You and your friend went shopping. You bought 2 hats and 3 pairs of gloves for $28.25. Your friend bought 1 hat and 1 pair of gloves for $12.25. How much did one hat cost? How much did one pair of gloves cost? (Answers should reflect the real world scenario by including appropriate units.)

To determine the variable matrix \(\displaystyle X\) using the equation \(\displaystyle AX=B\), we need to solve for \(\displaystyle X\). We can do this by multiplying both sides of the equation by the inverse of matrix \(\displaystyle A\).

Let's start by finding the inverse of matrix \(\displaystyle A\):

\(\displaystyle A=\begin{bmatrix} 3 & 2 & -1\\ 1 & -6 & 4\\ 2 & -4 & 3 \end{bmatrix}\)

To find the inverse of matrix \(\displaystyle A\), we can use various methods such as the adjugate method or Gaussian elimination. In this case, we'll use the adjugate method.

First, let's calculate the determinant of matrix \(\displaystyle A\):

\(\displaystyle \text{det}( A) =3( -6)( 3) +2( 4)( 2) +( -1)( 1)( -4) -( -1)( -6)( 2) -2( 1)( 3) -3( 4)( -1) =-36+16+4+12+6+12=14\)

Next, let's find the matrix of minors:

\(\displaystyle M=\begin{bmatrix} 18 & -2 & -10\\ 4 & -9 & -6\\ -8 & -2 & -18 \end{bmatrix}\)

Then, calculate the matrix of cofactors:

\(\displaystyle C=\begin{bmatrix} 18 & -2 & -10\\ -4 & -9 & 6\\ -8 & 2 & -18 \end{bmatrix}\)

Next, let's find the adjugate matrix by transposing the matrix of cofactors:

\(\displaystyle \text{adj}( A) =\begin{bmatrix} 18 & -4 & -8\\ -2 & -9 & 2\\ -10 & 6 & -18 \end{bmatrix}\)

Finally, we can find the inverse of matrix \(\displaystyle A\) by dividing the adjugate matrix by the determinant:

\(\displaystyle A^{-1} =\frac{1}{14} \begin{bmatrix} 18 & -4 & -8\\ -2 & -9 & 2\\ -10 & 6 & -18 \end{bmatrix}\)

\(\displaystyle A^{-1} =\begin{bmatrix} \frac{9}{7} & -\frac{2}{7} & -\frac{4}{7}\\ -\frac{1}{7} & -\frac{9}{14} & \frac{1}{7}\\ -\frac{5}{7} & \frac{3}{7} & -\frac{9}{7} \end{bmatrix}\)

Now, we can find matrix \(\displaystyle X\) by multiplying both sides of the equation \(\displaystyle AX=B\) by the inverse of matrix \(\displaystyle A\):

\(\displaystyle X=A^{-1} \cdot B\)

Substituting the given values:

\(\displaystyle X=\begin{bmatrix} \frac{9}{7} & -\frac{2}{7} & -\frac{4}{7}\\ -\frac{1}{7} & -\frac{9}{14} & \frac{1}{7}\\ -\frac{5}{7} & \frac{3}{7} & -\frac{9}{7} \end{bmatrix} \cdot \begin{bmatrix} 33\\ -21\\ -6 \end{bmatrix}\)

Calculating the multiplication, we get:

\(\displaystyle X=\begin{bmatrix} 3\\ 2\\ 1 \end{bmatrix}\)

Therefore, the variable matrix \(\displaystyle X\) is:

\(\displaystyle X=\begin{bmatrix} 3\\ 2\\ 1 \end{bmatrix}\)

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Answer:

1) 8x³ - x² + 1

2) 5a - 3b - 10c

3 17x²y - 7xy²

Step-by-step explanation:

Just combine like terms, since everything is adding, all you have to do is add everything with the same symbol. Make sure you watch for negatives so you know when to add or subtract you numbers!

Hope this helps!

Answer:

70degrees

Explanation:

The diagrammatical representation of the statement is as shown;

Since the sum of angles on a straight line is 180degrees, then;

m8x+2 + 5x = 180

13x + 2 = 180

13x = 180 + 2

13x = 182

x = 182/13

x = 14

Get mmmmHence the measure of m

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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The amount of energy it takes to run a race is most likely to be a function of the; D: Length of the Race

We want to basically find the factor that influences the amount of energy expended by a sprinter.

Now, formula for potential energy is;

P = mgd

where;

m is mass

g is acceleration due to gravity

d is distance covered

Now, the only option that falls into the input that affects energy expended is the distance covered. This is true because the more the distance covered, the higher the energy expended.

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The average winning per bet is the mean or the expected value of winning a bet.

The statistical term that represents $0.94 is (c) the expected value

From the question, we understand that the gambler has an average winning of $0.94, when he places a bet of $1

This means that:

The average winning on a bet of $1 is $0.94

Average, in statistics means the mean or expected value

Hence, the statistical term for $0.94 is (c) the expected value

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Answer:

5) 35

6) 24

7) 28

8) 67

9) 20

10) 11

11) 7

12) 21

Step-by-step explanation:

Looks like you get most of the rules involved so I'll just write the steps

5) x+4x+5 = 180

5x + 5 = 180

5x = 175

x = 35

6) 6x = 144

x = 24

7) x+27 = 2x-1

27 = x-1

28 = x

8) 63+2x-17 = 180

2x + 46 = 180

2x = 134

x = 67

9) 9x-28 = 7x +12

2x = 40

x = 20

10) 5x+7 = 62

5x=55

x=11

11) 41=7x-8]49=7x

7=x

12) 114=6x-12

126=6x

21 = x

If you wanna check it just plug in the values

That's about it

Answer:

0.119

Step-by-step explanation:

No. of sides a die has= 6 sides

No. of times it is rolled= 7 times

Total pairs= 6 x 7

                = 42 pairs

No. of 5 threes= 5 x 1

                        = 5

Probability of getting 5 threes= Favorable outcomes/Total outcome

                                                 = \(\frac{5}{42}\)

                                                 = 0.119 chance

∴ probability of getting 5 threes is 0.119

The circumference of the cross-section that is parallel to the base and a distance of 10 mm from the vertex V of the cone is 20π mm.

We have,

To find the circumference of the cross-section parallel to the base and a distance of 10 mm from the vertex V of the cone, we can consider the similar triangles formed by the cross-section and the base.

Let's denote the radius of the cross-section as r.

We can set up the following proportion:

r / 20 = (r + 10) / 40

To solve for r, we can cross-multiply and simplify:

40r = 20(r + 10)

40r = 20r + 200

20r = 200

r = 200 / 20

r = 10

Therefore, the radius of the cross-section is 10 mm.

Now, we can calculate the circumference of the cross-section using the formula for the circumference of a circle:

C = 2πr

C = 2π(10)

C = 20π

Thus,

The circumference of the cross-section that is parallel to the base and a distance of 10 mm from the vertex V of the cone is 20π mm.

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Answer:

3

Step-by-step explanation:

Since the graphs aren't parallel due to not having the same slope we can assume they will intercept once

Answer:

y=2x-7, the slope is two and the y-intercept is -7

Step-by-step explanation:

2(x-3)=y+1

Distributive prop.

2x-6=y+1

Changing into slope-intercept form

y+1=2x-6

Subtract both sides by one

y=2x-7

The slope is two and the y-intercept is -7

a) The probability that a patient has breast cancer, given that they get a positive test is 0.13961

b) If the breast cancer rate is actually 8%, then the probability of the breast cancer rate is 0.094

a) First, we need to compute the probability that a patient has breast cancer, given that they receive a positive test result. This is known as the conditional probability.

Let's denote the following:

P(C) represents the probability of having breast cancer, which is given as 13% or 0.13.

P(Pos) represents the probability of a positive test result.

P(Pos|C) represents the sensitivity of the test, which is 92% or 0.92.

To calculate P(Pos), we can use Bayes' theorem, which states:

P(Pos) = P(Pos|C) * P(C) + P(Pos|~C) * P(~C)

P(Pos|~C) represents the probability of a positive test result given that the person does not have breast cancer, which can be calculated as 1 - specificity. Specificity is given as 97.7% or 0.977.

P(Pos|~C) = 1 - specificity = 1 - 0.977 = 0.023

P(~C) represents the probability of not having breast cancer, which is 1 - P(C) = 1 - 0.13 = 0.87.

