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3 years ago

The difference of x and 7 is at most -28. Translate the sentence into an inequality

Mathematics

1 answer:

Mice21 [21]3 years ago

8 0

Answer:

x - 7 $\leq$ -28

Step-by-step explanation:

I guarantee you that this is correct. It's pretty simple to understand.

Please mark Brainliest. :)

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Zebras migrate in a circle with a round trip of about 300 miles. They travel at 64 km/h. How many hours does it take zebra to do

Tresset [83]

Answer:

7.5 hours (7 hours and 30 minutes)

Step-by-step explanation:

ok Let's start with 64km/h.

1.6 km=1 mile,

64÷1.6=40miles

so 64km/h changes into 40miles/hour.

Zebras's round trip =300miles,

300/40=7.5

so answer is 7.5 hours.

8 0

3 years ago

After breaking your penny bank, you notice that you have $4.87 in quarters ($0.25), dimes ($0.10), nickels ($0.05), and pennies

ira [324]

Answer: Option 'c' is correct.

Step-by-step explanation:

Let the number of dimes be 'x'.

Let the number of nickels be ' $\dfrac{3}{2}x$ '.

Let the number of pennies be $\dfrac{3}{2}\times 2x=3x$

Let the number of quarters be '3x-34'.

As we know that

1 quarter = $0.25

1 dime = $0.10

1 nickel = $0.05

1 penny = $0.01

According to question, we get that

$0.10x+0.05\times \dfrac{3x}{2}+0.01\times 3x+0.25(3x-34)=4.87\\\\0.10x+0.075x+0.03x+0.75x-8.5=4.87\\\\\\0.955x=4.87+8.5\\\\0.955x=13.37\\\\x=\dfrac{13.37}{0.955}\\\\x=14$

So, the number of pennies is given by

$3x=3\times 14=42$

Hence, Option 'c' is correct.

3 0

3 years ago

At a new exhibit in the Museum of Science, people are asked to choose between 94 or 220 random draws from a machine. The machine

Tresset [83]

Answer:

0.0869 = 8.69% probability of getting more than 61% green balls.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

The machine is known to have 99 green balls and 78 red balls.

This means that $p = \frac{99}{99+78} = 0.5593$

Mean and standard deviation:

$\mu = p = 0.5593$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5593*0.4407}{99+78}} = 0.0373$

a. Calculate the probability of getting more than 61% green balls.

This is 1 subtracted by the pvalue of Z when X = 0.61. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{0.61 - 0.5593}{0.0373}$

$Z = 1.36$

$Z = 1.36$ has a pvalue of 0.9131

1 - 0.9131 = 0.0869

0.0869 = 8.69% probability of getting more than 61% green balls.

8 0

3 years ago

1. What is the circumference of the given circle in terms of pi? radius= 14 in.

rusak2 [61]

Answer:

1. B 2. B

Step-by-step explanation:

1. The formula for circumference is C= pi times diameter

Radius is half of diameter, so you'd multiply 14 times 2 which gives you 28. Since it's asking for it in pi, it'll be 28 pi.

2. I think instead of circumference, it's asking for area because if it was asking for circumference the answer would have been 6.6 pi, but that answer isn't there. So if it's asking for area, the formula is A= pi(r²) They gave the diameter instead. Remember, the radius is half of the diameter, so in order to get the radius, you'd divide 6.6 by 2 and get 3.3. Then, multiply 3.3 with the number itself, and you'll get 10.89.

Hope this helps!

5 0

3 years ago

Someone plz help! thx

timurjin [86]

Convert each mixed number to an improper fraction

--------------------------------------------
Convert 6&1/2 to an improper fraction

6&1/2 = (6*2+1)/2
6&1/2 = (12+1)/2
6&1/2 = 13/2
--------------------------------------------
Do the same for 9&1/4

9&1/4 = (9*4+1)/4
9&1/4 = (36+1)/4
9&1/4 = 37/4
--------------------------------------------
Now multiply the improper fractions 13/2 and 37/4. Multiply straight across

(13/2)*(37/4) = (13*37)/(2*4)
(13/2)*(37/4) = 481/8
--------------------------------------------
The last step is to use long division to find the mixed number equivalent of 481/8

Or we an say
60*8 = 480
So 60*8+1 = 480+1
which means
481/8 = (480+1)/8 = 480/8+1/8 = 60&1/8

Making the final answer to be choice C

Another way to get the answer is to convert 481/8 into a decimal to get 60.125 and then convert that back to a mixed number. You should get 60&1/8

6 0

3 years ago