Find the surface area of the triangular prism shown below .

Answer:

It would be 18;24 or simplified it would be 3;4

Step-by-step explanation:

24-6=18 so there are 18 role playing games. So the ratio could be 18;24 but if it needs to be simplified you can divide both numbers by 6. 18/6=3 and 24/6=4

Given information:

We can use the Law of Sines to find angle B:

Substitute the given values:

Now, solve for angle B:

Now that we have angle B, we can find angle C using the fact that the sum of the interior angles in a triangle is always 180°:

Now, we can use the Law of Sines again to find the length of the other side (side c) opposite angle C:

Substitute the given values:

Now, solve for side c:

To the nearest meter, the other side length of the triangular lot is approximately 617 m. But, since there is not an option for the answer, the closest option is C. 616 m.

________________________________________________________

Answer:

  289 m  or  617 m

Step-by-step explanation:

You want the third side length of a triangle with side lengths 450 m and 200 m, with an angle of 28°.

The man's claim does not say which side the given angle is opposite. There are two possibilities. (1) It is opposite the unknown side; (2) it is opposite the side of length 450 m. (No triangle is possible having an angle of 28° opposite the shorter given side.)

If the angle is opposite the unknown side, the law of cosines can be used to find the third side length:

  c² = a² + b² - 2ab·cos(C)

  c² = 450² +200² -2·450·200·cos(28°) ≈ 83569.43

  c ≈ √83569.43 ≈ 289 . . . . meters

The other side length could be 289 meters.

The third side could also be figured using the law of sines.

  a/sin(A) = b/sin(B) = c/sin(C)

  450/sin(28°) = 200/sin(B)

  B = arcsin(200/450·sin(28°)) ≈ 12.043°

Then angle C is ...

  C = 180° -28° -12.043° = 139.957°

and side 'c' is ...

  c = 450·sin(139.957°)/sin(28°) ≈ 617 . . . . meters

The other side length could be 617 meters.

__

Additional comment

The problem tells us "one side" is 450 m, and it tells us the angle opposite "one side" is 28°. If both of the descriptors "one side" are referring to the same side, then Solution 2 is the intended one.

The description can be written in a less ambiguous way. As is, we are not sure that the second use of "one side" is referring to any side in particular. Hence the two possibilities.

<95141404393>

Answer:

The degrees of freedom are given by;

[tex] df =n-1= 5-1=4[/tex]

The significance level is 0.1 so then the critical value would be given by:

[tex] F_{cric}= 7.779[/tex]

If the calculated value is higher than this value we can reject the null hypothesis that the arrivals are uniformly distributed over weekdays

Step-by-step explanation:

For this case we have the following observed values:

Mon 25 Tue 22 Wed 19 Thu 18 Fri 16 Total 100

For this case the expected values for each day are assumed:

[tex] E_i = \frac{100}{5}= 20[/tex]

The statsitic would be given by:

[tex] \chi^2 = \sum_{i=1}^n \frac{(O_i-E_i)^2}{E_i}[/tex]

Where O represent the observed values and E the expected values

The degrees of freedom are given by;

[tex] df =n-1= 5-1=4[/tex]

The significance level is 0.1 so then the critical value would be given by:

[tex] F_{cric}= 7.779[/tex]

If the calculated value is higher than this value we can reject the null hypothesis that the arrivals are uniformly distributed over weekdays

Answer:

u=3

Step-by-step explanation:

(8u + 8)5 = 160

40u + 40 = 160

40u = 120

u = 3

Answer:

1.625 when convert it to 1.6 pounds

Step-by-step explanation:

The given bag of mill shrugged 1. 625 pounds.

1.625 ≈ 1.6 poundest to the nearest tenth.

Answer:

B) 0.0069

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 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.

Central Limit Theorem

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

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

In this question, we have that:

[tex]\mu = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846[/tex]

Find the probability that their mean rebuild time exceeds 9.1 hours.

This is 1 subtracted by the pvalue of Z when X = 9.1. So

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

By the Central Limit Theorem

[tex]Z = \frac{9.1 - 8.4}{0.2846}[/tex]

[tex]Z = 2.46[/tex]

[tex]Z = 2.46[/tex] has a pvalue of 0.9931

1 - 0.9931 = 0.0069

So the answer is B.

Answer:

OA. 12,155

Step-by-step explanation:

A paper company produces 4,675 notebooks in 5 days. How many notebooks can it produce in 13 days?

