Gray made a $3,500 tax-deductible contribution to his individual retirement account (IRA). Assuming he is in a 28 percent tax bracket, how much will this contribution save him on his taxes?

The smaller number is 14 and the larger number is 36.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let the smaller number would be x

And the larger number would be y

Given that the smaller of two numbers is 2 less than 1/3 the larger

So x - 2 = (1/3)y ⇒ 3x - 6 = y

The sum of the two numbers is 50

So x + y = 50

Substitute the value of equation 3x - 6 = y in the above equation,

⇒ x + 3x - 6 = 50

⇒ 4x = 50 + 6

⇒ x = 56/4

⇒ x = 14

Substitute the value of equation x = 14 in the equation x + y = 50,

⇒ 14 + y = 50

⇒ y = 36

Hence, the smaller number is 14 and the larger number is 36.

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Answer:

15.1 ?

Step-by-step explanation:

The cone has a volume of (D) 288in3.

To find the volume:

Given:

Formula:

The Pythagorean theorem is used to calculate height.

The volume of the cone:

Therefore, the volume of the cone is (D) 288in³.

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The complete question is given below:
Right triangle ABC, shown, has a vertical leg 6 inches long and a hypotenuse 10 inches long. If the triangle was rotated 360 degrees around the vertical leg to form a right circular cone, what would be the volume of this cone, in cubic inches?

A. 32

B. 96

C. 128

D. 288

E. 384

The  percent of phones have a battery life less than 5 hours or greater than 5.5 hours is 52.27%.

A z-score, also known as a standard score, provides information on how far a data point is from the mean. Technically speaking, however, it's a measurement of how many standard deviations a raw score is from or above the population mean.

You can plot a z-score on a normal distribution curve. The range of Z-scores ranges from -3 standard deviations (which would be on the far left of the normal distribution curve) to +3 standard deviations (which would fall to the far right of the normal distribution curve). You must be aware of the mean and population standard deviation in order to use a z-score.

Given the talk time battery life of a group of cell phones

Mean = μ = 5 hours

standard deviation = σ = 15 minutes = 0.25 hours

to calculate P(5 > x > 5.5)

formula for z score is

z = (x - μ)/σ

x = 5

z = (5 - 5)/.25

z = 0

P-value from Z-Table:

P(x < 5) = 0.5

P(x > 5) = 1 - P(x<5) = 0.5

at x= 5.5

z = (5.5 - 5)/.25

z = 2

P-value from Z-Table:

P(x < 5.5) = 0.97725

P(x > 5.5) = 1 - P(x < 5.5) = 0.02275

P(5 < x < 5.5) = P(x < 5.5) - 0.5 = 0.47725

for P(5 > x > 5.5) = 1 - P(5 < x < 5.5) = 1 -0.47725

P(5 > x > 5.5) = 0.52275

percent = 0.52275 x 100 = 52.27%

Hence the percent at   P(5 > x > 5.5) is 52.27%.

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The shock in part (c) leads to a decrease in capital per worker and consumption per worker, potentially affecting the standard of living. In contrast, the shock in part (d) leads to an increase in output per effective worker, which can positively impact the standard of living.

(c) When the tax funds are assumed to be gone without any goods or services purchased or government employees paid, it implies that the tax revenue is completely removed from the economy. In this case, the impact on the steady state levels of capital per worker and consumption per worker would depend on the specific economic model and assumptions.

Generally, the removal of tax revenue would lead to a reduction in both capital per worker and consumption per worker. The exact magnitude of the impact would depend on various factors, such as the marginal propensity to consume and the saving behavior of individuals. In steady state, the reduction in capital per worker could lead to lower productivity and potentially lower output per worker, affecting the standard of living.

To sketch a diagram showing the impact of this shock, you would typically have the levels of capital per worker and consumption per worker on the y-axis and time or steady state on the x-axis. The diagram would show a downward shift in both the capital per worker and consumption per worker curves, indicating a decrease due to the removal of tax revenue.

(d) When the tax funds are used by the government to implement plans that increase the growth rate of labor-augmenting technological change to 3% per year, it implies that the tax revenue is directed towards productivity-enhancing investments or policies. In this case, the impact on the steady state levels of capital per effective worker, output per effective worker, and consumption per effective worker can be analyzed.

