When translating the point (3,5) 5 units up and 3 units to the left, we should get:

Answer:

g(4) = 8/3

Step-by-step explanation:

g(4) = 5/6(4)-2/3

= 20/6 - 2/3

= 10/3 - 2/3

= 8/3

The formula for the volume of a cone is:

V = (1/3)πr²h

where r is the radius of the base, h is the height of the cone, and π is pi.

In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:

h² = s² - r²

h² = 17² - 8²

h² = 225

h = 15

Now that we have the height, we can plug in the values for r and h into the formula for the volume:

V = (1/3)π(8²)(15)

V = (1/3)π(64)(15)

V = (1/3)(960π)

V = 320π

Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.

Answer:

h= 180/41  

h=4 16/41

h≈4.390243902

Step-by-step explanation:

hope this helps

After solving the expression, the value obtained for the value of h will be equal to 4.5.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the data in the question, the given expression is,

16.5 + 2.75h = 9h + 7.5 - 4.25 h

2.75h + 4.25h - 9h = 7.5 - 16.5

-2h = -9

h = 4.5

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The probability that the sample mean of 77 speed typists would differ from the population mean by greater than 0.6 WPM is approximately 0.33 or 33%.

- Population mean (μ) = 73 WPM
- Population variance\((\sigma ^2)\)  = 144\(WPM^2\)
- Sample size (n) = 77 typists
- Difference from the population mean (d) = 0.6 WPM
First, let's find the standard deviation of the population (σ) by taking the square root of the variance:
σ = √144 = 12 WPM
Next, we need to find the standard error (SE) of the sample mean:
SE = σ / √n = 12 / √77 ≈ 1.37 WPM.
Now, we'll convert the difference (d) to a z-score:
z = (d - 0) / SE = (0.6 - 0) / 1.37 ≈ 0.44
Finally, we'll find the probability that the sample mean differs from the population mean by greater than 0.6 WPM.

To do this, we'll use the z-score we calculated and consult a z-table to find the area under the curve corresponding to the z-score.

For a z-score of 0.44, the area is approximately 0.670.
Since we're looking for the probability that the sample mean differs by greater than 0.6 WPM, we need to find the area in both tails of the distribution.

The area in one tail is given by 0.5 - 0.670/2 = 0.165.

To find the total area in both tails, simply multiply by 2:
Probability = 2 * 0.165 = 0.33.

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The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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The truth table for (p ∧ q) ∨ ( ∼ p ∧ ∼ q) a tautology, a contradiction is as follows:

p  q   |   p ∧ q    | ∼ p ∧ ∼ q  |  (p ∧ q) ∨ ( ∼ p ∧ ∼ q)
---|---|---|---
T | T | F |  T
T | F | T |  T
F | T | T |  T
F | F | T |  T

Therefore, (~p ∨ q) ∨ (p ∧ ~q) is a tautology.

5. The truth table for ∼ (p ∨ q) is as follows:

p  q   |  p ∨ q    | ∼ (p ∨ q)  |  ∼ p ∧ ∼ q
---|---|---|---
T | T | F |  F
T | F | F |  F
F | T | F |  F
F | F | F |  T

Therefore, ∼ (p ∨ q) is logically equivalent to ∼ p ∧ ∼ q. This law is called the De Morgan's Law.

6a. The truth table for p → q is as follows:

p  q   |  p → q  |  ∼ p ∨ q
---|---|---
T | T | T
T | F | F
F | T | T
F | F | T

Therefore, p → q and ∼ p ∨ q are logically equivalent.

6b. The truth table for ∼ (p → q) is as follows:

p  q   |  p → q  |  ∼ (p → q)  |  p ∧ ∼ q
---|---|---|---
T | T | F | F
T | F | T | F
F | T | T | F
F | F | T | T

Therefore, ∼ (p → q) and p ∧ ∼ q are not logically equivalent.

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The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.

In this case, we are estimating the difference in population means between two groups - upperclassmen and underclassmen. The point estimate is calculated by subtracting the sample mean of the underclassmen from the sample mean of the upperclassmen, which gives us

0.76 - 0.60 = 0.16.
the point estimate of the difference in population mean exercised between underclassmen and upperclassmen is 0.16 hours, which was calculated by subtracting the sample mean of underclassmen from the sample mean of upperclassmen.
Point Estimate = (Sample Mean of Upperclassmen) - (Sample Mean of Underclassmen)
Point Estimate = (0.76) - (0.60)
Point Estimate = 0.16

Hence, the point estimate of 0.16 suggests that, on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours. This is a rough estimate of the difference between the two population means based on the provided sample data.

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Answer:

C

Step-by-step explanation:

Begin by isolating y

-6y = - x - 1

Divide everything by -6

y = -x/-6 - 1/-6

y = x/6 + 1/6

Now you want the perpendicular

m1 * m2 = - 1

m1 = 1/6

1/6 * m2 = -1

multiply by 6

m2 = - 6

That's C

The equation to find the amount of space between the end of the wall and the painting is x = 16.9 - 2 * space, where 'x' represents the length of the painting and 'space' represents the unknown space.

To find the amount of space between the end of the wall and the painting, we need to subtract the length of the painting from the length of the wall and divide it by 2.

Given that the wall is 16.9 feet long and the painting is to be centered, we can assume the painting's length is unknown. Let's represent it as 'x'.

Therefore, the equation becomes (16.9 - x) / 2 = space between the end of the wall and the painting.

To solve for x, we can multiply both sides of the equation by 2 to get rid of the fraction, resulting in 16.9 - x = 2 * (space between the end of the wall and the painting).

Next, we simplify the equation to 16.9 - x = 2 * space.

To isolate x, we subtract 2 * space from both sides, resulting in x = 16.9 - 2 * space.

To determine the exact amount of space between the end of the wall and the painting, we would need to know the value of 'space'. Unfortunately, it is not provided in the question.

In summary, the equation to find the amount of space between the end of the wall and the painting is x = 16.9 - 2 * space, where 'x' represents the length of the painting and 'space' represents the unknown space.

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Answer:

4

Step-by-step explanation:

4/7 × 21÷3

4/7×7

=4

this is the answer ....thank you

Answer:

Question 1: Poll the potential viewers on what their favorite hobbies are. Then use that information to create a show or movie that includes their hobbies

Question 2: I can infer that football is the most liked sport. I can infer that soccer is the least liked sport.

Step-by-step explanation:

Using the hobbies will pull the viewers attention.

Your inferring how much people enjoy the sport.

To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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Answer:

CA = 22.6 ft

Step-by-step explanation:

For the known angle A, leg CA is the adjacent leg.

Side AB is the hypotenuse.

The trigonometric ratio that relates the adjacent leg tot eh hypotenuse is the cosine.

cos A = adj/hyp

cos 41° = CA/(30 ft)

CA = 30 ft * cos 41°

CA = 22.6 ft

The equation of the line will be y = -2x + 8.

An equation of a line is a mathematical expression that relates the x and y coordinates of points on the line. It can be written in different forms, but the most common form is the slope-intercept form, which is:

y = mx + b

where m is the slope of the line and b is the y-intercept (the point where the line intersects the y-axis). Another common form is the point-slope form:

y - y₁ = m(x - x₁)

where m is the slope of the line and (x₁, y₁) is a point on the line.

The slope of the line is -2. The value of the y-intercept is 8.

Therefore, the equation of the line will be y = -2x + 8.

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Answer:

2.8%

Step-by-step explanation:

(7.4 - 7.2) / 7.2 =

0.2 / 7.2 =

2.7777777777778%

Answer:

my name is katherine....

Step-by-step explanation:

its also 29% ^^

Answer:

99   (cm^2)

Step-by-step explanation:

Perpendicular to the AB segment at points D and C, the graph is divided into two triangles and a rectangle.

The area of the middle rectangle is equal to 8*9=72. The hypotenuse of the right triangle is 10cm, and one of the right sides is 9cm, so the other side is SQRT (10^2-9^2) = SQRT (19).

One side of the left triangle is 9cm long and the other side is 14-8-sqRT (19) = 6-sqRT (19) cm.

Then, add the area of the three parts.

72+9*sqrt（19）/2+9*（6-sqrt（19））/2=99    (cm^2)

Using the normal distribution, it is found that there is a 0.0139 = 1.39% probability that his systolic blood pressure will be greater than 160 mm.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

The probability that his systolic blood pressure will be greater than 160 mm is 1 subtracted by the p-value of Z when X = 160, hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{160 - 138}{10}\)

\(Z = 2.2\)

\(Z = 2.2\) has a p-value of 0.9861.

1 - 0.9861 = 0.0139

0.0139 = 1.39% probability that his systolic blood pressure will be greater than 160 mm.

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The consumption function for domestically produced goods and services is given by C(Y) = 0.75(Y - Taxes), where Taxes represent the tax payments made by individuals and businesses.

a) The consumption function for domestically produced goods and services as a function of national income Y is given by C(Y) = 0.75(Y - Taxes), where Taxes represent the tax payments made by individuals and businesses.

b) To determine the equilibrium level of national income for the economy in 2022, we use the equation Y = C(Y) + I + G + X - M, where I represents private investment, G is government spending, X denotes exports, and M represents imports.

c) Tax receipts can be calculated as Taxes = 0.20Y, and the budget surplus/deficit for 2022 is given by (Taxes + G) - (I + X - M).

d) If the government wants to run a deficit of $50 billion while maintaining the level of national income calculated in part b), the new tax rate would be Taxes = 0.20Y + 50 billion. The new level of government expenditure would be G = $80 billion + $50 billion.

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Answer:

- 2x² - 6x + 6 = 0

Step-by-step explanation:

A quadratic equation in standard form is

ax² + bx + c = 0 ( a ≠ 0 )

Given

6 - 2x² = 6x ( subtract 6x from both sides and rearrange )

- 2x² - 6x + 6 = 0 ← in standard form

It will take 527.09 years for the radioactive substance to reduce to 142 grams

The function is given as:

\(\mathbf{A = A_oe^{=0.0021t}}\)

And the parameters are given as:

\(\mathbf{A = 142}\) -- the current amount of the substance

\(\mathbf{A_o = 430}\) --- the initial amount

So, the equation becomes

\(\mathbf{142= 430 \times e^{-0.0021t}}\)

Divide both sides by 430

\(\mathbf{0.3302 = e^{-0.0021t}}\)

Take logarithm of both sides

\(\mathbf{log(0.3302) = log(e^{-0.0021t})}\)

This gives

\(\mathbf{log(0.3302) = log(0.9979^t})}\)

Apply laws of logarithm

\(\mathbf{log(0.3302) = tlog(0.9979})}\)

Make t the subject

\(\mathbf{t = \frac{log(0.3302)}{log(0.9979}}}\)

\(\mathbf{t = 527.09}\)

Hence, it will take 527.09 years to reduce to 142 grams

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25 * 20 is 244. to the nearest hundredth would be 240, because the two is ones, the first four is tens and the second four is hundreds

.244 in decimal points it's tenths hundreds and thousands

Check the picture below.

\(\stackrel{\textit{\Large Areas}}{\stackrel{rectangle}{(5)(3)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(4)(3)}~~ + ~~\stackrel{semi-circle}{\cfrac{1}{2}\pi (2)^2}}\implies 15~~ + ~~6~~ + ~~2\pi \stackrel{using~\pi =3.14}{\implies 27.28}\)

Answer:

True.

Explanation:

When solving equations with unknowns on both sides, it is generally recommended to first deal with the variable terms before dealing with the constant terms. This involves simplifying the equation by combining like terms and isolating the variable on one side of the equation. Once the variable is isolated, you can then solve for its value.\(\)

To evaluate the given integral, we can use the fact that D is symmetric with respect to both axes. This means that we can rewrite the integral as:
∫∫D g(x^2 tan(z) + ã¡ + 3) dA
= 4 ∫∫D g(x^2 tan(z) + ã¡ + 3) dxdy where we have used the symmetry of D to change the limits of integration.

Next, we can convert to polar coordinates, which is particularly convenient since D is defined in terms of x and y in terms of their distance from the origin. Specifically, we can substitute x = r cos(θ) and y = r sin(θ), and also use the identity tan(z) = sin(z) / cos(z) = y/x:
∫∫D g(x^2 tan(z) + ã¡ + 3) dxdy
= 4 ∫θ=0^2π ∫r=2^√(9 - r^2 cos^2(θ)) 0 g(r^2 sin(θ) cos(θ) + ã¡ + 3) rdrdθ where we have used the equation of the circle r^2 = x^2 + y^2 = 4 to set the limits of integration for r.
Now we can simplify the integrand by noting that r^2 sin(θ) cos(θ) = (r^2/2) sin(2θ). We also have the constant term ã¡ + 3, which does not depend on r or θ. Thus, we can pull it out of the integral:
4 ∫θ=0^2π ∫r=2^√(9 - r^2 cos^2(θ)) 0 g((r^2/2) sin(2θ) + ã¡ + 3) rdrdθ
= (ã¡ + 3) 4 ∫θ=0^2π sin(2θ) dθ ∫r=2^√(9 - r^2 cos^2(θ)) 0 g(r^2/2) rdr
The inner integral can be evaluated using the substitution u = r^2/2, so that rdr = du/sqrt(2), and the limits of integration become u = 0 to u = 9/2 cos^2(θ). We can then use the fact that g is an arbitrary function, so we can write:
∫r=2^√(9 - r^2 cos^2(θ)) 0 g(r^2/2) rdr
= ∫u=0^9/2cos^2(θ) g(u) du/sqrt(2)
Finally, we can substitute back into the original expression:
4 ∫θ=0^2π sin(2θ) dθ ∫r=2^√(9 - r^2 cos^2(θ)) 0 g(r^2/2) rdr
= (ã¡ + 3) 4 ∫θ=0^2π sin(2θ) dθ ∫u=0^9/2cos^2(θ) g(u) du/sqrt(2)
= 2π (ã¡ + 3) ∫u=0^9/2 g(u) du

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the given expression is

so the answer is - 141/4