Find the equation of the line

Y= __x + __

Answer:

6

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out expression

[9 × (10 - 2)] ÷ [2 + (5 × 2)]

Step 2: Bracket Parenthesis

[9 × 8] ÷ [2 + 10]

Step 3: Brackets

72 ÷ 12

Step 4: Divide

6

Answer:

13/20 of a mile

Step-by-step explanation:

2/5 x 4 = 8/20

1/4 x 5 = 5/20

8/20 + 5/20 = 13/20

Using the formula of compound interest and simple interest, the investment option that is better is at interest rate of 3.99% which is compounded monthly

To compare the investment options, you need to calculate the future value of each investment after 8 years. Here's a breakdown of each option:

A. 3.99% compounded monthly: This option earns interest every month and compounds, meaning the interest is added to the principal, so future interest is earned on the increased principal amount. This type of interest compound is the most advantageous to the investor. The formula for calculating the future value for this option is:

FV = P * (1 + r/n)^(nt)

FV = 12000(1 + 0.0399 / 12) * (12 * 8)

FV = $16,503.58

where P is the principal ($12,000), r is the annual interest rate (3.99%), n is the number of times the interest is compounded in a year (12 times), t is the number of years invested (8 years).

B. 4% compounded quarterly: This option earns interest every quarter and compounds. The formula for calculating the future value is the same as option A, with the only difference being the number of times the interest is compounded in a year (n=4).

Substituting the values into the formula;

FV = $16,499.29

C. 4.175% compounded annually: This option earns interest once a year and compounds. The formula for calculating the future value is the same as options A and B, with the only difference being the number of times the interest is compounded in a year (n=1).

Substituting the values into the formula

FV = $16,645.21

D. 4.2% simple interest: This option earns interest once a year based on the original principal amount and does not compound. The formula for calculating the future value for this option is:

FV = P(1 + rt)

FV = 12000 (1 +  0.042 * 8)

FV = $16032

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Answer:

10.8

Step-by-step explanation:

We need to use the cosine:

cos(26deg) * 12 ~= 0.89879404629 * 12 ~= 10.7855285556 ~= 10.8

The coefficient of determination is approximately 0.1348.

The coefficient of determination, denoted as R-squared, is a measure of how well the regression line (i.e., the line of best fit) fits the observed data points. It is calculated as the ratio of the explained variance to the total variance.

The coefficient of determination is the ratio of the explained variation to the total variation. It is calculated as follows:

R² = SS(regression) / SS(total)

From the ANOVA table, we have:

SS(regression) = 78.43

SS(total) = 582.19

Therefore, the coefficient of determination is: R² = 78.43 / 582.19 ≈ 0.1348

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The given series is Σ(126/ n^2 - n) and we have to determine whether the series is convergent or divergent.

The series Σ (126/ n^2 - n) can be written asΣ [126(1/n - 1/ n^2)]Then, 126 can be taken outside of the series.Σ [126(1/n - 1/ n^2)] = 126[1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +....+ 1/(n-1) - 1/n]The terms 1/n and -1/n cancel out and we are left withΣ [126(1/n - 1/ n^2)] = 126(1 - 1/2 + 1/3 - 1/4 +....+ 1/(n-1) - 1/n)

By comparing it to the series Σ [1/n], we can say that Σ [126(1/n - 1/ n^2)] is less than Σ [1/n].Σ [126(1/n - 1/ n^2)] < Σ [1/n]Now, Σ [1/n] is a divergent series and hence Σ [126(1/n - 1/ n^2)] is also divergent. Therefore, the given series Σ(126/ n^2 - n) is divergent.

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The given limit is: lim (x->0) (sin(9x) / x)

To estimate this limit, we can apply L'Hôpital's Rule since we have an indeterminate form (0/0 as x approaches 0). L'Hôpital's Rule states that if the limit of the ratio of the derivatives of the numerator and the denominator exists, then the limit of the original function exists and is equal to that value.

Taking the derivative of the numerator and the denominator with respect to x:

Numerator: d(sin(9x))/dx = 9cos(9x)
Denominator: d(x)/dx = 1

Now, we find the limit of the ratio of the derivatives:

lim (x->0) (9cos(9x) / 1)

As x approaches 0, cos(9x) approaches cos(0), which is 1. Therefore, the limit is:

lim (x->0) (9cos(9x) / 1) = 9(1) = 9

So, the limit exists and is equal to 9.

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The constant average rate of change is the slope of the line which can be used to write the linear function.

What is a Data Table ?

A table of data is linear if there is a constant average rate of change between all pairs of points.

Testing for Linearity

Finding a Function from a Table that is Linear

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Answer: We are given a expression:

1/4n-16

We have to find its equivalent expression.

1/4n-16

As we see the denominator ,the two  terms have 4 in common

The equivalent expression becomes

1/4 (n-4)

Hence, the expression equivalent to  1/4n-16 is:

1/ 4 (n-4)

The multiplier for the given economy is 4.

The multiplier represents the magnification effect of an initial change in autonomous spending on the overall output of an economy. It is calculated using the formula 1 / (1 - MPC), where MPC is the marginal propensity to consume.

In this case, the MPC is given as 0.75, which means that for every additional dollar of income, individuals spend 75 cents. The multiplier is calculated as 1 / (1 - 0.75) = 4.

The multiplier of 4 indicates that a change in autonomous spending, such as investment or consumption, will have a four times larger impact on the overall output of the economy. In other words, for every dollar increase in autonomous spending, the total output of the economy will increase by four dollars.

In this scenario, since the intended investment is $130, the total increase in output would be 4 * $130 = $520. Therefore, the multiplier effect amplifies the initial change in autonomous spending and leads to a larger increase in output in the economy.

