A right triangle with legs of lengths x and y has a hypotenuse of length z. Write an expression for the length of the hypotenuse, z. Show your work.

The probability that an 18-year-old man picked at random is taller than 74 inches is approximately 0.0228 or 2.28%.

We have,

We can use the standard normal distribution to solve this problem by standardizing the height value using the formula:

z = (x - μ) / σ

where:

x = the height value (in inches)

μ = the mean height (in inches)

σ = the standard deviation (in inches)

Substituting the given values, we get:

z = (74 - 68) / 3

z = 2.0

Using a standard normal table or calculator, we can find the probability that a random standard normal variable is greater than 2.0 to be approximately 0.0228.

Therefore,

The probability that an 18-year-old man picked at random is taller than 74 inches is approximately 0.0228 or 2.28%.

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The number of years that it will take to grow 8 inches is 32 years.

We know that the diameter grows at a constant rate of 1/4 inches per year.

Then the amount that the diameter grows after x years is given by the linear equation:

D(x) = x*(1/4) in

We want to find the number of years that it takes to grow 8 inches, then we need to solve the linear equation:

8in =  x*(1/4) in

Now we can solve that equation for x, we will get:

8in/((1/4) in) = x

8*4 = x

32 = x

It will take 32 years.

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As we have shown that both AE is congruent to CE and BE is congruent to DE.

Now, let's focus on the diagonals of the parallelogram, AC and BD. We are told that they intersect at point E.

To prove that AE is congruent to CE, we can use the fact that opposite sides of a parallelogram are congruent. Since AC is a diagonal of the parallelogram, it divides it into two congruent triangles, AEC and CED. This is because AE is parallel to CD (as they are opposite sides of the parallelogram), and EC is common to both triangles.

Therefore, by the Side-Angle-Side (SAS) congruence theorem, we can conclude that triangle AEC is congruent to triangle CED. In particular, this means that AE is congruent to CE.

Similarly, to prove that BE is congruent to DE, we can use the same reasoning. Since BD is a diagonal of the parallelogram, it divides it into two congruent triangles, AEB and DEC. This is because BE is parallel to AC (as they are opposite sides of the parallelogram), and ED is common to both triangles.

Therefore, by the SAS congruence theorem, we can conclude that triangle AEB is congruent to triangle DEC. In particular, this means that BE is congruent to DE.

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The volume of the triangular base prism is  120 inches³.

The prism above is a triangular base prism. The volume of the triangular base prism can be calculated as follows:

volume of the prism = base area × height

Therefore,

base area = 1 / 2 bh

base area = 1 / 2 × 8 × 10

base area = 80 / 2

base area = 40 inches²

Therefore,

volume of the prism = 40 × 3

volume of the prism = 120 inches³

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the Correct option of  coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 90° counterclockwise is A

A coordinate is a set of numbers that represents the position of a point in space. It is often used to describe the location of a point on a graph or a map

To determine the coordinates of polygon A′B′C′D′, we need to rotate each vertex of polygon ABCD 90° counterclockwise.

We can do this by using the following formulas for a 90° counterclockwise rotation of a point (x, y):

x' = -y

y' = x

Using these formulas, we can find the coordinates of each vertex of polygon A′B′C′D′ as follows:

A′(0, 0): Since (0, 0) is the origin, a 90° counterclockwise rotation will still result in (0, 0).

B′(-2, 5): To rotate the point (5, 2) 90° counterclockwise, we have x' = -y = -2 and y' = x = 5. So, B′ is (-2, 5).

C′(5, 5): To rotate the point (5, -5) 90° counterclockwise, we have x' = -y = 5 and y' = x = 5. So, C′ is (5, 5).

D′(3, 0): To rotate the point (0, -3) 90° counterclockwise, we have x' = -y = 0 and y' = x = 3. So, D′ is (3, 0).

Therefore, the coordinates of polygon A′B′C′D′ are A′(0, 0), B′(-2, 5), C′(5, 5), and D′(3, 0).

So, the answer is A) A′(0, 0), B′(−2, 5), C′(5, 5), D′(3, 0).

