Problem 1.1
The owner of a new restaurant is ordering tables and
chairs. She wants to have only tables for 2 and tables
for 4.
The total number of people that can be seated in the
restaurant is 120.
Describe some possible combinations of 2-seat tables
and 4-seat tables that will seat 120 customers.
Tables for 2
Tables for 4
0
30.

The prime factorization of the number 21 is:

21 = 3*7

We want to write the prime factorization of 21.

To do so, we just need to divide the number by prime numbers.

The first prime number we can try is 2, if we divide by 2 we get:

21/2 = 10.5

This is not an integer, so 2 is not a factor.

The next one is 3:

21/3 = 7

Now we can rewrite:

21 = 3*7

Where 3 and 7 are prime numbers, so that is the prime factorization.

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Collecting data on slugging percentage and average exit velocity from the top players at 5 local colleges allows the scout to assess the offensive talent and make informed evaluations that can contribute to their decision-making process in baseball scouting.

Assessing talent in baseball involves evaluating various performance metrics, and slugging percentage and average exit velocity are two important statistics used to measure a player's offensive abilities.

Slugging percentage represents the power of a hitter by measuring the number of bases they accumulate per at-bat, while average exit velocity measures how hard a player hits the ball off the bat.

By selecting the top 6 players from each of the 5 local colleges, the scout is likely focusing on the most skilled and promising athletes at each institution. By collecting data on their slugging percentage (x) and average exit velocity (y), the scout can gain insights into the offensive capabilities of these players and compare their performances across colleges.

Analyzing this data can help the scout identify standout players, assess the overall talent level at each college, and potentially make informed decisions about recruitment or player development. The slugging percentage and average exit velocity provide valuable information about a player's ability to hit for power and make solid contact with the ball, which are crucial skills in baseball.

The scout can use this data to compare the performance of players within and across colleges, identify trends or patterns, and make objective assessments about the talent level at each institution. This information can be used to inform scouting reports, player rankings, or even future team selections or drafts.

Overall, collecting data on slugging percentage and average exit velocity from the top players at 5 local colleges allows the scout to assess the offensive talent and make informed evaluations that can contribute to their decision-making process in baseball scouting.

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Answer:

Step-by-step explanation:

In Isosceles triangle base angles (angles oppoiste to equal sides) are congruent.

x + x + 98 = 180 {Angle sum proeprty of triangle}

   2x + 98 = 180   {Subtract 98 from both sides}

        2x = 180 - 98

       2x  = 82      {Divide both sides by 2}

        x   = 82/2

x = 41

Answer:

x = 41°

Step-by-step explanation:

An isosceles triangle has 2 opposite sides equal.

Therefore the angle opposite x is also x

Hence:

x + x + 98° = 180° (angles in a triangle add up to 180°)

2x + 98° = 180°

2x = 180° - 98°

2x = 82°

2x/2 = 82°/2

x = 41°

Answer:

14

Step-by-step explanation:

Given that T is the midpoint of line PQ, segments PT = 3x + 9, and TQ = 8x - 6 that are formed would be equidistant or congruent. PT = TQ.

Therefore:

\(3x+9=8x-6\)

Let's find the value of x

Rearrange the equation, so that the terms having x would be on your left, while those without x would be on your right.

\(3x-8x=-9-6\)

\(-5x=-15\)

Divide both sides by -5

\(x=3\)

Plug in the value of x into the expression, 3x + 5, to find PT.

PT = 3(3) + 5 = 14.

62.82 cm

Step-by-step explanation:

the formula of circumference of circle is 2 Pi R

so, 2 * 22/7 * 10 cm = 62.82 cm

The solution is : its circumference in terms of pi is 10π cm.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

here, we have,

given that,

The diameter of a circle is 10 cm.

now, we have to find its circumference in terms of pi.

the formula of circumference of circle is 2πr

here, we have,

d = 10

s, r = 10/2 = 5

so, we get,

2 * 22/7 * 5 cm

= 31.42 cm

=10π

Hence, its circumference in terms of pi is 10π cm.

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The variance of a sample or a population cannot be negative. Mathematically, variance is calculated as the average of the squared differences between each data point and the mean.

Variance is a measure of the spread or dispersion of a set of data points around their mean. It quantifies how much the individual data points differ from the average.

Since variance involves squaring the differences, all the terms in the calculation are positive or zero. Thus, the resulting variance value cannot be negative. Negative variance would imply that the data points are closer to the mean than they actually are, which contradicts the concept of dispersion.

Therefore, it is not possible for the variance of a sample or a population to be negative.

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COVARIANCE.S uses the number of data points minus one to adjust for the sample size. The functions COVARIANCE.P and COVARIANCE.S return different values when using the same data.

The reason why COVARIANCE.P and COVARIANCE.S return different values when using the same data is that they use different formulas to calculate covariance. COVARIANCE.P calculates the average of the product of deviations from the means of the two variables, while COVARIANCE.S calculates the sum of the product of deviations from the means of the two variables, divided by the number of data pairs minus one.

COVARIANCE.P assumes that the data represents the entire population, and therefore divides by the total number of data points. COVARIANCE.S, on the other hand, assumes that the data represents a sample of the population, and therefore divides by the number of data points minus one to account for the degree of freedom.

In summary, the difference between COVARIANCE.P and COVARIANCE.S lies in the way they account for the variance in the data, with COVARIANCE.P using the total number of data points, while COVARIANCE.S uses the number of data points minus one to adjust for the sample size.
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Answer:

12ft

Step-by-step explanation:

use sin cos tan method

here, we can see 6ft as adj to the angle and the ladder as hypotenuse

so, adj/hyp = cosθ

--> 6/hyp = cos60

--> hyp = 6/cos60

--> hyp, length of ladder =  12ft

The length of the ladder is 12ft.

Sine, Cosine, and Tangent are the main functions used in Trigonometry and are based on a Right-Angled Triangle.

Use the sin cos tan method:

Here, we can see 6ft as adj to the angle and the ladder as the hypotenuse

so,  

⇒ adj/hyp = cosθ

⇒ 6/hyp = cos60

⇒ hyp = 6/cos60

⇒ hyp, length of ladder =  12ft.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

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Answer:

uh huh she has 18 rolls of wrapping paper

Answer:

27

Step-by-step explanation:

The volume of the larger prism that is similar to the smaller prism is 625 cm³

Two figures are said to be similar if they are the same shape.

Similar figures are figures that are the same shape, but not necessarily the same size.

The prisms are similar and have edge length in the ratio of 2 to 5.

The volume of the smaller prism is 40 cm³. The volume of the larger prism can be found as follows:

(ratio of the edge length)³ = ratio of volume

Hence,

(2 / 5)³ = 40 / x

where

x = volume of the larger prism

Therefore,

8 / 125 = 40 / x

cross multiply

8x = 5000

x = 5000 / 8

x = 625 cm³

Therefore,

volume of the larger prism is 625 cm³

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Answer: Yes

Step-by-step explanation:

Yes, you can run different system voltages in the same conduit and boxes. The conductors must be rated for the highest voltage present and used on all circuits.

You need to get final payment for the cabinets before they enter the home. then bill for the installation the day of instillation and collect the check before you leave if possible

No, once installed they become part of the house, you can not remove the kitchen cabinets or any other cabinets that have been installed without the consent of the home owner in writing. if you are a good contractor why would you have to take the kitchen cabinets out of the house anyway. But if you have to you can take the doors.

Equation: y * 5 = 85

In this equation, 'y' represents the number of learners in class 9T, and '5' represents the number of pencils each learner receives. The equation states that the product of the number of learners (y) and the number of pencils each learner receives (5) is equal to the total number of pencils (85) that Mrs. Leclerc shares among the learners.

This equation can be used to solve for the value of 'y' by dividing both sides of the equation by 5. By doing so, we can determine the number of learners in class 9T based on the given information about the number of pencils shared.

For example, if we divide 85 by 5, the result is 17. Therefore, there are 17 learners in class 9T.

In summary, the equation y * 5 = 85 represents the situation where Mrs. Leclerc shares 85 pencils between the learners in class 9T, with each learner receiving 5 pencils. By solving the equation, we can find the number of learners in the class, which in this case is 17.

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Answer:

x = -4

y = -3

Step-by-step explanation:

-5y + 3x = 3

-8y + 9x = -12​

Time the first equation by -3

15y - 9x = -9

-8y + 9x = -12

7y = -21

y = -3

Now put -3 in for y and solve for x

-5(-3) + 3x = 3

15 + 3x = 3

3x = -12

x = -4

Let's Check

-5(-3) + 3(-4) = 3

15 - 12 = 3

3 = 3

So, x = -4 and y = -3 is the correct answer.

Answer:

400.00

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

The slope is 2/3 because you can look at the x-intercept which is -2. Find another point where the blue line crosses directly into the corner of the gray lines. The formula is rise/run. A point where the blue line crosses the gray line directly is (1,2). From the point (-2,0) you go up 2 places and then you go right three places to get to the other point. Therefore, your answer is 2/3.

You could also use the formula y1-y2/x1-x2. Now, you plot in the coordinates. 2-0/1--2= 2/3. Still, the answer would be 2/3.

Answer:

10

Step-by-step explanation:

32 - (5 x 3 + 7) first do the multiplication - order of operations is important!

32 - (15 + 7) then combine the numbers in the parentheses

32 - 22 now subtract

10

Answer:

(0, 50)

Step-by-step explanation:

The equation of a line is in the form of the y-intercept form

\(y = mx + b\)

where m is the slope and B is the y intercept. So in our case

\(y = 50 + 5x\)

if we use the commutative property we can rewrite our equation as

\(y = 5x + 50\)

therefore b = 50 is our why intercept

In order to convert centimeters (cm) into inches, we can use the conversion factor of 1 inch = 2.54 cm. So, 100 cm is equal to 39.37 inches.

