Help please! Quickly!

Staples recently charged $3.79 per ream (package of 500 sheets) of regular paper and $5.49 per ream of paper made of recycled fi

Ipatiy [6.2K]

<h3>Given</h3>

regular paper costs $3.79 per ream

recycled paper costs $5.49 per ream

$582.44 was spent for 116 reams

the numbers of reams of each type that were purchased

<h3>Solution</h3>

Let r and g represent the numbers of reams of regular and recycled ("green") paper, respectively.

... r + g = 116 . . . . . . . . 116 reams were purchased

... 3.79r + 5.49g = 582.44 . . . . this is the total cost of the purchase

Solve the first equation for r and substitute that into the second equation.

... r = 116 - g

... 3.79(116 - g) + 5.49g = 582.44 . . . . . use the expression for r

... 1.70g + 439.64 = 582.44 . . . . . . . . . simplify

... g = (582.44 -439.64)/1.70 = 84 . . . . subtract the constant, divide by 1.70

... r = 116 -84 = 32 . . . . . . . . . . . . . . . . . use the equation for r

32 regular reams and 84 recycled reams were purchased

3 0

3 years ago

Need help ASAP!! Write an informal proof to show triangles ABC and DEF are similar.

yaroslaw [1]

Answer:

Δ ABC and Δ DEF are similar because their corresponding sides are proportional

Step-by-step explanation:

Two triangles are similar if their corresponding sides are proportional which means the corresponding sides have equal ratios

In the two triangles ABC and DEF

∵ AB = 4 units

∵ DE = 2 units

∴ $\frac{AB}{DE}=\frac{4}{2}=2$

∵ BC = 6 units

∵ EF = 3 units

∴ $\frac{BC}{EF}=\frac{6}{3}=2$

∵ CA = 2 units

∵ FD = 1 units

∴ $\frac{CA}{FD}=\frac{2}{1}=2$

∴ $\frac{AB}{DE}=\frac{BC}{EF}=\frac{CA}{FD}=2$

∵ All the ratios of the corresponding sides are equal

∴ The corresponding sides of the two triangles are proportional

∴ Δ ABC is similar to Δ DEF

6 0

3 years ago

Suppose a sample of 100 families of four vacationing at Niagara Falls resulted in sample mean of $282.45 spent per day and a sam

Juli2301 [7.4K]

Given Information:

Mean = μ = $282.45

Standard deviation = σ = $64.50

Sample size = n = 100

Confidence level = 95%

Required Information:

95% Confidence interval = ?

Answer:

95% Confidence interval = ($269.81, $295.09)

Step-by-step explanation:

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

What is Confidence Interval?

The confidence interval represents an interval that we can guarantee that the target variable will be within this interval for a given confidence level.

The confidence interval is given by

$CI = \bar{x} \pm MoE\\$

Where $\bar{x}$ is the mean and MoE is the margin of error given by

$MoE = z_{\alpha/2}(\frac{\sigma}{\sqrt{n} } ) \\$

Where σ is the standard deviation, n is the sample size and $z_{\alpha/2}$ is the z-score corresponding to 95% confidence level.

$z_{\alpha/2} = 1 - 0.95 = 0.05/2 = 0.025\\\\z_{0.025} = 1.96$

$MoE = 1.96\cdot \frac{64.50}{\sqrt{100} } \\\\MoE = 1.96\cdot 6.45\\\\MoE = 12.64\\$

Finally, the confidence interval is

$CI = \bar{x} \pm MoE\\\\CI = 282.45 \pm 12.64\\\\CI = 282.45 - 12.64 \: and \: 282.45 + 12.64\\\\CI = \$269.81 \: and \:\:\$295.09\\$

Therefore, we are 95% sure that the true population mean amount spent per day by a family of four visiting Niagara Falls is within the interval of ($269.81, $295.09)

3 0

3 years ago

When you identify the author of a text, which of the following are you are specifically examining in the source?

ioda

I would say origin, but it's a hard choice.

3 0

3 years ago

Read 2 more answers

-5x+2y=4 solved algebraically

yan [13]

-5x + 2y - 4 = 0

= 5x - 2y + 4 = 0

5 0

3 years ago