The roof shingles are arranged so that each row has 7 fewer shingles than the row below it. If the first row has 75 shingles, how many shingles are in the 6th row?

Answers

Answer 1

The shingles are in the 6th row is 110 using arithmetic process.

What is arithmetic process?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The study of numbers and the operations on those numbers, which are relevant to all other branches of mathematics, is the focus of a branch of mathematics known as arithmetic operations. It includes addition, subtraction, multiplication, and division as its fundamental operations.

Given that A = 75 and d = 7, n = 6

A₆ = A + (n-1)d

A₆ = 75 + (6-1)7

A₆ = 75 + 5 * 7

A₆ = 75 + 35

A₆ = 110

To learn more about arithmetic process visit:

brainly.com/question/14340818

#SPJ1

Answer 2

Answer:

33

Step-by-step explanation:

it starts with 75 and decreases by 7 for each row. on the 6th row youll be at 33!

STARTS AT 75

row one: 68

row two: 61

row three:54

row four: 47

row five: 40

row six: 33


Related Questions

NO LINKS!!
58. You invest $200 in an annuity that earns 7% annual interest. After how many years will the value of the annuity double?

Answers

Answer:

The time taken for $200 invested at 7% annual interest compounded yearly:

[tex]\boxed{\mathrm{10.245 \; {years}}}[/tex]


which roughly works out to
[tex]\boxed{\mathrm{10\;years\;and\;3\;months}}[/tex]

Step-by-step explanation:

The formula for the accrued value of an amount P deposited at i% interest for a time period of t years compounded annually is given by the formula

[tex]\boxed{A = P(1 + r)^t\;\cdots[1]}[/tex]


Here A is the accrued value, P the principal and r = i/100

If you are given A, P and r we can compute t by taking the logarithms on both sides

In Equation [1] we get
[tex]\dfrac{A}{P} = (1 + r)^t \;\cdots[2][/tex]

Taking logs on both sides,
[tex]\log A - \log P = \log((1+r)^t)\\\\\log x^a = a \log x\\\\\\[/tex]

Therefore the right side becomes
[tex]t \log (1+r)[/tex]

Replacing right side of equation [2] with this expression yields

[tex]\log A - \log P = t \log (1+r)\\\\\textrm{Or, }\\\\t =\dfrac{ \log A - \log P}{\log (1 + r)}\\\\[/tex]

This is the general equation for determining how long it will take for the principal P to reach the value A if compounded annually at rate r(in decimal)

Since we are interested in seeing our principal P=200 double to A = 400 at r = 7% = 7/100 = 0.07
and
1 + r = 1 + 0.07 = 1.07

[tex]t = \dfrac{\log 400 - \log 200}{\log 1.07}\\\\[/tex]

[tex]t = \boxed{10.245 \; \textrm{years}}[/tex]

or approximately

[tex]\boxed{\mathrm{10\;years\;and\;3\;months}}[/tex]

Answer:

10.24 years (approx. 10 years 3 months)

Step-by-step explanation:

Most fixed annuities pay annual compound interest.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ A=P\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

A = $400 (double the principal)P = $200r = 7% = 0.07

To calculate after how many years the value of the annuity will double, substitute the given values into the formula and solve for t:

[tex]\implies 400=200(1+0.07)^t[/tex]

[tex]\implies 2=(1.07)^t[/tex]

[tex]\implies \ln 2=\ln (1.07)^t[/tex]

[tex]\implies \ln 2=t \ln 1.07[/tex]

[tex]\implies t=\dfrac{\ln 2}{\ln 1.07}[/tex]

[tex]\implies t=10.2447683...\rm years[/tex]

Therefore, the value of the annuity will double after 10.24 years (approximately 10 years 3 months).

Realiza el ejercicio utilizando las fórmulas para la curva normal.
Calcular la proporción de estudiantes que siguen una distribución normal, con media 78 y desviación estándar 36 y tienen puntuaciones que exceden por lo menos en cinco puntos de la puntuación que marca la frontera entre el Apto y No-Apto (es declarado No-Apto el 25 % de los estudiantes que obtuvieron las puntuaciones más bajas).
Datos:
Distribución normal
u = 78
O = 36

Answers

The proportion of students that had a grade at least 5 points greater than the 25th percentile is given as follows:

0.7054 = 70.54%.

How to obtain the z-scores?

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 78, \sigma = 36[/tex]

The 25th percentile is X when Z = -0.675, hence:

-0.675 = (X - 78)/36

X - 78 = -0.675 x 36

X = 53.7

The proportion of students with a grade of at least 58.7 is one subtracted by the p-value of Z when X = 58.7, hence:

Z = (58.7 - 78)/36

Z = -0.54

Z = -0.54 has a p-value of 0.2946.

1 - 0.2946 = 0.7054 = 70.54%.

More can be learned about z-scores at https://brainly.com/question/25800303

#SPJ1

56 parts were lost. 3% of the total parts were lost. How many total parts were there?

Answers

Answer:

3% = 56

100% = ?

Rule of three:

56 x 100

—————

3

Answer = 1,866.667 ≈ 1.867

Step-by-step explanation:

dont mind the answer below have a great day ______

                                                                                            \|/            

3% = 56
100% = ?

Rule of three:
56 x 100
—————
3

Answer = 1,866.667 ≈ 1.867

Have a good day ^^ ( and ignore the answer above)

As a town gets smaller the population of its high school decreases by 4% each year the senior class has 160 students now. In how many years will it have about 100 students? write an equation. then solve the equation without graphing.

Answers

The number of years that it will it have about 100 students is 11 years.

How to calculate the number of tears?

Final population = Initial population * (1-0.04)^years

Where 0.04 is the percentage decrease (4%) converted to decimal form, and "years" is the number of years in the future.

We can use this formula to find the number of years it will take for the senior class to have about 100 students:

Final population = 100

Initial population = 160

100 = 160 * (1-0.04)^years

We can solve for "years" by taking the natural logarithm of both sides:

ln(100) = ln(160 * (1-0.04)^years)

ln(100) = ln(160) + ln((1-0.04)^years)

and then we can solve for the power of (1-0.04)

ln(100) - ln(160) = ln((1-0.04)^years)

now we can get the value of years

years = (ln(100) - ln(160)) / ln(1-0.04)

which is around 10.72 , so it would take about 11 years for the senior class to have about 100 students.

Learn more about population on:

https://brainly.com/question/25630111

#SPJ1

suppose that a large influx of electric scooter rentals in a crowded downtown area results in a lot of new riders on the streets. for their safety, the mayor of the city decides to enact a law requiring helmets when renting scooters. these new helmets reportedly decrease the probability of injury by 29% in the event of a scooter crash. While the new helmets (increase/decrease) the probability of injury resulting from a scooter accident, they also incentivize individuals to ride (more/less) recklessly, which could (increase/decrease) the number of scooter collisions and therefore injuries to renters. Please choose one

Answers

While the new helmets decrease the probability of injury resulting from a scooter accident, but they also incentivize individuals to ride more recklessly, which could increase the number of scooter collisions and therefore injuries to renters.

The reason for the above statement is based on the concept of risk compensation. When the perceived risk of an activity is reduced, individuals may engage in more risky behavior. For example, if individuals believe that wearing a helmet makes them safer while riding a scooter, they may feel less concerned about the potential consequences of riding recklessly, leading to an increase in the number of accidents. On the other hand, the helmet does decrease the probability of injury in the event of a crash, but an increase in the number of crashes could lead to an overall increase in the number of injuries, offsetting the protective effect of the helmets. Therefore, the net impact of the new helmets on the number of scooter injuries is unclear, and further study is needed to determine their overall effect.

Read more about Risk Compensation:

https://brainly.com/question/28234991

#SPJ4

Please help, I really need this.

Answers

Answer:

Step-by-step explanation:

The slope's simplest form is 1/2.

When building a house, the number of days required to build is inversely
proportional to with the number of workers. One house was built in 85 days by 5
workers. How many days would it take to build a similar house with 25 workers?

Answers

It would take 17 days to build a similar house with 25 workers.

What is Inverse Proportion?

Inverse proportion is a type of proportionality relationship. If two quantities are inversely proportional then as one quantity increases, the other decreases.  In inverse proportion, the product of the given two quantities is equal to a constant value

One house was built in 85 days by 5 workers;

The relationship will be;

d ∝ 1/n

where

n = number of workers

d = number of days

d = k/n

when d = 5

k = 85

k = 5 x 85

k = 425

when n = 25

d = 425/25

d = 17

Learn more about inverse proportions here:

https://brainly.com/question/1266676

#SPJ1

The distribution of values taken by a statistic in all possible samples of the same size from the same population is None of the above The population parameter The sampling distribution of the statistic The probability that the statistic is obtained The variance of the values

Answers

The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population.

The population parameter is the true value of the statistic for the entire population. The probability that the statistic is obtained is the probability that it will be obtained in a single sample from the population. The variance of the values is the amount of variation among the values of the statistic in the sample. The formula for calculating the variance is the sum of the squared deviations from the mean, divided by the number of values in the sample. This can be written mathematically as: Variance = Σ (x - X)2/ n, where x is each value in the sample, X is the mean value, and n is the number of values in the sample.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ4

In exercises 5–8 tell whether a correlation is likely in the situation. If so tell her there’s a casual relationship. Explain your reasoning. 6. favorite color and color of shoes 

ANSWER FAST PLEASE
WILL GIVE BRAINLIEST

Answers

There may be a correlation, but there is no direct link. This is because it is more likely that you will get shoes in the color you want.

It's likely that the preferred color and the color of the shoes are related. A person's favorite color may or may not match the color of their shoes, so there is no direct correlation. Particularly, the color of the shoes may have influenced the preferred color.

There may be a correlation, but there is no direct link.

How does correlation work?

Correlation is a method for figuring out how two variables relate to each other. You learned that putting two variables on a "scatter plot" can help you figure out if they are usually connected. Despite the fact that there are other measures of association for variables measured at the ordinal or higher level of measurement, correlation is the strategy that is utilized the most frequently.

Learn more about Correlation work :

brainly.com/question/26998752

#SPJ1

Abdi and Bashir run in an ultra marathon. After 5 hours Abdi is 4 miles behind Bashir If at this point in the race, Abdi begins to run at a constant speed of 8 mph and Bashir runs at a speed of 6 mph. How long will it take for Adbi to catch up with Bashir?

Answers

Using the Time-Distance Formula, it will take Adbi 2 hours.

How to Use Time-Distance Formula to Calculate Time?

We can use the time-distance formula to find how long it will take for Abdi to catch up with Bashir. The time-distance formula is distance = speed x time.

Let t be the time in hours that it takes for Abdi to catch up with Bashir.

We know that the distance Abdi has covered is 4 miles more than Bashir, and the relative speed between the two runners is 8mph - 6mph = 2mph.

So we can write the equation:

4 = (8 - 6) * t

Solving for t, we get t = 4/2 = 2 hours.

So it will take Abdi 2 hours to catch up with Bashir.

Learn more about Time-Distance Formula on:

https://brainly.com/question/29251036

#SPJ1

In a garden 5/6 of the area is filled with native plants. The native plants take up to 107/4 m2 . Let g represent the total area of the garden. chooses 2 answers. pleas help me :(

Answers

The total area of the garden is given as follows:

32.1 m².

How to obtain the total area of the garden?

The total area of the garden is obtained applying the proportions in the context of this problem.

The area of native plants is given as follows:

107/4 = 26.75 m².

This area of 26.75 m² represents a fraction of 5/6 of the total area g of the garden, hence the total area of the garden is obtained applying the proportion as follows:

5g/6 = 26.75.

g = 26.75 x 6/5

g = 32.1 m².

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

division problem can be described using this model

Answers

The boxes are split in halves, and there is 4 boxes. The answer is 4 / 1/2.

What is division?

Division is a mathematical operation that involves dividing one number (the dividend) by another (the divisor). The result of this operation is called the quotient. Division is the inverse of multiplication, meaning that the product of a number divided by itself is equal to one. Division can also be used to find the number of times one number is contained in another. Division can be expressed in a variety of ways, such as by using fractions, decimals, or by using a long division algorithm.

When you look at the diagram, The boxes are split in halves, and there is 4 boxes. The answer is 4 / 1/2.

To learn more about Division, Visit

brainly.com/question/25289437

#SPJ1

If a particular sample has 36 participants and the other sample has 40 participants, the total degrees of freedom for the study is __________.

Answers

If a particular sample has 36 participants and the other sample has 40 participants, the total degrees of freedom for the study is

What is the degrees of freedom?

In Mathematics, the degrees of freedom in a sample are typically used to correct a possible bias that exists between the alternative and null hypotheses.

Mathematically, total degrees of freedom for the study can be calculated by using this mathematical expression:

v = n - k

Where:

v represents the total degree of freedom.n represents the number of individuals in a samplek represents the number of parameters being estimated.

Note: k is equal to 2 in this scenario.

Total degrees of freedom, v = n₁ + n₂ - k

Total degrees of freedom, v = 36 + 40 - 2

Total degrees of freedom, v = 74.

Read more on degrees of freedom here: brainly.com/question/22849398

#SPJ1

A ball is thrown straight down from the top of a 220-foot building with an initial velocity of - 22 feet per second. (Use the position function s(t)=−16t2+v0t+s0 for free-falling objects.)
(a) What is its velocity after 3 seconds?
(b) What is its velocity after falling 108 feet?

Answers

The velocity after 3 second is -118 ft/sec and the velocity after falling 108 feet is -87.6 ft/sec.

(a)

For the given position function

[tex]s(t)=-16t^2+v_0.t+s_0[/tex]

The ball is dropped from top of the building of height 220 ft, therefore

[tex]s_0=220ft[/tex]

Also, the initial velocity of the ball is −22 feet per second, thus.

[tex]v_0=22\frac{ft}{s}[/tex]

We will differentiate the position function to find the velocity function and then calculate velocity at (a) t=3sec and (b) after failing 108 ft.

Differentiate Position function to acquire the velocity function v(t).

[tex]s(t)=-16t^2+v_0.t+s_0\\\\s'(t)=-32t+v_0[/tex]

Now substitute t=3s,

v(3) = -32(3) + (-22)

v(3)= -118 ft/sec

b)

To find the velocity of ball after falling 108 ft, first we need to find the time at which ball is dropped 108 ft. and then find velocity at that time using velocity function.

let s(t)=108 ft, then using position function, we can write

[tex]s(t)=-16.t^2+v_0t+s_0\\\\108=-16t^2+(-22)t+220\\\\-16t^2-22t+112=0[/tex]

After solving the quadratic equation, we get

t= -3.42 and 2.05

Since time always positive,

therefore t=2.05 sec.

v (2.05) = -32(2.05)-22

v (2.05) = -87.6 ft/sec

learn more about Position function.

https://brainly.com/question/24112720

#SPJ4

The t-test takes into account the _____ and _____ of the data, and the p-value tells us _____.

Answers

The p-value is the chance of finding a t-value with an absolute value at least as great as the one we actually observed in the sample data assuming the null hypothesis is actually true. The t-value is a way to measure the difference between the population means.

We reject the null hypothesis of the test if the p-value is less than a predetermined threshold (for example, 0.05). We are primarily concerned with the p-value for each form of t-test, and we merely employ the t-value as a first step in that process.

You'll see that we merely used the t-value as a first step before determining the p-value. The genuine value in which we were most interested was the p-value, but first, we had to determine the t-value.

Therefore the p-value is the likelihood that, if the null hypothesis is correct, each test will result in a t-value with an absolute value at least as great as the one we actually observed in the sample data. The t-value is a way to measure the difference between population means.

To learn more about p-value and t-value, visit:https://brainly.com/question/6808433

#SPJ4

On the coordinate plane, the segment B(1-4) toC(7,4) forms, one side of triangle BCD. The triangle has an area of 15 square units select all points where D you could be

Answers

A coordinate plane is a two-dimensional graph that is used to locate points in a plane using an x-axis and a y-axis.

Explain about coordinate plane:Each point on the plane is defined by an x-coordinate (horizontal position) and a y-coordinate (vertical position). It is used in various branches of mathematics and sciences, such as geometry, algebra, and physics. It is a fundamental tool for graphing and analyzing mathematical equations and functions.To find the possible coordinates of point D, we first need to find the equation of the line that passes through points B(1, -4) and C(7, 4). We can use the slope-intercept form (y = mx + b) to find the equation of the line. Each point on the plane can be identified by its x and y coordinates, which are the distances from the point to the y-axis and x-axis, respectively. The x-coordinates are measured to the right of the y-axis, and the y-coordinates are measured upward from the x-axis. The coordinate plane is used to graph equations and inequalities, plot points, and identify patterns in data. It is a fundamental tool for understanding and manipulating mathematical concepts.

The slope of the line is (4-(-4))/(7-1) = 8/6 = 4/3.

The y-intercept is -4.

