Cole buys a new laptop for $335. He makes a down payment for $50, then makes 6 equal monthly payments ‘p'. Write an equation that represents the situation

*attachment contains the omitted graph

Answer:

\( y = -\frac{4}{3}x + 9 \)

Step-by-step explanation:

The equation that represents the path of the swimmer to the shoreline can be represented in the slope-intercept form, given as \( y = mx + b \).

Where,

Slope (m) = the negative reciprocal of the slope of the shoreline, since it is perpendicular to it = ??

y-intercept (b) = ??

Find the slope of the shoreline using, (0, 1) and (4, 4):

\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 1}{4 - 0} = \frac{3}{4} \).

Since the slope of the shoreline is ¾. The slope of the path of the swimmer would be the negative reciprocal of ¾.

The negative reciprocal of ¾ = -⁴/3.

The slope of the swimmer's path = -⁴/3.

Using the coordinate of the point of the swimmer (6, 1), and the slope of the path, we can find b, the y-intercept of the path.

Substitute x = 6, y = 1 and m = -⁴/3 into y = mx + b, to find b.

Thus:

1 = (-⁴/3)(6) + b

1 = -8 + b

Add 8 to both sides

1 + 8 = b

9 = b

b = 9

Substitute m = -⁴/3 and b = 9 into y = mx + b.

✅The equation that represents the path would be:

\( y = -\frac{4}{3}x + 9 \)

In a 45 · 45 · 90 triangle, the hypotenuse is √2 · legs, because a 45 · 45 · 90 triangle is isosceles, so the legs are the same length. So, we have 3√2 · √2 = 6, so the hypotenuse is 6.

x=6

The value of S, which represents the length of each side of the square, is 4 miles.

To find the value of S, we need to determine the length of each side of the square. Given that the perimeter of the square is 16 miles, we can use the formula for the perimeter of a square, which is 4 times the length of a side.

Perimeter = 4 × S

Given that the perimeter is 16 miles, we can substitute this value into the equation:

16 = 4 × S

To solve for S, we divide both sides of the equation by 4:

16 ÷ 4 = S

4 = S

Therefore, S, which stands for the square's side lengths, has a value of 4 miles.

So, S = 4 miles.

This means that each side of the square measures 4 miles, and the square has equal sides and right angles at each corner.

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The measurements associated with student life are categorized as follows: length of time to complete an exam is a ratio, time of first class is an interval, major field of study is nominal, course evaluation scale is ordinal, score on last exam is a ratio, and age of student is a ratio.

(a) Length of time to complete an exam - Ratio: This is measured on a scale of time, and can be expressed as a ratio (i.e. the amount of time spent on the exam divided by the total time allotted for the exam).

(b) Time of first class - Interval: The time of the first class is measured on a scale of minutes, hours, and days, and can be expressed as an interval (i.e. the amount of time between two classes).

(c) Major field of study - Nominal: This is a categorical measurement and can be expressed as a nominal variable (i.e. the student's major field of study is either engineering, business, etc).

(d) Course evaluation scale: poor, acceptable, good - Ordinal: This is a scale of quality and can be expressed as an ordinal variable (i.e. the quality of the course can be rated as poor, acceptable, or good).

(e) Score on last exam (based on 100 possible points) - Ratio: This is measured on a scale of points, and can be expressed as a ratio (i.e. the student's score on the exam divided by the total number of points possible).

(f) Age of student - Ratio: This is measured on a scale of years, and can be expressed as a ratio (i.e. the student's age divided by the total number of years they have been alive).

The measurements associated with student life are categorized as follows: length of time to complete an exam is a ratio, time of first class is an interval, major field of study is nominal, course evaluation scale is ordinal, score on last exam is a ratio, and age of student is a ratio.

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Students should be able to apply these concepts and tools in real-world situations, such as calculating the probability of winning a game or analyzing data from a scientific Experiment.

The probability is a measure of the possibility of an event happening. It is expressed as a fraction or decimal between 0 and 1, or as a percentage between 0% and 100%. Probability can be used to determine the likelihood of an event happening or not happening.

Data analysis is the process of analyzing data to extract valuable insights from it. It involves examining data sets to uncover trends, patterns, and relationships that can be used to make informed decisions. Data analysis is an important tool in many fields, including business, finance, and science.

The data analysis and probability unit test assesses students' understanding of these concepts and their ability to apply them in real-world situations.

The test typically includes questions that require students to use probability to determine the likelihood of an event happening or not happening, as well as questions that ask students to analyze data sets to extract valuable insights.In order to prepare for the data analysis and probability unit test, students should review the key concepts and formulas related to probability, such as the addition rule, the multiplication rule, and the complementary rule.

They should also practice analyzing data sets using tools like histograms, scatter plots, and box plots, and should be familiar with key concepts like mean, median, and mode.

