Evaluate j(k+2), when j=5 and k=3.

\((36911.22/500) = 12x ln(1 + r)ln(36911.22/500) = 12x(0.0083333333)ln(36911.22/500) = 0\).0083333333x

Multiply both sides by 1000 and divide both sides by 0.0083333333 to get: x = 35.

Let x be the age of the person. When the person was born, their parents opened an investment account in their name and deposited $500 into the account.

Let A be the value of the investment account when the person is x years old.

The interest rate is 10% compounded monthly. Then, the monthly interest rate is

\(:r = (10/12)/100 = 0.0083333333\)

The account has earned interest for 12 * x months.

Hence, we have:

\(A = 500(1 + r)^(12x)\)

Now, we can solve for x.

A = 36911.22.

Hence:\(36911.22 = 500(1 + r)^(12x)\)

Take the natural logarithm of both sides to solve for x.

\(ln(36911.22/500) = 12x ln(1 + r)ln(36911.22/500) = 12x(0.0083333333)ln(36911.22/500) = 0.0083333333x\)

Multiply both sides by 1000 and divide both sides by 0.0083333333 to get: x = 35.

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Answer:

=2/5

Step-by-step explanation:

Answer:

1.8 cm to the nearest tenth.

Step-by-step explanation:

The angle opposite side a = 180 - 105 - 15 = 60 degrees.

By the Sine Rule:

a / sin 60 = 2 / sin 105

a = 2 * sin60/ sin 105

= 1.79315

The line is given as

The slope is 1/5

The y-intercept is -9

Therefore, the first option is the correct one

Answer:

Yes, Mina is correct

Step-by-step explanation:

Let the triangles be A and B

Given

Triangle A:

\(Angles = 34, 57\)

Triangle B:

\(Angles = 89, 57\)

Required

Is Mina's claim correct?

First, we calculate the third angle in both triangles.

For A:

\(Third\ Angle = 180 - 34 - 57\)

\(Third\ Angle = 89\)

For B:

\(Third\ Angle = 180- 89 - 57\)

\(Third\ Angle = 34\)

For triangle A, the angles are: 34, 57 and 89

For triangle B, the angles are: 34, 57 and 89

Since both triangles have the same angles, then by the postulate of AAA (Angle-Angle-Angle), the triangles are similar.

Answer:

B

Step-by-step explanation:

The circumference of a circle can be described as the linear distance round the circle

The circumference of a circle = 2πr or πD

π = 3.14

r = radius

d = diameter

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

π  = circumference / 2r or circumference / D

37.68 / 12

Answer:

$70

Step-by-step explanation:

1. I = PRT

2. Sub in what you know into the equation:

I = $875 (principal amount) x 0.04 (4%) x 2 (24 months = 2 years)

3. 875 x 0.04 x 2 = 70

4. Anna will receive $70 in simple interest

Answer:

£70

Step-by-step explanation:

simple interest (I) is calculated as

I = \(\frac{PRT}{100}\)

where P is principal, R is rate of interest and T is time in years.

Note that 24 months = 2 years, thus

I = \(\frac{875(4)(2)}{100}\) = \(\frac{7000}{100}\) = £70

Answer:(1,4) (2,3) (3,2) (4,1) (5,0)

Step-by-step explanation:

An equation that mode the relationship between thee two variable is y=2x+3 .

Let x represent the number of 6-month period worked

Let y represent the total number of paid vacation day

According to the question,

When he started work, he was given three paid day of vacation. For each six-month period he pay at the job, his vacation is increased by two day.

Each year has 2 six-month periods. After 4.4 years Roberto will have worked 8.8 six-month periods. He will have been given vacation days for each of the 8 whole working periods he has completed. x=8 y=2*8+3 y=19

An equation that mode the relationship between thee two variable is y=2x+3 (Total vacation time equals 2 days times x plus the 3 days he was given at the start).

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Answer:

13/16

Step-by-step explanation:

Answer:

I hope they're not learned overtime haha (inborn responses)

Step-by-step explanation:

A) True. When we create a rectangle in ANSYS in the geometry step, we are defining the domain of the problem, which is an essential component of the mathematical model.

A) True. When we create a rectangle in ANSYS in the geometry step, we are defining the domain of the problem, which is an essential component of the mathematical model. The geometry defines the shape and size of the domain, which directly affects the governing equations and boundary conditions that will be applied to that domain. Therefore, creating a rectangle in ANSYS geometry step will have an impact on the mathematical model.

As for the "Save project " part of the question, saving the project in ANSYS does not affect the mathematical model in any way. Saving the project simply stores the information about the simulation, including the geometry, materials, loads, and boundary conditions, among others, in a file that can be retrieved and modified later. It does not alter the mathematical model, and the same solution can be obtained from the saved project at a later time.

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The absolute value of x minus one is equal to two. Therefore, x must be either one greater than two (x = 3) or one less than two (x = 1).

One less than x results in a value of two in absolute terms. As a result, x minus 1 has an absolute value of 2, which is a positive number. The separation of an integer from zero is its absolute value. As a result, x minus 1 is two units from zero in absolute terms. As x minus one has an absolute value of two, its real value must either be two or a negative two. That is to say, x must either be one more than two (x = 3) or one less than two (x = 1).In order to confirm this, let's look at a few examples. If x = 3, then |x - 1| = |2 - 1| = |1| = 1 which is not equal to two. Therefore, x = 3 is not the answer we are looking for. On the other hand, if x = 1, then |x - 1| = |1 - 1| = |0| = 0 which is not equal to two. Therefore, x = 1 is also not the answer we are looking for. The only two possible solutions for the equation |x - 1| = 2 are x = 3 and x = 1. Therefore, the result of |x - 1| = 2 is that x must be either one greater than two (x = 3) or one less than two (x = 1)

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Answer:

2ax(5x+7a) is your answer ☺️☺️☺️

i hope so it help you .........

In order to calculate the Mean Squared Error (MSE) for each region, you will need to have a dataset with values for each region.

Once you have this dataset, you can calculate the MSE using the following formula:

MSE = 1/n x ∑(yi - ŷi)²

where n is the number of data points in the region, yi is the actual value for the ith data point, and ŷi is the predicted value for the ith data point. Once you have calculated the MSE for each region, you can compare the values to determine if the variability around the fitted regression line is approximately the same for each region.

If the MSE values are similar for each region, then the variability around the fitted regression line is approximately the same. If the MSE values are different for each region, then the variability around the fitted regression line is not the same for each region.

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Answer:

This is an experiment because a treatment was applied to a group.

Step-by-step explanation:

There are two groups, The first group used the computer program while the second group did not therefore this is an experiment. An experiment involves changing an independent variable to see how it affects a dependent variable. The dependent variable in this case  determining the effect of a new computer program on learning while the independent variables was testing with the computer program and not testing with the program.

Answer:

Both angles are 51°

Step-by-step explanation:

By the Vertical Angles Theorem, both angles are congruent.

Step 1: Set up equation

68 - x = 3x

Step 2: Solve for x

68 = 4x

x = 17

Step 3: Find angles

68 - 17 = 51°

Answer:

4x=68

x=17

51°

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Step-by-step explanation:

multiply through by the LCM=3x-7

4(3x-7)-5=4(3x-7)

12x-28-5=12x-28

The integer coefficient of x on both sides of the equation=+12 so there's no integer solution for the equation

Answer:

I think the answer is C

Step-by-step explanation:

If you have a normal ginger bread cookie, its full size would be 100%. So, if you add the first 25%, 1.25%

The expression best describes the new length of the cookie will be 1.25y.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The initial length of the cookie is y after baking the length is increased by 25%

=   y  +  25%y

=   y   +  ( 25 / 100 ) y

=   y  +  0.25 y

=  1.25 y

Therefore the expression best describes the new length of the cookie will be 1.25y.

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Answer:

x is being multiplied by 7p so to find x you need to have it alone on one side of the problem, so you could divide both sides by 7p, making it look like 2n+3pm/7p=x (simplify if needed)

Step-by-step explanation:

The value of the test statistic is 1.177.

What is test statistic?

A test statistic is a numerical summary of sample data that is used in hypothesis testing. It is used to assess the strength of evidence against a null hypothesis by comparing the observed data to what would be expected if the null hypothesis were true.

To find the value of the test statistic, we need to use the formula:

test statistic = (sample statistic - hypothesized parameter) / (standard error of the sample statistic)

In this case, the hypothesized parameter is the standard deviation of pulse rates of adult males, which is stated to be more than 12 bpm. So, we have:

hypothesized parameter: σ > 12 bpm

sample size: n = 141

sample standard deviation: s = 13.4 bpm

To calculate the standard error of the sample standard deviation, we use the formula:

standard error of s = σ / √n

Since we don't know the value of σ, we will use the sample standard deviation s as an estimate for it:

standard error of s = s / √n = 13.4 / √141 = 1.126

Now, we can plug in the values into the formula for the test statistic:

test statistic = (s - σ) / (standard error of s)

= (13.4 - 12) / 1.126

= 1.177

Therefore, the value of the test statistic is 1.177.

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To find the average quarterly loads for the rest of the years, you can use the formula below:

Average Quarterly Load = Total Annual Load  4 For example, let's say the total annual load for Year 1 is 800.

To find the average quarterly loads for Year 1, we would divide 800 by 4 to get an average quarterly load of 200. Then, you can use this average quarterly load to find the seasonal indices for each quarter of each year.To find the seasonal index for a given quarter and year, you would divide the actual quarterly load by the average quarterly load for that year.

