brewer, a graduate student, would like to determine how often college students are going to local restaurants to eat lunch instead of eating on campus. which method should be used to gather data? case study

The value of your investment at maturity is $16,800. The interest is $9,800.

What is the meaning of initial investment?

The initial sum of money required to open an account or start a buy-in relationship is known as an initial investment. The two distinct but related industries of banking and long-term investment brokering are the main uses of the term "initial investment."

Given that the initial investment is $7,000. The rate of interest is 10% = 0.10. The number of years of investment is 14 years.

The formula of simple interest is

I = Prt

I = interest, P = principal, r = rate of interest, t = time.

Putting P = 7000, r = 0.10, t = 14 in I = Prt:

I = 7000 × 0.10 × 14

I = 9,800

The amount will be interest + principal = 9800+ 7000 = 16,800.

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The solution to the system of linear equations is: x = 5, y = (6x + 7 - 10/4)/(-5) = -4/5, z = -5/4.

To solve the system of linear equations using elimination, we can manipulate the coefficients of the variables to make one of the variables zero in one of the equations. Then, we can use this equation to eliminate that variable from the other equations.

Starting with the first two equations:

6x - 5y - 4z = -7

5x - 4y - 4z = -5

We can multiply the first equation by 5 and the second equation by 6 to get rid of the coefficients of x in both equations:

30x - 25y - 20z = -35

30x - 24y - 24z = -30

Now, we can subtract the first equation from the second equation to eliminate x:

0y - 4z = 5

So, z = -5/4

Next, we can use this value of z to solve for y in either of the first two equations:

6x - 5y - 4(-5/4) = -7

Expanding the right side:

6x - 5y + 10/4 = -7

And solving for y:

y = (6x + 7 - 10/4)/(-5)

Finally, we can use the value of y and z to solve for x in any of the first two equations:

6x - 5((6x + 7 - 10/4)/(-5)) - 4(-5/4) = -7

Expanding and solving for x:

6x - (6x + 7 - 10/4)/5 - 10/4 = -7

Multiplying both sides by 5:

30x - 6x - 7 + 2 = -35

And solving for x:

x = 5

Finally, we can use the values of x, y, and z to check the third equation:

3y + 6z = 6

Substituting the values we found:

3((6x + 7 - 10/4)/(-5)) + 6(-5/4) = 6

Expanding and solving:

The left side is equal to 6 and the right side is equal to 6, so the solution is consistent.

Therefore, the solution to the system of linear equations is:

x = 5, y = (6x + 7 - 10/4)/(-5) = -4/5, z = -5/4

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Answer: The answer is 1/4.

Step-by-step explanation:

Answer:To calculate the length and width of the original figure with a scale factor of 50%, you need to reverse the scaling by multiplying the new dimensions by 100% / 50% = 2.

So if the new length is L, the original length would be L * 2 = 2L. Similarly, if the new width is W, the original width would be W * 2 = 2W.

Step-by-step explanation:here's a step-by-step explanation:

Identify the new length (L) and new width (W) of the figure.

Multiply the new length by a factor of 2 to find the original length: 2L = L * 2

Multiply the new width by a factor of 2 to find the original width: 2W = W * 2

The original length is 2L and the original width is 2W.

Note: This process works for any scale factor, not just 50%. To find the original dimensions, simply multiply the new dimensions by 100% / the scale factor.

The sample space for choosing one card is, S={I, L, L, M, P, T, U, Y}

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.

Given that,

A set of eight cards were labeled with M, U, L, T, I, P, L, Y.

Here, the sample space is;

{ S, U, B, T, R, A, C, T}

Now, Elements in order is,

⇒ S = {I, L, L, M, P, T, U, Y}

Therefore, the sample space for the given cards is,

S = {I, L, L, M, P, T, U, Y}

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Answer: I think the answer would be C

The value of in x° is sin x = 3/z

The ratio of an angle's opposing side to its adjacent side, or its tan

tan x = 3/y

cos x = y/z

We choose 3 and y to represent the opposite and adjacent sides, respectively, because this ratio is 3:y.