Finally, students should be able to apply these concepts and tools in real-world situations, such as calculating the probability of winning a game or analyzing data from a scientific experiment.

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Answer:

I got this from one of my textbook for the previous years

Hope this helps:)

The equation of straight line having

(a) gradient -4 and coordinates (-2,1) is  4x + y \(=\) -7

(b) gradient 0 and coordinates (-1,21) is y = 21 .

In the question ,

the gradient and coordinates of the point on the line is given .

we have to find the equation of the straight line .

Part(a)

the gradient of the line \(=\) -4 ,

the coordinates of a point on the line = (-2,1)

So , the equation of the line is

(y - 1) = (-4)*(x -(-2))

y - 1 = -4(x + 2)

y - 1 = -4x - 8

4x + y = -8 + 1

4x + y = -7

the equation is 4x + y = -7  .

Part(b)

the gradient of the line = 0 ,

the coordinates of a point on the line = (-1 , 21)

So , the equation of the line is

(y - 21) = 0(x-(-1))

y - 21 = 0

y = 21

the equation of the line is y = 21  .

Therefore , The equation of straight line having  (a) gradient -4 and coordinates (-2,1) is 4x + y \(=\) -7  and (b) gradient 0 and coordinates (-1,21) is  y = 21  .

The given question is incomplete , the complete question is

Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.

(a) -4, (-2 , 1)

(b) 0, (-1, 21)

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(a) The sample size for the above sample is 15.

(b) The sample mean for these data is 3.8.

(c) The sample median is 3.6.

(d) To compute the 20% trimmed mean for the above data set is 3.7.

(e) The sample mean is less descriptive as the location's center (median) than the trimmed mean.

The following measurements were recorded for the drying time, in hours

3.4      2.5      4.8      2.9      3.6 is:

2.8      3.3      5.6      3.7      2.8

4.4      4.0      5.2      3.0      4.8

(a) We have to determine the sample size for the above sample.

The number of participants or observations included in a study is referred to as the sample size. This number is commonly represented by the symbol n.

Sample Size (n) = 15

(b) We have to calculate the sample mean for these data.

Sample Mean = Total Sum of data/Total Number

Sample Mean = (3.4 + 2.5 + 4.8 + 2.9 + 3.6 + 2.8 + 3.3 + 5.6 + 3.7 + 2.8 + 4.4 + 4.0 + 5.2 + 3.0 + 4.8)/15

Sample Mean = 56.8/15

Sample Mean = 3.8

(c) We have to calculate the sample median.

To define the sample median we first represent the data in ascending order.

2.5, 2.8, 2.8, 2.9, 3.0, 3.3, 3.4, 3.6, 3.7, 4.0, 4.4, 4.8, 4.8, 5.2, 5.6

Sample Size(n) = 15

So Median = (n+1)/2th term

Median = (15 + 1)/2th term

Median = 16/2th term

Median = 8th term

So the 8th term in the given data is 3.6. So,

Median = 3.6

(d) We have to compute the 20% trimmed mean for the above data set.

To compute the 20% termed mean, remove 20% of the largest and 20% of the smallest elements from the sample and compute the mean of the new sample.

New sample: 2.9 3.0 3.3 3.4 3.6 3.7 4.0 4.4 4.8

New Mean = 33.3/9

New Mean = 3.7

(e) We have to check is the sample mean for these data more or less descriptive as a center of location than the trimmed mean.

The mean value is 3.8, the median value is 3.6, and the trimmed mean value is 3.7. As a result, the sample mean is less descriptive as the location's center (median) than the trimmed mean.

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The complete question is:

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint.

3.4      2.5      4.8      2.9      3.6

2.8      3.3      5.6      3.7      2.8

4.4      4.0      5.2      3.0      4.8

Assume that the measurements are a simple random

sample.

(a) What is the sample size for the above sample?

(b) Calculate the sample mean for these data.

(c) Calculate the sample median.

(d) Compute the 20% trimmed mean for the above data set.

(e) Is the sample mean for these data more or less descriptive as a center of location than the trimmed mean?

General Formulas and Concepts:

Step 1: Define expression

Step 2: Expand

Steps:

Let's solve for f.

( 5 /7 x) (f)orx = −8

Step 1: Divide both sides by (5orx^2)/7.

For more steps see the attachment

Description:  

The first step is to simplify the equation step by step and to simplify an equation you can first multiplying the factors and use the exponent rules to remove the parentheses. After that you need to combine it a terms. Then you will get your answer.

Answer:  f=   −56  / 5orx²

Hope this helps.

Answer:

\(\sqrt{y}\) ÷ xz²

Step-by-step explanation:

multiply the exponent of 'x' by -2 to get -1

multiply the exponent of 'y' by -2 to get 1/2

multiply the exponent of 'z' by -2 to get -2

= (x^-1)(y^1/2)(z^-2)

= 1/x · \(\sqrt{y}\) · 1/z²

=  \(\sqrt{y}\) / xz²

Answer:

it is because the volume of the box is 200in^2

30 dollars

Step-by-step explanation:

Answer:

3 for every 45 students

Step-by-step explanation:

so 3 for 45

4 90

Answer:

2739 stickers

Step-by-step explanation:

So first, Derrick has 304 sheets of stickers and 12 stickers on each sheet. You need to find the total number of stickers he has before you do anything else. To find this out just multiply 304x12. When doing this you get 3648. Now that you have the total number of stickers you can subtract the amount he gives to his friends. Take 3648 and subtract 909 from it. When you do that you get 2739. So, Derrick has 2739 stickers left over. Make sure to add units!

Answer: 15

Step-by-step explanation: in 2 years its population grows by 30 so you divide that by 2 and you get 15.

The population in 4 year is 160 and in 6 year is 320.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

We have,

For, year= 0 the population= 10

and, Year=2 the population = 40

So, the changing factor is

= 40/10

= 4

Then, for 4 year the population

= 10 x 2⁴

= 10 x 16

= 160

and, For 6 year the population is

= 10 x 2⁶

= 10 x 32

= 320

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The A⁻¹ of the given matrix is \(\dfrac{1}{-12}\left[\begin{array}{cc}8&-4\\-2&-3\\\end{array}\right]\).

The inverse of the matrix is calculated by the ratio of the adjoint of the given matrix A to the determinant of the matrix A.

The inverse of a matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix.

The formula to calculate the inverse of a matrix is,

\(A_{Adj}=\left[\begin{array}{cc}8&-4\\-2&-3\\\end{array}\right]\).

The determinant of the matrix is,

D = [ad - bc ]

D = [ (-3 x 8 ) - ( 4 x -2 ) ]

D = -12

The inverse of the matrix will be,

\(A^{-1}=\dfrac{1}{ab-bc}\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right]\\A^{-1}=\dfrac{1}{(-3\times 8)-(4\times -2)}\left[\begin{array}{cc}8&-4\\2&-3\\\end{array}\right]\\\\A^{-1}=\dfrac{1}{-12}\left[\begin{array}{cc}8&-4\\2&-3\\\end{array}\right]\\\\\)

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Answer: The number is 192

Step-by-step explanation:

Ricardo's model of trade is an economic theory of comparative advantage that explains how trade can benefit all parties involved, even when one party has an absolute advantage in the production of all goods.

The model focuses on two countries: the US and Fiji, producing two goods - bananas (Y) and machines (X).

The labor unit requirements are as follows:

(i) Pattern of trade:

In this case, the US has a comparative advantage in machines, while Fiji has a comparative advantage in bananas. Therefore, the pattern of trade will be that the US will produce machines and trade them with Fiji, while Fiji will produce bananas and trade them with the US. The US will import bananas from Fiji and export machines to Fiji, while Fiji will import machines from the US and export bananas to the US.

(ii) Gains from trade:

The gains from trade are the benefits that both countries enjoy as a result of engaging in free trade. These gains can be illustrated using production possibility frontier (PPF) diagrams, which show the maximum combinations of two goods that a country can produce with its available resources.

Before trade, the PPF for the US shows that it can produce 800 machines or 400 bananas. The PPF for Fiji shows that it can produce 1000 machines or 250 bananas. Thus, the total world production before trade is 1800 machines and 650 bananas.

The autarky prices of machines and bananas in the US are 2 and 0.5, respectively, while in Fiji they are 4 and 1, respectively. The international price ratio of machines and bananas is 1:1.

(iii) Total world production of both goods before and after trade:

Before trade, the total world production of machines and bananas was 1800 machines and 650 bananas. After trade, the total world production of machines and bananas is 1000 machines and 750 bananas for the US, and 800 machines and 500 bananas for Fiji. Therefore, the total world production of machines and bananas has increased after trade.

(iv) Autarky and international price ratios:

Autarky prices refer to the prices of goods in a country that is not engaging in trade. In this case, the autarky prices of machines and bananas in the US are 2 and 0.5, respectively, while in Fiji they are 4 and 1, respectively. The international price ratio of machines and bananas is 1:1.

(v) Trade triangles:

Trade triangles demonstrate the gains from trade by comparing the pre-trade production and consumption of a good to the post-trade production and consumption. In this case, the trade triangle for the US shows that it exports 200 machines and imports 400 bananas. The trade triangle for Fiji shows that it exports 150 bananas and imports 300 machines. These trade triangles further illustrate the gains achieved through trade.

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Answer:

Step-by-step explanation:

12*15

180

Answer:

X=9

Step-by-step explanation:

15^2=12^2+x^2

225 = 144 +x^2

225-144=x^2

81 =x^2

squareroot(81) = x

Answer:

1,200

Steps down below

Step-by-step explanation:

Steps

1:  48=4% loaded on truck and they have 96% left to load

2: so set up a proportion and it should look like this

3: 48 over x = 4 over 100

4: 48/x=4/100

6: do cross multiplication 100×48= 4,800÷ 4 = 1,200 total on truck

Answer: 1,200 total on truck

Hope this helps.

Answer:

202

Step-by-step explanation:

4th answer

Answer:

9 is the answer u are looking for square root

Step-by-step explanation:

you take the specific number (males prefer cycling = 0.22) and the fitting total.

note there are 2 possibilities for that total :

all males

all people preferring cycling

the way it was phrased I would say the reference is all males.

the conditional relative frequency is then

0.22 / 0.54 = 0.407407407... ≈ 0.41

but if the meaning would be rather about how many of all people preferring cycling are male, then we would have

0.22 / 0.37 = 0.594594595... ≈ 0.59

both results are in your answer options.

I think the intended result is 0.41, because I understand the problem that way :

find the conditional relative frequency that a student athlete surveyed prefers cycling, given that the student is male.

the other should be phrased like

find the conditional relative frequency that a student athlete surveyed is male, given that the student prefers cycling.

6. r║s based on the: Consecutive Interior Angles Converse Theorem.

10. m<2 = 34°

The Consecutive Interior Angles Converse Theorem states that if two lines are intersected by a transversal, and the consecutive interior angles formed are congruent, then the lines are parallel.

6. Since m<7 + m<8 = 180°, therefore, lines r and s are parallel lines based on the Consecutive Interior Angles Converse Theorem.

10. m<1 = 180 - 72 [linear pair theorem]

m<1 = 108°

m<2 = 180 - 108 - 38 [triangle sum theorem]

m<2 = 34°

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The probability that the second card is higher in rank than the first card can be calculated using the fact that the probability of drawing a higher card is equal to the probability of drawing a lower card.

Let's denote P(higher) as the probability of the second card being higher than the first, P(lower) as the probability of the second card being lower than the first, and P(same) as the probability of the second card being the same rank as the first.

Using this notation, we can express the probability of the second card being higher in rank than the first as follows:

P(higher) = 1 - P(lower) - P(same)

Therefore, the probability that the second card is higher in rank than the first card is 1 minus the probability of the second card being lower than the first card minus the probability of the second card being the same rank as the first card.

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Answer:

It is, D

Step-by-step explanation:

Your welcome for raising your test score

Answer:

-12

Step-by-step explanation:

Answer:

1) Measure angle QWT and TWX are complementary because their measures add up to 90 degrees.

2) Both measure angles add up to 90 degrees because they're complementary.

3) Angle QWT = 2x and angle TWX = x + 6, and since angles QWT + TWX = 90 then 2x + x + 6 = 90.

4) (Made up?:) Angle measure QWX = 90. The quarter-turn, or the small square, indicates that the angle is 90 degrees.

5) (?)

6) x = 28 because it fulfills the equation, 2x + x + 6 = 90, or 3x + 6 = 90. 90 - 6 is 84, and 84/3 is 28.

Please, tell me if I did anything wrong. I'll gladly edit it.

Answer:

Step-by-step explanation:

2). Definition of complementary angles;

3). Substitution+combine like terms;

4). 3x+ 6 - 6 = 90 - 6   Subtraction Property

5). 3x/3 = 84/3    Division Property  

6). Q.E.D. ("that which was to be demonstrated")

a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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Based on this prediction, we can expect the pointer to land on the vowels (A and E) approximately 64 times in 200 trials.

To make a prediction for 200 trials based on the given data, we can assume that the probabilities observed in the 50 trials will remain consistent in the long run. We can use this assumption to estimate the number of times the pointer will land on the vowels (A and E) in 200 trials.

In the given data, the total number of spins recorded is 10 + 14 + 12 + 8 + 6 = 50 spins. We can calculate the proportion of spins for each letter by dividing the number of spins for that letter by the total number of spins:

Proportion of A = 10/50 = 0.2

Proportion of B = 14/50 = 0.28

Proportion of C = 12/50 = 0.24

Proportion of D = 8/50 = 0.16

Proportion of E = 6/50 = 0.12

Now, we can use these proportions to estimate the number of spins on the vowels in 200 trials. Since the vowels (A and E) have a combined proportion of 0.2 + 0.12 = 0.32, we can multiply this proportion by the total number of trials:

Number of spins on vowels = 0.32 * 200 = 64

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