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3 years ago

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Kay walks upstairs to make her legs stronger. Every day at work, she walks up 9 flights of stairs. If there are 13 steps in 1 fl

ight of stairs, how many steps does Kay climb in 5 days at work?

1 answer:

mr_godi [17]3 years ago

5 0

13*9*5 which will get you 585
585 steps

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Find the solution set of this inequality|10x+20| ≤10

Pavlova-9 [17]

Answer:

solution is

[-3,-1]

Step-by-step explanation:

we are given

$|10x+20|\leq 10$

Firstly, we will find critical values

so, let's assume it is equal

$|10x+20|= 10$

now, we can break absolute sign

For $|10x+20|= -(10x+20)$ :

$-(10x+20)= 10$

we can solve for x

$-10x-20= 10$

Add both sides by 20

$-10x-20+20= 10+20$

$-10x= 30$

Divide both sides by -10

and we get

$x=-3$

For $|10x+20|= (10x+20)$ :

$(10x+20)= 10$

we can solve for x

$10x+20= 10$

Subtract both sides by 20

$10x+20-20= 10-20$

$10x= -10$

Divide both sides by 10

and we get

$x=-1$

so, critical values are

$x=-3$

$x=-1$

now, we can draw a number line and locate these values

and then we can check inequality on each intervals

For $(-\infty,-3)$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=-5

$|10\times -5+20|\leq 10$

$|-50+20|\leq 10$

$30\leq 10$

so, this is FALSE

For $[-3,-1]$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=-2

$|10\times -2+20|\leq 10$

$|-20+20|\leq 10$

$0\leq 10$

so, this is TRUE

For $(-1,\infty)$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=0

$|10\times 0+20|\leq 10$

$|0+20|\leq 10$

$20\leq 10$

so, this is FALSE

so, solution is

[-3,-1]

7 0

3 years ago

A simple random sample of size nequals40 is drawn from a population. The sample mean is found to be 103.9, and the sample stand

yan [13]

Answer:

There is enough evidence to support the claim that the population mean is greater than 100

Step-by-step explanation:

<u>Step 1</u>: We state the hypothesis and identify the claim

$H_0:\mu=100$ and $H_1:\mu \:>\:100$ (claim)

<u>Step 2</u>: Calculate the test value.

$t=\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$

$\implies t=\frac{103.9-100}{\frac{21.9}{\sqrt{40} } }=1.1263$

<u>Step 3</u>: Find the P-value. The p-value obtained from a calculator is using d.f=39 and test-value 1.126 is 0.134

<u>Step 4</u>: We fail to reject the null hypothesis since P-value is greater that the alpha level. (0.134>0.05).

<u>Step 5</u>: There is enough evidence to support the claim that the population mean is greater than 100.

<u>Alternatively</u>: We could also calculate the critical value to obtain +1.685 for $\alpha=0.05$ and d.f=39 and compare to the test-value:

The critical value (1.685>1.126) falls in the non-rejection region. See attachment.

NB: The t- distribution must be used because the population standard deviation is not known.

5 0

3 years ago

Sliva [168]

Answer:

A. vertex, (3, 0); y-intercept 4.5

Step-by-step explanation:

Rewrite in vertex form and use this form to find the vertex

( h , k ) . ( 3 , 0 )

To find the x-intercept, substitute in 0 for y and solve for x . To find the y-intercept, substitute in 0 for x and solve for y .

x-intercept(s):

( 3 , 0 )

y-intercept(s):

( 0 , 4.5 )

3 0

2 years ago

Nadia solved the equation 4x-4=20!4x=16 x=4what error did she make

irakobra [83]

4(4) -4 = 16-4 = 12
She was wrong because she thought that x= 6

8 0

3 years ago

Read 2 more answers

Which equation demonstrates that use of a simple interest formula , l=PRT , to compute the investment earned on $70 at 3% For 12

Alenkinab [10]

Answer:

I = (70) x (0.03) x (12)

Step-by-step explanation:

The general formula of simple interest formula is: I = PRT where I = simple interest, P = principal amount, R = interest rate, T = time (in years). Given that the initial investment is $70, the interest rate is 3% (or 0.03 as a decimal) and the time is 12 years, you can form the following:

I = (70) x (0.03) x (12)

8 0

3 years ago