HELP!!!!!! Apply the distributive property to create an equivalent expression. 1/5 (15+10k) (7th grade)

Given the expressions, f(x)=√x+5, g(x)=3x-7, and h(x)=5x, the answer to f(g(5)) is 8. This is because when g(5) is substituted into f(x) we get f(g(5))=f(3x-7)=√(3x-7)+5. When 5 is substituted for x, this simplifies to f(g(5))=√(-2)+5 which equals 8.

The answer to g(f(78)) is 60. This is because when 78 is substituted into f(x) we get f(78)=√78+5 which simplifies to f(78)=9. When 9 is substituted into g(x) we get g(f(78))=3x-7 which simplifies to g(f(78))=3(9)-7 which equals 60.

Finally, the answer to h(g(f(2))) is 83. This is because when 2 is substituted into f(x) we get f(2)=√2+5 which simplifies to f(2)=3. When 3 is substituted into g(x) we get g(f(2))=3x-7 which simplifies to g(f(2))=3(3)-7 which equals 8. When 8 is substituted into h(x) we get h(g(f(2)))=5x which simplifies to h(g(f(2)))=5(8) which equals 83.

In summary, the answers to f(g(5)), g(f(78)), and h(g(f(2))) are 8, 60, and 83 respectively.

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The probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

To solve this problem, we'll use the M/M/1 queueing model with Poisson arrivals and exponential service times. Let's calculate the required values: (a) Percentage of time Judy is idle: The utilization of the system (ρ) is the ratio of the average service time to the average interarrival time. In this case, the average service time is 10 minutes, and the average interarrival time is 12 minutes. Utilization (ρ) = Average service time / Average interarrival time = 10 / 12 = 5/6 ≈ 0.8333

The percentage of time Judy is idle is given by (1 - ρ) multiplied by 100: Idle percentage = (1 - 0.8333) * 100 ≈ 16.67%. Therefore, Judy is idle approximately 16.67% of the time. (b) Average waiting time for a student:

The average waiting time in a queue (Wq) can be calculated using Little's Law: Wq = Lq / λ, where Lq is the average number of customers in the queue and λ is the arrival rate. In this case, λ (arrival rate) = 1 customer per 12 minutes, and Lq can be calculated using the queuing formula: Lq = ρ^2 / (1 - ρ). Plugging in the values: Lq = (5/6)^2 / (1 - 5/6) = 25/6 ≈ 4.17 customers Wq = Lq / λ = 4.17 / (1/12) = 50 minutes. Therefore, on average, a student spends approximately 50 minutes waiting in line.

(c) Average length of the line: The average number of customers in the system (L) can be calculated using Little's Law: L = λ * W, where W is the average time a customer spends in the system. In this case, λ (arrival rate) = 1 customer per 12 minutes, and W can be calculated as W = Wq + 1/μ, where μ is the service rate (1/10 customers per minute). Plugging in the values: W = 50 + 1/ (1/10) = 50 + 10 = 60 minutes. L = λ * W = (1/12) * 60 = 5 customers. Therefore, on average, the line consists of approximately 5 customers.

(d) Probability of finding at least one student waiting in line: The probability that an arriving student finds at least one other student waiting in line is equal to the probability that the system is not empty. The probability that the system is not empty (P0) can be calculated using the formula: P0 = 1 - ρ, where ρ is the utilization. Plugging in the values:

P0 = 1 - 0.8333 ≈ 0.1667. Therefore, the probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

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a) The coefficients of the regression equation are given as follows:

b) The regression equation is defined as follows: y = 0.9x + 7.6.

c) The estimate of y when x = 6 is given as follows: y = 13.

The slope-intercept definition of the regression equation is given as follows:

y = b1x + b0.

In which the parameters are given as follows:

The points from the table in this problem are given as follows:

(2,7), (6, 18), (9,9), (13, 26), (20,23).

Inserting these points into a linear regression calculator, the equation is given as follows:

y = 0.9x + 7.6.

Then the estimate of the value of y when x = 6 is obtained as follows:

y = 0.9(6) + 7.6 = 13.

