c) 2x(3x + 4)
expand the following:

Answer:

Yes

Step-by-step explanation:

A polygon is a 2D figure with at least three straight sides and angles. A pentagon has five sides and angles, so it qualifies as a polygon.

I hope this helped ^^ Good luck

Answer:

70

Step-by-step explanation:

180 minus 110 is 70

straight lines are 180 degrees

Answer:

100m/9.9 = ~10.1m/s

Step-by-step explanation:

Answer:

Option (3) x = 1

Step-by-step explanation:

f(x) represents a quadratic function as given in the graph (parabola).

Vertex of the parabola → (-2, -7)

Equation of function represented by the graph will be,

f(x) = (x + 2)² + (-7)

f(x) = (x + 2)² - 7

Option (1) For x = -1,

f(-1) = (-1 + 2)² - 7

     = -6

Another function has been given as,

h(x) = 4ˣ - 3

For x = -1,

h(-1) = 4⁻¹ - 3

      = 0.25 - 3

      = -2.75

Option (2). For x = 0

f(0) = (0 + 2)² - 7

     = 4 - 7

     = -3

h(0) = 4⁰ - 3

      = 1 - 3

      = -2

Option (3). For x = 1,

f(1) = 9 - 7 = 2

h(1) = 4¹ - 3

     = 4 - 3

     = 1

Option (4).For x = 2,

f(2) =  (2 + 2)² - 7

      = 16 - 7

      = 9

h(2) = 4² - 3

      = 16 - 3

      = 13

Therefore, for x = 1, function f(x) has a greater value than function h(x).

Option (3) will be the answer.

Answer:

She ate 5 apple slices

Step-by-step explanation:

25% of 20 is 5.

That means if she ate 5 slices, she ate 25% of the apple slices.

Hope this helped! Please give brainliest if it did help!

Answer:

5

Step-by-step explanation:

25% of 20 is 5

The variance of a distribution of means of samples of more than one is A) smaller than the original population variance.

When considering the distribution of means of samples, the central limit theorem states that as the sample size increases, the sampling distribution approaches a normal distribution regardless of the shape of the population distribution. Additionally, the standard error of the mean decreases as the sample size increases.

The variance of a population is denoted by σ^2.

The variance of the distribution of sample means, also known as the sampling distribution, is denoted by σ^2/N, where N is the sample size.

As the sample size (N) increases, the denominator increases, leading to a smaller value for the variance of the distribution of sample means (σ^2/N). Thus, the variance of the distribution of means of samples is smaller than the original population variance.

The variance of a distribution of means of samples of more than one is smaller than the original population variance. This is due to the central limit theorem and the decrease in standard error as the sample size increases.

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The equation of the line that has a gradient of -6 and passing through the point (4,-2) is y+2 = -6(x-4)

The gradient of the the line = -6

The line passing through the point = (4,-2)

The equation of the line y = mx+c

Here the gradient of the line is -6, which is the value of m in the equation of the line

Next we have to find the value of c

The line is passing through the point (4,-2)

y = mx+c

-2 = -6(4)+c

-2 = -24+c

c = -2+24

c= 22

The equation will be

y = -6x+22

Add  both sides by 2

y+2 = -6x+22+2

y+2  = -6x+24

y+2 = -6(x-4)

Hence, the equation of the line that has a gradient of -6 and passing through the point (4,-2) is y+2 = -6(x-4)

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Answer:

4th choice: y=-∛(x+2) - 1

Step-by-step explanation:

It's horizontal translation to left 2 units and vertical translation down 1 unit from y = -∛x

It's reflection of  y = ∛(x-2) - 1 over y axis

The statement is true. If a sequence {an} satisfies the condition an > 0 and lim n→∞ (an + 1)/an < 1, then the limit of the sequence as n approaches infinity, lim n→∞ an, is equal to 0.

To prove the statement, we use the limit comparison test. Let's assume that lim n→∞ (an + 1)/an = L, where L < 1. Since L < 1, we can choose a positive number ε such that 0 < ε < 1 - L. Now, there exists a positive integer N such that for all n ≥ N, we have (an + 1)/an < L + ε. Rearranging the inequality, we get an + 1 < (L + ε)an.

Now, let's consider the inequality for n ≥ N:

an + 1 < (L + ε)an < an.

Dividing both sides by an, we get (an + 1)/an < 1, which contradicts the given condition. Hence, our assumption that lim n→∞ (an + 1)/an = L is incorrect. Therefore, the only possible limit for the sequence {an} as n approaches infinity is 0, and hence the statement is true.

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Option b accurately interprets the slope coefficient in the context of the regression equation provided. b. As x increases by 1 unit, y is predicted to decrease by 17 units.

In the given sample regression equation, the slope coefficient (-17) represents the rate of change in the predicted value of y (y-hat) for each one-unit increase in x. Since the coefficient is negative, it indicates a negative relationship between x and y.

Specifically, for every one-unit increase in x, the predicted value of y is expected to decrease by 17 units. Therefore, option b accurately interprets the slope coefficient in the context of the regression equation provided.

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The simplified form of inequality -3x - 1 ≥ 20 is x ≤ -7.

The correct option is option (A).

A number line is a line on which numbers are pointed at some intervals, it is used to show numerical operations.

The given inequality is,

-3x - 1 ≥ 20.

To find the right number line from the options

Solve the inequality,

Add 1 to both the sides,

-3x -1 + 1 ≥ 20 + 1

-3x ≥ 21

-x ≥ 21 / 3

-x ≥ 7

x ≤ -7

The value of x are less than or equal to -7. Implies that, in number line graph close circle.

The number line in option (A), is correct option.

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The value of equation of 25x - 1 = 20x + 14 is x=3

Given,

25x - 1 = 20x + 14

5x=14+1

5x=15

x=3

Equations are fine statements that comprise two algebraic equations on each sides of an equal sign( =) . It depicts the equivalency link between the expression written on the left side and the expression written on the right side .L.H.S = R.H.S( left hand side = right hand side) appears in every fine equation. Equations can be used to calculate the value of an unknown variable that represents an unknown quantity. However, it isn't an equation, If the statement lacks the' equal to' sign.

Portions, variables, drivers, constants, terms, expressions, and an equal to are all factors of an equation. When we compose an equation, we must include a" = " symbol and terms on both sides.

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Answer:

False

Step-by-step explanation:

Hope it helps

We use the fundamental property of proportions where:

\( \space \)

\( \bf \frac{4x + 2}{39} = \frac{5x - 2}{42} \\ \\ \bf 39 \cdot (5x - 2) = 42 \cdot (4x + 2) \\ \\ \bf 195x - 78 = 168x + 84 \\ \\ \bf 195x - 168x = 84 + 78 \\ \\ \bf 27x = 162 \\ \\ \bf x = \frac{162}{27} \implies \bf \red{ \boxed{ \bf x = 6} } \)

The number is 6.

Hope that helps! Good luck! :)

1) The value of the investment after 8 years is approximately $2,069.36.

2) The value of the investment after 4 years is approximately $1,421.40.

3) The amount originally invested is approximately $1,150.00.

4) The nominal annual interest rate, compounded monthly, is approximately 6.5%.

5) The value of Nathan's account 10 years after the initial investment of $1000 is approximately $2,524.57.

9) The effective annual interest rate is approximately 4.57%.

10) The effective annual interest rate is approximately 7.34%.

1) To find the value of the investment after 8 years at a 4.5% annual rate, compounded monthly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (in decimal form)

n = Number of times interest is compounded per year

t = Number of years

Plugging in the values, we have:

P = $1,460

r = 4.5% = 0.045 (decimal form)

n = 12 (compounded monthly)

t = 8

A = 1460(1 + 0.045/12)^(12*8)

Calculating this expression, the value of the investment after 8 years is approximately $2,069.36.

2) To find the value of the investment after 4 years at a 5.8% annual rate, compounded quarterly, we use the same formula:

P = $1,190

r = 5.8% = 0.058 (decimal form)

n = 4 (compounded quarterly)

t = 4

A = 1190(1 + 0.058/4)^(4*4)

Calculating this expression, the value of the investment after 4 years is approximately $1,421.40.

3) If the value of the investment after 8 years is $1,786.77 at a 7.8% annual rate, compounded monthly, we need to find the original amount invested (P).

A = $1,786.77

r = 7.8% = 0.078 (decimal form)

n = 12 (compounded monthly)

t = 8

Using the compound interest formula, we can rearrange it to solve for P:

P = A / (1 + r/n)^(nt)

P = 1786.77 / (1 + 0.078/12)^(12*8)

Calculating this expression, the amount originally invested is approximately $1,150.00.

