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geniusboy [140]
3 years ago
5

There was one half of a pizza left. It was divided equally amongst 3 kids. What fraction of the pizza did each kid get?

Mathematics
1 answer:
alukav5142 [94]3 years ago
6 0

Answer:

one-sixth

multiply the numerator (2) by the number of kids (3) because you are accounting for the fraction of the whole pizza. By doing this you should get 3/6. divide the denominator by the number of kids (3/3) getting you to a value of 1, and replace the denominator, making the amount of pizza one-sixth.

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The product of a number and 3 more than twice that number is at most 152.
matrenka [14]

The quadratic equation that represents the product is 2n^{2}+3n-152\leq 0.

We are given in the question that the product of a number and 3 more than twice that number is at most 152.

It is also given that the smaller number is represented by the expression n.

Hence, according to the question, the larger number will be:-

2n+3

The product of the two numbers will be :-

n(2n+3)

It is given that the product of the two numbers is at most 152.

Hence,

n(2n + 3) ≤ 152

Hence, the quadratic inequality comes out to be:-

2n^{2}+3n\leq 152\\

Taking 152 to the left hand side , we get the quadratic inequality,

2n^{2}+3n-152\leq0

To learn more about quadratic equation, here:-

brainly.com/question/17177510

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8 0
1 year ago
The president of a small manufacturing firm is concerned about the continual increase in manufacturing costs over the past sever
mrs_skeptik [129]

Answer:

The answers to the question are

(a) The time series plot is given as attached

(b) The parameters for the line that minimizes MSE for the time series are;

y-intercept, b₀ = 19.993

Slope, b₁ =  1.77

MSE = 19.44

T_t = 19.993  + 1.774·t

(c) The average cost increase that the firm is realizing per year is $ 1.77

(d) The estimate of the cost/unit for next year is $35.96.

Step-by-step explanation:

(a) Using the provided data, the time series plot is given as attached

(b) Given hat the y-intercept, = b₀

Slope = b₁

Therefore the  linear trend forecast equation is given s

T_t = b₀ + b₁·t

The linear trend line slope is given as

b₁ = \frac{\Sigma^n_{t=1}(t-\overline{\rm t)}(Y_t-\overline{\rm Y)}}{\Sigma^n_{t=1}(t-\overline{\rm t} )^2}

b₀ = \overline{\rm Y} - b₁·\overline{\rm t}

Where:

Y_t = Time series plot value at t

n =  Time period number

\overline{\rm Y} = Time series data average value and

\overline{\rm t} = Average time, t

Therefore, \overline{\rm t} = \frac{\Sigma^n _{t=1} t}{n}  = \frac{36}{8} =4.5

\overline{\rm t} = 4.5

\overline{\rm Y}  =  \frac{\Sigma^n _{t=1} Y_t}{n}  = \frac{223.8}{8} =27.975

\overline{\rm Y}  =  27.975

Therefore the linear trend line equation T_t, is

b₁ = \frac{\Sigma^n_{t=1}(t-\overline{\rm t)}(Y_t-\overline{\rm Y)}}{\Sigma^n_{t=1}(t-\overline{\rm t} )^2} =  = \frac{74.5}{42} = 1.774

b₀ = \overline{\rm Y} - b₁·\overline{\rm t} = 27.975 - 1.774×4.5 = 19.993

Therefore the trend equation for the linear trend is

T_t = 19.993  + 1.774·t

MSE = \frac{1}{2} \Sigma(Y-\overline{\rm Y)^ }^2 = \frac{155.495}{8} = 19.44

(c) From the linear trend equation, the average is given as the slope of the curve or b₁ which is equal to 1.774

Therefore the average cost increase that the firm has been realizing per year is $ 1.77

(b) From the equation of the future trend, we have when y = 9

T_t  is given as

T_t = 19.993  + 1.774×9 = 35.96

The cost/unit for 9th year is $35.96

3 0
3 years ago
Will the following two equations have a solution? Explain. y = 3x + 5 y = 3x - 7
r-ruslan [8.4K]

Answer:

There is no solution because the slopes of the two lines are the same.

Step-by-step explanation:

3x + 5 = 3x - 7

-3x        - 3x             Subtract 3x from both sides

5 ≠ - 7                      No solution

If this answer is correct, please make me Brainliest!

7 0
3 years ago
8-c is at most -15 how do i translate this into a sentence?
emmainna [20.7K]

The largest number that 8c could be is -15

3 0
3 years ago
Which value of k makes 3- 3k -12 > 9 true ?
Nadya [2.5K]

Answer:

k

Step-by-step explanation

k can be 11. If u plug 11: 3-21-12 is bigger than 9

3 0
3 years ago
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