Solve the expression: x = 5, y = 8. x²

If the ratio of purple marbles to orange marbles is 3 to 8, how many orange marbles will I have if I have 48 purple marbles?

sveticcg [70]

Answer:

You will have 128 orange marbles

Step-by-step explanation:

Set this up as an equation

Variable x = number of orange marbles

3/8 = 48/x

Cross multiply

3 × x = 8 × 48

3x = 384

Divide both sides by 3 to isolate the variable

3x ÷ 3 = 384 ÷ 3

1x = 128

x = 128

128 orange marbles

Check work:

Substitute the variable x for the answer

3/8 = 48/128

Cross multiply

3 × 128 = 8 × 48

384 = 384

If the numbers equal, the answer is correct

6 0

3 years ago

Read 2 more answers

Water lilies are often used to decorate ponds, as shown in the photo. But they are also famous for their unusual growth pattern!

Alex17521 [72]

There really isn't a right or wrong answer since this is a prediction but to solve this look at the graph and try to see the pattern

5 0

3 years ago

Read 2 more answers

A company surveyed 2400 men where 1248 of the men identified themselves as the primary grocery shopper in their household. a) E

polet [3.4K]

Answer:

a) With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.

b) The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.

c) $\alpha =1-0.98=0.02$

Step-by-step explanation:

If np' and n(1-p') are higher than 5, a confidence interval for the proportion is calculated as:

$p'-z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }\leq p\leq p'+z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }$

Where p' is the proportion of the sample, n is the size of the sample, p is the proportion of the population and $z_{\alpha/2}$ is the z-value that let a probability of $\alpha/2$ on the right tail.

Then, a 98% confidence interval for the percentage of all males who identify themselves as the primary grocery shopper can be calculated replacing p' by 0.52, n by 2400, $\alpha$ by 0.02 and $z_{\alpha/2}$ by 2.33

Where p' and $\alpha$ are calculated as:

$p' = \frac{1248}{2400}=0.52\\\alpha =1-0.98=0.02$

So, replacing the values we get:

$0.52-2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\leq p\leq 0.52+2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\\0.52-0.0238\leq p\leq 0.52+0.0238\\0.4962\leq p\leq 0.5438$

With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.

The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.

Finally, the level of significance is the probability to reject the null hypothesis given that the null hypothesis is true. It is also the complement of the level of confidence. So, if we create a 98% confidence interval, the level of confidence $1-\alpha$ is equal to 98%

It means the the level of significance $\alpha$ is:

$\alpha =1-0.98=0.02$

4 0

3 years ago

What are four consecutive numbers if the sum is 604

antiseptic1488 [7]

Answer:

149.5, 150.5 , 151.5, 152.5

Step-by-step explanation:

n+(n+1)+(n+2)+(n+3)= 604

Combine Like Terms

4n + 6 = 604

Subtract 6

4n = 598

Divide by 4

n=149.5

Check Your Work:

149.5+150.5+151.5+152.5 = 604

5 0

3 years ago

Please Help Me.

My name is Ann [436]

They are Vertical Angles as they are directly across from one another.

7 0

3 years ago

Solve the expression: x = 5, y = 8. x² - 3y =