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2 years ago

Write this percentage as a fraction in its simplest form. 20%

Mathematics

1 answer:

Kobotan [32]2 years ago

7 0

Answer:

it is 1/5

Step-by-step explanation:

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Making handcrafted pottery generally takes two major steps: wheel throwing and firing. The time of wheel throwing and the time o

9966 [12]

Answer:

a) 8.23% probability that a piece of pottery will be finished within 95 minutes

b) 0.28% probability that it will take longer than 110 minutes.

Step-by-step explanation:

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Two variables:

Means $\mu_{a}, \mu_{b}$

Standard deviations $\sigma_{a}, \sigma_{b}$

Sum:

$\mu = \mu_{a} + \mu_{b}$

$\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}}$

In this question:

$\mu_{a} = 40, \mu_{b} = 60, \sigma_{a} = 2, \sigma_{b} = 3$

$\mu = \mu_{a} + \mu_{b} = 40 + 60 = 100$

$\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}} = \sqrt{4 + 9} = 3.61$

A) What is the probability that a piece of pottery will befinished within 95 minutes?

This is the pvalue of Z when X = 95.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{95 - 100}{3.61}$

$Z = -1.39$

$Z = -1.39$ has a pvalue of 0.0823

8.23% probability that a piece of pottery will befinished within 95 minutes.

B) What is the probability that it will take longer than 110 minutes?

This is 1 subtracted by the pvalue of Z when X = 110.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{110 - 100}{3.61}$

$Z = 2.77$

$Z = 2.77$ has a pvalue of 0.9972

1 - 0.9972 = 0.0028

0.28% probability that it will take longer than 110 minutes.

5 0

3 years ago

Please Answer THIS QUESTION ASAP ty!! First 2 answer right is BRAINLESS

pav-90 [236]

Hi there! :)

Answer:

$\huge\boxed{A = 119.44 cm^{2} }$

To find the area of the shaded region, we will need to find the areas of both the rectangle and the circle:

Rectangle: A = l × w

A = 11 × 12

A = 132 cm²

Circle: A = πr² (Let π = 3.14)

A = π(2)²

A = 4π

A ≈12.56 cm²

Subtract the area of the circle from the area of the rectangle:

132 - 12.56 = 119.44 cm².

4 0

3 years ago

Simon used 3 pears and 9 apples to make a fruit salad. What was the ratio of the number of pears to the number of apples in the

dlinn [17]

Answer:

Step-by-step explanation:

Ratio is an expression that shows the relationship between two items in terms of quantity. It shows how much of one item can be found in another.

Simon used 3 pears and 9 apples to make a fruit salad.

This is expressed in terms of quantity.

The ratio of the number of pears which simon used to the number of apples which simon used will be

Number of pears which simon used ÷ the number of apples which simon used.

The ratio is 3/9.

Simplifying further to its lowest term,

It becomes 1/3

This is done by dividing the numerator and denominator by 3

3 0

3 years ago

The length of a rectangular wall is 16.5 feet. The height of the wall is 8.625 feet. Cameron determines the area of the wall to

Drupady [299]

Answer:

Cameron’s solution is unreasonable because 17 times 9 is 153, and 153 is not close to his product.

Step-by-step explanation:

Area of a rectangle:

The area of a rectangle, of length l and height h, is given by:

$A = lh$

The length of a rectangular wall is 16.5 feet. The height of the wall is 8.625 feet.

This means that $l = 16.5, h = 8.625$

Estimate of the area:

To use an "easy" multiplication, lets consider $l = 17, h = 9$ . So

$A = lh = 17(9) = 153$

Cameron determines the area of the wall to be 1423.125 square feet.

Very far from the area of 153, which means that he made a confusion with the decimal places. Thus, the correct answer is:

Cameron’s solution is unreasonable because 17 times 9 is 153, and 153 is not close to his product.

4 0

2 years ago

Match the circle equations in general form with their corresponding equations in standard form. Not all will be used.

Xelga [282]

The standard form of the equation of a circumference is given by the following expression:

 $(x-h)^{2}+(y-k)^{2}=r^{2} \\ \\ where \ (h, k) \ is \ the \ center \ of \ the \ circumference \ and \ r \ the \ radius$

On the other hand, the general form is given as follows:

 $x^{2}+y^{2}+Dx+Ey+F=0 \\ \\ where: \\ D=-2h, \ E=-2k, \ F=h^{2}+k^{2}-r^{2}$ 

In this way, we can order the mentioned equations as follows:

Equations in Standard Form:

 $\bold{a)} \ (x-6)^{2}+(y-4)^{2}=56 \\ \bold{b)} \ (x-2)^{2} + (y+6)^{2}=60 \\ \bold{c)} \ (x+2)^{2}+(y+3)^{2}=18 \\ \bold{d)} \ (x+1)^{2}+(y-6)^{2}=46$

Equations in General Form:

$\bold{1)} \ x^{2}+y^{2}-4x+12y-20=0 \\ \bold{2)} \ x^{2}+y^{2}+6x-8y-10=0 \\ \bold{3)} \ 3x^{2}+3y^{2}+12x+18y-15=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 3, \ the \ equation \ becomes: \\ x^{2}+y^{2}+4x+6y-5=0 \\ \\ \bold{4)} \ 5x^{2}+5y^{2}-10x+20y-30=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 5, \ the \ equation \ becomes: \\ x^{2}+y^{2}-2x+4y-6=0 \\ \\ \bold{5)} \ 2x^{2}+2y^{2}-24x-16y-8=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 2, \ the \ equation \ becomes: \\ x^{2}+y^{2}-12x-8y-4=0$

$\bold{6)} \ x^{2}+y^{2}+2x-12y$

So let's match each equation:

$\bold{From \ a)} \\ \\ (h,k)=(6,4),\ r=2\sqrt{14} \\ D=-12, \ E=-8 \\ F=-4$

Then, its general form is:

$x^{2}+y^{2}-12x-8y-4=0$

First. a) matches 5) 

$\bold{From \ b)} \\ \\ (h,k)=(2,-6),\ r=2\sqrt{15} \\ D=-4, \ E=12 \\ F=-20$

Then, its general form is:

$x^{2}+y^{2}-4x+12y-20=0$

Second. b) matches 1) 

$\bold{From \ c)} \\ \\ (h,k)=(-2,-3),\ r=3\sqrt{2} \\ D=4, \ E=6 \\ F=-5$

Then, its general form is:

$x^{2}+y^{2}+4x+6y-5=0$

Third. c) matches 3)

$\bold{From \ d)} \\ \\ (h,k)=(-1,6),\ r=\sqrt{46} \\ D=2, \ E=-12, \ F=-9$

Then, its general form is: $x^{2}+y^{2}+2x-12y-9=0$

Fourth. d) matches 6)

6 0

3 years ago

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