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2 years ago

Which choice gives a valid first step to solve 2(w − 3) = 5? Exclude any choice where the explanation for the step is false.

Mathematics

1 answer:

UNO [17]2 years ago

7 0

Answer:

D. Use the Distributive Property. You clear the parentheses and then solve the two-step equation.

Step-by-step explanation:

Given problem;

2(w − 3) = 5

To solve this problem:

Use the distributive property to clear the parentheses;

2w - 6 = 5

Then, collect like terms, add 6 to both sides;

2w = 5 + 6

2w = 11

Now divide both terms by 2

w = $\frac{11}{2}$

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At most, Alana can spend $40 on carnival tickets. Ride tickets cost $4 each, and food tickets cost $2 each. Alana buys at least

attashe74 [19]

Answer:

Step-by-step explanation:

Here let the number of ride tickets be r, and the number of food tickets be f.

Hence

$r+f\ge16\\4r+2f\le40$

We first plot the two inequalities on graph as shown in attachment. From the graph we see that the two in-equation meet at (4,12)

Hence we can see that the maximum value of r is 4

7 0

2 years ago

Read 2 more answers

Mary deposits $550 in a savings account at 3% simple annual interest. The

kupik [55]

Answer:

Domain: $t \geq 0$

Range: $v \geq 550$

Step-by-step explanation:

Given

$v = 550 + 16.5t$

Required

Determine the domain and the range

Solving for domain:

From the question, we understand that t represent years.

Because years can't be negative;

Then, we can conclude that the domain, t is:

$t \geq 0$

Solving for Range:

We solved domain to be $t \geq 0$

This implies that the minimum value of t is $t = 0$ and the maximum is infinity

Substitute 0 for t in $v = 550 + 16.5t$

$v = 550 + 16.5(0)$

$v = 550 + 0$

$v = 550$

Hence;

The range is $v \geq 550$

6 0

2 years ago

If angle ABC is one degree less than three times angle ABD and angle DBC=47 find each measure

Contact [7]

It has not been indicated whether the figure in the questions is a triangle or a quadrilateral. Irrespective of the shape, this can be solved. The two possible shapes and angles have been indicated in the attached image.

Now, from the information given we can infer that there is a line BD that cuts angle ABC in two parts: angle ABD and angle DBC

⇒ Angle ABC = Angle ABD + Angle DBC

Also, we know that angle ABC is 1 degree less than 3 times the angle ABD, and that angle DBC is 47 degree

Let angle ABD be x

⇒ Angle ABC = 3x-1

Also, Angle ABC = Angle ABD + Angle DBC

Substituting the values in the above equations

⇒ 3x-1 = x+47

⇒ 2x = 48

⇒ x = 24

So angle ABD = 24 degree, and angle ABC = 3(24)-1 = 71-1 = 71 degree

8 0

2 years ago

A marketing firm wants to estimate how much root beer the average teenager drinks per year. A previous study found a standard de

Verdich [7]

Answer:

At least 832 teenargers must be interviewed.

Step-by-step explanation:

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

$\alpha = \frac{1-0.99}{2} = 0.005$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.005 = 0.995$ , so $z = 2.575$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval

At least n teenargers must be interviewed.

n is found when M = 0.1.

We have that $\sigma = 1.12$

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.1 = 2.575*\frac{1.12}{\sqrt{n}}$

$0.1\sqrt{n} = 2.575*1.12$

$\sqrt{n} = \frac{2.575*1.12}{0.1}$

$(\sqrt{n})^{2} = (\frac{2.575*1.12}{0.1})^{2}$

$n = 831.7$

Rounding up

At least 832 teenargers must be interviewed.

4 0

2 years ago

Simplify: StartRoot 64 r Superscript 8 Baseline EndRoot

patriot [66]

Answer:

8r^4

Step-by-step explanation:

$\sqrt{64r^8} =\sqrt{(8r^4)^2}=\boxed{8r^4}$

5 0

2 years ago