To convert 100 cm into inches, we can use this conversion factor by dividing the number of centimeters by 2.54.

100 cm ÷ 2.54 = 39.37 inches

So, 100 cm is equal to 39.37 inches.

It's important to note that this conversion factor is based on the international standard for length measurements, known as the International System of Units (SI). This system is widely used around the world, but it's important to be aware that some countries may use different units of measurement.

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1. As the graph is exponential the sequence is geometric.

2. - Find the ratio r betwen each k(x) value and the previous one:

Use the next formula to get the recursive formula:

Being k1 the first term (81)

r the ratio you find above: (1/3)

k(x-1) is the prevoius term

3. As x is the number of cuts, it cannot be a negative number. And it needs to be an inerger number (as the number of cuts cannot be a decimal number)

Then:

x can be any interger possitive number (example: 6,7,8) also, the number of cuts cannot be a very large number as you cannot cut an object in infinitely parts.

Answer:

-8 and 6

Step-by-step explanation:

you can use any positive or negative number, i just decided to use these. plz mark brainliest and have a great day

Answer:

7 over 2x-2

Step-by-step explanation:

Answer:

g^-1 •7

7g^-1

7•1/g

answer is 7/g

I hoped I helped!! :)

Answer:

8 yes

10 yes

11 yes

12 yes

13 yes

Answer:

I'm pretty sure they are all correct except number 12.

Explanation:

I just solved almost all of these a few minutes ago and i did my math slowly and checked it two times.

To find the area of the region bounded by the polar curve r = 12 sin θ and the rays θ = 0 and θ = 7/3, we need to integrate the area of small sectors of the circle.

The polar curve r = 12 sin θ represents a sinusoidal curve that oscillates between -12 and 12, and passes through the origin. The curve intersects the positive θ-axis at θ = π/2 and the negative θ-axis at θ = 3π/2.

To find the limits of integration for θ, we need to determine the angles at which the curve intersects the rays θ = 0 and θ = 7/3.

When θ = 0, we have r = 0, which corresponds to the origin.

When θ = 7/3, we have:

r = 12 sin (7/3)

≈ 9.82

Therefore, the limits of integration for θ are 0 and 7/3.

The area of a small sector of the circle with radius r and central angle dθ is given by:

dA = (1/2) r^2 dθ

In our case, we have r = 12 sin θ, so:

dA = (1/2) (12 sin θ)^2 dθ

= 72 sin^2 θ dθ

To find the total area of the region, we need to integrate dA over the limits of integration for θ:

A = ∫₀^(7/3) 72 sin^2 θ dθ

Using the identity sin^2 θ = (1/2) (1 - cos 2θ), we can simplify the integral as follows:

A = 36 ∫₀^(7/3) (1 - cos 2θ) dθ

= 36 [θ - (1/2) sin 2θ]₀^(7/3)

= 36 [7/3 - (1/2) sin (14/3)]

The area is approximately 10.37 square units, which is closest to answer choice 4: area 10 8 0 1.

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Answer:

All you have to do is find the diameter and divide it by 2. I'm sorry if I can't give you a direct answer because I cannot see the diagram.

Step-by-step explanation:

Answer:

7=2.75

8=18

9=3.625

10=29

Step-by-step explanation:

Answer:

4-7=-3

-5-7=-12

Step-by-step explanation:

-5-7=-12

4-7=-3

The complete statement is data analysis involves creating new ways of modeling and understanding the unknown by using raw data.

Data analysis can be defined as the process of cleaning, changing, and processing raw data, to relevant information that helps in the decision making of a business.

The procedure of data analysis helps in reducing the risks involved in decision-making by providing useful insights and statistics,.

Analyzed data are often presented in charts, images, tables, and graphs.

Some types of data analysis are;

Thus, the complete statement is data analysis involves creating new ways of modeling and understanding the unknown by using raw data.

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Answer:

-18700%

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:

a) To find the value of \(\sf 3(x - y) \\\):

\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)

b) To find the value of \(\sf 6x - 6y \\\):

\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)

c) To find the value of \(\sf y - x \\\):

\(\sf y - x = - (x - y) = -4 \\\)

Therefore:

a) The value of \(\sf 3(x - y) \\\) is 12.

b) The value of \(\sf 6x - 6y \\\) is 24.

c) The value of \(\sf y - x \\\) is -4.

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The given series alternates in sign and decreases in absolute value, so the alternating series test tells us that it converges.

The series given is (-1)^n-1/n, where n starts from 1. We can use the alternating series test to determine whether it converges or diverges. According to the alternating series test, if the terms of the series alternate in sign and decrease in absolute value, then the series converges. Here, the terms of the series alternate in sign since (-1)^n-1 changes from positive to negative as n increases. Also, the absolute value of the terms decreases as n increases. Thus, we can conclude that the given series converges.

To further explain, the alternating series test works by comparing the series to the sum of the absolute values of the terms. In this case, the sum of the absolute values of the terms is 1/1 + 1/2 + 1/3 + …, which is a harmonic series that diverges.

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