Brenna is going to swim the length of her rectangular swimming pool. The width of the pool is 36 feet, and the diagonal distance from one corner to the opposite corner is 60 feet. What is the length of the pool?

Answer:

x = 3/2

Step-by-step explanation:

Let b = x

3 - 2(x)

3 - 2x

2x = 3

x = 3/2

Answer:

3/4 is the correct answer

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Volume to fill =  1 x 2 x 3/2 = 3  cm^3

Volume of cube to fill this volume  1/2 * 1/2 * 1/2 = 1/8 cm^3

3/ (1/8) = 24

The cost of 1 bottle of water when sold in a 24-pack case with a case price of $7.50 is $0.3125 or 31.25 cents.

The given equation is 24b = t, where b is the cost of one bottle of water and t is the price of a case of 24 bottles.

We are given that the price of the case is $7.50. Substituting this value in the equation, we get:

24b = 7.50

To solve for b, we need to isolate it on one side of the equation. We can do this by dividing both sides by 24:

b = 7.50/24

Simplifying this expression, we get:

b = 0.3125

Therefore, the cost of 1 bottle of water when sold in a 24-pack case with a case price of $7.50 is $0.3125 or 31.25 cents. In other words, if you were to buy a case of 24 bottles of water for $7.50, each bottle of water would cost you about 31.25 cents.

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Answer:

---------------------

Formula for area of a rectangle with dimensions l and w is:

Substitute 10 for l and 4 for w:

Answer:

(0, 2)

Step-by-step explanation:

The equation that represent the number of penguins is (6 ×  4) + (3 × 6) + (3 × 6) = p.

A building has 6 homes per floor and 3 floors. On the first floor, there are 4 penguins per home. On the second and third floor, there are 3 penguins per home.

Therefore, the equation that can be used to find the total number of penguins living in the building is as follows:

Hence,

(6 ×  4) + (3 × 6) + (3 × 6) = p

where

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Answer:

Answer:

24 sq yds

Explanation:

9 sq ft per sq yd

24*9=216 sq ft

let's keep in mind that arc's get their angle value from the central angle they cover, so in this case whatever angle value the arcAFB has, will also be the same for the ∡AFB.

Check the picture below.

We have the following:

Since the sides are equal, it means that all the angles are equal, we also know that the sum of the 3 angles within a triangle is always 180°, therefore

The value of x is 12

Answer:

The area of this triangle is (1/2)(9)(8) = 36.

Answer:

$103,000

Step-by-step explanation:

teacher : 38,900 x 5 = 194,500

principal : 59,500 x 5 = 297,500

$297,500 - $194,500 = $103,000 more

Answer:

3

Step-by-step explanation:

The answer is three because u need to simply the fractions

\(f(x) + g(x) = - 2 {x}^{4} + 6 {x}^{3} + 8{x}^{2} - 9x + 7\)

Answer:

The geometric mean of 6 and 30 is 13.416407864999

Answer:

Step-by-step explanation:

Hello!

A pilot study was conducted to test if three food rewards are equally appealing to the participants.

Of 60 participants surveyed:

16 preferred cupcakes (CC)

26 preferred candy bars (CB)

18 preferred dried apricots (DA)

If the three types of food are equally appealing for the participants, you'd expect that their proportions will be equal: P(CC)=P(CB)=P(DA)= 1/3

1.

The objective of this pilot study is to test if the observed frequencies follow a theoretical model/ distribution. To analyze this, you have to apply a Chi Square Goodness to Fit test. \(X^2=sum \frac{(O_i-E_i)^2}{E_i} ~~X^2_{k-1}\) Where k= number of categories of the variable.

For this example the statistical hypotheses are:

H₀: P(CC)=P(CB)=P(DA)= 1/3

H₁: At least one of the proportions isn't equal to the others.

2.

To calculate the expected frequencies for each category you have to use the formula: \(E_i= n* P_i\) where Pi represents the theoretical proportion for the i category, stated in the null hypothesis.

\(E_{CC}= n* P(CC)= 60*1/3= 20\)

\(E_{CB}= n*P(CB)= 60*1/3= 20\)

\(E_{DA}= n* P(DA)= 60* 1/3= 20\)

3.

The cutoff or critical value indicates the beginning of the rejection region for the hypothesis test. For the Chi-Square tests, the rejection region is always one-tailed to the right, meaning that you'll reject the null hypothesis if the value of the statistic is big. For the goodness to fit test you have k-1 degrees of freedom, so the critical value will be:

Assuming α: 0.05

\(X^2_{k-1;1-\alpha /2}= X^2_{2;0.975}= 7.378\)

The rejection region is then X²₂ ≥ 7.378

4.

\(X^2_{H_0}= \frac{(O_{CC}-E_{CC})^2}{E_{CC}} + \frac{(O_{CB}-E_{CB})^2}{E_{CB}} + \frac{(O_{DA}-E_{DA})^2}{E_{DA}} = \frac{(16-20)^2}{20} +\frac{(26-20)^2}{20} +\frac{(18-20)^2}{20}= \frac{14}{5}= 2.8\)

I hope this helps!

To understand the algebra, go through the following equations below:

Part B

Algebra is defined as a branch of mathematics that deals with variables, symbols and finding of these unknown using arithmetic operation such as ( +,  -,  *,  ÷ )

Algebra is the study and understanding of mathematical symbols and how to manipulate them in mathematical problems and formulae.

In conclusion, the above are the solution to the questions on the attached image.

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Answer:

it should round up to 36000

Answer : 12z - 32

Explaination:

Uhhh yeah math?

Answer:

Step-by-step explanation:

You want the equation of the circle shown on the radar screen as having a radius of 8 miles, centered at the origin.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Your circle is shown as having a radius of 8 miles. It is centered at the same origin where the control tower is located. That means we have ...

  (h, k) = (0, 0)

  r = 8

Using these values in the circle equation gives ...

  (x -0)² +(y -0)² = 8²

The equation of the circle is x² + (y + 8)² = 13.

What is a circle?

All points in a plane that are at a specific distance from a specific point, the centre, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

We know that the standard equation of a circle is

(x - h)² + (y - k)² = r²

where (h,k) represents the center and r is the radius.

We are given the center of the circle to be (0, -8) and that the circle passes through the point (2,-5).

In order to find the radius, we will use the distance formula.

Using this, we get

⇒r = √ (2 - 0)² + (-5 - (-8))²

⇒r = √13

So, we get the equation as

⇒(x - 0)² + (y - (-8))² = √13²

⇒x² + (y + 8)² = 13

Hence, the equation of the circle is x² + (y + 8)² = 13.

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If the sum of 3 numbers is 150, then their average is 50. Then if they are consecutive even numbers, then they are 48, 50 and 52. The smallest 48.

Answer:

the smallest of the three numbers is 48

48+50+52 =150

Step-by-step explanation:

smaller number = x

next even number = x+2

next even number = x+4

x+x+2 + x+4 =150

3x+6= 150

3x=144

x= 48

48+2 = 50

48+4 = 52

48+50+52 = 150

The area of the sector is 37.68ft²

The region inside the portion of the circle formed by two radii and an arc is known as the area of a sector. It just covers a small portion of the circle's total area.

Area of a sector

The area of a sector can be gotten using the expression (θ/360º) × π r ² where

Using the expression we will get,(270/360) x 3.14 x 4²

From the solution, we will find the area to be 37.68ft²

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Answer:

2nd one

Step-by-step explanation:

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

Answer:

A

Step-by-step explanation:

The mean of the test is 20.

To determine the mean of the test, we need to use the information provided about the scores falling above the mean in terms of standard deviations.

Let's denote the mean of the test as μ, and the standard deviation as σ.

We are given that a score of 29 falls three standard deviations above the mean, so we can write this as:

29 = μ + 3σ

Similarly, we are told that a score of 23 falls one standard deviation above the mean, which can be expressed as:

23 = μ + σ

Now we have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the values of μ and σ.

From the second equation, we can isolate μ:

μ = 23 - σ

Substituting this value into the first equation, we have:

29 = (23 - σ) + 3σ

Simplifying the equation, we get:

29 = 23 + 2σ

2σ = 29 - 23

2σ = 6

σ = 3

Substituting the value of σ back into the second equation, we find:

μ = 23 - 3

μ = 20

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The sum of the numbers 8 × 10⁶ and 7.92 × 10⁹ in the form of scientific notation will be 7.928 × 10⁹.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The expression is given below.

8 × 10⁶ and 7.92 × 10⁹

The addition of both terms 8 × 10⁶ and 7.92 × 10⁹ will be

⇒ 8 × 10⁶ + 7.92 × 10⁹

⇒ 8 × 10⁶ + 7920 × 10⁶

⇒ 7928 × 10⁶

⇒ 7.928 × 10⁹

The sum of the numbers 8 × 10⁶ and 7.92 × 10⁹ in the form of scientific notation will be 7.928 × 10⁹.

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Answer:

= 0

Step-by-step explanation:

Let's solve your equation step-by-step.

2x−4=2(x−2)

Step 1: Simplify both sides of the equation.

2x−4=2(x−2)

2x+−4=(2)(x)+(2)(−2)(Distribute)

2x+−4=2x+−4

2x−4=2x−4

Step 2: Subtract 2x from both sides.

2x−4−2x=2x−4−2x

−4=−4

Step 3: Add 4 to both sides.

−4+4=−4+4

0=0