Planes T and X are parallel. Plane T contains line a. Plane X contains line b.

Planes T and X are parallel. Plane T contains line a and plane X contains line b.

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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answer attached

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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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Without seeing the graph of the linear function, it is impossible to determine if Tom's answer of 12 is correct or incorrect. However, it is important to understand the concept of slope and how it is calculated for a linear function.

The slope of a linear function represents the rate at which the y-coordinate changes for each unit increase in the x-coordinate. In other words, it measures the steepness of the line. Mathematically, the slope of a line is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line.

To calculate the slope of a line given its graph, one can choose any two points on the line and find the difference in their y-coordinates and x-coordinates. The slope is then the ratio of the change in y-coordinates to the change in x-coordinates. This can be expressed as:

slope = (change in y-coordinate) / (change in x-coordinate)

Now, if Tom has correctly identified two points on the line and calculated the difference in their y-coordinates and x-coordinates, and if he has obtained a ratio of 12 for the change in y-coordinate to the change in x-coordinate, then his answer of 12 for the slope would be correct.

However, it is also possible that Tom made an error in his calculation, or that he misread the graph, and obtained an incorrect answer. Therefore, it would be necessary to verify his calculations by checking the points he used and the formula he applied.

In conclusion, without further information about the graph of the linear function and the points chosen by Tom to calculate the slope, it is impossible to determine if his answer of 12 is correct or incorrect.

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The Surface area of figure is 396.896 unit².

We have,

x = 4 unit, y = 13 unit and z = 7 unit.

First Surface Area of Cylinder

= 2πrh

= 2(3.14)(4)(7)

=  175.84 unit²

and, Surface Area of Cone

= πrl

= (3.14)(4)(13.6)

= 170.816 unit²

Thus, the Surface area of figure is

= 175.84 + 170.816 + 50.24

= 396.896 unit²

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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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It is not appropriate to generalize the findings of the survey to the entire school population.

What is survey?

The conclusion that about 8.6% of the students in the school have a January birthday is not necessarily valid based on the information provided.

The sample size of the survey is too small (only 3 students with January birthdays) and limited to one math class, so it may not be representative of the whole school population. Additionally, the sample is not randomly selected, which introduces the possibility of selection bias.

Therefore, it is not appropriate to generalize the findings of the survey to the entire school population. A more reliable way to determine the percentage of students with a January birthday would be to collect data from a larger, randomly selected sample of students across the entire school population.

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The error which Mason made was subtracting 5 from both sides.

The correct solution is x < 16 and it is shown on the number line below.

The best way to describe the temperature in the greenhouse before the heater stopped working is that it was at least 71 degrees.

An inequality that represent this situation is x + 21 ≥ 47 and the solution is x ≥ 26.

The inequalities that can be used to represent the situation are;

D. x - 7.35 ≥ 2.87

E. x ≥ 10.22

Based on the information provided about the math test, the following inequality must be solved by students;

x - 5 < 11

By adding 5 to both sides of the inequality, we have the following:

x - 5 + 5 < 11 + 5

x < 16

Therefore, the error which Mason made was subtracting 5 from both sides.

Since the temperature dropped 6 degrees before it was fixed and it was still at least 67 degrees when the heater started working again, we can model it as follows;

x - 4 ≥ 67

x ≥ 71

Since Ramiro has $21 and wants buy a skateboard that cost $47, the amount of money that he needs can be modeled by this inequality;

x + 21 ≥ 47

x ≥ 47 - 21

x ≥ 26

In conclusion, the inequalities that can be used to represent the total amount, x, Kendra needs for the bead are;

x - 7.35 ≥ 2.87

x ≥ 2.87 + 7.35

x ≥ 10.22

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The height of the building is given by h = 93.5 m

Given data ,

Let the proportion be represented as A

Now , the value of A is

The height of the pole is 3.3 meters and its shadow is 1.71 meters long. We can set up a proportion to find the height of the building:

Height of pole / Length of pole's shadow = Height of building / Length of building's shadow

3.3 m / 1.71 m = x / 48.25 m

Now we can cross-multiply and solve for "x":

3.3 m * 48.25 m = 1.71 m * x

159.825 m² = 1.71 m * x

x = 159.825 m² / 1.71 m

x ≈ 93.5 m

Hence , the height of the building is approximately 93.5 meters

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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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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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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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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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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]

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)

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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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

Answer:

y = 2x

Step-by-step explanation:

If x > 5, then x - 5 is positive and x + 5 is also positive. So we can rewrite the equation as follows:

y = (x - 5) + (x + 5)

Simplifying the equation, we get:

y = 2x + 0

Therefore, the equation without using absolute value for the given conditions is y = 2x.

Hope this helps!

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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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 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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The length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

By Pythagoras rule we can evaluate for b as follows:

x = √(7.5² - 2.5²)

x = √50

x = x = 7.0711

f = √[(√78)² - 7²]

f = √(78 - 49)

f = √29

f = 5.3852

d = 2 × √(11² × 8²)

d = 2 × √53

d = 15.0996

Therefore, the length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.

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Answer:

102

Step-by-step explanation:

34 is d so 34×3=102

pls correct me if im wrong

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 volume of the triangular prism shown below is 48 cm²

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The area of triangular base = (1/2) * 12 cm * 8 cm = 48 cm²

The volume of triangular prism = area of base * height

Volume = 48 cm² * 34 cm = 1632 cm³

The volume of the triangular prism is 48 cm²

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Answer:

The answer choice that contains only equations is:

A. 2 + H = 14 and K - 25 = 2

Explanation:

A. Both expressions are equations because they have an equal sign and a variable.

B. C-14C-14 is not an equation because it doesn't have an equal sign.

C. Both expressions are equations, but 22-y is not a complete equation (missing an equal sign).

D. Both expressions are equations, but 55= r-1 is not a complete equation (missing an equal sign).

Step-by-step explanation:

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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Answer:

First, we need to find out how many people are male and female in the town:

Step-by-step explanation:

Male population = 48% of 42800 = 20544

Female population = 100% - 48% = 52% of 42800 = 22256

To find out how many more females there are than males, we need to subtract the male population from the female population:

Female population - Male population = 22256 - 20544 = 1712

Therefore, there are 1712 more females than males in the town.

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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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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