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3 years ago

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A restaurant has tables with three legs. Which of the following shows how the number of legs, y, changes as the number of tables

, x, changes?

1 answer:

alexandr1967 [171]3 years ago

5 0

Answer:

You have not written the following answers. But I think it should be

y = 3 * x

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Find two positive integers such that the sum of the first number and four times the second number is 1000, and the product of th

vladimir2022 [97]

Answer:

The two numbers are:

x = 500

y = 125

Step-by-step explanation:

We want to find two numbers x and y, such that:

x + 4*y = 1000

f(x, y) = x*y is maximum.

From the first equation, we can isolate one of the variables to get

x = 1000 - 4y

now we can replace it in f(x, y):

x*y = (1000 - 4*y)*y = 1000*y - 4*y^2

So now we want to maximize the function:

f(y) =- 4*y^2 + 1000*y

where y must be an integer.

Notice that this is a quadratic equation with a negative leading coefficient (so the arms of the graph will open downwards), thus, the maximum will be at the vertex.

Remember that for a general quadratic equation:

y = a*x^2 + bx + c

the x-value of the vertex is:

x = -b/(2*a)

so, in the case of:

f(y) =- 4*y^2 + 1000*y

the y-value of the vertex will be:

y = -1000/(2*-4) = 1000/8 = 125

So we found the value of y.

now we can use the equation:

x = 1000 - 4*y

x = 1000 - 4*125 = 1000 - 500 = 500

x = 500

Then the two numbers are:

x =500

y = 125

6 0

2 years ago

An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From pre

melamori03 [73]

Answer:

We conclude that a compact microwave oven consumes a mean of more than 250 W.

Step-by-step explanation:

We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W with a population standard deviation of 15 W.

They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.

Let $\mu$ = <u><em>mean power consumption for microwave ovens.</em></u>

So, Null Hypothesis, $H_0$ : $\mu$ $\leq$ 250 W {means that a compact microwave oven consumes a mean of no more than 250 W}

Alternate Hypothesis, $H_A$ : $\mu$ > 250 W {means that a compact microwave oven consumes a mean of more than 250 W}

The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean power consumption for ovens = 257.3 W

σ = population standard deviation = 15 W

n = sample of microwave ovens = 20

So, <em><u>the test statistics</u></em> = $\frac{257.3-250}{\frac{15}{\sqrt{20} } }$

= 2.176

The value of z test statistics is 2.176.

<u>Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.</u>

Since our test statistic is more than the critical value of t as 2.176 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.

Therefore, we conclude that a compact microwave oven consumes a mean of more than 250 W.

7 0

3 years ago

Eight friends went to a hockey game. The

ASHA 777 [7]

Step-by-step explanation:

Four bought a book at $6

4 x $6 = $24

8 x $x = $8x

Expression

$24 + $8x

3 0

3 years ago

Read 2 more answers

10q - 30 is equivalent to _____.

mr_godi [17]

For this case we must find an expression equivalent to:

$10q-30$

We look for the factors of 10 and 30:

10: 1,2,5,10

30: 1,2,3,5,6,10,15,30

The greatest common factor of both numbers is 10.

Then, we can rewrite the expression as:

$10 (q-3)$

Answer:

$10 (q-3)$

5 0

3 years ago

How do you write 11 thousands in standard form?

Afina-wow [57]

11,000 u think hope I helped

6 0

3 years ago