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3 years ago

The sum of two numbers is 53. if twice the first number minus three times the second number is 26, find both numbers.

1 answer:

6 0

Make an equation system based on the problem
eg. a is the first number and b is the seond number
An equation for "<span>The sum of two numbers is 53" is
</span>⇒ a + b = 53
An equation for "<span>twice the first number minus three times the second number is 26"
</span>⇒ 2a - 3b = 26
<span>
Solve the equations by elimination and subtitution method
Eliminate a to find the value of b
a + b = 53 (multiplied by 2)
2a - 3b = 26
--------------------------------------
2a + 2b = 106
2a - 3b = 26
------------------- - (substract)
5b = 80
b = 80/5
b = 16

Subtitute the value of b to one of the equations
a + b = 53
a + 16 = 53
a = 53 - 16
a = 37

The numbers are 16 and 37</span>

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Wren recorded an outside temperature of –2°F at 8 a.m. When she checked the temperature again, it was 4°F at 12:00 p.m. If x rep

Ksenya-84 [330]

Answer:

Step-by-step explanation:

We are given two points. Let the points be A and B

A ( 8 , -2 ) ------> ( x1 , y1 )

B ( 12 , 4 ) ------> ( x2 , y2 )

Now, let's find the slope of the given points:

$slope \: = \frac{y2 - y1}{x2 - x1}$

plug the values

$= \frac{4 - ( -2)}{12 - 8}$

When there is a ( - ) in front of an expression in parentheses , change the sign of each term in the expression

$= \frac{4 + 2}{12 - 8}$

Subtract the numbers

$= \frac{4 + 2}{4}$

Add the numbers

$= \frac{6}{4}$

Reduce the fraction with 2

$= \frac{3}{2}$

$= 1.5$

Hope this helps..

Best regards!!

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3 years ago

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valkas [14]

B is the correct answer. hope this helped:)

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2 years ago

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g A fair coin is tossed 20 times. The number of heads observed is the count X of successes. Give the distribution of X . Choose

Nuetrik [128]

Answer:

We assume that we have a fair coin that is $p(Head)=p(Tails)=0.5$

For this case we define the random variable X as "number of heads observed in 20 times". The distribution for X is given by:

$X \sim Binom(n=20, p=0.5)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Solution to the problem

We assume that we have a fair coin that is $p(Head)=p(Tails)=0.5$

For this case we define the random variable X as "number of heads observed in 20 times". The distribution for X is given by:

$X \sim Binom(n=20, p=0.5)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

3 0

3 years ago

Create an equation with one solution of x = −4.

katen-ka-za [31]

Answer:

What is missing is -5x - 20

Step-by-step explanation:

To find this, simply solve for the parenthesis as if it were a variable of its own. This will allow you to see exactly what is missing.

8x - (x - 20) = 2x - (_______)

8x - x + 20 = 2x - (_______)

7x + 20 = 2x - (_______)

5x + 20 = - (_______)

-5x - 20 = (_______)

So the answer for the parenthesis is -5x - 20

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3 years ago

If a car drove 180 miles in 3 hours and a truck drove 150 miles in 2 hours, what is the speed (in miles per hour) of the faster

grigory [225]

Step-by-step explanation:

Divide 180 by 3 = 60

Divide 150 by 2 = 75

The faster vehicle is truck and its speed is 75 mph

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2 years ago