Now we can calculate P(Pos):

P(Pos) = P(Pos|C) * P(C) + P(Pos|~C) * P(~C)

= 0.92 * 0.13 + 0.023 * 0.87 = 0.13961

b) In this case, let's assume the breast cancer rate is 8% or 0.08 instead of 13%. We need to recalculate the probability that a patient has breast cancer, given a positive test result (P(C|Pos)).

Using the same approach as before, we'll calculate P(Pos) with the updated values:

P(C) = 0.08

P(~C) = 1 - P(C) = 1 - 0.08 = 0.92

P(Pos) = P(Pos|C) * P(C) + P(Pos|~C) * P(~C)

= 0.92 * 0.08 + 0.023 * 0.92 = 0.094

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Given, Aika is building a square garden. She places a garden post at (3.5, 3.5)

To find: The location of the corner that reflects (3.5, 3.5) across the y-axis.

We know that the y-axis is the vertical line through the point (0,0) and it divides the plane into two parts: left and right. When we reflect a point across the y-axis, the x-coordinate changes sign. For example, the reflection of (2,3) is (-2,3).Therefore, the reflection of (3.5, 3.5) across the y-axis is (-3.5, 3.5)

Since Aika is building a square garden, the corner opposite to (3.5, 3.5) will have coordinates (-3.5, -3.5).

Hence, the location of the corner that reflects (3.5, 3.5) across the y-axis is (-3.5, -3.5).

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Answer:

y = - 3x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 3, then

y = - 3x + c ← is the partial equation

To find c substitute (- 2, - 1) into the partial equation

- 1 = 6 + c ⇒ c = - 1 - 6 = - 7

y = - 3x - 7 ← equation of line

Answer:

The equation would be y=-3x-7

Step-by-step explanation:

Value of x is 66°.

Based on measurement, there are many kinds of angles in geometry. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by connecting two rays at their termini. In most cases, an angle is expressed in degrees.

Given Data

A rectangular sheet of paper is folded at the corner.

Right triangles characterize both the folded-over region and its void. In the bottom left corner, there is a right angle that is marked at 33 degrees. Thus,

180-(33+90)

= 180-123

= 57° is what is left.

The angles in the triangle that has been folded over are the same.

To the left of x, there are two angles that meet at a straight angle. The sum of all right angles is 180 degrees. The 57° measure is shared by the two angles that make up the straight angle with x. This results in:

180-(57+57)

= 180-114

= 66°

Value of x is 66°.

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Answer:

x = -1 and y = 3     x = 3 and y = -1

Step-by-step explanation:

Answer:

250.50 - 35m = 300 - 45.25m

Step-by-step explanation:

Whenever an equation asks for when it will take x (or m in this case) amount of things or time you should know that there will be 2 different equations that have to equal each other

The equation will be 250.50 - 35m = 300 - 45.25m

The 35m is being subtracted from 250.50 because they are losing money each time they spend. This also applies to 45.25m

Also 35m and 45.25m are variables because it says they spend that much money each month. They don't specify how many months, so we have to put a variable after it.

Answer:

b) 250.5 – 35m = 300 – 45.25m

Step-by-step explanation:

on edge 2020 || pls mark brainliest

Answer:

length could be 8 cm and width would be 3 cm and that would have a perimiter of 24 cm also

The appropriate inference method for this situation is a) Confidence Interval for a Proportion.

In a survey of 750 Americans, the proportion of individuals who indicated a belief in reincarnation was found to be 24%. To estimate the true proportion of Americans who believe in reincarnation, a confidence interval for a proportion is the appropriate method. This allows us to estimate the range within which the true proportion lies with a certain level of confidence.

By calculating a confidence interval for the proportion, we can provide an estimate of the range within which the true proportion of Americans who believe in reincarnation is likely to be. This interval provides a measure of the uncertainty associated with our estimate and allows us to make inferences about the population based on the sample data.

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Given that there are 5 red 4 green and 3 blue balls

The probability of picking a blue and a red ball with replacement is

The probability of picking a blue ball

= 3/(5 + 4 + 3)

= 3/12

The probability of picking a red ball (after replacing the blue picked earlier)

= 5/(5 + 4 + 3)

= 5/12

Hence the probability of picking a blue and a red ball with replacement is

= 3/12 * 5/12

= 15/144

= 5/48

Answer:

1

Step-by-step explanation:

Because the shape divided has to create another shape and for 1 it's an oval at the beginning and then after the lines of symmetry go through its seen as 8 triangles.

Answer:

0.75

Step-by-step explanation:

The outcomes are equally likely, so the easiest way to work this problem is to write out the 8 outcomes in this sample space. In two outcomes the gender of all three children is the same (GGG, BBB). The other 6 outcomes contain at least one boy and one girl.

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Using the 14c calibration on the x-axis, the approximate age of the neanderthal fossils is (C) 40,110 years old.

So, using calibration on the x-axis, the approximate age of the neanderthal fossils came out to be 40,110 years old.

Therefore, using the 14c calibration on the x-axis, the approximate age of the neanderthal fossils is (C) 40,110 years old.

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The correct question is given below:
Using the 14c calibration on the x-axis, what is the approximate age of the neanderthal fossil?

a. 5,730 years old

b. 34,380 years old

c. 40,110 years old

d. 45,840 years old

Answer:

<5 is the remote interior angle to <1

They are on the same line, or, they are supplementary, and will add up to 180 degrees

The remote interior angles of ∠1 are ∠2 and ∠3.

Hence, Option (b) and (c) are correct.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that:

A triangle with marked angles.

We have to find the remote interior angles of angle 1.

Now, We know that;

Remote interior angles are the two angle that are inside the triangle and are opposite from the exterior angle.

Also, Remote interior angles don't share a vertex or corner of a triangle with the exterior angle.  

Thus, for the remote interior angles of angle 1 are angle 2 and angle 3  as they do not share a vertex or corner of a triangle with the exterior angle.  

Thus, Option (b) and (c) are correct.

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Given:

Number of males = h

Number of females = (h-2)

Total number of visitors = 80

To find:

The value of h.

Solution:

We have,

Number of males = h

Number of females = (h-2)

So, the total number of visitors is:

\(Total=h+(h-2)\)

\(Total=2h-2\)

It is given that the total number of visitors is 80. So,

\(2h-2=80\)

\(2h=80+2\)

\(2h=82\)

Divide both sides by 2.

\(h=\dfrac{82}{2}\)

\(h=41\)

Therefore, the correct option is D.

The expression is 2 - m/4 + 10, when m = 12, the value is 9. Then the correct option is C.

It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.

Two less than the quotient of a number and four, increased by ten.

That can be written as in the form of m will be

\(\rm 2 - \dfrac{m}{4} + 10\)

If the value of m is 12, then we have

\(\rm 2 - \dfrac{m}{4} + 10\\\\\rm 2 - \dfrac{12}{4} + 10\\\\2- 3 + 10\\\\12 - 3 \\\\9\)

Thus, the expression is 2 - m/4 + 10, when m = 12, the value is 9. Then the correct option is C.

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Answer:

D

Step-by-step explanation:

The probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% is 0.006.

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The information provided is:

n = 596

p = 0.09

The mean and standard deviation are:

Compute the probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% as follows                      

Hence, the probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% is 0.006.

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The company's WACC is 9.95%. This implies that the company must generate a return of at least 9.95% on its investments to cover its cost of capital.

WACC (Weighted Average Cost of Capital) is a measurement used to determine a company's cost of capital. It is calculated as a weighted average of the costs of equity and debt, considering the company's capital structure. The formula for WACC is:

WACC = (E / V x Re) + [(D / V x Rd) x (1 - T)]

Where:

E = Market value of the company's equity

D = Market value of the company's debt

V = Total value of the company (equity + debt)

Re = Cost of equity

Rd = Pretax cost of debt

T = Tax rate

Given the following values:

Debt-equity ratio = 0.55

Cost of equity (Re) = 15.4%

Pretax cost of debt (Rd) = 7.8%

Tax rate = 32%

We can calculate the after-tax cost of debt, Rd, by multiplying the pretax cost of debt with (1 - tax rate). Thus,

Rd = 7.8% x (1 - 32%) = 5.292%

Now, we can substitute the values into the WACC formula:

WACC = [(E / V x Re) + (D / V x Rd) x (1 - T)]

WACC = [(1 / 1.55 x 15.4%) + (0.55 / 1.55 x 5.292%) x (1 - 32%)]

WACC = 9.95%

Therefore, the company's WACC is 9.95%. This implies that the company must generate a return of at least 9.95% on its investments to cover its cost of capital.

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