The price of a holiday was increased by 11% to £870. What was the price before the increase?

Expand the expression 3(5p+1) using the distribution property PLEASE HELP

garri49 [273]

Answer:

15p + 3

Step-by-step explanation:

Multiply 3 by each number in the parentheses and keep the variable

7 0

2 years ago

Read 2 more answers

Each calendar will sell for $5 each write an equatio to model the total income for selling calendars

Brrunno [24]

To answer the question above, I let x be the number of calendars sold. You may use any other letter as this is just for representation. The total income generated in selling calendars is calculated by multiplying the number of calendars with the price. That is,
total income = 5x
If we let total income be y, our equation is further simplified into,
y = 5x

4 0

3 years ago

Solve.

artcher [175]

Answer:

x=1

Step-by-step explanation:

you would substitute the first equation in for the y in the second equation

x + 2x+3 =6

then you would combine the x's

3x +3 = 6

Then you would move the 3 to the other side with the six

3x =6-3 3x = 3

Then finally you would divide the three

3x/3 = 3/3 x=1

6 0

2 years ago

A researcher believes that the mean weight of competitive runners is about 140 pounds. A sample of 24 elite distance runners has

ExtremeBDS [4]

Answer:

$t=\frac{136-140}{\frac{11}{\sqrt{24}}}=-1.781$

$p_v =P(t_{(23)}$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean is less than 140 pounds at 5% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=136$ represent the sample mean

$s=11$ represent the sample standard deviation

$n=24$ sample size

$\mu_o =140$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is less than 140, the system of hypothesis would be:

Null hypothesis: $\mu \geq 140$

Alternative hypothesis: $\mu < 140$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{136-140}{\frac{11}{\sqrt{24}}}=-1.781$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=24-1=23$

Since is a one left tailed test the p value would be:

$p_v =P(t_{(23)}$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean is less than 140 pounds at 5% of signficance.

4 0

2 years ago

If Fran were to paint her living room alone, it would take 6 hours. Her sister Denise

GalinKa [24]

Answer:

It will take Fran and Denise $3\frac{3}{7}$ hours to paint the living room.

Step-by-step explanation:

Given that:

Time taken by Fran to paint living house = 6 hours

Time taken by Denise = 8 hours

Let,

x be the time taken by both of them.

$\frac{1}{Fran's\ share}+\frac{1}{Denise's\ share}=\frac{1}{x}\\\\\frac{1}{6}+\frac{1}{8}=\frac{1}{x}\\\\\frac{4+3}{24}=\frac{1}{x}\\\\\frac{7}{24}=\frac{1}{x}\\\\x = \frac{24}{7}$

$x = 3\frac{3}{7}$ hours

Hence,

It will take Fran and Denise $3\frac{3}{7}$ hours to paint the living room.

4 0

2 years ago