Type the correct answer in each box. If necessary, use/for the fraction bar(s).

In this triangle, the product of Sin B and tan C is_____, and the product of sin C and tan B is_____.

please view picture at the top

Answer:

      Lateral surface area is

≈

502.65cm²

      Base area is

=

πr^2

Answer:

Step-by-step explanation:

(-2,2) (2,-4)

(-4-2)/(2+2)= -6/4= -3/2 is the slope of the graph

Answer:

Thirty-one million, six hundred and twenty-four

Four billion, six million, eighty-five thousand, and twelve

six million five hundred thousad

twenty-five million, four hundred and thirty thousand and seven hundred and fifty-six

Step-by-step explanation:

Answer:

13, 21

Step-by-step explanation:

Fibonacci sequence-

Each number is added to the number before it.

1+1=2

2+1=3

3+2=5

5+3=8

Answer:

The missing numbers are 13, and 21.

The pattern given is the Fibonacci Sequence, where each number is the sum of the two numbers before it, starting with 0 and 1. (i.e. 5 is 2+3)

Answer:

x = 15

Step-by-step explanation:

Step 1: Write out equation

1/4x - 7/4 = 2

Step 2: Add 7/4 to both sides

1/4x = 15/4

Step 3: Divide both sides by 1/4

x = 15

Answer:

The highest altitude that the object reaches is 576 feet.

Step-by-step explanation:

The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be [tex]h(t) = -16\cdot t^{2} + 128\cdot t + 320[/tex], the first and second derivatives are, respectively:

First Derivative

[tex]h'(t) = -32\cdot t +128[/tex]

Second Derivative

[tex]h''(t) = -32[/tex]

Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:

[tex]-32\cdot t +128 = 0[/tex]

[tex]t = \frac{128}{32}\,s[/tex]

[tex]t = 4\,s[/tex] (Critical value)

The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:

[tex]h(4\,s) = -16\cdot (4\,s)^{2}+128\cdot (4\,s) +320[/tex]

[tex]h(4\,s) = 576\,ft[/tex]

The highest altitude that the object reaches is 576 feet.

Answer:

1 3 4 5

Step-by-step explanation:

The rotation does not change the angle measure, the side lengths and the shape of the shape that is being rotated.

An angle measure the size, the shape, and the position of center of rotation do not change after rotation.

If one thing is rotated then it will not change the angle measures, the side lengths and shape of the body. The rotation does not change the center of object.

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Hey there! :)

Answer:

3(d + 1)²

Step-by-step explanation:

Given 3d² + 6d + 3:

Begin by factoring out '3' from each term:

3(d² + 2d + 1)

Factor terms inside of the parenthesis:

3(d + 1)(d + 1) or 3(d + 1)².

Answer:

Options A, C and D are true.

- The average daily revenue for days when the Red Sox do not play away is $1,768.32.

- The average daily revenue for days when the Red Sox play away is $2,264.57.

- On average, the bar’s revenue is $496.25 higher on days when the Red Sox play away than on days when they do not.

Step-by-step explanation:

The complete Question is presented in the attached image to this solution.

Analyzing the options at a time

A) The average daily revenue for days when the Red Sox do not play away is $1,768.32.

This option is true as 1768.32 is the intercept which is the average daily revenue when the Red Sox=0, that is, 0=no, when red sox do not play away.

B) The average daily revenue for days when the Red Sox play away is $1,768.32.

This is false because when the Red Sox play away, the value is 1 and the average revenue = 1768.32 + 496.25 = $2,264.57

C) The average daily revenue for days when the Red Sox play away is $2,264.57.

This is true. I just gave the explanation under option B.

D) The average daily revenue for days when the Red Sox do not play away is $1,272.07.

This is false. The explanation is under option A.

E) On average, the bar’s revenue is $496.25 higher on days when the Red Sox play away than on days when they do not.

This is true. It is evident from the table that the 0 and 1 coefficient is 496.25. This expresses the difference in average daily revenue when the Red Sox games are played away and when they are not.

Hope this Helps!!!

Answer:

the probability that the number of heads is between 40 and 60 is 0.9535

the probability that the number of heads is between 50 and 55 is 0.3557

Step-by-step explanation:

From the given information:

A fair coin is tossed 100 times.

