Philip is going on a 400040004000-kilometer road trip with three friends. The car consumes 666 liters of gas per 100100100 kilometers, and gas costs \$1.50$1.50dollar sign, 1, point, 50 per liter.

The length of line segment WU is 4 cm.

Hence, 4 cm is correct.

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Now, As given that, RSTU is an parallelogram.

RT and SU are its two diagonals.

They intersect each other at point W.

Properties of parallelogram is that they bisect each other.

i.e SW = WU and RW = WT

As given that, SW = 4 cm.

So, WU = SW = 4 cm

Therefore, the length of line segment WU is 4 cm.

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Final answer:

To maximize the enclosed area, each kennel should be in the shape of a square with dimensions of 52.5 feet by 52.5 feet.

Explanation:

To maximize the enclosed area, each kennel should be in the shape of a square. Let's assume that each side of the square kennel has a length of x feet.

Each kennel has four sides, so the total length of fencing required for all four kennels is 4x feet.

Given that there are 210 feet of fencing available, we can set up the equation 4x = 210 and solve for x to find the length of each side of the square kennel.

Dividing both sides of the equation by 4, we get x = 52.5 feet.

Therefore, each kennel should have dimensions of 52.5 feet by 52.5 feet to maximize the enclosed area.

Final answer:

To find the length and width of the rectangle with an area of 156 square inches and a perimeter of 50 inches, we can set up and solve a system of equations based on the area and perimeter formulas. After solving, we determine that the length is 13 inches and the width is 12 inches.

Explanation:

The student has asked to find the length and width of a rectangle given that it has an area of 156 square inches and a perimeter of 50 inches. To solve this problem, we need to use the formulas for the area and perimeter of a rectangle.

Area and Perimeter Formulas

Area formula: A = length × width

Perimeter formula: P = 2(length + width)

Let's denote the length as 'l' and the width as 'w'. The area of the rectangle is 156, so we can write:

l × w = 156

The perimeter of the rectangle is 50, so we can write the perimeter formula as:

2(l + w) = 50

This simplifies to:

l + w = 25

Now, we have two equations:

l × w = 156

l + w = 25

We can solve this system of equations by expressing one variable in terms of another. Let's express 'w' in terms of 'l' from the second equation:

w = 25 - l

Now, substitute 'w' in the area equation:

l × (25 - l) = 156

This is a quadratic equation that can be solved to find the values of 'l'. Once we have 'l', we can find 'w' using the second equation.

After solving, we find that the length is 13 inches and the width is 12 inches. Therefore, the rectangle's dimensions are 13 inches by 12 inches.

Answer:

voluntary sampling

Step-by-step explanation:

Voluntary sampling involves someone opting to be a part of the sample.  In this situation, customers are given the option to stay on the line to answer a survey; this means it is on a voluntary basis.  Thus it is a voluntary sample.

The type of sampling is the cable company using is convenience sampling.

We do sampling so that we don't have to work on entire population of items but only on that sample in a way that we can predict information about population.

Most of the times, it isn't possible in real world to work on entire populations. Samples come out for rescue by assumptions that they will have some properties of the population pertained in them.

Thus, the sample should be taken out such that it includes data of the population as much  as it can in unbiased way so as to imitate population.

We are given that;

The cable company is using convenience sampling.

Convenience sampling involves selecting individuals who are convenient or readily available to participate in the study. In this case, the cable company is selecting individuals who call their customer service and happen to complete their call with a customer service representative. The individuals are not selected based on any specific criteria or randomly selected, but rather because they happen to call the cable company and complete a customer service call.

As the message specifically invites customers to stay on the line to answer the survey questions, it can also be considered a form of voluntary sampling, where individuals are invited to participate in a study and can choose whether or not to participate.

Therefore, by sampling the answer will be convenience sampling.

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Answer:

Step-by-step explanation:

To solve a triangle given two sides and included angle, use the law of cosines. This law is expressed as a² = b² + c² - 2bc cos(A), where a, b, c are the lengths of the sides, and A is the included angle.

To solve a triangle given two sides and the included angle, you would use the Law of Cosines. This law is used when you're given two sides and the included angle in a triangle (often abbreviated as SAS). The law states,

a² = b² + c² - 2bc cos(A)

where a, b, and c are the lengths of the sides of the triangle, and A is the included angle. So, in this case, if you're given sides b and c and included angle A, you would substitute these values into the formula to find side a.

For instance, if side b is 3 units, side c is 4 units, and angle A is 60 degrees, we would substitute these values into our formula like so:  a² = 3² + 4² - 2(3)(4) cos(60).

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The correct way to solve a triangles given two sides and the included angle is by the sine and cosine rule.

For angle placed in between two sides of a triangle, we can use the cosine rule to determine the unknown angle

According to the cosine formula, we will have:

[tex]a^2=b^2+c^2-2bc \ cos\theta[/tex]

where a, and c are the sides of the triangle and theta is the central angle.

Also, the remaining angles can be determined using the law of cosines as shown:
a/sinA = b/sinB = c/sinC

Hence the correct way to solve a triangles given two sides and the included angle is by the sine and cosine rule.

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Final answer:

The letter 'z' in mathematics can refer to various concepts including complex numbers with arguments measured in degrees, z-scores in statistics indicating deviation from the mean, and as a variable within equations and inequalities.