4) To find the nominal annual interest rate earned by the account where $559 grew to $895.41 after 5 years, compounded monthly, we can use the compound interest formula:

P = $559

A = $895.41

n = 12 (compounded monthly)

t = 5

Using the formula, we can rearrange it to solve for r:

r = (A/P)^(1/(nt)) - 1

r = ($895.41 / $559)^(1/(12*5)) - 1

Calculating this expression, the nominal annual interest rate, compounded monthly, is approximately 6.5%.

5) For Nathan's initial investment of $1000 at a 4.7% annual rate, compounded annually for 6 years, the value can be calculated using the compound interest formula:

P = $1000

r = 4.7% = 0.047 (decimal form)

n = 1 (compounded annually)

t = 6

A = 1000(1 + 0.047)^6

Calculating this expression, the value of Nathan's account after 6 years is approximately $1,296.96.

Then, if Nathan withdraws the money and deposits it into an account earning 7.9% interest annually for an additional 10 years, we can use the same formula:

P = $1,296.96

r = 7.9% = 0.079 (decimal form)

n = 1 (compounded annually)

t = 10

A

= 1296.96(1 + 0.079)^10

Calculating this expression, the value of Nathan's account 10 years after the initial investment is approximately $2,524.57.

9) To find the effective annual interest rate (or annual percentage yield) for an account earning 4.48% interest annually, compounded monthly, we can use the formula:

r_effective = (1 + r/n)^n - 1

r = 4.48% = 0.0448 (decimal form)

n = 12 (compounded monthly)

r_effective = (1 + 0.0448/12)^12 - 1

Calculating this expression, the effective annual interest rate is approximately 4.57%.

10) For an account earning 7.17% interest annually, compounded quarterly, we can calculate the effective annual interest rate using the formula:

r = 7.17% = 0.0717 (decimal form)

n = 4 (compounded quarterly)

r_effective = (1 + 0.0717/4)^4 - 1

Calculating this expression, the effective annual interest rate is approximately 7.34%.

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Answer:

25.28

Step-by-step explanation:

Answer:

25.28

Step-by-step explanation:

When a point is removed (i.e. \((130, -35)\)), both average and standard deviation are changed and a new least-squares line is created.

Given a minimum and representative set of points in a Cartesian plane, there is a given average and a standard deviation, of which slope and intercept of the least-squares line are determined.

When a point is removed, both average and standard deviation are changed and a new least-squares line is created. \(\blacksquare\)

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Answer:

Taking LHS:-

\( { | \overrightarrow{A} + \overrightarrow{B} | }^{2} - { | \overrightarrow{A} - \overrightarrow{B} | }^{2}\)

\( \boxed{ \mathsf{using \: \overrightarrow{a} . \overrightarrow{a} = { |a| }^{2} }}\)

\( \implies { | \overrightarrow{A} + \overrightarrow{B} | }^{2} = (\overrightarrow{A} + \overrightarrow{B})(\overrightarrow{A} + \overrightarrow{B})\)

\( \mathsf{using \: distributive \: property \: of \: vector \: multiplication}\)

eqn 1:-

\( \implies \mathsf{ \overrightarrow{A} \overrightarrow{A}+\overrightarrow{A} \overrightarrow{B} + \overrightarrow{B}\overrightarrow{A} + \overrightarrow{B}\overrightarrow{B}}\)

same with the other one

\( \boxed{ \mathsf{using \: \overrightarrow{a} . \overrightarrow{a} = { |a| }^{2} }}\)

\( { | \overrightarrow{A} - \overrightarrow{B} | }^{2} = (\overrightarrow{A} - \overrightarrow{B})(\overrightarrow{A} - \overrightarrow{B})\)

\( \mathsf{using \: distributive \: property \: of \: vector \: multiplication}\)

eqn. 2:-

\( \implies \mathsf{ \overrightarrow{A} \overrightarrow{A} - \overrightarrow{A} \overrightarrow{B} - \overrightarrow{B}\overrightarrow{A} + \overrightarrow{B}\overrightarrow{B}}\)

eqn. 1 - eqn. 2 :-

\( \implies \mathsf{ \overrightarrow{A} \overrightarrow{A}+\overrightarrow{A} \overrightarrow{B} + \overrightarrow{B}\overrightarrow{A} + \overrightarrow{B}\overrightarrow{B} - ( \overrightarrow{A} \overrightarrow{A} - \overrightarrow{A} \overrightarrow{B} - \overrightarrow{B}\overrightarrow{A} + \overrightarrow{B}\overrightarrow{B})}\)

after distributing the minus sign inside the braces AA and BB get canceled, while the other two add up.

