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3 years ago

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The length and width of a rectangle must have a sum of 80. Find the dimensions of the rectangle that will have the maximum area.

[Hint: Let x and 80−x be the length and width. The area can be described by the function f(x)=x(80−x).]

1 answer:

jok3333 [9.3K]3 years ago

6 0

I hope this helps you

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I need help (please show your work)

oksano4ka [1.4K]

Answer:

the solution is (-4, 3)

Step-by-step explanation:

if you were to graph y = -7/4x - 4 you could plot your first point at (0, -4) and get your second point by going up 7 units (from (0, -4) and to the left by 4

if you were to graph y = -1/4x + 2 you could plot your first point at (0, 2) and get your second point by going up 1 unit (from (0, 2) and to the left by 4

the second point plotted for each equation will be the point of intersection, (-4, 3)

6 0

3 years ago

A group of researchers wants to know whether men are more likely than women to contract a novel coronavirus. They surveyed two r

olasank [31]

Answer:

Test statistic Z= 0.13008 < 1.96 at 0.10 level of significance

null hypothesis is accepted

There is no difference proportion of positive tests among men is different from the proportion of positive tests among women

Step-by-step explanation:

<em>Step(I)</em>:-

Given surveyed two random samples of 390 men and 360 women who were tested

first sample proportion

$p_{1} = \frac{360}{390} = 0.9230$

second sample proportion

$p_{2} = \frac{47}{52} = 0.9038$

Step(ii):-

Null hypothesis : H₀ : There is no difference proportion of positive tests among men is different from the proportion of positive tests among women

Alternative Hypothesis:-

There is difference between proportion of positive tests among men is different from the proportion of positive tests among women

$Z = \frac{p_{1}- p_{2} }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } } }$

where

$P = \frac{n_{1}p_{1} +n_{2} p_{2} }{n_{1}+n_{2} }$

P = 0.920

$Z= \frac{0.9230-0.9038}{\sqrt{0.920 X0.08(\frac{1}{390}+\frac{1}{52} } )}$

Test statistic Z = 0.13008

Level of significance = 0.10

The critical value Z₀.₁₀ = 1.645

Test statistic Z=0.13008 < 1.645 at 0.1 level of significance

Null hypothesis is accepted

There is no difference proportion of positive tests among men is different from the proportion of positive tests among women

7 0

3 years ago

What are the first and second steps performed in solving the inequality 2(4w + 8) – 2w + 42 > 78? Name the property used.

Phoenix [80]

Hello :
<span>2(4w + 8) – 2w + 42 > 78
8w+16-2w+42 </span>> 78......(<span>distributivity × for + )
6w </span>> 20
w > 20/6

6 0

3 years ago

A detective has interviewed four witnesses to a crime. From the stories of the witnesses the detective has concluded

SVETLANKA909090 [29]

Answer:

Step-by-step explanation:

Step 1:we should turn the “facts” into logical expressions.

Step 2:Assign variables

Our variables are: b (for butler), c (for cook), g (for gardener), h (for handyman)

Step 3 . Let the value of true indicate that the person is telling the truth. For example, b = T means the butler is telling the truth. Then we can translate the statements as follows:

Check attachment

Step 4

We know all of these must hold. So we really want to know when (b→c)∧¬(c∧g)∧¬(¬g∧¬h)∧(h → ¬c) is true.

Step 5

Behold, another truth table task! If you work out the truth table, you see that this statement is only true when:

Check attachment

Step 6

Therefore we can say the butler and cook are definitely lying, but we can not determine if the gardener or handyman are lying. However, there are four variables in this problem. Instead, we can do this with some straight reasoning. Notice that:

If the butler is telling the truth, then by (a) the cook is telling the truth.

If the cook is telling the truth, then by (b) the gardener is lying.

If the gardener is lying, then by (c) the handyman is telling the truth.

If the handyman is telling the truth, they by (d) the cook is lying.

This leads to a contradiction (the cook can not be both telling the truth and lying)! Therefore the butler and cook must be lying. What about the gardener and the handyman? We don’t have enough information to figure out if they are lying. Since the cook is lying, we can’t use (b) to come to any conclusions about the gardener. Even if we are able to conclude that the gardener is telling the truth, we can’t use (c) to come to any conclusions about the handyman.

4 0

3 years ago

Arrange the polynomial so that the powers of x are in descending order.

Aleonysh [2.5K]

8x - 9x²y + 7y² - 2x⁴
-2x⁴ - 9x²y + 8x + 7y²

3 0

3 years ago