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The system of equations to determine the cost of a shirt and the cost of a pair of pants is 3s - 2p = $5 and 4s + 3p = $120

Define System of Equation

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given,

Jane bought 3 shirts and returned 2 pairs of pants

Laura bought 4 shirt and 3 pairs of pants.

Let, s = cost of shirt

and, p = cost of a pair of pants

The equation for Jane is

3s - 2p = $5

Here, -ve sign because Jane returned 2 pairs of pants and then bill was $5.

Now, the equation for Laura is

4s + 3p = $120

Here, +ve sign because Laura bought 4 shirt and 3 pairs of pants and then bill was $120.

So, the system of equation we get

3s - 2p = $5

4s + 3p = $120

After solving  simultaneously we get the values s = 15 and p = 20.

Now, if you want to cross check then put the values of s and p in equations and it should be equal to RHS value like this,

for 1st equation,

3 * 15 - 2 * 20 ⇒ 45 - 40 = 5 (which is correct)

for 2nd equation,

4 * 15 + 3 * 20 ⇒ 60 + 60 = 120 (which is correct)

Hence, The system of equations to determine the cost of a shirt and the cost of a pair of pants is 3s - 2p = $5 and 4s + 3p = $120.

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Most of the kinetic energy of the water is transferred into the water, then the thermal energy will increase. Hence, option C is correct.

Kinetic energy is the term used in physics to describe the force that a moving item has. It is described as the amount of effort necessary to accelerate anybody with a particular mass from rest to a given velocity. Except variations in speed, the body retains the kinetic energy it gains during acceleration.

The body uses exactly the same amount of energy when slowing down from its current rate to a state of rest. Formally, kinetic energy refers to any term in a system's Lagrangian that has a derivative with respect to time.

As per the given information in the question,

When the kinetic energy of the diver is transferred into the water, the thermal energy will increase.

The entity's thermal energy grows as the average kinetic energies of its particles rise. As a result, an object's thermal energy rises as its temperature does.

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Answer:

y = 0.028t + 230,000

Step-by-step explanation:

We know

t = number of years since the start of the study

y = be the city's population

Each year the population has grown by 2.8%, this is the slope

The city had 230,000 people, this is the y-intercept

2.8% = 0.028

The equation is y= mx + b

So, our equation in this case is

y = 0.028t + 230,000

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Answer:

10 cups

Step-by-step explanation:

120minutes divided into 60minutes = 2 hours

20 divided by 2 = 10 cups

The number of miles that a signal sent from Station 1 to the satellite and then to Station 2 will have to travel is; 48135 miles

Let us first find the distance from Station 1 to the satellite:

Using trigonometric ratio, we have;

tan 8.7 = length of longest leg/length of shortest leg

Thus;

tan 8.7 =  3963/length of longest leg

Length of longest leg = 3963/tan8.7°

Length of longest leg = 3963/0.15302150298

Length of longest leg = 25,898 miles

Distance from Station 2 to satellite:

Using trigonometric ratio again, we have;

sin 8.7 = length of longest leg/ length of hypotenuse

sin  8.7 =  3963/length of hypotenuse

Length of hypotenuse =3963/ sin 8.7

Length of hypotenuse =3963/0.1526082024

Length of hypotenuse = 26, 200 miles

Thus, the difference is;

26200 - 3,963 = 22237 miles

Total distance will calculated as;

25898 miles  + 22237 miles = 48135 miles

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The complete question is:

A satellite orbiting the earth uses radar to communicate with two control stations on the earth's surface. The satellite's orbit maintains a 10-degree angle of separation between the two stations, as shown in the picture below. Knowing that the earth's radius is 3,963 miles.

How many miles will a signal sent from Station 1 to the satellite and then to Station 2 have to travel?

Answer:

Step-by-step explanation:

We can use one of the properties of exponents to change the −2 into +2 by sending the base to the denominator as:24⋅2−2=24⋅12+2=244=6

Answer:

We can use one of the properties of exponents to change the −2 into +2 by sending the base to the denominator as:

24⋅2−2= 24⋅1/2 OVER +2= 24/4= 6

Step-by-step explanation:

Answer: 6 and 7

Step-by-step explanation: The square root of 41 is 6.4. Since you multiply it by itself, it’s the nearest square root to 41.

