By finding the size of each exterior angle of a regular polygon with 24 sides, calculate the size of each interior angle of the polygon.

The data set 25 "fast food" represents drive-through service times for Burger King lunches, with a lower class limit of 70 seconds and a class width of 40.

The data can be organized into frequency tables to visualize the distribution of service times. To create the first class, we group all service times from 70 to 109 seconds

(70 + 40 - 1 = 109).

Then, we continue creating classes by adding 40 to the upper limit of the previous class and repeat the process until all data points have been assigned to a class.

The frequency table shows how many times a service time falls within each class interval, allowing us to see the distribution and make inferences about the typical service times at Burger King.

Further analysis such as calculating the mean and standard deviation can also be performed to better understand the data.

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The question is -

Refer to data set 25 "fast food" and use the drive-through service times for Burger King lunches. Begin with a lower class limit of 70 seconds and use a class width of 40.

Data set - 5 0 1 0 2 0 5 0 5 0 3 8 5 0 5 0 5 6 0 0 0 0 0 0 8 5 5 0 4 5 0 0 4 0 0 0 0 0 8 0 9 5 3 0 5 0 0 0 5 8.

The solutions to the quadratic equation \(2x^2 + 6x - 1 = 0\), obtained by completing the square, are x = -3 + √10 and x = -3 - √10.

To solve the quadratic equation\(2x^2 + 6x - 1 = 0\)by completing the square, follow these steps:

Ensure that the coefficient of \(x^2\) is 1. In this case, it is already 2, so we don't need to make any changes.

Move the constant term to the other side of the equation. Add 1 to both sides:

\(2x^2 + 6x = 1\)

Divide the coefficient of x by 2 and square it. In this case, (6/2)^2 = 9.

Add the result from step 3 to both sides of the equation:

\(2x^2 + 6x + 9 = 1 + 9\)

Simplifying, we get:

\(2x^2 + 6x + 9 = 10\)

Write the left side of the equation as a perfect square trinomial. In this case, it is \((x + 3)^2.\)

\((x + 3)^2 = 10\)

Take the square root of both sides:

\(√[(x + 3)^2] = ±√10\)

Simplifying:

\(x + 3 = ±√10\)

Solve for x by subtracting 3 from both sides:

x = -3 ± √10

So, the solutions to the quadratic equation \(2x^2 + 6x - 1\)= 0, obtained by completing the square, are x = -3 + √10 and x = -3 - √10.

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Monetary conversion is essentially the price measure of one currency against another.

A conversion rate is the ratio between two currencies, most commonly used in foreign exchange markets, which designates how much of one currency is needed to exchange for the equivalent value of another currency. Conversion rates fluctuate regularly for all currencies traded in forex markets.

Given here: monetary conversion

Customers exchange their native currency for the currency of the country they are visiting. On the other hand, currency conversions are the process of converting prices to match the customer's native currency.

For example: Suppose you have 40 cents, how many cents would you need to make one dollar!

You can understand this through the following conversion. Since, $1 = 100¢, therefore, we subtract 40 cents from 100 cents. That is 100 cents – 40 cents = 60 cents. Since you already have 40¢, you would need 60¢ more to make it a dollar. This is how we can express 60 cents with different coins.

Hence, Monetary conversion is essentially the price measure of one currency against another.

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The triple integral ∫ ∫ ∫ e z dV, where e is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,5,0), and (0,0,2) is 15.

To find the triple integral ∫ ∫ ∫ e z dV, where e is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,5,0), and (0,0,2),

we can break it down into three separate integrals.
First, let's establish the limits of integration for each variable:
- For x, it ranges from 0 to 3

(since the x-coordinate varies between 0 and 3).
- For y, it ranges from 0 to 5

(since the y-coordinate varies between 0 and 5).
- For z, it ranges from 0 to 2

(since the z-coordinate varies between 0 and 2).
Now, we can write the triple integral as:
∫₀³ ∫₀⁵ ∫₀² z dz dy dx
Evaluating the integral, we get:
∫₀³ ∫₀⁵ [z²/2]₀² dy dx
= ∫₀³ ∫₀⁵ (2/2) dy dx
= ∫₀³ [2y]₀⁵ dx
= ∫₀³ 5 dx
= [5x]₀³
= 15
Therefore, the value of ∫ ∫ ∫ e z dV is 15.