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Answer:

You could divide 5 in half and then add that to the five to find the amount of flour to use in a triple recipe. Hope this helps.

Step-by-step explanation:

7) alternate interior angle, Angle measure = 71°

8) alternate interior angle, Angle measure = 90°

Using an illustration:

7) The angle type is alternate interior angle

Alternate interior angle angles are equal.

Hence, the angle measure which is represented with question mark = 71°

8) The angle type is alternate interior angle

Alternate interior angle angles are equal.

The square in red represents 90°

Hence, the angle measure which is represented with question mark is 90°

Answer:

600 cubic feet

Step-by-step explanation:

Answer:

9(5)-/y

9(5)-15/3

45-15/3

45-5

40

Answer:

can you show me the graph so I can't answer the question

Answer:

A

Step-by-step explanation:

Edge 2022

The equivalent expressions are  (b+3c)+(b+3c) and 2(b)+2(3c) or 2b+6c. Options B and C

An algebraic expression is simply described as an expression consisting of variables, coefficients, terms, constants, and factors.

Algebraic expressions are also made up of mathematical operations, such as;

Given the expression;

2(b+3c)

expand the bracket

2(b)+ 2(3c)

2b + 2×3×c

Multiply the values, we get;

= 2b +6c

It can also  be written as the sum of b+3c as (b+3c)+(b+3c)

Hence, the expressions are (b+3c)+(b+3c) and 2(b)+2(3c) or 2b+6c

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The complete question:

Which expressions are equivalent to 2(b+3c)2(b+3c)2, left parenthesis, b, plus, 3, c, right parenthesis ?

Choose all answers that apply:

A 3(b+2c)3(b+2c)3, left parenthesis, b, plus, 2, c, right parenthesis

B (b+3c)+(b+3c)(b+3c)+(b+3c)left parenthesis, b, plus, 3, c, right parenthesis, plus, left parenthesis, b, plus, 3, c, right parenthesis

C 2(b)+2(3c)2(b)+2(3c)2,

Yes, repeating two simple arithmetic operations will eventually transform every positive integer into 1.

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

f(n) = n/2 if n%2 = 0

f(n) = 3n + 1 if n%2 = 1

The above definition means that

f(n) = n/2 if n is even

f(n) = 3n + 1 if n is odd

To check if repeating operations would transform to 1, we can set n = 10

and then evaluate the function values

So, we have

f(10) = 10/2 = 5

f(5) = 3(5) + 1 = 16

f(16) = 16/2 = 8

f(8) = 8/2 = 4

f(4) = 4/2 = 2

f(2) = 2/2 = 1

See that the end result of the operations is 1

Hence, repeating two operations will transform every positive integer into 1

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Answer:

most likely next spring

Step-by-step explanation:

Step-by-step explanation:

Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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Step-by-step explanation:

Given that,

Length, l = (3d+2) m

Width, b = (d+5) m

(a) Perimeter of the rectangle,

P = 2(l+b)

P = 2(3d+2+d+5)

= 2(4d+7)

P = 8d+14

(b) If P = 30 cm.

8d+14 = 30

8d = 16

d = 2

(c) l = (3(2)+2) = 8 m

b = (2+5) = 7 m

The area of this rectangle,

A = lb

A = 8×7

A = 56 cm²

Hence, this is the required solution.

Answer:

The answer would be 14600 lbs

Step-by-step explanation:

take the days of the year (365) multiplied by how many lbs a day (40) which would be 14600 lbs

Answer:

The answer is 7.3 tons

Step-by-step explanation:

Answer:

4.1% ororor

Step-by-step explanation:

1/6 = 16.7%

3/8 = 37.5%

5/12 = 41.7%

= 95.9%

100% - 95.9% = 4.1%

Answer:

22

Step-by-step explanation:

the terms are counting by 3. making it by adding three to the lest term will give you the answer.

Answer:

D, The answer is D

Step-by-step explanation:

Answer:

I actually think its d because the slope is 1/4. Hopefully I'm correct.

Step-by-step explanation:

well, the volume of that triangular prism will just be the area of the triangle times the length.

now, what's the area of that triangular face?  well, let's say it has a base of "b" and a height of 3, whilst the prism has a length of 6, Check the picture below.

\(\stackrel{\textit{triangle's area}}{\cfrac{1}{2}(b)(3)}\stackrel{\textit{prism's length}}{(6)}~~ = ~~4\frac{1}{2}\implies 9b=\cfrac{9}{2}\implies b=\cfrac{9}{18}\implies b=\cfrac{1}{2}\)

Therefore , the solution of the given problem of surface area comes out to be 212 square feet of the wall are therefore covered by the design.

The total size of the object can be determined by calculating how much room would be required to completely cover its exterior. When choosing a similar product with a cylindrical form, the environment is taken into account. Anything's total dimensions are determined by its surface area. The amount of water that a cuboid can hold depends on the number of sides that link its four trapezoidal shapes.

Here,

We must first determine the area of each individual form before adding them together to determine the portion of the wall that the design covers.

Taking a look at the rectangle first, we can observe that it has the following area:

=> 120 square feet=  10 feet x 12 feet.

=> 40 square feet =  (1/2)(10 ft)(8 ft).

Consequently, the two triangles' combined area is:

=> 80 square feet =  2 x 40 square feet.

=> (12 square feet) = (1/2)(6 ft)(4 ft).

The total area of all the shapes is as follows:

=> 212 square feet=  120 square feet, 80 square feet, and 12 square feet.

=> 212 square feet of the wall are therefore covered by the design.

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Answer: the answer is 261 ^2 ft!

Step-by-step explanation: