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3 years ago

What is the slope of this line?

Mathematics

2 answers:

katen-ka-za [31]3 years ago

8 0

The slope of this line is -3/4

In order to find this, we look for two points on the line and then use the slope formula. Two points that are on the line are (0, 2) and (4, -1). Plug these into the following formula.

m (slope) = (y2 - y1)/(x2 - x1)

m = (-1 - 2)/(4 - 0)

m = -3/4

patriot [66]3 years ago

8 0

(0,2), (4,-1)
I got like that but i’am not sure

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The product of two consecutive even positive integers is 674 more than the sum of the two integers. Find the integers.

IrinaVladis [17]

$2n(2n+2)=2n+2n+2+674\\
4n^2+4n=4n+676\\
4n^2=676\\
n^2=169\\
n=-13 \vee n=13$
$-13\not\ \textgreater \ 0$

$n=13\\
2n=26\\
2n+2=28$

It's 26 and 28.

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3 years ago

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3 years ago

Read 2 more answers

(3x+4)^2=14 what are the solutions?

kherson [118]

$\bf (3x+4)^2=14\implies \sqrt{(3x+4)^2}=\pm\sqrt{14}\implies 3x+4=\pm\sqrt{14}
\\\\\\
3x=\pm \sqrt{14}-4\implies x=\cfrac{\pm \sqrt{14}-4}{3}\implies x=
\begin{cases}
\cfrac{\sqrt{14}-4}{3}\\\\
\cfrac{- \sqrt{14}-4}{3}
\end{cases}$

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3 years ago

Suppose that in a random selection of 100 colored candies, 28% of them are blue. The candy company claims that the percentage

Zigmanuir [339]

Answer:

We conclude that the percentage of blue candies is equal to 29%.

Step-by-step explanation:

We are given that in a random selection of 100 colored candies, 28% of them are blue. The candy company claims that the percentage of blue candies is equal to 29%.

Let p = population percentage of blue candies

So, Null Hypothesis, $H_0$ : p = 29% {means that the percentage of blue candies is equal to 29%}

Alternate Hypothesis, $H_A$ : p $\neq$ 29% {means that the percentage of blue candies is different from 29%}

The test statistics that will be used here is One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of blue coloured candies = 28%

n = sample of colored candies = 100

So, the test statistics = $\frac{0.28-0.29}{\sqrt{\frac{0.29(1-0.29)}{100} } }$

= -0.22

The value of the z-test statistics is -0.22.

Also, the P-value of the test statistics is given by;

P-value = P(Z < -0.22) = 1 - P(Z $\leq$ 0.22)

= 1 - 0.5871 = 0.4129

Now, at a 0.10 level of significance, the z table gives a critical value of -1.645 and 1.645 for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of z, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the percentage of blue candies is equal to 29%.

4 0

3 years ago

A square of side length s lies in a plane perpendicular to a line L. One vertex of the square lies on L. As this square moves a

user100 [1]

Answer:

Part (A) The required volume of the column is $s^2h$ .

Part (B) The volume be $s^2h=\frac{s^2h}{2}+\frac{s^2h}{2}$ .

Step-by-step explanation:

Consider the provided information.

It is given that the we have a square with side length "s" lies in a plane perpendicular to a line L.

Also One vertex of the square lies on L.

Part (A)

Suppose there is a square piece of a paper which is attached with a wire through one corner. As you blow it up it spins around on the wire.

This square moves a distance h along L, and generate a corkscrew-like column with square.

The cross section will remain the same.

So the cross section area of original column and the cross section area of twisted column at each point will be the same.

The volume of the column is the area of square times the height.

This can be written as:

$s^2h$

Hence, the required volume of the column is $s^2h$ .

Part (B) What will the volume be if the square turns twice instead of once?

If the square turns twice instead of once then the volume will remains the same but divide the volume into two equal part.

$s^2h=\frac{s^2h}{2}+\frac{s^2h}{2}$

Hence, the volume be $s^2h=\frac{s^2h}{2}+\frac{s^2h}{2}$ .

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3 years ago