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The radius of the cylindrical water bottle is approximately 2.34 cm.

The company designing the water bottle has given us the volume of the bottle, which is 220 cm³, and the height of the bottle, which is 8.9 cm. We can use the formula for the volume of a cylinder to relate the radius, height, and volume of the water bottle. The formula is:

Volume of a cylinder = π × radius² × height

We are given the volume of the cylinder as 220 cm³ and the height as 8.9 cm, so we can substitute these values into the formula to get:

220 = π × radius² × 8.9

To solve for the radius, we need to isolate it on one side of the equation. We can start by dividing both sides by π × 8.9:

220 ÷ (π × 8.9) = radius²

Now, we can take the square root of both sides to find the value of the radius:

√(220 ÷ (π × 8.9)) = radius

Using 3.14 for π, we can simplify the expression to get:

radius ≈ 2.34 cm

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She will fertilize 69.76 square feet outside of the circular flowers.

In order to get the area that she will fertilize outside of the circular flowers, we will calculate area of the entire rectangular garden and the area of the circular flowers.

The area of the rectangular garden is:

[tex]= 10 ft * 12 ft\\= 120 sq ft[/tex]

The area of the circular flowers is:

[tex]= \pi r^2\\= 3.14 * 4^2\\= 50.24 sq ft[/tex]

To find area to be fertilize outside of the circular flowers, we will subtract these area which gives us:

[tex]= 120 sq ft - 50.24 sq ft\\= 69.76 sq ft[/tex]

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Answer: If the daffodil start at 1 inch on day one, and only 1 day has passed, it will grow half of what it would in 2 days because half of 2 is 1. So the current height 1 inch + how much it will grow in one day (1.5 inches) = the final height (2.5 inches) Hope this helps :D

Step-by-step explanation:

The test statistic for the appropriate test to determine if there is a significant mean difference between the percent correct on the two sections for all candidates similar to the one in the investigation is given by t = 75 - 65 / [8 / √(50)], option (A) is correct.

The appropriate test to determine if there is a significant mean difference between the percent correct on the two sections is a two-sample t-test assuming equal variances.

The test statistic for this hypothesis test can be calculated using the formula:

t = x' / ([tex]s{p}[/tex] × √n')

where x' is the sample means for the first and second sections, respectively, [tex]s{p}[/tex] is the pooled standard deviation, and n' is the sample sizes for the first and second sections.

Using the information given in the question, we can calculate the values needed for the test statistic:

x₁ = 75, x₂ = 65, s₁ = 10, s₂ = 5, n' = 50

x’ = x₁ - x₂ = 75 - 65 = 10

The pooled standard deviation is given by [tex]s_{p}[/tex] = 8

We can calculate the test statistic:

t = (x') / [[tex]s_{p}[/tex] / √(n)]

t = 75 - 65 / [8 / √(50)]

Further simplifying:

t = 10 / [8 / √(50)]

t = 8.8356

Hence, option (A) is correct.

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– The question is incomplete, The complete question is:

To obtain certification for a certain occupation, candidates take a proficiency exam. The exam consists of two sections, and neither section should be more difficult than the other. To investigate whether one section of the exam was more difficult than the other, a random sample of 50 candidates was selected. The candidates took the exam and their scores on each section were recorded.

The summary of the statistics are as follows:

-For the first section, Mean Percent Correct is 75 and Standard Deviation Percent Correct is 10

-For the second section, Mean Percent Correct is 65 and Standard Deviation Percent Correct is 5

-The difference is, Mean Percent Correct is 10, and the pooled Standard Deviation Percent Correct is 8

Which of the following is the test statistic for the appropriate test to determine if there is a significant mean difference between the percent correct on the two sections (first minus second) for all candidates similar to the one in the investigation?

A) t = 75 - 65 / (8 / √(50))

B) t = 75 - 65 / [√(10² / 50 + 5² / 50)]

C) x² =(75 - 70)² / 70 + (65-70)² / 70

D) x² = (75-70)² / 65 + (65-70)² / 65

1.75 in or 1 3/4 in (which ever form you need it in)

youre given the diameter and so to find radius, you simply divide the diameter by 2.

The statement that correctly compares the two functions on the interval [-1, 2] is A. Both functions are increasing, but function g increases at a faster average rate.

For function f, as x increases from -2 to 2, we can see that the corresponding values of f(x) also increase, but at a decreasing rate. This is because the function is exponential and approaching a horizontal asymptote as x goes to infinity. Therefore, f(x) is increasing, but at a decreasing rate.

For function g, we don't have enough information to determine if it's increasing or not, since only its equation is given. The correct option is A.

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The mean, median, mode and range are 42.2, 30, 87 and 95 respectively.

