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3 years ago

The sum of three consecutive even numbers is one hundred sixty - two.

Mathematics

1 answer:

Alenkasestr [34]3 years ago

5 0

Answer:

Step-by-step explanation:

Let x represent the smallest of the three numbers. Then the other two are (x+2) and (x+4). Their sum is ...

x + (x+2) +(x+4) = 162

3x = 156 . . . . . . . . . . . .subtract 6

x = 156/3 = 52

The smallest of the three numbers is 52.

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I like to work problems like this by considering the average number. Here, the average of the three numbers is 162/3 = 54, the middle number of the three. Then the smallest of the three consecutive even numbers is 2 less, or 52.

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What is the probability of rolling a 5 on a dice? Provide answer as REDUCED FRACTION!

melisa1 [442]

Answer:

i mean, if its a 6 sided dice, then 1/6

Step-by-step explanation:

8 0

2 years ago

Find m Give explanation please

erik [133]

Answer: The measurement of ∠EFG is equal to 70°.

Step-by-step explanation:

Two interior angles who are always opposite to an exterior angle sums to that exterior angle. So we would start as the following:

(6x - 10) + 38 = 7x + 18

In order to find m∠EFG, we must first isolate x. In order to do that, we first add like terms together on both sides.

(6x - 10) + 38 = 7x + 18

6x + 28 = 7x + 18

We then substract 18 on both sides.

6x + 10 = 7x

We finally substract 6x from both sides in order to have the value of x.

x = 10

Now that we know the value of x, we substitute it in our the equation in order to find m∠EFG.

m∠EFG = 6x + 10

m∠EFG = 6(10) + 10

m∠EFG = 60 + 10

m∠EFG = 70

8 0

3 years ago

Read 2 more answers

In 2005, there are 705 cable users in the small town of Whoville. The number of users

OLga [1]

Answer:2008

Step-by-step explanation:

5 0

3 years ago

0.63 x 1.8 solve with the steps to get the answer

Xelga [282]

Answer:

key the numbers into your calculator and execute the multiplication function

Step-by-step explanation:

Details vary with calculator model. Read your manual.

_____

There are many ways to work a problem of this nature by hand or in your head. The second attachment shows a couple of them.

Long multiplication

Essentially, every digit in one number needs to be multiplied by every digit in the other number, and the results combined according to their place value. The diagram on the left is a method that has you put the product of the top digit and the right digit into the box with "tens" and "ones" separated by a diagonal line.

After you've filled in the products of all the digits, you add them along diagonal "columns", putting the sum at the bottom or to the left. Any "carry" from the sum will add to the next "column" to the left or above. For example, the product digit 3 is arrived at by adding the 8, 2, and 3 along the diagonal. That sum results in a "carry" of 1 that gets added to the 4, 6, and 0 in the diagonal "column" above it.

As with any multiplication of decimals, the number of decimal digits in the product is the same as the total of the numbers of decimal digits in the multiplicands. (2+1=3)

Mental math

Both these numbers are multiplies of 9, so the product can be found different ways using that fact. The number 1.8 is 2 - 0.2, so the product can be found as ...

0.63 × 1.8 = 0.63 × (2 -0.2) = (0.63×2) - (0.63×0.2)

= 1.26 -0.126 = 1.134

Multiplication by 2 is easily done in your head. The subtraction of one 3-digit number from another may be a little harder to do, but is probably less work than the long multiplicatin described above.

_____

Alternative mental math

The product of one number and the other, as described above, is the product of each digit in one number with each digit in the other number, paying attention to place value.

With decimal points removed, the numbers are 63 and 18, and their product is ...

6·1 × 100 + (6·8 +3·1) × 10 + 3·8

= 600 +510 +24

= 1110 +24

= 1134

The the desired product is this value with the decimal point put 3 places from the right: 1.134

3 0

3 years ago

Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with

Alexxandr [17]

Answer:

Step-by-step explanation:

Hello!

The SAT math scores have a normal distribution with mean μ= 540 and standard deviation σ= 119

Eleonor scored 680 on the math part.

X: score obtained in the SAT math test

*-*

The ACT Assessment math test has a normal distribution with mean μ= 18.2 and standard deviation σ= 3.6

Gerald took the test and scored 27.

X: score obtained in the ACT math test

To standardize the values you have to use the following formula:

Z= (X-μ)/σ ~N(0;1)

For each score, you have to subtract its population mean and divide it by the standard deviation.

Eleonor score:

Z= (680-540)/119= 1.176 ≅ 1.18

Gerald Score

Z= (27-18.2)/3.6= 2.44

Since both variables are very different you cannot compare the "raw" scores to know which one is higher but once both of them were standardized, you can make a valid comparison.

In this case, Eleonor's score is 1.18σ away from the mean, while Gerald's score is 2.44σ away, i.e. Gerald's score is further away from the mean score than Eleonor's so his score is higher.

In this item, you are asked to find the value that divides the top 10% of the population from the bottom 90%.

Symbolically you can express it as:

P(Z>c)=0.1

P(Z≤c)= 0.9

The tables of standard normal distribution show accumulative probabilities of P(Z<Z₁₋α), sois best to use the second expression.

In the body of the distribution table, you have to look for a probability of 0.90 and then reach the corresponding Z value looking at the table margins. The first column shows the integer and first decimal digit, the first row shows the second decimal digit. So the corresponding value of Z is 1.28

Now you have to reverse the standardization to know the corresponding scores for each test.

SAT test score:

Z= (c-μ)/σ

Z*σ = c-μ

c = (Z*σ ) + μ

c= (1.28*119)+540

c= 692.32

The student should score 692.32 in his SAT math test to be in the top 10% of the population.

ACT test score

Z= (c-μ)/σ

Z*σ = c-μ

c = (Z*σ ) + μ

c= (1.28*3.6)+18.2

c= 22.808 ≅ 22.81

The student should score 22.81 in his ACT math test to be in the top 10% of the population.

In this item, their vas a sample of students that took the ACT taken and you need to calculate the probability of the sample mean being greater than 25.

If you were to take a 100 random samples of ACT scores of 100 students and calculate the mean of all of them, you will get that the sample mean is a random variable with the same kind of distribution as the original variable but it's variance will be influenced by the sample size. In this case, the original variable is:

X: score obtained in the ACT math test

This variable has a normal distribution X~N(μ;δ²), then it's the sample mean will also have a normal distribution with the following parameters X[bar]~N(μ;δ²/n)

Remember when you standardize a value of the variable of interest you subtract its "mean" and divide it by its "standard deviation" in this case the mean is μ and the standard deviation will be √(δ²/n) ⇒ δ/√n and the formula of the standard normal is:

Z= (X[bar]-μ)/(δ/√n)~N(0;1)

with n=100

μ= 18.2

δ= 3.6

P(X[bar]>25)= 1 - P(X[bar]≤25)

1 - P(Z≤(25-18.2)/(6.3/√100))= 1 - P(Z≤10.79)= 1 - 1 = 0

The probability of the mean ACT score for a random sample of 100 students being more than 25 is zero.

I hope it helps!

4 0

3 years ago