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Arisa [49]
3 years ago
11

R = (–21 -5]

Mathematics
1 answer:
Hoochie [10]3 years ago
3 0
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2/3 of the sum of three times a number and six is 10. what is the number?
mestny [16]

9514 1404 393

Answer:

  3

Step-by-step explanation:

Let x represent the number. The problem statement tells you ...

2/3(3x +6) = 10

  2x +4 = 10 . . . . . . use the distributive property

  x +2 = 5 . . . . . . . . divide by 2

  x = 3 . . . . . . . . . . .subtract 3

The number is 3.

__

<em>Comment on the solution</em>

The above shows an "alternative" solution method. The more usual way this might be done is ...

  2(3x +6) = 30 . . . . . multiply by 3 to clear fractions

  6x +12 = 30 . . . . . . . eliminate parentheses

  6x = 18 . . . . . . . . . . . subtract 12

  x = 3 . . . . . . . . . . . . divide by 6

3 0
3 years ago
Read 2 more answers
A jar of peanut butter contains 454 g with a standard deviation of 10.2 g. Find the probability that a jar contains more than 46
Fofino [41]

Answer:

The probability that a jar contains more than 466 g is 0.119.

Step-by-step explanation:

We are given that a jar of peanut butter contains a mean of 454 g with a standard deviation of 10.2 g.

Let X = <u><em>Amount of peanut butter in a jar</em></u>

The z-score probability distribution for the normal distribution is given by;

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

where, \mu = population mean = 454 g

           \sigma = standard deviation = 10.2 g

So, X ~ Normal(\mu=454 , \sigma^{2} = 10.2^{2})

Now, the probability that a jar contains more than 466 g is given by = P(X > 466 g)

            P(X > 466 g) = P( \frac{X-\mu}{\sigma} > \frac{466-454}{10.2} ) = P(Z > 1.18) = 1 - P(Z \leq 1.18)

                                                                  = 1 - 0.881 = <u>0.119</u>

The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.

4 0
2 years ago
HELP ASAP The graph shows the relationship between time, in hours, and the population, in thousands of a culture of bacteria. y
Harrizon [31]

Answer:

I’m doing that exact question right now on a test so I just guessed

Step-by-step explanation:

3 0
3 years ago
What is the volume of the composite figure? Express the answer in terms of π.
topjm [15]

Answer:

312π mm³

Step-by-step explanation:

Given:

Oblique cone height, h = 14 mm

radius of half sphere = base radius of cone, r = 6 mm

Recall the volume of 1/2 - sphere

= 1/2 x volume of sphere

=  1/2 x (4π/3) r³

= 1/2 x (4π/3) (6)³

= 144π

Also volume of an oblique cone =

=volume of a right cone

= (π/3) r²h

= (π/3) 6²(14)

=168π

Volume of composite figure = 144π + 168π = 312π mm³

8 0
2 years ago
Read 2 more answers
The populations and land areas of four cities in Texas are shown.
dybincka [34]
We are given a table showing the population and the area of different cities, A, B, C and D. To calculate the population density, divide the population over the total area of the city. The following statements are true:

<span>--The population density of City B is greater than that of City C.

--City D has the lowest population density of the four cities.

</span><span>--The population density for City B can be found using the ratio 48,592 : 26.</span><span>
</span><span>
</span>
4 0
3 years ago
Read 2 more answers
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