A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli and measure the weight of cheese filling. They find a sample mean weight of 15 grams with a standard deviation of 1.5 grams. What is the margin of error at 90% confidence?

A. 0.3 grams

B. 0.5133 grams

C. 0.8391 grams

D. 1.5 grams

E. 0.06 grams

Answer:ABCD

Step-by-step explanation:

Alternate interior angles are congruent if two lines are parallel, leading to the similarity of triangles through the Angle Angle Angle theorem.

Alternate interior angles are congruent only if the two other lines are parallel. If the two other lines are not parallel, the angles will still be alternate interior angles but they will not have the same measure, that is, they will not be congruent. Two triangles are similar if all three corresponding angles are congruent, established by the Angle Angle Angle (AAA) theorem.

Answer:3 1/2

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

Answer:

r≈8

Step-by-step explanation:

Answer: 8 units

Step-by-step explanation:

C= 2*pi*r

50.24 = 2*3.14*r

50.24=6.28

50.24/6.28

8=r

Answer:

6.5

Step-by-step explanation:

Answer:

A true statement

Step-by-step explanation:

WHAT R THE STATEMENTS

Answer:

no

Step-by-step explanation:

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

5 m, 7 m, and 11 m do not form a right triangle.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

To determine whether 5 m, 7 m, and 11 m form a right triangle, we need to use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. That is:

c² = a² + b²

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

So, let's check if the Pythagorean theorem holds true for the lengths of 5 m, 7 m, and 11 m:

11² = 5² + 7²

121 = 25 + 49

121 = 74

This is not true, so 5 m, 7 m, and 11 m do not form a right triangle.

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The toy's height after 0-4 seconds can be found by substituting different values of t into the given equation.

The equation given to model the toy's height is h = -2t^2 + 7t + 4, where h is the height in feet and t is the time in seconds. To find the height of the toy after 0-4 seconds, we substitute different values of t into the equation.

For t = 0, h = -2(0)^2 + 7(0) + 4 = 4 feet.

For t = 1, h = -2(1)^2 + 7(1) + 4 = 9 feet.

For t = 2, h = -2(2)^2 + 7(2) + 4 = 12 feet.

For t = 3, h = -2(3)^2 + 7(3) + 4 = 11 feet.

For t = 4, h = -2(4)^2 + 7(4) + 4 = 4 feet.

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Answer:

11/100

Step-by-step explanation:

Answer:

The selling price of the remote control car is $36.3

Step-by-step explanation:

In this question, we are tasked with calculating the selling price of the remote control car.

From the first part of the question, we were made to know that he applies a markup of 21% and luckily for us, we are told that the expression for the retail price given the markup is 1.21 c

This means 1.21 × the cost price of the remote car

Hence, to calculate the selling price, we simply substitute $30.00 for the value of c.

The selling price is thus 1.21(30) = $36.3

Answer:

A = 36 pi in^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

A = pi (6)^2

A = 36 pi in^2

Answer:

36pi in²

Step-by-step explanation:

Area = pi × r²

= pi × 6²

= 36pi

Answer:

$5.75

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

First, convert all dimensions to be uniform.

1ft=0.08333 ft

90ft=90*0.0833=7.5ft

40 ft=40*0.0833=3.33 ft

The diagonal of the vehicle will be

[tex]\sqrt 7.5^{2}+3.33^{2}=8.20738150149675\ approx 8.2 ft[/tex]

Since the diagonal of vehicle is smaller than 12 ft, the pipe can't fit unless divided into two equal parts.

Final answer:

The 12-foot pipe can fit inside the van due to its dimensions.

Explanation:

The pipe is 12 feet long, which is equivalent to 144 inches. The interior dimensions of the van are 90 inches in length, which is shorter than the length of the pipe,

40 inches in width, and 40 inches in height, providing enough width and height for the pipe to fit. Therefore, the pipe will fit inside the plumber's van comfortably.

Answer:

7/25

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = expected outcome/total outcome

If the box contains 3 black pens, 7 blue pens, and 5 red pens, the total number of pens in the box is 3+7+5 = 15pens

Probability of pulling a red pen and replacing = 5/15 = 1/3

Probability of pulling a blue pen and replacing = 7/15

Probability of pulling a black pen and not replacing(using it) = 3/15

{Note that the total number of outcome used will still be 15 since the black pen was pulled out last even though it wasn't replaced.}

P(red, then blue, then black) = 1/3×7/15×3/15

= 63/225

= 7/25

Answer:

  12

Step-by-step explanation:

It is worthwhile memorizing the ratios of legs in a 30°–60°–90° triangle. Shortest to longest, the ratios are ...

  1 : √3 : 2

Then the sides marked will have the ratio ...

  6 : x = 1 : 2 = 6 : 12

  x = 12

_____

You can also get there using trigonometry.

  cos(60°) = 6/x

  x = 60/cos(60° = 60/0.5

  x = 12

Answer:39.3

Step-by-step explanation:

The volume of a right circular cone that has a height of 13 m and a base with a diameter of 3.4 m is 39.3 m^3

Suppose that the radius of considered right circular cone be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]

Right circular cone is the cone where the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.

Given that right circular cone that has a height of 13 m and a base with a diameter of 3.4 m.

Volume can be calculated as;

[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]

V = 22/7×3.4×3.4×13×3.4/ 24

V = 39.3 m^3

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Answer:

Dolls: 4,8,12

Balls: 6,12,18

Step-by-step explanation:

The completed ratio table is:

Dolls     4      4      12

Balls     6      12      6

Equivalent ratios: Dolls 1:3, Balls 1:2.

To find the missing values in the ratio table, we can set up proportions using the given ratios:

For Dolls:

4 dolls correspond to 12 dolls, so the missing value can be found using the proportion:

[tex]\(\frac{4}{12} = \frac{x}{12}\)[/tex]

[tex]\(x = \frac{4 \times 12}{12}\)[/tex]

x = 4

For Balls:

6 balls correspond to 12 balls, so the missing value can be found using the proportion:

[tex]\(\frac{6}{12} = \frac{y}{12}\)[/tex]

[tex]\(y = \frac{6 \times 12}{12}\)[/tex]

y = 6

The completed ratio table is:

Dolls     4      4      12

Balls     6      12      6

Equivalent ratio for Dolls:

[tex]\(\frac{4}{12} = \frac{1}{3}\)[/tex]

Equivalent ratio for Balls:

[tex]\(\frac{6}{12} = \frac{1}{2}\)[/tex]

Answer:

The perimeters of the square and the equilateral triangle are equal.

Which equation represents this scenario? ✔ 4(3x + 3) = 3(5x + 0.5)

What is the value of x? ✔ 3.5

What is the perimeter of the polygons?✔ 54 units

Step-by-step explanation:

Answer:

C,D, and C

Step-by-step explanation:

1 inch = 2.54 centimeters

Multiply.

57 * 2.54 = 144.78

Therefore, Tylers height is 144.78 centimeters.

Best of Luck!

Answer:

x=12

Step-by-step explanation:

2x - 3(x + 6) = -3(x - 2)

Distribute

2x -3x -18 = -3x +6

Combine like terms

-x -18 = -3x+6

Add 3x from each side

-x+3x -18 = -3x+3x +6

2x -18 = 6

Add 18 to each side

2x-18+18 = 6+18

2x = 24

Divide each side by 2

2x/2 = 24/2

x = 12

Answer:

[tex]x = 12[/tex]

Step-by-step explanation:

[tex]2x - 3(x + 6) = - 3(x - 2) \\ 2x - 3x - 18 = - 3x + 6 \\ 2x - 3x + 3x = 18 + 6 \\ 2x = 24 \\ \\ x = \frac{24}{2} \\ \\ x = 12[/tex]

Answer:

2,058

Step-by-step explanation:

first term :  a_1 = 6

common ratio   r = 7

a_n = (a_1) * r ^(n-1)

a_4 = 6 * 7^(4-1)

a_4 = 6 *7^3

a_4 = 6 * 343  = 2,058

Answer:

Student council's savings reduced by [tex]\$56[/tex]

Step-by-step explanation:

Given:

Volunteers buy 8 backpacks for $4 each and fill each backpack with paper and pens that cost $3

To find:

Change in student council's savings

Solution:

Cost of paper and pens in each backpack = [tex]\$3[/tex]

Total cost of paper and pens in 8 backpacks = [tex]\$8[/tex]× [tex]\$3[/tex] =[tex]\$24[/tex]

Cost of each backpack = [tex]\$4[/tex]

Total cost of 8 backpacks = [tex]8[/tex]×[tex]\$4[/tex] = [tex]\$32[/tex]

So,  student council's savings reduced by [tex]\$32+\$24=\$56[/tex]

x - 24 = 3 (-1) x

x - 24 = -3x

-24 = -4x

x = 6

Step-by-step explanation:

The number which decreased by 24 equals 3 times its opposite is 6

Let x represent the number to calculate

The opposite of the number is -x.

According to the problem, we have the following equation:

x - 24 = 3(-x)

Simplifying the equation:

x - 24 = -3x

Adding 3x to both sides:

4x - 24 = 0

Adding 24 to both sides:

4x = 24

Dividing both sides by 4:

x = 6

Hence, the number is 6.

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Answer:

3.07% probability that the​ newspaper's sample will lead it to predict​ defeat

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

For a proportion p with n voters, we use [tex]\mu = p, \sigma = \sqrt{\frac{p(1-p)}{n}}}[/tex]

In this problem, we have that:

[tex]p = 0.55, n = 354[/tex]

So

[tex]\mu = 0.55, \sigma = \sqrt{\frac{0.55*0.45}{345}}} = 0.0268[/tex]

What is the probability that the​ newspaper's sample will lead it to predict​ defeat?

That is, a percentage of 50% or less, which is the pvalue of Z when X = 0.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0.5 - 0.55}{0.0268}[/tex]

[tex]Z = -1.87[/tex]

[tex]Z = -1.87[/tex] has a pvalue of 0.0307.

3.07% probability that the​ newspaper's sample will lead it to predict​ defeat

Answer:

3/2 π

Step-by-step explanation:

If you realize that the sin is actually the y coordinate of a (unit) circle when you travel around it, you will know that it is -1 when you are 3 quarters round, assuming you started at (1,0).

The circumference is measured in radians, where one round is 2π.

So 3/4 of 2π is 3/2 π.

In degrees, the answer is 3/4 of 360°, which is 270°.

Hope that was helpful.Thank you!!!

Answer:

Step-by-step explanation:

1 case of note cards = 20 packs

1 pack = 50 note cards

50 x 20 = 1000 note cards in one case.

1000 / 10 = 100

Each person will receive 100 note cards.

Hope this helps!! :)

Answer:

(x+12)(x+5)

Step-by-step explanation:

Formula use: a²+bx+c

Original:

-7x-60 =x² +10x

New:

x² + 17x + 60

New:

(1)x x 60 = 60

New:

10 × 6, 60 × 1, 20 × 3, 5 × 12, 4 × 15

5 times 12 equal 60, but when added equal to 17.

New:

x² + 5x + 12x + 60

New:

x² + 5x  l  12x + 60

New:

x(x + 5)  l  +12(x+5)

Answer:

All corresponding sides and angles will be congruent

Step-by-step explanation:

To prove two triangles are congruent, we can use  SSS, SAS, ASA, and AAS method.

Prove all three sets of corresponding angles congruent is not method of to prove two triangles are congruent.

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Answer:

45

Step-by-step explanation:

a(1) = 20

a(n) = a(n - 1) x 3/2

---

start with  a(2) =  a(1) * (3/2) =  20* (3/2) = 30

a(3) = a(2) * (3/2) = 30 * (3/2) = 90/2 = 45

Answer:

45

Step-by-step explanation: