Compound interest: $8,765.58
Brainly keeps acting up if I go off or don't respond please understand it's brainly kicking me out. The last option for d is 309 yards
From the given diagram, let's find the length of the park's boundary.
We can see the side of the park's boundary is a circular arc and the top and bottom are the bases of triangles.
To find the length of the circular sides, apply the length of arc formula:
[tex]arc\text{ length=}2\pi r\ast\frac{\theta}{360}[/tex]Where:
Θ = 120 degrees
π = 3.14
radius, r = 50 yards
Hence, we have:
[tex]\text{arc length=2}\ast3.14\ast50\ast\frac{120}{360}=104.67\text{ yards}[/tex]This means the length of one circular side of the boundary is 104.67 yards.
We have two circular sides of the boundary.
The top and bottom sides form equilateral traingles.
Hence, the length of the top and bottom sides are 50 yards each.
To find the total length of the boundary, we have:
Total length = 104.67 + 104.67 + 50 + 50 = 309.34 yards
Rounding off to the nearest yard, the length of the park's boundary is:
309 yards
ANSWER:
D. 309 yards
boxes of nails are stacked on top of each other on a work bench. The table below shows how the height above the floor of the topmost box depends on the number of boxes. What is a rule for the height? Give the rule in words and as an algebraic expression.
The height is the sum of 39 and 9 times the number of boxes, n. The rule is 9n + 39.
What is algebraic expression?An algebraic expression is defined as the type of expression that is made up of a variable, a coefficient and a constant.
From the given box of nails,
The height of 2 boxes of nails = (9× 2) + 39 = 57 In
The height of 3 boxes of nails = ( 9 × 3) + 39 = 66 In
The height of 4 boxes of nails = ( 9× 4) + 39 = 75 ln
That is to say that the height of the box above the floor can be calculated by the sum of 39 and 9 times the number of boxes, n.
Therefore, the rule of heights is 9n + 39 where n is the number of boxes present.
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A woman saves $6000 at 2.5% compund interest. She adds $1000 to her amount at the end of each year. Find the total savings after 2 years
Answer:
$8303.75
Step-by-step explanation:
(6000x1.025^2)+2000=8303.75
what is the size of the angle between north west and south east?
180°
Step-by-step explanation:Size of the angle between:North and South: 180°East and West: 180°North East and South West: 180°North West and South East: 180°North West and North East: 90°South West and South East: 90°What is -5/7 times (-1/6)
Answer:
5/42 or 0.1190
hope this helps :)
5 : it is night. someone who is 4 feet tall is walking away from a street light at a rate of 8 feet per second. the street light is 12 feet tall. the person casts a shadow on the ground in front of them. how fast is the length of the shadow growing when the person is 3 feet from the street light? the length of the shadow is growing at a rate of
When a person is 3 feet from a street light, the length of the shadow grows at a rate of 4 feet per second.
See the figure that illustrates the in question statement, attached.
making use of the related triangle theorem;
4/y = 12/x+y
Cross multiply
4(x+y)=12y
4x+4y = 12y
4x=8y
x/y =2
x=2y
Divide the two sides of the equation by t, where dx/dt = 2 dy/dt. The speed at which the person is walking away from the street light is expressed as dx/dt
The growth rate of the shadow's length is measured by the ratio dy/dt.
Given that dx/dt = 8ft/s
by solving,
dy/dt = 4 ft/s
Hence the rate at which the length of the shadow growing when the person is 3 feet from the street light is 4ft/s
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devon has 15 dollars to spend on snacks. the corner store has candy bars for $1 and sports drinks for $3. he only wants to purchase at most 10 items.
Devon can have 6 candy bars and 3 sports drinks when he has $15 to spend.
According to the question,
We have the following information:
Devon has $15.
Cost of 1 candy bar = $1
Cost of 1 sports drink = $3
Devon wants to purchase at most 10 items.
It means that the total items should be less than or equal to 10.
Now, we have to spend $15 in such a way that number of items should be less than or equal to 10.
Now, we will look for the number of items for sports drink and change the number of candy bars accordingly.
Let's take 1 sports drink:
$3
We are left with $12. Now, there will be 12 candy bars.
So, this can not satisfy our conditions.
Let's take 2 sports drink:
$6
We are left $9. Now, there will be 9 candy bars. And the number of items is 11.
(This is not satisfying our condition.)
Let's take 3 sports drink:
$9
We are left with $6. Now, there will be 6 candy bars. And the number of items is 9.
This is satisfying all the conditions.
Hence, Devon can have 6 candy bars and 3 sports drinks when he has $15 to spend on snacks.
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Chad doesnt have any money, but he owes his sister $15, owes his brother $9 and owes his friend $24. What integer could be used to represent the amount of money chad has?
Answer:
- 48.00
Step-by-step explanation:
Add all the debt up.
Answer: -48
Step-by-Step Explanation:
Money that Chad owes his Sister = $15
Money that Chad owes his Brother = $9
Money that Chad owes his Friend = $24
Total Money he owes = 15 + 9 + 24 = $48
Hence, Total Money he has = -48 (since he doesn't have any money)
If ADAB ACBA,
ZD = 132° and ZC = x + 18
Answer:
x = 114
Step-by-step explanation:
since the triangles are congruent then corresponding angles are congruent, then
∠ C = ∠ D , that is
x + 18 = 132 ( subtract 18 from both sides )
x = 114
Area of circle when r is 14
Answer:
The area is 196π, or 615.752160 when evaluated to 6 decimal places.
Step-by-step explanation:
There is an equation for the area of a circle:
A=π[tex]r^{2}[/tex], Where A is the area and r is the radius. π is π, it is its own number. Plugging in the radius stated we can evaluate:
A=π([tex]14^{2}[/tex])
A=196π
If we write out π and evaluate with an (un)reasonable amount of decimal places:
π≅3.1415926536
A=196×(3.1415926536)
A≅615.752160
Answer:
A = [tex]\pi ^{2}[/tex]
Step-by-step explanation:
A≈615.75
15
4. If M is the midpoint of line segment EF. E is located at (10,-8) and M is located at (-6, -2). Find the other
endpoint.
Answer:
The other endpoint is F( - 22, 4)=============================
GivenSegment EF with:
Endpoint E = (10, - 8),Midpoint M = (- 6, - 2),Endpoint F = (x, y).SolutionUse midpoint equation:
x = (x₁ + x₂)/2, y = (y₁ + y₂)/2Find unknown coordinates of the point F:
- 6 = (10 + x)/2 ⇒ -12 = 10 + x ⇒ x = - 12 - 10 = - 22,- 2 = (- 8 + y)/2 ⇒ - 4 = - 8 + y ⇒ y = - 4 + 8 = 4.So the point is F = ( - 22, 4)
Answer:
F = (-22, 4)
Step-by-step explanation:
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\\\\ \textsf{where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.}[/tex]
Given information:
Midpoint = (-6, -2)E = (10, -8)Define the endpoints of the line segment EF:
Let (x₁, y₁) = endpoint E = (10, -8)Let (x₂, y₂) = endpoint FSubstitute the given information into the formula:
[tex]\implies (x_M,y_M)=\left(\dfrac{x_F+x_E}{2},\dfrac{y_F+y_E}{2}\right)[/tex]
[tex]\implies (-6,-2)=\left(\dfrac{x_F+10}{2},\dfrac{y_F-8}{2}\right)[/tex]
Find the x-coordinate of M:
[tex]\implies \dfrac{x_F+10}{2}=-6[/tex]
[tex]\implies x_F+10=-12[/tex]
[tex]\implies x_F=-22[/tex]
Find the y-coordinate of M:
[tex]\implies \dfrac{y_F-8}{2}=-2[/tex]
[tex]\implies y_F-8=-4[/tex]
[tex]\implies y_F=4[/tex]
Therefore, the coordinates of endpoint F are (-22, 4).
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The room numbers of two adjacent classrooms are two consecutive odd numbers. If their sum is 720, find the
classroom numbers.
The room numbers of two adjacent classrooms are 359 and 361.
What is consecutive odd numbers?
Consecutive odd numbers are odd integers that are separated by 2 and come after one another.
Suppose the first odd number is x, then the another consecutive odd number is x + 2.
The sum of these two numbers is 720.
So,
x + (x + 2) = 720
2x + 2 = 720
2x = 718
x = 359
Therefore, the first odd number is 359 and the second add number is 361 which gives the sum 720.
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By driving 10 miles per hour faster, Goldie was able to
Ishave 2 hours and 30 minutes off her 50-mile trip to visit
her grandmother who lives in the mountains. Select the
equation that could be used to solve this problem. Use x to
represent her faster driving rate.
The faster driving rate of Goldie is 20 miles/hour.
Given that, by driving 10 miles per hour faster, Goldie was able to have 2 hours and 30 minutes off her 50-mile trip.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Here, Speed = 10 miles/hour, Time = 2 hours and 30 minutes = 2.5 hours and Distance = 50 mile.
Now, Distance = Speed × Time
Let the faster driving rate be x.
50 = x × 2.5
⇒ x = 50/2.5
⇒ x = 20 miles/hour
Therefore, the faster driving rate of Goldie is 20 miles/hour.
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Answer:
Step-by-step explanation:
I don't agree with the other answer.
You need to you systems of equations
So
d=50 t=t-2.5 x=r+10
d=rt
50=(r+10)(t-2.5) (faster equation)
50=rt (slower equation)
t=[tex]\frac{50}{r}[/tex] (substitute into faster equation)
50 = (r+10)(50/r -2.5) mult both sides by r to get rid of fraction
50r = (r+10)(50-2.5r) FOIL
50r = 50r -2.5r² + 500 -25r Simplify
2.5r²+25r-500=0 divide all by 2.5
r²+10r-200 factor
(r-20)(r+10) eliminate negative answer
r=20
x=r+10 =20+10 =30 mph
A line that includes the point (3,10) has a slope of 4. What is its equation in slope intercept form?
The slope intercept form of equation of the line is y = 4x - 2
The slope intercept form of equation of the line that includes the point (3,10) has a slope of 4. is y = 4x - 2
What is equation of a straight line in slope intercept form?This is an equation of the form y = mx + c, where:
the coefficient of x is the slope
c is the intercept
To calculate the equation of the line that include point (3,10) has a slope of 4 we solve as follows
( y - y' ) / ( x - x' ) = 4
( y - y' ) = ( x - x' ) = 4
where y' = 10, and x' = 3
y - 10 = (x - 3 ) * 4
y - 10 = 4x - 12
y = 4x - 12 + 10
y = 4x - 2
The slope intercept form of equation of the line is y = 4x - 2
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What graph represents the system of linear inequalities? y>3x+1 y≤−2x−4
Answer:
Step-by-step explanation:
y>3x+1
y≤-2x-4
assume that your kidneys can filter out of 10% of a medication in your blood every 6 hours, you take 200 milligrams dose of the medicine how many milligrams of the medicine are in your blood after 2 days
Answer: 160 mg
Step-by-step explanation:
10% of 200 is 20
therefore, every 6 hours, 20 milligrams of medicine filters into your blood.
there are 24 hours in a day, and 48 hours in 2 days.
6 * 4 = 24
20 * 4 = 80
you get 80 mg of medicine every day.
80 * 2 = 160
you get 160 mg of medicine in two days.
FIND THE MEASURE OF EACH ANGLE<1 and <2 form a linear pair and m<2= 52 degrees.
Linear pair angles are the ones that form a straight line, in other words they will form a 180º angle. Therefore if the angle 2 measures 44 degrees we can find the angle 1 by doing as follows:
[tex]\begin{gathered} \measuredangle1+\measuredangle2=180 \\ \measuredangle1+52=180 \\ \measuredangle1=180-52 \\ \measuredangle1=128 \end{gathered}[/tex]The angle one is equal to 128 degrees.
which is true about box plots? group of answer choices boxplots show the number of datapoints between any two values boxplots present the shape of the distribution (density curve) boxplots can involve a categorical variable and a continuous numerical variable boxplots show the size of the data set (number of data points) boxplots visually present the mean and standard deviation boxplots show where the peak of the distribution is
Box plots present the shape of the distribution (density curve), Box plots can involve a categorical variable and a continuous numerical variable, Box plots show where the peak of the distribution is are the correct statement.
Instead of showing the raw data points, Box Plots takes the sample data and then present the ranges of values based on the quartiles and also display the asterisks for outliers that generally falls outside the whiskers.
Yes, the shape of distribution can be understood from a Box Plot. It can show whether a statistical data set is normally distributed or skewed.
A Box plot is a graph of the distribution that has Continuous variables. It is also applicable for Categorical variables.
Box Plot generally shows the below parameters: Maximum, Minimum, Median, 75th Percentile, 25th Percentile and Interquartile Range.
