Graph the function and identify the domain and range.
y=-0.25x^2

The lump-sum distribution includes employer securities and the payer reported an amount in box 7.

A lump-sum distribution is when all of a plan participant's remaining balance from all of the employer's eligible plans of one kind are distributed or paid to them in one tax year (for example, pension, profit-sharing, or stock bonus plans).

The net unrealized appreciation (NUA) in employer securities is typically not subject to tax until you sell the securities, even if the lump-sum distribution includes employer securities and the payer reported a sum in box 7 of your Form 1099-R, Distributions From Pensions, Annuities, Retirement or Profit-Sharing Plans, IRAs, Insurance Contracts, etc. for NUA in employer securities. You may, however, decide to include the NUA in your income in the year that you receive the securities.

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Answer:

C, D, E, and F

Step-by-step explanation:

C is correct because if you have a negative exponent in the denominator, you can make it positive by flipping the fraction over. Therefore, you end up with the simplified given expression.

D is correct because according to exponent rules, you subtract the exponents when you divide.

E is correct because they both equal 729 when calculated.

F is correct because the given expression equals 729 when calculated.

The equation of an arch for the given parabolic cross section is

y =  -2x² and its height is equal to 50 feet.

As given in the question,

Vertex of the parabola ( h , k ) = (0 , 0)

Focus is 0.5 foot below the given vertex.

Distance between focus and vertex 'a' = - 0.5

Standard equation of the parabola is given by:

( y - k ) = 4a ( x - h)²

Substitute the values we get,

( y - 0 ) = 4× (-0.5) ( x - 0)²

⇒ y = -2x²

Equation to represent the cross section of the given arch is

y = -2x²

Arch is 10 feet wide at ground level

⇒ x = 5 feet

Height of the arch is '( 0 - y)'

⇒ ( 0- y ) = 0 - 2(5)²

      = 50 feet

Therefore , the equation and height of the arch for the given parabolic cross section is equal to y =  -2x² and 50 feet respectively.

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Answer:

1÷12

Step-by-step explanation:

fractions can be converted to the decimal form by the long division method.

The fraction

can be written as

.

Let us do the long division for the given fraction.

What_is_1_12_as_a_decimal_img2

When the dividend is less than the divisor, add a decimal point to the quotient and add 0 to the dividend.

We can see that the dividend is still 10 and cannot be divided by 12. Hence add another 0 after the decimal point in the quotient and add 0 to the dividend to make it 0.

Carry out the division. It can be seen that the remainder 4 is recurring and hence the digit 3 in the quotient is repeated.

We can stop the division here as we know that the answer is a non-terminating decimal.

Hence the decimal form of the fraction

is 0.8333……

Here we can see that the digit 3 is repeating and hence it can be denoted with the help of a bar over the number.

Boost your score What is 1/12 as a decimal img

Note that the digit 8 is not repeated and hence the bar has to be drawn only for the digits that are repeated.

Remember

Here are some common terms you should be familiar with.

In the fraction

, the number 1 is the dividend (our numerator)

The number 12 is our divisor (our denominator).

Find More Fractions to Decimals

1/1 = 1

1/8 = 0.125

3/4 = 0.75

7/9 = 0.7

11/16 = 0.6875

8/9 = 0.8

7/8 = 0.875

4/5 = 0.8

1/2 = 0.5

1/9 = 0.1

2/5 = 0.4

3/10 = 0.3

15/32 = 0.4687

7/10 = 0.7

5/9 = 0.5

4/7 = 0.571

1/3 = 0.3

1/10 = 0.1

5/6 = 0.83

2/11 = 0.18

3/5 = 0.6

3/11 = 0.27

9/10 = 0.9

1/4 = 0.25

1/11 = 0.09

2/7 = 0.28571

5/11 = 0.45

3/7 = 0.428571

6/11 = 0.54

4/11 = 0.36

1/5 = 0.2

1/12 = 0.083

5/7 = 0.71428

8/11 = 0.72

6/7 = 0.85714

7/12 = 0.583

7/16 = 0.4375

1/6 = 0.16

1/16 = 0.0625

3/8 = 0.375

5/12 = 0.416

5/8 = 0.625

5/16 = 0.3125

15/16 = 0.9375

1/7 = 0.142857

2/3 = 0.6

2/9 = 0.2

3/16 = 0.1875

The giant box's surface area dwarfs that of the little box by = 8 times bigger than the tiny box.