Explanation:

The concept of 'z' seems to refer to multiple mathematical contexts, including complex numbers, z-scores in statistics, and equations involving z. Specific examples from the information provided include:

Complex numbers where z's argument could be positive or negative, and use of degrees in the context of a circle's 360 degrees showing that -30 and 330 degrees represent the same angle.

The z-score, which measures how many standard deviations a data point is from the mean in statistics, such as z = -4 indicating a data point four standard deviations to the left of the mean.

Equations where z is a variable representing a number, which could be within a certain range or satisfying a given condition.

Understanding these uses of z in the mathematical context allows for precise interpretation of equations, probabilities, and analyses of data sets.

The inequality that represents the statement "A number z is fewer than 34." is: z < 3/4.

How to express the inequality?

The inequality that represents the word sentence "A number z is fewer than 3/4" is z < 3/4.

To explain this, we can compare z to 3/4. If z is smaller than 3/4, we can use the less than symbol (<) to represent this relationship.

So, the inequality is z < 3/4.

For example, if z is 1/2, which is smaller than 3/4, the inequality holds true: 1/2 < 3/4.

Complete question is:

Write the word sentences as an inequality.

A number z is fewer than 3/4.

An inequality that represent this word sentences is?

After plugging the x-values from the table into the equation y = 115 + 32(x) and finding matching results with the y-values in the table, it is clear that the table and equation represent the same function.

To determine if the table and the equation y = 115 + 32(x) represent the same function, we can plug the x-values from the table into the equation and see if the resulting y-values match those provided in the table.

Since the y-values for all listed x-values in the table correspond exactly to those calculated using the equation, it is evident that the table and the equation do indeed represent the same function.

The place value of the '3' in 27.4359 is in the tenths place, and therefore its value is 0.3. The position of the '3' relative to the decimal point determines its place value.

The place value of the '3' in 27.4359 is determined by its position relative to the decimal point. In this example, the '3' is located in the first space to the right of the decimal point, which represents the tenths place.

So, the value of the '3' in this decimal is three-tenths, or 0.3. Looking at other numbers for comparison, consider 0.00347. Here, the '3' is three places to the right of the decimal, but the place value would be significantly lower, as it is in the thousandths place.

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Joey's sister takes 0.75 foot for each step she takes since she takes four steps for every three of Joey's, and Joey's step is 1 foot.

The question revolves around a ratio of steps taken by Joey and his sister. Since Joey's one step covers one foot and his sister takes four steps for his three, we need to determine how many feet his sister covers for each of Joey's steps. Let's use a ratio to figure this out.

First, we establish the ratio of steps: for every 3 steps Joey takes, his sister takes 4. If Joey's 3 steps equal 3 feet (because 1 step = 1 foot), we then find the length of his sister's step compared to his. We divide the 3 feet by Joey's 3 steps to find that each step Joey takes is 1 foot long. Then, we calculate his sister's step length in feet by dividing the 3 feet by 4 (since she takes 4 steps to his 3), which equals 0.75 foot per step for his sister.

So, for each of Joey's steps being 1 foot, his sister's step would be 0.75 foot. Therefore, Joey's sister covers 0.75 foot for each step she takes.

The answer is (B) Their measures should add up to be 100°.

We know that the sum of all angles of a triangle is equal to 180 degrees. Stefan has calculated the first angle and it came out to be 80 degrees. So the other two angles must be equal to 100 in order to complete the total measurement of triangle angles which is 180.

Answer:

Speed of the vehicle=[tex]\frac{5t^{4}-10t^{2}+6}{t+2}miles/min[/tex]

Step-by-step explanation:

Given that,

Distance traveled by the vehicle =  5t⁴ - 10t² + 6 miles

time = t + 2 minutes

We need to find the speed of vehicle. Use the formula of speed is:

[tex]Speed=\frac{Dstance}{Tme}[/tex]

[tex]Speed=\frac{5t^{4}-10t^{2}+6}{t+2}[/tex]

So, speed of the vehicle=[tex]\frac{5t^{4}-10t^{2}+6}{t+2}[/tex]

That's the final answer.

Answer:

The speed is 5t^3 - 10t^2 + 10t - 20 + 46/(t+2) miles per minute.

I believe you are finding the total cost of 5 shirts given the unit rate. To compute for the total cost, you have to multiply the unit rate to the number of shirts bought:

5 shirts x $75 unit rate = $375

Therefore, Sylvia will spend $375 to buy 5 shirts.

Final answer:

The slope of the line perpendicular to the line 4x + 2y = 12 is the negative reciprocal of the original line's slope, which in this case is 0.5 or 1/2.

Explanation:

The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. To find the slope of the line perpendicular to the line 4x + 2y = 12, we first need to rewrite the given equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.

First, we solve for y:

4x + 2y = 12

2y = -4x + 12

y = -2x + 6

From the equation y = -2x + 6, we can see that the slope (m) is -2. The slope of the perpendicular line will be the negative reciprocal of -2, which is ½ or 0.5. Therefore, the slope of the line perpendicular to the line 4x + 2y = 12 is ½.

Answer:(1.6,1.3)

Step-by-step explanation: