Help with question 3 please I’ll give brainlest

To approximate the area of the region bounded by the graph of f(t) = cos(t/2 - 3π/8) and the t-axis on the interval [3π/8, 11π/8] using 4 subintervals, we can use the midpoint rule.

The width of each subinterval is (11π/8 - 3π/8) / 4 = π/2.

We can calculate the height of each rectangle by evaluating the function at the midpoint of each subinterval.

The midpoints of the subintervals are:

t₁ = 3π/8 + π/4 = 5π/8

t₂ = 5π/8 + π/4 = 7π/8

t₃ = 7π/8 + π/4 = 9π/8

t₄ = 9π/8 + π/4 = 11π/8

Calculating the corresponding heights:

f(t₁) = cos(5π/16 - 3π/8)

f(t₂) = cos(7π/16 - 3π/8)

f(t₃) = cos(9π/16 - 3π/8)

f(t₄) = cos(11π/16 - 3π/8)

Now we can calculate the area of each rectangle by multiplying the width by the height.

Area of rectangle 1: (π/2) * f(t₁)

Area of rectangle 2: (π/2) * f(t₂)

Area of rectangle 3: (π/2) * f(t₃)

Area of rectangle 4: (π/2) * f(t₄)

Finally, we can approximate the total area by summing up the areas of all the rectangles:

Approximate area = Area of rectangle 1 + Area of rectangle 2 + Area of rectangle 3 + Area of rectangle 4

Please note that I cannot provide the exact numerical values as the calculation involves trigonometric functions and the specific values of π/8.

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The expected value of the bet is $5.

The expected value of the bet is calculated by multiplying each possible outcome by its corresponding probability and summing them up. In this case, there are two possible outcomes: winning $10 with a probability of 50% (0.5) and winning nothing with a probability of 50% (0.5).

To find the expected value, we multiply the value of each outcome by its probability:

Expected Value = ($10 * 0.5) + ($0 * 0.5) = $5 + $0 = $5.

Therefore, the expected value of the bet is $5. This means that, on average, for each bet placed, we can expect to win $5. It represents the long-term average outcome and is useful in assessing the overall value or profitability of the bet.

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Answer:

supplementary (add together to = 180°)

Step-by-step explanation:

Step-by-step explanation:

Supplementary angles add up to 180

complementary angles add up to 90

75+105=180

so the angles are supplementary

Hope that helps :)

Answer:

He won 6 games and lost 24 games.

a. the probability that the weight of a randomly selected candy bar is less than 8 ounces is approximately 0.1587 or 15.87%. b. the standard deviation of the sampling distribution is 0.1 / sqrt(40) ≈ 0.0159 ounces. c. the probability that the mean weight of the forty candy bars is less than 8 ounces is almost 0 or very close to 0.

(a) The probability that the weight of a randomly selected candy bar is less than 8 ounces can be found by calculating the cumulative probability using the Normal distribution. Given that the distribution of weights is Normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces, we want to find P(X < 8), where X represents the weight of a candy bar.

Using the properties of the Normal distribution, we can standardize the variable X using the formula Z = (X - μ) / σ, where Z is the standard normal random variable, μ is the mean, and σ is the standard deviation.

For our case, we have Z = (8 - 8.1) / 0.1 = -1.

Using a standard normal distribution table or a calculator, we find that the cumulative probability for Z = -1 is approximately 0.1587. Therefore, the probability that the weight of a randomly selected candy bar is less than 8 ounces is approximately 0.1587 or 15.87%.

(b) The mean of the sampling distribution of the sample mean can be calculated as the same as the mean of the population, which is 8.1 ounces.

The standard deviation of the sampling distribution of the sample mean, also known as the standard error of the mean, can be calculated using the formula σ / sqrt(n), where σ is the standard deviation of the population and n is the sample size.

In our case, the standard deviation of the population is 0.1 ounces, and the sample size is 40 candy bars. Therefore, the standard deviation of the sampling distribution is 0.1 / sqrt(40) ≈ 0.0159 ounces.

(c) To find the probability that the mean weight of the forty candy bars is less than 8 ounces, we can again use the properties of the Normal distribution. Since the mean and standard deviation of the sampling distribution are known, we can standardize the variable using the formula Z = (X - μ) / (σ / sqrt(n)).

In this case, we have Z = (8 - 8.1) / (0.0159) ≈ -6.29.

Using a standard normal distribution table or a calculator, we find that the cumulative probability for Z = -6.29 is extremely close to 0. Therefore, the probability that the mean weight of the forty candy bars is less than 8 ounces is almost 0 or very close to 0.

(d) The answers to (a), (b), and (c) would not be affected if the weights of chocolate bars produced by this machine were distinctly non-Normal. This is because of the Central Limit Theorem, which states that regardless of the shape of the population distribution, as the sample size increases, the sampling distribution of the sample mean approaches a Normal distribution.

In our case, we have a sufficiently large sample size of 40, which allows us to rely on the Central Limit Theorem. As long as the sample size is large enough, the sampling distribution of the sample mean will still be approximately Normal, even if the population distribution is non-Normal.

Therefore, we can still use the Normal distribution to calculate probabilities and determine the mean and standard deviation of the sampling distribution, regardless of the population distribution being non-Normal.

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Answer:

[tex]CI = (0.028636,0.071364)[/tex]

I am 95% confident that the true proportion of couples where the wife is taller than her husband is captured in the interval (.028, .071)

Step-by-step explanation:

Given

[tex]n = 400[/tex]

[tex]x = 20[/tex] --- taller wife

[tex]y = 380[/tex] --- shorter wife

Required

Determine the 95% confidence interval of taller wives

First, calculate the proportion of taller wives

[tex]\hat p = \frac{x}{n}[/tex]

[tex]\hat p = \frac{20}{400}[/tex]

[tex]\hat p = 0.05[/tex]

The z value for 95% confidence interval is:

[tex]z = 1.96[/tex]

The confidence interval is calculated as:

[tex]CI = \hat p \± z \sqrt{\frac{\hat p (1 - \hat p)}{n}}[/tex]

[tex]CI = 0.05 \± 1.96* \sqrt{\frac{0.05 (1 - 0.05)}{400}}[/tex]

[tex]CI = 0.05 \± 1.96 * \sqrt{\frac{0.0475}{400}}[/tex]

[tex]CI = 0.05 \± 1.96 * \sqrt{0.00011875}[/tex]

[tex]CI = 0.05 \± 1.96 * 0.01090[/tex]

[tex]CI = 0.05 \± 0.021364[/tex]

This gives:

[tex]CI = (0.05 - 0.021364,0.05 + 0.021364)[/tex]

[tex]CI = (0.028636,0.071364)[/tex]

Answer:

the amount that necessary to fund is $2,671.61

Step-by-step explanation:

The computation of the amount is shown below;

Given that

PMT = $270

NPER = 6 × 2 = 12

RATE = 6.2% ÷ 2 = 3.1%

FV = $0

The formula is shown below:

=-PV(RATE;NPER;PMT;FV;TYPE)

After applying the above formula the present value is $2,671.61

hence, the amount that necessary to fund is $2,671.61

Answer:

12

Step-by-step explanation:

12:18=2:3 multiply by four to get 8 as the first term

8:12

8:x

so x is 12.

*this could be wrong so check my work

Answer:

x = 12

Explanation:

8 : x

12 : 18

to find the value of x, we need to convert 12 into 8. since they both have a common factor of 4, we can divide 12 by 3 to get 4, and then multiply it by 2 to get 8. in numerical terms, this is:

12 ÷ 3 = 4

4 × 2 = 8

now, we can do the same for 18.

18 ÷ 3 = 6

6 × 2 = 12

thus, 12 : 18 is equivalent to 8 : 12. x = 12.

Answer and Step-by-step explanation:

Divide -5 from both sides of the inequality.

x < -5 is the answer.

Here's Why:

If you were to add 5x to both sides, it results in this:

0 > 25 + 5x

Now, we subtract 25 from both sides.

-25 > 5x

When we divide 5 from both sides, we see that it results in -5 > x, which is the same as x < -5.

#teamtrees #PAW (Plant And Water)

Answer:

4 cm

Step-by-step explanation:

The given statement “A correlation coefficient of −0.8 indicates strong indirect relationship” is true because it indicates a strong inverse or negative relationship between the variables.

A correlation coefficient is a statistical measure of the degree to which variables are related to one another. It is a numerical value that ranges from -1 to 1 and represents the strength and direction of the relationship between two variables.

If the correlation coefficient is -1, the relationship is strong and negative (inverse). On the other hand, if the correlation coefficient is 1, the relationship is strong and positive (direct).

When the correlation coefficient is zero, it indicates no relationship between the variables. When the correlation coefficient is near zero, it indicates a weak relationship between the variables.

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Answer:

Equally Likely

When x = 5, y = -1

When x = 6, y = 0

When x = 9, y = 1

When x = 14, y = 2

Answer:

696 39/100 meters

Step-by-step explanation:

Ben needs to replace two sides of his fence. One side is 367 9/100 meters long, and the other is 329 3/10 meters long. How much fence does Ben need to buy?

Side A = 367 9/100 meters

Side B = 329 3/10 meters

How much fence does Ben need to buy?

Total fence Ben needs to buy = Side A + side B

= 367 9/100 + 329 3/10

= 36709/100 + 3293/10

= (36709+32930) / 100

= 69639/100

= 696 39/100 meters

Ben needs to buy 696 39/100 meters

Answer:

I wanna say that it is 10-15

Step-by-step explanation:

Answer:

10-15

Step-by-step explanation:

#BeTheBest

Answer:

2010.62cm²

Step-by-step explanation:

The equation for the surface area of cylinder is:

A = 2πrh + 2πr²

Hope it was helpful

Answer:

b

Step-by-step explanation:

Answer:

DTI ratio in percentage = 42.36

Step-by-step explanation:

Annual salary = $47334

This means that gross monthly pay = 47334/12 = $3944.5

Now,

Total monthly debt payments = 1115 + 336 + 112 + 108 = $1671

Debt to income ratio = (1671/3944.5) × 100% = 42.36%

Since we are told not to put the % symbol, then answer is 42.36

Answer:

Pedro spent 9 weeks with his uncle and his friend.

Step-by-step explanation:

First, you need to find the amount of weeks Pedro spent with his friend. The statement indicates that he spent two weeks more with his friend than with his uncle which means that you have to add the number of weeks he spent with his uncle plus 2, which you can show in a number line:

       [tex]3\frac{1}{2}[/tex]                   2

___________________

1       2       3       4       5       6       7       8       9       10        

[tex]3\frac{1}{2}+2=5\frac{1}{2}[/tex]

Now, you can find the and answer by adding up the number of weeks he spent with his uncle plus the weeks he spent with his friend:

       [tex]3\frac{1}{2}[/tex]                                   [tex]5\frac{1}{2}[/tex]

__________________________________

1       2       3       4       5       6       7       8       9       10  

[tex]3\frac{1}{2} + 5\frac{1}{2}=9[/tex]

According to this, the answer is that Pedro spent 9 weeks with his uncle and his friend.

Answer:

y = 3x + 2

Step-by-step explanation:

If the line is parallel, then the slope remains the same.

To find the y-intercept, just plug the coordinates into the equation

y = 3x + b

14 = 3(4) + b

14 = 12 + b

2 = b

The equation is y = 3x + 2

Answer:

Slope intercept form

y=3x^2−19x+42

or

Point slope form

y−14=(3x−7)⋅(x−4)

Step-by-step explanation:

:)

I apologize, I cannot visually perceive or manipulate colors or lines directly. However, if you provide me with the equations of the lines or any additional information about their slopes, I would be more than happy to help you match the slopes with the corresponding lines.

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To match the lines (l1, l2, l3) with their corresponding slopes, we need to assign letters representing the slopes to each set.

Without specific information about the lines l1, l2, and l3, it is not possible to determine the exact slopes or their corresponding letters. In order to match the lines with their slopes, we would need additional details such as the equations of the lines or the coordinates of points on the lines.

The slope of a line represents the rate at which the line changes vertically (y-axis) with respect to the horizontal (x-axis). It is typically denoted by the letter "m" in mathematical notation.

To accurately match the lines l1, l2, and l3 with their respective slopes, we require more information about the lines themselves. Once the equations or coordinates are provided, we can calculate the slopes using the formula for slope, which is the change in y divided by the change in x.

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The new figure after the revolution is a cylinder of radius 5 and length 8

The volume is 200π

From the question, we have the following parameters that can be used in our computation:

The graph

The shape on the graph is a rectangle with

length = 5

width = 8

When revolved across the x-axis, we have the shape to be

A cylinder of radius 5 and length 8 (option a)

This is calculated as

V = πr²h

substitute the known values in the above equation, so, we have the following representation

V = π * 5² * 8

Evaluate

V = 200π

Hence, the volume is 200π

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Answer:

Option A

Step-by-step explanation:

The total shipping cost given was  $7.02.

C = 7.02

Solve for 'w'.

[tex]C = $3.50 + $0.55w\\\\7.02=3.50+0.55w\\\\3.52=0.55w\\\\\boxed{6.4=w}[/tex]

Hope this helps.

Answer:

15π cm²

Step-by-step explanation:

The total lateral area of a cone

= πr√h² + r²

= √h² + r² = l

h = Height = 4cm

r = radius = 3cm

Hence:

= π × 3 √4² + 3²

= 3π × √16 + 9

= 3π × √25

= 3π × 5

= 15π cm²

Answer:

The 20 subjects constitutes the sample

Step-by-step explanation:

Given

[tex]Total = 150[/tex]

[tex]Selected = 20[/tex]

Required

What does 20 represent?

The 150 patients being treated is the population of the study. When a certain amount is selected from a population, the selected is referred to as a sample.

So, this means that, 20 represents sample of the study.

The differences di = Xi - Yi for each pair of data are:

-1.1, -1.1, -4.2, -4.6, -2.9, -2.9, -0.8, -2.4.

To determine the differences di = Xi - Yi for each pair of data, we subtract the corresponding values of Xi and Yi:

Observations: 1 2 3 4 5 6 7 8

Xi: 45.4 45.5 45.5 42.9 45.2 47.4 51.4 43.1

Yi: 46.5 46.6 49.7 47.5 48.1 50.3 52.2 45.5

di = Xi - Yi: -1.1 -1.1 -4.2 -4.6 -2.9 -2.9 -0.8 -2.4

Therefore, the differences di = Xi - Yi for each pair of data are:

-1.1, -1.1, -4.2, -4.6, -2.9, -2.9, -0.8, -2.4.

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The number of units by which the graph of f(x) is translated vertically to obtain the graph of g(x) is -2 units. Since the value of d is negative, the direction of the translation is downwards. Thus, we can say that f(x) is translated 2 units downwards to form g(x).

f(x) = x⁴ and g(x) = x – 3, Since g is a vertical translation of f, we know that the graph of g(x) can be obtained by translating the graph of f(x) vertically up or down by some units, d. Thus, we can express g(x) as follows:g(x) = f(x) + d

Here, d represents the number of units by which the graph of f(x) is translated vertically to obtain the graph of g(x). Now, f(x) = x⁴, which means that the graph of f(x) is a standard cubic graph that has not undergone any transformation. We can represent this graph by the equation y = x⁴.

When g(x) is a vertical translation of f(x), we can write g(x) = y + d where d is the number of units by which f(x) is translated vertically to obtain g(x). Thus, we can rewrite g(x) as:

g(x) = f(x) + d

Substituting the values of f(x) and g(x), we get: x – 3 = x⁴ + d

Rearranging the equation, we have:x⁴ = x – 3 – d

Now, the number of units by which the graph of f(x) is translated vertically to obtain the graph of g(x), we need the value of d. To do this, we can use the fact that the graphs of f(x) and g(x) intersect at some point. At this point, the value of f(x) is equal to the value of g(x). Thus, we can write x⁴ = x – 3 – d

Solving this equation, we get x⁴ = x – (3 + d), the value of d by comparing the coefficients of x on both sides of the equation. On the left-hand side of the equation, the coefficient of x is 0, while on the right-hand side of the equation, the coefficient of x is 1. Thus, we can write:

0 = 1 – (3 + d)

Simplifying this equation, we get: d = -2

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Step-by-step explanation:

Area of square = Length x Length =

[tex] {length}^{2} [/tex]

Given Area of square =

[tex]256 {ft}^{2} [/tex]

[tex] {length}^{2} = 256 \\ length = \sqrt{256} \\ = 16ft[/tex]