So the equation of the line is y = (4/3)x - 4.

We know that the area of triangle BCD is 15 square units. To find the possible coordinates of point D, we can use the formula for the area of a triangle (A = (1/2)bh). Since we know the area and the base, we can find the height of the triangle and use that to find the possible coordinates of point D.

The equation of the line is y = (4/3)x - 4. We can use this equation to find the y-coordinate of point D.

y = (4/3)x - 4

15 = (1/2)(x)((4/3)x - 4)

By solving the equation above, we can find the possible x coordinate of point D, which are (-2, -4/3) and (12, 4). Therefore, the possible coordinates of point D are (-2, -4/3) and (12, 4).

Note: you can use the same formula to find the y coordinate if you were given the x coordinate of D, but it gives the same solution.

To learn more about coordinate plane refer to:

https://brainly.com/question/27481419

#SPJ1

In a right triangle, sin(7x+5)=cos(8x-5). Find the smaller of the triangles two acute angles

Answers

In a case whereby a right triangle, sin(7x+5)=cos(8x-5),  the smaller of the triangles two acute angles is 43°.

How can the  smaller of the triangles two acute angles be calculated?

The concept that will be used is  right triangle. An acute angle is one that is smaller than 90 degrees in length. The correct angle is larger than this angle (which is equal to 90 degrees).

We can see  that sin(7x+5)=cos(8x-5)

An it implies that 7x+5 -8x-5  =90°

15x=90

x= 6

Then 7(6)+5= 47°     8(6)-5 = 43°

Hence the smaller of the triangles two acute angle is 43°

Learn more about triangles at:

https://brainly.com/question/17335144

#SPJ1

A survey was done 1/4 voted for a restaurant 4/7 voted a library the rest voted for a gym what fraction voted for the gym

Answers

The fraction that voted for the gym is calculated as: 5/28.

How to Use Fractions to Solve Word Problems?

To find out what fraction voted for the gym, you have to subtract the fractions that voted for the restaurant and the library from 1, which represents the total number of people surveyed.

You can do this by adding the fractions that voted for the restaurant and the library and then subtracting the sum from 1.

(1/4) + (4/7) = (7/28) + (16/28) = (23/28)

so 1 - (23/28) = (5/28)

Therefore, 5/28 of the people surveyed voted for the gym.

Learn more about fractions on:

https://brainly.com/question/78672

#SPJ1

What is the sum of the geometric sequence −2, −6, −18, … if there are seven terms?

Group of answer choices

−728

−128

−1,458

−2,186

Answers

The sum of the first seven terms is given by -2186

What is a geometric progression?

Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar², ar³, ...

The geometric sequence is given here by -2,-6,-18...

We can observe that the common ratio is r=3

thus the sequence of upto 7 terms is given by

-2,-6,-18,-54,-162,-486.-1458

Thus the sum of all seven terms is given by

S=-2-6-18-54-162-486-1458

=-2186

Hence, The sum of the first seven terms is given by -2186

Learn more about the geometric sequence here:

https://brainly.com/question/4853032

#SPJ1

Today 5 friends went out for lunch. Their total bill was $35.20 including tax and gratitude. They decide to split the bill equally and each paid with a $10 bill how much money will each person get back
??

Answers

Answer: The total bill including tax and gratitude is $35.20

And each one of the 5 friends paid $10 for the bill.

So the total amount paid is $10*5 = $50

If each person paid $10 and the total bill was $35.20

then the change will be $50-$35.20 = $14.80

And since they split the bill equally then each one of them will get back $14.80/5 = $2.96

So each person will get back $2.96

Step-by-step explanation:

Expand a^2= (b-x)^2 +h^2

Answers

The expanded value of the given equation is a²+2bx = b² + x ²+ h² .

Expansion - what is it?

Multiplication distributes over addition, so an expansion of a product of sums represents it as a sum of products.

Expansion is a scale-increasing affine transformation, sometimes known as enlargement or dilatation. It is also frequently referred to as an enlargement and is the polar opposite of a geometric contraction. An expansion and a translation are equivalent to a central dilation.

We must multiply out the brackets in order to expand and simplify an expression, and we must then collect like words in order to simplify the resulting expression.

