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fiasKO [112]
3 years ago
7

The sum of four consecutive integers is 418. Find them.

Mathematics
1 answer:
cupoosta [38]3 years ago
5 0

Answer: 103, 104, 105, and 106

Step-by-step explanation: This problem states that the sum of 4 consecutive integers is 418 and it asks us to find the integers.

First represent your 4 consecutive integers as follows.

X ⇒ first integer

X + 1 ⇒ second integer

X + 2 ⇒ third integer

X + 3 ⇒ fourth integer

Since their sum is 418, our equation reads

x + (x + 1) + (x + 2) + (x + 3) = 418.

Simplifying on the left side we get 4x + 6 = 418.

Now we can subtract 6 from both sides of the equation and we have

4x = 412.

Now just divide both sides by 4 and we find that <em>x = 103</em>.

Finally, make sure you list all your answers.

If <em>x</em> is 103, then <em>x </em>+ 1 is 104, <em>x</em> + 2 is 105, and <em>x</em> + 3 is 106

Therefore, our 3 consecutive integers are 103, 104, 105, and 106.

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y = -4/3x - 1

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3 years ago
in the unted states, the height of men are normally distributed with the mean 69 inches and standard deviation 2.8 inches. If 16
yaroslaw [1]

Answer:

Probability that their mean height is less than 68 inches is 0.0764.

Step-by-step explanation:

We are given that in the united states, the height of men are normally distributed with the mean 69 inches and standard deviation 2.8 inches.

Also, 16 men are randomly selected.

<em>Let </em>\bar X<em> = sample mean height</em>

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

              Z = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \mu = population mean height = 69 inches

            \sigma = population standard deviation = 2.8 inches

            n = sample of men = 16

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 mean height of 16 randomly selected men is less than 68 inches is given by = P(\bar X < 68 inches)

 P(\bar X < 68 inches) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < \frac{68-69}{\frac{2.8}{\sqrt{16} } } ) = P(Z < -1.43) = 1 - P(Z \leq 1.43)

                                                           = 1 - 0.9236 = 0.0764

<em>Now, in the z table the P(Z  x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.43 in the z table which has an area of 0.92364.</em>

Therefore, probability that their mean height is less than 68 inches is 0.0764.

3 0
3 years ago
During the settlement of the west many towns were established by speculators who
USPshnik [31]

Answer:

could you finish the problem?

Step-by-step explanation:

Also this is in the wrong section

8 0
2 years ago
Please help, I will give brainliest, I am struggling badly.
Solnce55 [7]

Answer:

(8, -1)

Step-by-step explanation:

the solution is where they intersect. (x, y) and x is 8 while y is -1

7 0
3 years ago
Ciara is naking a new outfit she needs 2 1/2 yards of the fabric for the shawl and 1 3/4 yards of fabric for the dress. If she h
valentina_108 [34]

Answer:

1 1/4 yards

$20

Step-by-step explanation:

The amount of fabric more that she needs can be determined by subtracting the sum of the yards needed for the shawl and the dress from the fabric she has

sum of the yards needed for the shawl and the dress =

2\frac{1}{2} + 1\frac{3}{4}

3\frac{2 + 3}{4} = 3\frac{5}{4} = 4\frac{1}{4}

Yards needed

4\frac{1}{4} - 3 = 1\frac{1}{4}

cost of dance outfit = $16 x 1\frac{1}{4}

\frac{5}{4} × $16  = $20

6 0
3 years ago
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