Violets gross annual income is $57,903 she is paid biweekly and has 7% deducted from her paycheck for her 401(k) her employer matches her deduction up to 5%

A) How much is deducted from her paycheck for her 401(k)

B) How much is deposited into her retirement plan each day

The measure of DE, given that Triangle ABC is similar to Triangle DEF, is 53. 09 units .

To find the measure of DE, you need to use the corresponding sides of BC and EF to find the scale factor that shows the difference in the sizes of corresponding sides.

The scale factor is:

= 31 / 8

= 3. 875

Now, since the value of the corresponding side of AB is 13.7 units, the measure of DE would be :

= 13. 7 x 3. 875

= 53. 09 units

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The solution is,  the surface area of the parallelepiped is:444 cm²

Here, we have,

Area of parallelogram = a*h

                                     = 10*3

                                     = 30   ,

there are 2 such parallelograms in the prism

2 faces are rectangles with sides 12 and 6 ,

Area of this face is 12*6=72,  there are 2 such faces

we have,

2 faces are rectangles with sides 12 and 10

Area of this face is 12*10=120,  

there are 2 such faces

the surface area of the parallelepiped is:

2*30+2*72+2*120

= 444 cm²

Hence, The solution is,  the surface area of the parallelepiped is:444 cm²

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According to the table, the "Under 18" age group constitutes 24% of the total population, which is nearly 25 percent. Therefore, the answer is "nearly 25 percent".

The percentage of the population under the age of 18 can be calculated by dividing the total number of people in that age group by the total population, then multiplying by 100 to obtain a percentage.

From the table, we see that the total number of people under 18 is 74,181,467.

The total population is the sum of the total numbers in all age groups, which is 74,181,467 + 30,672,088 + 82,134,554 + 81,489,445 + 40,267,984 = 308,745,538.

Dividing the total number of people under 18 by the total population and multiplying by 100 gives

(74,181,467 / 308,745,538) × 100 ≈ 24%.

Therefore, nearly 25% of the population was under the age of 18 in 2010.

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Answer:

b. sin X and c. cos Y

Step-by-step explanation:

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

sin Y = 32/40 incorrect

sin X = 24/40 correct

cos Y = 24/40 correct

cos X =32/40 incorrect

So the answers are sin  X and cos Y

Answer:h

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

its 12.67 because like look at it this way

The solution to the initial value problem is [tex]y = 4e^{(5x^{10})[/tex]. The domain of the function is all real numbers.

Ordinary differential equations of the first order only take into account the dependent variable y's first derivative with regard to the independent variable x. They could be written as follows:

f(x,y) = dy/dx

where the supplied function of both x and y is f(x,y). There are numerous methods for solving first-order ordinary differential equations, which are crucial in many branches of science and engineering. One such method is variable separation. Other methods include Bernoulli equations, integrating components, and precise equations.

The given differential function is:

[tex]dy/dx = 10x{^9}y[/tex]

Separating the variables we have:

dy/y = 10x^9 dx

Now, integrating on both sides:

[tex]]int dy/y = \int 10x^9 dx\\ln (y) = 5x^{10} + C[/tex]

Solving for y:

[tex]y = ke^{(5x^{10})[/tex]

Now, for the initial values y = 4 and x = 0 we have:

[tex]4 = ke^{(0)}[/tex]

k = 4

Hence, the solution to the initial value problem is [tex]y = 4e^{(5x^{10})}[/tex].

The domain of the function is all real numbers.

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There is enough proof that the mean raw score for the school's applicants is more than 30 at a significance level of α = 0.01, therefore we reject the null hypothesis.

The null hypothesis H0: μ ≤ 30 mean raw score for the school's applicants is less than or equal to 30 and the alternative hypothesis Ha: μ > 30

We can utilize a one-tailed t-test since we don't know the population standard deviation and our sample size is less than 30. The test statistic is evaluated

t = (x' - μ) / (s / √n)

here
x'= sample mean = 31,
μ = hypothesized population mean = 30,
s =  standard deviation = 2.5,
n = sample size = 50.

t = (31 - 30) / (2.5 / √50)
= 3.16

Applying  t-distribution table with degrees of freedom (df) = n - 1 = 49 and a significance level of α = 0.01, we find that the critical value is
t-critical = 2.404.

The calculated t-value (3.16) is greater than our critical value (2.404), we reject the null hypothesis since there is enough evidence to support the student's claim that the mean raw score for the school's applicants is more than 30 at a significance level of α = 0.01.

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It is not possible for a subset of A to contain elements of Ac

To answer the question, "Can a subset of A contain elements of Ac?" we must first understand what these terms mean.

A subset of A is a set that contains only elements that are also in A. On the other hand, Ac is the complement of A, which is the set of all elements that are not in A. Therefore, an element that is in Ac is not in A.

Now, let us consider the possibility of a subset of A containing elements of Ac. If an element is in Ac, it is not in A. Therefore, it cannot be in any subset of A, as all elements of a subset must be in A. This means that it is not possible for a subset of A to contain elements of Ac.

In summary, It is not possible for a subset of A to contain elements of Ac because the complement of A includes all the elements that are not in A. Therefore, any element that is in Ac cannot be in any subset of A

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Complete Question:

Can a subset of A contain elements of Ac? Give reason.

Answer:

I put the equation on math-way and it gave me this:

Answer:

Starting at (0, 1), go up 4 units, then right 3 units. You will end at (3, 5). Plot that point, and then draw a line that goes through the two points.

Answer:

Kailey flipping heads: 3/4 as a fraction, 0.75 as a decimal, and 75% as a percent.

Olivia flipping tails: 9/20 as a fraction, 0.45 as a decimal, and 45% as a percent.

Step-by-step explanation:

Kailey flipped heads 15 times and tails 5 times.

First, find the total amount of times that Kailey flipped the coin.

15+5=20

Kailey flipped the coin 20 times.

Out of those 20 times, she flipped heads 15 times. We can rewrite this as:

[tex]\frac{15}{20}[/tex]

and simplify it:

[tex]\frac{3}{4}[/tex]

3/4 as a decimal is 0.75, and to find the percentage, simply multiply the decimal form by 100.

We can find that 3/4 as a percentage is 75%.

So, the probability of Kailey flipping heads is:

3/4 as a fraction, 0.75 as a decimal, and 75% as a percent.

Olivia flipped heads 11 times and tails 9 times.

Let's find how many times she flipped the coin.

11+9=20

Olivia flipped the coin 20 times.

Out of 20 times, Olivia flipped tails 9 times.

This can be rewritten as:

[tex]\frac{9}{20}[/tex]

This fraction is already in simplest form.

To find what 9/20 is as a decimal, divide 9 by 20. You'll get 0.45.

Now, multiply 0.45 by 100 to find the percent. You'll get 45%.

So, the probability of Olivia flipping tails is:

9/20 as a fraction, 0.45 as a decimal, and 45% as a percent.

The smallest number possible is 42.5 pound.

We have,

42 pounds 8 ounce.

We know 1 pound = 16 ounce

So, 42 pounds 8 ounce

= 42 + 8/16

= 42 + 1/2

= 42+ 0.5

= 42.5 pounds

Now, dividing by 5 we get

= 42.5/5

= 8.5

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Let's the weight of Case C = "x" grams.

From the information:

Case A = 12 times heavier than Case B,

Therefore, the weight of Case B = 1/12 of Case A's weight:

Weight of Case B = (1/12) * Weight of Case A

Case B = 16 times heavier than Case C,

so, weight of Case C = 1/16 of Case B's weight:

Weight of Case C = (1/16) * Weight of Case B

The weight of Case A = 8,640g,

Let's substitute the value into the equations to find the weight of Case C:

Weight of Case B = (1/12) * 8,640 = 720g

Weight of Case C = (1/16) * 720 = 45g

Thus, the weight of Case C is 45 grams.

The surface area of the square pyramid is 384 cm squared.

The surface area of the square base pyramid can be found as follows:

surface area of the square base pyramid = base area + 2al

where

Therefore,

base area = 12 × 12

base area = 144 cm²

Hence,

surface area of the square base pyramid = 144 + 2 × 12 × 10

surface area of the square base pyramid = 144 + 240

surface area of the square base pyramid = 384 cm²

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The formula for the volume (V) of a cylinder is given by:

V = πr^2h

where r is the radius of the cylinder and h is its height.

We are given the diameter of the cylinder as 28 meters, so the radius (r) is half of that, or 14 meters.

Using the given height of 7 and one half meters, we can now calculate the volume of the cylinder as follows:

V = πr^2h = (22/7) * (14)^2 * (7.5) = 4,620 cubic meters (rounded to the nearest whole number)

Therefore, the approximate volume of the cylinder is 4,620 cubic meters.

As per the triangle, the length of the other, shorter leg is 3.46 units.

We know that a is twice the length of b, so we can write:

a = 2b

We also know that c is the square root of three times b, or:

c = √3b

Now, let's say we're given the length of the longer leg, a. We can use our equation a = 2b to solve for b:

a = 2b

b = a/2

So, we know that the shorter leg is half the length of the longer leg. For example, if a is 8, then b is 4.

To double-check our answer, we can use the equation for the hypotenuse:

c = √3b

c = √3(4)

c = 2√3 = 3.46

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If [tex]5[/tex] grammes are rounded to the closest tenth, that would be  [tex]0.175[/tex] ounces.

The conversion factor that states [tex]1[/tex] gramme is about equivalent to [tex]0.035[/tex]ounces can be used to convert grammes to ounces.

we may multiply  [tex]5[/tex] by  [tex]0.035[/tex] to convert [tex]5[/tex] grammes to ounces:

[tex]5 grams \times 0.035 \ oz/gram = 0.175[/tex] ounces

It's vital to remember that the ratio of 1 gramme to  [tex]0.035[/tex] ounces is merely an estimate; the precise ratio is 1 gramme to [tex]0.03527396195[/tex] ounces.

However, utilizing the streamlined conversion factor of [tex]1[/tex] gramme to [tex]0.035[/tex] ounces is accurate enough for the majority of routine uses.

Therefore,If [tex]5[/tex] grammes are rounded to the closest tenth, that would be  [tex]0.175[/tex] ounces.

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The graph K must represent an investment that was compounded continuously because investments that are compounded continuously increase at a faster rate than investments that use either simple interest or are compounded monthly.

In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):

[tex]A(t) = P_{0}e^{rt}[/tex]

Where:

By critically observing the given graph, we can reasonably infer and logically deduce that the graph with line K represent an investment that was compounded continuously because the principal (initial amount of money) increases at a faster rate

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

There are 775 - 91 + 1 = 685 integers.

In the given range, the smallest multiple of 14 is 98, and the largest multiple of 14 is 770. ((770-98)/14) + 1 = 49 multiples of 14.

So the probability of choosing a multiple of 14 from this range is 49/685.

Selina will get £153.78 of interest by the end of 3 years.

To calculate the total amount of interest Selina will get by the end of 3 years, we need to use the compound interest formula:

A = P[tex](1 + r/n)^{(nt)}[/tex]

where:

A = the amount of money at the end of the time period

P = the principal amount (the amount initially invested)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period (in years)

In this case, we have:

P = £2000 (the amount initially invested)

r = 2.5% per annum = 0.025 (as a decimal)

n = 1 (the interest is compounded annually)

t = 3 (the time period is 3 years)

So, plugging in the values into the formula, we get:

A = 2000[tex](1 + 0.025/1)^{(1×3)}[/tex]

= 2000[tex](1.025)^{3}[/tex]

= 2000(1.07689)

= £2,153.78 (rounded to the nearest penny)

To find the total amount of interest Selina will get, we need to subtract the principal amount from the final amount:

Total interest = £2,153.78 - £2,000

= £153.78

Therefore, Selina will get £153.78 of interest by the end of 3 years.

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Answer: by watching videos

Step-by-step explanation:

Answer: Watch a video or do your best to scroll down as soon as the website loads. The scrolling worked for me before but you get about 5 seconds before you can't see it anymore.

Step-by-step explanation:

The radius of the pool is changing at a rate of 3 / (20π) cm/min when the radius is 10 cm.

To solve this problem, we'll use the given information and the area formula for a circle.
Write the formula for the area of a circle:

[tex]A = \pi r^2[/tex],

where A is the area and r is the radius.
Differentiate both sides of the equation with respect to time (t): [tex]dA/dt = d(\pi r^2)/dt.[/tex]
Apply the chain rule on the right side: [tex]dA/dt = 2\pi r(dr/dt),[/tex]

where dr/dt is the rate of change of the radius.
Plug in the given values:

dA/dt = 3 cm²/min (given) and r = 10 cm (given at the moment of interest).
Solve for dr/dt:
3 = 2π(10)(dr/dt).

Isolate dr/dt:
dr/dt = 3 / (20π)
Simplify:
dr/dt = 1 / (20π/3) = 3 / (20π).

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The surface area of the prism is 78 square units, which corresponds to option A.

You provided three dimensions: 5 units, 3 units, and 3 units. I assume these are the dimensions of a rectangular prism.

Let's label the dimensions: length (l) = 5 units, width (w) = 3 units, and height (h) = 3 units.

There are two bases, and their areas are equal:

Base Area = l * w = 5 * 3 = 15 square units

There are also three pairs of lateral faces. The areas of the lateral faces are:

Two faces with dimensions l and h: 2 * (l * h) = 2 * (5 * 3) = 30 square units

Two faces with dimensions w and h: 2 * (w * h) = 2 * (3 * 3) = 18 square units

Now, add the areas of all the faces together:

Surface Area = Base Area * 2 + Lateral Area = 15 * 2 + 30 + 18 = 30 + 30 + 18 = 78 square units

So, the surface area of the prism is 78 square units, which corresponds to option A.

