An object moving with a speed of 21 m/s and has a kinetic energy of 140 J, what is the mass of the object?

We want to find a polynomial

f(x) = a x³ + b x² + c x + d

such that the roots of f are x = -3, x = -1, and x = 4, and f(x) takes on a value of -24 when x = -2.

The factor theorem for polynomials tells us that we can factorize f(x) as

a x³ + b x² + c x + d = a (x + 3) (x + 1) (x - 4)

Expand the right side:

(x + 3) (x + 1) (x - 4) = x³ - 13x - 12

So we have

a x³ + b x² + c x + d = a x³ - 13a x - 12a

In order for both sides to be equal, the coefficients of both polynomials on terms of the same degree must be equal. This means

a = a (of course)

b = 0 (there is no x² term on the right)

c = -13a

d = -12a

We also have that f (-2) = -24, which means

f (-2) = a (-2 + 3) (-2 + 1) (-2 - 4)

-24 = 6a

a = -4

which in turn tells us that c = 52 and d = 48.

So we found

f(x) = -4x³ + 52x + 48

If you are 25yr old and single with no kids/dependents.  The total Federal Income Taxes is $11,218 and FICA paid is $6,478.

First, you need to determine your taxable income.

Gross income: $84,649

Itemized deductions: $10,211

Tax-deferred retirement contributions: $3,288

Taxable income: $71,150

Next, you can use the tax brackets and rates for the 2023 tax year to calculate your federal income tax liability.

The first $10,950 is taxed at 10%: $1,095

The next $32,250 is taxed at 12%: $3,870

The next $28,425 is taxed at 22%: $6,253

The remaining $0 is taxed at 24%: $0

Total federal income tax liability: $11,218

b. For 2023, the Social Security tax rate is 6.2% on the first $147,000 of income, and the Medicare tax rate is 1.45% on all income.

Social Security tax: $5,240.80

Medicare tax: $1,237.20

Total FICA taxes: $6,478

Therefore the total Federal Income Taxes is $11,218 and FICA paid is $6,478.

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About 88.49% of cellphone plans have charges that are less than $83.60.

To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.

z = (x – μ) / σ

where x = 83.60, mean, μ =  62 and standard deviation, σ = 18

Thus, the z-score of $83.60 is:

z = (83.60 - 62) / 18 = 1.2

Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).

Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.

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Answer

sum of all 3 digit even number = 247050

The series is 100 + 102 + 104 + .... + 998

which by using formula Sn = N/2 ( a + an)

where N = number of terms

a = first term = 100

an = last term = 998

The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)

For the first question:

The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.

The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.

Now, let's analyze the answer options:

A. A line passes through the point (0, 0) and continues through the point (3, 12).

This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.

B. A line passes through the point (0, 0) and continues through the point (2, 8).

This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).

C. A line passes through the point (0, 0) and continues through the point (6, 24).

This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.

D. A line passes through the point (0, 0) and continues through the point (12, 3).

This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).

Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.

For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?

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Answer:

96.25%

Step-by-step explanation:

The empirical rule regarding mean and standard deviation is that

Therefore between mean and +2 standard deviation or between mean and -2 standard deviation you will find  approximately 95/2 = 47.5% of the values

Between mean and ± 3 standard deviations you will find approximately 97.5/2 = 48.75% of the values

Therefore between 2 standard deviations above and 3 standard deviations below you will find approximately 47.5 + 48.75 = 96.25% of values

Given:

CDEF is dilated by a scale factor of \(\dfrac{3}{4}\) to form the quadrilateral C'D'E'F'.

To find:

The measure of side E'F'.

Solution:

If a figure is dilated by a scale factor of k, then the side of dilated figure is k times of corresponding side of original figure.

CDEF is dilated by a scale factor of \(\dfrac{3}{4}\) to form the quadrilateral C'D'E'F'. So,

\(E'F'=\dfrac{3}{4}\times EF\)

From the given figure it is clear that \(EF=12\). So,

\(E'F'=\dfrac{3}{4}\times 12\)

\(E'F'=9\)

Therefore, the measure of side E'F' is 9 units.

The height of the shipping container is 7 feet

A volume is the amount of space occupied by a three dimensional shape or object.

Let h represent the height of the shipping container. The volume of the prism is given by:

Volume = length * width * height

1120 = 20 * 8 * h

h = 7 feet

The height of the shipping container is 7 feet

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Answer:12

for every 2 boys that is 3 girls

there are 4 sets of two boys so you would have 4 sets of 3 girls

4×3=12

I hope this is good enough:

Arcs get their angle measure from the central angle they're in, in this case the central angle of 86°, central to arcED, has a counterpart of a twin vertical angle across the center, since both vertical angles are identical twins that means the central angle for arcAB is 86° also, and that's the arcAB's measure too.

Answer:

1) 3√5

2) -7√2

3) 4√3

5) 6√6k^2

6) 10v^3/2

7) 4√5p^3/2

8) 3√5p

9) 7√3m^3/2n^3/2

10) 10m^√2n

11) 5x√3y

12) 8m^3/2n^3/2

Step-by-step explanation:

Answer:

31 + 32 + 33 = 96.

Step-by-step explanation:

I think you are meaning 96 not -96

Answer:

day 2

Step-by-step explanation:

day 1 had a 26.19-degree change while day 2 had a 33.47

Answer:

Day 2 is a bigger change.

Step-by-step explanation:

Day 1 change: 26.19

Day 2 change: 33.47

Add the positive version of each number together to find the change, like so:

Day 1: -12.75 to 12.75 and 13.44 to 13.44   12.75+13.44= 26.19

Day 2: -8.83 to 8.83 and 24.64 to 24.64   8.83 + 24.64=33.47

PS: Next time, please be a little nicer with your question.

The area of the sector with an angle of 285 degrees and a radius of 6 units is 28.5π square units.

To find the area of a sector, we can use the formula:

Area of Sector = (Central Angle / 360 degrees) × π ×  (Radius²)

Given that the central angle is 285 degrees and the radius is 6, we can substitute these values into the formula:

Area of Sector = (285 degrees / 360 degrees) ×  π ×  (6²)

Area of Sector = (19/24) ×  π × 36

Area of Sector = (19/24) ×  36π

Area of Sector = (19 × 36π) / 24

Area of Sector = 684π / 24

Area of Sector = 28.5π

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Answer:

undefined

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2  x_1)

slope = (-3 - 4)/(6 - 6)

slope = -7/0

Since division by zero is undefined, this line has undefined slope.

Answer:

4:3

Step-by-step explanation:

They list first first but then ask for turtles to fish.

\(\frac{24}{18}\)  Divide the top and the bottom by 6 to get \(\frac{4}{3}\) or 4:3

The dataset represented by the given box plot is 12, 15, 15, 17, 19, 19, 20, 22, 24 option B.

A box plot, sometimes called a box whisker plot, shows the distribution of a dataset graphically. The minimum value, the first quartile (25th percentile), the median (50th percentile), the third quartile (75th percentile), and the maximum value are the five main values used to standardise this method of displaying the distribution of data.

Two whiskers that extend from a rectangular box make up a box plot. The range of values between the first and third quartiles is represented by the box, which is known as the interquartile range (IQR).

From the given box plot we observe that the minimum value is 12 and the maximum value is 24.

Here, the median is 19.

From the information the two data set that have the corresponding values are:

12, 15, 15, 17, 19, 19, 20, 22, 24

12, 15, 17, 17, 19, 19, 22, 22, 24

The lower quartile is 15.

The upper quartile is 21.

Calculating the lower quartile for the data sets:

12, 15, 15, 17, 19, 19, 20, 22, 24

Lower quartile = 15

Hence, the dataset represented by the given box plot is 12, 15, 15, 17, 19, 19, 20, 22, 24 option B.

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Answer:

midsegment = 23

Step-by-step explanation:

the midsegment is half the sum of the bases, that is

midsegment = \(\frac{18+28}{2}\) = \(\frac{46}{2}\) = 23

Answer: None of the choices is correct.

6,714÷103 is about 65.184

Step-by-step explanation:

The closest answer is the second choice. But there must be a typo in the question.

6,714÷100 = 67.14

I hope this helps. You might be able to ask your teacher about the mistake in the question.

The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

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Answer:

The answer is -136

Step-by-step explanation:

you multiply -34 by 4 which gives you -136

(Hope this help)

Answer:

$5.88 Divided by 12 = $0.49

$10.20 Divided by 20 = $0.51

So Turbo Taste costs $0.02 more.  

I hope this helped.

Answer:

infinite. the line goes on diagonally crossing thru infinite points.

Answer:

Step-by-step explanation:

You equal both angles to each other and solve. You should get x=5, the you plug in x giving you 44 for both angles and 88 for ABC

Answer:0.0081  or 0.81%

Step-by-step explanation:

The required probability is P(3,5,0.1)= C5 3 * p^3*q^2, where

C5 3=  5!/3/2=4*5/2=10

p is the probability that one randomly selected calculator is defective= 10%=0.1

q is the probability that one randomly selected calculator is non-defective.

q=1-p=1-0.1=0.9

So P(3,5,0.1)= 10*0.1^3*0.9^2=0.01*0.81=0.0081

Answer:

15/2 minutes

Step-by-step explanation:

Class duration= 45 minutes

For 6 songs = 45 minutes

For 1 song = 45/6 = 15/2 minutes

Given:

Colin’s piano lesson is 45 minutes, or Three-fourths of an hour, long. If he practices 6 different songs and spends an equal amount of time on each song, what fraction of an hour does he spend practicing each song ?

Solution:

we have,

→ Colin’s piano lesson is = 45 minutes .

and,

→ he practices total different songs = 6

also, given that, he spends an equal amount of time on each song .

So,

→ Time he spend on each song = Total time of lesson / Total number of songs he practice = 45/6 = (15/2) Minutes.

now, we know that,

→ 60 minutes = 1 hour .

→ 1 minute = (1/60) hour .

then,

→ (15/2) minutes = (1/60) * (15/2) = (1/8) hours.

hope this helps......

Answer: not related

Step-by-step explanation: Statistical tests are employed when trying to establish the existence or non-existence of relationship between two variables. Variables may be numerical or categorical, in most cases, regression is employed in establishing relationship between. numerical variables. However, the Chisquare test of independence is employed when analysing and trying to establish if a relationship exists between two categorical variables. With the null hypothesis maintain that both variables are independent are hence unrelated while the alternative hypothesis states otherwise.

Answer:

Outcome Y is independent of Factor X.

Step-by-step explanation:

The null hypothesis for the Chi-Square Tables Test is:

Outcome Y is independent of Factor X.

A 99% confidence interval for the population proportion is; CI = (0.164, 0.194)

We are given;

Sample size; n = 4096

Number that opposed transgender students; x = 733

Thus;

Proportion; p^ = x/n = 733/4096 = 0.179

Formula for confidence interval of proportions is;

CI = p^ ± z√[p^(1 - p^)/n]

The z-value for confidence level of 99% is z = 2.576

Thus;

CI = 0.179 ± 2.576√[0.179(1 - 0.179)/4096]

CI = 0.179 ± 0.015

CI = (0.164, 0.194)

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