Questions 1

Questions 2

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B.<

C.=

Questions 3

Questions 4

Questions 5

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B.<

C.=

The test statistic value is -2.03.

What is the mean and standard deviation?

In statistics, the measurement of variability known as the standard deviation (SD) is frequently utilised. It displays the degree of variance from the mean (average). While a high SD shows that the data are dispersed throughout a wide range of values, a low SD suggests that the data points tend to be close to the mean.

We can use a one-sample t-test to test whether the mean endurance time of the tires is significantly different from the claimed value of 40000 km. The test statistic is given by:

\(t = (x - \mu) / (s / \sqrt{(n)})\)

where x is the sample mean (39750 km), μ is the claimed mean (40000 km), s is the sample standard deviation (387 km), and n is the sample size (25).

Substituting the values, we get:

\(t = (39750 - 40000) / (387 / \sqrt{25})\)

t = -250 / (387/5)

t = -2.03

Therefore, the test statistic value is -2.03.

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Answer:

$50 - $9.99 = $40.01

$40.01 ÷ $3.99 = 10

so the answer is 10

Step-by-step explanation:

if thats not whats being asked sorry

Inequality shows a relationship between two numbers or two expressions.

The inequality describes the number of movies Parv can buy.

9.99 + 3.99x ≤ 50

Where x is the number of movies.

The number of movies Parv can buy is 10.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal= ≥

We have,

Gift card = $50

Cost of a pack of games = $9.99

Cost of each movie = $3.99

x = number of movies

The inequality describes the number of movies Parv can buy.

9.99 + 3.99x ≤ 50

Where x is the number of movies.

Solve for x.

9.99 + 3.99x ≤ 50

Subtract 9.99 on both sides.

3.99x ≤ 50 - 9.99

3.99x ≤ 40.01

Divide both sides by 3.99

x ≤ 40.01/3.99

x ≤ 10

This means the number of movies Parv can buy is 10.

We can cross-check.

9.99 + 3.99 x 10 ≤ 50

9.99 + 39.9 ≤ 50

49.89 ≤ 50

Thus,

The number of movies Parv can buy is 10.

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12) There were about 557 principals in attendance. 13) Option A: The college will have about 480 students who prefer cookies. 14) Option C: bar graph, title favorite sport and the x axis labeled sport and the y axis.

The relationship between two quantities that are measured on the same scale and in the same units is known as a percentage. The relative size or magnitude of one thing in comparison to another is represented by proportions, which are frequently stated as ratios, fractions, or percentages. For instance, if there are 8 girls and 12 boys in a class, the girl-to-boy ratio is 8:12, or 2:3, which indicates that there are 3 guys for every 2 girls. Statistics, geometry, and physics are just a few of the mathematical and scientific disciplines that use proportions. Proportions are frequently used in statistics to describe the distribution of a population or a sample.

12) For the number of principals in conference we set up a proportionality with total people as follows:

We know that, 52 principals out of 70 people thus:

52/70 = x/750

Now,

x = (52/70) * 750

x = 557.14

Hence, we can predict that there were about 557 principals in attendance at the conference.

13) Given that, out of 225 students 27 prefer cookies thus,

27/225 = 0.12

That is 12% students like cookies.

Now, for the total number of students we have:

0.12 * 4000 = 480

Thus, option A: The college will have about 480 students who prefer cookies.

14) For the collected data the best representation is option C: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44.

15) For the given description of the line plot the median is:

For Bus 47 = 16

For Bus 18 = 13

The faster bus is Bus 47, with a median of 16.

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We will have the following:

First, we have that:

\(m<\text{VSW}+m<\text{WSR}=90\)And we have that:

m\(m<\text{VSW}+4m<\text{VSW}=90\Rightarrow5m<\text{VSW}=90\)\(\Rightarrow m<\text{VSW}=18\)So, the measurement of angle VSW is 18°.

2x-3y=-5

2x−3y+8=0

⇒−3y=−2x−8

⇒3y=2x+8

⇒y=  

3

2

​  

x+  

3

8

​ That's how I knew it

hopes  it helps you

And

your welcomeee

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The relationship between the ratios of sin x° and cos yº is that they are reciprocals. The correct answer is option c. The ratios of sin x° and cos yº are reciprocals of each other.

In trigonometry, sin x° represents the ratio of the length of the side opposite the angle x° to the length of the hypotenuse in a right triangle. Similarly, cos yº represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Since the hypotenuse is the same in both cases, the ratios sin x° and cos yº are related as reciprocals. This means that if sin x° is equal to 12/13, then cos yº will be equal to 13/12. The reciprocals of the ratios have an inverse relationship, where the numerator of one ratio becomes the denominator of the other and vice versa.

It's important to note that the signs of the ratios can vary depending on the quadrant in which the angles x° and yº are located. However, the reciprocal relationship remains the same regardless of the signs.

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The sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

To find a sinusoidal function with the given attributes, we can use the general form of a sinusoidal function:

f(x) = A * sin(Bx + C) + D

where A represents the amplitude, B represents the frequency (related to the period), C represents the phase shift, and D represents the vertical shift.

Amplitude: The given amplitude is 10. So, A = 10.

Period: The given period is 5. The formula for period is P = 2π/B, where P is the period and B is the coefficient of x in the argument of sin. By rearranging the equation, we have B = 2π/P = 2π/5.

Midline: The given midline is y = 31, which represents the vertical shift. So, D = 31.

f(3) = 41: We are given that the function evaluated at x = 3 is 41. Substituting these values into the general form, we have:

41 = 10 * sin(2π/5 * 3 + C) + 31

10 * sin(2π/5 * 3 + C) = 41 - 31

10 * sin(2π/5 * 3 + C) = 10

sin(2π/5 * 3 + C) = 1

To solve for C, we need to find the angle whose sine value is 1. This angle is π/2. So, 2π/5 * 3 + C = π/2.

2π/5 * 3 = π/2 - C

6π/5 = π/2 - C

C = π/2 - 6π/5

Now we have all the values to construct the sinusoidal function:

f(x) = 10 * sin(2π/5 * x + (π/2 - 6π/5)) + 31

Simplifying further:

f(x) = 10 * sin(2π/5 * x - 2π/10) + 31

f(x) = 10 * sin(2π/5 * x - π/5) + 31

Therefore, the sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

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The variance of X, where X takes the values 28, 46, 73, and 73 with equal probability, is 364.5.


To find the variance of a random variable X, you need to follow these steps:
1. Calculate the mean (average) of X.
2. Calculate the squared difference between each value of X and the mean.
3. Calculate the expected value of the squared differences.
4. The result obtained in step 3 is the variance of X.
Let’s apply these steps to the given values of X: 28, 46, 73, and 73.
Step 1: Calculate the mean (average) of X.
Mean(X) = (28 + 46 + 73 + 73) / 4 = 220 / 4 = 55
Step 2: Calculate the squared difference between each value of X and the mean.
(28 – 55)^2 = 27^2 = 729
(46 – 55)^2 = 9^2 = 81
(73 – 55)^2 = 18^2 = 324
(73 – 55)^2 = 18^2 = 324
Step 3: Calculate the expected value of the squared differences.
Expected value = (729 + 81 + 324 + 324) / 4 = 1458 / 4 = 364.5
Step 4: The result obtained in step 3 is the variance of X.
Variance(X) = 364.5
Therefore, the variance of X, where X takes the values 28, 46, 73, and 73 with equal probability, is 364.5.

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Answer:

=18,581,360,437,009

Answer:

The equation that can be use to determine the price of a sandwich is 5x + $1.25 = $38.75

Step-by-step explanation:

The equation that can be use to determine the price of a sandwich is as follows:

Let us assume the price of a sandwich be x

So,

The equation would be

5x + $1.25 = $38.75

5x = $38.75 - $1.25

x = $37.5 ÷ 5

x = $7.5

hence, the equation that can be use to determine the price of a sandwich is 5x + $1.25 = $38.75

Answer:

1

Step-by-step explanation:

y2 - y1 divided by x2 - x1

-9 + 5 = -4

3 - 7 = -4

-4/-4 = 1

Answer:

19) x=21

20) x=22

21) m∠1=70°

Step-by-step explanation:

19)

\(5x+75=180\)

\(5x=105\)

\(x=21\)

20)

\(90+68+x=180\)

\(x+158=180\)

\(x=22\)

21)

Because ∠1 and ∠3 are vertical, they are also congruent.

m∠3=m∠1=70°

Answer:

the answer is ç

Step-by-step explanation:

because π=3.14

Answer:

\(\huge\boxed{\sf 62.5 \%}\)

Step-by-step explanation:

Given that,

Completed problems = 5

Total = 8

\(\displaystyle = \frac{completed}{total} \times 100 \%\\\\= \frac{5}{8} \times 100\%\\\\= 0.625 \times 100 \%\\\\= 62.5 \%\\\\\rule[225]{225}{2}\)

The parametrization for C inducing a counterclockwise orientation and starting at (8, 0) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π, the parametrization for C inducing a clockwise orientation and starting at (0, 8) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π and parametrization for C if it is now centered at the point (2, 4) is C(t) = (4+ 8 cos, 2+ 8 Sin), 0 ≤ t ≤ 2π

The circle C of radius 8, centered at the origin, parametrization for C inducing a counterclockwise orientation and starting at (8, 0). c(t) :0 ≤ t ≤ 2π,

a) equation of the circle is x² + y² = 64.

starting point it (80) and orientation Counterclockwise.

c(t) (8cos, 8sin) 0 ≤ t ≤ 2π

b) Starting point is (0,8) and orientation is clockwise

c(t) (8cos, 8sin) 0 ≤ t ≤ 2π

c) equation of circle is (x-4)²+ (4-2)² - 64

For counterclockwise orientation

C(t) = (4+ 8 cos, 2+ 8 Sin), 0 ≤ t ≤ 2π

Therefore, the parametrization for C inducing a counterclockwise orientation and starting at (8, 0) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π, the parametrization for C inducing a clockwise orientation and starting at (0, 8) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π and parametrization for C if it is now centered at the point (2, 4) is C(t) = (4+ 8 cos, 2+ 8 Sin), 0 ≤ t ≤ 2π

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Answer:

2nd answer choice

Step-by-step explanation:

they are congruent aka equal or in the same spot

12 km / 3 hours = 4 km in 1 hour

1 hour / 4 km = 1/4 hour per km

Answer: 1/4 hour to run 1 km

Answer:

1/4 hours=0.25 hours

Step-by-step explanation:

Ntate runs 12 km in 3 hours.

Ntate runs 1 km in 3/12=1/4 hours.

The exact area of the surface obtained by rotating the given curve y = Sqrt(x2 +1) about the x-axis is (2π/3)(3√5 - 1).

To find the area of the surface obtained by rotating the given curve y = Sqrt(x2 +1) about the x-axis, we need to use the formula for the surface area of a revolution. This formula is given by:
\(S = 2π ∫a^b y √(1 + (dy/dx)2\)) dx

In this case, the limits of integration are from 0 to 2, as given in the problem. We first need to find dy/dx by taking the derivative of y with respect to x. We get:
dy/dx = x/(Sqrt(x2 +1))

Substituting this into the formula above, we get:
\(S = 2π ∫0^2 Sqrt(x2 +1) √(1 + x2/(x2 +1)) dx\)

Simplifying this expression and evaluating the integral, we get: \(S = 2π ∫0^2 Sqrt(2x2 +1) dx\)
\(S = 2π/3 [(2x2 +1)3/2]0^2\)
S = (2π/3)(3√5 - 1)

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The radius of the cylinder is found to be 6 cm.

A right circular cylinder is a three dimensional figure having its base and top as a circle and the height is perpendicular to circular base. The volume is given as V = πr²h.

Given that,

The height of the cylinder is 17 cm.

And, the volume is 1921.68 cm³.

Suppose the radius be r cm.

Substitute the corresponding values in the expression of volume V = πr²h as follows,

V = πr²h

=> 1921.68 = π × r² × 17

=> π × r² = 1921.68/17

=> r² =  1921.68/17π    

=> r = 6

Hence, the radius of the cylinder is obtained as 6 cm.

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Answer:

multiply

Step-by-step explanation:

Cause it just is

There is a 34% chance that the randomly purchased item from the manufacturer will last longer than 8 years.

The question is asking for the probability that a randomly purchased item from a manufacturer will last longer than 8 years. To answer this question, we must use the normal distribution formula and find the area under the curve between 8 and infinity.

The formula for the normal distribution is as follows:

\(1/(\sigma\sqrt{2\pi}) e^{-((x-\mu)^2)2\sigma^2}\)

Where μ is the mean and σ is the standard deviation.

In this problem, μ = 6.5 years and σ = 0.8 years.

Using the formula, the probability of the randomly purchased item lasting longer than 8 years is 0.34.

To calculate the probability, we use the z-score formula, which is \((x-\mu)/\sigma\). Plugging in 8-6.5/0.8 gives us a z-score of 1.875.

Using the z-table, we can find the area under the curve, which is 0.34. This means that the probability of the randomly purchased item lasting longer than 8 years is 0.34.

Therefore, the answer to the question is that there is a 34% chance that the randomly purchased item from the manufacturer will last longer than 8 years.

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Answer:

26

Step-by-step explanation:i used a caluculator

Answer: 9

Step-by-step explanation: there are 36 students in total. Since 25% of students wore a jacket, you would multiply 36 by 1/4 which gets you 9, so 9 students wore jackets

Answer:

The area of the park is 1,11,739 square feet.

Step-by-step explanation:

Since, the area of a triangle is,

Where,  and  are the adjacent sides and  is the included angle of these sides,

Here, the two adjacent sides of the park are 533 feet and 525 feet, while, the angle included by these sides is 53°.

