Mrs. Jameson paid $22.50 for each student to visit an amusement park. Write an equation relating the total cost, y, and the number of students, x, attending the park.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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The surface area of the largest sphere that could fit into the rectangular box of dimensions 12 in x 14 in x 18 in is 324π inches²

The surface area of sphere = 324π inches²

What is a Sphere?

A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.

The Surface Area of a Sphere = 4πr²

The Volume of a Sphere = ( 4/3 ) πr³

where r is the radius of the sphere

Given data ,

Let the surface area of the Sphere be = S

Let the dimensions of the rectangular box be L x W x H

12 inches x 14 inches x 18 inches

Now , for the surface area of the sphere to have the largest surface area , the radius should be maximum

From the rectangular box , we can see that the height of the rectangle is best suited as the diameter of the sphere

So , Height of the Box = Diameter of the Sphere

And , Radius of the sphere = Height of the Box / 2

                                             = 18 / 2

Radius of the sphere = 9 inches

Now ,

Surface Area of a Sphere = 4πr²

r = 9 inches

Substituting the values in the equation , we get

Surface Area of a Sphere S = 4 x π x ( 9 )²

                                              = 4 x π x 81

                                              = 324π inches²

Therefore , the value of S is 324π inches²

Hence , The surface area of sphere = 324π inches²

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Answer:

the first and third equation

Step-by-step explanation:

when you divide 1/4 by 5, you get 1/20. dividing 1/4 by 5 is also the same as multiplying 1/4 by 1/5.

Answer: The area is  (800)

Step-by-step explanation: (10x 10= 100)

(100 x 8= 800)

FINAL ANSWER: 800m

~ i really hope this is correct, have a gr8 day/night my friend!~

Answer:

AB = 28 , BC = 17.5 , X = 13.2

Step-by-step explanation:

since the figures are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{AB}{PQ}\) = \(\frac{AD}{PS}\) ( substitute values )

\(\frac{AB}{8}\) = \(\frac{14}{4}\) ( cross- multiply )

4 AB = 8 × 14 = 112 ( divide both sides by 4 )

AB = 28

and

\(\frac{BC}{QR}\) = \(\frac{AD}{PS}\) ( substitute values )

\(\frac{BC}{5}\) = \(\frac{14}{4}\) ( cross- multiply )

4 BC = 5 × 14 = 70 ( divide both sides by 4 )

BC = 17.5

similarly for the 2 similar figures

\(\frac{x}{6}\) = \(\frac{11}{5}\) ( cross- multiply )

5x = 6 × 11 = 66 ( divide both sides by 5 )

x = 13.2

Answer:

\(\overline{AB}=28\)

\(\overline{BC}=17.5\)

\(x=13.2\)

Step-by-step explanation:

If quadrilateral PQRS is similar to quadrilateral ABCD, their corresponding sides are in the same ratio:

\(\overline{PQ} : \overline{AB} = \overline{QR} : \overline{BC} = \overline{RS} : \overline{CD} = \overline{SP}:\overline{DA}\)

From inspection of the two quadrilaterals, the given side lengths are:

\(\overline{PQ} = 8\)

\(\overline{QR} = 5\)

\(\overline{RS} = 6\)

\(\overline{SP} = 4\)

\(\overline{DA} = 14\)

Substitute these into the ratio equation:

\(8 : \overline{AB} = 5 : \overline{BC} = 6 : \overline{CD} = 4:14\)

Solve for AB:

\(8 : \overline{AB} = 4:14\)

   \(\dfrac{8}{\overline{AB}}= \dfrac{4}{14}\)

 \(8 \cdot 14=4 \cdot{\overline{AB}}\)

   \(\overline{AB}=\dfrac{8 \cdot 14}{4}\)

  \(\boxed{\overline{AB}=28}\)

Solve for BC:

\(5 : \overline{BC} = 4:14\)

  \(5 \cdot 14=4 \cdot \overline{BC}\)