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i) The multiplication of (3.1x\(10^0\)) and (1.5x10) results in 4.65x\(10^1\).

j) The division of (3.1x10) by (1.5x\(10^{-1\)) equals 2.07x\(10^1\).

i) To multiply numbers in scientific notation, we multiply the coefficients (3.1 and 1.5) and add the exponents (0 and 1) together. In this case, 3.1 multiplied by 1.5 gives us 4.65. Adding the exponents, \(10^0\) multiplied by \(10^1\) results in \(10^1\). Therefore, the final result is 4.65x\(10^1\).

j) When dividing numbers in scientific notation, we divide the coefficients (3.1 and 1.5) and subtract the exponents (1 and -1) from each other. Dividing 3.1 by 1.5 gives us approximately 2.07. Subtracting the exponents, \(10^1\)divided by \(10^{-1\) is equivalent to \(10^{(1-(-1))}\) which simplifies to 10^2. Hence, the result is 2.07x\(10^1\).

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Answer:

1: +

2: +

3: -

4: +

5: -

6: -

Step-by-step explanation:

hope this helps!

Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

Answer:

if it takes 4 people for 2 days

4+4= 8

so it would only take 8 people for 1 day

Answer:

1 day

Step-by-step explanation:

4 people = 2 days

→ Work out how long 1 person takes

4 people = 2 days

( ÷ 4 )            ( × 4 )

1 person = 8 days

→ Work out how long 8 people can do it

1 person = 8 days

( × 8 )            ( ÷ 8 )

8 people = 1 day

Answer:

Log 8 a - Log 8 2

Step-by-step explanation:

the 8 thing is the number under btw

plz brainliest :)

Answer:1. C2. D3. A4. A5. D6. B7. A

Step-by-step explanation:

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Answer:

,,Answer:

The given equation 3x − 7 = 4 + 6 + 4x has one solution.

Step-by-step explanation:

Given : Equation 3x − 7 = 4 + 6 + 4x

We have to find the number of solutions of the given equation.

Consider the given equation 3x − 7 = 4 + 6 + 4x

Simplify, we have,

3x − 7 = 10 + 4x

Now subtract 3x both side, we have

-7 = 10 + 4x - 3x

Simplify, we have,

- 7 = 10 + x

Subtract 10 both side, we have,

-7 - 10 = x

x = - 17

Thus, The given equation 3x − 7 = 4 + 6 + 4x has one solution.

Thank you❤

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Answer:

16.22%

Explanation:

The percent of increase can be calculated as:

Where vf is the final value and vi is the initial value. So, replacing vf by 10.75 and vi by 9.25, we get:

Therefore, the percent of the increase is 16.22%

Answer:

-6 and -10

Step-by-step explanation:

Three times negative two equal to negative six

Negative two plus negative eight equal to negative ten

The length of the indicated side of the trapezoid is 10 inches

From the question, we have the following parameters that can be used in our computation:

The trapezoid

The length of the indicated side of the trapezoid is calculated as

Length² = (18 - 12)² + 8²

Evaluate the sum

So, we have

Length² = 100

Take the square root of both sides

Length = 10

Hence, the length of the indicated side of the trapezoid is 10 inches

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Answer:

See below.

Step-by-step explanation:

There are four ticks between each term, meaning that any point in between would be represented in fourths.

B is located at the first tick between 2 and 3, so the fraction is 2 1/4.

-hope it helps

Answer:

The correct answer is 2 1/4

Step-by-step explanation:

There are 4 dashes in the number line from 2 to 3 so the fraction has to be /4

It is 1/4 because B is on the first dash after 2

Answer:

D. Malleability because he is most likely going to show how you can easily roll pizza dough

Step-by-step explanation:

Answer:

malleability or D

Step-by-step explanation:

70% i guess

mark brainiest if correct

Answer:

35% hope this helps have a nice day please give me brainliest :)

Step-by-step explanation:

The measure of ZAFD is 50 degrees.

Based on the given information:

ZCFE is congruent to ZCFA.

mZCFB = 68°.

mZEFD = 62°.

To find the measure of ZAFD, we can use the fact that angles in the same segment of a circle are equal.

Since ZCFE and ZCFA are congruent, angle ZCFE is equal to angle ZCFA.

Therefore, mZCFA = mZCFE.