Given : a^2= (b-x)^2 +h^2

          a² = (b-x)² + h²

we know that (c-d)² = c²+d² + 2cd

So,    a² = b² + x² -2bx + h²

         a²+2bx = b² + x ²+ h²

To learn more about Numbers, visit the link :

brainly.com/question/24644930

#SPJ1

for 14-21 write two equivalent fractions for each

Answers

The fractions with different numerators and denominators but the same value are said to be equivalent fractions.

What is an equivalent fraction about?

For instance, since 2/4 and 3/6 both equal the 1/2, they are equivalent fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.

A rule that says the result of multiplying the numerator and denominator of a fraction by the same nonzero number is a fraction equal to the original fraction.

Equivalent fractions are those that, despite their visual differences, represent the same value. For instance, if you have a cake and cut it into two equal pieces, you will have consumed half of the cake.

In this case, it should be noted 1/2 is the same as 3/6.

Note that an overview was given as your information is incomplete.

Learn more about fractions on:

https://brainly.com/question/17220365

#SPJ1

Hassan's history class is taking a field trip to the state capitol building. The capitol building is
50 miles from Hassan's school. The class plans to stop after 45 minutes, or 0.75 hours, to
view a local monument. The bus driver plans to drive at an average speed of 40 miles per
hour.
Which equation can you use to find how many hours, x, the second part of the trip will take?

Answers

The equation that can be used to find how many hours, x, the second part of the trip will take is:

distance = rate x time

Which equation can you use to find how many hours?Where distance is the remaining distance from the capitol building to the school, rate is the average speed of the bus, and time is the time it takes to travel that distance.So, if we know that the distance is 50 miles and the rate is 40 miles/hour, we can find the time it takes to travel the remaining distance by plugging these values into the equation and solving for x:50 miles = 40 miles/hour x xthen by dividing both sides by 40 miles/hourx = 50/40 = 1.25 hours The equation to use to find how many hours, x, the second part of the trip will take is:distance = rate x timeIn this case, the distance is the remaining distance from the capitol building to the school, which is 50 miles - (40 miles/hour x 0.75 hours) = 35 miles. The rate is the average speed of the bus, which is 40 miles/hour. Therefore, the equation to find the time, x, of the second part of the trip is:35 miles = 40 miles/hour x xTo solve for x, divide both sides of the equation by 40 miles/hour:x = 35 miles / 40 miles/hour = 0.875 hours, or 52.5 minutes.

To learn more about capitol building refer to;

https://brainly.com/question/30190474

#SPJ1

Find the point on the curve y = -x^2 - 2 that is closest to the point (0, 1)

Answers

Answer:

[tex](0,-2)[/tex]

Step-by-step explanation:

Let the coordinates of the desired point be [tex](a, -a^2-2)[/tex]. Let the distance of this point from [tex](0,1)[/tex] be [tex]f(a)[/tex].

By the distance formula, [tex]f(a)=\sqrt{a^2+(a^2+3)^2}[/tex].

Clearly, [tex]f(a)[/tex] is minimized when the radicand is minimized.

Clearly, the radicand is always increasing, so the minimum is achieved at the left endpoint of the maximal domain of [tex]f(a)[/tex], which is [tex]a=0[/tex].

So, the coordinates are [tex](0,-2)[/tex].

The point on the curve y = -x^2 - 2 that is closest to the point (0, 1) will be (0, -2)

How to calculate the value?

From the information, we want to know the point on the curve y = -x^2 - 2 that is closest to the point (0, 1).

Let the coordinates of the desired point be illustrated as (a - a² - 2).

The distance of the point from (0, 1) is depicted as f(a).

When the radicand is minimized, f(a) is minimized.

In this case, the minimum will be achieved at the left endpoint of the maximal domain of f(a) which is a = 0.

Therefore, the coordinates will be (0, -2).

Learn more about coordinate on:

brainly.com/question/17206319

#SPJ1

Sine/Cosine of Complementary Angles Solve for x
In a right triangle,sin (8x-9) = cos (x+6) Round to the nearest tenth if nessecary

Answers

The value of the variable , x is 10. 33

How to determine the value of the variable

It is important to note that in mathematics, complementary angles are defined as angles that sum up to 90 degrees.

Some properties of complementary angles are;

If the addition of  two angles add up to 90 degrees in a right angle, they are called complementary anglesC represents complement and also for the corner of a right angleComplementary angles can be adjacent or non-adjacent angles

From the information given, we have the angles as;

8x - 9x + 6

Equate the angles to 90 degrees

8x - 9 + x + 6 = 90

collect like terms

8x + x = 90 +3

add the like terms, we get;

9x = 93

Make 'x' the subject of formula by dividing both sides by 9

x = 93/9

x = 10. 33

Hence, the value is 10.33

Learn about complementary angles on:

https://brainly.com/question/98924

#SPJ1

4. A distributor of fasteners is opening a new plant and considering whether to use a mechanized process or a manual process to package the product. The manual process will have a fixed cost of $36,234 and a variable cost of $2.14 per bag. The mechanized process would have a fixed cost of $84,420 and a variable cost of $1.85 per bag. The company expects to sell each bag of fasteners for $2.75. a) What is the break-even point for the manual process (in units)?

Answers

166158  is the break-even point for the manual process

What is Expression?

An expression is combination of variables, numbers and operators.

Given that The manual process will have a fixed cost of $36,234 and a variable cost of $2.14 per bag.

Let the number of bags will be x

36234+2.14x..(1)

The mechanized process would have a fixed cost of $84,420 and a variable cost of $1.85 per bag.

84420+1.85x..(2)

From equation 1 and 2

36234+2.14x=84420+1.85x

2.14x-1.85x=84420-36234

0.29x=48186

Divide both sides by 0.29

x=166158

Hence, 166158  is the break-even point for the manual process

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ1

The initial bacterium count in a culture is 500. A biologist later makes a sample count ofbacteria in the culture and finds that the relative rate of growth is 40% per hour.(a)Find a function that models the number of bacteria after t hours.(b)What is the estimated count after 10 hours?(c)When will the bacteria count reach 80,000?(d)Sketch the graph of the function . n(t)

Answers

a) The function is P = 500e^0.4t

b) The count after 10 hours is 27299

c) it would reach 80000 in 13 hours

What is the function?

We know that at this time we are dealing with the population of the bacteria and we have to invoke the exponential growth ideology and we would have;

P = Poe^rt

P = population at time t

Po = Initial population

r = Population growth rate
t = Time taken

Then we have;

P = 500e^0.4t

After ten hours;

P= 500e^0.4 * 10

P = 27299

The count would reach 80000 when;

80000 = 500e^0.4 t

80000/500 = e^0.4 t

160 = e^0.4 t

ln160 = e^0.4 t

ln160 = 0.4t

t = ln160/0.4

t = 13 hours

Learn more about population growth:https://brainly.com/question/18415071

#SPJ1

Use the Empirical The mean speed of a sample of vehicles along a stretch of highway is 70 miles per hour, with a standard deviation of 5 miles per hourEstimate the percent of vehicles whose speeds are between 60 miles per hour and 80 miles per hour(Assume the data set has a bell-shaped distribution )

Answers

Using the empirical rule, 95% of vehicles travel between 60 miles per hour and 80 miles per hour.

What is the empirical rule?

Generally, Given that

Mean = 66 and Standard deviation 4

To find the percent of vehicles whose speeds are between 60 miles per hour and 80 miles per hour

60 = 70-(2*5) ,

this shows that the 58 value is 2 standard deviations below the mean

and

80 = 70 +( 2*5)

This shows that the 74 value is 2 standard deviations above the mean

Using the empirical rule, we know that 95% of data fall within 2 standard deviations from the mean.

Read more about the empirical rules

https://brainly.com/question/11266206

#SPJ1

How to solve -7=5x-2. 2 step equations using inverse operations

Answers

Answer:

-1

Step-by-step explanation:

Add 2 to both sides of the equation: -7 + 2 = 5x - 2 + 2. This gives you -5 = 5x.

Divide both sides of the equation by 5: -5/5 = 5x/5. This gives you -1 = x.

So the solution to the equation is x = -1.

Alternatively, you can also use inverse operations to solve the equation by isolating x to one side.

Add 2 to both sides of the equation: -7 + 2 = 5x - 2 + 2. This gives you -5 = 5x

Divide both sides of the equation by 5: -5/5 = 5x/5. This gives you -1 = x

So the solution to the equation is x = -1.

-7=5(-1)-2
-7=-5-2
-7=-7

in trigonometry it is important that the right triangles (reference triangles) have a consistent orientation. the reference triangles always have a leg perpendicular to the [ select ] , the value of the hypotenuse is [ select ] , and is the angle adjacent to the [ select ] .