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The value for a is equal to 4.

In Mathematics and Geometry, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

By applying the basic proportionality theorem to the given triangle, we have the following:

EG/CE = GF/DF

(a + 12)/8 = (3a + 2)/7

By cross-multiplying, we have the following:

7a + 84 = 24a + 16

24a - 7a = 84 - 16

17a = 68

a = 68/17

a = 4.

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The rate of change of the circular area is increasing at a constant rate of 12π square feet per second when the radius is exactly 3 feet.

To solve this problem, we need to use the formula for the area of a circle:

[tex]A = πr^2[/tex],

where A is the area and r is the radius.

We also need to use the chain rule of differentiation because we are dealing with a changing radius over time.

First, we can find the rate of change of the area with respect to time (dA/dt) by differentiating the formula for the area:

dA/dt = 2πr(dr/dt)

where dr/dt is the rate of change of the radius with respect to time, which is given as 2 feet per second in the problem.

Therefore, we can substitute these values into the formula to get:

dA/dt = 2π(3)(2)

dA/dt = 12π

So, the rate of change of the circular area is increasing at a constant rate of 12π square feet per second when the

radius is exactly 3 feet.

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Answer:

The mean is 8.6 minutes.

Step-by-step explanation:

"mean" is the average, the way people might talk about it in common language (not necessarily math class language.)

To calculate the mean, you ADD and DIVIDE. You add up all the numbers in your list and divide by however many numbers there are.

ADD:

5+5+15+12+14+6+3

= 60

Then DIVIDE by 7 (bc there are 7 items in the list)

60/7

= 8.5714285714

They said to round to the nearest tenth.

8.5714285714 rounds to 8.6

The mean is 8.6 minutes.

The velocity and direction of the jet and the velocity and direction of the wind, expressed as vectors are;

(a) (0. 45)

(b) (450, 0)

(c) (450, 45)

(d) 452

84.3 °E

A vector quantity is one that has both magnitude and direction.

The direction of the pilot is heading = Due east

The speed of the jet relative to the air = 450 mi/h

The direction of the wind = Due north

Speed of the wind = 45 mi/h

(a) The velocity of the wind expressed as a vector is therefore;

[tex]\vec{v}_w[/tex] = 0·i + 45·j

Which indicates that the vector component form of the velocity of the wind is (0, 45)

(b) The velocity of the jet relative to the wind expressed as a vector therefore is; [tex]\vec{v}_j[/tex] = 450·i + 0·j

Which indicates that the vector form of the velocity of the jet relative to the wind is; (450, 0)

(c) The true velocity of the jet expressed as a vector is the sum of the two vectors, which indicates;

The true velocity of the jet = 0·i + 45·j + 450·i + 0·j = 450·i + 45·j

The vector form of the true velocity of the jet is (450, 45)

(d) The true speed of the jet is the magnitude of the vector of the true velocity of the jet, which is;

Speed = √((450 mi/h)² + (45 mi/h)²) ≈ 452 mi/h

The direction of the jet is the arctangent of the ratio of the components of the vector of the true velocity of the jet

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Length of the new rectangle = 28 x 2 = 56,Width of the new rectangle = 7 x 2 = 14These are indeed the dimensions of the new rectangle we considered, so we can conclude that it is similar to the given rectangle.

How to solve the question?

In order for two rectangles to be similar, their corresponding sides must be in proportion. This means that the ratio of the length to the width in one rectangle must be equal to the ratio of the length to the width in the other rectangle.

Let's consider a rectangle with a length of 56 and a width of 14. We can check if this rectangle is similar to the given rectangle by calculating the ratio of the length to the width in each rectangle:

Ratio in the given rectangle = 28/7 = 4

Ratio in the new rectangle = 56/14 = 4

As we can see, the ratio of the length to the width is the same in both rectangles. Therefore, the rectangle with a length of 56 and a width of 14 is similar to the given rectangle.

To confirm this, we can calculate the dimensions of the new rectangle by scaling up the dimensions of the given rectangle by a factor of 2. That is, we can multiply the length and width of the given rectangle by 2:

Length of the new rectangle = 28 x 2 = 56

Width of the new rectangle = 7 x 2 = 14

These are indeed the dimensions of the new rectangle we considered, so we can conclude that it is similar to the given rectangle.

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