Rick wants to determine if there is a correlation between the age and the cost of a used car.

What can be interpreted from this data?

The inverse of the matrix A by getting its determinant value is equal to [tex]A^{-1} = \left[\begin{array}{ccc}1&-1\\\frac{-3}{2} &2\end{array}\right][/tex]

The matrix is equal to,

A = [tex]\left[\begin{array}{ccc}4&2\\3&2\end{array}\right][/tex]

To find the inverse of a matrix,

we first need to calculate its determinant of the matrix A  we have,

|A| = [tex]\left|\begin{array}{ccc}4&2\\3&2\end{array}\right|[/tex]

⇒ |A| = 4(2) - 2(3)

        = 8 - 6

        = 2

Now we can proceed to find the inverse of A.

Set up the matrix of cofactors.

The matrix of cofactors C is obtained by replacing each element of A with its corresponding cofactor,

which is the determinant of the submatrix obtained by deleting the row and column that contain that element.

For our matrix A, we have,

C = [tex]\left[\begin{array}{ccc}2&-3\\-2&4\end{array}\right][/tex]

Transpose the matrix of cofactors.

The transpose of a matrix is obtained by flipping its rows and columns. For our matrix C, we have.

[tex]C^{T} = \left[\begin{array}{ccc}2&-2\\-3&4\end{array}\right][/tex]

Divide by the determinant.

The inverse of A is obtained by dividing the transpose of the matrix of cofactors by the determinant of A.

For our matrix A, we have,

A⁻¹ = [tex]C^{T}[/tex] / |A|

   [tex]C^{T} = (1/2)\left[\begin{array}{ccc}2&-2\\-3&4\end{array}\right][/tex]

   [tex]C^{T} = \left[\begin{array}{ccc}1&-1\\\frac{-3}{2} &2\end{array}\right][/tex]

Therefore, the inverse of the matrix A is equal to [tex]A^{-1} = \left[\begin{array}{ccc}1&-1\\\frac{-3}{2} &2\end{array}\right][/tex]

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Answer:

hope it helps

Step-by-step explanation:

The given equation is as follows:

3x + 7 = 19

To solve for x, we need to isolate x on one side of the equation.

First, we can start by subtracting 7 from both sides of the equation to get rid of the constant term:

3x + 7 - 7 = 19 - 7

Simplifying, we get:

3x = 12

Next, we can find x by dividing both sides of the equation by 3:

3x/3 = 12/3

Simplifying, we get:

x = 4

Therefore, the solution to the equation 3x + 7 = 19 is x = 4.

Using simplification of equations, we can find the value of x to be = 4.

Equations are mathematical statements with the equals (=) symbol and two algebraic expressions on either side. This illustrates the equality of the relationship between the expressions printed on the left and right sides. The formula LHS = RHS (left hand side equals right hand side) is utilised in all mathematical equations. To determine the value of an unknown variable that represents an unknown quantity, you can solve equations. A statement is not regarded as an equation if it has no "equal to" symbol. It'll be regarded as a term.

This is the equation that is provided:

3x + 7 = 19

We must isolate x on one side of the equation in order to find its value.

To eliminate the constant term, we can begin by deducting 7 from both sides of the equation:

3x + 7 - 7 = 19 - 7

To put it simply, we obtain 

3x = 12.

Then, by multiplying both sides of the equation by 3, we can determine x:

3x/3 = 12/3

To put it simply, we obtain x = 4.

Consequently, x = 4 is the answer to the equation 3x + 7 = 19.

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The height of the rectangular pyramid is calculated as:

h = 17 units.

The formula for calculating the volume of a rectangular pyramid is expressed as:

Volume (V) = 1/3 * lwh, where:

Given the following:

l = 9 units

w = 14 units

Volume of rectangular pyramid (V) = 714 cubic units.

Plug in the values:

714 = 1/3 * 9 * 14 * h

714 = 42h

714/42 = h

h = 17 units.