That is,   = 533 ft,  = 525 ft and  = 53°,

Hence, the area of the park is,

Step-by-step explanation:

Two adjacent sides of the park say x and y are,

x=533feet

y=525feet

A=53º

area=1/2*b*c*sin(A)

111739 feet^2

Answer:

h = 10/15

Step-by-step explanation:

Isolate the variable, h. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, add 4 to both sides of the equation:

15h - 4 (+4) = 6 (+4)

15h = 6 + 4

15h = 10

Next, divide 15 from both sides of the equation:

(15h)/15 = (10)/15

h = 10/15 or 0.667 (rounded)

The critical value of 2.576. If |z| > 2.576, reject the null hypothesis; otherwise, fail to reject the null hypothesis.

To test the manufacturer's claim at a 1% significance level, we need to perform a hypothesis test. Let's define the null and alternative hypotheses:

Null hypothesis (H₀): The medicine is 90% effective in relieving backache.

H₀: p = 0.9

Alternative hypothesis (H₁): The medicine is not 90% effective in relieving backache.

H₁: p ≠ 0.9

Where p represents the true proportion of people who experience relief from backache after taking the medicine.

To conduct the hypothesis test, we will use the sample proportion and perform a z-test.

Calculate the sample proportion:

p = x/n

where x is the number of people who experienced relief (160) and n is the sample size (200).

p= 160/200 = 0.8

Calculate the standard error:

SE = √(p(1 - p)/n)

SE = √((0.8 * (1 - 0.8))/200)

Calculate the test statistic (z-score):

z = (p - p₀) / SE

where p₀ is the hypothesized proportion (0.9 in this case).

z = (0.8 - 0.9) / SE

Determine the critical value for a two-tailed test at a 1% significance level.

Since we have a two-tailed test at a 1% significance level, the critical value will be z* = ±2.576 (obtained from a standard normal distribution table or calculator).

Compare the absolute value of the test statistic to the critical value to make a decision:

If the absolute value of the test statistic is greater than the critical value (|z| > z*), we reject the null hypothesis.

If the absolute value of the test statistic is less than or equal to the critical value (|z| ≤ z*), we fail to reject the null hypothesis.

Substituting the values into the equation, we can determine the test statistic and compare it to the critical value.

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Step 1

Multiple both fractions

Step 2

Multiply numerator with numerator and denominator with denominator.

Final answer

The first four nonzero terms in the power series expansion for the general solution to the given differential equation about x0 are determined by setting coefficients of each power of (x - x0) to zero.

To find the power series expansion for the general solution to the given differential equation, let's assume the solution can be expressed as a power series:

y(x) = ∑[n=0 to ∞] a_n(x - x0)^n

Differentiating the series term by term, we have:

y'(x) = ∑[n=0 to ∞] n * a_n * (x - x0)^(n-1)

y''(x) = ∑[n=0 to ∞] n * (n-1) * a_n * (x - x0)^(n-2)

Substituting these into the differential equation (x^2 - 1)y'' - xy' = 0, we get:

(x^2 - 1) * ∑[n=0 to ∞] n * (n-1) * a_n * (x - x0)^(n-2) - x * ∑[n=0 to ∞] n * a_n * (x - x0)^(n-1) = 0

Now, we can expand and collect terms:

∑[n=0 to ∞] n * (n-1) * a_n * (x^2 - 1) * (x - x0)^(n-2) - ∑[n=0 to ∞] n * a_n * x * (x - x0)^(n-1) = 0

To find the first four nonzero terms, we can start with the term with the lowest power of (x - x0) and proceed with increasing powers. Let's go through the terms:

For n = 0:

0 * (-1) * a_0 * (x^2 - 1) * (x - x0)^(-2) - 0 * a_0 * x * (x - x0)^(-1) = 0

For n = 1:

1 * 0 * a_1 * (x^2 - 1) * (x - x0)^(1-2) - 1 * a_1 * x * (x - x0)^(1-1) = 0

For n = 2:

2 * 1 * a_2 * (x^2 - 1) * (x - x0)^(2-2) - 2 * a_2 * x * (x - x0)^(2-1) = 0

For n = 3:

3 * 2 * a_3 * (x^2 - 1) * (x - x0)^(3-2) - 3 * a_3 * x * (x - x0)^(3-1) = 0

By simplifying these equations, we can determine the first four nonzero terms in the power series expansion for the general solution to the given differential equation about x0.

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As a car dealer lowers a vehicle that was worth 18300 to 16000 by applying the formula of change in percentage we get that by 12.569 percentage (approximately) the price gets lowered .

The initial price of the car is set at P = 18300 (units)

The price after lowering drom P becomes A= 16000 (units)

Hence the change in price (or value) of the car, that is the price of the car is lowered by, C = (initial price - lowered price) = (P - A) = (18300 - 16000) units = 2300 units.

The formula for calculating percentage change is given as follows,

Change in percentage = [(Change in value)/ ( Initial value) ]*100

⇒Change in percentage = (C/ P)*100

⇒ Change in percentage =( 2300/ 18300)*100 = 12.569% (approximately)

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