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The equation of the transformed logarithmic function that passes through the points (1,0) and (-3,3) is f(x) = 4.366*log10(x+4)

To find the equation of the transformed logarithmic function that passes through the points (1,0) and (-3,3), we need to determine the values of a, b, h, and k.

First, we know that the function passes through (1,0), so we can substitute x=1 and y=0 in the general equation of the transformed logarithmic function to get:

0 = a x log b(1-h) + k

Since log b(1-h) = 0 for any base b and any value of h, we can simplify the equation to:

0 = k

Therefore, k=0 and the equation becomes:

f(x) = a x log b(x-h)

Now, we have two equations with two unknowns (a and h), which we can solve by substitution or elimination. For simplicity, we can substitute b=10 (base 10 logarithm) since it is a common base and the values of a and h do not depend on the base of the logarithm. We get:

10⁶/ᵃ = 3-h

Since h is the horizontal shift of the graph, we can choose any value of h that makes the expression inside the logarithm positive. For example, we can choose h=-4, which makes x-h=-3-(-4)=1, the same as the x-coordinate of the point (1,0).

Taking the logarithm of both sides with base 10, we get:

log(4) = (6/a)*log(10)

Solving for a, we get:

a = 6/(log(4)*log(10)) ≈ 4.366

Now, we can substitute the values of a and h in the equation of the transformed logarithmic function to get:

f(x) = 4.366*log10(x+4)

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The surface area of the composite solid is calculated to the nearest hundredth as: 113.09 square feet.

To find the surface area of the composite solid which is composed of a cone and a cylinder, do the following:

Find the surface area of the cone:

Surface area of cone = πrl

radius (r) = 4 ft

l = √(3² + 4²) = 5 ft

Plug in the values:

Surface area of cone = π * 4 * 5 ≈ 62.83 square feet.

Find the surface area of the cylinder:

Surface area of cylinder = 2πr(h + r)

radius (r) = 4 ft

h = 2 ft

Plug in the values:

Surface area of cylinder = 2 * π * 4 * (2 + 4) ≈ 150.80 square feet.

Find area of the surface both meet:

Area = πr² = π * 4² ≈ 50.27 square feet.

Surface area of the composite solid = 62.83 + 150.80 - 2(50.27)

= 113.09 square feet.

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The cost for wall-to-wall carpeting is equal to $ 318.

In this problem we need to compute the cost for wall-to-wall carpeting, that is, the cost of covering the floor of the entire room. This can be done by using the following formula:

C = (1 / 9) · c · w · l

Where:

If we know that c = 13.25, w = 12 and l = 18, then the cost of the wall-to-wall carpeting is:

C = (1 / 9) · 13.12 · 12 · 18

C = 318

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The answer of given question is 9/16.

An equation is a mathematical statement that shows the equality between two expressions. It typically consists of mathematical symbols, such as numbers, variables, operators, and equal signs. Equations are used to represent relationships between quantities and are commonly used in various fields of mathematics, science, and engineering to solve problems, make predictions, and describe phenomena.

A fraction is a mathematical representation of a part or parts of a whole. It consists of two numbers, separated by a horizontal or diagonal line, called the numerator and the denominator. The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts that make up the whole.

3/8+4/5-5/16-3/10

(30+64-25-24)/80

45/80

=9/16

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The images best represents the result is image W.

We have, the image is rotated about the x-axis.

Now, rotating around x axis can give the other half of the image.

Also, rotating about x axis gives the mirror image of the figure.

So, the rotation leads to a circle.

and, In three dimensional we can say that Sphere.

Thus, the required image is W.

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The end behavior is if  x becomes very large the value of f(x) also becomes very large, The function will approach zero more slowly as x approaches negative infinity, because 7 is greater than 1.

To describe the end behavior of f(x), we need to consider the limit of f(x) as x approaches positive infinity and negative infinity. We can write this as:

lim f(x) as x → ±∞ = ±∞

This means that as x becomes very large (either positive or negative), the value of f(x) also becomes very large (either positive or negative).

b. If we change the base of the exponential function from 5/7 to 7, the graph of f(x) will change in the following ways:

The function will grow faster, because 7 is greater than 5/7.