Now, let's find the measure of angle ZCFE:

mZCFE = mZCFB + mZEFD (Angle Addition Postulate)

mZCFE = 68° + 62°

mZCFE = 130°

Since ZCFA is congruent to ZCFE, we can conclude that mZCFA is also equal to 130°.

Now, to find the measure of ZAFD, we need to consider the angles in the quadrilateral ZAFD.

The sum of the angles in a quadrilateral is always 360°.

mZAFD + mZAFB + mZBFD + mZBFA = 360°

We know that mZAFB and mZBFD are equal to 90° because they are right angles (angle AFB and angle BFD are right angles in the diagram).

Therefore, we can rewrite the equation as:

mZAFD + 90° + 90° + mZBFA = 360°

Simplifying:

mZAFD + 180° + mZBFA = 360°

Rearranging the equation:

mZAFD + mZBFA = 360° - 180°

mZAFD + mZBFA = 180°

We know that mZBFA is equal to mZCFA, which is 130°.

Substituting the known values into the equation:

mZAFD + 130° = 180°

Subtracting 130° from both sides:

mZAFD = 180° - 130°

mZAFD = 50°

Therefore, the measure of ZAFD is 50 degrees.

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Answer:

19

Step-by-step explanation:

Rearranging the number in ascending order,

12,15,17,19,19,20,24,26

Median = The average of the 4th and 5th number

\( = \frac{19 + 19}{2} \\ = 19\)

Answer:

19

Step-by-step explanation:

so first you have to order the values from least to greatest.

12, 15, 17, 19, 19, 20, 24, 26

there are 8 terms (note that 2 of them are 19)

n = 8

median = (n + 1) ÷ 2

            =(8 + 1)/2

            =9/2 = 4.5

it's 19 because the median falls between those two (19) data points.

The proababilities are: i) P(Aᶜ) = 0.6, ii) P(Bᶜ) = 0.4

iii) Probability that exactly one of the events A, B occurs = 0.7

Let A and B be any two disjoint events such that P(A) = 0.4 and P(A ∪ B) = 0.7. We need to find the following probabilities:

i) P(Aᶜ): This is the probability of the complement of event A, which represents the probability of not A occurring. Since A and B are disjoint, Aᶜ and B are mutually exclusive and their union covers the entire sample space.

Therefore, P(Aᶜ) = P(B) = 1 - P(A) = 1 - 0.4 = 0.6.

ii) P(Bᶜ): This is the probability of the complement of event B, which represents the probability of not B occurring. Since A and B are disjoint, Bᶜ and A are mutually exclusive and their union covers the entire sample space.

Therefore, P(Bᶜ) = P(A) = 0.4.

iii) Probability that exactly one of the events A, B occurs: This can be calculated by subtracting the probability of both events occurring (P(A ∩ B)) from the probability of their union (P(A ∪ B)).

Since A and B are disjoint, P(A ∩ B) = 0.

Therefore, the probability that exactly one of the events A, B occurs is P(A ∪ B) - P(A ∩ B) = P(A ∪ B) = 0.7.

To summarize:

i) P(Aᶜ) = 0.6

ii) P(Bᶜ) = 0.4

iii) Probability that exactly one of the events A, B occurs = 0.7

Note: The provided values of P(A), P(A ∪ B), and the disjoint nature of A and B are used to derive the above probabilities.

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Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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Answer:

4 40 divided by 4 equals 10 and 24 divided by 4 equals 6

Step-by-step explanation:

step-by-step explanation: 8 goes into both but where are the answers

Answer:

Well we know that it's a linear because it has a exponent so what we do to answer this question

Step-by-step explanation:

------

- b+ v. b2 -4ac

x= ____________

2a

x2+ 12x +20 =0

a=1

b=12

c=20

_______

X= -12+v 12 2 -4 • 1 • 20

___________________

2•1

Answer:

2; 10

Step-by-step explanation:

12/2 = 6

\((x+6)^{2}\) = \(x^{2}\) +12x + 36

   \(x^{2}\) +12x + 20

-   \(x^{2}\) +12x + 36

    0 + 0  - 16

\((x+6)^{2}\) - 16 = 0

\((x+6)^{2}\) = 16

x + 6 = \(\sqrt{16}\)

x = -4 + 6 = 2

x = 4 + 6 = 10

Answer:

y = -2x + 12

Step-by-step explanation:

Slope-intercept form

\(y=mx+b\)

where:

Therefore, to find the slope-intercept form of the given linear equation, isolate y:

\(\implies 4x+2y=24\)

\(\implies 4x+2y-4x=-4x+24\)

\(\implies 2y=-4x+24\)

\(\implies \dfrac{2y}{2}=\dfrac{-4x}{2}+\dfrac{24}{2}\)

\(\implies y=-2x+12\)

Answer:

y = -2x + 12

Step-by-step explanation:

Given equation,

→ 4x + 2y = 24

The slope-intercept form is,

→ y = mx + b

Converting into slope-intercept form,

→ 4x + 2y = 24

→ 2y = -4x + 24

→ y = (-4x + 24)/2

→ [ y = -2x + 12 ]

Hence, the solution is y = -2x + 12.

The simple interest rate that will ensure that Bob's investment of R6,500 equals Alice's 3% compound interest per year investment is 3.2%.

The difference between simple interest and compound interest is that simple interest computes interest on the principal only for each period.

Compound interest computes interest on both the principal and accumulated interest for each period.

Alice:

Principal investment = R6,500

Compound interest rate per year = 3%

Investment period = 5years

Future value = R7,535.28 (R6,500 x 1.03⁵)

Total Interest R1,035.28 (R7,535.28 - R6,500)

Bob:

Principal invested = R6,500

The simple interest rate = r

Investment period = 5years

The future value of the simple interest investment, A = P(1+rt)

7,535.28 = 6,500(1 + 5r)

Dividing each side b 6,500:

1.15927 = (1 + 5r)

5r = 0.15927

r = 0.031854

r - 0.032

r = 3.2% (0.32 x 100)

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Calculate r, giving your answer correct to 1 decimal place.

Answer:   11

\(\sqrt{114}\) = 10.67707825

rounded to nearest whole number would be 11

Answer:

11

Step-by-step explanation:

Answer:

i swear to God if anyone else criticizes me for not getter parentheses I'm going to frikinf punch a hole through my wall

Answer:

42

Step-by-step explanation:

4×9+3×2

You will multiply it and then add

36+6

You add the numbers

Which is going to be;

42

Answer:

Only 18

Step-by-step explanation:

18 / 3 = 6 is a whole number.

Also,

3 x 6 = 18

Hence,

18 is a multiple of 3.

If Aaron is designing a party game in which he needs exactly 24 possible outcomes, then he can use the following sets of actions to have a statistically fair game from the Statistics point  of view,

Toss a coin twice, and then then roll a 6-sided number cube.

How can he play a statistically fair game to get exactly 24 outcomes?

The game has 24 alternative outcomes, as far as we know. The next step is to identify a series of activities that produces 24 distinct outcomes with equal probabilities.

The first of the alternatives is the only one with a sample space of 24 elements.

Flip two coins, then roll a D6.

The results of each coin toss are 2:  (tails and heads).

There are 6 outcomes for the D6: (1, 2, 3, 4, 5, 6)

The combined outcomes of the two throws and rolling the number are then given by the product between the numbers of outcomes for each individual part, as solved below:

C = 2 × 2 × 6

C = 24

Thus, by tossing a coin twice, and then then rolling a 6-sided number cube, Aron can play a statistically fair game if h needs exactly 24 outcomes.

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Sin 7° is equal to sin(0.1221) = 0.1218693.

We must multiply the supplied value by \(\pi\)/180 to convert the angle's degree value to its counterpart in radians.

According to the given information

The angle 7°, or sin 7 degrees, is located between 0° and 90°. (First Quadrant).

Sin 7° value = 0.1218693 because the sine function is positive in the first quadrant.

Sin 7 degrees has a numeric value of 0.121869343.

Another way to define sin 7 degrees is to use the radian equivalent of the angle (7 degrees) (0.12217 . . .).

Using the degree to radian conversion, we can see that 7 degrees equals 7° (\(\pi\)/180°) in radians. rad = 0.1221 . . .

Sin 7° is equal to sin(0.1221) = 0.1218693.

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Answer:

1) 4 × 4× 4 = 64

2) 6⁴ = 1296

3) 25 = 25

4) 5² = 2

3) 3⁴= 81