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4 years ago

A pencil company used 49 grams of rubber to make 7 pencils, which is a rate of grams per pencil?

Mathematics

1 answer:

sineoko [7]4 years ago

6 0

Answer:

7 grams per pencil

Step-by-step explanation:

49 grams/7 pencils

divided both parts of the fraction by 7 to simplify to the number of grams for just one pencil so you end up with:

7 grams/1 pencil

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Please help me on question 6

saveliy_v [14]

Answer:

123.5

Step-by-step explanation:

4 0

3 years ago

On a coordinate plane, the segment with endpoints (10, 40) and (70, 120) is

OlgaM077 [116]

Answer:

The length of the resulting segment is 500.

Step-by-step explanation:

Vectorially speaking, the dilation is defined by following operation:

$P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]$ (1)

Where:

$O(x,y)$ - Center of dilation.

$P(x,y)$ - Original point.

$k$ - Scale factor.

$P'(x,y)$ - Dilated point.

First, we proceed to determine the coordinates of the dilated segment:

( $P(x,y) = (10, 40)$ , $Q(x,y) = (70, 120)$ , $O(x,y) = (0,0)$ , $k = 5$ )

$P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]$

$P(x,y) = (0,0) +5\cdot [(10,40)-(0,0)]$

$P'(x,y) = (50,200)$

$Q'(x,y) = O(x,y) + k\cdot [Q(x,y)-O(x,y)]$

$Q' (x,y) = (0,0) +5\cdot [(70,120)-(0,0)]$

$Q'(x,y) = (350, 600)$

Then, the length of the resulting segment is determined by following Pythagorean identity:

$l_{P'Q'} = \sqrt{(350-50)^{2}+(600-200)^{2}}$

$l_{P'Q'} = 500$

The length of the resulting segment is 500.

3 0

3 years ago

Which scale factors produce a contraction under a dilation of the original image?

Leokris [45]

Answer:

1/2

-1/2

Step-by-step explanation:

we know that

If a dilation produce a contraction that means that the absolute value of the scaling factor is less than 1

If a dilation produce an enlargement that means that the absolute value of the scaling factor is greater than 1

<u><em>Verify each case</em></u>

case 1) 2

$\left|2\right|=2$

$2 > 1$ ----> is a enlargement

case 2) 1/2

$\left|1/2\right|=1/2$

$1/2 < 1$ ----> is a contraction

case 3) -2

$\left|-2\right|=2$

$2 > 1$ ----> is a enlargement

case 4) -1/2

$\left|-1/2\right|=1/2$

$1/2 < 1$ ----> is a contraction

7 0

3 years ago

The major and minor axes of an ellipse are 25 inches and 4 inches in length. What is the area of the ellipse?

Nostrana [21]

Answer:

Therefore, the area of the ellipse is:

Area = 78.5 inches

Step-by-step explanation:

The formula to find the area of the ellipse is

$\:a\:\times \:b\:\times \:\pi$

The major axis of an ellipse = 25 inches

The minor axis of an ellipse = 4 inches

The value of a = major axis/2 = 25/2 = 12.5 inches

The value of b = minor axis/2 = 4/2 = 2 inches

Thus

The area of the ellipse:

Area = $\:a\:\times \:b\:\times \:\pi$

$=\:12.5\:\times\:2\:\times\:\pi$

$=25\pi$

$=78.5$ inches ∵ $\pi =3.14$

Therefore, the area of the ellipse is:

Area = 78.5 inches

5 0

3 years ago

Two types of plastic are suitable for an electronics component manufacturer to use. The breaking strength of this plastic is imp

Allushta [10]

Answer:

(a) Null Hypothesis (H₀) = Mean of x₁ > Mean of x₂

Alternative Hypothesis (H₁) = Mean of x₁ ≠ Mean of x₂

(b) We will use here t-test for two sample means which is given by,

$[tex]t = \frac{\bar_{x_{1}}-\bar_{x_{2}}}{\sqrt{s^2(\frac{1}{n_{1}}+\frac{1}{n_{2}} )}}$ [/tex]

Putting all values we get, t = 17.5 with 20 degree of freedom

At α = 0.05

p-value = 95% Confidence Interval for the Difference ( 6.6068 , 8.3932 )

8 0

3 years ago