Answers

In trigonometry it is important that the right triangles (reference triangles) have a consistent orientation. the reference triangles always have a leg perpendicular to the y-axis , the value of the hypotenuse is positive , and is the angle adjacent to the y-axis and hypotenuse.

A right angle triangle has six trigonometric ratios: Sin, Cos, Tan, Cosec, Sec, and Cot. They represent, successively, Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent.

So, when we graph a right angle triangle, we draw a side of triangle perpendicular to y-axis and another side will be on y-axis. The remaining side left would be hypotenuse that will always be positive and is adjacent to the side perpendicular to y-axis and the side on the y-axis.

To learn more about trigonometry here:

https://brainly.com/question/29002217

#SPJ4

Other Questions
The equation of the plane passing through the point (-8,3,7) and parallel to the plane 4x + 8y ~ 2z = 45, is given by 4x - 8y - 2z = -22 4x + 8y + 2z = -22 4x + 8y _ 2z = -22 4x + 8y - 2z = 22 What are the similarities between "Romeo and Juliet" and Zakia and Ali? Why does the narrator keep his real identity a secret until his last conversation with Pete from the book born worker Write an equivalent expression by distributing the "-" sign outside the parentheses:-(-3.4c + 1) which of the following is not true? no area of comparable size in north america, or perhaps in the world, contained a greater variety of native languages and cultures than did pre-european california. the primary staple of most native californians was corn. some native californians practiced agriculture. the native californians were among the world's best basket makers. 1. Aflatoxins grow on raw beef, poultry, and shellfish.A. FalseB. True2. Cook all raw beef, pork, lamb and veal steaks, chops, and roasts to a minimum internal temperature of _____ as measured with a food thermometer before removing meat from the heat source.A. at least 100 degrees FB. about 125 degrees FC. 145 degrees FD. 141 degrees F3. Fungi are multi-celled organisms such as mold, yeast, and mushrooms.A. TrueB. False4. The leading cause of food-borne illness in the U.S. is _____.A. Toxoplasma gondiiB. Salmonella spp.C. cheese moldD. norovirus5. Someone whose skin turns yellow may have jaundice which is a symptom of hepatitis A.A. FalseB. True Find the volume of the solid of revolution obtained by rotating the region bounded by the curve y=3xx2 and the line y=2x about the y-axis. Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. Blood Platelet Count of Males (1000 cells/muL) Frequency 0-99 3 100-199 54 200-299 76 300-399 21 400-499 0 500-599 0 600-699 1 Identify the lower class limits (in 1000 cells/muL). TRAVEL Marion is travelling 500 miles by car. She drives 250 miles at an average rate of x miles per hour the first day and the remaining 250 miles at an average rate of x5 miles per hour. Select the expression that represents the amount of time Marion spent traveling the 500 miles. (Hint: Write out the units to determine how to solve the problem.)Multiple choice question.A)x(x5)/500x1250B)62,500/x(x5)C)500x1250/x(x5)D)500/2x5 Our mission is to promote academic and personal development by providing growth opportunities o global youth in the areas of literacy; community awareness and engagement; mentoring, success planning, global enterprise; social-emotional wellness; and athletic skills development. What does it mean? josh has just been asked to complete a rhetorical analysis for his political science class. his professor asked him to use at least one empirical source in this rhetorical analysis. which of the following is an example of an empirical source that josh could use in his essay why are entrepreneurs important in a free enterprise economy A number increased by 7 gives 20, what is the number?with steps pls HELP ME ASAP ITS DUE IN 5 minutes HELPPP A______ is a government in which political power or influence overinstitutions, leaders, and policies-rests in the hands of the people Which of the following is not required by the employer following an exposure incident to human blood or OPIM? Fever 1793 pages 1-3 gist PLEASE HELP ME!What are symptoms of Nomophobia? (fear of being without a mobile phone) Has to be both physical and emotional symptoms. Describe how it appeared. (is it heredity?) on jan. 2, callie taylor invests $40,000 into the business in exchange for common stock. she journalized the transaction as follows but something is wrong with the journal entry. use your knowledge of what a correct journal entry should look like to identify everything that is wrong. select all answers which apply. each state retains its sovereignty, freedom and independence, and every power, jurisdiction and right, which is not by this confederation expressly delegated to the united states, in congress assembled.T/F