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3 years ago

Suppose y varies inversely with x, and y = 32 when x = 4. What is the value of y when x = 8?

Mathematics

1 answer:

bulgar [2K]3 years ago

6 0

Answer:

Step-by-step explanation:

Inverse variation is of the form

xy = k where k is a constant

x=4 and y = 32

4*32 = k

128 = k

xy = 128

Let x = 8

8y = 128

Divide each side by 8

8y/8 = 128/8

y =16

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1,8,27,64...<br><br> What are the three next numbers in the pattern.<br><br> PLEASE ANSWER FAST!

Sav [38]

Answer:

125, 216, 343,

Step-by-step explanation:

7 0

3 years ago

3 3/5 + 9 3/5 answer with a mixed number in simplest form

Romashka [77]

Both fractions have the same denominator so it's going to be easy. First set up your equation:

$3 \frac{3}{5} + 9 \frac{3}{5}$

Add the whole numbers:

$3 + 9 = 12$

Now add the fractions:

$\frac{3}{5} + \frac{3}{5} = \frac{6}{5}$

add both together:

$12 + \frac{6}{5} = 12 \frac{6}{5}$

$\frac{6}{5}$ is an improper fraction so change it:

$12 \frac{6}{5} = 13 \frac{1}{5}$

Since 6 is one more than 5, add 1 to the whole number and subtract the numerator and denominator(6 - 5 = 1) and make the remaining the new numerator. That leaves you with $13 \frac{1}{5}$

Your answer is $13 \frac{1}{5}$

3 0

3 years ago

Answers should be exact decimals (please do not leave as fractions or unfinished calculations).

aksik [14]

Answer:

P(rolling the die results in a 3 or a 6)=0.3333

P(rolling the die results in not getting a 6)=0.8333

P(rolling the die results in the number being either greater than 2 or less than 5)=0.3333

P(rolling the die results in an even number or a 5)=0.6667

P( rolling the die twice results in a 6 followed by a 4)=0.0278

P(rolling the die three times results in all 6's)=0.0046

Step-by-step explanation:

As the all outcomes are equally likely, so each number has equal probability of occurring.

For six sided die the sample space is {1,2,3,4,5,6} and each outcome has equal probability of 1/6.

P(rolling the die results in a 3 or a 6)

P(rolling the die results in a 3 or a 6)=P(3)+P(6)=1/6+1/6=2/6=1/3

P(rolling the die results in a 3 or a 6)=0.3333

P(rolling the die results in not getting a 6)

P(rolling the die results in not getting a 6)=1-P(6)=1-1/6=5/6

P(rolling the die results in not getting a 6)=0.8333

P(rolling the die results in the number being either greater than 2 or less than 5)

number either greater than 2 or less than 5={3,4}

P(rolling the die results in the number being either greater than 2 or less than 5)=2/6=1/3

P(rolling the die results in the number being either greater than 2 or less than 5)=0.3333

P(rolling the die results in an even number or a 5)

number is an even number or a 5={2,4,5,6}

P(rolling the die results in an even number or a 5)=4/6=2/3

P(rolling the die results in an even number or a 5)=0.6667

P( rolling the die twice results in a 6 followed by a 4)

For six sided die rolled twice the sample space is

S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}.

n(S)=6²=36.

rolling the die twice results in a 6 followed by a 4={(6,4)}

P( rolling the die twice results in a 6 followed by a 4)=1/36.

P( rolling the die twice results in a 6 followed by a 4)=0.0278

P(rolling the die three times results in all 6's)

When three die are rolled the number of outcomes=n(S)=6³=216.

rolling the die three times results in all 6's={(6,6,6)}

P(rolling the die three times results in all 6's)=1/216

P(rolling the die three times results in all 6's)=0.0046

Note: All answers are rounded to four decimal places.

8 0

3 years ago

Factor this trinomial. Your answer should consist of two binomials.

Sergeu [11.5K]

Y² + 8y - 33 :

Break the expression into groups for formula ax²+ bx+c :

= (y²- 3y) + (11y - 33 )

Factor y from y² - 3y => y (y - 3)

Factor out 11 from 11 y - 33 => 11 (y - 3)

= y ( y- 3 ) + 11 ( y - 3 )

Factor out common term (y - 3 ) :

= ( y - 3 ) ( y + 11 )

hope this helps!

5 0

3 years ago

Spaulding is the leading maker for basketballs in the US. Spaulding prides itself on the quality that its basketballs have the r

Vesna [10]

Answer:

0 < 0.05, which means that we reject the null hypothesis, meaning that the air pressure of the balls is different of the target value of 7.9.

Step-by-step explanation:

The air pressure of a particular ball has a target value of 7.9 PSI.

This means that the null hypothesis is:

$H_{0}: \mu = 7.9$

The alternate hypothesis is:

$H_{a}: \mu \neq 7.9$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

The hypothesis tested means that $\mu = 7.9$

Suppose the basketballs have a normal distribution with a standard deviation of 0.20 PSI.

This means that $\sigma = 0.2$

When a shipment of basketballs arrive, the consumer takes a sample of 21 from the shipment and measures their PSI to see if it meets the target value, and finds the mean to be 7.3 PSI.

This means that $X = 7.3, n = 21$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{7.3 - 7.9}{\frac{0.2}{\sqrt{21}}}$

$z = -13.74$

pvalue:

We are testing that the mean pressure is different than the target value of 7.9, and since the test statistic is negative, the pvalue is 2 multiplied by the pvalue of z = -13.74, which we find looking at the z-table.

$z = -13.74$ has a pvalue of 0.

2*0 = 0

0 < 0.05, which means that we reject the null hypothesis, meaning that the air pressure of the balls is different of the target value of 7.9.

8 0

2 years ago