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3 years ago

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One of Maria and Josie’s early tasks is printing and laminating signs to hang at local businesses around town. Working alone, Ma

ria could print and laminate the signs in 4 hours. Josie, however, has better laminating equipment, so she could get the job done by herself in 2 hours. If each works for the same amount of time, how long will it take them working together to print and laminate the signs? Start by filling in the table with the missing values or expressions. Note that rate of work is a unit rate that describes the amount of the job completed in one hour.

2 answers:

nignag [31]3 years ago

7 0

Answer:

Maria and Josie working together can complete the work in= 1 hour and 20 minutes

Step-by-step explanation:

Given:

Time taken by Maria to print and laminate signs = 4 hours

Time taken by Josie to print and laminate signs = 2 hours

Solution:

Rate of work done by Maria = $\frac{1}{4}$ per hour

Rate of work done by Josie = $\frac{1}{2}$ per hour

Let them work for $x$ hours together.

In $x$ hours work done by Maria = $\frac{x}{4}$

In $x$ hours work done by Josie = $\frac{x}{2}$

Total work done by both = $\frac{x}{4}+\frac{x}{2}=\frac{3x}{4}$

If they complete the work in $x$ hours, then we can write as:

$\frac{3x}{4}=1$

Solving for $x$

Multiplying both sides by $\frac{4}{3}$

$\frac{4}{3}\times\frac{3x}{4}=1\times \frac{4}{3}$

∴ $x=\frac{4}{3}=1\frac{1}{3}$ hours = 1 hour and 20 minutes [As $\frac{1}{3}$ of an hour =20 minutes.

So, Maria and Josie working together can complete the work in= 1 hour and 20 minutes

Trava [24]3 years ago

5 0

Answer:

part of task completed for josie is 1/2

Step-by-step explanation:

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marysya [2.9K]

In order to solve equations like these, you need to move all terms involving the variable on one side, and all the numeric constants on the other side.

To do so, we can add/subtract the same quantity to both sides.

For example, we can add 5.2 to both sides to get

$-0.7+2.8+5.2=-3.14x-5.2+5.2 \iff -0.7+2.8+5.2=-3.14x$

Then, we can add all the terms on the left hand side, and we have

$-0.7+2.8+5.2=-3.14x \iff 7.3=-3.14x$

Finally, we can divide both sides by -3.14:

$\dfrac{7.3}{-3.14} = \dfrac{-3.14x}{-3.14} \iff x = -\dfrac{7.3}{3.14}$

In order to check the solution, we have to plug the value we found for x in the initial equation:

$-0.7+2.8=-3.14x-5.2 \iff -0.7+2.8=-3.14\cdot \left(-\dfrac{7.3}{3.14}\right) -5.2 \iff -0.7+2.8 = 7.3-5.2 \iff 2.1=2.1$

which is clearly true.

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3 years ago

Can someone help me with this

zimovet [89]

Answer:

Step-by-step explanation:

It pretty simple, you need to read the sentence and match the number.

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Seven more than one half = 7 more than 1/2

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For the hypothesis test H0: μ = 10 against H1: μ >10 and variance known, calculate the Pvalue for each of the following test

Basile [38]

Answer:

a) $p_v =P(Z>2.05)=1-P(z$

b) $p_v =P(Z>-1.84)=1-P(z$

c) $p_v =P(Z>0.4)=1-P(z$

Step-by-step explanation:

Some previous concepts

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.

A z-test for one mean "is a hypothesis test that attempts to make a claim about the population mean(μ)".

The null hypothesis attempts "to show that no variation exists between variables or that a single variable is no different than its mean"

The alternative hypothesis "is the hypothesis used in hypothesis testing that is contrary to the null hypothesis"

Hypothesis

Null hypothesis: $\mu=10$

Alternative hypothesis: $\mu >10$

If the random variable is distributed like this: $X \sim N(\mu,\sigma)$

We assume that the variance is known so the correct test to apply here is the z test to compare means, the statistic is given by the following formula:

$z_o=\frac{\bar X -\mu}{\sigma}$

Since we have the values for the statistic already calculated we can calculate the p value using the following formulas:

Part a

$p_v =P(Z>2.05)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(2.05,0,1,TRUE)"

Part b

$p_v =P(Z>-1.84)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(-1.84,0,1,TRUE)"

Part c

$p_v =P(Z>0.4)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(0.4,0,1,TRUE)"

Conclusions

If we use a reference value for the significance, let's say $\alpha=0.05$ . For part a the $p_v$ so then we can reject the null hypothesis at this significance level.

For part b the $p_v>\alpha$ so then we FAIL to reject the null hypothesis at this significance level.

For part c the $p_v>\alpha$ so again we FAIL to reject the null hypothesis at this significance level.

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Answer:

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