    \(\overline{BC}=\dfrac{5 \cdot 14}{4}\)

   \(\boxed{\overline{BC}=17.5}\)

\(\hrulefill\)

Assuming the two figures are similar, their corresponding sides are in the same ratio. Therefore:

\(x:6=11:5\)

   \(\dfrac{x}{6}=\dfrac{11}{5}\)

   \(x=\dfrac{11 \cdot 6}{5}\)

   \(x=\dfrac{66}{5}\)

  \(\boxed{x=13.2}\)

The sample size needed to be 99​% confident that the sample proportion will not differ from the true proportion by more than ​4% is given as follows:

n = 1037.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The margin of error is given as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

As we have no estimate, the parameter is given as follows:

\(\pi = 0.5\)

Then the sample size for M = 0.04 is obtained as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.04\sqrt{n} = 2.575 \times 0.5\)

\(\sqrt{n} = \frac{2.575 \times 0.5}{0.04}\)

\((\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2\)

n = 1037.

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Answer:

1

Step-by-step explanation:

Answer: 1

Step-by-step explanation: Parentheses first, so (7-2), which is equal to 5, and then divide by 5 and you get 1 as the answer.

Answer:

Inequality form: x<1 or x>4

Interval Notation:

(-∞,1)∪(4,∞)

I hope this helps you

Answer:

30 units

Hope this answer is right!!

Step-by-step explanation:

Perimeter of Parallelogram Formula With Sides

Then the perimeter of the parallelogram is a + b + a + b (or) 2a + 2b (or) 2 (a + b). Thus, the perimeter (P) of a parallelogram with sides is, P = 2 (a + b) units.

Answer:C

Step-by-step explanation:

The bicycle is traveling at a speed of 19.46 miles per hour.

What is a circumference of a circle?

The circumference of a circle is the length of the circle. it is calculated by the formula  2πr where π is the mathematical constant whose value is 3.14

First, we convert the radius of the bicycle wheels from inches to feet

We get,

r = 14.0 in. = (14.0/12) ft = 1.1667 ft

Next, we calculate the circumference of the circle, which is equal to the distance traveled in one revolution.

distance = 2πr

Now we calculate the distance traveled in one minute

distance traveled in one minute = 2π(1.1667) * 215

                                                      = 1604.4 ft/min

Finally, we convert this to miles per hour:

We know that,

1 mile = 5280 ft

60 minutes = 1 hour

So, the speed of the bicycle in miles per hour is:

1604.4 ft/min * (1 mile/5280 ft) * (60 min/1 hour) = 19.46 mph (rounded to two decimal places)

Hence, The bicycle is traveling at a speed of 19.46 miles per hour.

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Step-by-step explanation:

b²-4ac

(10)²-4(-4)(-8)

=100+16+32

=148

Answer:

1.25 serving(s)?

Step-by-step explanation:

3/4 is a serving yes?

if you add the 1/4, than you get a cup getting 1 1/4 a serving

i changed the 1/4 to .25 because it makes more sense

The mean age of the U.S. presidents at inauguration is 54.7 years and the population standard deviation is approximately 5.7 years.

To find the mean and population standard deviation of the ages of the U.S. presidents at inauguration, we first need to calculate the sum of the ages and the number of presidents in the data set.

The sum of the ages is:

57 + 61 + 57 + 57 + 58 + 57 + 61 + 54 + 68 + 51 + 49 + 64 + 50 + 48 + 65 + 52 + 56 + 46 + 54 + 49 + 50 + 47 + 55 + 55 + 54 + 42 + 51 + 56 + 55 + 51 + 54 + 51 + 60 + 62 + 43 + 55 + 56 + 61 + 52 + 69 + 64 + 46 + 54 + 47 = 2,405

There are 44 presidents in the data set.

