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2 years ago

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To make purple plum paint, the paint store mixes blue and red paint in a ration of 8:5 if a customer needs 65 gallon of paint ho

w many gallons blue and red paint needs to go in the mix

1 answer:

Olegator [25]2 years ago

3 0

Answer:

Number of gallons of blue paint = 40 gallons

Number of gallons of red paint = 25 gallons

Step-by-step explanation:

We are given the ratio:

Blue paint : Red paint =

8 : 5

Sum of proportion = 8 + 5 = 13

If the customer need 65 gallons of paint,

a) Number of gallons of blue paint needed =

8/13 × 65 gallons = 40 gallons

b) Number of gallons of red paint needed =

5/13 × 65 gallons = 25 gallons

Therefore:

Number of gallons of blue paint = 40 gallons

Number of gallons of red paint = 25 gallons

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The following measurements were added: 5.45 + 6.1 + 2.84. what should

Natali [406]

Answer: 14.39

Explanation:

5.45+2.84= 8.29
Then for 6.1 you add a zero to the end and make it 6.10 which is the same thing
Now 8.29+6.10= 14.39

3 0

2 years ago

is the sum of two polynomials of degree 5 always a polynomial of degree 5? Give an example to explain your answer

ddd [48]

A counter example is

f(x)=5x^5+2x^3+3x
g(x)=-5x^5-x^4+x^2-4

Then f(x)+g(x) = -x^4+2x^3+x^2+3x-4 which is a polynomial of degree 4.

So the answer is no. Counter-example is given above.

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3 years ago

Please i will give brainliest if right

pishuonlain [190]

Answer:

s = 156.25 square meters

Step-by-step explanation:

s = 2lw + 2lh + 2wh

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s = 33 + 43.5 + 79.75

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6 0

2 years ago

Read 2 more answers

Solve each system of equations algebraically. For each one, explain what the solution (or lack thereof) tells you

Paul [167]

Answer:

a: no solutions

b: (2, 3)

Step-by-step explanation:

a:

In both equations, the slope of x is the same, but the y-intercept is not, which means they are parallel. Therefore, this system of equations has no solutions.

b:

Since both of the equations are equal to y, we can set them equal to each other:

$\frac{1}{2}x^2+1= 2x-1\\x^2 + 2 = 4x - 2\\x^2-4x+4=0$

We can solve by factoring (by finding a number that multiplies to 4 and adds up to -4):

(x-2)^2 = 0

x = 2

Now, to find y, plug-in x to any of the equations:

y = 2*2-1 = 3

Therefore, the solution to this system of equation is (2, 3)

I hope this helped.

4 0

3 years ago

A national survey conducted in 2011 among a simple random sample of 1,507 adults shows that 56% of Americans think the Civil War

Drupady [299]

Answer:

a) $z=4.658$

$p_v =P(z>4.65)=1-P(z$

b) Using the significance level assumed $\alpha=0.05$ we see that $p_v$ so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life is higher than 50%.

c) The 90% confidence interval would be given (0.527;0.593).

We are confident that about 54% to 59% of all Americans think the Civil War is relevant.

Step-by-step explanation:

I )Part a

1) Data given and notation

n=1507 represent the random sample taken

X represent the Americans who thinks that the Civil War is still relevant to American politics and political life

$\hat p$ estimated proportion of Americans who thinks that the Civil War is still relevant to American politics and political life in the sample

$p_o=0.5$ is the value that we want to test since the problem says majority

$\alpha=0.05$ represent the significance level (no given, but is assumed)

z would represent the statistic (variable of interest)

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

p= population proportion of Americans who thinks that the Civil War is still relevant to American politics and political life

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life exceeds 50%(Majority). :

Null Hypothesis: $p \leq 0.5$

Alternative Hypothesis: $p >0.5$

We assume that the proportion follows a normal distribution.

This is a one tail upper test for the proportion of union membership.

The One-Sample Proportion Test is "used to assess whether a population proportion $\hat p$ is significantly (different,higher or less) from a hypothesized value $p_o$ ".

Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

$np_o =1507*0.5=753.5>10$

$n(1-p_o)=1507*(1-0.5)=753.5>10$

3) Calculate the statistic

The statistic is calculated with the following formula:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o(1-p_o)}{n}}}$

On this case the value of $p_o=0.5$ is the value that we are testing and n = 1507.

$z=\frac{0.56 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1507}}}=4.658$

The p value for the test would be:

$p_v =P(z>4.65)=1-P(z$

II) Part b

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

Based on the alternative hypothesis the p value would be given by:

$p_v =P(z>4.65)=1-P(z$

Using the significance level assumed $\alpha=0.05$ we see that $p_v$ so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life is higher than 50%.

III) Part c

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 90% confidence interval the value of $\alpha=1-0.9=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

And replacing into the confidence interval formula we got:

$0.56 - 2.58 \sqrt{\frac{0.56(1-0.56)}{1507}}=0.527$

$0.56 + 2.58 \sqrt{\frac{0.56(1-0.56)}{1507}}=0.593$

And the 90% confidence interval would be given (0.527;0.593).

We are confident that about 54% to 59% of all Americans think the Civil War is relevant.

And this result agrees with the result of part b, since the interval not contains the value of 0.5 we can conclude that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life it's higher than 0.5 at 90% of confidence.

7 0

2 years ago