What are some benefits of representing data sets using frequency distributions What are some benefits of using graphs of frequency distributions? What are some benefits of representing data sets using frequency distributions? Organizing the data into frequency distribution can make patterns within the data more evident: Organizing the data into frequency distribution makes it possible to graph quantitative data_ It is easier t0 determine the minimum and maximum values of a data set when has been arranged into a frequency distribution. What are some benefits of using graphs of frequency distributions? It can be easier t0 determine the class boundaries by looking at a graph of the frequency distribution_ Graphing a frequency distribution makes possible to determine the relative frequencies of each of the classes_ It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution_ Graphing frequency distribution makes it possible to find the total number of observations.

The percentage of the down payment in the purchase is 15% and the down payment of $67500 will be 45% of the purchase price.

The ratio of the actual worth to the total value multiplied by 100 is the formula for calculating the percentage.

The percentage formula is given by

Here we have

A family buys a studio apartment for $ 150,000

The down payment paid by the family is $ 22500

a. Percentage of down payment in the purchase

From the above data,

The percentage of the down payment = [tex][ \frac{22500 }{150,000} \times 100 ][/tex]  

= [tex][ \frac{22500 }{1500} ][/tex] =  15

Therefore,

The percentage of the down payment is 15%  

b. The percentage of the purchase price would be a $67500 down payment?    

Let x  be the percentage of the down payment in the purchase amount  

=>  [tex]\frac{x}{100} \times $ 150,000 = 67500[/tex]  

=>  [tex]x \times 1500 = 67500[/tex]

=>  x = 67500/1500

=>  x = 45%

Therefore,

The percentage of the down payment in the purchase is 15% and the down payment of $67500 will be 45% of the purchase price.

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-x2+3x-3=0 is the equation that  has the sum of its roots as 3.

A quadratic equation's roots are equal to the second term's coefficient negated, divided by the leading coefficient. The constant term (the third term), divided by the leading coefficient, is equivalent to the product of the roots of a quadratic equation.

Sum of roots= -b/a

Sum of root is defined as:

Sum of root = -b/a

Consider option B -x^2+3x-3

a=-1 , b=3

Sum of root= - 3/(-1)=3

So B is the correct option of the following question.

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Answer: x= -1

Step-by-step explanation:

5(x+2)= 3(x+3)-1

5x + 10 = 3x + 9 -1

5x + 10 = 3x + 8

2x = -2

x= -1

A student who obtained a percentile rank of 75 on an achievement test is best characterized as having scored higher than 75% of the test takers.

What is percentile rank?

A percentile rank describes a student's performance in relation to other students in the same grade and subject who made up the specific norm group. The percentile rank of a student indicates whether their score was equal to or higher than the percentage of students in the norm group.

The percentage of scores in a frequency distribution that are lower than a given score is known as the percentile rank of that score in statistics.

A percentile rank of 75 indicates that the student outperformed 75% of the other students in his or her norm group, and 25% of the students outperformed your student.

Hence, a student who obtained a percentile rank of 75 on an achievement test is best characterized as having scored higher than 75% of the test takers.

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There are 144 ways to place 4 pairs of shoes per shelf in the store.

What is a permutation?

The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged. Put simply, a permutation is a word that describes the number of ways things can be ordered or arranged. With permutations, the order of the arrangement matters.

This question can be solved using basic logic . One can also solve this by using permutations.
Since 12 different models arrive and 4 pairs of shoes should be placed per shelf , the answer can be sort by

4!×3! = [ 4×3×2×1] × [3×2×1] = 24×6 = 144.

( Because 4 pairs of shoes can be interchanged among themselves , therefore 4! , and 12/4=3 , so the 12 pair of shoes can be organised amongst 3 shelves , and hence 3!)
Therefore , none of the options is correct. The correct answer is 144 ways.
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Answer:

Step-by-step explanation:

2,637

The number of nickels is 173.

The number of dimes is 258.

The number of quarters is 69.

The coins are worth $51.7.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

For every 2 nickles, there are 3 dimes.

For every 2 dimes, there are 5 quarters.

This means,

Let,

Nickles = N

Dimes = D

Quarters = Q

2N = 3D

N = 3D/2

2D = 5Q

Q = 2D/5

Now,

N + D + Q = 500

3D/2 + D + 2D/5 = 500

15D + 10D + 4D = 500 x 10

29D = 5000

D = 5000/29

D = 173

Now,

N = 3 x 172 / 2

N = 3 x 86

N = 258

Q = 2 x 172 / 5

Q = 69

Now,

Total coins = 500

173 + 258 + 69 = 500

Now,

20 nickels = $1

10 dimes = $1

4 quarters = $1

So,

173 nickels = $1 x 173 / 20 = $8.65

258 dimes = $1 x 258 / 10 = $25.8

69 quarters = $1 x 69 / 4 = $17.25

The total worth.

= $8.65 + $25.8 + $17.25

= $51.7

Thus,

The number of nickels is 173.

The number of dimes is 258.

The number of quarters is 69.

The coins are worth $51.7.

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It means 3 km in 1 minutes.

I think this is a speed of an object which shows that it can run or walk 3km in 1 minutes.

hope you understand.

The results of the evaluation of the given expression; (2t+3g) divided by 4 as required is; 7.

It follows from the task content that the result of the evaluation of the given expression is to be determined according to the information provided.

Therefore, since the expression to be evaluated is; ( 2t + 3g ) / 4.

Where; g = 2, r = 3 and t = 11.

Therefore, we have;

( 2(11) + 3(2) ) / 4

= ( 22 + 6 ) / 4

= 28 / 4

= 7.

Therefore, the result of the expression evaluation is; 7.

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Answer:

Step-by-step explanation:

4/14

Divided both by 2

2/7

Answer: 29%

Step-by-step explanation:

To find the percent of decrease, you need to first calculate the difference between the original cost and the current cost of the TV. You can do this by subtracting the current cost from the original cost: $700 - $500 = $200.

Next, divide the difference by the original cost and multiply by 100% to express the result as a percentage: ($200 / $700) * 100% = 28.57%.

Rounding this result to the nearest whole percent, we get that the percent of decrease is 29%.

Rounded to the nearest whole percent, the answer is 29%.

B. 5/3 is the evaluation of [tex]log_{8} 32[/tex] using the base conversion method.

using the base conversion - [tex]log_{a} p= \frac{log_{b} p}{log_{b} a}[/tex]

convert the base 8 into the base 2 algorithm

[tex]\frac{log_{2} 32}{log_{2} 8}[/tex]

since 32=[tex]2^{5}[/tex]

then, [tex]log_{2}(32)=5[/tex]

similarly, since [tex]8=2^{3}[/tex]

then, [tex]log_{2} (8)=3[/tex]

this makes our expression 5/3.

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Answer:

5/3

Step-by-step explanation:

The change of base formula says logb b a = [logc c a] / [logc c b].

To evaluate log8 32, you need to use the following equation: log8 32 = x, where x is the unknown value.

This can be rewritten as 8^x = 32.

Solving for x gives x = 5/3.

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Answer:

B

Step-by-step explanation:

Based on the provided table and equation when the class size is 1, gymnastics is less expensive, and when the class size is 3 or 4, ice skating is less expensive.

Given that y denotes the price and x denotes the number of classes, the gymnastics programmed is completed by the table, whereas the ice skating program is concluded by the equation y = 18x + 20.

Find the cost of the ice skating programmed for classes 1, 2, 3, and 4 as the table already lists the price for each specified number of gymnastics courses.

For 1 class, substitute x = 1 into y = 18x + 20:

y = 18(1) + 20

y = $38

For 2 class, substitute x = 2 into y = 18x + 20:

y = 18(2) + 20

y = $56

For 3 class, substitute x = 3 into y = 18x + 20:

y = 18(3) + 20

y = $74

For 4 class, substitute x = 4 into the equation y = 18x + 20:

y = 18(4) + 20

y = $92

We may infer from the foregoing that gymnastics is less expensive when the number of lessons is 1. When there are three or four courses, ice skating is less expensive.

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The value of x in the first question is 11 and the value of y is 3.

The value of x in the second question is 4 and the value of y is 4.