The cube's surface area is calculated as six times the square of its side lengths. 6a2, where an is the cube's side length, serves as its representation. In essence, it is the overall surface area. Study Cube Volume as well.

given

Large boxes with a side length of 6 feet are produced by Z-Grand Shipping Company.

The business also produces little boxes with 3-foot sides.

surface are of large box is = 6*6*6

= 216 feet3

surface area of small box = 3*3*3

= 27 feet3

The giant box's surface area dwarfs that of the little box by = 8 times

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Differentiating F(x) gives  10[tex]x^{9}[/tex] - 72[tex]x^{5}[/tex] + 72[tex]x[/tex].

Differentiation, also referred to as derivatives, determines the rate at which one variable changes in relation to another, in this case, f(x) in relation to x. Finding the greatest or minimum conditions, or the best solution, is possible through differentiation. There are certain fundamental guidelines for differentiating functions.

lf c is any real number and if f(x) = c for all x, then f ' (x) = 0 for all x . That is, the derivative of a constant function is the zero function.

Partial derivatives in calculus are derivatives of multivariate functions taken with respect to only one variable in the function, treating other variables as though they were constants.

F(x) = ([tex]x^{5}[/tex] -6[tex]x[/tex])²

= [tex]x^{10}[/tex] -12[tex]x^{6}[/tex] + 36[tex]x^{2}[/tex]

dF(x)/dx = d( [tex]x^{10}[/tex] -12[tex]x^{6}[/tex] + 36[tex]x^{2}[/tex] )/dx

= 10[tex]x^{9}[/tex] -12 (6[tex]x^{5}[/tex]) + 36([tex]2x[/tex])

= 10[tex]x^{9}[/tex] - 72[tex]x^{5}[/tex] + 72[tex]x[/tex]

Thus, differentiating F(x) gives  10[tex]x^{9}[/tex] - 72[tex]x^{5}[/tex] + 72[tex]x[/tex].

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No, it is not safe to assume that the sampling distribution of the sample means is about normal given the sample size.

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Answer:

9x^2-12x+4=0

Step-by-step explanation:

you can use factorization method or Quadratic method (Almighty formular).

‍

The number of the solution of the equation is 2 and the solution is equal and real which is 2/3.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,

D = b² - 4ac

The equation is given below.

9x² - 12x + 4 = 0

The discriminant is given as,

D = (-12)² - 4 x 9 x 4

D = 144 - 144

D = 0

Then the roots of the equation is given as,

9x² - 12x + 4 = 0

(3x)² - 2 · 3x · 2 + (2)² = 0

(3x - 2)² = 0

x = 2/3

The number of the solution of the equation is 2 and the solution is equal and real which is 2/3.

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The sample mean is 75.

Margin of error is 6.

Sample standard deviation is 17.53 .

What is the relationship between margin of error and confidence level?

Confidence level and marginal of error As the confidence level increases, the critical value increases and hence the margin of error increases. This is intuitive; the price paid for higher confidence level is that the margin of errors increases.

Part A:

The sample mean is at the midpoint of the lower and the upper values of the confidence interval.

Thus, the sample mean is given by:

=(69 + 81) / 2

= 150/2 = 75

Therefore, the sample mean is 75.

Part 2:

The margin of error is the distance between the upper and the lower confidence interval values from the sample mean.

Thus, margin of error is given by 81 - 75 = 75 - 69 = 6 .

Therefore, margin of error is 6.

Part 3:

The margin of error is given by

ME = t₍ᵃ/₂₎ ([tex]\frac{s}{\sqrt{n} }[/tex] )

where t₍ᵃ/₂₎  is the value of the t-distribution given the degree of freedom; s is the sample standard deviation and n is the sample size.

Since the sample size is 25, the degree of freedom is 25 - 1 = 24.

[tex]\frac{a}{2}[/tex] = [tex]\frac{1-0.9}{2}[/tex] = [tex]\frac{0.1}{2}[/tex] = 0.05

From the t-distrbution table, we have:

t₍ᵃ/₂₎ = 1.710882

Thus, margin of error is given by:

6=1.710882 [tex](\frac{s}{\sqrt{25} })[/tex]

⇒[tex]\frac{s}{\sqrt{25} }[/tex]   = [tex]\frac{6}{1.710882}[/tex]

⇒s= 17.53

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Answer:

3x2a2-15xa+10

Step-by-step explanation:

The measure of ∠WRS is 25°.

