Solve this using a number line.<br> 3 1/8 ÷ 1/8

A line passes through the points (3,7) and (5,19) Part A: find the slope

nikklg [1K]

Answer:

The slope is 6. For the first line you could do y=6x+7, and the line parallel to that could be y= 6x+3

Step-by-step explanation:

For it to be parallel the slopes have to be the same and the y intercepts (b) have to be different. And I found the slope by doing y-y/x-x

plug in you numbers 19-7/5-3= 12/2 = 6

7 0

3 years ago

5. How many solutions will the following system of equations have?<br> y = -x +4<br> x² + y² = 16

alekssr [168]

Answer:

x = 0 and y = 4

x = 4 and y = 0

thus: 2 solutions

Step-by-step explanation:

8 0

3 years ago

In the past decades there have been intensive antismoking campaigns sponsored by both federal and private agencies. In one study

DIA [1.3K]

Answer:

$z=\frac{0.384-0.362}{\sqrt{0.374(1-0.374)(\frac{1}{4276}+\frac{1}{3908})}}=2.055$

The p value can be calculated from the alternative hypothesis with this probability:

$p_v =2*P(Z>2.055)=0.0399$

And the best option for this case would be:

C. between 0.01 and 0.05.

Step-by-step explanation:

Information provided

$X_{1}=1642$ represent the number of smokers from the sample in 1995

$X_{2}=1415$ represent the number of smokers from the sample in 2010

$n_{1}=4276$ sample from 1995

$n_{2}=3908$ sample from 2010

$p_{1}=\frac{1642}{4276}=0.384$ represent the proportion of smokers from the sample in 1995

$p_{2}=\frac{1415}{3908}=0.362$ represent the proportion of smokers from the sample in 2010

$\hat p$ represent the pooled estimate of p

z would represent the statistic

$p_v$ represent the value for the pvalue

System of hypothesis

We want to test the equality of the proportion of smokers and the system of hypothesis are:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

The statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{1642+1415}{4276+3908}=0.374$

Replacing the info given we got:

$z=\frac{0.384-0.362}{\sqrt{0.374(1-0.374)(\frac{1}{4276}+\frac{1}{3908})}}=2.055$

The p value can be calculated from the alternative hypothesis with this probability:

$p_v =2*P(Z>2.055)=0.0399$

And the best option for this case would be:

C. between 0.01 and 0.05.

7 0

2 years ago

The diameter of a circle is 14 inches. Find the circumstance and area use 22/7

s344n2d4d5 [400]

Answer:

Circumference= 44 in

Area= 154 in²

Step-by-step explanation:

$\boxed{circumference \: of \: circle = 2\pi r}$

Radius

= diameter ÷2

= 14 ÷2

= 7 in

Circumference of circle

$= 2( \frac{22}{7} )(7)$

= 44 in

$\boxed{area \: of \: circle = \pi {r}^{2} }$

Area of circle

$= \frac{22}{7} ( {7}^{2} )$

= 154 in²

3 0

3 years ago

A cylindrical tank with radius 3 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increas

Fittoniya [83]

Height of the water increasing is at rate of $#(dh)/(dt)=3/(25 pi)m/(min)#$

<h3>How to solve?</h3>

With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:

$#V=pi r^2 h#$

There is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:

$#V=pi (5m)^2 h#$

Since the rate in this problem is time related, we need to implicitly differentiate wrt (with respect to) time:

$#(dV)/(dt)=(25 m^2) pi (dh)/(dt)#$

In the problem, we are given $#3(m^3)/min# which is #(dV)/(dt)#.$

So we need to substitute this in:

$#(dh)/(dt)=(3m^3)/(min (25m^2) pi)=3/(25 pi)m/(min)#$

Hence, Height of the water increasing is at rate of $#(dh)/(dt)=3/(25 pi)m/(min)#$

<h3>Formula used: </h3>

$#V=pi r^2 h#$

To Learn more visit:

brainly.com/question/4313883

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4 0

2 years ago

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