Over the course of two hockey seasons, a star hockey player scored 39 goals while playing in 74 games. Express his scoring rate as a unit rate. Round your answer to the thousandths place.

Answer: Graph A shows the correct probability distribution.

Step-by-step explanation:

The probability of the spinner landing on "A" is 1/2. Similarly, the probability of the spinner landing on "B" is 3/8. Therefore, the probability of the spinner landing on "C" is 1-1/2-3/8=1/8. So:

probability of landing on "A" is 1/2 = 0.5,

probability of landing on "B" is 3/8 = 0.375, and

probability of landing on "C" is 1/8 = 0.125.

Thus the correct probability distribution should be answer choice \(\boxed{\text{A}}.\)

Total courses =5

Each course has 3 options

5 courses has

Hence

Answer: m = 15

Explanation:

Each (1 course) has 3 options

By multiplication,

5 courses shall have: (5 × 3) = 15 choices

By addition,

Sum of choices for 5 courses: (5 + 5 + 5) = 15 choices

Answer:

322.777778

Step-by-step explanation:

Answer:

11-8 =3

3*0.25=0.75

0.75+(0.49)8

0.75+3.92=4.67

The domain of the function f(x) = log_b(x) in interval notation is (0, +∞). The range of the function depends on the base b.

The domain of the logarithmic function f(x) = log_b(x) is determined by the requirement that the argument of the logarithm, x, must be positive. Since the logarithm is undefined for zero and negative numbers, the domain excludes these values. Therefore, the domain is expressed in interval notation as (0, +∞), where the parentheses indicate that zero is not included and the positive infinity symbol indicates that the domain extends indefinitely towards positive numbers.

The range of the logarithmic function depends on the base b. If the base b is greater than 1, the function can output any real number as the exponent increases or decreases, leading to a range of (-∞, +∞), covering all possible real numbers. However, if the base b is between 0 and 1, the logarithmic function only outputs negative numbers. As the exponent increases or decreases, the value of the logarithm approaches negative infinity, resulting in a range of (-∞, 0). This signifies that the range consists of all negative real numbers, but does not include zero or positive numbers.

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Answer:

49/16

Step-by-step explanation:

make the fraction into a mixed number then multiply have answer

Answer:

Feb 27, 2010 · Annette has 5 more dimes than quarters. The total amount of money she has is $3.30. How many of each coin?

Step-by-step explanation:

Answer:

Step-by-step explanation:

4 quarter is a dollar

another 4 is 2

8 quarter so far

then we are left with 1.30

i takes 13 dimes to get to 1.30

13 dimes is 1.30

8 quarter is 2 dolalrs

together it equals 3.30

and the dimes is five more than quarters

The experimental probability of randomly drawing a green marble is 56%

The table of values is given as:

| Red | Blue | Green |

| 10 | 12 | 28 |

So, we have

P(Green) = Green/Total

This gives

P(Green) = 28/(10 + 12 + 28)

Evaluate

P(Green) = 56%

Hence, the experimental probability of randomly drawing a green marble is 56%

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The system equation that models the amount of calories from fats (f) and proteins (p) that the individual can consume to reach 1,800 calories is: f + p = 1,200. The equation that relates calories from protein (p) to calories from fat (f) based on the prescribed diet is: p = 3f. Solving the system of equations, we find that the individual should consume 300 calories from fats and 900 calories from proteins.

To find the equation that models the amount of calories from fats and proteins that the individual can consume in order to reach 1,800 calories, we consider that 600 calories will come from carbohydrates. Since the total goal is 1,800 calories, the remaining calories from fats and proteins should add up to 1,800 - 600 = 1,200 calories. Therefore, the equation is f + p = 1,200.

Based on the prescribed diet, the individual is required to consume calories from protein that are three times the calories from fat. This relationship can be expressed as p = 3f, where p represents the calories from protein and f represents the calories from fat.

To solve the system of equations, we substitute the value of p from the second equation into the first equation: f + 3f = 1,200. Combining like terms, we get 4f = 1,200, and dividing both sides by 4 yields f = 300. Substituting this value back into the second equation, we find p = 3(300) = 900.

Therefore, the individual should consume 300 calories from fats and 900 calories from proteins to meet the diet requirements and achieve a total of 1,800 calories.

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Answer:

5uv+35uw+7sv-49sw

Step-by-step explanation:

u(5v+35w)+s(7v-49w)

=5uv+35uw +7sv-49sw

You need to multiply the numbers in the brackets by the number in front of the bracket.

hope it helps !!!!!

The angle between vectors u and v is approximately 43.7 degrees to the nearest tenth of a degree.

To find the angle between two vectors, we can use the dot product formula and the magnitude of the vectors. The dot product of two vectors u and v is given by:

u · v = |u| |v| cos(theta)

where |u| and |v| are the magnitudes of vectors u and v, respectively, and theta is the angle between the vectors.

Given vectors u = <6, 4> and v = <7, 5>, we can calculate their magnitudes as follows:

|u| = sqrt(6^2 + 4^2) = sqrt(36 + 16) = sqrt(52) ≈ 7.21

|v| = sqrt(7^2 + 5^2) = sqrt(49 + 25) = sqrt(74) ≈ 8.60

Next, we calculate the dot product of u and v:

u · v = (6)(7) + (4)(5) = 42 + 20 = 62

Now, we can substitute the values into the dot product formula:

62 = (7.21)(8.60) cos(theta)

Solving for cos(theta), we have:

cos(theta) = 62 / (7.21)(8.60) ≈ 1.061

To find theta, we take the inverse cosine (arccos) of 1.061:

theta ≈ arccos(1.061) ≈ 43.7 degrees

Therefore, the angle between vectors u and v is approximately 43.7 degrees to the nearest tenth of a degree.

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Answer: C

Step-by-step explanation: because d is different from the others by default

Answer:

c. 412.5 cm^2

Step-by-step explanation:

first triangle: 5 x 15 = 75

75/2 = 37.5

rectangle:  15 x 19 = 285

triangle 2: 15 x 12 = 180

180/2 = 90

37.5 + 285 + 90 = 412.5

$39.99+238.8+1.75x and  $4.99=1.99x+$40 are the algebraic expressions of given data.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Given that $39.99 /month, unlimited texting , 120MB data (Overages $1.99 /MB talk is $1.75 /minutes

$39.99+120(1.99)+1.75x

$39.99+238.8+1.75x

$4.99 /month, unlimited texting ,$40 for 80MB data talk is $1.99 /minutes

$4.99+1.99x+$40

Hence, $39.99+238.8+1.75x and  $4.99+1.99x+$40 are the algebaic expressions of given data.

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Answer:

a ) 7a + 12

b) b - 15

Step-by-step explanation:

a)2a+5a +8+8

= 7a + 12

b) b - 7 - 8

= b-15

Answer:

sin M = \(\frac{12}{13}\), tan M = \(\frac{12}{5}\), cos M = \(\frac{5}{13}\)

Step-by-step explanation:

The sine of an angle is equal to \(\frac{opposite}{hypotenuse}\).  The opposite (opposite from the angle) side is 12 and the hypotenuse is 13.

The tangent of an angle is equal to \(\frac{opposite}{adjacent}\).  The opposite side is 12 and the adjacent (next to the angle) side is 5.

The cosine of an angle is equal to \(\frac{adjacent}{hypotenuse}\).  The adjacent (next to the angle) side is 5 and the hypotenuse is 13.

Answer:

21.20%

Step-by-step explanation:

85-67=18

18/85=0.2112

0.2112x100 = 21.20

For a sample of 64 low-income children, the estimate of the true mean complexity score is 7.64

Parameter refers to the mathematical quantity calculated using population while statistics refers to the mathematical quantity calculated using sample.

Given, the sample mean of 64 children is 7.64 and the estimated population parameter value is equal to its statistics. So, here the estimated value of the mean sentence complexity score is equal to its sample mean value which is 7.64

So, an estimate of the true mean is sample mean=\(\bar x\)=7.64

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The complete question is given below:

Each child in a sample of 64 low-income children was administered a language and communication exam. The sentence complexity scores had a mean of 7.64 and a standard deviation of 8.94. Complete parts a through d. a. From the sample, estimate the true mean sentence complexity score of all low-income children.

The researcher used a within-subjects design in this study, which involves measuring the same group of participants under different conditions.

The research design used in this study is a within-subjects design, also known as a repeated measures design, where the same group of participants is measured twice, once during a period of abstinence and once during a period of red wine consumption with dinner.

This design allows the researcher to compare the cholesterol levels of the same group of participants under two different conditions, with and without red wine consumption, and therefore, eliminate potential individual differences between participants that could influence the results.

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Answer: Choice D

Explanation:

As you send more texts, the total phone bill goes up. We can see that the texts are the independent variable, and that the total bill relies (aka depends) on the number of texts sent.

To accumulate $2,176,097.00 in his retirement account by age 65, Derek needs to make annual deposits of $5,000.00 starting on his 27th birthday and ending on his 65th birthday, assuming an 8.00% interest rate.

To determine the annual deposits Derek needs to make, we can use the future value of an ordinary annuity formula. First, we calculate the number of years between Derek's 25th and 65th birthdays, which is 65 - 25 = 40 years. Next, we calculate the future value of the retirement account using the given interest rate of 8.00%. Using the formula:

Future Value = Present Value * (1 + interest rate)^number of periods

In this case, the future value is $2,176,097.00, the interest rate is 8.00%, and the number of periods is 40. We can rearrange the formula to solve for the present value:Present Value = Future Value / (1 + interest rate)^number of periods

Substituting the values:Present Value = $2,176,097.00 / (1 + 0.08)^40 = $123,529.31 (rounded to 2 decimal places)

Now, we need to find the annual deposit amount. Since Derek starts making deposits on his 27th birthday and ends on his 65th birthday, he makes deposits for 65 - 27 = 38 years.Annual Deposit = Present Value / ((1 + interest rate)^number of periods - 1)Substituting the values:

Annual Deposit = $123,529.31 / ((1 + 0.08)^38 - 1) = $5,000.00 (rounded to 2 decimal places)Therefore, Derek must make annual deposits of $5,000.00 into his retirement account starting on his 27th birthday and ending on his 65th birthday to accumulate $2,176,097.00 by the time he turns 65.

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The required probability for the parts which are examined for defects are ;

1. Probability of both the parts are good is equal to 0.375.

2. Probability represents exactly one part has major defect is 0.2333.

Here, we have,

Total number of parts to be examined for defects = 16

Number of good parts = 10

Number of parts with minor defects = 4

Number of parts with major defects = 2

Number of parts to be chosen at random without replacement = 2

Total number of outcomes = ¹⁶C₂

                                            = (16!) / ( 16 - 2 )!2!

                                            = 120

1. Probability of both the parts to be good

Number of favourable outcomes = ¹⁰C₂

                                                       = 10! / (8!)(2!)

                                                       = 45

Required Probability = 45 / 120

                                  = 0.375

2. Probability of exactly one major defect

Number of favourable outcomes= ²C₁ × ¹⁴C₁

                                                     = 2 × 14

                                                     = 28

Required Probability = 28/ 120

                                  = 0.2333

Therefore, the probability of both are good is 0.375 and probability of exactly one major defect is 0.2333.

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The above question is incomplete, the complete question is:

'16 parts are examined for defects. It is found that 10 are good, 4 have minor defects, and 2 have major defects. Two parts are chosen at random from the 16 without replacement; that is; the first part chosen is not returned to the mix before the second part is chosen:

1. What is the probability that both parts are good?

2. What is the probability that exactly one part has major defect?'

Answer: 9 feet, 22 feet and 23 feet

Step-by-step explanation:

Let the smallest side be x.

The middle length side is 4feet greater than twice the length of the smallest​ side. This will be:

= (2 × x) + 4 = 2x + 4

The longest side is 4feet less than 3 times the length of the smallest side. This will be:

= (3 × x) - 4 = 3x - 4

Perimeter = x + 2x + 4 + 3x - 4

x + 2x + 4 + 3x - 4 = 54

Collect like terms

6x = 54

x = 54/6

x = 9

The three sides are

Smallest side = 9 feet

Middle side = 2x + 4 = 2(9) + 4 = 18+4 = 22 feet

Longest side = 3x - 4 = 3(9) - 4 = 27 - 4 = 23feet

Answer:

A lower price and quantity would result.

The approximate profit the company makes on the item on a day when the item price is $40 is $9077.45.

Given the equation, y= −5.62x²+475.81x−962.95 represents the total y dollars of profit a company makes in one day on the item when the price of the item that day is x dollars.

The question asks to find the approximate profit the company makes on the item on a day when the item price is $40.

So, we need to substitute x = 40 in the given equation to find the value of y. We have:

y = -5.62(40)² + 475.81(40) - 962.95y

= -5.62(1600) + 19032.4 - 962.95y =

-8992.2 + 18069.45y

= $9077.45

Therefore, the approximate profit the company makes on the item on a day when the item price is $40 is $9077.45.

Option (c) is the correct answer.

Note: We know that 1 dollar = 100 cents. Therefore, 1 cent = 1/100 dollars. Hence, 0.45 dollars can be expressed as 0.45 x 100 cents = 45 cents.

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Answer:

0.333

Step-by-step explanation:

From the total of 300 workers in the factory :

a. Number of men = 200 and Women = 100

b. Number of workers works in the morning = 225

c. Number of workers unionized are 150.

d. Number of workers trustworthy are 50.

Total number of workers in the factory are 300.

a. Fraction of men in the factory are ( 2/3)

= 2/3 of 300

= 200

Women

= 300 -200

= 100

b. Number of workers in the morning shift are

= 3/4 of 300

= 225

c. Total number of workers unionized

= 1/ 2 of 300

= 150

d. Number of trustworthy workers

= 1/6 of 300

= 50

Therefore, out of 300 workers in the factory answer of the following questions are:

a. Number of men and women work in the factory are 200 and 100 respectively.

b. Number of workers works in the morning is 225.

c. Unionized workers = 150

d. Trustworthy workers = 50.

The above question is incomplete , the complete question is :

The Factory has 300 workers of which 2/3 are men, 3/4 work in the morning, 1/2 are unionized and 1/6 are trusted personnel.

a. How many men work in the factory and how many women?

b. How many workers work in the morning?

c. How many are unionized?

d. How many are trustworthy?

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Answer:

x=30

Step-by-step explanation:

dive 3x both sides then u should get 10