A group of students was asked about the number of times they had been water-skiing. The data is shown in the histogram.

A histogram titled Water Skiing Trips. The x-axis is labeled Number of Times Water Skiing and has intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every 1 units up to 6. There is a shaded bar for 6 to 10 that stops at 3, for 11 to 15 that stops at 5, for 16 to 20 that stops at 6, and for 21 to 25 that stops at 1. There is no shaded bar for the 1 to 5 interval.
Which of the following best describes the spread of the data?

Explain its meaning in this situation.

The data has a possible range of 19, which is a wide spread. This might mean that the most common number of water-skiing trips is 10.
The data has a possible range of 19, which is a wide spread. This might mean that there is a large difference in the number of water-skiing trips taken by the students.
The data has a possible range of 6, which is a narrow spread. This could mean that most of the students have taken a similar number of water-skiing trips.
The data has a range of 6, which is a narrow spread. This might mean that the most common number of water-skiing trips was 6.

The student is correct because we can factorize x² - x - 56 to get (x - 8)(x + 7).

How to Factorize an Expression?

In order to determine if -56 is the integer that can replace the box in the expression, we can try to factorize the expression and see if it works.

Factorize x² - x - 56 using the sum-product pattern:

x² - x - 56

Take out the common factors from each pair:

(x² + 7x) - (8x - 56)

x(x + 7) -8(x + 7)

Rewrite in factored form:

(x - 8)(x + 7)

Thus, this shows that the student is correct.

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Answer:B

Step-by-step explanation:i did the quiz

ΔPQR and ΔMNR are similar  and if  MN = 15 ft then the side length of QP is 52.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

ΔPQR and ΔMNR are similar are similar because both have the corresponding angles are congruent and the corresponding sides are in proportion .

If MN=15 feet we have to find QP

As sides are proportional

45/13=QP/15

Apply cross multiplication

45×15=13QP

675=13QP

Divide both sides by 13

QP=52

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In total, Christian had 62 customers in the last week.

The rate of car is 35 mph.

Given that engineer traveled 140 mi by car and then an additional 750 mi by plane. The rate of the plane was three times the rate of the car.

Let c be the rate of wind.

215 + c = rate of plane with wind

215 - c = rate of plane against wind

Therefore, the travel time =distance/rate

⇒ 750/(215+c) = 540/(215-c)

Cross multiplying we get,

540(215+c) = 750(215-c)

116100+540c = 161250-750c

1290c = 45150

c=35

Hence, the rate of car is 35 mph.

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In the words that your describing it, I supposed we are talking about the pythagorean theorem

What is the formula for the theorem?

a^2+b^2= C^2

A being the height

B being the Bottom

C being the slant or hypotenuse

How to Solve?

Well supposed 9 is a and 6 is b

[tex]9^{2}[/tex]+[tex]6^{2}[/tex]=[tex]c^{2}[/tex]

9 squared is 81 and 6 squared is 36

81+36= 117

So, 117=[tex]c^{2}[/tex]

Which means [tex]\sqrt{117}[/tex] is the answer or 10.8

Hope this helped!

Answer: 4:42

Step-by-step explanation:

4:30 + 0:12 = 4:42

The answer is : No, this time there is not a fixed number of trials,

Fixed Number of Trials (n): Established beforehand, the experiment consists of a specified set of trials or repetitions.

Binary Outcomes: Every trial possess just two feasible outcomes typically referred to as "success" and "failure."

Independent Trials: The result of a single trial will not affect the outcome of any subsequent trials.

Constant Success Probability (p): Per trial, the chances of success remain unchanging.

Taking into account the given circumstances, Ms. Lee intends on giving out another homework pass consequently, she will keep pulling names until concluding with a statistics student. She rearranges and shuffles the papers which contain the names in-between each trial.

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If 5 is subtracted from the square of a number, the positive solution is √5.

In this exercise, you are required to determine or solve for an unknown number as follows. First of all, we would assign a variable to the unknown number and then translate the word problem into an algebraic expression as follows;

Assuming the unknown number is represented by the variable x.

Therefore, the required algebraic expression is given by;

x² - 5

In order to determine the positive solution, we would have to equate the algebraic expression to zero as follows;

x² - 5 = 0

x² = 5

x = ±√5

x = √5 (positive solution)

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The solution to the equation as it is given in (8) above is -21.

According to the subtraction property of equality, If you subtract the same number from both sides of an equation, the equation remains true.

Also by the multiplication  property of equality,  If you multiply both sides of an equation by the same number (except zero), the equation remains true.  These can be used to solve the question in (7) above

Given;

280 = -8(-14 + x)

280 = 112 - 8x

280 - 112 = -8x

x = -21

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The wingspan (in feet) of the actual airplane is equal to 87.5 feet.

