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At PRMS, 25% of the 124 students Mrs. Pasternak teaches buy their lunches in the cafeteria. How many students buy their lunches

Ksju [112]

25% = 0.25
124 x 0.25 = 31

31 students bought their lunch.

Part = 31
Percent = 25%
Whole = 124

Hope this helps! ✨

6 0

2 years ago

Please Help). Use the figure below to answer the questions. A) Describe in words a sequenc of transformations that maps □ABC to

lesya [120]

Answer:

See below

Step-by-step explanation:

The initial ordered-pairs are $(x, y)$

We have a rotation of 90 degrees counterclockwise with respect to origin

Note. Previously the points were

$A(-3, 4), B(-3, 0), C(-1, 3)$

After the rotation, we have

$A(-4, -3), B(0, -3), C(-3, -1)$

Thus, $(x, y) \rightarrow (-y, x)$

Then shifting horizontally to the right 2 units, we get ΔA'B'C'

Thus,

$(x, y) \rightarrow (-y, x) \rightarrow (x+2, y)$

7 0

2 years ago

The sum of two non-zero numbers a and b equals the sum of their reciprocals. If a+b≠0, what is the product of the two numbers?

Vadim26 [7]

Answer:

ab = 1

Step-by-step explanation:

A Reciprocal of a number is a number which when multiplied by the original number yields the multiplicative number, 1.

So the reciprocal of x would be x⁻¹ or ¹⁄ₓ

The information we are given states that the sum of the two non-zero numbers a and b equals the sum of their reciprocals.

So we can write this into an equation and solve,

(See image)

Once we solve, we get the equation (ab-1)(a+b) = 0

We are given info that a+b≠0

So for the above equation to be true, ab-1 has to equal 0

For <em>this</em> to be true, the product ab must equal 1

7 0

2 years ago

If carlos did some work and got 3x + 2x - 6 = 24 what mistake did he make

Makovka662 [10]

Carlos made the mistake that he did not combine like terms (3 x and 2 x) properly and did not use addition property of equality.

<u>Step-by-step explanation:</u>

Carlos did the work as 3 x + 2 x - 6 = 24

We need to find his mistake that he made in above given.

Here, he did not add the like terms (3 x and 2 x)

3 x + 2 x = 5 x

Therefore, his work should be

5 x - 6 = 24

Also, he did not use addition property of equality. It means the equation remains same even though the same number gets added on both sides. It would be

5 x - 6 = 24

+ 6 = + 6

-----------------------

5 x = 30

Dividing 30 by 5, we get answer as '6'. Hence,

$x=\frac{30}{5}$ = 6

So, stated the above two are the mistakes found in carlos work.

4 0

3 years ago

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.18 millimeters and a standard deviat

dimulka [17.4K]

As per the concept of normal distribution, the two diameters of the bolt that has separate the top 3% and the bottom 3% are 5.2836 mm and 5.0764 mm respectively .

Normal distribution:

Normal distribution means the probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean and it has the bell shaped curve.

Given,

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.18 millimeters and a standard deviation of 0.07 millimeters.

Here we need to find the two diameters that separate the top 3% and the bottom 3% and these diameters could serve as limits used to identify which bolts should be rejected. we have also round off the result into nearest hundredth.

Here we have the given question with the values of,

The value of Mean is 5.18 millimeters

The value of Standard deviation is 0.07 millimeters.

Here we have to consider the following two cases, they are.

Case 1

We need to find x₁ such that that is P(X > x₁) = 3% when we convert it into decimal then we get P (X > x₁) = 0.03

So, as per the probability,

P (X ≤ x₁) = 1 - 0.03 = 0.97

So, z corresponding to the value of p = 0.97 is 1.48

Apply the given values to the formula of normal distribution then we get,

=> 1.48 = (x₁ - 5.18) /0.07

=> 0.1036 = x₁ - 5.18

Therefore, the value of x₁ is 5.2836

So, the diameter of the both with separate top 3% is 5.2836.

Case 2:

Next we have to take P(X < x₂) = 3% when we convert it into decimal then we get P (X < x₂) = 0.03

So, as per the given probability, the value of

P (X ≤ x₂) = 1 - 0.03 = 0.97

So, z corresponding to but here we have to use the negative because of the less than concept p = 0.97 is -1.48

Apply the values on the formula of normal distribution then we get,

-1.48 = (x₂ - 5.18) /0.07

Move the value to the other side

-0.1036 = x₂ - 5.18

When we simplify it,

x₂ = 5.0764

So, the diameter of the both with separate bottom 3% is 5.0764

To know more about Normal distribution here.

brainly.com/question/12421652

#SPJ1

7 0

6 months ago

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