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goblinko [34]
3 years ago
7

The sum of two consecutive integers is 51. What are the numbers?

Mathematics
2 answers:
Naddika [18.5K]3 years ago
7 0

x is the 1st integer

x + 1 is the 2nd integer

x + (x+1) = 51

x + x + 1 = 51

2x + 1 = 51

subtract 1 to both sides

2x + 1 - 1 =51 -1

simplify

2x = 50

divide both sides by 2

2x/2 = 50 /2

simplify

x = 25

x + 1 = 25 +1 = 26

Answer: the numbers are 25 and 26

proof: sum of two consecutive integers is 51

25 + 26 =51


kolbaska11 [484]3 years ago
6 0
<span> OK

x + x + 1 =51
2x +1 =51
2x =50
x=25

The two numbers are 25, and 26.

Hope that helps  :)</span>
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Answer:

\bar x = 260.1615

\sigma = 70.69

The confidence interval of standard deviation is: 53.76 to 103.25

Step-by-step explanation:

Given

n =20

See attachment for the formatted data

Solving (a): The mean

This is calculated as:

\bar x = \frac{\sum x}{n}

So, we have:

\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 +.....+250.61}{20}

\bar x = \frac{5203.23}{20}

\bar x = 260.1615

\bar x = 260.16

Solving (b): The standard deviation

This is calculated as:

\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}

\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2+.....+(250.61- 260.1615)^2}{20 - 1}}\sigma = \sqrt{\frac{94938.80}{19}}

\sigma = \sqrt{4996.78}

\sigma = 70.69 --- approximated

Solving (c): 95% confidence interval of standard deviation

We have:

c =0.95

So:

\alpha = 1 -c

\alpha = 1 -0.95

\alpha = 0.05

Calculate the degree of freedom (df)

df = n -1

df = 20 -1

df = 19

Determine the critical value at row df = 19 and columns \frac{\alpha}{2} and 1 -\frac{\alpha}{2}

So, we have:

X^2_{0.025} = 32.852 ---- at \frac{\alpha}{2}

X^2_{0.975} = 8.907 --- at 1 -\frac{\alpha}{2}

So, the confidence interval of the standard deviation is:

\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} } to \sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }

70.69 * \sqrt{\frac{20 - 1}{32.852} to 70.69 * \sqrt{\frac{20 - 1}{8.907}

70.69 * \sqrt{\frac{19}{32.852} to 70.69 * \sqrt{\frac{19}{8.907}

53.76 to 103.25

8 0
3 years ago
1 A line passes through (0, 2) and has a slope of 3. Which function's graph is parallel to this line?
motikmotik
D. y=mx+b. m being slope and b being the y intercept. so the equation for the line is y=3x+2 and to be parallel your m must be the same number so D. 3x
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3 years ago
A livestock pen is built in the shape of a rectangle that is 2 times as long as it is wide. The perimeter is 30 feet. If the mat
shutvik [7]

Answer:

$57.5 is the total cost to build the pen.

Step-by-step explanation:

We are given the following in the question:

A livestock pen is built in the shape of a rectangle.

The length of rectangle is two times the width.

Let l be the length of rectangle and w be the width of rectangle. Thus, we can write

l = 2w

Perimeter = 30 feet

\text{Perimeter of rectangle} = 30\\2\times (l\times w) = 30

Putting values,

2(2w + w) = 30\\6w = 30\\w = 5\\l = 2w = 10

The length of rectangle is 10 feet and width of rectangle is 5 feet.

If the material used to build the pen is $ 1.75 per foot for the longer sides and $ 2.25 per foot for the shorter sides

Cost of building =

=2\times(\text{Cost of length}\times \text{Length} + \text{Cost of width}\times \text{Width})\\=2\times(1.75\times 10 + 2.25\times 5)\\=57.5

Thus, $57.5 is the total cost to build the pen.

7 0
3 years ago
si franco comió 8/3 de pizza y Fabián comió 5/6 de la misma pizza. ¿quien comió más ? si quedó 4/9 de pizza.​
devlian [24]

Answer:

Franco comió 8/3 de pizza.

Fabián comió 5/6 de pizza.

Queremos saber quien comió más.

Entonces básicamente queremos ver cuál número es más grande, 8/3 o 5/6,

Podemos reescribir el primero como:

8/3 = (2 + 3 + 3)/3 = 2/3 + 3/3 + 3/3 = 2/3 + 1 + 1

      = 2 + 2/3

En cambio, para el número 5/6, el numerador es menor que el denominador, entonces sabemos que:

5/6  < 1

Claramente podemos ver que 8/3 > 5/6

Entonces podemos concluir que Franco comió más.

8 0
3 years ago
A grading scale is set up for 1000 students' test scores. It assumes the
astra-53 [7]

Answer:

464 students will score between 48 and 75. Using the z-distribution, we measure how many standard deviations each score is from the mean, then find the p-value associated with each score to find the proportion, and from the proportion, we find how many out of 1000.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

It assumes the scores are normally distributed with a mean score of 75 and a standard deviation of 15.

This means that \mu = 75, \sigma = 15

How many students will score between 48 and 75?

First we find the proportion, which is the pvalue of Z when X = 75 subtracted by the pvalue of Z when X = 48. So

X = 75

Z = \frac{X - \mu}{\sigma}

Z = \frac{75 - 75}{15}

Z = 0

Z = 0 has a p-value of 0.5

X = 48

Z = \frac{X - \mu}{\sigma}

Z = \frac{48 - 75}{15}

Z = -1.8

Z = -1.8 has a p-value of 0.0359

1 - 0.0359 = 0.4641

Out of 1000:

0.4641*1000 = 464

464 students will score between 48 and 75. Using the z-distribution, we measure how many standard deviations each score is from the mean, then find the p-value associated with each score to find the proportion, and from the proportion, we find how many out of 1000.

7 0
3 years ago
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