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

Therefore mean = (23+87+19+34+37+37+5+14+100+26)/10

= 422/10 = 43.2

The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

median = 26+34/2 = 60/2 = 30

Mode is the number with the highest frequency

Therefore, the mode is 87

Range Is the difference between the highest and the lowest

= 100-5 = 95

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Approximately 30% of the sampled baseballs are too lively based on a cutoff coefficient of restitution of 0.630. The 95% lower confidence bound on this proportion is  0.154.

To find the proportion of the baseballs in the sampled population that are too lively, we need to count the number of baseballs in the sample that have a coefficient of restitution greater than 0.630 and divide by the total sample size

Number of baseballs with coefficient of restitution > 0.630 = 12

Total sample size = 40

Proportion of baseballs in the sample that are too lively = 12/40 = 0.3 = 30%

To find a 95% lower confidence bound on this proportion, we can use the formula

lower bound = p - zsqrt(p(1-p)/n)

where p is the sample proportion, z is the z-score associated with the desired confidence level (95% confidence level has a z-score of 1.96), and n is the sample size.

Substituting the values, we get:

lower bound = 0.3 - 1.96sqrt(0.3(1-0.3)/40) ≈ 0.154

Therefore, we can be 95% confident interval that at least 15.4% of the baseballs in the population are too lively.

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The correct answer is option c) A circle graph, also known as a pie chart, would be the best graphical representation for the teacher's data on the subject preferences of the 100 students in the school.

What is graphical representation?

A graphical representation is a way of presenting data or information visually using charts, graphs, diagrams, or other visual aids. It helps to convey complex information in an easy-to-understand manner, enabling the viewer to quickly grasp the main points and trends.

A circle graph, also known as a pie chart, would be the best graphical representation for the teacher's data on the subject preferences of the 100 students in the school.

A circle graph can effectively display the relative proportions of different categories in a data set, making it a useful tool for showing the distribution of categorical data such as subject preferences.

A stem-and-leaf plot is more suitable for displaying numerical data, while a histogram and box plot are typically used for showing the distribution of continuous data.

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Answer:

Step-by-step explanation:

The answer is attached below. There isn't much explanation for this. You just translate the word problem into a mathematical inequality.

Answer: 7

Step-by-step explanation:

i did it a weird way

Answer: Just simply replace the letter with the number that it equals in the equation. Then solve the equation using PEMDAS order of operations, (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction).

Step-by-step explanation:

We can deduce here that the experimental probability that the next time Lea rolls the number cubes, they will land with a 1 showing on the top face of one number cube and a 5 showing on the top face of the other number cube is: 1/36.

Probability is a measure for determining the possibility or chance that a specific event will take place. It is typically stated as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

We can see that there is only one roll where one number cube that shows a 1 and the other number cube shows a 5. Therefore, the number of successful outcomes is 1.

The total number of rolls seen are: 36 rolls = 6 possible outcomes on the first number cube × 6 possible outcomes on the second number cube.

We can then see here that the probability will be = 1/36.

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Answer:

12

Step-by-step explanation:

to divide by a fraction use the acronym K.C.F or keep change flip to re-arrange the problem.

[tex]\frac{3}{\frac{1}{4} }[/tex] can be re-written as

[tex]\frac{3}{1} *\frac{4}{1}[/tex]

or 3*4 which equals 12

The length of the second shelf is 98 centimeters.

Let's denote the length of the first shelf as x centimeters. According to the problem, we have the following equations for the lengths of the other shelves:

Second shelf: 2x + 18 cm

Third shelf: x - 12 cm

Fourth shelf: x + 4 cm

Robert must use the entire 2.5-meter board for the shelves, so the sum of the lengths of the four shelves should be equal to 2.5 meters, or 250 centimeters. Thus, we can write an equation:

x + (2x + 18) + (x - 12) + (x + 4) = 250

Simplify the equation:

x + 2x + 18 + x - 12 + x + 4 = 250

Combine like terms:

6x + 10 = 250

Subtract 10 from both sides:

6x = 240

Now, divide by 6:

x = 40

Now that we have the length of the first shelf (x = 40 cm), we can find the length of the second shelf:

Second shelf = 2x + 18 = 2(40) + 18 = 80 + 18 = 98 cm

So, the length of the second shelf is 98 centimeters.

Answer:

114 cm

Step-by-step explanation:

Let's start by finding the shortest shelf.

The second shelf is 18 centimeters longer than twice the length of the first shelf. The first shelf is smaller than the second shelf.

The third shelf is 12 centimeters shorter than the first shelf. The third shelf is shorter than the first shelf, so, the third shelf is the shortest shelf.

Let's call the length of the third shelf s.

We know that the third shelf is 12 centimeters shorter than the first shelf. In other words, s is 12 centimeters shorter than the first shelf. So, we can write the length of the first shelf as:

[tex]s+12[/tex]

We also know that the second shelf is 18 cm longer than twice the length of the first shelf.

Start by multiplying the length of the first shelf by 2.

[tex]2(s+12)=2s+24[/tex]

Now, let's add 18.

[tex]2s+24+18=2s+42[/tex]

So, the length of the second shelf is 2s+42.

The remaining shelf is 4 centimeters longer than the first shelf. Remember that the first shelf is s+12. Let's add 4.

[tex]s+12+4=s+16[/tex]

So, the first shelf is s+12, the second shelf is 2s+42, the third shelf is s, and the remaining shelf is s+16.

When you add them all together, you will get the 2.5 meter board.

2.5 meters is equal to 250 cm.

So, the first shelf plus the second shelf plus the third shelf plus the remaining shelf is equal to the entire board, or 250 cm.

Let's rewrite that in terms of s:

[tex](s+12)+(2s+42)+s+(s+16)=250=\\5s+70=250=\\5s=180=\\s=36[/tex]

We now know that s=36 cm.

The problem asks how long the second shelf is. Recall that the second shelf is 2s+42.

Let's plug in 36 to this expression:

[tex]2s+42=\\2(36)+42=\\72+42=\\114[/tex]

So, the second shelf is equal to 114 cm.

The measure of AC, in circle ABCD can be found to be 20 cm.

In Circle ABCD, O is the midpoint of the circle which means that OB is the radius.

As A and C are on opposite sides of the circle, it means that the value of the measure of AC would be the diameter of the circle which can be found if we have the radius.

The diameter which is AC would then be:

= Radius x 2

=  OB x 2

= 10 x 2

= 20 cm

In conclusion, the measure of AC is 20 cm.

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Marilyn needs 3 and 1/3 cups of brown sugar to make 5 batches of the recipe.

To find the total amount of brown sugar Marilyn needs, we need to multiply the amount required for one batch by the number of batches.

One batch requires 2/3 cup of brown sugar. To find the amount required for five batches, we can multiply 2/3 by 5.

2/3 * 5 = 10/3

So Marilyn needs 10/3 cups of brown sugar to make 5 batches of the recipe. However, it's usually easier to work with mixed numbers or whole numbers.

To convert the fraction 10/3 to a mixed number, we divide the numerator (10) by the denominator (3) and get a quotient of 3 with a remainder of 1. So:

10/3 = 3 1/3

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At a function x = 4 has a vertical asymptote and at y = -15 has a horizontal asymptote.

The general form of a function is x= a and y = b.

f(x) = (kx + m) / (x - a) + b

k and m are constants.

We require a factor of (x - 4) in the denominator to get a vertical asymptote at x = 4. It is necessary for the fraction to approach -15 when x approaches positive or negative infinity in order to obtain a horizontal asymptote at y = -15.

One potential function that meets these specifications is:

H(x) = 6/(x - 4) - 15 + k

where k is a constant that establishes the function's vertical shift (i.e., its value at x = 0).

By entering a point on the graph, such as the x-intercept (where y = 0), the value of k can be determined:

0 = 6/(x - 4) - 15 + k

15 - k = 6/(x - 4)

x - 4 = 6/(15 - k)

x = 6/(15 - k) + 4

We may enter this value of x into the original equation to find k since y = 0 at the x-intercept:

0 = 6/((6/(15 - k) + 4) - 4) - 15 + k

0 = 6/(6/(15 - k)) - 15 + k

0 = 15 - k - 15 + k

The x-intercept and asymptotes are unaffected by the value of k, and any value of k will result in a function with the same asymptotes. K does, however, have an impact on the function's vertical shift.

We can select a value for k and then search for a specific function that has the specified asymptotes.

For instance, if we select k = 0, we obtain:

H(x) = 6/(x - 4) - 15

This function has the same shape as the original function H(x) presented in the problem and asymptotes at x = 4 and y = -15, respectively.

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Answer:

They are length, thickness and temperature

yes very cool math problem

The angle x subtended by the arc of the circle between the two tangents is 130 degrees.

In trigonometry, the tangent (often abbreviated as tan) is a mathematical function that describes the ratio of the length of the side opposite to an angle in a right-angled triangle to the length of the adjacent side.

The formula 50=180-x represents the fact that the angle between two tangents drawn to a circle from an external point is equal to the difference of the angles subtended by the tangents in the opposite segment of the circle.