\( \implies \mathsf{2 \overrightarrow{A}\overrightarrow{B} + 2\overrightarrow{B}\overrightarrow{A}}\)

\( \boxed{ \mathsf{\overrightarrow{A} \overrightarrow{B}= \overrightarrow{B}\overrightarrow{A}} }\)

\( \implies \mathsf{ 4\overrightarrow{A}\overrightarrow{B} }\)

LHS = RHS

Hence, Proved! =D

Step-by-step explanation:

m(x) = x+3

y = x+3

=> x = y-3

m`¹(x) = x-3

Answer:

2:10 or 1:5

Step-by-step explanation:

Answer: 4 squares to 1 triangle

Step-by-step explanation: both can be divided by two and that is the largest number they can be divided into

If the resulting value is positive, it means buying from Marley would yield higher profits. If negative, making internally would result in higher profits.

To determine the effect on Paibec's profits if MT-RF is purchased from Marley in 2021, we need to compare the costs of manufacturing it internally (make costs) versus purchasing it from Marley (buy costs). Let's calculate both scenarios:

Make Costs:

Direct materials: $168,000 (30,000 units * $5.60 per unit)

Direct labor: $108,000 (30,000 units * $3.60 per unit)

Plant space rental (fixed): $75,000

Equipment lease (fixed): $38,000

Other overhead:

Variable: $84,000 (30,000 units * $2.80 per unit)

Fixed: $126,000

Total make costs: $599,000

Buy Costs:

Cost per unit from Marley: $18.40

Total buy costs: $662,400 (36,000 units * $18.40 per unit)

Now, let's consider the additional information provided by Hart's estimates:

If MT-RF is not outsourced, direct material costs per unit are 9% higher in 2021.

Adjusted direct materials cost per unit: $5.60 + ($5.60 * 9%) = $6.104, rounded to $6.10

If MT-RF is not outsourced, direct labor costs per unit are 4% higher in 2021.

Adjusted direct labor cost per unit: $3.60 + ($3.60 * 4%) = $3.744, rounded to $3.74

If MT-RF is purchased from Marley, the termination costs for space rental are $8,500 (instead of $9,500) and for equipment lease are $3,500 (instead of $4,500).

Adjusted space rental termination cost: $8,500

Adjusted equipment lease termination cost: $3,500

If MT-RF is purchased from Marley, $10,000 of fixed overhead costs can be saved.

Now, let's calculate the updated costs for both scenarios:

Updated Make Costs:

Direct materials: 36,000 units * $6.10 per unit = $219,600

Direct labor: 36,000 units * $3.74 per unit = $134,640

Plant space rental (fixed): $75,000

Equipment lease (fixed): $38,000

Other overhead:

Variable: $84,000 (36,000 units * $2.80 per unit)

Fixed: $116,000 (original $126,000 - $10,000 saved)

Total updated make costs: $667,240

Profit from making internally: Total revenue - Updated make costs

Profit from making internally: (36,000 units * $18.40 per unit) - $667,240

Updated Buy Costs: Total buy costs + Termination costs

Updated Buy Costs: $662,400 + $8,500 + $3,500

Profit from buying from Marley: Total revenue - Updated buy costs

Profit from buying from Marley: (36,000 units * $18.40 per unit) - (updated buy costs)

To determine the effect on Paibec's profits, we compare the profits from both scenarios:

Effect on Profits: Profit from buying from Marley - Profit from making internally

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Correct question:

Lynn Hart is a managerial accountant at Paibec Corporation. Paibec is under intense cost competition, and Hart has been asked to evaluate whether Paibec should continue to manufacture part MT-RF or purchase it from Marley Company. Marley has submitted a bid to supply the 36,000 MT-RF units that Paibec will need for 2021 at a price of $18.40 each.

From plant records and interviews with Jane Porter, the plant manager, Hart gathered the following information regarding Paibec's costs to manufacture 30,000 units of MT-RF in 2020:

Direct materials $168,000

Direct labor 108,000

Plant space rental [fixed] 75,000

Equipment lease [fixed] 38,000

Other overhead

Variable 84,000

Fixed 126,000

Total $599,000

Porter also tells her that:

if MT-RF is not outsourced, all variable costs per unit, space rental costs, and equipment lease costs will be the same in 2021 as in 2020,

if MT-RF is purchased from Marley, plant space will not have to be rented, and equipment will not have to be leased, but it will cost $9,500 and $4,500, respectively, to terminate the two contracts, and

if MT-RF is purchased from Marley, none of the fixed overhead costs can be avoided.

Hart recognizes that Porter is probably concerned that outsourcing MT-RF will result in some of her close friends being laid off. She therefore performs her own independent analysis, and determines that:

if MT-RF is not outsourced, direct material and direct labor costs per unit are more likely to be higher in 2021 by 9% and 4%, respectively,

if MT-RF is purchased from Marley, the contract termination costs will actually be $8,500 for the space rental and $3,500 for the equipment lease, and

if MT-RF is purchased from Marley, $10,000 of the fixed overhead costs can actually be saved.

Hart estimates that 36,000 units of MT-RF will be needed in 2021.

REQUIRED [Note: Round unit cost computations to the nearest cent]

Based on Hart's estimates, if MT-RF is purchased from Marley in 2021, what will be the effect on Paibec's profits? [Note: if the buy costs are less than the make costs, enter the difference as a positive number; if the make costs are less than the buy costs, enter the difference as a negative number.]

Answer:

{A) X=5} {B) X=2.75}

Step-by-step explanation:

A) (2)4x-1/2=x+7(2) - multiply each side by denominator

4x-1=x+14

-x + 1 -x +1

3x=15

÷3. ÷3

x=5

B) (2)3x+2=2x+13/2(2)

6x+2=2x+13

-2x -2. -2x -2

4x=11

÷4. ÷4

x=2.75

Answer:

x = 7.5 , x = 1

Step-by-step explanation:

(a)

\(\frac{4x-1}{2}\) = x + 7 ( multiply both sides by 2 to clear the fraction )

4x - 1 = 2(x + 7)

4x - 1 = 2x + 14 ( subtract 2x from both sides )

2x - 1 = 14 ( add 1 to both sides )

2x = 15 ( divide both sides by 2 )

x = 7.5

(b)

3x + 2 = \(\frac{2x+13}{3}\) ( multiply both sides by 3 to clear the fraction )

3(3x + 2) = 2x + 13

9x + 6 = 2x + 13 ( subtract 2x from both sides )

7x + 6 = 13 ( subtract 6 from both sides )

7x = 7 ( divide both sides by 7 )

x = 1

"If n is not odd and n is not 2, then n is not prime." "If n is even and n is not 2, then n is not prime."

Using the logical equivalences, we can rewrite the sentence "If n is prime, then n is odd or n is 2" in two different ways:

"If n is not odd and n is not 2, then n is not prime."

This is the contrapositive of the original statement. It states that if n is not odd and n is not 2, then n cannot be prime.

"If n is even and n is not 2, then n is not prime."

This is another equivalent form of the original statement. It states that if n is even and n is not 2, then n cannot be prime.

By using logical equivalences, we can rephrase the original statement to provide alternative perspectives and logical relationships between the variables involved.

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The ways in which companies can attract and retain employees are given below.

The term human resources (HR) refers to the department responsible for managing employee-related resources.

It's an essential partner in an organization's success.

Given is that to answer some ways in which companies can attract and retain employees.

The ways in which companies can attract and retain employees are -

Therefore, the ways in which companies can attract and retain employees are given above.

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Answer:

No

I hate pokemon.

Answer: 260 m

Step-by-step explanation:

Let's say the length of NR is x m, using the similarity rule, we get the equation

175/130 = (175+175)/x

x = 260

So NR is 260 m

Answer:

in 7 mins she can hop 21 times

Step-by-step explanation:

24 divided by 8 = 3

24-3=21

Answer:

Natalie can hop 21 times in 7 minutes

Step-by-step explanation:

To figure out how many times she can hop in 7 minutes you need to find the average hop each minute.

First, you write 24/8. You simply that to 3/1.

So Natalie can jump 3 times in 1 minute.

If you want 7 minutes, you multiply 1 by 7, and 3 by 7, which gets you 21 hops for 7 minutes.

-I hope this helps!

Answer: 80%

Step-by-step explanation: If ten of the marbles are red, that means the remaining 40 of the marbles in the bag are not. So 40 non-red marbles out of 50 marbles in total (40/50) is 0.8. After multiplying by 100 to get the percentage, it is 80%.

The percent of the marbles in the bag are not red will be 80%.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

A bag contains 50 total marbles.

And, Number of red marbles = 10

Now,

Since, A bag contains 50 total marbles.

And, Number of red marbles = 10

Hence, The percent of red marbles = 10/50 × 100

                                                       = 10 × 2

                                                        = 20%

Thus, The percent of the marbles in the bag are not red = 100% - 20%

                                                                                       = 80%

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