--------

in 5 days= 4675

in 13 days= 4675/5*13= 12155

Answer

A OR D

Step-by-step explanation:

The interval of the data if, The mean of 73.5 years and the standard deviation of 6.5 years, is  (67,80) so, option D is correct.

Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

Given:

The mean of 73.5 years and the standard deviation of 6.5 years,

the middle 99.7% of ages of residents living at the facility,

Calculate the interval as shown below,

The coordinates of x in the interval = Mean - Standard deviation

The coordinates of x in the interval = 73.5 - 6.5

The coordinates of x in the interval = 67

The coordinates of y in the interval =  Mean + Standard deviation

The coordinates of y in the interval = 73.5 + 6.5

The coordinates of y in the interval = 80

Thus, the interval will be (67, 80).

To know more about mean:

https://brainly.com/question/2810871

#SPJ5

Answer:

The downtown angle measures about 22.62° and the town pool angle measures about 67.38°.

The hypotenuse measures 13 miles. Each third measures 4 1/3 miles.

Step-by-step explanation:

Use trigonometric ratios to solve this problem.

a. Find the measure of each acute angle of the right triangle shown.

Let's start with the acute angle that's marked near downtown. We can use the trigonometric ratio tangent to find the measure of this angle. (Remember, tangent = opposite/adjacent!)

We can divide the opposite side from the angle by the adjacent side to find the tangent:

5/12

= 0.4166666...

Now, we do the inverse tangent to find the measure of the angle:

≈ 22.62°

Now, we can find the angle near the town pool. This time, we can use tangent again, but the 12 mi side is the opposite and the 5 mi side is the adjacent:

12/5

= 2.4

Now, calculate the inverse tangent:

≈ 67.38°

b. Find the length of the hypotenuse. Also find the length of each of the three congruent segments forming the hypotenuse.

We can use the Pythagorean theorem to find the length of the hypotenuse. Remember, given legs a and b and hypotenuse c, the Pythagorean theorem states:

a² + b² = c²

Plug the values in this triangle into this equation:

5² + 12² = c²

25 + 144 = c²

169 = c²

13 = c

The hypotenuse measures 13 miles.

Now, we find the length of the three congruent segments that form the hypotenuse. (to be honest, I'm not sure that there are three congruent segments, but oh well, I'll just go with what it says there).

Since all the segments are the same length, we can just divide 13 by 3 to find the length of each of them:

13/3 = 4 1/3.

Each of the segments measures 4 1/3 miles.

Answer:

d. Because of the small sample size of differences in times required between machine A and machine B, the distribution of differences for all workers must be normal.

Step-by-step explanation:

A paired t- test conclusion is said to be valid if one of the assumptions that must be satisfied is that: the distribution of the differences must be normal in most cases for which the sample size is small.

From the given information:

the sample size n = 15 ;which is far less than 30

Therefore;we require the distribution of differences in times required between machine A and machine B for all workers to be normal.

From the first option; it is incorrect because even if the sample size is small; the distribution of sample means of the differences will be normal but in the first option ; it is stated that the differences cannot be normal. That makes the first option to be incorrect.

From the second option; is not correct because the sample size (for differences) is 15 and therefore that is a minimal sample which makes the Central Limit Theorem to be invalid and not applicable here.

From the third option; we all know that the sample size is small and not large since it is lesser than 30.

hope it helps :] !!!!!!

Answer:

15 grams  hope this helps

Answer:

42%

Step-by-step explanation:

Given: P(M) = 0.52, P(A) = 0.33, and P(M and A) = 0.27.

Find: P(not M and not A).

P(not M and not A) = 1 − P(M or A)

P(not M and not A) = 1 − (P(M) + P(A) − P(M and A))

P(not M and not A) = 1 − (0.52 + 0.33 − 0.27)

P(not M and not A) = 1 − 0.58

P(not M and not A) = 0.42

Treating these probabilities as Venn probabilities, it is found that there is a 0.42 = 42% probability of a random student being chosen who is a female and is not between the ages of 18 and 20.

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

The events are:

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

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

The probability of a random student being chosen who is a female and is not between the ages of 18 and 20 is given by:

[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]

Inserting the probabilities we found:

[tex]P(A \cap B) = 0.48 + 0.67 - 0.73 = 0.42[/tex]

0.42 = 42% probability of a random student being chosen who is a female and is not between the ages of 18 and 20.

