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Tpy6a [65]
3 years ago
9

BD bisects LABC. M LABD

Mathematics
1 answer:
Sergio [31]3 years ago
5 0

Answer:

a. x=4

b. 45

Step-by-step explanation:

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A woodworking artist makes two types of carvings: type X and type Y. He
ivolga24 [154]

Answer:

part C. 3x + 2y <u>< </u>30, 5x + 7y <u><</u> 105

Step-by-step explanation:

Part 1:

spends 3 hours making each type X (3x)-each type x will take 3 hours so as the number of type x increases, the hours will increase by 3.

spends 2 hours making each type Y (2y)-each type y will take 2 hours so as the number of type y increases, the hours will increase by 2.

Part 2:

he can spend up to 30 hours each week making carvings. (<u><</u>30)-because he cannot spend more than 30 hours

Therefore, He has to spend 30 hours or less to make type X and type Y.

3x + 2y <u>< </u>30

Part 3:

His  materials cost him $5 for each type X carving. (5x)-each type x will take $5 so as the number of type x increases, the cost will increase by 5.

His materials cost him $7 for each type Y carving, (7y)-each type y will take $7 so as the number of type y increases, the cost will increase by 7.

Part 4:

he must keep his weekly cost for materials to $105 or less (<u><</u>105)-total cost cannot be more than $105.

Therefore, the total cost of making x and y should be $105 or less.

5x + 7y <u><</u> 105

!!

6 0
3 years ago
A manager records the number of hours, X, each employee works on his or her shift and develops the probability distribution belo
Reika [66]

Answer:

c. 2

Step-by-step explanation:

Given : X = No. of hours worked

           No. of people work for the manager = 50

           X = 3, 4 , 5 , 6 , 7, 8

           P(X) = 0.1 , ? , 0.14 , 0.3 , 0.36 , 0.06

To Find : No. of people work for four hours

Solution : First understand the fact that sum of all probabilities is equal to 1

So, sum of all values of P(X) = 1

⇒0.1+?+0.14+0.3+0.36+0.06 = 1

⇒0.96+? = 1

⇒?= 1-0.96

⇒? = 0.04

So, the probability of no. of people worked for 4 hours is 0.04.

⇒P(4)=0.04

Thus , To calculate no. of people work for four hours :

0.04\times 50

⇒ 2 no. of people work for four hours per shift .


5 0
3 years ago
Read 2 more answers
The figures below are made out of circles, semicircles, quarter circles, and a square. Find the area and the perimeter of each f
WITCHER [35]

Answer:

Part 1) A=36(\pi-2)\ cm^2

Part 2) P=6(\pi+2\sqrt{2})\ cm

Step-by-step explanation:

<u><em>The picture of the question in the attached figure</em></u>

Part 1) Find the area

we know that

The area of the shape is equal to the area of a quarter of circle minus the area of an isosceles right triangle

so

A=\frac{1}{4}\pi r^{2}-\frac{1}{2}(b)(h)

we have that the base and the height of triangle is equal to the radius of the circle

r=12\ cm\\b=12\ cm\\h=12\ cm

substitute

A=\frac{1}{4}\pi (12)^{2}-\frac{1}{2}(12)(12)\\A=(36\pi-72)\ cm^2

simplify

Factor 36

A=36(\pi-2)\ cm^2

Part 2) Find the perimeter

The perimeter of the figure is equal to the circumference of a quarter of circle plus the hypotenuse of the right triangle

The circumference of a quarter of circle is equal to

C=\frac{1}{4}(2\pi r)=\frac{1}{2}\pi r

substitute the given values

C=\frac{1}{2}\pi (12)\\C=6\pi\ cm

Applying the Pythagorean Theorem

The hypotenuse of right triangle is equal to

AC=\sqrt{12^2+12^2}\\AC=\sqrt{288}\ cm

simplify

AC=12\sqrt{2}\ cm

Find the perimeter

P=(6\pi+12\sqrt{2})\ cm

simplify

Factor 6

P=6(\pi+2\sqrt{2})\ cm

4 0
3 years ago
Determine whether the given value is a solution of the equation.
serious [3.7K]

Answer:

84 is a solution.

Step-by-step explanation:

To find out if 84 is a solution or not, we plug in the value and simplify.

  • (84)/14 = 6
  • 6 = 6

Therefore, 84 is a solution.

6 0
3 years ago
Annual starting salaries in a certain region of the U. S. for college graduates with an engineering major are normally distribut
defon

Answer:

0.8665 = 86.65% probability that the sample mean would be at least $39000

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean $39725 and standard deviation $7320.

This means that \mu = 39725, \sigma = 7320

Sample of 125:

This means that n = 125, s = \frac{7320}{\sqrt{125}} = 654.72

The probability that the sample mean would be at least $39000 is about?

This is 1 subtracted by the pvalue of Z when X = 39000. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{39000 - 39725}{654.72}

Z = -1.11

Z = -1.11 has a pvalue of 0.1335

1 - 0.1335 = 0.8665

0.8665 = 86.65% probability that the sample mean would be at least $39000

4 0
3 years ago
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