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If the expression is  10x2-18x-4.:

a. The greatest common factor of the expression 10x^2 - 18x - 4 is 2.

b. The expression 10x^2 - 18x - 4 can be factored completely as: 10x^2 - 18x - 4 = 2(5x + 1)(x - 2)

C.  the factoring from Part B is correct.

Part A: To find the greatest common factor of the expression 10x^2 - 18x - 4, we need to find the largest factor that divides all three terms of the expression evenly. One way to do this is to factor out the greatest common factor using the distributive property.

10x^2 - 18x - 4 = 2(5x^2 - 9x - 2)

Now, we need to factor the expression inside the parentheses further to see if we can find any additional common factors.

5x^2 - 9x - 2 can be factored using the quadratic formula, but it does not have any common factors other than 1.

Therefore, the greatest common factor of the expression 10x^2 - 18x - 4 is 2.

Part B: To factor the expression completely, we can start by using the greatest common factor of 2.

10x^2 - 18x - 4 = 2(5x^2 - 9x - 2)

Next, we need to factor the expression 5x^2 - 9x - 2 further. We can use the factoring method of product and sum:

The product of 5 and -2 is -10, and the sum of the factors that multiply to -10 and add to -9 is -10 and 1.

So, we can write 5x^2 - 9x - 2 as:

5x^2 - 10x + x - 2

= 5x(x - 2) + 1(x - 2)

= (5x + 1)(x - 2)

Therefore, the expression 10x^2 - 18x - 4 can be factored completely as:

10x^2 - 18x - 4 = 2(5x + 1)(x - 2)

Part C: To check our factoring from Part B, we can multiply the factors using the distributive property and simplify:

2(5x + 1)(x - 2) = 2(5x)(x) + 2(5x)(-2) + 2(1)(x) + 2(1)(-2)

= 10x^2 - 20x + 2x - 4

= 10x^2 - 18x - 4

Therefore, the factoring from Part B is correct.

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Answer:  The base should be 4.

Step-by-step explanation:

1. We draw a triangle shape like the image.

(The steps was showed in the image).

Answer:

5

Step-by-step explanation:

The information that a slope of 0.416 represents in the scatterplot is the crime index will increase 416 for every 1000 increment in the population.

The information that an intercept of -669.96 represents in the scatterplot is the value of the crime index when the population is zero.

A graph is a pictorial representation of data. It is used by as many fields that uses data. Graphs helps to make information that the data represents easier to understand the relationship existing within the variables

The graph plots the crime index against the population. The slope is the represents how the crime index will behave with respect to the population. While the intercept is the point where the graph intercept the y axis which represents the crime index

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Coordinates are numerical lengths or angles that uniquely identify locations on two-dimension. The missing coordinates are coordinates 3 and 4.

A Cartesian coordinate plane is a two-dimensional plane with infinite dimensions. On an endless 2d plane, any two-dimensional figure may be drawn. A location is assigned to each point on a Cartesian plane.

It is the perpendicular distance between that point and the horizontal and vertical axes, which are commonly referred to as the x-axis and y-axis.

Location is then written as (a,b), where 'a' is the point's shortest distance from the y-axis, 'b' is the point's shortest distance from the x-axis, and 'c' is the point's shortest distance from the x-axis.

Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ).

Mathematics, scientists, and engineers frequently employ a variety of coordinate systems.

Hence the missing coordinates are coordinates 3 and 4.

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The answer is B.

Answer:

3

Step-by-step explanation:

i wont explan

To plot the original function x(t) and its sampled versions, we need to consider different sampling periods and apply the sampling process.

The original function is given by:

x(t) = t * 3cos(10πt) * p2(t−1)

(a) For ts = 1s:

The sampling period is 1 second. We need to evaluate x(t) at every 1-second interval within the range -2 to 5.

Sampling points: -2, -1, 0, 1, 2, 3, 4, 5

Evaluate x(t) at each sampling point to get the corresponding sampled values x5(t).

(b) For ts = 0.1s:

The sampling period is 0.1 seconds. We need to evaluate x(t) at every 0.1-second interval within the range -2 to 5.