Therefore, the mean age is:

mean = sum of ages / number of presidents = 2,405 / 44 = 54.7

To find the population standard deviation, we first need to calculate the sum of the squared deviations from the mean:

(57 - 54.7)² + (61 - 54.7)² + ... + (47 - 54.7)² = 3,391.5

Then, we divide the sum of squared deviations by the number of presidents and take the square root:

population standard deviation = √(3,391.5 / 44) ≈ 5.7

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Option A. The statement that can be said to be true for h is h(2) = 16

If we look at the domain and range, we can rule out some straight away.

For h - 3 = -1

this is outside of the range of the such that -1 ∉ 1 ≤ hx ≤ 25

When h is 13 = 18

This is also outside of the domain such that 13 ∉ -3 ≤ x ≤ 11

When h is 8 = 21

there is going to be a contradiction with what the question has stated earlier. This is because we are told that h(8) = 19

Therefore on h(2) = 16

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Answer:

I think you need to know the value of X to get this answer.

Step-by-step explanation:

Answer:

El raigañu cuadráu corresponder cola radicación d'índiz 2 o, equivalentemente, cola potenciación d'esponente 1/2.

Cualquier númberu real non negativu {\displaystyle x}x tien un únicu raigañu cuadráu positiva o raigañu cuadráu principal[2] y denotada como {\displaystyle {\sqrt {x}}}{\displaystyle {\sqrt {x}}} onde {\displaystyle {\sqrt {\;}}}{\displaystyle {\sqrt {\;}}} ye'l símbolu raigañu y {\displaystyle x}x ye'l aniciando.

Cuando se riquir denotar dos raigaños cuadraos una negativa, {\displaystyle -{\sqrt {x}}}{\displaystyle -{\sqrt {x}}}, y otra positiva, {\displaystyle {\sqrt {x}}}{\displaystyle {\sqrt {x}}}, suelen denotarse curioso como {\displaystyle \pm {\sqrt {x}}}{\displaystyle \pm {\sqrt {x}}} o bien como {\displaystyle \mp {\sqrt {x}}}{\displaystyle \mp {\sqrt {x}}} según l'orde precisáu.

El conceutu de raigañu cuadráu puede estendese a cualquier aniellu alxebraicu, asina ye posible definir el raigañu cuadráu d'un númberu real negativu o'l raigañu cuadráu de delles matrices. Nos númberos cuaterniónicos los reales negativos almiten un númberu infinitu de raigaños cuadraos, sicasí'l restu de cuaterniones distintos de cero almiten solu dos raigaños cuadraos. Nel aniellu non conmutativu de les funciones reales de variable real cola adición y la composición de funciones si fºf = g, puede plantegase que f ye la "raigañu cuadráu" de g.[3]

Step-by-step explanationY segun todos mis calculos es 2 :

Answer:

75

Step-by-step explanation:

All the angles would add up to 360

145+55+35+55=285

Then:

360-285=75

>ZUW=75

is △ABC equilateral?  well, we dunno, however let's check for all sides' length.

\(~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{-6}~,~\stackrel{y_2}{-2}) ~\hfill AB=\sqrt{(~~ -6- (-3)~~)^2 + (~~ -2- 2~~)^2} \\\\\\ ~\hfill AB=\sqrt{( -3)^2 + ( -4)^2} \implies AB=\sqrt{ 25 }\implies \boxed{AB=5}\)

\(B(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad C(\stackrel{x_2}{0}~,~\stackrel{y_2}{-2}) ~\hfill BC=\sqrt{(~~ 0- (-6)~~)^2 + (~~ -2- (-2)~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 6)^2 + ( 0)^2} \implies BC=\sqrt{ 36 }\implies \boxed{BC=6} \\\\\\ C(\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\qquad A(\stackrel{x_2}{-3}~,~\stackrel{y_2}{2}) ~\hfill CA=\sqrt{(~~ -3- 0~~)^2 + (~~ 2- (-2)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -3)^2 + (4)^2} \implies CA=\sqrt{ 25 }\implies \boxed{CA=5}\)

well, not quite.

