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2 years ago

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Mathematics

1 answer:

Firdavs [7]2 years ago

3 0

Answer:

It will take 1 week for both classmates to catch up with each other
Each child has passed about 9 tests.

Step-by-step explanation:

We know that:

Q = 8 + 1(w)
S = 4 + 5(w)
Q = S

Work:

8 + w = 4 + 5w
=> 8 - 4 = -w + 5w
=> 4 = 4w
=> w = 1

Hence, it will take 1 week for both classmates to catch up with each other. Now, let's substitute the value of w into the first equation to find how many tests have each child passed.

Q = 8 + (w)
=> Q = 8 + 1
=> Q = 9

Hence, each child has passed about 9 tests.

Hoped this helped.

$BrainiacUser1357$

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36x^3a+45xa^2=9xa( ) complete the statement.

Dafna1 [17]

9xa is the common factor.

You can complete the statement by dividing the two terms of the expression of the left side by 9xa, and you will get:

36x^3a + 45xa^2 = 9xa ( 4x^2 + 5a)

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4 years ago

Solve the proportion

algol13

Answer: 78

Step-by-step explanation:

The rest of the answers are too small to be the length.

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3 years ago

What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean

Elena-2011 [213]

Answer:

0.658 is the probability that a sample 90 test takers will provide a sample mean test score within 10 points of the population mean of 502.

Step-by-step explanation:

The following information is missing:

The standard deviation of population is 100.

We are given the following information in the question:

Population mean, μ = 502

Standard Deviation, σ = 100

Sample size, n = 90

Standard error =

$\dfrac{\sigma}{\sqrt{n}} = \dfrac{100}{\sqrt{90}} = 10.54$

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(test score within 10 points)

$P(492 \leq x \leq 512) \\\\= P(\displaystyle\frac{492 - 502}{10.54} \leq z \leq \displaystyle\frac{512-502}{10.54}) \\\\= P(-0.9487 \leq z \leq 0.9487)\\= P(z \leq 0.9487) - P(z < -0.9487)\\= 0.829 -0.171 = 0.658 = 65.8\%$

$P(492 \leq x \leq 512) = 65.8\%$

0.658 is the probability that a sample 90 test takers will provide a sample mean test score within 10 points of the population mean of 502.

7 0

3 years ago

A local company rents a moving truck for $750 plus $0.59 per mile driven over 1000 mi. What is the maximum number of miles the t

Katen [24]

The maximum number of miles the truck can be driven so that the rental cost is at most $\$1000$ is $\boxed{1423{\text{ miles}}}.$

Further explanation:

Given:

A local company rents a moving truck for $\$ 750.$

Rent per mile is $\$ 0.59$ if the truck moves more than 1000 miles.

Explanation:

The rental cost of the truck is $\$ 750$ if he drove less than 1000 miles.

${\text{Cost}} = \$ 750{\text{ }}x \leqslant 1000$

The rental cost of the truck can be expressed as follows,

${\text{Cost}} = 750 + 0.59x{\text{ }}x > 1000$

The rental cost is at most $\$1000.$

$750 + 0.59x \leqslant 1000$

The maximum number of miles can be obtained as follows,

$\begin{aligned}0.59x &\leqslant 1000 - 750\\0.59x &\leqslant 250\\x &\leqslant \frac{{250}}{{0.59}}\\x &\leqslant 423.7\\\end{aligned}$

The maximum number of miles can be obtained as follows,

$\begin{aligned}{\text{Maximum miles}} &= 1000 + 423\\&= 1423 \\\end{aligned}$

The maximum number of miles the truck can be driven so that the rental cost is at most $\$1000$ is $\boxed{1423{\text{ miles}}}.$

Learn more:

Learn more about inverse of the function brainly.com/question/1632445.
Learn more about equation of circle brainly.com/question/1506955.
Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear inequality

Keywords: local company, rents, moving, truck, $750, $0.59, maximum, 1000 miles, $1000, at most, at least, number of miles, rental cost, driven over

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3 years ago

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4 years ago