What is meaning of intersect point?

A graph intersection is a location where two or more graphs meet. It is a point that is the answer to an equational system. The intersection of two curves is the sole application of the TI series.

Given the points on a line are T, R, W.

The points on another line are V, R, S.

Both lines intersect at R.

Then another line that extends from point R to point Z between ∠VRW.

The angle ∠VRT is 5x° and the angle ∠TRS is (25x + 30)°.

∠VRS is a linear angle means ∠VRS = 180°.

Again,

∠VRS = ∠VRT + ∠TRS

Putting the value of ∠VRS, ∠VRT, ∠TRS

180° =  5x° + (25x + 30)°

180 =  30x + 30

Subtract 30 from both sides:

150 = 30x

Divide both sides by 30:

x = 5.

∠WRS is vertically opposite angle of ∠VRT.

Therefore ∠WRS = ∠VRT = 5x° = (5×5)° = 25°

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The car's value will decreases to $6,200 in about 8.65 years.

First, let's find the annual depreciation of the car. The car is purchased for $19,000 and depreciates at 7.75% per year, so the annual depreciation is:

⇒ 0.0775 x $19,000 = $1,478.50.

Now that we know the annual depreciation of the car, we can divide the difference in value by the annual depreciation to find out how long it will take for the value of the car to reach $6,200.

The value of the car decreases from $19,000 to $6,200, so the difference in value is :

⇒ $19,000 - $6,200 = $12,800.

Dividing this difference by the annual depreciation of $1,478.50:

⇒ $12,800 / $1,478.50 = 8.65 years.

Therefore, it will take approximately 8.65 years for the value of the car to reach $6,200.

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Here each tea mug has 60 milliliters of tea.

What is division?

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

2.4 liters of tea were equally distributed to 40 mugs.

2400 milliliter of tea.

So each tea mug has = 2400/40 = 60 milliliters of tea.

Hence, each tea mug has 60 milliliters of tea.

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The measure of the angle PQR is 90° as Segment QR is tangent to the circle with center P. Hence, option C is the correct answer.

A tangent draw to a circle always makes a right angle with the radius of the circle. In simple words, we can say that the radius of the circle and the tangent segment are always perpendicular to each other.

Now we have, PQ as the radius of the circle, and segment QR is tangent to the circle with center P.

Thus, segment PQ is perpendicular to segment QR, so the angle PQR is equal to 90°.

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Answer:

n = 113°

Step-by-step explanation:

⭐What is an isosceles triangle?

⭐What is the exterior angles theorem?

In this case, n is the exterior angle, because it is outside of the triangle.

The 46° is opposite of n.

Thus, we need to find the left base angle, because it is opposite of n, and use the exterior angles theorem to find n.

Knowing that the triangle is an isosceles triangle, we can make an equation to find the base angles.

The internal angles of a triangle sum to 180°. Let the base angles = x.

[tex]46 + x + x = 180[/tex]

[tex]46 + 2x = 180[/tex]

[tex]2x = 134[/tex]

Solving for one base angle:

[tex]x = 67[/tex]

∴ The left base angle is 67°

Now, apply the exterior angles theorem knowing the two angles opposite of n.

[tex]n = 46 + 67[/tex]

[tex]n = 113[/tex]

∴ n = 113°

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Using the concept of similar triangle and rule for the proportionality of it's sides, The answer is x=2.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the internal angles of a triangle add up to 180 degrees.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

Triangle ADE and Triangle ABC are similar in nature.

using the rule of proportionality of sides of the similar triangle, We have,

[tex]\frac{2+x}{2} = \frac{2}{1}[/tex]

x+2=4

x=4-2

x=2

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When a relationship is plotted on a graph, a linear relationship results in a straight line; a nonlinear relationship, on the other hand, results in a curve.

There are a total of four components in a time series model.

Trend, Seasonal, Cyclical, and Error.

Seasonal Component is a wavelike pattern that is repeated throughout a time series and has a recurrence period of at most one year.

Cyclical Component is a wavelike pattern within the time series that repeats itself throughout the time series and has a recurrence period of more than one year.

Error Term represents the changes in time series data that are unpredictable and can't be associated with a seasonal , cyclical component.

Trend Component is the long-term increase or decrease in a variable being measured over time.

When a relationship is plotted on a graph, a linear relationship results in a straight line; a nonlinear relationship, on the other hand, results in a curve.

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Answer:

The number is 28.35

Step-by-step explanation:

45% of 36

[tex]\frac{x*y}{100}[/tex]

= [tex]\frac{45*36}{100}[/tex]

= [tex]\frac{2835}{100}[/tex]

= 28.35

The answer is false because the answer will be 0.04863%

To find the periodic interest rate we have to know about the following terms:-

Interest Rate (R)

It is the nominal interest rate or "stated rate" in percent. r = R/100

Compounding Periods (m)

It is the number of times compounding will occur during a period.

Periodic Interest Rate (P)

This is the rate per compounding period, such as per month when your period is year and compounding is 12 times per year.

R ={  (1 + i/m) to the power m/n - 1 }

Where,

i = nominal annual rate

n = number of payments per year i.e., 12 for monthly payment, 1 for yearly payment and so on.

m = number of compounding periods per year

The period interest rate per payment is integral to the calculation of annuity instruments including loans and investments.

So, R = 0.04863%

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As per the concept of hypothesis testing, the p-value of the test static is  0.0837

Hypothesis testing:

In statistics, when the alternative hypothesis is of the "greater than or greater than or equal to" type, the p-value can be calculated by calculating the probability of the z statistic being greater than the test statistic value.

Given,

Here we have the mayor of a town has proposed a plan for the annexation of a new community. and the political study took a sample of 800 voters in the town and found that 63% of the residents favored annexation. using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is more than 60%. testing at the 0.02 level.

Here we need to find the p-value of the test statistic.

While we looking into the given question we have identified the following hypothesis,

=> H0 : p <=0.6

=> H1: p > 0.6

And the value of alpha=0.02 p{reject H0 | H0 true} test statistic is a z from a 1 way 1 proportion test

So, the z value is z> 7.1286

Then the z value is calculated as,

=> 0.03/sqrt(0.6*0.63/800)

=> z = 1.3801

Therefore, the reject H0, the true proportion is greater than 60% and the p-value is 0.0837

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It is insufficient proof that more than half of the students at the school recycle.

Given :

suppose that in the sample, 55 students said that they recycle.

It is insufficient proof that more than half of the students at the school recycle because: "Yes" was replied by 55 out of 100 pupils.

= 55 / 100

= 0.55

We can see that the proportion 0.55 of has a lot of dots above it in the dot plot.

As a result, a proportion of 0.55 is quite likely to be obtained when the genuine proportion is 0.5, and there is insufficient evidence to support the assertion that more than half of the school's students recycle.

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The standard deviation of the distribution is 8.60

From the question, we have the following parameters that can be used in our computation:

Sample size = 40

Standard error of the mean = 1.36

These parameters mean that

n = 40

SE = 1.36

The standard deviation is then calculated as

SE = σ/√n

Where

σ = standard deviation

Make σ the subject

σ = SE * √n

So, we have

σ = 1.36 * √40

Evaluate

σ = 8.60

Hence, the standard deviation is 8.60

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The total income tax paid by Isabel last year was $3,230.

Now, for the question.

Tax rate - 15% upto $8500.

Tax rate - 17% from $8500.

Total amount - $20,000.

Total income tax = 15% of $8500 + 17% of (20,000 - 8500)

Total income tax = 1,275 + 1,955

Total income tax = 3,230

Thus, the total income tax paid by Isabel last year was $3,230.

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14 2/7 as a fraction can be rewritten as 100/7. This is a Mixed fraction which is converted into Improper Fractions.

Fractions indicate pieces of a whole or group of items. A fraction is made up of two components. The number at the top of the line is referred to as the numerator. It specifies the number of equal sections of the whole or collection that are taken. The denominator is the number below the line. It displays the total number of equal sections into which the whole is divided or the total number of identical objects in a collection.

By multiplying the whole integer by the denominator and then adding it to the numerator, mixed fractions can be transformed into improper fractions. The denominator stays the same, but it becomes the new numerator.

Like for converting the mixed fraction to improper fraction we follow the below steps :

14 2/7 = ((14 X 7) + 2)/7

= (98 + 2) / 7

= 100/7

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50%. students (in percent) who passed the second exam also passed the first exam.

Let's imagine that there are 100 kids in the teacher's class. We know that 40 of them passed BOTH tests, and 80 passed the second test.

Because if they weren't, they wouldn't have passed the first test and consequently wouldn't have passed both, we can be sure that the group of students who passed BOTH tests is only made up of the 80 who passed the second test.

