HELP EMERGENCY ITS DUE TODAY 4100 people attended a football game. If 20% of the people who attended were teenagers, how many teenagers attended the game?

We choose option B: The P-value gives strong evidence against H_0. The P-value indicates that the null hypothesis is not plausible.

a. To find the test statistic z, we use the formula:

z = (p - P) / sqrt [P(1-P) / n]

where p is the sample proportion, P is the hypothesized proportion under the null hypothesis, and n is the sample size.

Plugging in the values given, we get:

z = (0.43 - 0.5) / sqrt [0.5(1-0.5) / 100] = -1.96

b. To find the P-value for H_a: p < 0.50, we look up the probability of getting a z-score less than -1.96 in a standard normal distribution table. The P-value is the area under the standard normal curve to the left of -1.96.

The P-value is approximately 0.025.

c. Since the P-value is less than the significance level of 0.05, we can reject the null hypothesis at the 5% level of significance. The P-value gives strong evidence against H_0. Therefore, we choose option B: The P-value gives strong evidence against H_0. The P-value indicates that the null hypothesis is not plausible.

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Here by Using identity –

\( {a}^{m} \times {a}^{n} = {a}^{(m + n)} \)

Now , According to your question /–

\(( {x}^{ - 8} ) \: ( {x}^{3} ) \)

\( =( {x}^{( - 8) + 3} )\)

\( =( {x}^{ - 5} )\)

\(Hence, \: value \: of \: |n| \: is \: \: ( - 5). \)

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The question is asking for the roots of the polynomial f(x) = 5x4 - 2x3 - 25x2 - 6x + 45. Therefore, the roots of f(x) = 5x4 - 2x3 - 25x2 - 6x + 45 are approximately -1.2 and 1.6.

To find the roots of a polynomial, we need to set f(x) equal to zero and solve for x. This means we are looking for values of x that make the equation f(x) = 0 true. We can do this through factoring or by using numerical methods such as the quadratic formula or Newton's method. To find the roots of f(x) = 5x4 - 2x3 - 25x2 - 6x + 45, we can use various methods. One approach is to try to factor the polynomial.

However, it is not immediately clear how to factor this polynomial, so we can turn to numerical methods. One way to find the roots is to use a graphing calculator or software to plot the function and look for the x-intercepts (where the function crosses the x-axis). This can give us an approximate idea of where the roots are located. Another method is to use iterative numerical techniques such as Newton's method or the bisection method to find the roots with increasing accuracy.


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The value of y so that the line has a slope of 1 is given as follows:

y = -2.

The slope of a linear function represents the rate of change of the output variable y relative to the input variable x.

Hence, given two points, the slope is calculated as the change in y divided by the change in x.

The points for this problem are given as follows:

(-1, y) and (4,3).

The change in y is of:

3 - y

The change in x is of:

4 - (-1) = 5.

The slope will have a value of one when:

(3 - y)/5 = 1

3 - y = 5

y - 3 = -5

y = -2.

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The value of a and b are 1 and -8 respectively.

Quadratic expressions are polynomial expressions of second degree.

The general form of a quadratic expression is ax² + b x + c.

The given quadratic expression is x² + 2x - 7.

We have to write this in the form (x + a)² + b.

We have the algebraic identity a² + 2ab + b² = (a + b)²

x² + 2x - 7 = x² + 2x - 7 + 1 - 1

                 = (x² + 2x + 1) - 7 - 1

                 = (x + 1)² - 8, which is in the form (x + a)² + b.

a = 1 and b = -8

Hence the value of a is 1 and the value of b is -8.

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The correct answer is D. an approximation of the time and expense of the research report.

A research request agreement typically includes all of the following items:

A. the scales for the measures: This refers to the specific measurement scales or instruments that will be used to collect data in the research.

B. the decision problem confronting the manager: This outlines the specific problem or issue that the research aims to address and provide insights for decision-making.