Let consider n to be the number of time the coin is tossed, So n = 100 times

In a fair toss of a coin; the probability of getting a head P(Head) = 1/2 = 0.5

If we assume X to be the random variable which follows a binomial distribution of n and p; therefore , the mean and the standard deviation can be  calculated as follows:

Mean μ = n × p

Mean μ = 100 × 1/2

Mean μ = 100 × 0.5

Mean μ =  50

Standard deviation σ =  [tex]\sqrt{n \times p \times (1-p)}[/tex]

Standard deviation σ =  [tex]\sqrt{100 \times 0.5 \times (1-0.5)}[/tex]

Standard deviation σ = [tex]\sqrt{50 \times (0.5)}[/tex]

Standard deviation σ = [tex]\sqrt{25}[/tex]

Standard deviation σ = 5

Now, we've made it easier now to estimate  the probability that the number of heads is between 40 and 60 and the probability that the number is between 50 and 55.

To start with the probability that the number of heads is between 40 and 60 ; we have:

P(40 < X < 60) = P(X < 60)- P(X < 40)

Applying  the central limit theorem , for X is 40 which lies around 39.5 and 40.5  and X is 60 which is around 59.5 and 60.5 but the inequality signifies less than sign ;

Then

P(40 < X < 60) = P(X < 59.5) - P(X < 39.5)

[tex]P(40 < X < 60) = P( \dfrac{X - \mu}{\sigma}< \dfrac{59.5 - 50 }{5}) - P( \dfrac{X - \mu}{\sigma}< \dfrac{39.5 - 50 }{5})[/tex]

[tex]P(40 < X < 60) = P( Z < \dfrac{9.5 }{5}) - P( Z< \dfrac{-10.5 }{5})[/tex]

[tex]P(40 < X < 60) = P( Z <1.9}) - P( Z< -2.1)[/tex]

[tex]P(40 < X < 60) =0.9713 -0.0178[/tex]

[tex]P(40 < X < 60) =0.9535[/tex]

Therefore; the probability that the number of heads is between 40 and 60 is 0.9535

To estimate the probability that the number is between 50 and 55.

P(50 < X < 55) = P(X < 55)- P(X < 50)

Applying  the central limit theorem , for X is 50 which lies around 49.5 and 50.5  and X is 55 which is around 54.5 and 55.5 but the inequality signifies less than sign ;

Then

P(50 < X < 55) = P(X < 54.5) - P(X < 49.5)

[tex]P(50 < X < 55) = P( \dfrac{X - \mu}{\sigma}< \dfrac{54.5 - 50 }{5}) - P( \dfrac{X - \mu}{\sigma}< \dfrac{49.5 - 50 }{5})[/tex]

[tex]P(50 < X < 55) = P( Z < \dfrac{4.5 }{5}) - P( Z< \dfrac{-0.5 }{5})[/tex]

[tex]P(50 < X < 55) = P( Z <0.9}) - P( Z< -0.1)[/tex]

[tex]P(50 < X < 55) =0.8159 -0.4602[/tex]

[tex]P(50 < X < 55) =0.3557[/tex]

Therefore; the probability that the number of heads is between 50 and 55 is 0.3557

Answer:

3c^3+2c^2

Step-by-step explanation:

Answer:

3c^3 +2c^2

Step-by-step explanation:

–c^2(3c – 2)

Distribute

=c^2 * 3c - c^2 * -2

3c^3 +2c^2

Answer:

Step-by-step explanation:

Answer:

The Pythagorean Triplet that has 5 is 3-4-5

Step-by-step explanation:

We can prove this using Pythagorean Theorem: a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

25 = 25

Answer:

4.11% probability that he has lung disease given that he does not smoke

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Does not smoke

Event B: Lung disease

Lung Disease/Nonsmoker 0.03

This means that [tex]P(A \cap B) = 0.03[/tex]

Lung Disease/Nonsmoker 0.03

No Lung Disease/Nonsmoker 0.7

This means that [tex]P(A) = 0.03 + 0.7 = 0.73[/tex]

What is the probability of the following event: He has lung disease given that he does not smoke?

[tex]P(B|A) = \frac{0.03}{0.73} = 0.0411[/tex]

4.11% probability that he has lung disease given that he does not smoke

Probabilities are used to determine the chances of an event.

The  probability that he has lung disease given that he does not smoke is 0.231

The required probability is calculated as:

[tex]\mathbf{P = \frac{P(Lung\ Disease\ and\ Non\ Smoker)}{P(Lung\ Disease)}}[/tex]

From the question, we have:

[tex]\mathbf{P(Lung\ Disease\ and\ Non\ Smoker) = 0.03}[/tex]

[tex]\mathbf{P(Lung\ Disease) = P(Has Lung Disease/smoker) + P(Lung Disease/Nonsmoker)}[/tex]

[tex]\mathbf{P(Lung\ Disease) = 0.1 + 0.03}[/tex]

[tex]\mathbf{P(Lung\ Disease) = 0.13}[/tex]

So, we have:

[tex]\mathbf{P = \frac{P(Lung\ Disease\ and\ Non\ Smoker)}{P(Lung\ Disease)}}[/tex]

[tex]\mathbf{P = \frac{0.03}{0.13}}[/tex]

[tex]\mathbf{P = 0.231}[/tex]

Hence, the  probability that he has lung disease given that he does not smoke is 0.231

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Answer:

x=3y

Step-by-step explanation:

divide both sides by 20

20x = 60y

------   -------

20        20

x=3y

Answer:

x = 3y

Step-by-step explanation:

20x = 60y

Divide 20 into both sides.

20x/20 = 60y/20

1x = 6/2y

x = 3y

Answer:

B

Step-by-step explanation:

It can be figured out by using graph transformations.

When when subtracting directly next to x, it shifts the graph to the left while doing the opposite when adding. Since the graph is to the left, we know it has to be A or B since those are subtracting by 5

Outside of the absolute value, when subtracting, it makes the graph move down. That means we are looking for a -4 which is found in  B

Answer: (5, 42)

Step-by-step explanation:

22 + 4x= 42

if we test the options we will see this is the only one that works

42 - 22 = 20

4x = 20

x= 5

which is equal to X the number of weeks they have gotten the allowance.

Answer:

16

Step-by-step explanation:

The sum of the 12 numbers is 12 * 24 = 288 and the sum of the 24 numbers is 24 * 12 = 288 so the sum of the 36 numbers is 288 + 288 = 576 which means the average is 576 / 36 = 16.

Answer:

Area: 7 units²

Perimeter: 14 units

Step-by-step explanation:

Area of each square:

1 unit × 1 unit = 1 unit²

There are 7 squares:

1 unit² × 7 (squares) = 7 units²

The area of the shape is 7 units².

The perimeter of the shape is the length of the outer sides.

1 + 1 + 1 + 1/2 + 1/2 + 1 + 1 + 1/2 + 1 + 1/2 + 1 + 1 + 1 + 1 + 1 + 1 =  14 units

Answer:

(1+√481/2,0),(1−√481/2,0)

Step-by-step explanation:

You find this by substituting 0 for y and then solving.

Answer:

(1+√481/2,0),(1−√481/2,0)

Step-by-step explanation:

Answer:

A. The student scored better on the geography test.

Step-by-step explanation:

The z-score for a normal distribution, for any value X, is given by:

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

Where is μ the mean score, and σ is the standard deviation.

For the Geography test:

X = 74

μ = 80

σ = 5

[tex]z_g=\frac{74-80}{5}\\ z_g=-1.2[/tex]

For the Mathematics test:

X = 273

μ = 300

σ = 18

[tex]z_m=\frac{273-300}{18}\\ z_m=-1.5[/tex]

The z-score for the Geography test is higher than the score for the Mathematics test, which means that the student had a better relative score in the Geography test.

The answer is  A. The student scored better on the geography test.

Answer:

Always the numerator for the statistic needs to be higher than the denominator. And replacing we got:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{38}{32}=1.19[/tex]

And the best option would be:

d. 1.19.

Step-by-step explanation:

Data given and notation  

[tex]n_1 = 24 [/tex] represent the sampe size 1

[tex]n_2 =16[/tex] represent the sample size 2

[tex]s^2_1 = 32[/tex] represent the sample variance for 1

[tex]s^2_2 = 38[/tex] represent the sample variance for 2

The statistic for this case is given by:

[tex]F=\frac{s^2_1}{s^2_2}[/tex]

Hypothesis to verify

We want to test if the true deviations are equal, so the system of hypothesis are:

H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]

H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]

Always the numerator for the statistic needs to be higher than the denominator. And replacing we got:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{38}{32}=1.19[/tex]

And the best option would be:

d. 1.19.

Answer:

[tex]\frac{1}{13}[/tex]

Step-by-step explanation:

The probability P(A) that an event A will occur is given by;

P(A) = [tex]\frac{number-of-possible-outcomes-of-event-A}{total-number-of-sample-space}[/tex]

From the question,

=>The event A is selecting a king the second time from a 52-card deck.

=> In the card deck, there are 4 king cards. After the first selection which was a king, the king was returned. This makes the number of king cards return back to 4. Therefore,

number-of-possible-outcomes-of-event-A = 4

=> Since there are 52 cards in total,

total-number-of-sample-space = 52

Substitute these values into equation above;

P(Selecting a king the second time) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]

Answer:

x = 465 km

y = 735 km

Step-by-step explanation:

Step 1: Write out equations

x + y = 1200

y = x + 270

Step 2: Find x using substitution

x + (x + 270) = 1200

2x + 270 = 1200

2x = 930

x = 465

Step 3: Plug in x to find y

y = 465 + 270

y = 735

Answer:

They traveled 780

Step-by-step explanation:

Got it right on the test

Answer: On a coordinate plane, 2 lines are parallel to each other.

Step-by-step explanation:

The solution of the system of equations of two lines is the intersecting point where both lines intersect.

When two lines intersect at one point then, we say it has a unique solution.

When two lines coincide, then we say it has an infinite number of solutions.

But when two lines are parallel to each other then, we say it has no solution.

Hence, the graph represents a system of equations with no solution:

On a coordinate plane, 2 lines are parallel to each other.

On a coordinate plane, [tex]2[/tex] lines are parallel to each other.

A graph is a diagram that depicts the relationship between two or more variables measured along one of a pair of axes at right angles.

A coordinate plane is a two-dimensional plane formed by the intersection of a vertical line called [tex]y-[/tex]axis and a horizontal line called [tex]x-[/tex]axis.

A system of equations has no solution if the lines are parallel.

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Answer:

The z–score corresponding to 45 is z=2.

Step-by-step explanation:

We have a random variable X represented by a normal distribution, with mean 35 and standard deviation 5.

The z-score represents the value X relative to the standard normal distribution. This allows us to calculate probabilities for any given normal distribution with the same table.

The z-score for X=45 can be calculated as:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{45-35}{5}=\dfrac{10}{5}=2[/tex]

The z–score corresponding to 45 is z=2.

Answer:

A.

Step-by-step explanation:

It's the first one. The angles are supplementary not complementary.

Answer:

I would have to say A

Step-by-step explanation:

Answer:

Step-by-step explanation:

(4+1)/(8-2)= 5/6

y + 1 = 5/6(x - 2)

y + 1 = 5/6x - 5/3

y + 3/3 = 5/6x - 5/3

y = 5/6x - 8/3

6(y = 5/6x - 8/3)

6y = 5x - 16

-5x + 6y = -16

Answer:

Function

Step-by-step explanation:

The following is a one-on-one function since neither the domain nor the range is being repeated.

Answer:

Function

Step-by-step explanation:

A relation has a connection between the input and output.

You can determine whether each element of the domain is paired with exactly one element of the range.

A function can only have one y value for each x value, so you can't repeat the same x value.

Answer:

2^5

Step-by-step explanation:

The base is the same

2^3 * 2^2

We are multiplying, so we can add the exponents

2^3 * 2^2 = 2^(3+2) = 2^5

Answer: [tex]2^{5}[/tex]

Explanation: I have written this problem on the whiteboard.

For the problem on the board, since our two powers have like bases of 2, we can multiply them together by simply adding their exponents.

So 2³ · 2² is just [tex]2^{5}[/tex].

A common mistake in this problem would

be for students to say that  2³ · 2² is [tex]4^{5}[/tex].

It's important to understand however that when applying your

exponent rules, your base in this case 2 will not change.