Using this formula, we can solve for x as follows:

50 = 180 - x (given)

x = 180 - 50 (subtracting 50 from both sides)

x = 130 (simplifying)

Therefore, the angle x subtended by the arc of the circle between the two tangents is 130 degrees.

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Answer:

The correction definition of a resume is a document describing the applicant's experience, strengths, skills, education and other qualifications.

The circumference of a circle is proportional to its diameter. The constant of proportionality for this relationship is pi (π). Therefore, we can use the equation C = πd (where C is the circumference and d is the diameter) to determine the circumference of a circle.

Pi (π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159, but its decimal representation goes on infinitely without repeating.

The radius of a circle is half the length of its diameter. Therefore, the relationship between diameter and radius is that the diameter is twice the length of the radius, or d = 2r.

If given the diameter of a circle, you can calculate its radius by dividing the diameter by 2 (r = d/2). Conversely, if given the radius of a circle, you can calculate its diameter by multiplying the radius by 2 (d = 2r).

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Answer: 3. is 13

4. is 36

5. is 21

6. is 15

7. is 21

8. is 2

9. is 6

10. is 45

Step-by-step explanation:

the letters are there to just confuse you. i promise its all right <-- the answers

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The dimensions of the net for the cube lampshade which fits into the sheet of plastic with dimensions 20 cm by 15 cm indicates;

5. The area of each square of (5 cm)² on the sheet of plastic, indicates that the area of the net comprising of six squares is 150 cm²

6. The percentage of the plastic sheet wasted is 50%

What is a cubic shape?

A cubic shape is a shape that consists of six square faces, twelve edges and eight vertices. The area of each square face of side length s = Side length, s × Side length, s.

5. The surface area of the net in the figure can be calculated by finding the sum of the area of the squares within the area of the net.

The number of squares in the figure are 6 squares

The area of each square = (5 cm)²

The area of the sheet of plastic = 20 cm × 15 cm = 300 cm²

The area of the net containing six squares is therefore;

Area = 6 × (5 cm)² = 150 cm²

6. The amount of plastic sheet wasted can be obtained by finding the difference between the area of the plastic and the area of the net

Area of the sheet of plastic = 20 cm × 15 cm = 300 cm²

Area of the net = 150 cm²

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The area of the composite figure for this problem is given as follows:

A = 90 in².

The area of the composite figure is given by the sum of the areas of all the parts that compose the figure.

The right triangle has a side length of 5 in and an hypotenuse of 13 units, hence the missing side is given as follows:

5² + x² = 13²

25 + x² = 169

x² = 144

x = 12.

Thus the entire base is of:

12 + 4 = 16 in.

Then the figure is composed as follows:

Hence the area is given as follows:

A = 3 x 16 + 0.5 x 12 x 5 + 4 x 3

A = 90 in².

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Answer:

y = 4x

Step-by-step explanation:

To find the constant of proportionality, we need to calculate the ratio of y to x for any two corresponding values in the table.

Let's choose the first set of values: x = 6, y = 24.

y/x = 24/6 = 4

So the constant of proportionality is 4.

We can check this for the other sets of values as well:

- for x = 8, y = 32: y/x = 32/8 = 4

- for x = 10, y = 40: y/x = 40/10 = 4

- for x = 12, y = 48: y/x = 48/12 = 4

In each case, the ratio of y to x is equal to 4, so the constant of proportionality is indeed 4. Therefore, the relationship between x and y is:

y = 4x

Answer:10 40

Step-by-step explanation:

Answer: 12

Step-by-step explanation:

Using Phytagorean theorem

[tex]r^{2} = \sqrt{} y^{2} +x^{2}[/tex]

given: r=20 and y=16

[tex]20^{2} =\sqrt16^{2} +x^{2} \\400=\sqrt{256+ x^{2} \\[/tex]

move x to the other side (when x is moving to the other side the sign change)

x²= √400-256       subtract  

x= √144      take the square root

x=  12

the answer to the problem is that one angle measures 19.1 degrees and its complementary angle measures 70.9 degrees.

How to solve the question?

Let's first define the problem. Complementary angles are two angles whose sum is 90 degrees. Let x be the measure of one of the angles, then the measure of its complementary angle is 90 - x. According to the problem, one angle measures 51.8 degrees less than its complementary angle, so we can write:

x = (90 - x) - 51.8

Simplifying this equation, we get:

2x = 90 - 51.8

2x = 38.2

x = 19.1

Therefore, one angle measures 19.1 degrees and its complementary angle measures 90 - 19.1 = 70.9 degrees.

We can check that these angles are indeed complementary by verifying that their sum is 90 degrees:

19.1 + 70.9 = 90

So the answer to the problem is that one angle measures 19.1 degrees and its complementary angle measures 70.9 degrees.

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