The increase in the growth rate of labor-augmenting technological change would lead to higher productivity and potentially higher output per effective worker in steady state. This increase in output per effective worker could also translate into higher consumption per effective worker, depending on the saving and consumption behavior.

To sketch a diagram showing the impact of this shock, you would typically have the levels of capital per effective worker, output per effective worker, and consumption per effective worker on the y-axis and time or steady state on the x-axis. The diagram would show an upward shift in the output per effective worker curve, indicating an increase due to the improved technological change.

Overall, the shock in part (c) leads to a decrease in capital per worker and consumption per worker, potentially affecting the standard of living. In contrast, the shock in part (d) leads to an increase in output per effective worker, which can positively impact the standard of living.

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Answer: 24 is 96% of 25.

Step-by-step explanation: You can apply the rule of three in order to answer this question. If 24 represents 96%, you can put this as 24/96. Then, use x as the value that represents 100%, you can put it as x/100. Order the data in a way you can cross multiply them; 24/96 = x/100. The answer is x = 25.

Answer:

Expressions A,C and E

Step-by-step explanation:

Collecting like terms will give us :

-5.5z +7y - 5

This is expression E

Expressions A and C are equivalent expressions meaning that they are the same thing but just in a different order.

Answer:

4.9 × \(10^3\)

Step-by-step explanation:

Start by doing what is in the paranthesis from right to left.

\(9 * 10^2 = 900\)

and

\(4 * 10^3 = 4000\)

So if we add them we get:

\(900 + 4000 = 4900\)

Now to put it into standard form we just put a decimal to the right of the first number and see how many times we need to move right in order to make the number. In this case it's 3 times so we tack on × \(10^3\)

So our answer is:

\(4.9\) × \(10^3\)

Answer:

2400cm^3 I believe

Step-by-step explanation:

(a) The firm's output supply function is given by q = (p + 199) / 2.

(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.

(c) Each firm sells 70 computers in the long run.

(39 - 0.009q) = (2q - 2) / q

Simplifying the equation, we find:

q = (p + 199) / 2

This represents the firm's output supply function.

p = 39 - 0.009((p + 199) / 2)

Simplifying and solving for p, we get:

p ≈ $32.56

Substituting this price back into the output supply function, we find:

q = (32.56 + 199) / 2 ≈ 115.78

Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:

Number of firms = q / 70 ≈ 10

70 * 10 = 700

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The inequality that represents the area of the rectangle is: y(2y - 2) ≥ 15

Given:

width of rectangle = y cm

length of rectangle = (2y - 2) cm

Area = y(2y - 2)

We are given that the area of the rectangle is at least 15 sq cm.

Therefore, the inequality that represents the area of the rectangle is: y(2y - 2) ≥ 15

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Answer:

Step-by-step explanation:

The error involved in approximating the sum of the given series by the sum of the first five terms of the series is `R5 = 1/6³ + 1/7³ + ...`.

To estimate the error that is made by approximating the sum of the given series by the series the first 5 terms 1/k³, we can use the remainder term of a convergent series.

The given series is ∑ 1/k³ from k = 1 to infinity.We have to find the error involved in approximating the sum of the given series by the sum of the first five terms of the series.

That is, we need to find the difference between the actual sum of the series and the sum of the first five terms of the series.

The sum of the series is given by: `S = 1/1³ + 1/2³ + 1/3³ + 1/4³ + ... + 1/n³ + ...` We can use the remainder term of the series to find the error in approximation.

The remainder term `Rn` is given by: `Rn = Sn - S` where `Sn` is the sum of the first `n` terms of the series. Thus, we have to find the remainder term for `n = 5`.

The remainder term `Rn` is given by: `Rn = S - Sn = 1/6³ + 1/7³ + ...` Since the given series is convergent, the remainder term `Rn` tends to zero as `n` tends to infinity.

So, if we take the sum of the first five terms of the series, the error involved in approximation is given by the remainder term `R5`.

The error involved in this approximation is very small and can be neglected.

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Answer:

A ≈ 3.9

Step-by-step explanation:

How to solve

A=πr2

C=2πr

A=C2

4π=72

4·π ≈ 3.8993

Therefore, the circle in square meters in the nearest tenths is A ≈ 3.9

Answer:

5/3

Step-by-step explanation:

is equivalent to 30 18 because 5 x 18 = 3 x 30 = 90. 10 6 is equivalent to 30 18 because 10 x 18 = 6 x 30 = 180. 15 9 is equivalent to 30 18 because 15 x 18 = 9 x 30 = 270. 20 12 is equivalent to 30 18 because 20 x 18 = 12 x 30 = 360.

Answer:

5/3 is equivalent to 30/18

I hope this helps have a good day!

Answer:

y<1/2+2

Step-by-step explanation:

Answer:

I think the answer is A because I learned about slope last year

There are several main types of negotiated contracts, including Cost Plus contracts. These contracts have certain disadvantages, such as potential cost overruns and lack of cost control.

Cost Plus contracts are a type of negotiated contract where the buyer agrees to reimburse the seller for the actual costs incurred in performing the contract, along with an additional fee or percentage of costs to cover profit. One disadvantage of Cost Plus contracts is the potential for cost overruns. Since the seller is reimbursed for actual costs, there may be little incentive to control expenses or find cost-saving measures. This can result in project costs exceeding the initial estimates, leading to financial strain for the buyer.

Another disadvantage of Cost Plus contracts is the limited cost control for the buyer. With this type of contract, the buyer may have limited insight and control over the seller's expenses. The seller may have little incentive to minimize costs or find more efficient ways to complete the project, as they will be reimbursed for all actual expenses. This lack of cost control can make it challenging for the buyer to manage their budget effectively and ensure that the project stays within the desired cost parameters.

In summary, Cost Plus contracts can suffer from potential cost overruns and limited cost control. The reimbursement of actual costs without strong incentives for cost savings can lead to higher expenses than initially estimated, creating financial challenges for the buyer. Additionally, the buyer may have limited visibility and control over the seller's expenses, making it difficult to effectively manage the project's budget.

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Answer:

9x2x1 and 6x3x1

Step-by-step explanation:

This question has multiple answers to it. A sandbox of 18 cubic feet with a height of a foot is actually quite simple. If it is confusing I would try to visualize the sandbox. Since volume is b x h x w the first thing you should do is divide 18 by 1. This would be more important if the height was more than one. Now you just have to find two other numbers that can divide 18. 9x2=18 and 6x3=18 so two possible dimensions for the sandbox are 9x2x1 and 6x3x1

Answer:

3 hours

Step-by-step explanation:

If a car is traveling 50 miles an a hour, then divide 150 into 3, we are using 3 because it is 3 hours.

Answer:it will take the car 3 hours

Answer: 7.35 inches

Step-by-step explanation:

The formula for the surface area of a cylinder is 2πrh + 2πr^2, where r is the radius and h is the height of the cylinder.

Given that the diameter of the tub is 10 inches, the radius (r) is half of that, which is 5 inches.

So, the equation for the surface area of the cylinder can be written as:

2π(5)(h) + 2π(5)^2 = 387.79

Simplifying the equation gives:

10πh + 50π = 387.79

Dividing both sides by 10π gives:

h + 5 = 12.34

Subtracting 5 from both sides gives:

h = 7.34

Therefore, the height of the tub is 7.35 inches (rounded to two decimal places).

Using a 35-bag sample with a mean of 406.0 grams, a known standard deviation of 25.0 grams, and a level of significance of 0.05, you can perform a one-tailed Z-test to determine whether to reject or fail to reject the null hypothesis.

To test if the potato chip manufacturer's bag filling machine is working correctly at the 411.0-gram setting, we will state the hypotheses using the given terms.

Null Hypothesis (H0): The machine fills bags correctly, with a mean weight of 411.0 grams (µ = 411.0 grams)
Alternative Hypothesis (H1): The machine is underfilling bags, with a mean weight less than 411.0 grams (µ < 411.0 grams)

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Answer: Should be 13

Step-by-step explanation:

The length of the segment M′E′ when segment ME  is rotated 270∘ counterclockwise about the origin is 13 inches.

Rotation of a figure is the transformation of it about a point in either clockwise or anticlockwise direction. By rotating, a figure changes the point of the figure.

For example, let suppose a line segment has the end point (0,3) and (0,6). By rotating it from one of its end point (0,3) 90 degree clockwise will change its location.

The new location of the line will be (0,3) and (3,3) as it is rotated  90 degree clockwise. Here, the initial length of the line is 3 units. After the rotation, the length is still 3 units long.