C. the target population from which a sample will be drawn: This defines the specific group or population that the research will focus on and from which a representative sample will be selected.

D. an approximation of the time and expense of the research report: This item is not typically included in a research request agreement. The time and expense of the research report are usually discussed separately during project planning and budgeting.

Therefore, the correct answer is D. an approximation of the time and expense of the research report.

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Answer:

(12+17)-(3x2)

Step-by-step explanation:

Answer:

12+17-(3x2)

Step-by-step explanation:

You do multiblecation before addition so you put it in parenthesis

Answer:

y-(-8) = 7(x-3) or

y+8 = 7(x-3)

The statement "The Taylor series centered at 0 (aka MacLaurin Series) for f(x) = \(x^{11}\) sin x has only even powers of x" is false.

The Taylor series centered at 0 (or MacLaurin series) for the function f(x) = \(x^{11}\) sin(x) includes terms with both even and odd powers of x. The general form of the Taylor series for this function is:

f(x) = f(0) + f'(0)x + f''(0)\(x^{2}\)/2! + f'''(0)\(x^{3}\)/3! + ...

The derivative of f(x) = \(x^{11}\) sin(x) involves both the derivative of \(x^{11}\) (which has only even powers) and the derivative of sin(x) (which has both even and odd powers). Therefore, when the Taylor series is expanded, terms with both even and odd powers of x will be present.

Hence, the statement is false.

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Answer:

\(\csc A - \sec A = \dfrac 83 + \dfrac{8}{\sqrt{55}}\\\\\csc A - \sec A = \dfrac 83 - \dfrac{8}{\sqrt{55}}\)

Step by step explanation:

\(\text{Given that,}\\\\~~~~~~\sin A = \dfrac 38 \\\\\implies \sin^2 A = \dfrac 9{64}\\\\\implies 1 - \cos^2 A = \dfrac{9}{64}\\\\\implies \cos ^2 A = 1 - \dfrac 9{64}\\\\\implies \cos^2 A = \dfrac{55}{64}\\\\\implies \cos A =\pm\sqrt{\dfrac{55}{64}}\\ \\\implies \cos A = \pm\dfrac{\sqrt{55}}8\\\\\)

\(\implies \dfrac 1{\cos A} = \pm\dfrac{8}{\sqrt{55}}\)

\(\text{Now,}\\\\\csc A - \sec A\\\\=\dfrac{1}{\sin A}- \dfrac{1}{\cos A}\\\\=\dfrac 83 -\left(\pm \dfrac 8{\sqrt {55}} \right)\\ \\\text{Hence,}\\\\\csc A - \sec A = \dfrac 83 + \dfrac{8}{\sqrt{55}}\\\\\csc A - \sec A = \dfrac 83 - \dfrac{8}{\sqrt{55}}\)

The histogram doesn't support Alfonso's claim and the correct option is 5: No, the distribution is skewed to the left with a mean age greater than 36.

What is a histogram?

A histogram is a graphic depiction of a frequency distribution with continuous classes that has been grouped. A series of rectangles with bases equal to the distances between class boundaries and areas proportional to frequencies in the associated classes make up the area diagram.

Consider the given histogram at the photo below. It is an left-skew histogram, since it has a long tail to the left side.

We need to estimate the mean of the given data. To do so, we need to multiply each class midpoint with its probability, and sum them.

For example, for the first one, the midpoint is 32 and the probability is 0.03 (read the value on the y-axis). For, the second one, the midpoint is 33 and the probability is 0.04, for the third the midpoint is 34 and the probability is 0.05, and so on. All needed values are presented below.

1. midpoint = 32, probability= 0.03

2. midpoint = 33, probability = 0.04

3. midpoint = 34, probability = 0.05

4. midpoint = 35, probability = 0.1

5. midpoint = 36, probability =0.11

6. midpoint = 37, probability = 0.13

7. midpoint = 38, probability = 0.2

8. midpoint = 39, probability = 0.09

So, it is obtained that -

μ = 0.03 · 32 + 0.04 · 33 + 0.05 · 34 + 0.10 · 35 + 0.11 · 36 + 0.13 · 37 + 0.25 · 38 + 0.20 · 39 + 0.09 · 40

μ = 37.15

Therefore, this histogram is left-skewed with mean greater than 36.

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If f(x) = 10 - 4x...

f(18) = 10 - 4(18) = 10 - 72 = -62 ≠ -2

This rules out answer a, since (18,-62) would be a point, not (18,-2).

f(-18) = 10 - 4(-18) = 10 + 72 = 82 ≠ -2

This rules out answer b, since (-18,82) would be a point, not (-18,2).

f(-2) = 10 - 4(-2) = 10 + 8 = 18

Answer c seems to be ok so far, since (-2,18) is a point in answer c.

f(2) = 10 - 4(2) = 10 - 8 = 2 ≠ =18

This rules out answer d, since (2,2) would be a point, not (2,-18).

The only answer that wasn't ruled out by check the first point in each answer is answer C.

Answer:

6.13 days

Step-by-step explanation:

Hello,

This question directly relates to radioactivity of a substance.

Data,

k = 0.113

Initial mass (No) = 38g

Half life of the substance (T½) = ?

To solve this question, we don't need the value of the initial mass because the variables in half life (T½) formula does not require it.

T½ = ln2 / k

Note : ln2 is a constant derived while k is the decay constant of the substance

T½ = 0.693 / 0.113

T½ = 6.13 days

The half life of the substance is 6.13 days

Answer:

456.63

Step-by-step explanation:

The value of the postfix expression 6 3 2 4 + - * is 18, which falls between 15 and 100. Therefore, the correct answer is d) Something between 15 and 100.

Here is the step-by-step  of how to evaluate the postfix expression:

1. Start with the first two numbers, 6 and 3, and the first operator, *. Multiply 6 and 3 to get 18.
2. Move on to the next two numbers, 2 and 4, and the next operator, +. Add 2 and 4 to get 6.
3. Now you have 18 and 6, and the last operator, -. Subtract 6 from 18 to get 12.
4. The final result is 12.

Therefore, the value of the postfix expression 6 3 2 4 + - * is 12, which falls between 15 and 100. The correct answer is d) Something between 15 and 100.

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Is the relation a function: C. No, because for each input there is not exactly one output.

In Mathematics, a function is typically used for uniquely mapping an independent value (input variable or domain) to a dependent value (range or output variable).

This ultimately implies that, an independent value represents the value on the x-axis of a cartesian coordinate while a dependent value represents the value on the y-axis of a cartesian coordinate.

Since the independent value (12) is mapped to multiple dependent values (-4 and -2), we can logically deduce that the relation does not represent a function.

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Answer:

x = 5

Step-by-step explanation:

Add all of the angles together. We know that the third one is 90° because it is a right triangle and the little square indicates a 90° angle.

7x + 16 + 39 + 90 = 180

Simply.

7x + 145 = 180

     -145    -145

7x = 35

/7      /7

x = 5

^-^

Solution:

Note that:

Simplify the equation:

we can take the two equations and divide them

so is option 4

Answer:

0.20

Step-by-step explanation:

The table F shows a proportional relationship.

A proportional relationship, also known as direct variation, exists when two variables are related in such a way that their ratio remains constant.

As one variable increases or decreases, the other variable changes by a consistent factor.

In the given tables, the table F represents a proportional relationship.

x/y=1/2=2/4=4/8=5/10

The ratio is constant x/y=1/2.

Hence, the table F shows a proportional relationship.

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Ten: 7,810

Hundred: 7,800

Thousand: 8,000

Answer:

1. 7810, 2. 8000, 3. 7800

Step-by-step explanation:

1. 12 is closer to 10 than it is to 20

2. 812 is closer to 1000 (188 away from 1000)than it is to 0(812 away)

3. 812 is close to 800 than 900

The general solution to the differential equation is given by y(x) = y_c(x) + y_p(x), where y_c(x) is the complementary solution and y_p(x) is the particular solution obtained using the method of undetermined coefficients.