(a) {2, 3, 4, 5, 6, 7, 8}

(b) {2, 4, 5, 9, 11, 12, 14}

(c) No next largest 7-subset; this is the last one in lexicographic order.

(d) {2, 4, 5, 6, 11, 12, 13}

(e) No next largest 7-subset; this is the last one in lexicographic order.

If all of the items in a set A are also in a set B, then the sets A and B are subsets of one another. To put it another way, the set A is contained within the set B. A and B stand for the subset connection.

For instance, if A represents the set of natural numbers and B represents the set of all whole numbers, then B is a subset of A since the set of whole numbers contains all natural numbers. This is how we may comprehend it: Natural numbers 1, 2, 3, and so on make up the set A. B = A collection of whole numbers, such as "0, 1, 2, 3,..."

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The mean number of pages is 13.8.

What is the mean?

There are various mean types in mathematics, particularly in statistics. Each mean helps to summarize a certain set of data, frequently to help determine the overall significance of a specific data set.

We have,

Kamari is reading a novel for his English class.

For the first 10 days, he records the number of pages he reads each day.

14,10,8,20,15,15,12,10,14,20

We have to calculate the mean of the number of pages he has red.

The mean is calculated by dividing the sum of all values in a data set by the number of values.

so,

14  + 10 + 8 + 20 + 15 + 15 + 12 + 10 + 14 + 20

= 138

Mean = 138 ÷ 10

= 13.8

Hence, the mean number of pages is 13.8.

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Answer:

There are 8! (8 factorial) ways for 8 people to be seated in an 8-passenger van. This is because there are 8 choices for the first person to sit, 7 choices for the second person, 6 choices for the third person, and so on, until there is only 1 choice for the last person. Therefore, the total number of ways for the 8 people to be seated is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 8!, which is equal to 40,320.

The relation between the vertices of a cube or cuboid is  V, the side is E, and the surface, F is  V - E + F = 2. Option 3) is the correct answer.

The vertice, face, and side of a cube or cuboid are related by Euler's Theorem. This theorem states that the number of faces, vertices, and edges of any polyhedron are related by Euler's formula.

Euler's formula can be stated as:

F + V = E + 2.

or

F + V - E = 2

where,

F = equal to the number of faces,

V = equal to the number of vertices

E = equal to the number of edges.

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Answer: Shape P is similar to shape Q, however, shape P, is smaller than shape Q.

A single transformation that takes shape P to shape Q is; a dilation by a scale factor of 3 with a center of dilation at .

Reasons:

The give figure shows;

The preimage figure = P

The image figure = Q

The image P is larger than the preimage Q, therefore, the figure, Q is a

dilation of the preimage P

(x₁, y₁) = A point on the preimage, P = (2, 3)

(x₂, y₂) = The corresponding point on the dilated image, Q = (4, 9)

k = The scale factor = 3

Therefore;

The center of dilation, (x₀, y₀) = (1, 0)

Therefore;

The single transformation that takes shape P to shape Q is a dilation by a scale factor of 3 with a center of dilation at (1, 0).

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Step-by-step explanation:

Yes, there is evidence that the level of significance is taken at 0.05 or 5% when the p-value is low.

Level of significance: The fixed probability of incorrectly eliminating the null hypothesis when it is actually true is what is meant by the term "level of significance." The probability of type I error is defined as the level of significance, which is set by the researcher using the results of the error. The statistical significance is measured by the level of significance. It specifies whether or not the null hypothesis is thought to be true. It is anticipated to determine whether the outcome is statistically significant enough to reject or prove the null hypothesis wrong.

The significance level is set at 0.05 or 5%. Low p-values indicate that the observed values differ significantly from the population value that was initially hypothesized. If the p-value is as small as possible, it is said to be more significant. Additionally, if the p-value is very low, the outcome would be highly significant. However, since obtaining a p-value below 0.05 is quite uncommon, p-values less than 0.05 are typically considered significant.

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The standardized distribution known as the T distribution is a member of the one-parameter family. The degrees of freedom are the only input for the t distribution.

A measure of the distribution of a set of data points is called population variance. It measures the mean squared departure from the mean, specifically. As a result, the variance will be minimal if all of the data points are very near to the mean. The variation will be high if the data points are dispersed throughout a wide range.