So, it can be concluded that rotation of a figure does not change the length of it.

The rotation of a line segment does not change the length of it. Hence, the length of the segment M′E′ when segment ME  is rotated 270∘ counterclockwise about the origin is 13 inches.

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Answer:

D

Step-by-step explanation:

Answer: C

Step-by-step explanation:

it is 10% shades

Answer:

Last option) 3

Step-by-step explanation:

For having no real solutions, discriminant of this equation must be be less than 0.

D=\(\sqrt{b^{2}-4ac }<0\)

b²-4ac<0

b²<4ac

b²/4a<c

c>b²/4a

c>\(\frac{(-4^{2} )}{8}\)

c>16/8

c>2

Answer:

t=-3

Step-by-step explanation:

2x²-4x-t=0

disc=b²-4ac=(-4)²-4×2×(-t)=16+8t

it has no solution if 16+8t<0

8t<-16

t<-2

so t=-3

2.

\(\sqrt{x-a} =x-4\\if a=2\\\sqrt{x-2} =x-4\\squaring\\x-2=x^2-8x+16\\x^2-9x+18=0\\\)

x²-6x-3x+18=0

x(x-6)-3(x-6)=0

(x-6)(x-3)=0

x=6,3

when x=6

√(6-2)=6-4

√4=2

2=2

when x=3

√(3-2)=3-4

√1=-1

1=-1

which is not true.

Hence x=3 is an extraneous solution.

x=6 is real solution.

Mathland is more likely to be sunny than rainy, with a probability of 19/30 for sunny and 11/30 for rainy. So, on average, mathland is a more sunny place than a rainy place.

In this problem, we are given that in mathland, the weather is either sunny or rainy, and there are no other possible weather conditions. We are also given that on a sunny day, there is an equal chance that it will rain on the following day or be sunny. On a rainy day, there is a 70% chance it will rain on the following day and a 30% chance it will be sunny.

To determine whether mathland is a more rainy or sunny place, we need to calculate the probabilities of the two weather conditions, sunny and rainy.

We can use the law of total probability to calculate the probabilities of the events R (it is rainy) and S (it is sunny):

P(R) = P(R|S)P(S) + P(R|R)P(R)

where P(R|S) is the probability of it being rainy given that it is currently sunny, P(S) is the probability of it being sunny, P(R|R) is the probability of it being rainy given that it is currently rainy, and P(R) is the probability of it being rainy.

We are given that on a sunny day, there is an equal chance that it will rain or be sunny the next day. Therefore, P(R|S) = 1/2 and P(S|S) = 1/2.

We are also given that on a rainy day, there is a 70% chance it will rain the next day and a 30% chance it will be sunny. Therefore, P(R|R) = 0.7 and P(S|R) = 0.3.

Finally, we know that the probability of it being sunny or rainy must be equal to 1. Therefore, P(R) + P(S) = 1.

Substituting the values we have into the law of total probability formula and using the fact that P(R) + P(S) = 1, we can solve for P(R) and P(S):

P(R) = P(R|S)P(S) + P(R|R)P(R) = (1/2)(1/3) + (7/10)(2/3) = 11/30

P(S) = 1 - P(R) = 1 - 11/30 = 19/30

Therefore, mathland is more likely to be sunny than rainy, with a probability of 19/30 for sunny and 11/30 for rainy. So, on average, mathland is a more sunny place than a rainy place.

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The image point for the given rule and preimage is (6 - 8)

When we apply a rule T<a, b> to a preimage point (x, y) we get the image (x + a, y + b), so this is like a translation.

So if we apply the rule T<4, -1> to the preimage point (2, -7), the image will be:

(2 + 4, - 7 + (-1)) = (6 - 8)

Concluding, the image point is (6 - 8)

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Answer:

C

Step-by-step explanation:

f(x) • g(x)

= \(\sqrt{x^2+12x+36}\) × (x³ - 12)

= \(\sqrt{(x+6)^2}\) × (x³ - 12)

= (x + 6)(x³ - 12)

= x(x³ - 12) + 6(x³ - 12) ← distribute parenthesis

= \(x^{4}\) - 12x + 6x³ - 72

= \(x^{4}\) + 6x³ - 12x - 72

Answer:

See photo

Step-by-step explanation:

Plato/Edmentum