A similar problem is given at https://brainly.com/question/21421475

Answer:

Change in temperature = -9 degrees

Step-by-step explanation:

Given

[tex]Start Temperature = 10 deg[/tex]

[tex]Change = 3 deg/hr[/tex]

[tex]Time= 3hr[/tex]

Required

Change in temperature;

First, the total change in 3 hours has to be solved for. This is done as follows:

[tex]Total Change = Change* Time[/tex]

[tex]Total Change = 3 deg/hr * 3 hr[/tex]

[tex]Total Change = 9 deg[/tex]

From the question, we understand that the temperature dropped.

So,  we can conclude that the temperature changed by -9 degrees;

This means that at the end of the third hour is temperature is 1 degrees

Answer: it’s A

Step-by-step explanation:

Answer:

I check the answer was a or Subtract 6 from the x value to get the y value

Answer:

Step-by-step explanation:

A quart is 1/4 gallon, so the total of liquid ingredients for the punch is ...

  (1 2/4 gal) +(3/4 gal) +(1 3/4 gal) = 2 8/4 gal = 4 gal

Samantha made 4 gallons of punch.

__

1 cup is 1/16 gallon, so 2 cups each for 25 students requires ...

  (1/16 gal)(2)(25) = 50/16 gal = 3 1/8 gal

Samantha made more punch than that, so there will be enough for 2 1-cup servings for each student.

Answer:

The percent increase was of 464%.

Step-by-step explanation:

To find the percent increase, first we find how much the current amount is of the original amount. Then, we subtract the current amount from the original amount.

Percentage of current amount:

We solve this using a rule of three.

The original amount(94 cities), was 100% = 1.

The current amount(530 cities) is x. So

94 cities - 1

530 cities - x

94x = 530

x = 530/94

x = 5.64

5.64 = 564% of the original amount

What was the percent​ increase?

The current amount is 564%

The original amount is 100%

564 - 100 = 464

The percent increase was of 464%.

Answer:

x = 48

Step-by-step explanation:

Since it's given that these two shapes are similar, you can set up a proportion to solve for x, like so:

[tex]\frac{27}{18} =\frac{72}{x}[/tex]

Cross multiply:

[tex]\frac{27x}{1296}[/tex]

Divide 1296 by 27:

x = 48

Frank can build a fence in twice the time it would take Sandy. Working together, they can build it in 7 hours. How long will it take each of them to do it alone?

Answer

If Frank and Sandy can build the fence in 7 hours, they must be building

1

7

of the fence every hour.

Now, let the amount of time it takes Sandy be

x

hours so that Frank takes

2

x

hours. Sandy can build

1

x

of the fence every hour and Frank can build

1

2

x

of the fence every hour.

We now have the following equation to solve.

1

x

+

1

2

x

=

1

7

2

+

1

2

x

=

1

7

21

=

2

x

x

=

21

2

=

10.50

Thus, Sandy takes

10.50

hours and Frank takes

21

hours.

Answer:

[tex]6x^2-2x-6[/tex]

Step-by-step explanation:

[tex]f(x)=6x^2-4 \\\\g(x)=2x+2 \\\\(f-g)(x)= (6x^2-4)-(2x+2)=6x^2-2x-6[/tex]

Hope this helps!

Answer:

[tex]P(21<X<28)=P(\frac{21-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{28-\mu}{\sigma})=P(\frac{21-24}{3}<Z<\frac{28-24}{3})=P(-1<z<1.33)[/tex]

And we can find the probability with this difference

[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)[/tex]

And using the normal standard distribution or excel we got:

[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)=0.908-0.159=0.749[/tex]

Step-by-step explanation:

Let X the random variable that represent the soft drink machine outputs of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(24,3)[/tex]  

Where [tex]\mu=24[/tex] and [tex]\sigma=3[/tex]

We want to find this probability:

[tex]P(21<X<28)[/tex]

The z score is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula we got:

[tex]P(21<X<28)=P(\frac{21-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{28-\mu}{\sigma})=P(\frac{21-24}{3}<Z<\frac{28-24}{3})=P(-1<z<1.33)[/tex]

And we can find the probability with this difference

[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)[/tex]

And using the normal standard distribution or excel we got:

[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)=0.908-0.159=0.749[/tex]

Answer:

See explanation below

Step-by-step explanation:

Given a mean of 32. The claim here is that the mean is 32.

Therefore, the null hypothesis and alternative hypothesis, would be:

H0 : u = 32

Ha: u ≠ 32

b) When we fail to reject null hypothesis, H0. This means that the mean weight, u = 32

Conclusion:  There is not enough evidence to conclude that there is overfilling or underfilling.

c) When null hypothesis, H0 is rejected. This means the mean weight, u ≠ 32.

Conclusion: There is enough evidence to conclude that overfilling or underfilling exists

The null hypothesis in the sampling is u = 32 and the alternative is that u isn't equal to 32.

It should be noted that based on the information, when the null hypothesis is rejected, it implies that the weight is 32.

Also, there's no enough evidence to conclude that there's either overfilling or underfilling. When the null hypothesis is rejected, it means that the mean weight is not equal to 32.

Learn more about sampling on:

https://brainly.com/question/17831271

Answer:

20

Step-by-step explanation:

x is the radius of the circle.  The tangent line is perpendicular to the radius line at that point.  Using Pythagorean theorem:

x² + 15² = (x + 5)²

x² + 225 = x² + 10x + 25

225 = 10x + 25

200 = 10x

x = 20

Answer is:

x = 20. hope this helps

Answer:

Step-by-step explanation:

The data is incorrect. The correct data is:

Deluxe standard

39 27

39 28

45 35

38 30

40 30

39 34

35 29

Solution:

Deluxe standard difference

39 27 12

39 28 11

45 35 10

38 30 8

40 30 10

39 34 5

35 29 6

a) The mean difference between the selling prices of both models is

xd = (12 + 11 + 10 + 8 + 10 + 5 + 6)/7 = 8.86

Standard deviation = √(summation(x - mean)²/n

n = 7

Summation(x - mean)² = (12 - 8.86)^2 + (11 - 8.86)^2 + (10 - 8.86)^2 + (8 - 8.86)^2 + (10 - 8.86)^2 + (5 - 8.86)^2 + (6 - 8.86)^2 = 40.8572

Standard deviation = √(40.8572/7

sd = 2.42

For the null hypothesis

H0: μd = 10

For the alternative hypothesis

H1: μd ≠ 10

This is a two tailed test.

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 7 - 1 = 6

2) The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (8.86 - 10)/(2.42/√7)

t = - 1.25

We would determine the probability value by using the t test calculator.

p = 0.26

Since alpha, 0.05 < than the p value, 0.26, then we would fail to reject the null hypothesis.

b) Confidence interval is expressed as

Mean difference ± margin of error

Mean difference = 8.86

Margin of error = z × s/√n

z is the test score for the 95% confidence level and it is determined from the t distribution table.

df = 7 - 1 = 6

From the table, test score = 2.447

Margin of error = 2.447 × 2.42/√7 = 2.24

Confidence interval is 8.86 ± 2.24

Answer:

Step-by-step explanation:

there is a pressure difference between inside and outside the container and if the — bag, bottle, whatever — is flexible enough it will either expand as the ambient air pressure decreases when climbing or collapse when the aircraft is descending and the pressure is increasing.......

this is ur answer ....

Answer:

The solutions for the equations are x = 0.1644 and x = -12.1644

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]x^{2} + 12x - 2 = 0[/tex]

So

[tex]a = 1, b = 12, c = -2[/tex]

[tex]\bigtriangleup = 12^{2} - 4*1*(-2) = 152[/tex]

[tex]x_{1} = \frac{-12 + \sqrt{152}}{2} = 0.1644[/tex]

[tex]x_{2} = \frac{-12 - \sqrt{152}}{2} = -12.1644[/tex]

The solutions for the equations are x = 0.1644 and x = -12.1644

Answer:

21.6m

Step-by-step explanation:

Brian throws a ball from point 'a'

The ball travels a distance of:

The ball travels a total distance of 0.6m + 1.2m + 1.8m + 2.4m + 3.0m + 3.6m + 4.2m + 4.8m = 21.6m from point 'a' to point 'b'.

9.4 units.

Because,

Formula for arc length is 2times pie times radius times angle divided by 360.

Answer:

The answer is option 2.

Step-by-step explanation:

You have to use length or arc formula, Arc = θ/360×2×π×r where θ represents degrees and r is radius. Then substitute the following values into the formula :

[tex]arc = \frac{θ}{360} \times 2 \times \pi \times r[/tex]

Let θ = 45,

Let r = 12,

[tex]arc = \frac{45}{360} \times 2 \times \pi \times 12[/tex]

[tex]arc = \frac{1}{8} \times 24\pi[/tex]

[tex]arc = 9.42 \: units \: (3s.f)[/tex]