Thus, both tests were passed by 40 of the 80 pupils who passed the second one:                                      

40/80 = 1/2 = 50%.

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Let's say you run a test, and your p-value comes out to be equal to 0.93. Do not reject [tex]H_{o}[/tex] at alpha equal to 0.10, 0.05, or 0.01 according to this conclusion.

The significance level is the likelihood that the researcher will conclude that the null hypothesis is false even though it is true. The validity and correctness of the data set are increased when the lower values of the significance level are used during the hypothesis testing.

The null hypothesis is disregarded if the p-value is less than the significance level.

Information Given: p=0.93

The test findings would be insignificant because the p-value is higher than the thresholds of 0.01, 0.05, and 0.10. This leads to the conclusion that at 0.01 and 0.05 and 0.10, the null hypothesis cannot be ruled out.

Therefore, option (b)—Do not reject [tex]H_{o}[/tex] at alpha equal to 0.10, 0.05, or 0.01—is the appropriate response.

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The value of the condensed logarithm is, log(dq^8).

What is logarithm?

The opposite of exponentiation in mathematics is the logarithm. The exponent to which b must be raised in order to produce a number x is therefore the logarithm of a number x to the base b. For instance, since 1000 = 10^3, log10 of 1000 is 3, or [tex]log_1_0[/tex] = 3.

Given: log d + 8 log q.

We have to condense the given logarithm

Frist to simplify 8 log q by moving 8 inside the logarithm.

⇒ log(q)^8

⇒ log d + log(q^8)

Applying the product rule of logarithm

log(a) + log(b) = log(ab)

⇒ log d + log (q^8) = log(dq^8)

Hence, the condensed logarithm form of the given logarithm is, log(dq^8).

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A weight training program for a friend that will increase his or her muscular endurance:

Legs: barbell back squats — 3 sets of 5 reps.

Chest: flat barbell bench press — 3 set of 5 reps.

Back: seated cable rows — 3 sets of 6–8 reps.

Shoulders: seated  shoulder press — 3 sets of 6–8 reps.

The ability of a muscle or group of muscles to perform repetitive contractions against a force for an extended period of time is referred to as muscular endurance. The more muscular endurance you have, the more repetitions you can do.

Muscular endurance is the ability to contract a muscle or group of muscles against resistance, such as weights or body weight, for an extended period of time. Increasing these muscles' performance means they can continue to contract and work against these forces.

The workouts should be done on Mondays, Wednesdays, Fridays, and Saturdays. That way, you can take a day off between upper-body-focused workouts. Each of the four weekly workouts consists of five moves that you will perform in straight sets.

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The probability that it was that of a male is 2/5 .

This problem of probability can be solved using Baye's Theorem . In simple terms , Bayes' Theorem states that the conditional probability of an event, based on the occurrence of another event, is equal to the likelihood of the second event given the first event multiplied by the probability of the first event. Hence , proceeding accordingly -
Given in the question is :

P(Males reacting negatively = M) = 1-40%= 60% = 60/100

P(Females reacting negatively = F) = 1-70%= 30% = 30/100

Now , P(Females' response being selected= f) = 15/20
P(Males' response being selected = m ) = 5/20
P(M/m) = P(M) P(m)/ P(M) P(m) + P(F) P(f)
⇒ 5/30 × 60/100 ÷ 5/30 × 60/100 + 15/20 × 30/100

⇒ 300/300+450
⇒ 300/750

⇒ 2/5
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absolute maximum =  3.033

absolute minimum = -1.846

A point where the function achieves its highest value is known as an absolute maximum point. Similar to this, an absolute minimum point is the location at which the function's maximum value is obtained.

f(x) = x[tex]e^{-x^{2}/50 }[/tex] , [−2, 10]

f'(x) = x[tex]e^{-x^{2}/50 }[/tex] (-2x/50) + [tex]e^{-x^{2}/50 }[/tex] (1)  = 0

-2[tex]x^{2}[/tex]/50 + 1 = 0

2[tex]x^{2}[/tex]/50 = 1

2[tex]x^{2}[/tex] = 50

[tex]x^{2}[/tex] = 25

x = +5 , -5

f(-2) = -2 [tex]e^{-2^{2} /50}[/tex] = -1.846

f(10) = 1.3353

f(5) = 3.033

absolute maximum = 3.033

absolute minimum = -1.846

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