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Step-by-step explanation:

First, let's find the area of the rectangular sides using the dimensions given.

16 x 7 = 112 [tex]in^2[/tex]

112 is just for one rectangle. We need to find the area for 3 rectangles.

112 x 3 = 336 [tex]in^2[/tex]

Now, we need to find the area of the triangle. Using the formula let's find the area.

bh/2

7 x 8/2

56

Our answer is 56 as we find the area of two triangles and 28 x 2 equals 56.   To find the prism's total area, we have to add the areas altogether.

56 + 336 =

Answer: 392 [tex]in^2[/tex]

The ship moved almost 72.5 degrees north of west to arrive at its destination.

1.: According to a trigonometrical rule, the square of a side in a plane triangle is equal to the sum of the squares of the other sides minus twice that amount plus the cosine of the angle between the other two sides.

BC² is equal to AB² + AC² - 2AB AC cosx

BC² = 17657 - 22068 cosx BC² = 942 + 1192 - 2 94 119 cosx

BC ≈ 105.2

cos(x) = (2 BC AB) / (BC² + AB² - AC²)

cos(x) = (105.2² + 94² - 119²) / (2 × 105.2 × 94)

cos(x)=0.301 = 72.5 degrees

As a result, the ship moved almost 72.5 degrees north of west to arrive at its destination.

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Since the angle at the center of the circle is 120 degrees, the angle subtended by the minor arc XY at the center of the circle is also 120 degrees.

The circumference of a circle with radius r is given by 2πr, where π is the constant pi (approximately equal to 3.14).

The total circumference of the circle is 2π(23 cm) ≈ 72.4 cm.

Since the minor arc XY subtends an angle of 120 degrees at the center of the circle, it will have a length that is 120/360 = 1/3 of the total circumference.

Therefore, the approximate length of the minor arc XY is (1/3)(72.4 cm) ≈ 24.1 cm.

So the closest option to this value is option D, 24 cm.

Answer: A. 48 cm

Step-by-step explanation:

I just did it :)

Answer:

x

Step-by-step explanation:

[tex] \frac{1}{5} (25x - 10x) - 2x \\ = \frac{1}{5} (15x) - 2x \\ = 3x - 2x \\ = x[/tex]

Answer: You might want to know how many 24 apples are, individually, also being an accountant, mathematician, scientist, all require Math and math follows PEMDAS [Parenthesis, exponents, multiplication, division, addition, subtraction.] normally.

Step-by-step explanation:

Also, if you multiple something let's say 378x54 and get 20,412 and let's say you want to divide this huge number to a smaller number you can divide from 2 all the way up! Mathematics is not just something we have to learn, it's also something we can use!

Answer:

Step-by-step explanation:

The b is area of the base which is l x w

so if you substituted in you get V= l x w x h

So they are the same

We can plot 7/10 as 0.7 and 1(1/5) as 1.2 on the number line.

We have,

To plot 7/10, we need to divide the number line into 10 equal parts and then count 7 parts starting from 0.

We can label this point as 7/10.

To plot 1(1/5), we first note that 1 is to the left of the 1/5 mark on the number line.

We can divide the section between 0 and 1/5 into 5 equal parts and count 1 part starting from 0.

Then, we can move to the left of 1 and count 1 more part starting from the 1/5 mark.

We can label this point as 1(1/5).

Alternatively,

We can convert 1 1/5 to an improper fraction first:

1 (1/5) = (5 x 1 + 1) / 5 = 6/5

Then, we can plot 6/5 by dividing the number line into 5 equal parts and counting 6 parts starting from 0.

We can label this point as 6/5 or 1(1/5).

Thus,

We can plot 7/10 as 0.7 and 1(1/5) as 1.2 on the number line.

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The probability term that best describes these events is D. complementary.

Complementary events are those that cannot occur simultaneously and are mutually exclusive and exhaustive in probability, meaning that their probabilities add up to 1. Nikoli rolls a number cube with six possible outcomes in this scenario: 1, 2, 3, 4, 5, and 6.

Because events A and b have no common outcomes and their union encapsulates all outcomes that could result from rolling a number cube, they are complimentary events.

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Answer:

3√2

Step-by-step explanation:

We can find the value of x using the following equation:

x² = 2×9

x² = 2×9

x² = 18

x = 3√2

Answer:

40

Step-by-step explanation:

Perimeter of rectangle = 2(l + w)

L= 12

W = 8

Let's solve

2(12 + 8) = 40

So, the perimeter of the rectangle is 40

To find the height of the tissue box, we use the formula for the volume of a rectangular prism, substituting the given values. We get a height of approximately 11.0 inches, rounded to the nearest tenth.

To find the height of the tissue box, we need to use the formula for the volume of a rectangular prism, which is:

volume = length x width x height

We are given the volume of the tissue box as 1,001 cubic inches, and its width and length as 7 inches and 13 inches, respectively.  We can enter these values as substitutes in the formula to obtain:

1,001 = 13 x 7 x height

The right side of the equation is simplified, and the outcome is:

1,001 = 91 x height

Dividing both sides by 91 gives:

height = 1,001 / 91

We can evaluate this expression with a calculator to obtain:

height ≈ 11.0

Therefore, the height of the tissue box is approximately 11.0 inches, rounded to the nearest tenth.

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The the freshness half-line of milk is 10h, (b) The milk keep fresh at 22°C  for 31.1h (c) The milk keep fresh at 4°C for 55.7h

Recal that Storage temperature refers to the temperature at which food product is stored immediately after preparation and maintained at a safe holding temperature until it is dispensed to the customer

The given relation is T = 190 (1/2)^t/10

a. From the relation, T = 190 (1/2)^t/10

So the freshness half life of milk is 10 hours

b.  22 =  190 (1/2)^t/10

t = 10log₁/₂(190/22) = 31.1 hours

c. = 190 (1/2)^t/10

t= 10log₁/₂(190/22 = 55.7 hours

Milk can keep fresh for 55.7 hours at 4°C

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The perimeter and the area of the rectangle are given as follows:

Considering dimensions l and w, the perimeter of the rectangle is given as follows:

P = 2(l + w).

The dimensions in this problem are of 7 in and 3.2 in, hence the perimeter is given as follows:

P = 2(7 + 3.2)

P = 10.4 inches.

The area of a rectangle is given as follows:

A = lw.

Hence:

A = 7 x 3.2

A = 22.4 in².

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Answer: f(−3) = -5/2

f(−1) = -5/2

f(3) = 3/4

Step-by-step explanation: For x ≤ -1, we have:

f(x) = 7/2 + 2x

For x = -3, we have:

f(-3) = 7/2 + 2(-3)

f(-3) = 7/2 - 6

f(-3) = -5/2

For x = -1, we have:

f(-1) = -5 + 3(-1)/2

f(-1) = -5/2

For -1 < x < 3, we have:

f(x) = -5 + 3x/2

For x = 3, we have:

f(3) = 1/4 (3)

f(3) = 3/4

Answer: [tex]0.4x=360,000[/tex]

Step-by-step explanation:

From the problem it can be seen that 360,000 is 40% of the sales she got this year. So, 40% of her sales is 360,000.

40% of x is mathematically 0.4 times x.

Therefore the equation you could use is:  [tex]0.4x=360,000[/tex]

If you want to solve this for x, simply divide 0.4 from both sides to get x by itself.

[tex]x=(\frac{360,000}{0.4})=900,000[/tex]

So this year she made 900,000 dollars.

The solution is:

a) 22-t mph; is the rate of the boat when it travels upstream.

b) 22+t mph. is the rate of the boat when it travels downstream.

Here, we have,

a) When the boat travels​ upstream, the current hinders the boat (the speed of the boat decreases). Thus, the speed of the boat upstream becomes

22-t mph.

b) When the boat travels​ downstream, the current helps the boat (the speed of the boat increases). Thus, the speed of the boat downstream becomes

22+t mph.

Hence, The solution is:

a) 22-t mph; is the rate of the boat when it travels upstream.

b) 22+t mph. is the rate of the boat when it travels downstream.

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The requried completely factored form of the given polynomial is (q+w)(c+y).

We can group the first two terms and the last two terms together, then factor out the common factors:
= cq+cw+qy+wy
= c(q+w) + y(q+w)
= (q+w)(c+y)

Therefore, the completely factored form of the given polynomial is (q+w)(c+y).

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It would take the assistant 17 hours, 30 minutes to do it alone

Algebraic expressions are defined as expressions that are composed of terms, variables, constants, factors and coefficients.

They are also made up of arithmetic operations, such as;

From the information given, we have that;

Josephine makes the correction in 7 hours

They both do it for 5 hours

Let the assistant be x, we then have;

7x/7 + x = 5

cross multiply the values

7x = 37 + 5x

collect the like terms

2x = 35

x = 35/2

x = 17. 5 hours

x =17 hours, 30 minutes

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Answer:

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

Convert the equation in below steps to solve for x:

Divide both sides by a:

Log both sides with base b:

Here is the answer:

Based on their unit rates (hourly rates), William earns $3.20 less per hour than Carson.

The unit rates can be determined as the quotients of the total earnings divided by the number of hours worked by each worker.

Total earnings in 21 hours = $451.50

The total number of hours worked = 21 hours

Hourly rate = $21.50 ($451.50 ÷ 21)

Hours (x)  Earnings (y)   Hourly Rate

   8             $146.40        $18.30 ($146.40 ÷ 8)

 32             $585.60      $18.30 ($585.60 ÷ 32)

 36             $658.80      $18.30 ($658.80 ÷ 36)

40             $732.00       $18.30 ($732.00 ÷ 40)

William's hourly rate = $18.30

Difference between Carson's and William's hourly rate = $3.20 ($21.50 - $18.30)

Thus, judging from their hourly rates, we can conclude that Carson earns more per hour than William.

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William's Earnings

Hours (x)  Earnings (y)

   8             $146.40

 32             $585.60

 36             $658.80

40             $732.00

Step-by-step explanation:

cutive Function Test aimed at elderly individuals be a useful tool?

Using the standard thumb, we can say that any brain volume that falls outside the range of 878.6 cm³ to 1333.8 cm³ is significantly low or significantly high. Therefore, any brain volume below 878.6 cm³ or above 1333.8 cm³ would be considered significantly low or significantly high.

As for whether a Brain Executive Function Test aimed at elderly individuals would be a useful tool, the information given is not enough to answer that question. The Brain Executive Function Test is a cognitive assessment tool that measures various cognitive skills such as attention, problem-solving, working memory, and decision-making. The usefulness of this test depends on the purpose of the assessment and the population being tested. The given information only provides brain volume data of 20 brains and does not give any indication of the age or cognitive status of the individuals. Therefore, it is not possible to determine whether a Brain Executive Function Test aimed at elderly individuals would be useful based on this information alone.

Answer:

Median: As this is a set of 8, add the two numbers which are in the middle (11 and 13) and then divide them by two.

Mean: Add all of the numbers in the set and then divide the answer by the total number of the numbers in the set, which is 8.

Answer:

Step-by-step explanation:

A randomized controlled trial is the best type of study to conduct to establish causality due to its ability to control for confounding factors, and its ability to measure the true effects of a particular treatment.

What is statistics?
Statistics is the science of collecting, organizing, analyzing, and interpreting data. It involves describing, summarizing, and making inferences about a given set of data. Statistics is used to make decisions in various fields, such as business, economics, medicine, psychology, and engineering. Statistical methods are used to help scientists understand the behavior of complex systems, to analyze the relationships between different variables, and to test hypotheses. Additionally, statistics can be used to draw conclusions from data, to identify patterns, to estimate probabilities, and to make predictions.