For example, let's say the actual load for Quarter 1, Year 1 is 240. To find the seasonal index for this quarter and year, we would divide 240 by 200 to get a seasonal index of 1.2. You would repeat this process for each quarter and year to find the seasonal indices for all quarters and years.

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Answer:

Touchdowns: 6

Field goals: 3

PATS: 5

Step-by-step explanation:

6*6 = 36

3*3 = 9

5*1 = 5

9+5+36 = 50 points

6+3+5 = 14 scored times

Answers:

6 touchdowns (TD)

3 field goals (FG)

5 points after touchdown (PAT)

===============================================

Explanation:

Acronyms used in football

Define the following variables

"They had 3 more touchdowns than field goals", so,

TD = FG + 3

x = y + 3

They scored 14 times which means we can say

x+y+z = 14

Let's look at the point breakdown per type of score

Then we can add up those expressions to get us to 6x+3y+1z = 50 points total. This is the same as saying 6x+3y+z = 50.

--------------------------

Here's our system of equations

x = y+3

x+y+z = 14

6x+3y+z = 50

Let's replace each x with y+3 in the second equation. Then solve for z.

x+y+z = 14

y+3+y+z = 14

2y+z = 14-3

2y+z = 11

z = 11-2y

Now replace every x with y+3 in the third original equation

6x+3y+z = 50

6(y+3)+3y+z = 50

6y+18+3y+z = 50

9y+z = 50-18

9y+z = 32

Then plug in z = 11-2y and solve for y

9y+z = 32

9y+11-2y = 32

7y+11 = 32

7y = 32-11

7y = 21

y = 21/7

y = 3 is the number of FGs scored

Use this to find z

z = 11-2y

z = 11-2(3)

z = 11-6

z = 5 is the number of PATs scored

Now let's find x

x = y+3

x = 3+3

x = 6 is the number of TDs scored

--------------------------

Checking the answers:

x+y+z = 6+3+5 = 9+5 = 14 times they scored

6x+3y+z = 6*6+3*3+5 = 36+9+5 = 50 points scored

There are 3 more TDs than FGs since x = y+3 leads to 6 = 3+3 which is a true statement.

All three original equations we set up for the system of equations are true. Therefore, the final answers are confirmed.

Answer:

Step-by-step explanation:

Draw the altitude from the vertex angle to the base. You have two congruent, right triangles. The hypotenuse of each triangle is

√[(56/2)²+45²] = √[28²+45²] = √2809 = 53 mm

perimeter of larger triangle = 2×53 + 56 = 162 mm

Part A: To find the total surface area of the rectangular prism, we need to calculate the areas of all six faces and then add them together.

Given dimensions:

Length = 7 feet

Width = 3 feet

Height = 4.8 feet

Surface Area of each face:

Front and back faces: Length * Height

= 7 feet * 4.8 feet

= 33.6 square feet

Top and bottom faces: Width * Length

= 3 feet * 7 feet

= 21 square feet

Side faces: Width * Height

= 3 feet * 4.8 feet

= 14.4 square feet

Total Surface Area:

2 * (Front and back faces) + 2 * (Top and bottom faces) + 2 * (Side faces)

= 2 * 33.6 square feet + 2 * 21 square feet + 2 * 14.4 square feet

= 67.2 square feet + 42 square feet + 28.8 square feet

= 137 square feet

Therefore, the total surface area of the bench is 137 square feet.

Part B: To calculate the cost of covering the bench with ceramic tiles, we need to multiply the total surface area by the cost per square foot.

Cost per square foot = $0.89

Total Surface Area = 137 square feet

Total cost to cover the bench:

= Cost per square foot * Total Surface Area

= $0.89 * 137 square feet

= $121.93

Therefore, it will cost $121.93 to cover the bench with ceramic tiles.

The best linear approximation to the function f(x) = e^x near x = 0 is L(x) = x + 1.

The given function is f(x) = e^x near x = 0.

To find the best linear approximation, L(x), we use the formula:

L(x) = f(a) + f'(a)(x-a),

where a is the point near which we are approximating.

Let a = 0, so that a is near the point x = 0.

f(a) = f(0) = e^0 = 1

f'(x) = d/dx (e^x) = e^x;

so f'(a) = f'(0) = e^0 = 1

Substituting these values into the formula: L(x) = 1 + 1(x-0) = x + 1

Therefore, the best linear approximation to f(x) = e^x near x = 0 is L(x) = x + 1.

For instance, linear approximation is used to approximate the change in a physical quantity due to a small change in another quantity that affects it.

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Answer:

No, 15/21 and 40/56 do not form a proportion.

Step-by-step explanation:

Answer:

7x-7=0

5x-9=4x

4x(9)=36

x=36

Answer:

negative 1.16 million

Step-by-step explanation:

P = 1.38 - 2.54 = -1.16 = a negative profit of $1.16 million = a loss of $1.16 million