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3 years ago

Please help me .......

Mathematics

1 answer:

V125BC [204]3 years ago

8 0

9514 1404 393

Answer:

65°

Step-by-step explanation:

Any sort of bisector divides a geometry into two congruent parts. Here, we have an angle bisector that divides the larger (130°) angle into two equal parts. The measure of each of the resulting smaller angles will be 130°/2 = 65°.

∠JAE = 65°

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The amount of warpage in a type of wafer used in the manufacture of integrated circuits has mean 1.3 mm and standard deviation 0

valina [46]

Answer:

a) $P(\bar X >1.305)=P(Z>\frac{1.305-1.3}{\frac{0.1}{\sqrt{200}}}=0.707)$

And using the complement rule, a calculator, excel or the normal standard table we have that:

$P(Z>0.707)=1-P(Z$

b) $z=-0.674$

And if we solve for a we got

$a=1.3 -0.674* \frac{0.1}{\sqrt{200}}=$

So the value of height that separates the bottom 95% of data from the top 5% is 1.295.

c) $P( \bar X >1.305) = 0.05$

We can use the z score formula:

$P( \bar X >1.305) = 1-P(\bar X$

Then we have this:

$P(z< \frac{1.305-1.3}{\frac{0.1}{\sqrt{n}}}) = 0.95$

And a value that accumulates 0.95 of the area on the normal distribution z = 1.64 and we can solve for n like this:

$n = (1.64*\frac{0.1}{1.305-1.3})^2= 1075.84 \approx 1076$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Part a

Let X the random variable that represent the amount of warpage of a population and we know

Where $\mu=1.3$ and $\sigma=0.1$

Since the sample size is large enough we can use the central limit theorem andwe know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

We can find the probability required like this:

$P(\bar X >1.305)=P(Z>\frac{1.305-1.3}{\frac{0.1}{\sqrt{200}}}=0.707)$

And using the complement rule, a calculator, excel or the normal standard table we have that:

$P(Z>0.707)=1-P(Z$

Part b

For this part we want to find a value a, such that we satisfy this condition:

$P(\bar X>a)=0.75$ (a)

$P(\bar X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=-0.674$

And if we solve for a we got

$a=1.3 -0.674* \frac{0.1}{\sqrt{200}}=$

So the value of height that separates the bottom 95% of data from the top 5% is 1.295.

Part c

For this case we want this condition:

$P( \bar X >1.305) = 0.05$

We can use the z score formula:

$P( \bar X >1.305) = 1-P(\bar X$

Then we have this:

$P(z< \frac{1.305-1.3}{\frac{0.1}{\sqrt{n}}}) = 0.95$

And a value that accumulates 0.95 of the area on the normal distribution z = 1.64 and we can solve for n like this:

$n = (1.64*\frac{0.1}{1.305-1.3})^2= 1075.84 \approx 1076$

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3 years ago

Chase a has locker that is 2 ft. wide, 2 ft. deep, and 5 ft. high. How many boxes of fundraising candy can he fit into his locke

madreJ [45]

Answer:

16 boxes of candy

Step-by-step explanation:

since 12 inches fit in one foot, 3 inches are basically 3/12 or 1/4

the volume of the locker = width x depth x height. 2x2x5=20

20 divided by 1 1/4=20 divided by 5/4=20*4/5=80/5=16

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2 years ago

a patrolman gives a speeding ticket 15% over the posted speed the speed limit is 40 miles per hour a driver can go without recei

Alexus [3.1K]

0.15 x 40 = 6 and 40+6 = 46
So you can drive below 46 miles per hour without getting a ticket
Hope this helps!

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3 years ago

Decide if the function is an exponential growth function or exponential decay function, and describe its end behavior using limi

Tems11 [23]

Answer:

Exponential Decay

Its end behavior on the left is as follows as x approaches negative infinity y approaches positive infinity. Its end behavior on the right is as follows as x approaches positive infinity y approaches negative infinity.

Step-by-step explanation:

We can graph the function by graphing two points when x=0 and x=1.

x=0 has $y=7^{-x} =7^{0} =1$

x=1 has y= $7^{-x} =7^{-1} =\frac{1}{7}$

This function starts with higher output values and decreases over time. This is Exponential Decay. Its end behavior on the left is as follows as x approaches negative infinity y approaches positive infinity. Its end behavior on the right is as follows as x approaches positive infinity y approaches negative infinity.

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3 years ago

Read 2 more answers

2. The cost that a carpet cleaning company charges is directly proportional to the number of rooms cleaned. The cost is $22 for

Artemon [7]

Let c represent the cost and r represent the number of rooms, then
a.) c = 22r

b.) 200 = 22r
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c.) 200 - 40 = 22r
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3 years ago