The school that Scott goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold 12 adult tickets and 10 student tickets for a total of $196. The school took in $59 on the second day by selling 3 adult tickets and 5 student tickets. What is the price each of one adult ticket and one student ticket

Based on the dimensions of the floor plan given, and the city code, the perimeter of the floor plan is 446 feet.

This means that it is NOT within code.

The perimeter can be found by adding the lengths of all the sides of the floor plan. This gives:

= 135 + 49 + 54 + 39 + 81 + 88

Solving gives:

= 135 + 49 + 54 + 39 + 81 + 88

= 446 feet

This means that the porch does not stay within code as it is larger than the recommended maximum.

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Answer:

7

Step-by-step explanation:

Do the brackets first

X+8= 8x

X+8= 8x

then you plus 8x + 8x =16x

16x -9 =7x

Answer:

20

Step-by-step explanation:

The factors of 20 are 1, 2, 4, 5, 10, and 20. The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80. You can see that they have some of the same factors, but the greatest they share is 20

The greatest common factor of 80 and 20 is 20.

In Mathematics, factors can be defined as the fundamental building blocks of a number. This ultimately implies that, factors simply refers to numbers which can be multiplied together to get another number.

The factors of 20 include the following: 1, 2, 4, 5, 10, and 20.

The factors of 80 include the following: 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.

By critically observing the factors above, we can logically deduce that the greatest common factor of 80 and 20 is equal to 20.

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Answer:

V = (1/2)(4/3)π(6.5^3) = 575.17 cubic inches

V = (1/2)(4/3)(3.14)(6.5^3) =

574.88 cubic inches

The correct answer is 574.9 cubic inches.

Answer: 44 degrees

Step-by-step explanation: 59+77+x=180

x=44

Use the quadratic formula to find the values of x:

Where a, b and c are the coefficients of the quadratic equation.

The equation has two solutions for x.

As decimal numbers:

Answer:

C and E are correct

Step-by-step explanation:

We simply substitute the value of x to see if we can get y for each of the equations

A. y = -3x

2 is not -3(6)

This is wrong

B. y = -3/2x + 6

-3/2x + 6 = -3/12 + 6

This cannot be equal to 2 so this is wrong also

c. y = -1/6x + 3

y = -1/6(6) + 3

= -1 + 3 = 2

This is correct

d. y = 2/3x - 1

This is wrong

2/3(6) - 1 cannot be 2

e. y = 1/2x - 1

2 = 1/2(6) -1

This is correct

F. y = 4(6) - 2 = 24-2 = 22

Answer:

64

Step-by-step explanation:

Looking at the number 63.62, you see that 6 comes immediately after the decimal point.

Now if the number after the decimal point is more than 5 we round up by adding one to the number just before the decimal point which is 3 in this case.

Assuming the number after the decimal point was less than 5 we would round down adding nothing to the number just before the decimal point.

Answer:

x = 3

x = -3 + √ 10

x = -3 - √ 10

Step-by-step explanation:

I used a calculator

** I'm not sure if the x's are multiplication symbols or they're variables. (I'm assuming they're variables).

If it's wrong, I'm sorry!!

Answer:

example...

2/3 = 4/6 has the same meaning as 2:3 = 4:6

Hope this helped!

Answer:

Explanation: 250 x 0.40 = 100

The limit of the given function as x approaches 1 is 0.

To find the limit of the given function as x approaches 1, we need to evaluate the expression by substituting x = 1. Let's break it down step by step:

1. Begin by substituting x = 1 into the numerator:

\(\[12\sin\left(\frac{\pi}{2}\cdot 1\right)\ln(1) = 12\sin\left(\frac{\pi}{2}\right)\ln(1) = 12(1)\cdot 0 = 0\]\)

2. Now, substitute x = 1 into the denominator:

(1³ + 5)(1 - 1) = 6(0) = 0

3. Finally, divide the numerator by the denominator:

0/0

The result is an indeterminate form of 0/0, which means further analysis is required to determine the limit. To evaluate this limit, we can apply L'Hôpital's rule, which states that if we have an indeterminate form 0/0, we can take the derivative of the numerator and denominator and then evaluate the limit again. Applying L'Hôpital's rule:

4. Take the derivative of the numerator:

\(\[\frac{d}{dx}\left(12\sin\left(\frac{\pi}{2}x\right)\ln(x)\right) = 12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{x} + \frac{\sin\left(\frac{\pi}{2}x\right)\ln(x)}{x}\right)\]\)

5. Take the derivative of the denominator:

\(\[\frac{d}{dx}\left((x^3 + 5)(x - 1)\right) = \frac{d}{dx}\left(x^4 - x^3 + 5x - 5\right) = 4x^3 - 3x^2 + 5\]\)

6. Substitute x = 1 into the derivatives:

Numerator: \(\[12\left(\cos\left(\frac{\pi}{2}\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{1} + \sin\left(\frac{\pi}{2}\right) \cdot \frac{\ln(1)}{1}\right) = 0\]\)

Denominator: 4(1)³ - 3(1)² + 5 = 4 - 3 + 5 = 6

7. Now, reevaluate the limit using the derivatives:

lim as x approaches 1 of \(\[\frac{{12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{{-1}}{{x}} + \sin\left(\frac{\pi}{2}x\right) \cdot \frac{{\ln(x)}}{{x}}\right)}}{{4x^3 - 3x^2 + 5}}\]\)

= 0 / 6

= 0

Therefore, the limit of the given function as x approaches 1 is 0.

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Explanation:

The question wants us to obtain the circumference of the circle given that the diameter of the circle is 13 meters.

To do so, we will use the formula:

Therefore, the circumference will be

Rounding off to the nearest whole number, we will have 41 meters

The sum of the measure of angles ∠AVC + ∠CVB is C. ∠AVB.

An angle bisector is a line segment that divides an angle into two equal parts.

The angle addition postulate states, if a line segment is in between an angle sum of two smaller angles created by the line segment, is equal to the measure of the larger angle.

The measure of angle AVB is 62°.

The measure of the angle AVC is 39° and the measure of the

angle CVB is 23°.

As the point, C is inside ∠AVB, ∠AVC + ∠CVB = ∠AVB.

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Answer:

80 degrees

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees so we can create the equation 70+30+x=180. This solves out to 80 so x=80 degrees.

Answer:

i think it is c or b but go with you gut feeling

Step-by-step explanation:

Answer:

\(\displaystyle \sqrt[4]{7^3}=7^{\frac{3}{4}}\)

Step-by-step explanation:

Exponential Form of Radicals

A radical of the form

\(\displaystyle \sqrt[n]{x^m}\)

Can be expressed in exponential form as follows:

\(\displaystyle \sqrt[n]{x^m}=x^{\frac{m}{n}}\)

We are given the number 4th root of 7 cubed. Writing in radical form:

\(\displaystyle \sqrt[4]{7^3}\)

It can be expressed in exponential form as:

\(\boxed{\displaystyle \sqrt[4]{7^3}=7^{\frac{3}{4}}}\)

Answer:

Step-by-step explanation:

According to intersecting secants theorem we have:

Correct choice is B

Answer:

Answer:

AC = 12

Step-by-step explanation:

If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore

ΔABC is similar to ΔADE.

The sides of smaller triangle are in proportion with sides of bigger triangle.

Therefore we have the equation:

AC/AE = AB/AD

Substitute the given numbers:

x/x+15 =8/18

18x= 8(x+15)

18x = 8x+120

10x = 120

x = 12

AC=12

Answer: Your answer is 23.5in²

Hope it helped :D

Good Luck!

Answer:

calculator gave me 6.5732

Step-by-step explanation:

Answer:

1100

Step-by-step explanation:

8 = 1000

9 = 1001

10 = 1010

11 = 1011

12 = 1100

hope this helps :)

The expression of the total amount is 0.3p + 0.0575(0.3p)

From the question, we have the following parameters that can be used in our computation:

Number of pencils = p

tax = 5.75%

Cost of pencils = $0.30

Using the above as a guide, we have the following:

Total amount = Number of pencils * cost of pencils * (1 + tax

Substitute the known values in the above equation, so, we have the following representation

Total amount = p * 0.3* (1 + 5.75%)

So, we have

Total = 0.3p + 0.0575(0.3p)

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Answer:

6.25

Step-by-step explanation:

Using the rules of exponents

\((\frac{a}{b}) ^{-\frac{m}{n} }\) = \((\frac{b}{a}) ^{\frac{m}{n} }\)

\(a^{\frac{m}{n} }\) = \((\sqrt[n]{a} )^m\)

Given

\((\frac{8}{125}) ^{-\frac{2}{3} }\)

= \((\frac{125}{8}) ^{\frac{2}{3} }\)

= \((\sqrt[3]{125} )^2\) × \(\frac{1}{(\sqrt[3]{8})^2 }\)

= 5² × \(\frac{1}{2^2}\)

= 25 × \(\frac{1}{4}\)

= \(\frac{25}{4}\)

= 6.25

Answer:

G and J

Step-by-step explanation:

Answer:

b) The data is bell shaped hence the assumption of X been normally distributed is correct

c) The categories are

  <  5, 5-6, 6-7, 7-8,  8-9, 9-10

d) attached below

e) The probability of < 7 gallons = 0.167

Step-by-step explanation:

a) stem and leaf diagram for these data

stem             leaf

5               .3

6               .1, .2, .2, .2, .5, .7, .7, .8

7               .1, .1, .1, .3, .4, .4, .4, .6, .6, .6, .7, .7, .8, .9, .9, .9

8              .0, .1, .1, .2, .2, .2, .4, .5, .7, .7, .7, .8, .8

9              .0, .1, .2, .3, .5, .5, .6, .6, .7

10             0

b) The data is bell shaped hence the assumption of X been normally distributed is correct

c) The categories are

  <  5, 5-6, 6-7, 7-8,  8-9, 9-10

d) attached below

e) The probability of < 7 gallons = 0.167