The standardized distribution known as the T distribution is a member of the one-parameter family. The degrees of freedom are the only input for the t distribution. Because sample size is used to assess this degree of freedom, degrees of freedom are dependent on sample size.

The t distribution tends to follow a normal distribution as sample size rises. The degree of freedom is ultimately determined by the sample size, so as the degree of freedom rises, the t distribution tends to be a normal distribution.

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We know that (D) 3xy is the factor of the given equation (x+y)³-(x³+y³) using the algebraic identity.

An identity element, also known as a neutral element, in a binary operation on a set is a set element that, when the operation is applied, leaves each element of the set untouched.

In algebraic structures like groups and rings, this idea is applied.

The left side of the equation equals the right side of the equation in an algebraic identity.

As an illustration, (a+b)2 = a2+2ab+b2 is true for all values of and b.

So, we have the equation:

(x + y)³ - (x³ + y³)

Now, get factors as follows:
Use the algebraic identity: (a + b)³ = a³ + b³ + 3ab (a + b)

x³ + y³ + 3xy (x + y) - x³ - y³

Simplify one more step to obtain:
3xy (x + y)

Therefore, we know that (D) 3xy is the factor of the given equation (x+y)³-(x³+y³) using the algebraic identity.

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Correct question:

Which of the following is a factor of (x + y)3 - (x3 + y3 )

a. x² + y² + 2xy

b. x² + y² - xy

c. xy²

d. 3xy

Answer:

246.5

Step-by-step explanation:

86275÷35

= 246.5

approximately 247

Answer:

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

Calculate it from end to start.

Before guard 3 he had:

Before guard 2 he had:

Before guard 1 he had:

This is the number of plants stolen.

The exponential function that represents the employee’s salary, S, after t years since the employee began working with the company is given as follows:

S(t) = 35400(1.08)^t.

An increasing exponential function is modeled according to the rule presented as follows:

A(t) = A(0)(1 + r)^t.

The parameters are given as follows:

An employee receives a salary increase of 8% at the end of each full year working with a company, hence the growth rate is given as follows:

r = 0.08.

The employee receives an initial salary of $35,400, hence the initial value is given as follows:

A(0) = 35400.

Thus the exponential function for this problem is defined as follows:

S(t) = 35400(1.08)^t.

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If 5 dollars can be exchanged for 7.7095 units of some foreign​ currency, the unit of that currency that can be obtained for 6 ​dollars will be

5 dollars can be exchanged for 7.7095 units. This means that 1 dollar equals to:

5 dollars / 5 = 7.7095 units / 5

1 dollar = 7.7095 units / 5

1 dollar = 1.5419 units.

Now, for 6 ​dollars, the foreign currency that can be obtained is:

= 6 * 1.5419 units

= 9.2514 units. Therefore, 9.2514 unit of the foreign​ currency can be obtained for 6 ​dollars.

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The complex number in each case will be 11 - 3i, 2 + i, and 5 - 6i.

The complex number is the combination of the real part and the imaginary part. Then the complex number is given as a+bi where the value of i is √(-1) and the value of i² is -1.

The real part is 11 and the imaginary part is -3i. Then the complex number is given as,

⇒ 11 - 3i

The real part is 2 and the imaginary part is i. Then the complex number is given as,

⇒ 2 + i

The real part is 5 and the imaginary part is -6√(-1). Then the complex number is given as,

⇒ 5 - 6√(-1)

⇒ 5 - 6i

The complex number in each case will be 11 - 3i, 2 + i, and 5 - 6i.

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The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles is 244 minutes.

When the distribution is normal, we use the z-score formula.

In a set with mean µ and standard deviation σ , the z-score of a measure X is given by:

Z = (X – µ) / σ

The Z-score shows how many standard deviations the measure is from the mean. After finding the Z-score, need to look at the z-score table and discover the p-value associated with the z-score. This p-value is the probability that the value of the measure is smaller than X, means, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

So, in this case, given that:

µ = 249, σ = 20

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles:

100 – 80 = 20th percentile, which is X when Z has a p-value of 0.2. So, X when Z = –0.253.

Now, put all the values into the formula:

Z = (X – µ) / σ

–0.253 = (X – 249) / 20

X – 249 = –0.253 * 20

X = 244

Hence, the candle burns for 244 minutes.

