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3 years ago

A direct variation function contains the points (-8,-6) and (12,9) which equation represents the function

Mathematics

1 answer:

brilliants [131]3 years ago

7 0

Answer:

y = 0.75x

Step-by-step explanation:

Given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k substitute either of the 2 points into the equation

Using (12, 9 ), then

k = $\frac{y}{x}$ = $\frac{9}{12}$ = 0.75, so

y = 0.75x ← equation of variation

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Zinaida [17]

Answer:

The 3rd one 50 - 12p = 26

Step-by-step explanation:

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6s-4=8 (2+ 0.25s) solve for s

pentagon [3]

Answer:

s=5

Step-by-step explanation:

6s-4=16+2s

6s=20+2s

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Biologists have found that the number of chirps some crickets make per minute is related to temperature. the relationship is ver

aalyn [17]

Answer:

It is $74.24$ degrees Fahrenheit when the crickets are chirping $150$ times a minute.

Variables $x = Chirps$ and $y = Degrees$

y-intercept $= 38.24$

slope $= 0.24$

Step-by-step explanation:

As the chirps are $124$ times per minute for $68$ degrees Fahrenheit we will consider it in $(x_1,y_1) = (124,68)$ .

Now when the chirps are $172$ times and temperature is $80$ degrees we consider it $(x_2,y_2) = (172,80)$ .

To find the slope we can use point-slope formula.

Where $m$ is the slope and $m=\frac{y_2-y_1}{x_2-x_1} =\frac{80-68}{172-124}= 0.24$

To find y-intercept we will plug out the value of slope in $y=m(x)+b$ choosing point $(x_1,y_1) = (124,68)$ .

So $b=y-m(x) =68-124(0.24) =68-29.76=38.24$

And the equation is $y=0.24(x)+b$

To calculate temperature for $150$ chirpings we have to plug $x=150$ and $b=38.24$ in our above equation which is in form of $y=m(x)+b$

$y=0.24(x)+b$

$y=0.24(150)+38.24=74.24\approx 75$ degrees Fahrenheit.

Finally we have :

Temperature $74.24$ degrees Fahrenheit.

With variables $x = Chirps$ and $y = Degrees$

y-intercept $= 38.24$ and

slope $= 0.24$

6 0

3 years ago

In 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alc

Fynjy0 [20]

Answer:

We conclude that the proportion of adults who totally abstain from alcohol has changed.

Step-by-step explanation:

We are given that in 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?"

Of the 1100 adults surveyed, 429 indicated that they were total abstainers. In a recent survey, the same question was asked of 1100 adults and 352 in

Let p = proportion of adults who totally abstain from alcohol.

where, p = $\frac{429}{1100}$ = 0.39

So, Null Hypothesis, $H_0$ : p = 39% {means that the proportion of adults who totally abstain from alcohol has not changed}

Alternate Hypothesis, $H_A$ : p $\neq$ 39% {means that the proportion of adults who totally abstain from alcohol has changed}

The test statistics that would be used here One-sample z proportion statistics;

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

where, $\hat p$ = sample proportion of adults who totally abstain from alcohol = $\frac{352}{1100}$ = 0.32

n = sample of adults surveyed = 1100

So, test statistics = $\frac{0.32-0.39}{\sqrt{\frac{0.32(1-0.32)}{1100} } }$

= -4.976

The value of z test statistics is -4.976.

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

Since our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the proportion of adults who totally abstain from alcohol has changed.

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3 years ago

Solve the expression (-24) + (+6)

ASHA 777 [7]

Answer:

-18

Step-by-step explanation:

The answer is -18 because a negative plus a positive is always a negative.

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