A property of equality which you would use to solve the equation -15 = x/3 + 18 is: D. Subtraction property of equality and multiplication of equality.

The solution of the equation 280 = -8(-14 + x) is: B. x = -21.

Based on the scale model, we can logically deduce that the airplane has a length of 12.2 inches and a wingspan of 12.5 inches. This ultimately implies that, we would convert from inches to feet as follows;

1 inch = 1/12 feet

12.2 inches = 12.2 × 1/12 = 12.2/12 feet.

Therefore, the scaled factor is given by;

Scale factor = (85.4 × 12/12.2)

For the actual length of the wingspan with a scaled length of 12.5 inches, we have:

12.5 inches = 12.5/12 feet

Actual length of wingspan = 12.5/12 × (85.4 × 12/12.2)

Actual length of wingspan = 87.5 feet.

-15 = x/3 + 18

x/3 = -15 - 18 ⇒ (Subtraction property of equality)

x/3 = -33

x = 3(-33) ⇒ (Multiplication property of equality)

x = -99

280 = -8(-14 + x)

280 = 112 - 8x

8x = 112 - 280

x = -168/8

x = -21

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Answer:

1st one is b.  2nd one is A

Step-by-step explanation:

i did the quiz

The missing term of the factorization equation is A = ( -15x - 1 ) ( x + 2 )

Given data ,

Let the equation be represented as A

Now , the value of A is

A = -15x² - 31x - 2

On simplifying , we get

The expanded form of the expression ( -15x - 1 ) ( x + 2 ) can be calculated using the distributive property of multiplication over addition

So , on factorizing , we get

A = ( -15x - 1 ) ( x + 2 )

Hence , the factorized equation is A = ( -15x - 1 ) ( x + 2 )

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The complete question is attached below :

Fill in the missing terms to complete the factorization. 15x² + x - 2 = (? -1) (? + 2)

a- 3x, 5x

b- x, 15x

c- 5x, 3x

d- 15x, x

Answer:g=g(9)

Step-by-step explanation:

The total at 0 id 100 hours and rate if increasing is 50 per hour.

From the given graph;

Let x represents the total hours

And y represents total pay

Then,

(a) When x = 0

Then from graph we have y = 100

So total pay is 100 dollars.

(b) When x = 1 then y = 150

Therefore,

Rate of increasing = (150-100)/(1-0) = 50

So it is increasing 50 per hour.

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The approximate value of the median is 25

The median is the middle number in a sorted, ascending, or descending, list of numbers and can be more descriptive of that data set than the average.

The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values.

To find the median, calculate the value mean by adding together the middle values and dividing them by two.

Hence, the approximate value of the median is Median

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What is the approximate value of the median?

A 18

B 20

C 25

D 27

The value of the angle y is 86 degrees

To determine the value of the variable, we need to take note of the properties of a parallelogram. They include;

Also, note that angles on a straight line is equal to 180 degrees.

From the information shown on the diagram, we have;

y + 94 = 180

collect the like terms

y = 180 - 94

Subtract the terms

y =86 degrees

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Answer:

To find the probability that a person surveyed is under 40 given that he or she gets the news by reading the paper, we need to use Bayes' theorem:

P(Under 40 | Read paper) = P(Read paper | Under 40) * P(Under 40) / P(Read paper)

where

P(Under 40 | Read paper) is the probability that a person is under 40 given that he or she gets the news by reading the paper

P(Read paper | Under 40) is the probability that a person under 40 reads the paper (36/80)

P(Under 40) is the overall probability of selecting a person under 40 (40/80)

P(Read paper) is the overall probability of selecting a person who reads the paper, calculated as the sum of those who are under 40 and read the paper and those who are 40 or older and read the paper (36+24)/(80)

Plugging in the values, we get:

P(Under 40 | Read paper) = (36/80) * (40/80) / ((36+24)/80)

P(Under 40 | Read paper) = 0.6

So the probability that a person surveyed is under 40, given that he or she gets the news by reading the paper, is 60%.

The requried probability that Luc gets both questions correct is 1/16 or approximately 0.0625.

The probability of guessing a single question correctly is 1/4, since there are 4 answer choices and only 1 is correct. Since the questions are independent, the probability of guessing both questions correctly is the product of the probability of guessing each question correctly.

Therefore, the probability that Luc gets both questions correct is:

P(both correct) = P(first correct) * P(second correct)

P(both correct) = (1/4) * (1/4)

P(both correct) = 1/16

Thus, the probability that Luc gets both questions correct is 1/16 or approximately 0.0625.