The value of x in the third question is -5 23/26 and the value of y is -1/13

2x + y = 25 equation 1

2x - 3y = 13 equation 2

The first step is to subtract equation 2 from equation 1:

-4y = -12

Divide both sides of the equation by -4

y = -12 / -4

y = 3

Substitute for y in equation 1:

2x + 3 = 25

2x = 25 - 3

2x = 22

x = 22 / 2

x = 11

-3x + 4y = -18 equation 1

x = -2y - 4

x + 2y = -4 equation 2

Multiply equation 2 by 2

2x + 4y = -8 equation 3

Subtract equation 3 from equation 2:

-5x = -20

Divide both sides of the equation by -5

x = -20 / -5

x = 4

Substitute for x in equation 2:

4 + 2y = -4

4 + 4 = 2y

8 = 2y

y = 8/2

y = 4

-2x + 3y = -15 equation 1

3x + 2y = -23 equation 2

Multiply equation 1 by 3 and equation 2 by 2

-6x + 9y = -45 equation 3

6x + 4y = -46 equation 4

Add equation 3 and equation4 together

13y = -1

y = -1/13

Substitute for y in equation 1:

-2x + 3(-1/13) = -15

-2x  -3/13 = -15

-2x = -15 + 3/13

-2x = 11 10/13

x = 11 10/13 ÷ -2

x = 153/13 x -1/2

x = -153/26

x =-5 23/26

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Answer:  D

Step-by-step explanation:

Answer: D

Step-by-step explanation:

We are trying to find out how this situation leads to 30 miles for d.

We know he has 14 miles to the gas station, and he has gone an unknown amount in 2 hours, t.

30=Xt+14

Solving for X: 30=X(2)+14

X=8

They both make 3 baskets. The number of points Norma and vincent have after first time out are 6 points and 9 points respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time.

If the number of basket is x, and the total point is y, thus

for Norma, the total point = 19+2x=y equation 1

for vincent, the total point = 16+3x= y equation 2

subtract equation 1 from 2

16-19+3x-2x = 0

-3+x = 0

x= 3

substitute 3 for x in equation 1

19+2(3)= y

25= y

y = 25

therefore they both made 3 basket after the first time out and Norma make extra 6 points and Vincent made extra 9 points

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Answer:

48/7

Step-by-step explanation:

8/7/6

= 8 × 1/7/6

= 8× 6/7

48/7

D. At the end of 20 years, the policy's cash value will equal $100,000 is INCORRECT regarding a $100,000 20-year level term policy.

A $100,000 20-year level term policy is a type of life insurance policy that provides a fixed amount of coverage for a set period of time. The premiums for this policy will remain level for the entire 20 years and, if the insured dies during that time, the beneficiary will receive the full $100,000. However, the policy will expire at the end of the 20-year period and the cash value will not equal the $100,000. As a result, it is untrue to say that $100,000 will be the policy's cash value after 20 years.

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On solving the provided graph question, we got to know that - the area below the line will be taken into account.

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph.

Given : equation  2x + 3y ≤ 6

Out of the options provided, we must select the graph that displays the graph of the solution set for the equation 2x + 3y 6.

Consider the given equation   2x + 3y ≤ 6

We first find the points where the equation cut x- axis and y-axis.

Thus,

[tex]For x - axis put y = 0 ,\\We get 2x + 3(0) \leq 6 =2x \leq 6 x \leq 3\\Thus, point (3,0)\\For y - axis put x = 0 ,\\We get 2(0) + 3y \leq 6 = 3y \leq 6 = y \leq 2\\Thus, point (0,2)[/tex]

For each region, we select a test point, determine the values of x and y there, and then determine whether or not the inequality is satisfied.

Take into account the point (0, 0), and inequality becomes,

[tex]2(0) + 3(0) \leq 6 = 0 \leq 6 (true)\\[/tex]

So, the area below the line will be taken into account.

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The compass needle always points north because it is magnetic north pole.

Earth has magnetic field due to magnetic elements present in Earth's core in molten form. They are assumed to be in the form of giant bar to ease the calculations concerning magnetic field and polarity. The assumptions are geographic south pole harbours magnetic north pole and vice versa for the opposite pole.

So, we know that like poles attract each other and unlike poles repel each other. The north end of magnetic needle will point towards the magnetic south pole which is geographic north pole. Thus, we see compass needle directed to North pole.

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Classification model

What is Classification model?

A subset of supervised machine learning is classification models. A categorization model takes in some input and produces an output that categorises the input. For instance, after reading an email, a model may binary identify it as spam or not.

This is a classification model. This is a categorization model because we are categorising people here according to their age and location.

