If y = 27x + 405, what does x equal?

Multiply. (give answer as a mixed number.) 6 1/4 x 3 3/5 =

sladkih [1.3K]

Okay, I went through a lot of work to try solving this, so here goes! First, turn the mixed numbers into improper fractions. 6 1/4 --> 25/4 3 3/5 --> 18/5 Next, we need to multiply the two improper fractions together. 25 x 18 450 --- --- = --- 4 x 5 20 Then, we need to turn 450/20 into a mixed number. To do this, we divide. 450/20=22 10/26 We're almost done. Last step is to simplify the mixed number, specifically 10/26. We need to find GCF of 10 and 26, which is 2. 10/2=5 26/2=13 = 5/13 FINAL ANSWER - 22 5/13 You're welcome.

3 0

4 years ago

Canine Crunchies Inc. (CCI) sells bags of dog food to warehouse clubs. CCI uses an automatic filling process to fill the bags. W

KatRina [158]

Answer:

a) 0.9999 = 99.99% probability that a filled bag will weigh less than 49.5 kilograms

b) 0.0018 = 0.18% probability that a randomly sampled filled bag will weight between 48.5 and 51 kilograms.

c) 46.24 kilograms

d) The standard deviation would have to be of 3.41 kilograms.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 45 kilograms and a standard deviation of 1.2 kilograms.

This means that $\mu = 45, \sigma = 1.2$

a. What is the probability that a filled bag will weigh less than 49.5 kilograms?

This is the pvalue of Z when X = 49.5. So

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

$Z = \frac{49.5 - 45}{1.2}$

$Z = 3.75$

$Z = 3.75$ has a pvalue of 0.9999

0.9999 = 99.99% probability that a filled bag will weigh less than 49.5 kilograms

b. What is the probability that a randomly sampled filled bag will weight between 48.5 and 51 kilograms?

This is the pvalue of Z when X = 51 subtracted by the pvalue of Z when X = 48.5.

X = 51

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

$Z = \frac{51 - 45}{1.2}$

$Z = 5$

$Z = 5$ has a pvalue of 1

X = 48.5

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

$Z = \frac{48.5 - 45}{1.2}$

$Z = 2.92$

$Z = 2.92$ has a pvalue of 0.9982

1 - 0.9982 = 0.0018

0.0018 = 0.18% probability that a randomly sampled filled bag will weight between 48.5 and 51 kilograms.

c. What is the minimum weight a bag of dog food could be and remain in the top 15% of all bags filled?

This is the 100 - 15 = 85th percentile, which is X when Z has a pvalue of 0.85. So X when Z = 1.037

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

$1.037 = \frac{X - 45}{1.2}$

$X - 45 = 1.037*1.2$

$X = 46.24$

46.24 kilograms.

d. CCI is unable to adjust the mean of the filling process. However, it is able to adjust the standard deviation of the filling process. What would the standard deviation need to be so that no more than 2% of all filled bags weigh more than 52 kilograms?

X = 52 would have to be the 100 - 2 = 98th percentile, which is X when Z has a pvalue of 0.98, so X when Z = 2.054. We would need to find the value of $\sigma$ for this.

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

$2.054 = \frac{52 - 45}{\sigma}$

$2.054\sigma = 7$

$\sigma = \frac{7}{2.054}$

$\sigma = 3.41$

The standard deviation would have to be of 3.41 kilograms.

5 0

3 years ago

If line T is a transversal of lines I and m, name the angel relationship of the given angle pairs

kolbaska11 [484]

Answer:

a. corresponding angles (congruent)

b. alternate exterior angles (congruent)

c. same-side interior angles (supplementary)

Step-by-step explanation:

The vocabulary associated with angles created by a transversal and parallel lines is not so difficult.

If angles are on the same side of the transversal, they are same-side angles. If not, they are alternate angles.

If angles are between the parallel lines, they are interior angles. If not, they are exterior angles.

If the angles are in the same direction from the point of intersection of the transversal with the parallel line, they are corresponding. Corresponding angles are same-side; one is interior and the other is exterior.

These names generally apply to angles with different vertices.

__

a. Both angles are northwest of the intersection point; they are same-side, and one is interior and one is exterior. They are corresponding angles. (congruent)

__

b. The angles are on opposite sides of the transversal and are outside the parallel lines. They are alternate exterior angles. (congruent)

__

c. The angles are on the same side of the transversal, and both are between the parallel lines. The are same-side interior angles. (supplementary)

3 0

3 years ago

Is this true or false

Bas_tet [7]

Answer:

true is the answer off this question

8 0

3 years ago

Read 2 more answers

What is the correct answer to this?

EleoNora [17]

8x^2 + 7
hope this helps

8 0

3 years ago