A size can be determined by using these parameters but is not directly seen in a Box Plot
Generally a Standard Deviation is not visualized by Box Plot. It mainly visualizes Maximum, Minimum, Median, 75th Percentile, 25th Percentile and Interquartile Range.
Yes, the peak of the distribution can be analyzed from Box Plot
Generally for Normal Distribution, Mean = Median and this is the point where the peak is seen.
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oncerns about climate change and co2 reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). random samples of 47 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. (a) if the true mean is .9340 with a standard deviation of 0.0030, within what interval will 98 percent of the sample means fall? (round your answers to 4 decimal places.)
The interval is from 0.9330 to 0.9350
For given condition;
mean = 0.9340
standard deviation = 0.0030
z-score at 98% = 2.33
n = size of sample = 47
Step 1: calculate the standard error of the mean
standard error of mean = z-score * standard deviation/sqrt(n)
= 2.33 * 0.0030/[tex]\sqrt{47}[/tex]
= 0.0010
step 2: upper limit = mean + standard error
= 0.9340 + 0.0010
= 0.9350
lower limit = mean - standard error
= 0.9340 - 0.0010
= 0.9330
Hence, the interval is from 0.9330 to 0.9350
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+) The expression 5p represents the total price of buying 5 movie tickets. ) What do the parts of the expression 5p represent? • The variable p represents the ? The number 5 represents the ?
Since the expression 5p represents the total price of buying 5 movie tickets, divide the expression 5p by 5 to find the price of a single ticket:
[tex]\frac{5p}{5}=p[/tex]Then, the price of a ticket is p.
Therefore, the variable p represents the ticket price, while the number 5 represents the number of tickets.
Chris and Sarah's dinner bill was $28.67. They want to leave an 18% tip. How much gratuity will they leave?
Please help me!
Answer:
Tip- $5.16
Total cost- $33.86
Step-by-step explanation:
To find a 18% tip, turn 18% into 0.18.
Multiply 28.67 by 0.18.
28.67x0.18=
5.16
If you add that to the bill, it would be 33.86
I am not sure how to find out if the number is an integer or not I don’t need you to answer all those number that are in the pic I want to understand how to figure that out on my own
An integer number is a number that can be written without using a rational component. In other words, if a number can be written without using a fraction, then that number is considered an integer.
For example, let's take the first number:
[tex]-\frac{64}{8}[/tex]This number is written as a fraction. But, this is also equivalent to:
[tex]-\frac{64}{8}=-8[/tex]Since it can also be written without making use of a fraction then this number is an integer.
Also, there are numbers that are written in decimal form. For example:
[tex]-8.92[/tex]These types of numbers are not integers.
a list of 20182018 positive integers has a unique mode, which occurs exactly 1010 times. what is the least number of distinct values that can occur in the list?
The least number of distinct values that can occur in the list is 225.
what is mode?The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. However, occasionally there is either no mode or more than one mode. When every observed value occurs exactly once in a data collection, there is no mode.
The mode appears 10 times. That leaves 2008 numbers.
The least number of distinct values will occur if all but one of the remaining values appears 9 times
= 2008/9
=223 1/9.
So, The list can include a maximum of 225 distinct values, with the mode appearing 10 times, 223 other values nine times, and the last value once.
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betty and karen have been hired to paint the houses in a new development. working together, the women can paint a house in two-thirds the time that it takes karen working alone. betty takes 4 h to paint a house alone. how long does it take karen to paint a house working alone?
Betty takes 6 hours to paint a house alone, that indicates she can paint 1/6 of the house in 1 hour then Karen working alone will paint a house in 3 hours.
How long does it take paint a house working alone?Since Betty takes 6 hours to paint a house alone, that indicates she can paint 1/6 of the house in 1 hour.
Karen can even paint 1/x in 1 hour
Both of them will paint the house in 3/2 hours.
We then add them together which gives:
1/6 + 1/x = 3/2x
The lowest common multiple is 6x
1x/6x + 6/6x = 9/6x
We then leave out the denominators
1x + 6 = 9
simplifying the above equation, we get
x = 9 - 6
x = 3
Therefore, the value of x = 3.
Karen working alone will paint a house in 3 hours.
The complete question is:
Betty and Karen have been hired to paint the houses in a new development. Working together, the women can paint a house in two-thirds the time that it takes Karen working alone. Betty takes 14 h to paint a house alone. Betty takes 6 h to paint a house alone.
Required:
How long does it take Karen to paint a house working alone?
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Hi please help me on the q
Answer:
x = 30°
Step-by-step explanation:
The angles of a pentagon add up to 540°
Make an equation adding up the angles to equal 540°
x + 4x + 4x + 135° + 135° = 540°
Simplify
9x = 270°
Divide
x = 30°
What measure of variance is best to describe Mr. Mack’s 1st period scores?Choose the correct one MeanMedianModeInterquartile range Standard deviation Variance
Step 1
The measures of variance include;
[tex]\begin{gathered} 1)\text{ Interquartie Range} \\ 2)\text{ Range} \\ 3)\text{ Standard deviation} \\ 4)\text{ Variance} \end{gathered}[/tex]Step 2
For a bar chart, we have that;
[tex]undefined[/tex]The value of x =5 is a solution to each of the following except which ?
A 3x+2=4x-3
B (x+2)(x-5)=0
C4x+2=15
D 3x-10=x
Answer:
The answer is C
Step-by-step explanation:
If you substitute every x value for 5, you know that every equation can have 5 as an answer but C.
A. 3x+2=4x-3
Isolate the x(s) and combine like terms
3x+2-2=4x-3-2
3x=4x-5
3x-4x=4x-4x-5
-x=-5
-x(-1)=-5(-1)
x=5
Therefore A is a solution
B. (x+2)(x-5)=0
Substitution--Substitute every x for a 5
(7)(0)=0
anything multiplied by 0 will be 0
B. Is a solution because it is true.
C. 4x+2=15
Isolating the x(s) and combine like terms
4x+2-2=15-2
4x=13
4x÷4=13÷4
x=3.25
C is not a solution because x should equal to 5 but in this equation x can only be equal to 3.25. C is wrong.
We know our answer so we don't have to keep solving the rest of the equations.
But I'll just do D
D. 3x-10=x
Isolate the x(s) and combine like terms
3x-x-10=x-x
2x-10=0
2x=10
2x÷2=10÷2
x=5
D is a solution.
Find the distance between the points (10, 1) and (9, -4) using the distance formula. Round to the hundredths
place.
A: 3.16
B: 5.00
C: 3.00
D: 5.10
Please explain.
Answer:
3.16
Step-by-step explanation:
the number after the decimal point you add the and before are added s example0.1=one is tenth1.6=one is tensKennedy has $0.81 worth of pennies and nickels. she has 9 more nickels than pennies. write a system of equations that could be used to determine the number of pennies and the number of nickels that kennedy has. define the variables that you use to write the system.
Variable used to write the equation are x, Number of pennies and y, Number of nickels and the system of equations used is x+y=0.81 and x+9=y.
An equation is a mathematical statement that shows that two mathematical expressions are equal.
Let the variables defined to form the system of equation are as follows:
x= Number of pennies
y= Number of nickels
Total worth of pennies and nickels is 0.81
mathematically, x+y=0.81
Given condition, she has 9 more nickels than pennies
mathematically, x+9=y
So, the system of equation which can be used to determine the number of pennies and the number of nickels that Kennedy has are x+y=0.81 and x+9=y, where variables used are x and y.
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at a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 20 cubic feet per minute. the diameter of the base of the cone is approximately three times the altitude. at what rate (in ft/min) is the height of the pile changing when the pile is 22 feet high? (hint: the formula for the volume of a cone is v
When the pile is 22 feet high, the height of the pile changes to 20/1089π.
Given (dV)/(dt) = 20, h = 22 feet , dh /dt =?
The volume of cone is V = 1/3 * pi * r ^ 2 * h
d=3h
2r = 3h
r = (3h)/2
V = 1/3 * pi * r ^ 2 * h
= 1/3 * pi * ((3h)/2) ^ 2 * h
= 1/3 * pi((9 * H ^ 2 )/4) * h
= (9pi)/12 * h ^ 3
Differentiate w.r.to t
(dV)/(dt) = (3pi)/4 * (3h * h^ 2) * (dh)/(dt)
(dV)/(dt) = (9pi)/4 * (h ^ 2) * (dh)/(dt)
(dV)/(dt)=20, h=22 feet
20 = (9pi)/4 * (22 ^ 2) * (dh)/(dt)
(dh)/(dt) = 80/ (9pi * (22^ 2))
h^ t = 20/ 1089 *pi ft / min
Therefore, The height of the pile changing when the pile is 22 feet high is 20/1089π
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