If u + 6 = 3 and v- 4= -2, what is the value of u + v?

1.The formula for the volume of a right circular cylinder is V = πr^2h, where r is the radius of the base and h is the height of the cylinder.

We are given that the base diameter is 20cm, so the radius is half of that, which is 10cm.

Therefore, the volume of the cylinder is:

V = πr^2h

V = π(10cm)^2(5cm)

V = π(100cm^2)(5cm)

V = 500π cm^3

Hence, the volume of the cylinder is 500π cubic centimeters.

2.We are given that the height of the cylinder is 22 1/4 and the diameter is 2 2/5 times its height. First, we need to find the radius of the base.

The diameter of the base is 2 2/5 times the height, so we can write:

d = (12/5)h

Substituting in the given value of h, we get:

d = (12/5)(22 1/4) = 54.4 cm

Therefore, the radius of the base is:

r = d/2 = 27.2 cm

Now, we can use the formula for the volume of a cylinder:

V = πr^2h

Substituting in the values of r and h, we get:

V = π(27.2cm)^2(22 1/4 cm)

V ≈ 50,873.36 cm^3

Rounding to the nearest hundredth, we get:

V ≈ 50,873.36 cm^3 ≈ 50,873.35 cm^3

Hence, the volume of the cylinder is approximately 50,873.35 cubic centimeters.

The probability is 0.375, which means that out of 4 people, one person is likely to have the disease. Given,The fraction of people x years old with the disease is modeled by f(x) = x / (100 + x).

Here, (a) Evaluate f(20) and f(60). Interpret the results.

f(20) = 20 / (100 + 20) results to 0.1667

f(60) = 60 / (100 + 60) results to 0.375

Here, f(20) is the probability that a person who is 20 years old or younger has the disease. Therefore, the probability is 0.1667, which means that out of 6 people, one person is likely to have the disease. On the other hand, f(60) is the probability that a person who is 60 years old or younger has the disease. Therefore, the probability is 0.375, which means that out of 4 people, one person is likely to have the disease.

(b) To find the age at which the fraction of people with the disease is half of its maximum value, we need to substitute

f(x) = 1/2.1/2

= x / (100 + x)50 + 50x

= 100 + x50x - x

= 100 - 505x

= 50x = 10

Hence, the age at which the fraction of people with the disease is half of its maximum value is 10 years.

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The percentage of the distribution that lies between $5 and $11 is 86.62%.

To find the percentage of the distribution that lies between $5 and $11, we need to calculate the area under the normal distribution curve within this range. We can use the Z-score formula to standardize the values and then use a standard normal table to find the corresponding area. The Z-score formula is:

Z = (X - μ) / σ

Where X is the value of the stock, μ is the mean, and σ is the standard deviation.

For X = 5, the Z-score is:

Z = (5 - 8.52) / 2.38 = -1.49

For X = 11, the Z-score is:

Z = (11 - 8.52) / 2.38 = 1.49

Now we can use a standard normal table to find the area under the curve for Z = -1.49 and Z = 1.49. This will give us the percentage of the distribution that lies between 5 and 11.

From the table, we find that the area under the curve to the left of Z = -1.49 is 0.0669, and the area under the curve to the left of Z = 1.49 is 0.9331. So the area between these two values is 0.9331 - 0.0669 = 0.8662, which represents 86.62% of the distribution.

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Given

Find the first 5 terms of the sequence setting n=1, 2, 3, 4, and 5 as shown below

Answer:

The answer is C 39 and i am very sure and positive you will know

Step-by-step explanation:

We are 99% confident that the true average stance duration among elderly individuals lies within the range of 744.56 ms to 857.44 ms.

To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test. The null hypothesis (H0)

Using the t-test, we compare the means and standard deviations of the two samples and calculate the test statistic

a) To calculate a 99% confidence interval for the true average stance duration among elderly individuals, we can use the sample mean, sample standard deviation, and the t-distribution.

Given:

Older adults: n = 28, sample mean = 801, sample standard deviation = 117

Using the formula for a confidence interval for the mean, we have:

Margin of error = t * (sample standard deviation / √n)

Since the sample size is relatively large (n > 30), we can use the z-score instead of the t-score for a 99% confidence interval. The critical z-value for a 99% confidence level is approximately 2.576.

Calculating the margin of error:

Margin of error = 2.576 * (117 / √28) ≈ 56.44

The confidence interval is then calculated as:

Confidence interval = (sample mean - margin of error, sample mean + margin of error)

Confidence interval = (801 - 56.44, 801 + 56.44) ≈ (744.56, 857.44)

b) To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test.

The null hypothesis (H0): The true average stance duration among elderly individuals is equal to or less than the true average stance duration among younger individuals.

The alternative hypothesis (Ha): The true average stance duration among elderly individuals is larger than the true average stance duration among younger individuals.

. With the given data, perform the t-test and obtain the p-value.

c) To construct a 95% confidence interval for the difference in means between older and younger adults, we can use the formula for the confidence interval of the difference in means.

Given:

Older adults: n1 = 28, sample mean1 = 801, sample standard deviation1 = 117

Younger adults: n2 = 16, sample mean2 = 780, sample standard deviation2 = 72

Calculating the standard error of the difference in means:

Standard error = √((s1^2 / n1) + (s2^2 / n2))

Standard error = √((117^2 / 28) + (72^2 / 16)) ≈ 33.89

Using the t-distribution and a 95% confidence level, the critical t-value (with degrees of freedom = n1 + n2 - 2) is approximately 2.048.

Calculating the margin of error:

Margin of error = t * standard error

Margin of error = 2.048 * 33.89 ≈ 69.29

The confidence interval is then calculated as:

Confidence interval = (mean1 - mean2 - margin of error, mean1 - mean2 + margin of error)

Confidence interval = (801 - 780 - 69.29, 801 - 780 + 69.29) ≈ (-48.29, 38.29)

Comparison with part (b): In part (b), we performed a one-tailed test to determine if the true average stance duration among elderly individuals is larger than among younger individuals. In part (c), the 95% confidence interval for the difference in means (-48.29, 38.29) includes zero. This suggests that we do not have sufficient evidence to conclude that the true average stance duration is significantly larger among elderly individuals compared to younger individuals at the 95% confidence level.

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Answer:

61 degrees

Step-by-step explanation:

The angle measure must be less than 90 degrees (4x+15) (10x-3) is 61 degrees

Answer:

Step-by-step explanation:

The area of the wall is the sum of the areas of the different sections of the wall. The cost to paint it will be the product of the cost of a tin of paint and the number of tins required.

__

Here, the shape of the wall can be divided into two trapezoids and a rectangle. Each shape has a corresponding area formula. Left-to-right, their areas are ...

Left Trapezoid

  A = 1/2(b1 +b2)h

  A = 1/2(10 m +11 m)(4 m) = 42 m²

Middle Rectangle

  A = LW

  A = (13 m)(11 m) = 143 m²

Right Trapezoid

  A = 1/2(b1 +b2)h

  A = 1/2(11 m +8 m)(10 m) = 95 m²

Wall Area

The total area to be painted is the sum of the above areas:

  total area = 42 m² +143 m² +95 m² = 280 m²

The area that needs to be painted is 280 m².

__

A tin of paint covers 15 m², so the number of tins needed is ...

  (15 m²)t = 280 m²

  t = 280/15 = 18 2/3 . . . . . . divide by the coefficient of t

We can only buy whole tins, so we need to buy 19 tins. Their cost will be ...

  (£7 /tin)(19 tins) = £133

It will cost £133 to paint the wall.

Answer:

A pentagon, any side with 5 sides is a pentagon.

Step-by-step explanation:

Answer:

step 1: x+50+4x=90

the angle of a right-angled triangle is 90 degrees, therefore if we add everything together ,we could work out what x is.

step 2: x+50+4x=90

                  x+4x=50

                      5x=50

                        x=10

then you solve the equation, x is 10

In the real world, circularity is used for various applications, including assembly, sealing surfaces, rotating clearance, and support.

When it comes to verifying circularity tolerance, the inspection method must be able to determine either the circle that inscribes or the circle that circumscribes the set of points.

Circularity plays a crucial role in applications such as assembly, where a shaft and a hole need to fit together with precision. It is also important for sealing surfaces found in engines, pumps, and valves to ensure effective sealing and prevent leakage. Additionally, circularity is essential in achieving proper rotating clearance between components like a shaft and housing. Lastly, circularity ensures equal load distribution along a line element, providing stability and support.

When verifying circularity tolerance, the inspection method should determine either the circle that inscribes the set of points or the circle that circumscribes the set of points. The circle that inscribes the points is the smallest circle that can contain all the points, while the circle that circumscribes the points is the largest circle that encloses all the points. The inspection method should accurately identify and measure the properties of these circles to assess circularity tolerance.

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The probability that the second student chosen is a boy, given that the first one was a girl, is 8/21. So the correct answer is option c.

The probability that the second student chosen is a boy, given that the first one was a girl, can be calculated by considering the remaining number of boys and girls after the first student is chosen.

Initially, there are 14 girls and 8 boys in the class. If the first student chosen is a girl, there will be 13 girls and 8 boys left in the class.

Therefore, the probability of choosing a boy as the second student, given that the first one was a girl, is the number of remaining boys divided by the total number of remaining students:

Probability = Number of remaining boys / Total number of remaining students

          = 8 / (13 + 8)

          = 8 / 21

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Answer:

268

Step-by-step explanation:

366 minus 98= 268

CAN I GET BRAINLIEST

There are 33.814 fluid ounces in a liter, in unit of measurement.

A unit of measurement is a predetermined, acknowledged by law, and frequently used magnitude of a quantity that acts as a standard for evaluating other quantities of the same kind. A multiple of the measurement unit can be used to express any additional quantity of that type.

An example of a physical quantity is length. The word "metre" is a measurement that stands in for a particular, predetermined length, and it begins with the letter "M." A length is 10 times the precise, predetermined length known as "metre" when the term "10 metres" is used (or 10 m).

Human endeavour has relied on the definition, acceptance, and practical application of units of measurement from antiquity to the present.

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To determine the price of widgets that a company should sell to maximize profit, you need to find the value of x at which the given equation will produce the highest y value.

Here's how to solve this:

Step 1: Rewrite the equation in standard form y = -44x² + 1375x - 6548 becomes

y = -44(x² - 31.25x) - 6548

Step 2: Complete the square by adding and subtracting the square of half of the coefficient of x:

y = -44(x² - 31.25x + (31.25/2)² - (31.25/2)²) - 6548

y = -44((x - 15.625)² - 244.141) - 6548

y = -44(x - 15.625)² + 10723.564

Step 3: The maximum value of y occurs when

(x - 15.625)² = 244.141/44.

Therefore,

x - 15.625 = ±sqrt(244.141/44)

x = 15.625 ± 2.765

x = 18.39 or 12.86

Since the company cannot sell at a negative price, x must be $12.86 or $18.39.

The company should sell widgets at $12.86 or $18.39 to maximize profit to the nearest cent.

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The Maclaurin series for the function f(x) = 1 + x^2 + cos(x) is D. 2 + x + 3x^2 + ...

The Maclaurin series is a special case of the Taylor series, where the expansion is centered at x = 0. To find the Maclaurin series of the function f(x) = 1 + x^2 + cos(x), we need to compute the derivatives of the function and evaluate them at x = 0.

The first derivative of f(x) is f'(x) = 0 + 2x - sin(x), and evaluating it at x = 0 gives f'(0) = 0. The second derivative is f''(x) = 2 - cos(x), and f''(0) = 2. The third derivative is f'''(x) = sin(x), and f'''(0) = 0.

By plugging these values into the formula for the Maclaurin series, we get the series 2 + x + 3x^2 + ..., where each term represents the coefficient of the corresponding power of x.

Therefore, the Maclaurin series for the function f(x) = 1 + x^2 + cos(x) is D. 2 + x + 3x^2 + ..., as provided in the options.

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Answer:

so the smallest side would be associated with the smallest angle, and the angle is directly across from the side. To write from smallest to largest angle would be:

angle V because it's across from the smallest side

angle S because it's across the second smallest side

angle T because it's across the largest side

The area of the rectangular area is 12,800 sq ft and the side of the building has a length of 100 ft. The total length of fencing is 400 ft and the dimension of the side opposite the building is 128 ft.

The area of the rectangular area to be enclosed is 12,800 sq ft. The side of the building has a length of 100 ft. One side of the rectangle will be the length of the building and the other three sides will be bounded by fencing.Let the width of the rectangular area be x ft. Since the area of the rectangular area is 12,800 sq ft,x × (100) = 12,800x = 128 ft The total length of fencing to be used is 400 ft. Let the length of the fencing be y ft.2 (y + 100) = 400y + 100 = 200 ft The dimension (in feet) of the side of the rectangle that is opposite the building is 128 ft. Therefore, the required dimension is 128 ft. Note: Whenever solving a geometry problem, draw a diagram to understand the given information and to formulate an equation.

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Answer:

C. 36 degrees

Step-by-step explanation:

90 + 54 = 144

180 - 144 = 36

you were correct

Answer:

68 kilometers per hour

Step-by-step explanation:

Rosetta's average speed is 85 kilometers per hour. This can be determined by dividing the total distance traveled (85 kilometers) by the total time taken (1 hour and 15 minutes, or 1.25 hours). Therefore, 85 kilometers divided by 1.25 hours is equal to 68 kilometers per hour.

Answer: 68 kilometers per hour (look at the image for the explanation)

Step-by-step explanation:

If the degree of freedom is 24, your sample size when conducting a t-test for dependent means must be 25. Option C is the correct answer.

The sample size when conducting a t-test for dependent means depends on the specific study design and the level of significance desired, and cannot be determined solely based on the degrees of freedom.

However, if we assume that the sample size is equal for both groups, then the formula to calculate the degrees of freedom for a t-test for dependent means is:

df = n - 1

Where "n" is the number of pairs of observations in the sample.

Therefore, if the degree of freedom is 24, then the number of pairs of observations in the sample would be:

n = df + 1 = 24 + 1 = 25

Hence, the answer is 25.

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The amount owed in 20 years is $712.08.

Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.

Compound interest is when you receive interest on both your interest income and your savings.

Given:

P= $325

R= 4%

n= total years = 20 year

So, A = P \((1+ r)^n\)

A = 325 \((1+ 4/100)^{20\)

A = 325  \((1+ 0.04)^{20\)

A = 325 x 2.191

A = 712.08

Hence, the amount is $712.08

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Answer:

Step-by-step explanation:

11 and 12

Answer:

  b) x = - 1

Step-by-step explanation:

You want the equation of the axis of symmetry for a parabola with x-intercepts of 5 and -7.

The given x-intercepts are symmetrical about the axis of symmetry, so its x-intercept is the midpoint of the segment between (5, 0) and (-7, 0).

That midpoint is ...

  ((5, 0) +(-7, 0))/2 = (-2, 0)/2 = (-1, 0)

The vertical line through this point has equation ...

  x = -1

Answer: 4 dresses

Step-by-step explanation:

Hope you get it right!

answer:

provided in the explanation.

step-by-step explanation:

the graph would contain the points (0,0), (1,10), (2,20), etc. the slope is 10, which represents the number of coordinate video games practiced in x number of hours. the representation for the slope depends on whether coordinate video game or hours practiced is on the x or y axis. hope that helps!

(a) The conditional probability mass function of X₁ given X₂ = 1 is P(X₁ = 1 | X₂ = 1) = 7/18.

(b) The conditional probability mass function of X₁ given X₂ = 0 is P(X₁ = 1 | X₂ = 0) = 2/18 = 1/9.

(c) Assuming balls are selected with replacement, the conditional probability mass function of X₁ given X₂ = 1 is P(X₁ = 1 | X₂ = 1) = 12/19.

(d) Assuming balls are selected with replacement, the conditional probability mass function of X₁ given X₂ = 0 is P(X₁ = 1 | X₂ = 0) = 7/19.

(a) When the balls are selected without replacement and X₂ is known to be 1 (black), there are 12 black balls left out of 18 remaining balls. Therefore, the probability of X₁ being 1 (black) is 12/18 = 7/18.

(b) When the balls are selected without replacement and X₂ is known to be 0 (white), there are still 7 black balls left out of 18 remaining balls. Therefore, the probability of X₁ being 1 (black) is 7/18.

(c) When the balls are selected with replacement, the probability of selecting a black ball remains constant at 12/19, regardless of the outcome of the second draw. Therefore, P(X₁ = 1 | X₂ = 1) = 12/19.

(d) When the balls are selected with replacement, the probability of selecting a black ball remains constant at 12/19, regardless of the outcome of the second draw. Therefore, P(X₁ = 1 | X₂ = 0) = 12/19.

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