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Answer:

Step-by-step explanation:

It is

4

√

12

=

4

√

3

⋅

4

=

4

⋅

2

⋅

√

3

=

8

√

3

The value of the side length h is 19.1 cm.

The figure in the image is a right triangle:

Angle θ = 47 degrees

Opposite to angle θ = 14cm

Hypotenuse = h

To solve for side length h, we use trigonometric ratio.

Note that: sine = opposite / hypotenuse

Plug in the values and solve for h.

sin( 47° ) = 14 / h

h = 14 / sin( 47° )

h = 19.1 cm

Therefore, the value of h is 19.1 cm.

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a) An equation representing Christina's investment's value, y, after x years is y = 10,000(1.05)^x.

b) Using the above equation, Christina's investment will be worth a future value of $26,532.98 after 20 years.

The principal = $10,000

Annual compound interest rate = 5%

The investment period = 20 years

Let the value of the investment after x years = y

Let the number of investment periods = x

y = 10,000(1.05)^20

= $26,532.98

Online finance calculator, the future value is determined as follows:

N (# of periods) = 20 years

I/Y (Interest per year) = 5%

PV (Present Value) = $10,000

PMT (Periodic Payment) = $0

Results:

FV = $26,532.98

Total Interest = $16,532.98

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The investment compounds at a 5% interest rate yearly.

The 99% confidence interval for the proportion of Americans who believe that the minimum wage should be raised is: 0.56 < P < 0.64

We are given:

Sample size: n = 1000

Sample proportion: p = 600/1000 = 0.6

Formula for confidence interval for proportion is:

CI = p ± z√(p(1 - p)/n)

where:

p is sample proportion

n is sample size

z is z-score at confidence level

z at 99% CL = 2.576

Thus:

CI = 0.6 ± 2.576√(0.6(1 - 0.6)/1000)

CI = 0.6 ± 0.04

CI = (0.56, 0.64)

CI = 0.56 < P < 0.64

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The checkbook balance is $5703.25.

To find the checkbook balance, we need to start with the original balance and then subtract the amounts of the checks written and add the amount of the deposit.

Original balance: $7349.44

Checks written: $1349.67 + $344.12 = $1693.79

Deposit: $956.60

To find the checkbook balance, we can subtract the total amount of the checks written from the original balance and then add the deposit:

Checkbook balance = Original balance - Checks written + Deposit

Checkbook balance = $7349.44 - $1693.79 + $956.60

Checkbook balance = $5703.25

Therefore, the checkbook balance after store manager deposited $956.60 is $5703.25.

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The simplified expression is 120x³ + 120x².

To simplify the expression 5x(2x+2)12x, we can use the distributive property of multiplication over addition and simplify the resulting terms.

First, we distribute 5x to the expression (2x+2), which gives us:

5x(2x+2) = 10x² + 10x

Next, we can multiply the result by 12x:

12x(10x² + 10x) = 120x³ + 120x²

Therefore, the simplified expression is 120x³ + 120x².

We can see that the original expression was a multiplication of three factors, and we used the distributive property to simplify it by expanding and multiplying the resulting terms. The final expression has a common factor of 120x², which we can factor out to get 120x²(x+1).

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The value of the expression 5z - 3z, when z is equal to 3, is 6.

Given the expression in the question:

Evaluating an expression simply means substituting the given value of a variable into the expression and simplifying the result.

Given the expression 5z - 3z, we are given the value of z as 3.

Hence, we substitute z with 3 in the expression:

5z - 3z

Plug in z = 3

5(3) - 3(3)

Simplifying further using the order of operations (multiplication before subtraction), we get:

15 - 9

= 6

Therefore, the value of the expression is 6.

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Answer:

a₈₁ = - 482

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 2 and d = a₂ - a₁ = - 8 - (- 2) = - 8 + 2 = - 6 , then

a₈₁ = - 2 + (80 × - 6) = - 2 + (- 480) = - 2 - 480 = - 482

The correct box plot is

A box plot uses a number line from 7 to 46 with tick marks every one unit. The box extends from 22.5 to 33.5 on the number line. A line in the box is at 30. The lines outside the box end at 10 and 40.

We have the data:

10, 14, 20, 25, 29, 30, 30, 31, 32, 35, 39, 40 .

So, First Quartile(Q1) = ((n + 1)/4)th Term.

= (12+1)/4

= 13/4

= 3.25 th term

=  (20+25)/2

= 22.5

and, Second Quartile or median (Q2) = ((n + 1)/2)th Term.

Q₂ = ((12 + 1)/2)th term

   = 6.5th term

   = 30

and, Third Quartile(Q3) = (3(n + 1)/4)th Term.

Q₃ =3 (3.25)

    = 9.75

   = 33.5

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