The Present value is $6,139.132.

We have,

FV=100000, pmt = 4000, I =5%, n=10

So, The present value formula is

PV=FV / (1 + \(i)^n\)

So, PV =  100, 000 / (1+ 5/100\()^{10\\\)

PV = 100,000 / (1+ 0.05\()^{10\\\)

PV = 100, 000/ (1.05\()^{10\\\)

PV = 100,000 / 1.6288946

PV= $6,139.132

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Answer:

One answer is x = 1, y = -1, and z = 2.

this is the answer to your question x=50

Step-by-step explanation:

3x-2x=50

1x=50

The value of x for the given equation is given as x = 50.

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

The given equation is as below,

3x = 2x + 50

It can be solved as follows,

3x = 2x + 50

=> 3x - 2x = 50

=> x = 50

Hence, the solution of the given linear equation is x = 50.

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Answer:

answer is 36

Step-by-step explanation:

The cost of each ratchet set at full price was $36.

Given that in a sale a ratchet set cost $8 less than its full price. Austin paid a total of $56.

We to find the cost of each ratchet set at full price,

Let's denote the cost of each ratchet set at full price as "x" dollars.

According to the information given, each ratchet set was marked down by $8, so their sale price would be (x - $8) dollars each.

Austin purchased 2 ratchet sets, so the total cost of his purchase would be:

2 (x - $8) = $56

Now we can solve for "x":

2 (x - $8) = $56

2x - $16 = $56

2x = $56 + $16

2x = $72

x = $72 / 2

x = $36

So, the cost of each ratchet set at full price was $36.

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Answer:

C.

Step-by-step explanation:

If by "turns in" they mean order, than its not a 3:4 ratio

Answer: 5:8

Step-by-step explanation:

There are 5 cows and 8 horses as outlined by the question. Thus, the ratio of horses to pigs is 5:8

Answer:

yeah as they said it is 5:8

Answer:

d,c,a

Step-by-step explanation:

guess it helps

Answer:

1/6

Step-by-step explanation:

A (6,1)

B (12,2)

slope = (2-1)/(12-6)

1/6

Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.

To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.

Rental: 1/5

Food: 1/10

Bank: 1/4

To find the fraction spent on miscellaneous:

Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)

Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40

Fraction spent on miscellaneous = 1 - 17/40 = 23/40

So, Mr. Marshal spent 23/40 of his salary on miscellaneous.

To find the amount spent on rental, we multiply the fraction spent on rental by his salary:

Amount spent on rental = (1/5) \(\times\) $8,400 = $1,680

Therefore, Mr. Marshal spent $1,680 on rental.

If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.

Fraction spent on the trip = (4/9) \(\times\) (23/40) = 92/360 = 23/90

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The researcher claim is invalid and the p-value based on alpha = 0.05 is   approx. = 0.

In the question ,

it is given that ,

a researches claims that per person yearly consumption (μ) is 52 gallons .

sample size (n) = 50 .

the mean of the consumption (x) = 56.3 .

the standard deviation (σ) is = 3.5 gallons .

the α = 0.05 .

let the null hypothesis ,

H₀ : μ = 52 and

H₁ : μ ≠ 52 .

the test statistics is : z = (x - μ)/(σ/√n)

the critical value ( rejection region ) : {z : |z| ≥ z₀.₀₂₅ = 1.96 }

So , z = (56.3 - 52)/(3.5/√50)

Simplifying further ,

we get ,

z = 8.69

We reject the null hypothesis H₀ , since the absolute value of the test statistics 8.69 is greater than the critical value 1.96 .

Since this is a two tailed test,  p-value must be multiplied by two

2 × P(z > 8.69) ≈  0

Since the p-value is less than α(0.05), So ,we reject the claim of the researcher that the mean yearly consumption of soft drinks per person is 52 gallons

Hence , the claim is not valid .

Therefore , The claim is invalid and p-value is ≈ 0 .

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