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2 years ago

The sum of 2 numbers is 46. One number is 12 more than the other. What are the numbers?

Mathematics

2 answers:

harkovskaia [24]2 years ago

5 0

Answer:

two numbers are 29 and 17

Step-by-step explanation:

let the number be x

12+x+x=46

2x=46-12

x=34/2

x=17

another number is 12+x

12+17

Alex73 [517]2 years ago

3 0

The two numbers would be 29 and 17

29+17=46
29-17=12

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2 years ago

The length of a rectangle is four times its width.

Irina-Kira [14]

Answer:

Length = 24 yd

Width = 6 yd

Step-by-step explanation:

To start out, we can begin by saying that "l" is the length of the rectangle, and "w" is the width.

Since we know that the length (l) is 4 times its width we can say that 4 times the width is equal to its length. We would write this out this way :

4w = l

Next, we know that the perimeter is 60yd (as it is given in the question). We also know that the perimeter of a rectangle is all of its sides, added. Meaning the length plus the length, plus the width and the width. So, we can use the equation :

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"p" being the perimeter. And, since the perimeter is 60, we can place in 60 for "p"

2l + 2w = 60

Now we can use this information to combine the terms, and find the width and length. We first do this by noticing that in the first equation, it shows that "l" (the length) is equal to 4w. This means that we can put 4w in place of the "l" in the second equation. We can do this, becuase we know that "l" is equal to 4w. (from the first eqaution)

2 (4w) + 2w = 60

Now, we solve

2 * 4w = 8w

8w + 2w = 10w

So now we have :

10w = 60

To get the width, all we have to do is simply get "w" alone. We can do this by dividing both sides by 10.

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Therefore, the width is 6.

Now, going back to the first equaiton, we already know that the length is 4 times the width, meaning all we have to do is multiply 6 by 4 to get the length.

6 * 4 = 24.

Therefore, the length is 24.

Lastly, to check and make sure we are correct, we can go back to the second equation. 2l + 2w = 60

2 (24) + 2 (6) = 60

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Now, we officially know that the length of the rectangle is 24 and the width is 6.

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1 year ago

5. Suppose that a particular candidate for public office is in fact favored by p = 48% of all registered voters. A polling organ

mart [117]

Answer:

Probability that the sample proportion will be greater than 0.5 is 0.8133.

Step-by-step explanation:

We are given that the a particular candidate for public office is in fact favored by p = 48% of all registered voters. A polling organization is about to take a simple random sample of voters and will use the sample proportion to estimate p.

Suppose that the polling organization takes a simple random sample of 500 voters.

Let $\hat p$ = sample proportion

The z-score probability distribution for sample proportion is given by;

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

where, $\hat p$ = sample proportion

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n = sample of voters = 500

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the sample proportion will be greater than 0.5 is given by = P( $\hat p$ > 0.50)

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Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.89 in the z table which has an area of 0.8133.

Therefore, probability that the sample proportion will be greater than 0.50 is 0.8133.

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