A stadium has 53,600 seats. Seats sell for $40 in section A, $30 in section B, and for $15 in section C. The number of seats in section A equals the sum of the number of seats in sections B and C. For each sold-out event, the stadium takes in $1,682,500. How many seats does each section hold?

The length of the second trial will be equal to 2(⁵/₈) miles.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that two bicycle trails were developed in a new housing development. One trail is 3¹/₂ miles long. The other trail is 3/4 as long.

The length of the second trial will be calculated as,

Length =  3/4 x ( 3¹/₂ )

Length = 2(⁵/₈)

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Answer:

No, the Normal/large sample condition is not met. A confidence interval assumes that the underlying population follows a normal distribution and that the sample size should be at least 30. Since the sample size in this case is only 10, the Normal/Large Sample condition is not met and the conditions for constructing a confidence interval are not met.

(A) The formula for n swing \(a_n = 30(6/7)^n\).

(B) The arc length of the tire on 11th swing is 5.504 feet.

(C)  It takes 22 swings before the arc length is less than 1 foot.

An algebraic expression is consists of variables, numbers with various mathematical operations,

Given that,

The initial arc length of the tire = 30 feet

Also, the tire swings  and on each swing the arc length of the tire becomes 6/7 of the previous length.

(A)

The formula for n swing can be given as

\(a_n = 30(6/7)^n\)

(B)

The arc length of the tire on 11th swing = 30(6/7)¹¹ = 5.504 feet

(C)

To find number of swing when arc length in less than 1 foot,

The expression can be written as,

aₙ < 1

30(6/7)ⁿ < 1

(6/7)ⁿ  < 1/30

Take log both the sides,

log (6/7)ⁿ  < log (1/30)

n log (6/7) < log (1/30)

n < log(1/30)/log(6/7)

n < 22.064

Therefore, it takes 22 swings before the arc length is less than 1 foot.

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Answer:

x=sqrt(28)

Step-by-step explanation:

x^2+2^2=9^2-7^2

x^2=28

 x=sqrt(28)

Answer: The value of x is 26
In the given quadrilateral, it is given that, two angles have measurements

And two have measurement

And sum of measurement of angles of a quadrilateral is 360 degree, that is

SO for the given quadrilateral, the value of x is 26 .

Step-by-step explanation:

Answer:

  x = 30

Step-by-step explanation:

You want the value of x given that adjacent angles in a parallelogram are (3x+30)° and (2x)°.

Adjacent angles in a parallelogram total 180°, so ...

  (3x +30)° +2x° = 180°

  5x +30 = 180 . . . . . . . . . divide by °, simplify

  x +6 = 36 . . . . . . . . . divide by 5

  x = 30 . . . . . . . . . subtract 6

The value of x is 30.

__

Additional comment

The angles are (3·30 +30)° = 120°, and 2·30° = 60°.

Answer:

(a) We conclude that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism at 5% significance level.

(b) Yes, we can conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child.

Step-by-step explanation:

We are given that Autism and Maternal Antidepressant Use A recent study 41 compared 298 children with Autism Spectrum Disorder to 1507 randomly selected control children without the disorder.

Of the children with autism, 20 of the mothers had used antidepressant drugs. Of the control children, 50 of the mothers had used the drugs.

Let \(p_1\) = proportion of mothers who had used drugs having Autism Spectrum Disorder in their children.

\(p_2\) = proportion of mothers who had used drugs not having Autism Spectrum Disorder in their children.

(a) Null Hypothesis, \(H_0\) : \(p_1=p_2\)      {means that there is no significant association between prenatal exposure to antidepressant medicine and the risk of autism}

Alternate Hypothesis, \(H_A\) : \(p_1\neq p_2\)     {means that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism}

The test statistics that would be used here Two-sample z test for proportions;

                         T.S. =  \(\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }\)  ~ N(0,1)

where, \(\hat p_1\) = sample proportion of mothers who had used drugs having Autism Spectrum Disorder in their children = \(\frac{20}{298}\) = 0.067

\(\hat p_2\) = sample proportion of mothers who had used drugs not having Autism Spectrum Disorder in their children = \(\frac{50}{1507}\) = 0.033

\(n_1\) = sample of children with Autism Spectrum Disorder = 298

\(n_2\) = sample of children without Autism Spectrum Disorder = 1507

So, the test statistics  =  \(\frac{(0.067-0.033)-(0)}{\sqrt{\frac{0.067(1-0.067)}{298}+\frac{0.033(1-0.033)}{1507} } }\)

                                       =  2.281

The value of z test statistics is 2.281.

Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism.

(b) Yes, we can conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child because if we reconsider our hypothesis for one-tailed test in which the null hypothesis states that the prenatal exposure to antidepressant medicine does not increases the risk of autism in the child.

For this hypothesis also, our test statistics will be more than the critical value of z and due to which we reject our null hypothesis and conclude that prenatal exposure to antidepressant medicine increases the risk of autism.

Answer:

29 degrees

Step-by-step explanation:

Note how both triangles are isosceles triangles, which mean two angles will be equivalent. In the triangle with the marked angle measurement, since the total of angles in a triangle is 180, then the measurement of the unmarked angles have a sum of 180-64, which is 116. Then, as stated before, this triangle is isosceles, so the measurement of each unmarked angle is 116/2, which is 58.
Next, notice how the angle below angle x in that triangle shares a line with one of the 58 degree angles. This means that angle is 180-58, which is 122. Now, since the total of angles in a triangle is 180 and the triangle is isosceles, then angle x is (180-122)/2, which is 58/2, or 29 degrees

Answer:

28.0

Step-by-step explanation:

The circumference is diameter*3.14 (pi). So for this you divide to get the diameter. Hope this helps! :)\

88/3.14=28.0

Answer:

7 < x < 12

Step-by-step explanation:

To solve this inequality, solve it the same way you do a normal function. Perform the same actions on both sides of the inequality.