Taking the second derivative of y_p(x), we have:

d²y_p/dx² = -Ab²cos(bx) - Bb²sin(bx)

Substituting this back into the differential equation, we get:

(-Ab²cos(bx) - Bb²sin(bx)) + a²(Acos(bx) + Bsin(bx)) = cos(bx)

For this equation to hold, the coefficients of cos(bx) and sin(bx) must be equal on both sides. Therefore, we have the following equations:

-Ab² + a²A = 1 ... (1)

-Bb² + a²B = 0 ... (2)

Solving equations (1) and (2) simultaneously for A and B, we can express the particular solution y_p(x) in terms of a and b.

The complementary solution y_c(x) can be found by solving the homogeneous equation d²y/dx² + a²y = 0, which yields y_c(x) = C₁cos(ax) + C₂sin(ax), where C₁ and C₂ are constants.

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Answer:

160/11 or 14 and 6/11

Step-by-step explanation:

6.4/0.44=6 4/10 divided by 100/44

64/10÷100/44=64/1÷10/44

11/1*10/11=160/11

The center of mass of the portion of the disk in the first quadrant, x^2+y^2=36, with mass density ρ(x,y) is 10yx/√(x^2+y^2), is  (14.4, 2.9).

To find the center of mass (CM) of the given portion of the disk, we need to first find the mass and the coordinates of the centroid.

Firstly, Find the mass of the portion of the disk. The mass of the portion of the disk can be found using double integrals

m = ∬R ρ(x,y) dA

where R is the region in the first quadrant defined by

x^2 + y^2 <= 36 and x >= 0, and ρ(x,y) = 10y√(x^2+y^2).

Using polar coordinates,

m =\(\int\limits^0_\(pi /2\)  \(\int\limits^0_6\) 10r^2sinθ dr dθ

 = 450π

Therefore, the mass of the portion of the disk is 450π.

Now, Find the coordinates of the centroid. The coordinates of the centroid can be found using the following formulas

x¯ = (1/m) ∬R x ρ(x,y) dA

y¯ = (1/m) ∬R y ρ(x,y) dA

Using polar coordinates again to evaluate the integrals

x¯ = (1/m) \(\int\limits^0_\(pi /2\) \(\int\limits^0_6\) 10r^3sin^2θ dr dθ

  = 72/5

y¯ = (1/m)\(\int\limits^0_\(pi /2\) \(\int\limits^0_6\) 10r^3sinθcosθ dr dθ

  = 144/5π

Therefore, the coordinates of the centroid are (x¯, y¯) = (72/5, 144/5π).

Hence, the center of mass of the portion of the disk in the first quadrant is located at (x¯, y¯) = (14.4, 2.9).

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Answer:

The area of the shaded region is 240 ft.

Step-by-step explanation:

Area Formula: A = L * H

First, find the area of the WHOLE shape. (300 = 25 * 12)

Next, find the area of the WHITE section. (60 = 5 * 12)

Lastly, subtract the area of the entire shape to the area of the white section. (300 - 60 = 240)

Your final answer should be 240 ft. Hope this helps! :D

Answer:

f^3 + 5f^2 +12f +8

Step-by-step explanation:

Answer:

R = 8,228,571.43 (Approx)

Step-by-step explanation:

Given:

R = x²/y

x = 4.8 x 10⁵

y = 2.8 x 10⁴

Find:

Value of R

Computation:

R = x²/y

R = (4.8 x 10⁵)²/ (2.8 x 10⁴)

R = 23.04 x 10¹⁰ / (2.8 x 10⁴)

R = 8.22857.. x 10⁶

R = 8,228,571.43 (Approx)

Answer:

8.2x10^6

Step-by-step explanation: