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austin is riding his bicycle. He rides for 27.5 kilometers at a speed of 11 kilometers per hours for how many hours did he ride?

Ludmilka [50]

Divide 27.5/11, and you get 2.5.
Austin rode for 2.5 hours (2 and a half hours).

4 0

3 years ago

Which expressions have a value less than 1? Choose all the correct answers.

Lemur [1.5K]

Answer:

A and D

Step-by-step explanation:

-7/2-4= -15/2

-7+1/2(-4)

-7-2

-9

5 0

3 years ago

What is the value of (f-3)?

almond37 [142]

Simply substitute the value of

3

given. In other words,

f

(

3

)

is the function of

f

(

x

)

, however, in this case,

x

is

3

f

(

3

)

=

3

(

3

)

−

4

Distribute

3

through the parenthesis

f

(

3

)

=

9

−

4

Simplify

f

(

3

)

=

5

8 0

3 years ago

a rectangle has a perimeter of 76 cm. Its length is 5 more that twice its width. The system of equation below can be use to fine

Juliette [100K]

Answer:

$l=27cm$ and $w=11cm$

Step-by-step explanation:

the perimeter of a rectangle is given by the following equation:

$p=2(l+w)=2l+2w$

if a rectangle has a perimeter of 76cm and its length is 5 plus the double of its width we can use a system of equations to find the length $l$ , and the width $w$ .

For the perimeter of the rectangle

$2l+2w=76$ where $l$ is its length, and $w$ is its width, 76 is the perimeter of the rectangle in cm.

We know that the lengh of the rectangle is 5 plus the double of its width, writing the equation:

$l=5+2w$

Substituting the equation above in $2l+2w=76$

$2(5+2w)+2w=76\\10+4w+2w=76\\6w=76-10\\w=66/6\\w=11$

We got that the rectangle width is w=11cm

Substituting w in the equation $2l+2w=76$

$2l+2(11)=76\\2l+22=76\\l=(76-22)/2=54/2\\l=27$

We got that the rectangle length is l=27cm

Verifying the values obtained

$2l+2w=76$ with l=27 and w=11

$2(27)+2(11)=76$

$54+22=76$

Satisfying the equation

5 0

3 years ago

A quality-conscious disk manufacturer wishes to know the fraction of disks his company makes which are defective. Step 2 of 2: S

Anna35 [415]

Answer:

The 98% confidence interval for the population proportion of disks which are defective is (0.082, 0.118).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

Suppose a sample of 1536 floppy disks is drawn. Of these disks, 1383 were not defective.

1536 - 1383 = 153

This means that $n = 1536, \pi = \frac{153}{1536} = 0.1$

98% confidence level

So $\alpha = 0.02$ , z is the value of Z that has a pvalue of $1 - \frac{0.02}{2} = 0.99$ , so $Z = 2.327$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1 - 2.327\sqrt{\frac{0.1*0.9}{1536}} = 0.082$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1 + 2.327\sqrt{\frac{0.1*0.9}{1536}} = 0.118$

The 98% confidence interval for the population proportion of disks which are defective is (0.082, 0.118).

6 0

3 years ago