\(10 < 2x-4 < 20\\14 < 2x < 24\\7 < x < 12\)

The volume of the great Khafre Pyramid, given the height, and length of bases would be 74, 433, 109.33 cubic feet.

To find the volume of the pyramid, we can use the formula:

V = (1/3) x B x h

where B is the area of the base and h is the height of the pyramid.

Since the base is a square, the area of the base can be found by:

B = s^2

where s is the length of a side.

In this case, s = 706 feet, so:

B = 706 ^ 2 = 498, 436 square feet

Now we can plug in the values for B and h:

V = (1/3) x 498,436 x 448

V = 74, 433, 109.33 cubic feet

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The full question is:

The great Khafre Pyramid, the second tallest and second largest of the three ancient pyramids of Egypt, is 448 feet tall, and the length of a side at the base is 706 feet. The base of the pyramid is a square. What is its volume, rounded to the nearest cubic foot?

Answer: 74,433,109

Step-by-step explanation:

Answer:

VALUE OF X:

3x-13+61 = 90

3x+48 = 90

3x = 42

x = 14

MEASURE OF <MNQ:

3x-13

= 3(14)-13

= 42-13

= 29

Answer:

3/4 to 9/6

Step-by-step explanation:

Answer:

c=y×z

Step-by-step explanation:

the answer is this because z would be the number of dozens you have times y the cost of one by multiplying those together you will get the cost of the z dozens of eggs

5x - 4y = 12

Isolating y

In this equation, the slope is 5/4 and the y-intercept is -3.

From the answer choices, y = 2x - 3 has the same y-intercept.

Answer:

0

Step-by-step explanation:

distributive property

6x + 6 - 5x = 8 + 2x - 2

combine like terms

x + 6 = 6 + 2x

subtract x from both sides

6 = 6 + x

subtract 6 from both sides

0 = x

Answer:

6-13=7 , 7-13=6

6+1=7,7-1=6,

Step-by-step explanation:

A= h*b/2=4*16/2=32

Hope it helps!

Step-by-step explanation:

I think the Answer is option A

The standard error tells us how much we can expect the sample proportion to vary from the true proportion in repeated samples of the same size. Option (d) correctly states that "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion." This means that if we were to take many samples of 100 students from the same school and calculate the proportion of students who bring a reusable water bottle from home in each sample, about 95% of the sample proportions would fall within +/-0.048 of the true proportion.

The correct option is (d) "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion."

The standard error of the sample proportion can be calculated using the formula:

SE = √[p*(1-p) / n]

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 37/100 = 0.37 and the sample size is 100. Plugging in these values, we get:

SE = sqrt[0.37*(1-0.37) / 100] = 0.048

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Answer:

4 lb/month

Step-by-step explanation:

loss of 144 lb in 36 months

144/36 = 4

Answer: 4 lb/month

The result of the percentage increase = 72.24

number = 43

percentage Increase = 68%

increase = number × percentage Increase

increase = 43 × 68% = 43 × 0.68

increase = 29.24

The result of the percentage increase = initial number + the increase

The result of the percentage increase = 43 + 29.24

The result of the percentage increase = 72.24

Answer:

x = 63.5°

Step-by-step explanation:

To find the value of x in the given right triangle, we would apply trigonometric function.

Reference angle = x

Side length Opposite to x = 17

Hypotenuse length = 19

Apply SOH:

\( sin(x) = \frac{Opp}{Hyp} \)

\( sin(x) = \frac{17}{19} \)

\( x = sin^{-1}(\frac{17}{19}) \)

x = 63.474648° ≈ 63.5° (nearest tenth)

Answer:

50

Step-by-step explanation:

Median is found by locating the middle of a data. You have a total of 9 numbers. the 5th number would be the answer(you would have to sort the numbers from least to greatest).

Answer:

h bxbdbbdbdbdbdvxbdbd

l am not sure but I think it's Y

1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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Answer:

7 brown M&Ms.

Step-by-step explanation:

This question is not complete, but I will assume that the final question is how many brown M&Ms will be in this package.

0.14 × 52 is our equation.

The answer is 7.28. We cannot have .28 of a brown M&M in a package (unless you count the broken ones) so there will be, on average, 7 brown M&Ms in a package.

(again, the question is incomplete, so this may not be the answer)

The graph of the pH function can be created by plotting the output of

input values of the hydronium ions, x, in the range 0 < x ≤ 1.

Correct responses:

First part:

Please find attached the graph of the pH function

From the attached graph of the pH function, we have;

Second part

First part

The pH function is; f(x) = -log₁₀x

Please find attached the graph of the pH function created with MS Excel

Where;

x = Amount of hydronium ions

f(x) = pH level

When the pH is 0, we have;

-log₁₀x = 0

Which gives;

x = 10⁰ = 1

When the pH value is 1, we have;

-log₁₀x = 1

log₁₀x = -1

x = 10⁻¹ = 0.1

Second Part

The given transformations are;

f(x) + 1, and f(x + 1)

At the y-intercept, x = 0

From the transformation, f(x) + 1, we have;

At x = 0, the transformation = -log₁₀(0) + 1

log₁₀(0) = Does not exist (DNE)

Therefore;

f(x) + 1 = -log₁₀(0) + 1 = DNE

The transformation, f(x + 1), at x = 0, gives;

f(0 + 1) = -log₁₀(0 + 1) = -log₁₀(1) = 0

Therefore;

The function f(x + 1) = -log₁₀(x + 1) is defined at x = 0, and therefore, has a y-intercept

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