Sampling points: -2, -1.9, -1.8, ..., 4.9, 5

Evaluate x(t) at each sampling point to get the corresponding sampled values x5(t).

(c) For ts = 0.09s:

The sampling period is 0.09 seconds. We need to evaluate x(t) at every 0.09-second interval within the range -2 to 5.

Sampling points: -2, -1.91, -1.82, ..., 4.91, 5

Evaluate x(t) at each sampling point to get the corresponding sampled values x5(t).

Plot the original function x(t) and the sampled versions x5(t) on separate graphs for each sampling period, showing the sampling points and the waveform.

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Expression is not equal to zero, we cannot find a vector field G such that curl G = (xyz, -y⁶z⁵, y⁵z⁶). Therefore, the answer is no.

There is no such G because the divergence of curl G is not equal to zero. The divergence of curl G is given by the scalar triple product identity:

div(curl G) = dot(grad, curl G)

Using this identity and the given components of curl G, we have:

div(curl G) = x(∂/∂x)(-y⁶z⁵) + y(∂/∂y)(y⁵z⁶) + z(∂/∂z)(xyz)
div(curl G) = -6xy⁵z⁵ + 5y⁶z⁵ + xz

Since this expression is not equal to zero, we cannot find a vector field G such that curl G = (xyz, -y⁶z⁵, y⁵z⁶). Therefore, the answer is no.

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The percent increase in the conversion rate from 4.25% to 7% is 64.7%.

To find the percent increase, we need to calculate the difference between the new conversion rate and the old conversion rate, and then divide that difference by the old conversion rate. Finally, we need to multiply that result by 100 to get the percent increase. Here are the steps:

1. Calculate the difference between the new conversion rate and the old conversion rate: 7% - 4.25% = 2.75%
2. Divide the difference by the old conversion rate: 2.75% ÷ 4.25% = 0.6470588235294118
3. Multiply the result by 100 to get the percent increase: 0.6470588235294118 × 100 = 64.70588235294118%

So the percent increase is 64.70588235294118%. To round to the nearest tenth, we look at the digit to the right of the tenths place (the hundredths place), which is 0. If that digit is 5 or greater, we round up. If it's less than 5, we round down. In this case, the digit is 0, so we round down to get a final answer of 64.7%.

Therefore, the percent increase in the conversion rate from 4.25% to 7% is 64.7%.

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Given a triangle ABC with angles A, B, C and side lengths b, c, a respectively, B = 139.1°, c = 5.7, b = 159, we need to find the unknown angle of the triangle.  

To find the unknown angle of triangle ABC, we can use the law of cosines: \(c^2 = a^2 + b^2 - 2ab*cos(C)\). where a is the opposite side of angle A and b is the opposite side. Angles B and c are opposite angles C.

Since b = 159 and c = 5.7, we can plug these values ​​into the equation. \(5.7^2 = a^2 + 159^2 - 2(5.7)(159)cos(C)\). A further simplification is\(32.49 = a^2 + 159^2 - 181.8cos(C)\).

From this equation we can solve \(a^2 + 159^2 - 181.8*cos(C)\) = 32.49. However, without the value of angle A or side a, it is not possible to determine the specific value of angle A, angle C, or side a of that triangle.

Therefore, the correct choice would be to state that it is impossible to determine the unknown angles of triangle ABC from the information given. 

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Answer:

1.84

Step-by-step explanation:

25.38-23.54

The actual weight is 0.0042 pounds lighter than the labeled weight.

The actual weight of the chocolates is 0.3798 pounds, while the label on the bag states it should weigh 0.384 pounds. To determine how much lighter the actual weight is, we can calculate the difference between the two weights.

Subtracting the actual weight from the labeled weight, we get:

0.384 pounds - 0.3798 pounds = 0.0042 pounds.

Therefore, the actual weight is 0.0042 pounds lighter than the labeled weight.

It's important to note that this difference may seem small, but it can be significant depending on the context. Accuracy in labeling is crucial for various reasons, such as complying with regulations, providing precise information to consumers, and ensuring fair trade practices. Even minor discrepancies can impact trust and customer satisfaction.

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The volume of the pentagonal prism is 645 cubic millimeters.

