Given the expression 2(3x + 1), what would be the resulting equivalent expression after the distributive property is applied?

1. The monthly payments for 2 of these options are:

2. The total payments for 2 of these options are:

3. The percentage of the total amounts to be paid back as interest is:

4. The percentages above represent the accumulated interests of the total payments.

The APR (annual percentage interest) represents the yearly financing cost of the financing institution for extending credit.

5. Ramona should choose the Online Construction Business to remodel her kitchen because the total cost she will incur is less than the total cost for the Local Small Business Home Improvement Company.

Home improvement cost = $13,200

Financing:

Year 1 0% monthly payment of $100 = $1,200

Balance after Year 1 = $12,000

APR 16.99%

Remaining payment period = 3 years

N (# of periods) = 36 months

I/Y (Interest per year) = 16.99%

PV (Present Value) = $12,000

FV (Future Value) = $0

Results:

PMT = $427.77

Sum of all periodic payments = $15,399.83

Total Interest = $3,399.83

Total costs = $16,599.83 ($15,399.83 + $1,200)

Home improvement cost = $11,800

Financing:

3% origination fee = $354 ($11,800 x 3%)

APR = 7.5%

Payment period = 5 years

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 7.5%

PV (Present Value) = $11,800

FV (Future Value) = $0

Results:

PMT = $236.45

Sum of all periodic payments = $14,186.87

Total Interest = $2,386.87

Total costs = $14,540.87 ($14,186.87 + $354)

Interest as a percentage of the total payment = 16.41% ($2,386.87/$14,540.87 x 100)

Home improvement cost = $10,200

Additional applied amount = $1,000

Total = $11,200

APR = 11.9%

Payment period = 4 years

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 11.9%

PV (Present Value) = $11,200

FV (Future Value) = $0

Results:

PMT = $294.39

Sum of all periodic payments = $14,130.69

Total Interest = $2,930.69

Total cost = $14,130.69

Interest as a percentage of the total payment = 20.74% ($2,930.69/$14,130.69 x 100)

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a)Perimeter of given right angle triangle is 48.

Perimeter of dilated right angle triangle is 192.

b) Area of given figure is 96cm²

Area of figure after dilation is 1536cm².

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.

Given,

Triangle given,

Base = 12

hypotenuse = 20

Leg =  16

Dimensions of new triangle after dilatated by scale factor of 4:

Base = 48

hypotenuse = 80

Leg = 64

Area of right angled triangle:

Base × Leg/2

Area of given figure:

12 × 16/2

12 × 8

96

Area of given figure is 96cm²

Area of figure after dilation:

48 × 64/2

24 × 64

1536

Area of figure after dilation is 1536cm².

Perimeter of right angle triangle:

Perimeter of given figure:

12 + 20 + 16

48

Perimeter of given right angle triangle is 48.

Perimeter of dilated figure:

48 + 80 + 64

192

Perimeter of dilated right angle triangle is 192.

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Answer:

Addition and subtraction are inverse operations, as are multiplication and division. To solve an equation means to isolate the unknown, x, on the left of the = sign.

volumes of cone: V= TT ×R2 × H ÷ 3

Answer:

I believe for a cylinder the volume is the base times the height.

Step-by-step explanation:

this is just from my own head

Answer:

- The value of the 2 test statistic is 6.98

- There is no sufficient evidence to reject the claim of the specific distribution

Step-by-step explanation:

Given

Proportion (p)

\(ABC = 29\% = 0.29\\CBS = 28\% = 0.28\\NBC = 25\% = 0.25\\Others = 18\% = 0.18\\\)

Samples

\(ABC = 95\\CBD = 65\\NBC = 87\\Others = 53\\\alpha = 0.05\)

First, we formulate a table for chi square totals:

\(x^2 = \frac{(O - E)^2}{E}\)

Where

O = Observed Frequency and E = Expected Frequency

So, we have:

\(\begin{array}{cccccc}{\ } & {O} & {E = np} & {O - E} & {(O -E)^2} & {x^2 = \frac{(O - E)^2}{E}} \ \\ \\ {0.29} & {95} & {87} & {8} & {64} & {0.736} &{0.28} & {65} & {84} & {-19} & {361} & {4.300} & {0.25} & {87} & {75} & {12} & {144} & {1.920} & {0.18} & {53} & {54} & {-1} & {1} & {0.019}\ \end{array}\)

For ABC

\(E = np = 300 * 0.29= 87\)

\(O-E =95 - 87 = 8\)

\((O-E)^2 = 8^2 = 64\)

\(x^2 = \frac{(O - E)^2}{E} = \frac{64}{87} = 0.736\)

For CBS

\(E =np = 300 * 0.28 = 84\)

\(O -E = 65 - 84 = -19\)

\((O -E)^2 = (-19)^2 = 361\)

\(x^2 = \frac{(O - E)^2}{E} = \frac{361}{84} = 4.300\)

For NBC

\(E =np = 300 * 0.25 = 75\)

\(O -E = 87 - 75 = 12\)

\((O -E)^2 = (12)^2 = 144\)

\(x^2 = \frac{(O - E)^2}{E} = \frac{144}{75} = 1.920\)

For others:

\(E = np = 300 * 0.18 =54\)

\(O - E = 53 - 54 = -1\)

\((O - E)^2 = (-1)^2= 1\)

\(x^2 = \frac{(O - E)^2}{E} = \frac{1}{54} = 0.019\)

\(\sum x^2 = 0.736 + 4.300 + 1.920 + 0.019\)

\(\sum x^2 = 6.975\)

\(\sum x^2 = 6.98\) --- approximated

The value of the 2 test statistic is 6.98

Next, is to determine the p value:

Calculate the degree of freedom

\(df = n - 1\)

\(df = 4 - 1\)

\(df = 3\)

Using the \(x^2\) table in the 3rd row,

\(\sum x^2 = 6.98\) corresponds to:

\(p = 0.072699\)

The value of p is:

\(0.05 < P < 0.10\)

This implies that, we fail to reject H o

The matrix shown represents its elements in rows and columns

The operation performed by the student is R3 -> 2R2 + R3.

The matrix is given as:

\(\left[\begin{array}{cccc}-4&1&2&4&0&-1&3&1&3&2&4&5\end{array}\right]\)

Multiply the elements on the second row (Row 2) by 2.

So, we have:

2R2 = 0 -2 6 2

Add these elements to the third row (Row 3).

So, we  have:

2R2 + R3 = 3 0 10 7

Replace the row 3 by the above elements.

i.e.

R3 -> 2R2 + R3.

So, we have:

\(\left[\begin{array}{cccc}-4&1&2&4&0&-1&3&1&3&0&10&7\end{array}\right]\)

Hence, the operation performed by the student is R3 -> 2R2 + R3.

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Answer:

Step-by-step explanation:

h hubuj

ANSWER:

EXPLANATION

so this is an easy question ur mom and dad they are smart that how th

Answer:

=−6x−24

Step-by-step explanation:

Answer:

The answer is (-7)

Step-by-step explanation:

f(x) = -2x - 3, if f(2)

f(2) = -2(2) - 3 = -4 - 3 = (-7)

Thus, The answer is (-7)

Answer:

57%

Step-by-step explanation:

the table shows the following:

test scores for Test 1 = 62, 62, 66, 70, 70, 70, 78, 82, 82, 86

test scores for Test 2 = 68, 72, 72, 72, 72, 76, 80, 80, 80, 84, 88, 88

there are 7 tests with scores greater than or equal to 70 on test 1

there are 11 tests with scores greater than or equal to 70 on test 2

the percent change is the difference of the two amounts, 7 and 11, divided by the original amount, 7

4/7 = 57%

Answer:

$1.70 per share

Step-by-step explanation:

37.90-36.20=1.70

The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42

A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.

The six o'clock position on the Ferris wheel is level with the loading platform.

The wheel completes 1 full revolution in 2 minutes.

We have to find how many minutes of the ride are spent higher than 26 meters above the ground.

So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters

So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)

Also, the height of a person at the lowest point = 4 - 15 = -11 meters

Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.

So, the total distance travelled will be = 19 + 11 = 30 meters.

Also, we are given that the wheel completes 1 full revolution in 2 minutes.

We need to calculate the time spent higher than 26 meters above the ground.

So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.

This angle can be calculated as follows:

Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees

Angle = 30 / (pi * 30) * 360 degrees

Angle = 360 degrees / pi

= 114.59 degrees

So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.

Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.

This can be calculated as follows:

Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken

Time = (180 - 114.59) / 360 * 2 minutes

Time = 0.42 minutes

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

set O

set P

median = ?

Step 02:

P: 19, 19, 26, 36, 49, 50, 81

median = 36

O: 25, 26, 32, 33, 37, 60, 71

median = 33

The answer is:

Set P has the larger median, 36.

Answer:

6 miles

Step-by-step explanation:

You Can make a proportion

\(\frac{26/3 miles}{60 minutes}\)=\(\frac{x}{45 minutes}\)

Now cross multiply

45*26/3 is 360

and 60*x is 60x

make an equation

60x=360

x=6

So 6 miles

Answer:

6 miles

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

\( {x3 \: - 4 {x \: }^{2} + 3x \: = 0}^{} \)

solve for x

\(x 1 = 0 \\ x2 \: = 1 \\ x3 \: = 3\)

Answer:

C. 20 feet

Step-by-step explanation:

Let x = width

Let y = length

If the length is at least 10 feet longer than the width:

⇒ x + 10 ≤ y

⇒ x ≤ y - 10

If the perimeter is to be no more than 100 ft:

⇒ 2x + 2y ≤ 100

⇒ x + y ≤ 50

⇒ x ≤ 50 - y

Equate the equations for x and solve for y:

⇒ y - 10 = 50 - y

⇒ 2y = 60

⇒ y = 30

Substitute found value of y into one of the inequalities for x:

⇒ x ≤ 30 - 10

⇒ x ≤ 20

Therefore, the maximum possible width of the fence is 20 feet.

Answer:

The question has some missing details such as ; Use cylindrical shells to find the volume of the remaining solid if the remaining solid is 8cm high. I have however solved it using the value of 8cm, you can use the same approach to solve for the volume irrespective of the value of the height you are given.

Step-by-step explanation:

The detailed step by step analysis and appropriate Integration by susbtitution in order to get the volume of the remaining solid is as shown in the attached file.

Answer:

126

Step-by-step explanation:

\(V = A * h = \frac{1}{4} * \pi * d^{2} * h = A * h = \frac{1}{4} * 3.14 * 36 * 5 = 141.3\\ \\V_{empty} = A * h = \frac{1}{4} * \pi * d^{2} * h = \frac{1}{4} * \pi * 4 * 5 = 15.7\)

\(V_{full} = V - V_{empty} = 141.3 - 15.7 = 125.6 \approx 126\)

Answer: A, B and C

Step-by-step explanation:

Step-by-step explanation:

Given any three side lengths of a right triangle, the longest side is the hypotenuse.

The side lengths  of a right triangle must satisfy the Pythagorean Theorem.

Pythagorean Theorem:

Option A:

True

Option B: 2.5, 6, 6.5

Option C:

Since all are true, the side lengths in Options A, B and C forms a right triangle,

Answer:

Side lengths a , b , c form a right triangle if, and only if, they satisfy a² + b² = c² . We say these numbers form a Pythagorean triple

Step-by-step explanation:

Answer:

a. 125.0714; 11.1835.

b. 109.4375; 10.4612.

Step-by-step explanation:

Given the following data;

70, 65, 71, 78, 89, 68, 50, 75.

Mean = 70.75

The deviation for the mean of the data is -0.75, -5.75, 0.25,7.25,18.25,-2.75,-20.75, and 4.25.

We would then find the square of this deviation;

\(=(-0.75)^2+(-5.75)^2+( 0.25)^2+(7.25)^2 +(18.25)^2+(-2.75)^2+(-20.75)^2 +(4.25)^2\)

\(=0.5625+33.0625+0.0625+52.5625+333.0625+7.5625+430.5625+18.0625\)

= 875.5

Next is to find the population variance;

\(V = \frac{875.5}{8}\)

Variance, V = 109.4375

The population standard deviation is the square root of the population variance;

\(Sd = \sqrt{109.4375}\)

Standard deviation, Sd = 10.4612

To find the sample variance;

\(V = \frac{875.5}{8-1}\)

\(V = \frac{875.5}{7}\)

Variance, V = 125.0714

The sample variance is;

\(Sd = \sqrt{125.0714}\)

Standard deviation, Sd = 11.1835

Therefore,

a. The sample variance is 125.0714 and the sample standard deviation is 11.1835.

b. If this is a population data, the population variance is 109.4375 and the population standard deviation is 10.4612.

Answer:

C. 20.67

Step-by-step explanation:

I got it right on edge :)

The meer-kitty survey feedback tab has limitations in its data. The survey results must have at least 120 unique responses to be considered useful and aligned with the business objective. The current data, however, only has 40 total responses, with 11 of them coming from one user. This skews the results and makes it difficult to accurately analyze the feedback.

To address these limitations, it is recommended to remove the duplicates, in this case the 11 responses from one user, and focus on the remaining 29 unique responses. This will provide a clearer picture of the survey results and a more accurate representation of the feedback. By doing so, the analysis of the data will be better aligned with the original business objective and provide more valuable insights.

It is important to consider the limitations of the data when conducting any type of analysis, especially when it comes to surveys and feedback. By taking the necessary steps to ensure the data is as accurate and reliable as possible, the results of the analysis will be more meaningful and relevant to the business.

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Answer:

5/3

Step-by-step explanation:

In this question, we are trying to find the slope of the line with the given points.

To find the slope, we would use the slope equation: m = y2-y1/x2-x1

Plug in the coordinates and solve:

-5 - 5/-3 - 3

-10/-6

Simplify further while canceling out the negative.

5/3

The slope of the line would be 5/3

The Fraction 9/18 should be multiplied by 1/4 to get the value Equivalent to 9/18 ÷ 2.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

We have to solve,

9/18 ÷ 2

As, Fraction does not support the division as usually number does.

So, we have to perform the multiplication by reciprocating the number,

9/18 x 1/2

= 9/ 36

= 1/4

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Answer:

6.4 miles

Step-by-step explanation:

24 minutes is 2/5 of an hour, meaning that we can just multiply 16 and 2/5 to get how many miles he traveled in 24 minutes.

16 x 2/5 = 32/5

Tom traveled 32/5, or 6 and 2/5 of a mile in 24 minutes.

In decimal form, this would be 6.4 miles as a 2/5 = 0.4

Answer:

76.5in²

Step-by-step explanation:

First we will find the area of the square. This is done by multiplying the side length (9in) by itself.

\(9 * 9 = \boxed{81}\)

The area of the square is 81in².

Next we will find the area of the triangular hole. We can use the formula \(\frac{1}{2}bh\), where b is the base of the triangle (3) and h is the height of the triangle (3).

\(\frac{1}{2}bh\\\frac{1}{2}(3)(3)\\\frac{9}{2}\\\boxed{4.5}\)

The area of the triangle is 4.5in².

Now we can find the area of the figure by subtracting the area of the square and the area of the triangular hole.

\(81 - 4.5 = \boxed{76.5}\)

The area of the figure is 76.5in².

That is the answer

- Kan Academy Advance

Answer:

-6/49

Step-by-step explanation:

this is the answer it is very easy

Answer:

A = 8.75 cm²

Step-by-step explanation:

Given that,

Radius, r = 5 cm

The arc length, l = 3.5 cm

We need to find the area of a sector. Let \(\theta\) be the angle. So,

\(\theta=\dfrac{l}{r}\\\\\theta=\dfrac{3.5}{5}\\\\\theta=0.7\ rad\)

The formula for the area of sector when \(\theta\) is in radian is  given by :

\(A=\dfrac{1}{2}\times \theta r^2\\\\A=\dfrac{1}{2}\times 0.7\times 5^2\\\\A=8.75\ cm^2\)

So, the area of the sector is 8.75 cm².

Answer: (b)

Step-by-step explanation:

Given

the radius of circle r=5 cm

arc length  \(l=3.5\ cm\)

Arc length is also given by

\(l=\dfrac{\theta }{360^{\circ}}\times 2\pi r\)

\(\Rightarrow 3.5=\dfrac{\theta }{360^{\circ}}\times 2\pi \times 5\\\\\Rightarrow \theta =40.10^{\circ}\)

Area of the sector is given by

\(\Rightarrow A=\dfrac{\theta }{360^{\circ}}\times \pi r^2\\\\\Rightarrow A=\dfrac{40.101^{\circ}}{360^{\circ}}\times 3.142\times 5^2\\\\\Rightarrow A=8.749\approx 8.75\ cm^2\)

Answer:

Its English :))))))

Answer:

i would go fro the first one

Step-by-step explanation:

its asking whitch maple have the more absolute deviations

Answer:

\($(x-h)^2+(y-k)^2= (r+ 40 )^2$\)  

Step-by-step explanation:

It is given that a meteorologist is using a Doppler radar to find out the distance of the storm as it passes using a polar grid.

The origin of the radar screen is its center.

And the distance between each ring is 10 miles from the center.

So let :

r = radius

h and k = be the coordinates of the center.

So the equation of a circle is :

\($(x-h)^2+(y-k)^2= r^2 $\)

Now the equation of the fourth circle when the radius changes by 10 miles is :

\($(x-h)^2+(y-k)^2= (r+ 40 )^2$\)  

The experimental probability that the next train to pull into Lakeside Station will be full is 7/10.

The experimental probability of the next train to pull into Lakeside Station being full can be calculated by dividing the number of times a full train occurred by the total number of trains observed.

Given that out of the last 20 trains, 14 were full, we can express the experimental probability as a fraction:

P(full) = Number of full trains / Total number of trains observed

P(full) = 14 / 20

Simplifying the fraction, we get:

P(full) = 7 / 10

Therefore, the experimental probability that the next train to pull into Lakeside Station will be full is 7/10.

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