The function will start at a higher value, because f(0) = 4(7)^0 = 4.

The function will approach zero more slowly as x approaches negative infinity, because 7 is greater than 1.

c. If we add a constant to the exponential function, the graph of f(x) will be shifted vertically by the amount of the constant. In this case, the graph of f(x) will be shifted downwards by 2 units, because we are subtracting 2 from the function.

The equation of the new function is:

f(x) = 4(5/7)ˣ - 2

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Answer: Well that wouldn't work quite as well.

Step-by-step explanation:

From the information provided, according to the table, if the purchase price of a car was less than $20,000, what is the probability that its Trepair costs were less than about 46%.

If a car had total repair costs of less than $10,000, what is the probability that its purchase price was more than $40.000 Express your about 20%.

Probability is a measure of the likelihood of an event happening. It is a numerical value between 0 and 1, where 0 indicates an event is impossible, and 1 indicates an event is certain.

So, calculating the probability of the events above happening in percentage is as follows:

A. 86/ (86+67+35) =

18/188 ≈ 46%.

Therefore, Blank 1 is about 46%

B. 40/(88+71+40) =

40/197 ≈ 20%.

Therefore, Blank 2 is about 20%.

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The gross premium for the endowment insurance is 73.

To calculate the gross premium for the endowment insurance, we can use the equivalence principle, which states that the present value of the premiums must equal the present value of the benefits.

We can break down the problem into two parts: the present value of the death benefit and the present value of the endowment benefit.

First, let's calculate the present value of the death benefit. The death benefit is payable at the moment of death, and the probability of dying at age x is given by qx, where qx is the probability of surviving to age x.

Since deaths are uniformly distributed between integral ages, we can assume that deaths occur at the midpoint of the age interval. Therefore, the probability of dying at age x can be approximated by

.

Let's denote the present value of the death benefit as DB. Using the equivalence principle, we can write:

DB = A*(1+0.35) - E0 - C1 - 0.05A(1+0.05)

- 0.05A(1+0.05)

- ... - 0.05A(1+0.05)

where A is the annual premium, E0 is the expense paid at the beginning of the first year, and C1 is the commission and tax paid at the beginning of the first year.

The factor (1+0.35) accounts for the commission and tax on the first year premium.

Using the formula for the present value of a perpetuity, we can simplify the above equation to:

DB =

= 116.22

where q65/2 is the probability of dying at age 65. We can obtain q65/2 from the Illustrative Life Table, which gives

q65/2 = 0.112488.

Therefore, the gross premium for the endowment insurance is 73.

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The increase in crime was caused by D. Both are the result of implementing social service programs.

Significant modifications made to a society's social and political structures can cause periods of instability and uncertainty, leading to a rise in crime rates. The daunting tasks of restructuring society that came with the abolishment of apartheid in South Africa and Germany's reunification represent examples of such changes.

When power structures, economic systems, and social norms abruptly shift, gaps in authority may arise, thereby presenting opportunities for criminal activity to escalate. Criminal elements can capitalize on these unexpected power vacuums.

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The additional information is required to prove the triangles are congruent with ASA Postulate is [tex]\bar{RS} \cong \bar{CS}[/tex] (option d)

In order to prove that two triangles are congruent using the ASA postulate, we need to know that they have two pairs of congruent angles and a congruent side that is in between those angles. The image below shows two triangles, but we do not have enough information to prove that they are congruent with the ASA postulate.

To use the ASA postulate, we need to have a congruent side in between the two congruent angles. In this case, we do not know if side RS is congruent to side CS. Therefore, we cannot use the ASA postulate to prove that these triangles are congruent.

In summary, to prove that two triangles are congruent using the ASA postulate, we need to have two pairs of congruent angles and a congruent side in between those angles. Without this information, we cannot use the ASA postulate to prove congruency.

Hence the correct option is (d)

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a. The basketball player is 19.50 cm tall. (Assuming you meant to write

195 cm instead of 1950 cm)

b. A new piece of chalk is about 81.00 cm long.

c. The speed limit in town is 40.0 km/hr. (Assuming you meant to write 40 km/hr instead of 400 km/hr).

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

By placing a decimal point in the appropriate location, we can make the numbers more reasonable.

a. The basketball player cannot be 1950 cm tall, as that is almost 20 meters or over 65 feet.

The average height of a basketball player in the NBA is around 6'7'' (or about 2 meters).

Therefore, we can assume that the correct height of the basketball player is 195 cm, or about 6'5''.

b. A piece of chalk that is 8100 cm long is over 80 meters long, which is clearly too long for a piece of chalk.

Therefore, we can assume that the correct length of the chalk is 81.00 cm or about 32 inches.

c. A speed limit of 400 km/hr is unreasonably high, as it is equivalent to over 248 miles per hour.

The highest speed limits in the world are typically around 80-85 mph (130-140 km/hr), so 400 km/hr is clearly incorrect.

Therefore, we can assume that the correct speed limit is 40.0 km/hr, which is a more reasonable speed limit for a town or residential area.

Hence,

a. The basketball player is 19.50 cm tall. (Assuming you meant to write

195 cm instead of 1950 cm)

b. A new piece of chalk is about 81.00 cm long.

c. The speed limit in town is 40.0 km/hr. (Assuming you meant to write 40 km/hr instead of 400 km/hr).

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Answer:

Step-by-step explanation:

Given:

Proportion of students who are late for class in the population: p = 0.12

Sample size: n = 538

Margin of error: E = 0.03

The standard error of the proportion can be calculated using the formula:

SE = sqrt(p*(1-p)/n)

SE = sqrt(0.12*0.88/538)

SE = 0.019

The margin of error corresponds to a z-score at the 97.5th percentile (since we want the probability of the sample proportion being within 3% of the population proportion in either direction, which gives us a two-tailed test with an alpha level of 0.025 on each side). This z-score can be found using a standard normal distribution table or calculator and is approximately 1.96.

The margin of error can also be calculated using the formula:

E = z*(SE)

0.03 = 1.96*(0.019)

To find the probability that the sample proportion differs from the population proportion by less than 3%, we need to find the area under the standard normal distribution curve between the z-scores of -1.96 and 1.96. This area is equivalent to the probability of the sample proportion being within 3% of the population proportion. This probability can be found using a standard normal distribution table or calculator and is approximately 0.8534.

Therefore, the probability that the proportion of late students in a sample of 538 students would differ from the population proportion by less than 3% is 0.8534 or 85.34% (rounded to four decimal places)

Caden needs to use 126 cubes to fill the box without empty space.

The volume of the box is:

42 in. x 1 in. x 3 in. = 126 cubic inches

The volume of each small cube is:

1 in. x 1 in. x 1 in. = 1 cubic inch

To fill the box, the number of cubes needed is the volume of the box divided by the volume of each cube:

126 cubic inches ÷ 1 cubic inch per cube = 126 cubes

Therefore, Caden needs to use 126 cubes to fill the box without empty space.

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Answer: The 290 millimeters long is the ribbon.

Step-by-step explanation:

To convert centimeters to millimeters

1 cm =10 millimeters

therefore,

29cm= 290 millimeters

Therefore, the ribbon is 290 millimeters long.

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Answer:

8a^2 + 6ats - 2t^2s^2

Step-by-step explanation:

(4a-ts)(2a+2ts)

4a(2a+2ts) -ts(2a+2ts)

8a^2 + 8ats - 2ts - 2t^2s^2

= 8a^2 + 6ats - 2t^2s^2

The inequalities that could show the weight of each horse are:

h ≤ 1248

t ≤ 352

To determine the inequalities that could show the weight of each horse, we can use the fact that the total weight of the horses and tack must be less than or equal to the capacity of the horse trailer. We can set up the following inequalities:

5h + 5t ≤ 8000

where h represents the average weight of each horse.

However, we don't know the value of t, so we need to express it in terms of h. We are given that the combined weight of the horses is 6,240 pounds, so we can write:

5h ≤ 6240

Solving for h, we get:

h ≤ 1248

This means that the weight of each horse must be less than or equal to 1,248 pounds.

Now we can substitute this upper bound for h into the first inequality to get:

5(1248) + 5t ≤ 8000

6240 + 5t ≤ 8000

5t ≤ 1760

t ≤ 352

This means that the average weight of tack per horse must be less than or equal to 352 pounds.

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Answer:

102

Step-by-step explanation:

34 is d so 34×3=102

pls correct me if im wrong

Answer:

Step-by-step explanation:

temperature is heated half an hour

19°c+71°c=90°c

{since its increased by 71°c}

90°c-[2°c*30]=30°c

The graph of y=|x| is a v-shaped graph that starts at the origin and continues infinitely in both the positive and negative x-directions. The graph of y=|x|+2 is the same v-shaped graph, but it has been shifted up two units so that it no longer intersects the x-axis. Finally, the graph of y=|x|-1 is a v-shaped graph that has been shifted down one unit so that it intersects the x-axis at (1,0) and (-1,0). All three graphs are symmetric with respect to the y-axis.

The solution to the Quadratic equation x², when x satisfies the equation 6x - 24 = 0, is x²= 16.

A quadratic equation is a polynomial equation of the second degree, meaning it contains one or more terms that involve a variable raised to the power of two. The standard form of a quadratic equation is:

ax^2 + bx + c = 0,where a, b, and c are constants, and x is the variable.

The given equation is 6x - 24 = 0.

To solve for x, we can isolate x on one side by adding 24 to both sides of the equation:

6x - 24 + 24 = 0 + 24

6x = 24

Then, we can solve for x by dividing both sides by 6:

6x/6 = 24/6

x = 4

Therefore, the solution to the equation 6x - 24 = 0 is x = 4.

Now, to solve for x², we can simply substitute x = 4 into the equation x²:

x² = 4²

x^2 = 16

Therefore, the solution to the equation x², when x satisfies the equation 6x - 24 = 0, is x² = 16.

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An compound inequality that describes the acceptable weights for a 20 oz box is 19.25 ≤ x ≤ 20.75.

We have,

The absolute value of a number is defined as its magnitude irrespective of the sign of the number. To determine the absolute value of a real number, we consider only the number and remove the sign. It can only be a non-negative value.

We are Given that, cereal manufacturer has a tolerance of 0.75 oz for a box of cereal that is supposed to weigh 20 oz.

Let the weight of cereal box be; w

Now, the inequality is

20-0.75 ≤ x ≤ 20+0.75

Add 20 on both sides of an inequality, we get

19.25 ≤ x ≤ 20.75

Here, 19.25 ≤ x ≤ 20.75

Therefore, an absolute value inequality to find the range of acceptable weights is 19.25 ≤ x ≤ 20.75.

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Hope it helps :)

[tex]x + 4y = 9 \\

-x - 2y = 3 \\ eliminate \: one \: variable \: by \\ adding \: the \: equations \\ 2y = 12 \\ divide \: both \: sides \\ y = 6 \\ substitute \: the \: value \: of \: y \\ \: into \: equation \: ...2 \\ - x - 2(6) = 3 \\ solve \: the \: equation \\ - x - 12 = 3 \\ - x = 3 + 12 \\ - x = 15 \\ x = - 15 \\ SOLUTION \\ x = - 15 \\ y = 6 \\ Hope \: it \: helps :)[/tex]

The value of the derivative of the composite function h(x) = f[g(x)] is equal to h'(3) = 2.

In this problem we find a function in the form of a composite function of the form h(x) = f[g(x)], whose derivative is defined by the chain rule:

h'(x) = f'(g) · g'(x)

If we know that g'(3) = 2 and f'(2) = 1, then the exact value of the derivative of the composite function is:

h'(3) = 2 · 1

h'(3) = 2

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