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4 years ago

The large rectangle below was created from the small rectangle using a scale factor of 2.5

Mathematics

1 answer:

kaheart [24]4 years ago

7 0

Given:

The large rectangle below was created from the small rectangle using a scale factor of 2.5.

Dimensions of small rectangle are 6 cm and 4cm.

To find:

The area of the large rectangle, in square centimeters.

Solution:

If the scale factor is 2.5. So, each side of large rectangle is 2.5 times of corresponding side of small rectangle.

Dimensions of large rectangle are

Length = $6\times 2.5=15\text{ cm}$

Width = $4\times 2.5=10\text{ cm}$

Area of the large rectangle is

$Area=length\times width$

$Area=15\times 10$

$Area=150$

Therefore, the area of the large rectangle is 150 square centimeters. Hence, the correct option is D.

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This exercise illustrates that poor quality can affect schedules and costs. A manufacturing process has 120 customer orders to f

Aliun [14]

Answer:

a. P(X = 0) = 0.02586

b. $\mathbf{P(X \leq 2 ) =0.2879}$

c. $\mathbf{P(X \leq 5 ) =0.8387}$

Step-by-step explanation:

From the given information:

a. If the manufacturer stocks 120 components, what is the probability that the 120 orders can be filled without reordering components?

$P(X = 0)=(^{120}_{0}) (0.03)^0 (1-0.03)^{n-0}$

$P(X = 0)=\dfrac{120!}{0!(120-0)!} (0.03)^0 (1-0.03)^{n-0}$

P(X = 0) = 1 × 1 ( 0.97)¹²⁰ ⁻ ⁰

P(X = 0) = 0.02586

b. ) If the manufacturer stocks 122 components, what is the probability that the 120 orders can be filled without reordering components?

$P(X \leq 2 ) = [ P(X=0) + P(X =1) + P(X = 2) ]$

$P(X \leq 2 ) = [(^{122}_{0})(0.03)^0 (0.97)^{122-0}+(^{122}_{1})(0.03)^1 (0.97)^{122-1}+(^{122}_{2})(0.03)^2 (0.97)^{122-2}]$ $P(X \leq 2 ) = [\dfrac{122!}{0!(122-0)! } \times 1 \times (0.97)^{122}+\dfrac{122!}{1!(122-1)! } \times (0.03) (0.97)^{121}+\dfrac{122!}{2!(122-2)! } \times 9 \times 10^{-4} \times (0.97)^{120}]$

$P(X \leq 2 ) = [(1 \times 1 \times 0.02433 )+(122 \times (0.03) \times 0.025083)+(7381 \times 9 \times 10^{-4} \times 0.02586)]$

$\mathbf{P(X \leq 2 ) =0.2879}$

(c) If the manufacturer stocks 125 components, what is the probability that the 120 orders can be filled without reordering components?

$P(X \leq 5 ) = [ P(X=0) + P(X =1) + P(X = 2) +P(X = 3)+P(X = 4)+ P(X = 5) ]$

$P(X \leq 5 ) = [(^{122}_{0})(0.03)^0 (0.97)^{122-0}+(^{122}_{1})(0.03)^1 (0.97)^{122-1}+(^{122}_{2})(0.03)^2 (0.97)^{122-2} + (^{122}_{3})(0.03)^3 (0.97)^{122-3} + (^{122}_{4})(0.03)^4 (0.97)^{122-4}+ (^{122}_{5})(0.03)^5 (0.97)^{122-5}]$ $P(X \leq 5 ) = [\dfrac{122!}{0!(122-0)! } \times 1 \times (0.97)^{122}+\dfrac{122!}{1!(122-1)! } \times (0.03) (0.97)^{121}+\dfrac{122!}{2!(122-2)! } \times 9 \times 10^{-4} \times (0.97)^{120} + \dfrac{122!}{3!(122-3)! }*(0.03)^3(0.97)^{122-3)}+ \dfrac{122!}{4!(122-4)! }*(0.03)^4(0.97)^{122-4)} +\dfrac{122!}{5!(122-5)! } *(0.03)^5(0.97)^{122-5)}]$

$\mathbf{P(X \leq 5 ) =0.8387}$

5 0

3 years ago

How do I solve this?

zzz [600]

Yeah use this app bro u welcome

6 0

2 years ago

I need help with math please!!!

kvasek [131]

To simplify you would:
3x+1+2x-6=135
3x+2x=5x
1+-6= -5
5x-5=135
Then add 5 to both sides, so on (5x-5) the negative 5 would cancle out.
5x=140
Then divide 5 on both sides.
Then your answer will be 28.

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4 years ago

The graph of the equation (given below) will intersect the y-axis when y equals what value?

Svetllana [295]

When y=5 because five is the y intercept

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3 years ago

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HELP <br> what is 5.476 rounded to hundreths and how do you round the numbers <br> GIVING 12 POINTS

Bond [772]

Hundredths are the second number after the decimal, which is the 7. The number, 5.476, rounded is 5.48. You round numbers by looking at the number after what place you want to round by. For example, if I had 5.28 and wanted to round it to the nearest tenths, I would look at the number after 2, which is 8. If the number is 5 or higher and one to the place you need to the round. If it’s 4 or lower, just take away the numbers after the place you need to round, so it would be 5.3. However, if it was 5.23 and I wanted to round it to the tenths, I would just take away the three, making it 5.2

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3 years ago