Technically, we ought to write 3t and yt, but we'll take a chance since y appears in the second ratio as well!

Since y is already used to represent the adjacent side, z is used to represent the length of the hypotenuse.

The right triangle's sides are now finished.

Because tan x = sin(x)/cos(x), therefore

sin x = tan(x)*cos(x)

        = (3/y)*(y/z)

        = 3/z

Answer: a) sin x = 3/z

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Answer:

X=5 Cars

Y=6 Vans

Step-by-step explanation:

Let's assume the number of cars used is x and the number of vans used is y.

We can set up two equations based on the information given:

x + y = 11 (the total number of vehicles used)

5x + 8y = 73 (the total number of students that went on the trip)

We can use substitution to solve for one of the variables in terms of the other:

y = 11 - x

5x + 8(11 - x) = 73

5x + 88 - 8x = 73

-3x = -15

x = 5

So the class used 5 cars and 11 - 5 = 6 vans.

The transaction should be recorded as an Accounts Payable (A/P) liability in Sanford’s financial accounting system.

Accounts Payable is a liability account that records the amount of money a company owes to its suppliers for goods and services that have been received, but not yet paid for. In this case, Sanford is responsible for paying the supplier $15,000 for the helmets that have been delivered to its warehouse.

This payment should be recorded in the Accounts Payable account as a debit of $15,000 and a credit to the Cash account of $15,000. By doing this, Sanford’s Accounts Payable balance will be reduced to reflect that the invoice has been paid, and the Cash account will be increased to reflect the payment made. This will keep the company’s financial records up to date and accurate.

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[tex]\cfrac{PQ}{XY}=\cfrac{QR}{YZ}\implies \cfrac{5}{30}=\cfrac{6}{YZ}\implies 5YZ=180\implies YZ=\cfrac{180}{5}\implies YZ=36 \\\\\\ \cfrac{PQ}{XY}=\cfrac{PR}{XZ}\implies\cfrac{5}{30}=\cfrac{10}{XZ}\implies 5XZ=300\implies XZ=\cfrac{300}{5}\implies XZ=60 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Perimeter of }XYZ}{30~~ + ~~36~~ + ~~60}\implies \text{\LARGE 126}[/tex]

First, we can find the total number of calendars sold by Rosie and Suzy combined:

19 (calendars sold by Rosie) + 26 (calendars sold by Suzy) = 45 calendars

Next, we can find the number of calendars sold by Juan:

Juan sold 4 times as many calendars as Rosie and Suzy combined, so Juan sold 4 * 45 = 180 calendars.

The theorem that proves that the two triangles are similar is the SAS Similarity Theorem. The theorem states that if two sides of one triangle are proportional to two sides of another triangle, and the included angle between these sides is the same in both triangles, then the two triangles are similar.

In this case, the ratio of the corresponding sides of the two triangles are:

AB/DE = 3/18 = 1/6

BC/EF = 7/42 = 1/6

Since the ratio of corresponding sides is equal, and the included angle between them (angle B and angle E) is the same, the two triangles are similar by the SAS Similarity Theorem.

The expression is factorized to give x(x+ 12) + 8( y + 12)

From the information given, we have that the expression as;

(x+y)²+8(x+y)+12

Now, expand the bracket, we get;

(x + 2) (x+2) + 8x + 8y + 12

expand the squared bracket, we get;

x² + 2x + 2x + 4 + 8x + 8y + 12

Now, collect like terms

x² 2x + 2x + 8x + 8y + 4 + 12

Add the collected like terms, we get;

x² + 12x + 8y + 16

Now, let's factorize in airs by grouping, we get;

(x² + 12x) + (8y + 16)

Factor the common terms

x(x+ 12) + 8( y + 12)

Hence, the expression is x(x+ 12) + 8( y + 12)

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Answer:

Multiply by the inverse.

Answer: 45

Step-by-step explanation:

(15)/(1/3) is the same thing as multiplying the top (numerator), by the inverse of the bottom (denominator).

So we have the following: [tex]\frac{15/1}{1/3}[/tex]

Taking the inverse means flipping the fraction. The inverse of [tex]\frac{1}{3}[/tex] is [tex]\frac{3}{1}[/tex]. So we can keep the top, and multiply by the inverse.

[tex]\frac{15}{1}[/tex] X [tex]\frac{3}{1}[/tex] = 15 x 3 = 45.

Does this make sense?

Answer: 12 11/26 laps

Step-by-step explanation:

9 3/13= 9 6/26

9 6/26+ 3 5/26=12 11/26.

The probability of odd or less than 6 is 0.75 which is 75%

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

From the question, there are 4 numbers

These include: 5,6,7,8

Pr(odd) 2/4

Pr(x<6) 1/4

Adding the fractions we have

1/2  + 1/4  = 3/4  = 0.75

Converted to percentage = 75%

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The shortest distance between planet Q and planet R is  1.64 × 10⁷ .

RP = 1.6 * 10⁷

most compact distance

The Pythagoras theorem x₂ = R * P² + Q * P² is then used to determine the shortest distance (x).

This results in x = (3.6 * 10⁶) + (1.6 * 10⁷) = 2.

x² = 12.96 * 10¹²  + 2.56 * 10¹⁴ should be evaluated.

Write the equation as: x²= 12.96 * 10¹² + 256 * 10¹²

Sums x² = 268.96*10¹² should be evaluated.

multiply both sides' square roots.

x = 16.4 * 10⁶

Replace with: x = 1.64 * 10⁷

In light of this, the distance between planet Q and planet R is 1.64 * 10⁷ km.

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The complete  question is

The distances between some planets are given below.

Planet Q is 3.6 x 10⁷ to the power of 6 km from planet P.

Planet R is 1.6 x 10⁷ to the power of 7 km from planet P.

Work out the shortest distance between planet Q and planet R. Give your answer in standard form.

The area of the shaded region is 17.4 rounded up to the nearest tenth.

The unshaded region forms a circle with a radius of 9/2, so to get the area of the shaded region, we subtract the area of the circle from the area of the square as follows:

area of square = 9 m × 9 m = 81 m²

area of the circle = 22/7 × 9/2 × 9/2

area of the circle = 891/14 m²

area of the shaded region = 81 m² - 891/14 m²

area of the shaded region = (1134 - 891)/14

area of the shaded region = 243/14

area of the shaded region = 17.3571

Therefore, the area of the shaded region is 17.4 rounded up to the nearest tenth.

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The number of ways you can select n elements from N elements by using factorial (!) when n=2 and N=10 is 45.

Factorial is a crucial mathematical operation that is used to determine the number of possible arrangements or the ordered set of numbers. Daniel Bernoulli is credited with discovering the factorial function's well-known interpolating feature. Numerous mathematical ideas, including probability, permutations and combinations, sequences and series, etc., use the factorial concept. A factorial function, in essence, multiplies a number by each number below it until it equals 1. For instance, the factorial of 3 is equal to 6 and reflects the multiplication of the integers 3, 2, and 1.

Now,

The number of ways you can select n elements from N elements when n=2 and N=10 is [tex]\frac{N!}{n!(N-n)!}[/tex]

=[tex]\frac{10!}{2!(8)!}[/tex]

=[tex]\frac{10 \times 9 \times \times 8!}{8! \times 2 !}[/tex]

=45

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True. The variance and standard deviation both quantify how far spaced apart a set of data is from the mean. They cannot be used to calculate the dispersion around the median or mode, or any other center-of-mass metric.

The variance and standard deviation both quantify how far spaced apart a set of data is from the mean. They can therefore be used to calculate the difference between the highest and lowest values in a data set. The standard deviation, which is the square root of the variance, is used to calculate how far away from the mean each result is on average. The average of the squared deviations between each data point and the mean is the variance. The variance and standard deviation cannot be used to quantify the dispersion of data around other measures of center, such as the median or mode, because they only measure the dispersion of data around the mean.

