The state fair is a popular field trip destination. This year the senior class at High School A and the
senior class at High School B both planned trips there. The senior class at High School A rented and
filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54
students. Every van had the same number of students in it as did the buses. Find the number of students
in each van and in each bus.

Answer:

Step-by-step explanation:

Answer:

(a) D y = 6x + 7

(b) A 6

Step-by-step explanation:

6x -6 = -7   Subtract 6x from both sides

6x - 6x - y = -6x - 7

-y = -6x - 7    Divide all the way through by -1

y = 6x + 7

The slope is the number before the variable x. (6)

Answer:

since t takes 11 days for 200 the answer should be from 60 to 590

Step-by-step explanation:

it will take 53 days for 590

Answer:

The length of the longer base is 5mm.

Step-by-step explanation:

The area of a trapezoid:

\(A=\frac{1}{2}h(b_1+b_2)\)

With the given information, we can write some equations to represent the problem:

\(b_1=2b_2-7\\48=\frac{1}{2}(12)(b_1+b_2)\)

There's only 2 equations and 2 variables, so it's a relatively simple system of equations to solve. Ill solve by substitution:

\(b_1=2b_2-7\\48=\frac{1}{2}(12)(b_1+b_2)\\\\48=\frac{1}{2}(12)((2b_2-7)+b_2)\\48=(6)(3b_2-7)\\48=18b_2-42\\18b_2=90\\b_2=5\)

Now, plug that back into the first equation to solve for the other variable:

\(b_2=5\\b_1=2b_2-7\\\\b_1=2(5)-7\\b_1=10-7\\b_1=3\)

Now we have the measures of both of the bases.

To check that, calculate the area using these bases:

\(A=\frac{1}{2}(12)(3+5)\\A=6(8)\\A=48\)

It works fine.

Answer:

Step-by-step explanation:

it think it 23 becasue u add

1 divide it by 2

Answer:

b)60

Step-by-step explanation:

3/5 of 150 is 90 and 2/3 of 90 =60

so the anwser is 60

The end behavior of the function is as x tends to infinity, f(x) tends to zero. It is power function.

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function given is determine the end behavior of the graph.

Given that function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2.

The end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity.

The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).

Hence, we can conclude that the end behavior of the function is as x tends to infinity, f(x) tends to zero.

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Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

your answer is B

Step-by-step explanation:

Germany, Austria-Hungary, Bulgaria, and the Ottoman Empire

The score Julia has to have on her last test to have an A for the term is 102.

The first step is to determine the sum of her scores on the first three tests: 85 + 88 + 97 = 270

Now determine the score on the last test that would give an average of 93

(270 + x)/ 4 = 93

270 + x = 93 x 4

372 - 270 = x

x = 102

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Answer:

169

Step-by-step explanation:

Larger Number = 196

Smaller Number = 169

Step-by-step explanation:

larger sum = 196/

smaller sum = 169/

hope it helps. :)

Answer:

Step-by-step explanation:

You want the solution to right triangle RST with RS = 15, R = 72°, T = 90°.

The mnemonic SOH CAH TOA reminds you ...

  Sin = Opposite/Hypotenuse   ⇒   r = 15·sin(72°) ≈ 14.3

  Cos = Adjacent/Hypotenuse   ⇒   s = 15·cos(72°) ≈ 4.6

The acute angles in a right triangle are complementary, so ...

  S = 90° -R = 90° -72° = 18°

Answer:

48

Step-by-step explanation:

About 40 millions of aluminum cans can be recycled each month in the US. A quarter of these aluminum cans are used to make one aluminum boat. How many aluminum boats can be made in one year in the US?

Given that:

Approximate Number of cans that can be recycled per month in the US = 40 million

Fraction of recycled cans that can be used to make an aluminum boat = 1/4

The number of aluminum boats that can be made in the US in one year :

If about 40 million cans are recycle per month :

The number of boat that can be made from each monthly recycled aluminum cans will be :

Number of monthly recycled can needed to make one boat:

1/4 * 40 million = 10 million cans

Hence, 40,000,000 / 10,000,000 = 4

4 aluminum boats can be made in one month :

Number of months in a year = 12

Number of aluminum boats that can be made in a year :

4 per month * 12 = 48 aluminum boats

Answer:

the answer is y= √x/4

Step-by-step explanation:

f(x)= 4x^2

 y= 4x^2

  x= 4y^2

  4       4

   x/4= y^2

√x/4 = √y^2

y=  √x/4

The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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The value of \(b\) in the cubic polynomial is -4.

After a quick analysis, we find that given cubic function is equivalent to the following equivalence:

\(x^{3}+b\cdot x^{2}+c\cdot x + d = (x-1)^{2}\cdot (x-2)\)

\(x^{3}+b\cdot x^{2}+c\cdot x + d = (x^{2}-2\cdot x + 1)\cdot (x-2)\)

\(x^{3}+b\cdot x^{2}+c\cdot x + d = x^{3}-2\cdot x^{2}+x-2\cdot x^{2}+4\cdot x-2\)

\(x^{3}+b\cdot x^{2}+c\cdot x + d = x^{3}-4\cdot x^{2}+5\cdot x -2\)

After a quick observation, we conclude that the value of \(b\) in the cubic polynomial is -4. \(\blacksquare\)

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9514 1404 393

Answer:

Step-by-step explanation:

The area of each triangular face is given by the formula ...

  A = 1/2bh

The triangular faces have a base of b=8 cm, and a height of h=6 cm. Their area is ...

  A = 1/2(8 cm)(6 cm) = 24 cm²

__

Each of the rectangular faces has a length of 20 cm. The width depends on which face is of interest. In each case, the area is given by ...

  A = LW

Bottom face: A = (20 cm)(8 cm) = 160 cm²

Back face: A = (20 cm)(6 cm) = 120 cm²

Sloped face: A = (20 cm)(10 cm) = 200 cm²

__

The total area is the sum of the areas of all of the faces and bases. There are two triangular bases, so the total area is ...

  (2×24 + 160 +120 +200) cm² = 528 cm²

Answer:

Step-by-step explanation:

(0, -1) (3,3)

(3 + 1)/(3 - 0) = 4/3

y + 1 = 4/3(x - 0)

y + 1 = 4/3x - 0

y = 4/3x - 1

answer is A

Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.

We have,

Let's start by finding the total number of points that Carlos can earn in the class:

Total points

= 5 quizzes x 20 points per quiz

= 100 points

If Carlos needs an average of 90% or greater, that means he needs to earn at least 90 points out of 100.

Total points earned.

= 18 + 19 + 17 + 20

= 74 points

To find the minimum score Carlos needs on the final quiz, we can set up an inequality:

(74 + x) / 5 ≥ 0.9

where x is the score on the final quiz.

Simplifying this inequality.

74 + x ≥ 90

x ≥ 16

Therefore,

Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.

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Answer:

Step-by-step explanation:

If cakes of 4 small and 4 large tiers serve 288 guests, and 3 small and 5 large tiers serve 316 guests, you want to know the number of guests served by a tier of each size.

Let 's' and 'l' represent the numbers of guests served by small and large cake tiers, respectively. The first cake serves ...

  4s +4l = 288

And the second cake serves ...

  3s +5l = 316

Subtracting 3/4 of the first equation from the second gives ...

  (3x +5l) -3/4(4s +4l) = (316) -3/4(288)

  2l = 100

  l = 50

  4s +4(50) = 288 . . . substitute for l in the first equation

  4s = 88 . . . . . . . . . . subtract 200

  s = 22 . . . . . . . divide by 4

A small tier will serve 22 guests; a large tier will serve 50 guests.

Answer: It's not equal to 20% discount.

Step-by-step explanation:

Let's assume the cost of a good is $100. Since there's 10% off on every item, the cost of the good will be:

= $100 - (10% × $100)

= $100 - $10

= $90

Since the coupon states that one will receive an additional 10% off, therefore the amount that the person will pay will be:

= $90 - (10% × $90)

= $90 - (0.1 × $90)

= $90 - $9

= $81

If the same good is $100 and there's a 20% discount, the amount that'll be paid will be:

= $100 - (20% × $100)

= $100 - (0.2 × $100)

= $100 - $20

= $80

Therefore, it's not equal to 20% discount.

Some of the tips which is used to conduct a survey are:

Conducting a survey is an important tool for gathering information from a large and diverse group of people. Its allows allow researchers to obtain data from a representative sample of the population, which can then be used to make informed decisions, identify trends, and measure changes over time.

Also important, its can provide insight into people's attitudes, beliefs, and behaviors, which can be valuable in developing marketing strategies, designing programs and policies, and making important decisions.

A paragraph in a designed questionnaire which can remind participants why your doing the survey and that their information will kept confidential is as follows: "Thank you for taking the time to participate in this survey. The purpose of this questionnaire is to gather information about your experiences and opinions on a particular topic. Your participation is crucial to help us gain insights and make informed decisions. All of the information provided in this survey will be kept strictly confidential and will only be used for research purposes".

Full question "In a designed questionnaire, remind participants why your doing the survey and that their information will kept confidential".

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Answer: $5.10

Step-by-step explanation:

14.50 - 4.25 - 5.15 = 5.10

Answer: 4 pt + 2 c

Step-by-step explanation:

You add 2 + 2 = 4 and 1 + 1 = 2.

4 pt + 2 c

Add 2+2 and 1+1 which gives you 4 pt and 2 c.

Final result 4 pt + 2 c.

The general solution to the given differential equation is:

y = (x/12) - (1/288)

How to solve the Differential Equation?

We want to solve the differential equation given as: y' - 24xy = -2x

The integrating factor is given by the exponential of the integral of the coefficient of y, which in this case is -24x. Therefore, the integrating factor is e^(-24x).

Multiplying the entire equation by the integrating factor, we get:

e^(-24x)y' - 24xe^(-24x)y = -2xe^(-24x)

The left side of the equation is the derivative of (e^(-24x)y) with respect to x:

(d/dx)(e^(-24x)y) = -2xe^(-24x)

Integrating both sides with respect to x, we have:

e^(-24x)y = ∫(-2xe^(-24x))dx

Integrating the right side, we get:

e^(-24x)y = -∫(2xe^(-24x))dx

To evaluate the integral on the right side, we can use integration by parts. Let's differentiate -2x and integrate e^(-24x):

u = -2x (differential of u = -2dx)

dv = e^(-24x) (integral of dv = -1/24e^(-24x)dx)

Using the integration by parts formula:

∫uv dx = uv - ∫v du

We can compute the integral as follows:

-∫(2xe^(-24x))dx = -[(-2x)(-1/24e^(-24x)) - ∫(-1/24e^(-24x))(-2dx)]

= -[x/12e^(-24x) + 1/12∫e^(-24x)dx]

= -[x/12e^(-24x) + 1/12(-1/24)e^(-24x)]

= -[x/12e^(-24x) - 1/(12*24)e^(-24x)]

= -[x/12e^(-24x) - 1/(288e^(-24x))]

= -[x/12 - 1/288]e^(-24x)

Substituting this back into the previous equation, we have:

e^(-24x)y = -[-(x/12 - 1/288)e^(-24x)]

Simplifying further:

e^(-24x)y = (x/12 - 1/288)e^(-24x)

Canceling out e^(-24x) on both sides:

y = x/12 - 1/288

Therefore, the general solution to the given differential equation is:

y = x/12 - 1/288

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For the expression \(x^64 + ax^b + 25\) to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = \(y^2.\)

To determine the values of a and b such that the expression\(x^64 + ax^b\) + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.

A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of\((x^n)^2,\) where n is an even integer.

Let's examine the given expression: \(x^64 + ax^b\) + 25

For it to be a perfect square, the quadratic term \(ax^b\)must have the same exponent as the leading term\(x^6^4.\) This means b must be equal to 64.

So we have:\(x^64 + ax^64 + 25\)

Now, we can rewrite this as:\((x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2\)

By comparing this with the standard form of a perfect square, (\(x^n +\sqrt{k} )^2\), we can deduce that √a must be equal to x^32 and \(\sqrt{25}\) must be equal to \(\sqrt{k.}\)

Therefore, we have: \(\sqrt{a} = x^3^2\)and\(\sqrt{25} = \sqrt{k}\)

From the second equation, we know that k = 25.

Now, substituting the value of k back into the first equation, we have: \(\sqrt{a} = x^3^2\)

To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =\(y^2\), where y is an integer.

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Answer:

\(y=-4x+5\)

Step-by-step explanation:

The equation of a line with slope \(m\) and \(y\)-intercept \((0,b)\) is \(y=mx+b\).

Answer:

1232 is the answer

Step-by-step explanation:

distance= 22/7 ×7/2 ×112

=1232

Answer:

1232 ft.

Step-by-step explanation:

Distance travelled = circumference of the wheel * number of revolutions

= 7/2 * 22/7 * 112

= 22/2 + 112

= 11 * 112

= 1232 ft.