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1 year ago

Laura will go for a run during her lunch break if the temperature is between 60∘F

Mathematics

1 answer:

balu736 [363]1 year ago

8 0

Answer:

D(t) = 3 + 0.0(80 - t)

Step-by-step explanation:

The average of speed of Laura in miles per hour is given by:

S(t) = 6 + 0.1(80 - t) Equation 1

where, t is the temperature in degrees Fahrenheit.

The distance D, Laura covers at x miles per hour is given as:

D(x) = 0.5x Equation 2

We need to find the expression that models the distance that Laura runs in terms of the temperature "t"

The "x" in Equation 1 represents the average speed of Laura in miles per hour. S(t) in Equation 1 also represent the speed of Laura in miles per hour. So, we can replace x by S(t) in Equation 2 and generate an equation of Distance in terms of temperature "t" as shown below:

D(S(t)) = 0.5 (6 + 0.1(80-t))

D(t) = 3 + 0.0(80 - t)

This expression models the distance that Laura runs in 30 minutes given that it is t∘F outside at the start of her run.

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lions [1.4K]

The triangles are similar because corresponding angles are congruent, however no congruency statement can be made because the side lengths are unknown.

The 4th selection is appropriate.

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2 years ago

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A direct variation function contains the points (-9, -3) and (-12,4). Which equation represents the function?

Triss [41]

Answer:

$y = -\frac{7x}{3} - 24$

Step-by-step explanation:

We can model this function using the equation of a line:

$y = ax + b$

Where a is the slope of the line and b is the y-intercept.

To find the values of a and b, we can use the two points given:

(-9, -3):

$-3 = a * (-9) + b$

$-9a + b = -3$

(-12, 4):

$4 = a * (-12) + b$

$-12a + b = 4$

If we subtract the second equation from the first one, we have:

$-12a + b - (-9a + b) = 4 - (-3)$

$-12a + 9a = 4 + 3$

$-3a = 7$

$a = -7/3$

Then, finding the value of b, we have:

$-12a + b = 4$

$28 + b = 4$

$b = -24$

So the equation is:

$y = -\frac{7x}{3} - 24$

3 0

1 year ago

A teacher handed out m notebooks which came in packs with c notebooks in each pack. How many packs were there?

Roman55 [17]

Let’s throw some numbers in here just so it becomes clear what we are asked for.

Let’s say the teacher hands out 12 notebooks that came in packs with 4 notebooks in each pack. If you are asked for the number of packs here you would see that it’s 3. That is 3 packs of 4 give 12.

So you divide the number of notebooks handed out (m) by the number of notebooks per pack (c) to get the number of packs.

The number of packs is m/c

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1 year ago

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A quality control technician works in a factory that produces computer monitors. Each day, she randomly selects monitors and tes

jeka94

Answer:

There is enough evidence to support the claim that the true proportion of monitors with dead pixels is greater than 5%.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 300

p = 5% = 0.05

Alpha, α = 0.05

Number of dead pixels , x = 24

First, we design the null and the alternate hypothesis

$H_{0}: p = 0.05\\H_A: p > 0.05$

This is a one-tailed(right) test.

Formula:

$\hat{p} = \dfrac{x}{n} = \dfrac{24}{300} = 0.08$

$z = \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

Putting the values, we get,

$z = \displaystyle\frac{0.08-0.05}{\sqrt{\frac{0.05(1-0.05)}{300}}} = 2.384$

Now, we calculate the p-value from excel.

P-value = 0.00856

Since the p-value is smaller than the significance level, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

Conclusion:

Thus, there is enough evidence to support the claim that the true proportion of monitors with dead pixels is greater than 5%.

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1 year ago

What is the solution set of the quadratic inequality 6x^2+1 greater than or equal to 0?

Ratling [72]

Answer:

Step-by-step explanation:

6x^2 + 1 <= 0

6x^2 <= -1

x^2 <= -1/6

Since we cannot take the square root of a negative number, there is no solution.

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1 year ago