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3 years ago

How do the expressions 4(3+x) and (3+3+3+3) + (x+x+x+x) compare to one another

Mathematics

2 answers:

valina [46]3 years ago

6 0

Answer:

Well they represent the same answer as the second expression is the distributive property of the first expression.

Step-by-step explanation:

4(3+x) is basically 4 • (3+x)since we are working with addition and multiplication you can use the distributive property. That can be written out as (4•3) + (4•x). If you wanted to simplify it even more then it could be written as (3+3+3+3) + (x+x+x+x)

Dafna1 [17]3 years ago

3 0

Answer:

Step-by-step explanation:

If we expand 4(3+x), we get (4*3)+(4*x).

Then we do 4*3 to get 12 and 4*x to get 4x

(3+3+3+3) is the same thing as 4*3, because we are adding 3 together 4 times. (3+3+3+3) gives us 12 as well, since they are the same thing.

(x+x+x+x) is the same thing because we are adding x together 4 times, which is the same thing as (4*x). (x+x+x+x) gives us 4x as well.

Hope this helps.

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a recipe uses 1 1/4 cups of milk to make 10 servings. if the same amount of milk is used for each serving, how many servings can

Anestetic [448]

Answer:

128 servings can be made using 1 gallon of milk.

Step-by-step explanation:

Given that:

$1\frac{1}{4}$ cups of milk make 10 servings

$1\frac{1}{4}$ can also be written as 1.25

Ratio of cups of milk to servings = 1.25 : 10

1 gallon = 16 cups

Let,

x be the number of servings made from 1 gallon

Ratio of cups of milk to servings = 16 : x

This is a direct proportion

1.25 : 10 :: 16 : x

Product of mean = Product of extreme

10*16 = 1.25x

160 = 1.25x

1.25x=160

Dividing both sides by 1.25

$\frac{1.25x}{1.25}=\frac{160}{1.25}\\x=128$

Hence,

128 servings can be made using 1 gallon of milk.

3 0

3 years ago

A researcher studying stress is interested in the blood pressure measurements of chief executive officers (CEOs) of major corpor

sesenic [268]

Answer:

Null Hypothesis, $H_0$ : $\mu$ = 136 mm Hg

Alternate Hypothesis, $H_A$ : $\mu\neq$ 136 mm Hg

In this context type I error is rejecting that the μ is equal to 136 mm Hg when in fact μ is equal to 136 mm Hg.

Step-by-step explanation:

We are given that the mean systolic blood pressure, μ, of CEOs of major corporations is different from 136 mm Hg, which is the value reported in a possibly outdated journal article.

He measures the systolic blood pressures of a random sample of CEOs of major corporations and finds the mean of the sample to be 126 mm Hg and the standard deviation of the sample to be 18 mm Hg.

So, Null Hypothesis, $H_0$ : $\mu$ = 136 mm Hg {means that the mean systolic blood pressure, μ, of CEOs of major corporations is 136 mm Hg}

Alternate Hypothesis, $H_A$ : $\mu\neq$ 136 mm Hg {means that the mean systolic blood pressure, μ, of CEOs of major corporations is 136 mm Hg}

Type I error states that the null hypothesis is rejected when in fact the null hypothesis was true. So, in this context type I error is rejecting that the μ is equal to 136 mm Hg when in fact μ is equal to 136 mm Hg.

Suppose the researcher decides not to reject the null hypothesis. It means the researcher is making a type I error.

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3 years ago

Determine the Y intercept PLEASE HELP!! X Y -3 -3 0 -1 3 1

BartSMP [9]

You are adding two each time

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3 years ago

2 candy bars cost $.98 at this rate how much do 5 candy bars cost? I NEED ASAP

alisha [4.7K]

Answer:

2.45$

Step-by-step explanation:

98/2 =49

49x5 equals 2.45

7 0

3 years ago

14. The maximum capacity for seating in a theater is 500 people. The theater sells two types of

Eva8 [605]

Taking into account the definition of a system of linear equations, the amount of adult tickets sold is 356 and the amount of child tickets sold is 144.

<h3>System of linear equations</h3>

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

<h3>Amount of ticket sold</h3>

In this case, a system of linear equations must be proposed taking into account that:

"x" is the amount of adult tickets sold.
"y" is the amount of child tickets sold.

The maximum capacity for seating in a theater is 500 people. If they sold out on a certain showtime, this is represented by x+y=500.

On the other side, the theater sells two types of tickets, adult tickets for $7.25 each and child tickets for $4 each and the made a total of $3,157. This is represented by 7.25x +4y=3157.

So, the system of equations to be solved is

$\left \{ {{x+y=500} \atop {7.25x+4y=3157}} \right.$

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable x from the first equation you get:

x=500 - y

Substituting this expression in the second equation you get:

7.25× (500 -y) +4y=3157

7.25×500 - 7.25y +4y=3157

3625 - 7.25y +4y=3157

- 7.25y +4y=3157 -3625

-3.25y= -468

y= (-468)÷ (-3.25)

y= 144

Substituting this value in the expression x=500 - y you get:

x=500 - 144

x=356

Remembering that "x" is the amount of adult tickets sold and "y" is the amount of child tickets sold, you get that the amount of adult tickets sold is 356 and the amount of child tickets sold is 144.

Learn more about system of equations:

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2 years ago