In order to establish causality, the best type of study to conduct is a randomized controlled trial (RCT). An RCT is a type of experiment designed to establish a cause-and-effect relationship between variables. This study involves randomly assigning individuals to different experimental groups, and then comparing the outcomes between the groups. This helps to determine the effects of a particular treatment or intervention on a population.

For example, if we wanted to study the effects of a new medication on a particular condition, we would create two groups of people – one group would receive the medication and the other would receive a placebo. We would then measure the outcomes of the two groups to see if the medication has an effect on the condition. This type of study helps to establish a causal relationship between the treatment and the outcome, as the randomization helps to control for other confounding factors that could influence the results.

Therefore, a randomized controlled trial is the best type of study to conduct to establish causality due to its ability to control for confounding factors, and its ability to measure the true effects of a particular treatment.

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(a) The test statistic is z = -1.788 and (b) P-value = 0.0734.

Hypothesis testing is a statistical method used to make decisions about a population based on a sample of data.

The process involves setting up a null hypothesis (H₀) and an alternative hypothesis (Hₐ), collecting data from a sample, calculating a test statistic based on the sample data, and using the test statistic to determine whether to reject or fail to reject the null hypothesis

Here we have

An article published in the Washington Post claims that 45 percent of all Americans have brown eyes.

A random sample of n = 78 college students found 30 who had brown eyes. Consider testing = H₀: p =0 .45 Hₐ:p + 0.45

(a) The test statistic can be calculated using the formula:

z = (p' - p) / √(p(1-p) / n)

where p' is the sample proportion, p is the hypothesized proportion under the null hypothesis, and n is the sample size.

In this case, the hypothesized proportion is p = 0.45, the sample proportion is p' = 30/78 = 0.3846 (rounded to four decimal places), and the sample size is n = 78. Therefore:

z = (0.3846 - 0.45) / √(0.45 × 0.55 / 78)

z = -1.788

So the test statistic is z = -1.788.

(b) To find the p-value, we need to look up the area in the standard normal distribution table corresponding to the test statistic z = -1.788. The area to the left of z = -1.788 is 0.0367 (rounded to four decimal places). Since this is a two-tailed test (Ha: p > 0.45), we need to double this area to get the p-value:

p-value = 2 × 0.0367

p-value = 0.0734 (rounded to four decimal places)

Therefore,

(a) The test statistic is z = -1.788 and (b) P-value = 0.0734.

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Complete Question:

REMINDER: DO NOT use your calculator or an app to obtain normal curve areas such as you would for finding a p-value. Use the table in your formula packet. DO NOT use another method or the difference in precision may cause you to lose points. An article published in the Washington Post claims that 45 percent of all Americans have brown eyes. A random sample of n = 78 college students found 30 who had brown eyes. Consider testing = H₀: p= 0.45 Hₐ:p + 0.45 (a) The test statistic is z = -1.161 (b) P-value =

Based on the given table, the annual premium per $100 of coverage for a wood house in the country would be 0.74.

To calculate the annual premium for the $200,000 house, we first need to determine the coverage amount. Assuming a coverage of 80% of the house's value, the coverage amount would be:

Coverage amount = 80% of $200,000 = $160,000

Next, we can calculate the annual premium as follows:

Annual premium = (Coverage amount / $100) x Annual premium per $100 of coverage

= ($160,000 / $100) x 0.74

= $1,184

Therefore, the annual premium to insure the $200,000 wood house in the country would be $1,184.

Answer:

  (b)  0.4

Step-by-step explanation:

You want the experimental probability that Antonia will make both of her next two free throw attempts.

The "experimental" probability is the fraction of times the outcome of interest occurred in the trials used for the experiment.

Here, Antonia made both free throws in trials 2, 5, 9, and 10 of the ten trials, so her record for making both free throws is 4 out of 10 trials. We are to assume this 4/10 ratio is the probability that the next 2 attempts will result in Antonia making both free throws.

The experimental probability of making both free throws is 0.4, choice B.

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