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The statement that can be concluded from the fact that the area of square ABHI plus the area of square BCDE is equal to the area of square EFGH is of:

D. BE² + BH² = EH².

The area of a square of side length s is given by the side length squared, as follows:

A = s².

Hence the areas of each square on the image given at the end of the answer are given as follows:

Hence the correct statement regarding the areas is given as follows:

BE² + BH² = EH².

Meaning that statement D is correct.

The problem is given by the image shown at the end of the answer.

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The measure of angle EBF is 40 degrees

The complete question is added at the end of this solution

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

EBF = 6x + 4

CBF = 7x - 2

Also from the question, we understand that the measures of angle EBF and the measure of angle CBF are congruent

This can be represented mathematically as follows

EBF = CBF

Substitute the known values in the above equation, so, we have the following representation

6x + 4 = 7x - 2

Multiply through by 1

6x + 4 = 7x - 2

Collect the like terms

7x - 6x = 4 + 2

Evaluate the like terms

x = 6

Recall that

EBF = 6x + 4

Substitute the known values in the above equation, so, we have the following representation

EBF = 6 x 6 + 4

Evaluate

EBF = 40

Hence, the measure is 40 degrees

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Complete question

If the measures of angle EBF and the measure of angle CBF are congruent and EBF = 6x+4 and CBF = 7x-2 find EBF

Answer:

first you need to write the given equation in a standard form

4x - 7y = 9

-7y = -4x + 9

y = 4/7x - 9/7

*parallel lines have equal gradient

m = 4/7

y - y1 = m(x - x1)

y - 3 = 4/7(x -7)

y - 3 = 4/7x - 4

y = 4/7x - 1

your equation is y = 4/7x - 1

Answer:

[tex]y = \frac{4}{7} + 5[/tex]

Step-by-step explanation:

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponent (& Root)

Multiplication

Division

Addition

Subtraction

~

First, subtract 4x from both sides of the equation:

4x (-4x) - 7y = 9 (-4x)

-7y = -4x + 9

Next, divide -7 from both sides of the equation:

(-7y)/-7 = (-4x + 9)/-7

[tex]y = \frac{-4x}{-7} + \frac{9}{-7}[/tex]

[tex]y = \frac{4}{7}x - \frac{9}{7}[/tex]

Next, as long as your slope (4/7) is the same, you can adjust the b (-9/7 for original) to get a parallel line.

In this case, I will utilize 5

[tex]y = \frac{4}{7}x + 5[/tex]

See attached image for the result. The blue line is the adjusted parallel line, while the red line is the original line given by the question.

~

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Answer:

2? – (-6)x +(-27), x² + 6x – 27 = 0

Step-by-step explanation:

i used a calculator

Answer:

x = [tex]\frac{y-b}{a}[/tex]

Step-by-step explanation:

y = xa + b ( subtract b from both sides )

y - b = xa ( isolate x by dividing both sides by a )

[tex]\frac{y-b}{a}[/tex] = x , that is

x = [tex]\frac{y-b}{a}[/tex]

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

y = xa - b ( add b to both sides )

y + b = xa ( isolate x by dividing both sides by a )

[tex]\frac{y+b}{a}[/tex] = x , that is

x = [tex]\frac{y+b}{a}[/tex]

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

assuming you mean

y = [tex]\frac{x+2}{2}[/tex] ( multiply both sides by 2 to clear the fraction )

2y = x + 2 ( subtract 2 from both sides )

2y - 2 = x , that is

x = 2y - 2

Answer:

Tom will pay a total of $58,064 in interest over the 30 year loan.

Step-by-step explanation:

The purchase price of the home is $144,000, and Tom will make a down payment of 10%, or $144,000 * 10/100 = $14,400.

Therefore, Tom borrows $144,000 - $14,400 = $129,600.

Next, we need to calculate the total number of payments he will make over the 30 year loan. Since the loan is for 30 years and the payments are made monthly, there will be 30 years * 12 months/year = <<30*12=360>>360 payments.

Finally, we can use the mortgage formula to calculate the total amount of interest Tom will pay over the loan:

I = P * r * t

Where:

I is the total interest

P is the principal (the amount borrowed)

r is the annual interest rate (in decimal form)

t is the number of payments

Plugging in the values, we get:

I = $129,600 * 0.045 * 360 payments

= $58,064