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The number which satisfies the given condition is 28.

According to the question

The number 28 is less than 50 and has a multiple of 7. It becomes 82, which is also a multiple of 8 when its digits are inverted. As a result, the criteria can only be satisfied by the number 28. This may be verified by quickly determining whether any other number less than 50 that is a multiple of 7 has its digits switched around to become a multiple of 8. However, it is clear that none of the other figures satisfy both requirements.

In light of this, the answer to this issue is 28.

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The number which satisfies the given condition is 28.

According to the question

The number 28 is less than 50 and has a multiple of 7. It becomes 82, which is also a multiple of 8 when its digits are inverted. As a result, the criteria can only be satisfied by the number 28. This may be verified by quickly determining whether any other number less than 50 that is a multiple of 7 has its digits switched around to become a multiple of 8. However, it is clear that none of the other figures satisfy both requirements.

In light of this, the answer to this issue is 28.

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Answer:

Step-by-step explanation:

You're right; it's 97 degrees. The angles of a triangle add up to 180, so to solve for each triangle's unknown angle value, subtract the known angles from 180. For the left triangle, that's 33 and for the right triangle it's 50. Those missing angles plus the one the question is asking for should add up to 180 degrees as well. Hence, 180 - 33 - 50 = 97.

The area of the logo is 6 square feet.

We start wit a logo of 4 inches by 6 inches, and we want to make it 6 times larger, so the new dimensions are:

6*(4 inches) = 24 inches.

6*(6 inches) = 36 inches.

Remember that:

1ft = 12 in

Writting that in feet, we will get:

24 inches = (24/12) ft = 2ft

36 inches = (36/12) ft = 3ft

Then the area of the logo is:

A = 2ft*3ft = 6 ft²

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The equation of a radical function can be determined by using the transformation rules for x- and y- shifts, stretches/compressions, reflections, and rotations.

The equation of a radical function can be determined by applying various transformation rules. The most common transformations are shifts, stretches/ compressions, reflections, and rotations. For example, a radical function that is shifted left two units would have an equation of y = sqrt(x + 2). This is because the function is shifted two units to the left of the origin, so the equation must include an x + 2 term. Similarly, if the function is reflected in the x-axis, the equation would be y = -sqrt(x). This is because the reflection inverts the sign of the y-coordinate, so the equation must include a negative sign in the radical. For stretches and compressions, the equation must include a coefficient in front of the radical. For example, if the function is stretched horizontally by a factor of 3, then the equation would be y = 3 sqrt(x). This is because the function is stretched by a factor of three, so the equation must include a coefficient of 3 in front of the radical. Finally, for rotations, the equation must include a term for the angle of rotation. For example, if the function is rotated counterclockwise by 45 degrees, then the equation would be y = sqrt(x + y/tan45). This is because the angle of rotation is 45 degrees, so the equation must include a tan45 term.

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The average rate of change over for the interval 1 < x < 5 k(x) greater than the average rate of change over of g(x)

A function is a relationship between inputs where each input is related to exactly one output.

We have,

g(x) = 1.8 [tex]x^{2}[/tex]

The average rate of change of g(x) over the interval 1 < x < 5:

= [tex]$\frac{g(5)-g(1)}{5-1}[/tex]

= [tex]$\frac{1.8 \times (5)^{2} -1.8 \times(1)^{2} }{5-1}[/tex]

= [tex]$\frac{43.2}{4}[/tex]

= 10.8..............(1)

The average rate of change of f(x) = [tex]x^2[/tex] in the interval 1 < x < 5:

= [tex]$\frac{25-1}{4}[/tex]

= [tex]$\frac{24}{4}[/tex]

= 6..............(2)

The average rate of change of g(x) = 1.2 [tex]x^2[/tex] in the interval 1 < x < 5:

= [tex]$\frac{28.8}{4}[/tex]

= 7.2.................(3)

The average rate of change of h(x) =1.5 [tex]x^2[/tex] in the interval 1 < x < 5:

= [tex]$\frac{36}{4}[/tex]

= 9...........(4)

The average rate of change of k(x) = 2 [tex]x^{2}[/tex] in the interval 1 < x < 5:

= [tex]$\frac{48}{4}[/tex]

= 12.........(5)

From (1), (2), (3), (4), and (5) we see that,

The average rate of change of [tex]$\mathbf{k}(x)=2 x^2$[/tex] is larger than the average rate of change of [tex]$g(x)=1.8 x^2$[/tex].

12 > 10.8

Thus,

Option D is the correct answer.

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When rotated about its center, a regular heptagon has 7 rotational symmetries. In addition to rotational symmetry, a regular heptagon has 1 line of reflectional symmetry.

Rotation symmetry, also known as radial symmetry or circular symmetry, is a fundamental concept in geometry that refers to the property of a shape to remain unchanged after rotating it about a fixed point. This point is typically the center of the shape, although it can be any point within the shape.

The amount of rotation required for the shape to become congruent to its original form is called the "angle of rotation." If a shape can be rotated multiple times and still remain unchanged, it is said to have multiple rotational symmetries.

For example, a circle has an infinite order of rotational symmetry, as it can be rotated 360 degrees and still look exactly the same. On the other hand, a square has 4 rotational symmetries, as it can be rotated 90 degrees and still look the same 4 times.

Rotational symmetry is a useful concept in mathematics and science as it provides a way to describe the symmetry of objects and shapes in the real world. It also helps us understand how objects and shapes change when they are rotated, and it provides a way to classify objects based on their symmetrical properties.

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The length d for the angle of depression 3° and altitude 1m is equal to 19 m to the nearest metre using the trigonometric ratio of cosine for the angle 87°

The angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards.

Considering the right triangle formed by the length d and the altitude of 1 m, we shall derive a complementary angle as:

90° - 3° = 87°

such that;

cos 87° = 1/d {adjacent/hypotenuse}

d = 1/cos 87°

d = 19.1073.

Therefore, the length d for the angle of depression 3° and altitude 1m is equal to 19 m to the nearest metre using the trigonometric ratio of cosine for the angle 87°.

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It is not possible to describe the standard deviations of salary, hourly rate, years worked, education, and age without having the data.

Standard deviation is a measure of the spread or dispersion of a set of data. It is calculated as the square root of the variance and is used to give an idea of how far the individual values in a data set are from the mean or average.

In order to describe the standard deviations of salary, hourly rate, years worked, education, and age, we would need to have the actual data for those variables. Without the data, it is not possible to calculate the standard deviations and describe what they tell us about the variables.

It is important to note that the standard deviation can give us information about the distribution of the data and the variability of the values. For example, if the standard deviation is small, this means that the majority of the values are close to the mean, while a larger standard deviation indicates that the values are more spread out. This information can be useful in making inferences about the variables and in making predictions about future values.

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The inequality and number line that shows the solution is x>-7.

Given,

-4x <28

(-4x) (-1) > 28 (-1)

Simplify

4 x>-28

Divide both sides by 4

[tex]\frac{4 x}{4} > \frac{-28}{4}[/tex]

Simplify

x>-7

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The area enclosed between the graph of Æ and the x-axis for 1 ≤ x ≤ 3 is estimated to be 4/3.

Ram's Rule is a numerical integration method used to estimate the area under a curve by dividing it into trapezoids. The formula for calculating the area under the curve is given by A = (1/2) x (b - a) x (f(a) + f(b)), where A is the area, b and a are the limits of the integration and f(a) and f(b) are the values of the function at the limits a and b respectively.

In this case, the area enclosed between the graph of Æ and the x-axis for 1 ≤ x ≤ 3 can be estimated using Ram's Rule as follows:

A = (1/2) x (3 - 1) x (1/1 + 1/3)

 = (1/2) x (2) x (4/3)

 = 4/3.

Therefore, the area enclosed between the graph of Æ and the x-axis for 1 ≤ x ≤ 3 is estimated to be 4/3.

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