it is estimated that 45% of the senior class will go to prom this year. if you randomly choose 10 seniors and ask them if they are going to prom, would you use the normal approximation to predict these results?

The area of the trapezoid is 70 square centimeters.

locating a right trapezoid's area. A = (a + b) x h/2 is the formula to calculate the area of a right trapezoid.

We must apply the following calculation to determine the area of the trapezoid:

A = (b1 + b2) * h/2

where A is the area, h is the height, b1 and b2 are the lengths of the parallel sides (or the distance between the parallel sides).

We can observe that in this instance, b1 = 12 cm, b2 = 8 cm, and h = 7 cm. When we plug these numbers into the formula, we get:

A is equal to (12 + 8) x 7 cm / 2.

A = 20 cm * 7 cm / 2

A = 70 cm²

Hence, the trapezoid has a surface area of 70 square centimetres.

To know more area of trapezoid about visit:

https://brainly.com/question/15640807

#SPJ1

Answer:

Step-by-step explanation:

All you have to do is subtract 6 from 14. The answer is 8. If the question is something like this one, always take the remainder and subtract it from how many you had in the beginning to get the answer.

Good luck

Peyton

We can claim that after answering the above question, the Therefore, the solution to the original equation is: [tex]q = 9^x\\[/tex]

In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" states that the sentence "2x Plus 3" equals the value "9". The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.

given equation:

[tex]1/4xln(16q^8) - ln3 = ln24\\1/4xln(16q^8) = ln(24 * 3)\\1/4xln(16q^8) = ln72\\ln(16q^8)^(1/4x) = ln72\\16q^8^(1/4x) = 72\\16q^8 = 72^(4x)\\ln(16q^8) = ln(72^(4x))\\[/tex]

[tex]ln(16) + ln(q^8) = 4x ln(72)\\ln(q^8) = 4x ln(72) - ln(16)\\ln(q^8) = ln(72^(4x)) - ln(16^1)\\ln(q^8) = ln((72^(4x))/16)\\q^8 = e^(ln((72^(4x))/16))\\q^8 = (72^(4x))/16\\q^8 = 9^(8x)\\q = 9^x\\[/tex]

Therefore, the solution to the original equation is:

[tex]q = 9^x\\[/tex]

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

the y-coordinate must be 7 in order for the point to lie on the line.

A line in the xy-plane passes through the origin and has a slope of 1/7. Point B (1, 7) lies on the line, as the slope of the line is calculated by the equation y = mx + b, where m is the slope of the line, and b is the y-intercept. Since the line passes through the origin, the y-intercept is 0. This can be expressed as y = (1/7)x + 0

Learn more about coordinate

brainly.com/question/16634867

#SPJ11

Answer: 7.286

Step-by-step explanation:  To find the average, here is the formula =

Sum of all values in a data set ÷ the number of values = mean (average)

Step 1: We add the sum of the values

We do=

9 + 3 + 10 + 5 + 8 + 8 + 8 = 51

Step 2: We find the number of values

9  3  10  5  8  8  8  

1    2  3   4  5  6   7

So there are 7 values.

Step 3: We divide the sum of values by the number of values

51 ÷ 7 = 7.286

So the answer is 7.285714....

We round it to the nearest 3 decimal places (3 d.p).

This becomes 7.286

A horizontal curve is to be designed with a 2000 feet radius. The curve has a tangent length of 400 feet and its pi is located at station 103+00. Determine the stationing of the PT.

A horizontal curve is a curve that is used to provide a transition between two tangent sections of a roadway. To connect two tangent road sections, horizontal curves are used. Horizontal curves are defined by a radius and a degree of curvature. The curve's radius is given as 2000 feet. The tangent length is 400 feet.

The pi is located at station 103+00.

To determine the stationing of the PT, we must first understand what the "pi" means. PC or point of curvature, PT or point of tangency, and PI or point of intersection are the three primary geometric features of a horizontal curve. The point of intersection (PI) is the point at which the back tangent and forward tangent of the curve meet. It is an important point since it signifies the location of the true beginning and end of the curve. To calculate the PT station, we must first determine the length of the curve's arc. The formula for determining the length of the arc is as follows:

L = 2πR (D/360)Where:

L = length of the arc in feet.

R = the radius of the curve in feet.

D = the degree of curvature in degrees.

PI (103+00) indicates that the beginning of the curve is located 103 chains (a chain is equal to 100 feet) away from the road's reference point. This indicates that the beginning of the curve is located 10300 feet from the road's reference point. Now we need to calculate the degree of curvature

:Degree of curvature = 5729.58 / R= 5729.58 / 2000= 2.8648 degrees. Therefore, the arc length is:

L = 2πR (D/360)= 2π2000 (2.8648/360)= 301.6 feet.

The length of the curve's chord is equal to the length of the tangent, which is 400 feet. As a result, the length of the curve's long chord is: Long chord length = 2R sin (D/2)= 2 * 2000 * sin(2.8648/2)= 152.2 feet To determine the stationing of the PT, we can use the following formula: PT stationing = PI stationing + Length of curve's long chord= 10300 + 152.2= 10452.2Therefore, the stationing of the PT is 10452+2.

A horizontal curve is to be designed with a 2000 feet radius : https://brainly.com/question/31078631

#SPJ11

There was 88% increase in maintenance and repair costs from the first year to the second year. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

The four fundamental operations, often referred to as "arithmetic operations", are thought to be able to properly represent all real numbers. The mathematical operations quotient, product, sum, and difference come after division, multiplication, addition, and subtraction.

We are given that during the first year she owned her car, Barbara spent $732 on repairs and maintenance and she  spent $1,377 the second year she owned the car.

So, the more amount she spent in the second year is obtained using subtraction operation which gives:

⇒ $1,377 - $732

⇒ $645

Now, the percentage increase is

⇒ $645 ÷ 7.32

⇒ 88.11%

Hence, there was 88% increase in maintenance and repair costs from the first year to the second year.

Learn more about arithmetic operations from the given link

brainly.com/question/30283549

#SPJ1

Answer:

There were 62 people on the train to begin with.

Step-by-step explanation:

Firstly,i I subtracted 21 with 18 so i got 3.

It means that the train got 3 more people from the start.

Then i subtracted 65 with 3.

And so i got 62.

If on a monte carlo roulette wheel, there are 37 slots: 18 red, 18 black, and 1 green, the probability of getting 26 straight blacks is approximately 3.143 x 10^-16.

The probability of duplicating the exact sequence of 26 straight blacks that occurred on August 18, 1913, is extremely low. Each spin of the wheel is an independent event, so the probability of getting a black on any given spin is always 18/37, regardless of what happened on previous spins.

To calculate the probability of getting 26 straight blacks, we can use the formula for the probability of a sequence of independent events, which is the product of the probabilities of each event. Therefore, the probability of getting 26 straight blacks is (18/37)^26, which is an extremely small number, approximately 3.143 x 10^-16.

Therefore, the probability of duplicating the 26 straight blacks that occurred on August 18, 1913, is so low that it's effectively impossible. It's important to note that each spin of the wheel is independent, so even if the wheel had produced 25 straight blacks, the probability of the next spin being black would still be 18/37.

To learn more about probability click on,

https://brainly.com/question/20717881

#SPJ4

The closest option is (A) (3,3), which is the correct solution to the system of equations.

To find the solution to the system of equations, we need to substitute the value of y in the first equation with the value given in the second equation:

-6x + y = -21 ...(1)

2x - 1/3 y = 7 ...(2)

Substituting y=7 in the first equation, we get:

-6x + 7 = -21

Simplifying the above equation:

-6x = -28

Dividing both sides by -6, we get:

x = 28/6 = 14/3

Substituting x=14/3 and y=7 in the second equation, we get:

2(14/3) - 1/3(7) = 7

Simplifying the above equation, we get:

28/3 - 7/3 = 7

21/3 = 7

Therefore, the solution to the system of equations is (14/3, 7).

Hence, the answer is not in the given options, but the closest option is (A) (3,3), which is not the correct solution to the system of equations.

To know more about Linear Equations in two variables, click here,

https://brainly.com/question/30339221

#SPJ1

The circle at -6 is closed because the inequality does not include the possibility of y being equal to -6.

Inequality refers to a situation in which there is a difference or disparity between two or more things, usually in terms of value, opportunity, or outcome. Inequality can take many forms, including social, economic, and political inequality.

by the question.

the solution set of the inequality 1/2y < -3

Graph the solution set of the inequality 1/2y &lt; -3 - 1

To solve the inequality 1/2y < -3, we can begin by isolating the variable y on one side of the inequality:

1/2y < -3

Multiplying both sides by 2 yields:

y < -6

So, the solution set of the inequality is all real numbers y that are less than -6.

To graph the solution set on a number line, we can draw a closed circle at -6 and shade to the left of it, indicating that all values to the left of -6 are solutions to the inequality. The graph would look like this:

<=======o----------------------

To learn more about number:

https://brainly.com/question/13465215

#SPJ

To calculate the number of days it will take Ivan to read both books, we need to divide the total number of pages by the number of pages Ivan can read per day.

The first book has c pages, and the second book has d pages, so the total number of pages is c + d. If Ivan reads eight pages per day, then he will read a total of 8[tex]*[/tex]n pages in n days. Therefore, the number of days it will take Ivan to read both books can be calculated as: n = (c + d) / 8

This formula tells us that we need to divide the total number of pages by the number of pages Ivan can read per day, which is eight. The result of this division will give us the number of days it will take Ivan to read both books.

For example, if the first book has 100 pages and the second book has 200 pages, then the total number of pages is 300. plugging this into the formula, we get: n = (100 + 200) / 8 = 37.5 Since Ivan can't read a fraction of a day, we round up to the nearest whole number. Therefore, it will take Ivan 38 days to read both books.

Learn more about whole number here:

https://brainly.com/question/29766862

#SPJ4

The number of distinct sequences of letters is 8 × 26⁷.

How many distinct sequences of letters can you make if each sequence is ten letters long and contains the subsequence die?

We have to find the number of distinct sequences of letters that can be made. Here, the word 'die' can occur in any position of the ten-letter sequence. Therefore, we have to find the number of distinct sequences of seven letters that can be formed, which are not related to the word 'die'. The number of distinct sequences of seven letters that can be formed with no restrictions is:

26 × 26 × 26 × 26 × 26 × 26 × 26 = 26⁷

The word 'die' has three letters, and it can be placed in any of the eight positions of the seven-letter sequence (that is not related to the word 'die'). We have a total of 8 possibilities to choose where to put the word 'die'.Thus, the number of distinct sequences of letters is:

8 × 26⁷ (or) 703, 483, 260, 800.

The number of distinct sequences of letters is 8 × 26⁷.

To learn more about distinct sequences refer :

https://brainly.com/question/14575469

#SPJ11

13.33 hrs long would it take juan to do the same job alone.

Here, we have,

given that,

carlos and juan take 5 hours to do a job.

carlos alone takes 8 hours to do the same job.

let, x hr long would it take juan to do the same job alone.

now, we have,

1 hr work of carlos = 1/8

1 hr work of juan = 1/x

1 hr work of both = 1/8 + 1/x = (x+8)/8x

we have,

So they together can do this job in = 5 hours

so, ATQ, we get,

(x+8)/8x = 1/5

or, (5x+40) = 8x

or, 3x = 40

or. x = 13.33

Hence, 13.33 hrs long would it take juan to do the same job alone.

To learn more on simplification click:

brainly.com/question/28996879

#SPJ12

Answer: It is 160

Step-by-step explanation:

I just completed the test

Therefore , the solution of the given problem of surface area comes out to be the right response is option c 160 in².

Calculating how much space would be needed to fully cover the outside will reveal its overall size. The surroundings are considered when determining the same surface with a rectangular form. The surface area of something determines its overall dimensions. The amount of edges present in the space between a cuboid's four trapezoidal corners determines how much water it can hold inside.

Here,

the base's outermost boundary is:

=> Perimeter = 4s

To locate s,

=> Base  Area = s² = 64 in².

To solve for s, we obtain:

=> √(64 in²) = 8 in

We can now determine the perimeter:

=> perimeter: 4s

=> (4 * 8 inches)/(32 inches)

Finally, we can enter the numbers into the surface area formula as follows:

=>  Base Area + (1/2) x Perimeter x Slant Height

=> Surface Area Surface Area = 64 in² + (1/2) x 32 in x 6 in

=> Surface area = 64 in² + 96 in².

160 in² is the surface area.

Consequently, the cone has a surface area of 160 in².

The right response is (c) 160 in².

To know more about surface area visit:

https://brainly.com/question/2835293

#SPJ1

Answer:c

Step-by-step explanation:

Answer: C

Step-by-step explanation:

We can conclude that the end behavior of the function [tex]$h(x)$[/tex] is that it approaches negative infinity as [tex]$x$[/tex] approaches either positive or negative infinity.

What is meant by end behavior?

End behavior refers to the behavior of a function as the input (usually denoted by x) becomes extremely large (approaches positive or negative infinity). It describes the trend of the function as the input approaches infinity or negative infinity, and is determined by the highest-degree term of the function.

To determine the end behavior of the function [tex]$h(x)=-4x^2+11$[/tex], we can use limits. Specifically, we can evaluate the limit of [tex]$h(x)$[/tex] as [tex]$x$[/tex] approaches positive infinity and as [tex]$x$[/tex] approaches negative infinity.

As [tex]$x$[/tex] approaches positive infinity, we have:

[tex]\lim_{x \to \infty} h(x)= \lim_{x \to \infty} (-4x^2+11) = - \infty[/tex]

This tells us that as [tex]$x$[/tex] gets larger and larger, the value of [tex]$h(x)$[/tex] becomes more and more negative, eventually approaching negative infinity.

Similarly, as [tex]$x$[/tex] approaches negative infinity, we have:

[tex]\lim_{x \to -\infty} h(x)= \lim_{x \to -\infty} (-4x^2+11) = - \infty[/tex]

This tells us that as [tex]$x$[/tex] gets more and more negative, the value of [tex]$h(x)$[/tex] becomes more and more negative, also approaching negative infinity.

Therefore, we can conclude that the end behavior of the function [tex]$h(x)$[/tex] is that it approaches negative infinity as [tex]$x$[/tex] approaches either positive or negative infinity.

To learn more about end behavior visit:

https://brainly.com/question/1365136

#SPJ1

Answer:

Step-by-step explanation:

he's rich

Xavier will have $1278 left over from his paycheck after spending 20% on a new mattress and 29% on fixing a leak.

To find out how much will be left over from Xavier's paycheck after he spends 20% on a new mattress and 29% on fixing a leak, we can follow these steps:

Therefore, Xavier will have $1278 left over from his paycheck.

https://brainly.com/question/33576466

#SPJ2

The probability of Kim getting a 2 and a head is 1/12.

A subfield of mathematics known as probability studies random occurrences and the possibility that they will occur. It is a technique of putting a number on the degree of ambiguity surrounding a situation or result. A number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event, is used to express probability. The probability of an occurrence is determined by dividing the number of possible outcomes by the number of ways the event may occur. Several disciplines, including science, engineering, economics, and statistics, employ probability.

For a fair dice, the probability of getting a 2 on the dice is 1/6.

The probability of getting a head on the coin is 1/2.

Thus,

P(getting a 2 and a head) = P(getting a 2) × P(getting a head)

= (1/6) × (1/2)

= 1/12

Hence, the probability of Kim getting a 2 and a head is 1/12.

Learn more about probability here:

https://brainly.com/question/31120123

#SPJ1

Answer:

5a² + 4ab = a(5a+4b)

6p - pq - 5pr = p(6-q-5r)

8st +9su + 7sv = s(8t+9u+7v)

8pq² +9qr+ 7pqr = q(8p²+7pr+9r)

2a²b + ab² - 6ab = ab(2a+b-6)

6t²u +8tu²y + 5tuw = tu(6t+8uy+5w)

18abc²-42a²bc + 18ab²c = 6abc(3c-7a+3b)

24pqrs +56q²rs - 40qrs = 8qrs(3p+7q-5)

The GCF (Greatest Common Factor) of the variables of a polynomial has the least exponent of any variable term in the polynomial because it represents the largest factor that is common to all the terms in the polynomial.

To understand this better, consider a polynomial like 6x²y³ + 9x³y². The GCF of this polynomial would be 3x²y², which is the largest factor that can divide both terms evenly.

Notice that the exponent of each variable in the GCF is the smallest exponent among the corresponding variable terms in the polynomial.

This is because any factor that is common to all terms in the polynomial must be able to divide each term without leaving a remainder. Therefore, the exponent of each variable in the GCF must be less than or equal to the exponent of that variable in every term of the polynomial.

In summary, the GCF of the variables of a polynomial has the least exponent of any variable term in the polynomial because it represents the largest factor that can divide all terms in the polynomial evenly, and therefore, it must have the smallest exponent of each variable among all terms in the polynomial.

To know more about greatest common factor click on below link:

https://brainly.com/question/11221202#

#SPJ11

Answer:

Step-by-step explanation:well work it out use ur brain

Answer:

Step-by-step explanation:you need to multiply 120x40=20 your get $2,408

Answer:

7/20

Step-by-step explanation:

ok so it has 30 members, 7 are seniors it's possible. if there is multiple choice just let me know if it is not on there.

The value of angle ACB in triangle is 30°.

A triangle is a closed, two-dimensional shape made up of three line segments and has both inner and exterior angles. According to the triangle sum theorem, a triangle's internal angles may be added up to make 180, and its exterior angle equals the total of its two opposite interior angles.

∠ACB=8x-2

∠ABC=19x+4(vertically opposite angle)

∠BAC=180°-110°=70°( the sum of angles on a straight line is equal to 180°)

∠ACB+∠ABC+∠ABC=180°

8x-2+19x+4+70=180°

27x=108

x=4

Hence, value of angle∠ ACB=30°

to know more about line, visit:

https://brainly.com/question/2696693

#SPJ1

Answer:

11°

Step-by-step explanation:

The sum of the angles in a triangle is always 180°. Therefore, we can find the measure of ∠z by subtracting the measures of ∠x and ∠y from 180°:

∠z = 180° - ∠x - ∠y

∠z = 180° - 110° - 59°

∠z = 11°

Therefore, the measure of ∠z is 11°

The shape is an identical parallelogram and the area is equal to 30 square centimeters.

In calculating for the area of parallelogram, the base is multiplied by the height, as the same way for calculating the area of a rectangle.

we shall calculate for the area of the shape by evaluating the area of the one parallelogram and then multiply the result by two as follows:

area of one identical parallelogram = 5 cm × 3 cm

area of one identical parallelogram = 15 cm²

area of identical parallelogram shape = 2 × 15 cm²

area of identical parallelogram shape = 30 cm²

Therefore, the area for the identical parallelogram shape is equal to 30 square centimetres.

Know more area of parallelogram here: https://brainly.com/question/970600

#SPJ1

The probability of randomly chosen, a 50-year-old or older voter from the winning party is 45.84%

Given the table of values

From the table of values, we have the winning party to be

New Democratic

From the column of New Democratic, we have

Total = 9422

50-year-old or older voter = 4319

So, the required probability is

Probbaility = 4319/9422

Evaluate

Probbaility = 0.45839524517

This gives

Probbaility = 45.839524517%

Approximate

Probbaility = 45.84%

Hence, the probability is 45.84%

Read more about probability at

https://brainly.com/question/24756209

#SPJ1

The side opposite to angle Y is the longest, and angle Y is the largest angle in triangle XYZ. So, the angles can be ordered from greatest to least as follows:

angle Y > angle Z > angle X.

What is triangle ?

A triangle is a three-sided polygon, or a closed two-dimensional shape with three straight sides and three angles. The sum of the angles in a triangle always adds up to 180 degrees. The sides of a triangle can be of different lengths, and the angles can be acute (less than 90 degrees), right (equal to 90 degrees), or obtuse (greater than 90 degrees).  

To order the angles from greatest to least in triangle XYZ, we need to determine which side is the longest. By the Law of Cosines, we know that:

[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]

where c is the side opposite to angle C, and a and b are the other two sides.

So, let's calculate [tex]c^2[/tex] for each angle:

For angle X: [tex]c^2 = 25^2 + 27^2 - 2(25)(27)*cos(X)[/tex] ≈ 173.65

For angle Y: [tex]c^2 = 24^2 + 27^2 - 2(24)(27)*cos(Y)[/tex] ≈ 267.43

For angle Z: [tex]c^2 = 24^2 + 25^2 - 2(24)(25)*cos(Z)[/tex] ≈ 121.97

Therefore, the side opposite to angle Y is the longest, and angle Y is the largest angle in triangle XYZ. So, the angles can be ordered from greatest to least as follows:

angle Y > angle Z > angle X

To know more about triangle visit:

https://brainly.com/question/1058720

#SPJ1

The length of side x in simplest radical form with a rational denominator is equal to 4.472 units.

An isosceles triangle is a triangle with two equal sides. Also, the angles opposite to the two equal sides are also congruent.

According to Pythagoras' theorem, the square on the hypotenuse of a right-angled triangle equals the sum of the squares on the remaining two sides.

So, the length of other side is also equal to [tex]\sqrt{10}[/tex].

Now, lets use Pythagoras theorem to find the length of x.

Length of Hypotenuse is equal to [tex]\sqrt{y^2 + y^2}[/tex]

x = [tex]\sqrt{y^2 + y^2}[/tex]

x = [tex]\sqrt{\sqrt{10}^2+\sqrt{10 ^2} }[/tex]

x = [tex]\sqrt[2]{10+10}[/tex]

x = 4.472 units

Therefore, the length of side x in simplest radical form with a rational denominator is equal to 4.472 units.

Learn more about Pythagoras theorem:

https://brainly.com/question/343682

#SPJ1