A categorization model takes in some input and produces an output that categorises the input.

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Answer:

Step-by-step explanation:

23

Answer:

Step-by-step explanation:

2^x + 7 = 3

2^x = -4          this cannot be solved

Maybe you meant

2^(x+7) = 3    

LOG both sides to get

 (x+7)  LOG 2 =  LOG 3

x+7 = log3/log2      subtract 7 from both sides to get

x = - 5.415

All veterinarians that responded to the questionnaire were included in the sample.

Complete Question : Veterinarians often use non-steroidal anti-inflammatory drugs to treat lameness in horses. A group of veterinary researchers wanted to find out how widespread the practice was in the United States. They obtained a list of all veterinarians treating large animals, including horses. They sent questionnaires to all the veterinarians on the list. Such a survey is called a census. The response rate was 40%. Which of the following statement is correct?

a. The sample consisted of all veterinarians on the list and therefore equaled the target population.

b. The sample consisted of all veterinarians who returned the questionnaire.

c. The sample consisted of all veterinarians who treat horses with NSAIDs.

d. None of the choices are correct.

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The function represented in graph is f(x) = 4cos(x) - 1. We can find it by putting given points in following options and checking whether it is matching to graph or not  (hit and trial method)

What are trigonometric functions?

6 trigonometric functions are Sine, Cosine, Tangent, Cotangent, Secant, Cosecant .

Cosine ranges from (-1 to 1) for x.

Given points are 0, pi, and 2pi

For 0 , cos(0)= 1

For pi, cos(pi) = -1

For 2pi, cos(2pi) = 1

In f(x) = 4cos(x)-1

For x = 0,

f(0)=4cos(0)-1

3 = 3 i.e. correct.

For x = pi

f(pi) = 4cos(pi)-1

-5 = -5 i.e.  correct

also correct for 2pi.

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Answer:

there should be 1 customer waiting in line at the ticket outlet.

Step-by-step explanation:

To calculate the expected number of customers in the queue, we can use the following formula:

Expected number of customers = Arrival rate * Average waiting time

In this case, the arrival rate is 10 customers per hour and the average waiting time is 6 minutes. Converting the waiting time to hours, we get:

Expected number of customers = 10 customers/hour * (6 minutes / 60 minutes/hour) = 1 customer

So the expected number of customers in the queue is 1. This means that on average, there should be 1 customer waiting in line at the ticket outlet.

Answer:

y = 1.50x

the graph is shown below

Step-by-step explanation:

We are told that y is equal to the total cost of the amount of grapefruit purchased. The amount of grapefruit is represented by x. The price of $1.50 would be our rate or slope for the graph.

With this information, we can create the expression:

y = 1.50x

To find the graph you need, either type it in a graphing calculator, or put in your choice of "x" values to find different coordinate that would be on the graph.

For example:

y = 1.50(2)

y = 3

Coordinate 1 would be (2,3)

y = 1.50(0)

y = 0

Coordinate 2 would be (0,0)

With these two coordinates you can draw a line and match your graph with the right one you need for the answer.

Answer:

The second one

Step-by-step explanation:

The first graphic would be correct if the connector was "AND" instead of "OR"

"AND" --> Both conditions must ALWAYS be fulfilled

"OR" ---> It's only necessary that one of the conditions is fulfilled

A sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.

We have that to find our  level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.96}{2} =0.02[/tex]

Now, we have to find z in the Z table as such z has a p value of [tex]1-\alpha[/tex] .

So it is z with a p value of 1-0.02 = 0.98, so z= 2.055

Now, find the margin M as such

[tex]M = Z*\frac{\sigma }{\sqrt{n} }[/tex]

In which [tex]\sigma[/tex]  is the standard deviation of the population and n is the size of the sample.

In this problem, we have that:

[tex]\sigma = 40 , M = 10\\\\M = Z*\frac{\sigma}{\sqrt{n} } \\\\10 = 2.055*\frac{40}{\sqrt{n} } \\\\\sqrt{n} = 8.22\\\\n= 67.6[/tex]

Hence , a sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.

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1. Move 12 to the right side.

2. Divide both sides by -7.

3. Simplify.

4. Square both sides.

5. Solve [tex]x-5=\frac{64}{49}[/tex]

Hence, our solution.

_______________________

Hope this helps!