We have,

The formula for the volume of a pentagonal prism is:

V = A x h

where A is the area of the pentagonal base and h is the height of the prism.

In this case, we are given the area of the base as 43 square millimeters and the height as 15 millimeters.

Therefore, we can calculate the volume as:

V = 43 x 15

V = 645 cubic millimeters

Therefore,

The volume of the pentagonal prism is 645 cubic millimeters.

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Answer:

Erin's office will have recycled a total of 10 kg of paper in 9 weeks.

Step-by-step explanation:

First write out the formula for the total weight of paper recycled, and then solve this equation for time:

AmtRecycled(t) =  1 kg + (1 kg/wk)(t)

In this problem, AmtRecycled(t) = 10 kg, and so the following is true:

    10 kg              = 1 kg + (1 kg/wk)(t)

Then    9 kg = (1 kg/wk)(t)

and so:

   9 kg

------------- = 9 wk

1 kg/wk

Erin's office will have recycled a total of 10 kg of paper in 9 weeks.

Answer:

subtracting 7.84 from 12.48 will give 15.44 this is equal to 12 packets if you dived 12 by the price of 15.44 you will get your answer you may need to round

$0.03 pretzels cost more than cost of bag of chips.

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

price of 16 snack- size bags of chips = 7.84

Cost of 1 bag of chip = 7.84 /16

                                  = $0.49

and, price of 24 snack-size bags of pretzels = 12.48

Cost of 1 snack-size bags of pretzels = 12.48 / 24

                                                              = 0.52

Hence, by $0.03 pretzels cost more than cost of bag of chips.

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Answer:

The time it takes Ms. Croft to reach the cruise ship by speedboat = 6.11 hours

The time it takes Ms. Croft to reach the cruise ship by helicopter = 6.25 hours

since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.

Step-by-step explanation:

The given parameters are;

The elapsed time by which Ms. Croft missed the boat = 5 hours

The speed of the cruise ship = 528 mi/day

The speed of the speedboat = 100 miles in 2.5 hours

The speed of the helicopter = 90 mph

The time it would take Ms. Croft to arrive at the harbor = 3.5 hours

Therefore, we have;

The cruise ship's speed = 528 miles per 24 hours = 528/24 mph = 22 mph

The location of the cruise after the first 5 hours = 5 × 22 = 110 miles

The speed of the speedboat = 100 miles per 2.5 hours = 100/2.5 = 40 mph

By traveling with a speed boat

The time at which Ms. Croft will intercept the cruise ship is given by the following relation;

40 mph × t = 22 mph × t + 110 miles

Which gives;

40 mph × t - 22 mph × t = 110 miles

18 mph = 110 miles

t = 110 miles/(18 mph) = 55/9 hours ≈ 6.11 hours

By taking the helicopter, we have;

Upon arrival at the harbor, after 3.5 hours, we find

90 mph × t = 22 mph × t + 22 mph × 3.5 hours + 110 miles

90 mph × t - 22 mph × t = 22 mph × 3.5 hours + 110 miles

68 mph × t = 77 miles + 110 miles = 187 miles

t = 187 miles/(68 mph) = 11/4 hours = 2.75 hours

The total time it takes Ms. Croft to reach the cruise ship by taking the helicopter = 3.5 + 2.75 = 6.25 hours

Therefore, since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.

Answer:

Step-by-step explanation:

These angles are equal because the parallel lines are traversed by a straight line.

17x-6=15x+10 add 6 to each side

17x=15x+16. Subtract 15x from each side

2x=16. divide each side by 2

x=8

Answer:

1. 1.5 inches per minute

2. 90 inches per hour

Step-by-step explanation:

speed = \(\frac{distance}{time}\)

1. total distance covered = \(\frac{9}{8}\) + \(\frac{27}{8}\)

                                      = \(\frac{9+27}{8}\)

                                      = \(\frac{36}{8}\)

                                      = 4\(\frac{1}{2}\) inches

Total time taken = \(\frac{3}{4}\) + \(\frac{9}{4}\)

                           = \(\frac{3 +9}{4}\)

                           = \(\frac{12}{4}\)

                           = 3 minutes

The ants average speed = \(\frac{4.5}{3}\)

                                         = 1\(\frac{1}{2}\)

                                         = 1.5

The ants speed is 1\(\frac{1}{2}\) inches per minute.

2. Since;

60 minutes = 1 hour

3 minutes = x hours

x = \(\frac{3}{60}\)

  = \(\frac{1}{60}\)

  = 0.05 hours

Speed = \(\frac{4.5}{0.05}\)

           = 90 inches per hour

The red ants speed is 90 inches per hour.

Answer:

mode: none

median: 4

mean: 4.2

Step-by-step explanation:

when dealing with mean, median, mode the first thing you should do is arrange the numbers in order from least to greatest. Once you have done so the easiest thing to do first is see which number is in the very middle, this is your median. Mode is the number that appears the most. Mean is another word for average. To find the mean, add up all the numbers then divide the sum of all the numbers by how many numbers are listed. In this case, 2+3+4+5+7=21.

21 divided by 5 (how many numbers there are) = 4.2

Answer:he should build them 25x10

Step-by-step explanation:

Encik Ahmad can build 10 square plots with three different sizes.

Rectangle is a polygon in two dimensional geometry which has four sides and four angles and each angle being right angles.

Length of the rectangular plot = 85 m

Width of the rectangular plot = 30 m

We have to find the number of square plots Encik Ahmad can built of three different sizes.

For that first we take a 45 m length of the plot.

Divide it to three equal lengths. We get three lengths with each 15 m length.

Along the width also, divide into two equal width, each having a width of 15 m.

Each 15 m length, we will get two square plots.

Along 45 m length, we get 3 × 2 = 6 square plots.

The remaining rectangle has length 40 m and width 30 m.

Divide this length as 30 m and 10 m.

So we get a square of dimension 30 m.

Remaining is a rectangle whose remaining length is 10 m and width 30 m.

Along the width, divide into three equal widths, each 10 m.

So there we get three square plots with side length 10 m.

So we have 10 square plots, 6 having the side length 15m, 1 having the side length 30 m and 3 having the side length 10 m.

Hence he get 10 square plots having three different sizes as 15 m, 30 m and 10 m.

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Answer:

11. Slope of the line is 7/10.

12. Slope of the line is \(-\frac{1}{3}\)

Step-by-step explanation:

11. Given points are:

(-6, 1) and (4, 8)

Slope of a line is given by the formula;

m = \(\frac{y_2-y_1}{x_2-x_1}\)

m = \(\frac{8-1}{4-(-6)}\)

m = \(\frac{7}{4+6}\)

m = \(\frac{7}{10}\)

Slope of the line is 7/10.

12. Given points are:

(2, -3) and (5, -4)

Slope of the equation is;

m = \(\frac{-4-(-3)}{5-2}\)

m = \(\frac{-4+3}{3}\)

m = \(\frac{-1}{3}\)

Hence,

Slope of the line is \(-\frac{1}{3}\).

Answer:

2x+10

Simplifying

2x + 10

Reorder the terms:

10 + 2x

Factor out the Greatest Common Factor (GCF), '2'.

2(5 + x)

Final result:

2(5 + x)

Step-by-step explanation:

choose as brainliest

Answer:

2(x+5)

Step-by-step explanation:

Looking at 2x+10, they all are factorable with 2. Divide 2x and 10 by two and bring the two outside. Which you will get:

2(x+5)

Answer:

r = p - q

Step-by-step explanation:

Write the two given vectors using i and j components.

i = unit vector in x direction

j = unit vector in y direction

p = -i - 3j

q = 3i - 4j

Now how can you combine these two vectors and get r when

r = -4i + j?

Adding p and q gives this:

p + q = -i - 3j + 3i - 4j = 2i - 7j

That is not r, so the addition of the vectors p and q does not work.

How about subtraction?

Start with -i from p and subtract 3i from q. You do get -4i which is the x-component of r.

Then start with -3j from p and subtract -4j from q. You get -3j - (-4j) = -3j + 4j = j which is the y-component of r.

That subtraction works.

p - q = -i - 3j - (3i - 4j) = -i - 3j - 3i + 4j = -4i + j which is exactly what r is.

Answer: r = p - q

Answer:

Step-by-step explanation: