on a recent shopping trip, you see a sale advertising 5 pairs of socks and 2 pairs of shoes for $100. write an equation using x to represent the cost of socks and y to represent the cost of shoes.

According to this information, investments with 4.2, 1.3 and 2.8 interest have a profit of more than $100. On the other hand, investments with interest of 0.75 and 5.2 have a profit of less than $100.

To calculate the profit of these investments we must carry out the following procedure:

1. We must divide the interest in 100

2. We must multiply the interest by the total value of the investment ($1500).

3. We must multiply the result by the number of years of the investment.

4. We must classify the result as less than or greater than $100.

According to the above, investments with 4.2, 1.3 and 2.8 interest have a profit of more than $100. On the other hand, investments with interest of 0.75 and 5.2 have a profit of less than $100.

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According to the central limit theorem, difference of sample mean of two normal populations will also fill normal distribution if the sample size is at least 30 .

What does a statistical sample distribution mean?

An example of a sampling distribution is a probability distribution of a statistic that is derived from repeated sampling of a particular population. It describes a variety of potential possibilities for a statistic, such the mean or mode of some variable in a population.

What are the different forms of sample distribution?

This idea, which is a sort of probability distribution, is frequently used to gather precise data from a huge population that has been divided into a number of samples that have been chosen at random.

                             This idea is further broken down into three categories: sampling Distribution of the mean, percentage, and T-Sampling.

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The complete question is -

Ata large university, the division of computing services surveyed random sample of 45 biologv majors and 55 business majors from populations of over 1,000 biology and O00 business majors. The sampled students were asked how many hours they spend per week using any university computer lab. Let represent the average hours per week spent in any university computer lab by the 45 biology majors, and let 1, represent the average hours per week spent in any university computer lab by the 55 business majors. Which of the following Is the best explanation for why the sampling distribution of can be modeled with a normal distrlbution? A) The two sample standard deviations are assumed to be equal_

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is always the same. In this case, the common difference is 3, so every term is 3 more than the previous term.

The [tex]$n^{th}$[/tex] term in the arithmetic sequence can be found using

[tex]$a_n = a_1 + (n - 1)d$[/tex]

where $a_1$ is the first term (2 in this case), $d$ is the common difference (3 in this case), and $n$ is the term number.

To find the page number that $11{,}111$ appears on, we need to find the term number that corresponds to this value:

[tex]$11{,}111 = 2 + (n - 1) \cdot 3$[/tex]

Solving for $n$, we have:

$11{,}109 = 3n - 1$

$3n = 11{,}110$

$n = 37{,}037$

Since each page contains 100 numbers, the number 11,111 appears on page $\left\lceil \frac{37{,}037}{100} \right\rceil = 371$.

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Answer:

12w+19

Step-by-step explanation:

[tex]3(4w + 2) + 13[/tex]

[tex]3(4w) + 3(2) + 13[/tex]

[tex]12w + 6 + 13[/tex]

[tex]12w + 19[/tex]

12suitcase

The height of the cone is 0.083 inches

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

Volume = 1024π cubic inches

Radius = 16 feet

Convert the radius to inches

So, we have the following representation

Radius = 192 inches

The volume of a cone is

Volume = 1/3πr^2h

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

1/3πr^2h =  1024π

So, we have

r^2h =  3072

This gives

h = 3072/(192^2)

Evaluate

h = 0.083

Hence, the heightt is 0.083 inches

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Answer:  Richard is 22 and Teo is 9

Step-by-step explanation:

The solution to the given inequality  [tex]-5f + 6 > 10f - 10[/tex] is [tex]f < 16/15[/tex].

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The inequality is given in the question, as follows:

[tex]-5f + 6 > 10f - 10[/tex]

To solve the inequality [tex]-5f + 6 > 10f - 10[/tex], we need to isolate the variable [tex]f[/tex] on one side of the inequality.

We will first subtract 6 from both sides to isolate the [tex]-5f[/tex] term:

[tex]-5f + 6 - 6 > 10f - 10 - 6[/tex]

Simplifying the left side:

[tex]-5f > 10f - 16[/tex]

Next, we will subtract [tex]4f[/tex] from both sides to isolate the [tex]-5f[/tex] term on the left side:

[tex]-5f - 10f > 10f - 10f - 16\\-15f > -16[/tex]

Finally, we will divide both sides by -9,

[tex]-( 15 f )/9 > -16/15[/tex]

Dividing both sides by -15:

[tex]f < 16/15[/tex]

This is the required solution to the given inequality.

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The probability that candidate B is going to win the election is 2.

The probability of candidate A winning the election is 0.5, the probability of candidate B winning the election is 2, the probability of candidate C winning the election is 1/3 and the probability of candidate D winning the election is 2/3.

Therefore, the candidate most likely to win the election is candidate B, and the probability that they are going to win is 2. This can be calculated using the formula for probability, which states that the probability of an event occurring is the number of favourable outcomes divided by the total number of outcomes. In this case, the number of favourable outcomes is 1 and the total number of outcomes is 3, so the probability of candidate B winning is 1/3.

Therefore, the probability that candidate B is going to win the election is 2.

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The length of the diagonal is 12.6 feet.

"Information available from the question"

The perimeter of a rectangle is 32 feet.

The length is three times as long as the width.

We have to find the length of the diagonal.

Let w = width

then

3w = length.

Because we know the perimeter:

Perimeter of the rectangle is : 2(l + w)

32 = 2(w + 3w)

32 = 2(4w)

16 = 4w

4 feet = w (width)

Length:

3w = 3(4) = 12 feet

Diagonal, we use the Pythagorean theorem:

Let d = diagonal

then,

[tex]d^2 = 4^2 + 12^2[/tex]

[tex]d^2[/tex] = 16 + 144

[tex]d^2[/tex] = 160

d = 12.6 feet

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The value of x is obtained as follows:

128º.

The measure of angle A is given as follows:

m < A = 132º.

For a parallelogram, the opposite angles are congruent, meaning that they have the same measure, hence the value of x is obtained as follows:

5x - 508 = x + 4.

4x = 512

x = 512/4

x = 128.

Then the measure of angle A is given as follows:

m < A = 5(128) - 508

m < A = 132º.

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The value of the trigonometric function is -

sin(θ) = 21 / 29,

cos(θ) = 20/29,

csc(θ) = 29/21,

sec(θ) = 29/20,

cot(θ) = 20/21.

In a nutshell, trigonometric functions, also referred to as circular functions, are the functions of a triangle's angle. This suggests that these trig functions provide the relationship between a triangle's angles and sides. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given that,

tan (θ) = - 21 / 20

We can infer from the value that the triangle's two legs are 21 and 20, respectively.

Using the Pythagorean theorem, we can:

[tex]a^{2} + b^{2} = c^{2}[/tex]

[tex](21)^{2} + (20)^{2} = c^{2}[/tex]

441 + 400 =[tex]c^{2}[/tex]

c = 29

The value of :

sin(θ) = 21 / 29

cos(θ) = 20/29

csc(θ) = 29/21

sec(θ) = 29/20

cot(θ) = 20/21

Hence, the value of the trigonometric function is

sin(θ) = 21 / 29,

cos(θ) = 20/29,

csc(θ) = 29/21,

sec(θ) = 29/20,

cot(θ) = 20/21.

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Answer:

250

Step-by-step explanation:

190 students = 76%

190/76=2.5

2.5 x 100 =250

In a residual plot, the residuals are plotted against the predictor variable. Ideally, the residuals should be randomly scattered around zero, without any patterns or trends.

If there is a pattern, it suggests that the linear model is not an adequate representation of the data and a more complex model may be necessary.

In this case, the residual scatter plot shows that the residuals are randomly scattered around zero, which suggests that a linear model is appropriate for summarizing the relationship between the predictor and response variables. This means that a straight line can be used to approximate the relationship and make predictions based on the data.

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The water's height at 8:30 PM is approximately 0.69 feet.

As per the data given in the question,

We have the equation,

depth = 4 * sin (0.5 * t)

where t is the number of hours after midnight.

As we need to find the depth of the water at 8:30 PM,

For finding the value of the depth at 8:30 PM we need to first convert 8:30 PM to the number of hours after midnight.

8:30 PM = 20.5 hours after midnight

So, substituting t = 20.5 into the equation,

we will get it as:

depth = 4 * sin (0.5 * 20.5)

depth = 4 * sin (10.25)

depth = 4 * 0.1736481776669303

depth = 0.6945971520676809

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The volume of one carton of strawberries is 200 in³.

The volume of all of the cartons of strawberries is 6,000 in³.

The volume of each carton can be determined by multiplying the length, width and height together.

Volume = length x width x height

10 x 4 x 5 = 200 in³

The volume of all the boxes of strawberries can be determined by multiplying the number of cartons by the volume of one carton.

Volume of the 30 cartons of strawberries = 200 in³ x 30 = 6,000 in³

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The formula to solve for the height of a given triangle is =h=2A/b

Given the area of a triangle formula = A=1/2×b×h

where , A=area of the triangle.

b=base of the triangle.

h=height of the triangle.

To find the height of the triangle using this formula=

A=1/2×b×h

2A=b×h

h=2A/b

thus,h=2A/b is the formula to solve for the height of a given triangle.

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Answer: 900

Step-by-step explanation:

The Interior Angle formula is (n-2)x180. So you take 7 minus 2 times 180 and that gives you 900

Answer3rd one and 1st

Step-by-step explanation:

The system of equations graphically on the set of axes is given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

y = (1/6)x + 7

y = -2x - 6

The graph of each equation is given below.

The point of intersection is (-6, 6).

i.e,

(1/6)x + 7 = -2x - 6

(1/6)x + 2x = -6 - 7

13x/6 = -13

x/6 = -1

x = -6

So,

y = -2x - 6

y = -2 x -6 - 6

y = 12 - 6

y = 6

Thus,

The system of equations graphically is given above.

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The simplified expression for this problem is given as follows:

9 - 13j/7.

The expression for this problem is defined as follows:

16 + (-4) - 5j/7 - 6j/7 + 7.

The plus sign means that the sign is maintained, hence:

16 + (-4) - 5j/7 - 6j/7 + 7 = 12 - 5j/7 - 6j/7 + 7.

Then we combine the like terms, as follows:

Hence the simplified expression is given as follows:

9 - 13j/7.

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The probability that a tire of this brand will last longer than 58,000 miles is  0.8413 or 84.13%.

Given in the question that the tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2000 miles.

We have to calculate the probability that a particular tire of this brand which will last longer than 58,000 miles.

The standard normal variable corresponding to the given tire's tread life being longer than 58,000 miles can be calculated using the z-score formula:

The formula for computing a z-score is =(DataValue-Mean)/StDev

Therefore , we can write z = (58,000 - 60,000) / 2000

Hence, z = -1

Next, we can use a standard normal table to find the probability that a standard normal variable will be less than -1:

P(Z < -1) = 0.1587

Hence P = 1 - 0.1587

            P = 0.8413

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To create a scale illustration of her bedroom, Elena must draw a 10cm by 6cm rectangle.

To create a scale illustration of her bedroom she must take into account the scale she will be using. In this case it would be 1:50, that is, each original unit must be divided into 50 parts. Therefore, we must divide the lengths into 50 as shown below. Additionally we must take the values in cm.

According to the above, a scale model would be 10cm by 6cm.

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Given the following subset phrases are neither is a subset of the other. A set whose elements are all members of another set is simply referred to as a subset.

Because U.S. citizenship can also be acquired through other means, the group of people born in the country is a subset of the group of people who are citizens of the country. The group of Java learners all belong to the group of learners of a programming language, so Because Java is simply one of the many distinct kinds of programming languages, the group of students studying Java is a subset of the group of students studying a programming language. Since fish are just one of the many different marine species that dwell in the ocean, fish are a subset of the animals that live in the ocean.

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Answer: 4

Step-by-step explanation:

(-88) - (-44) = -36

remove the (-) = 36

36 ÷ 9 = 4