A. name 3 different angles which could have a reference angle of 20 degrees. how did you arrive at this answer?.

b. what are the characteristics of a reference angle?

c. how is it possible that angles can have different measurements, but still have the exact same reference angle?

Answer: B

Step-by-step explanation:

Points from the graph

Points from f(x)                         points from g(x)

(1,2)                                                (1, 1/2)

(4, 16)                                             (4, 4)

f(x) was multiplied by 1/4 to get to g(x)

The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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Step-by-step explanation:

- 22 = -8u + 6(u-7)

-22 = -8u + 6u - 42

8u - 6u = 22 - 42

2u = -20

u = -20/2

u = -10

Answer:

Step-by-step explanation:

\( \mathrm{ - 22 = - 8u + 6(u - 7)}\)

Distribute 6 through the parentheses

⇒\( \mathsf{ - 22 = -8u + 6u - 42}\)

Collect like terms

⇒\( \mathrm{ - 22 = - 2u - 42}\)

Swap the sides of the equation

⇒\( \mathrm{ -2u - 42 = - 22}\)

Move constant to R.H.S and change it's sign

⇒\( \mathrm{ - 2u = - 22 + 42}\)

Calculate

⇒\( \mathrm{ - 2u = 20}\)

Divide both sides of the equation by -2

⇒\( \mathrm{ \frac{ - 2u}{ - 2} = \frac{20}{ - 2} }\)

Calculate

⇒\( \mathrm{u = - 10}\)

Hope I helped!

Best regards!

Answer:

Step-by-step explanation:

Initial length of the cardboard was y cm, and width was x cm.

The new dimensions are:

length = (y - 25) cm

width = (x - 15) cm

Area of the new rectangle = length x width

                                            =  (y - 25) x (x - 15)

                                            =  (y - 25) (x - 15) \(cm^{2}\)

Perimeter = 2 ( length + width)

                = 2 ((y - 25)  + (x - 15))

                = 2(y - 25) + 2(x - 15)

Therefore:

2(x + y) - 40 is neither of these

2(x - 15) + 2(y - 25) is the perimeter

(x - 15)(y - 25)  is the area

(x - 25)(y - 15) is neither of these

2(x - 15)(y - 25)  is neither of these

2x + 2y - 80 is the perimeter

xy - 375 is neither of these

x + y - 40 is neither of these

Scaling a dataset by a constant value changes the standard deviation proportionally by the same constant value.

Scaling (multiplying or dividing) a set of data by a constant value changes the standard deviation of the data.

If you multiply every value in a dataset by a constant value, the standard deviation will also be multiplied by the same constant. For example, if you have a set of data with a standard deviation of 2 and you multiply every value by 3, the new standard deviation will be 6.

On the other hand, if you divide every value in a dataset by a constant value, the standard deviation will also be divided by the same constant. For example, if you have a set of data with a standard deviation of 6 and you divide every value by 3, the new standard deviation will be 2.

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(a) 95% confidence interval for the difference between female and male times is (11.954, 255.591).

(b) The assumptions and conditions for the two-sample t-test are met, so we can use the results of the test and confidence interval.

a) To construct a 95% confidence interval for the difference between female and male times, we can use a two-sample t-test. Let's denote the mean time for female swimmers as μf and the mean time for male swimmers as μm. We want to test the null hypothesis that there is no difference between the two means (i.e., μf - μm = 0) against the alternative hypothesis that there is a difference (i.e., μf - μm ≠ 0).

The formula for the two-sample t-test is:

t = (Xf - Xm - 0) / [sqrt((s^2f / nf) + (s^2m / nm))]

where Xf and Xm are the sample means for female and male swimmers, sf and sm are the sample standard deviations for female and male swimmers, and nf and nm are the sample sizes for female and male swimmers, respectively.

Using the data from the plots, we get:

Xf = 917.5, sf = 348.0137, nf = 15

Xm = 783.7273, sm = 276.0625, nm = 28

Plugging in these values, we get:

t = (917.5 - 783.7273 - 0) / [sqrt((348.0137^2 / 15) + (276.0625^2 / 28))] = 2.4895

Using a t-distribution with (15+28-2) = 41 degrees of freedom and a 95% confidence level, we can look up the critical t-value from a t-table or use a calculator. The critical t-value is approximately 2.021.

The confidence interval for the difference between female and male times is:

(917.5 - 783.7273) ± (2.021)(sqrt((348.0137^2 / 15) + (276.0625^2 / 28)))

= 133.7727 ± 121.8187

= (11.954, 255.591)

Therefore, we can be 95% confident that the true difference between female and male times is between 11.954 and 255.591 minutes.

b) Assumptions and conditions for the two-sample t-test:

Independence, We assume that the observations for each group are independent of each other.

Normality, We assume that the populations from which the samples were drawn are approximately normally distributed. Since the sample sizes are relatively large (15 and 28), we can rely on the central limit theorem to assume normality.

Equal variances, We assume that the population variances for the female and male swimmers are equal. We can test this assumption using the F-test for equality of variances. The test statistic is,

F = s^2f / s^2m

where s^2f and s^2m are the sample variances for female and male swimmers, respectively. If the p-value for the F-test is less than 0.05, we reject the null hypothesis of equal variances. If not, we can assume equal variances. In this case, the F-test yields a p-value of 0.402, so we can assume equal variances.

Sample size, The sample sizes are both greater than 30, so we can assume that the t-distribution is approximately normal.

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Answer:

$4.20

Step-by-step explanation:

The Writing Emporium sells pencils and pens individually.

Step 1

We have to first find the price of a pencil and a pen

Let:

The price of a pencil = x

The price of a pen = y

Alana buys a pencil and two pens for $1.10.

x + 2y = 1.1 ......Equation 1

x = 1.1 - 2y

Jeffrey buys two pencils and a pen for $1.00.

2x + y = 1 ........ Equation 2

We substitute 1.1 - 2y for x in Equation 2

2(1.1 - 2y) + y = 1

2.2 - 4y + y = 1

-4y + y = 1 - 2.2

-3y = -1.2

y = -1.2/-3

y = $0.4

Solving for x

x = 1.1 - 2y

x = 1.1 - 2(0.4)

x = 1.1 - 0.8

x = $0.3

Hence:

The price of a pencil = x = $0.3

The price of a pen = y = $0.4

Step 2

How much does Edward spend to buy six pencils and six pens from the Writing Emporium?

6x + 6y

6($0.3) + 6($0.4)

$1.8 + $2.4

= $4.20

Therefore, Edward spent $4.20 to buy six pencils and six pens from the Writing Emporium.

Answer:

x=3, y=5

Step-by-step explanation:

Allura, this is the solution:

As you can see we have two right triangles in the figure:

Therefore,

Step 1: Let's calculate the hypotenuse of the left triangle, as follows:

c² = a² + b²

c² = 12² + 18²

c²= 144 + 324

c² = 468

c = 21.63

Step 2: Let's calculate the sides of the right triangle on the right, this way:

Leg 1 = 21.63

Leg 2 = x

Hypotenuse = 12 + y

Height of the right triangle = 18

In consequence, to find the value of the hypotenuse and y, we have:

c = 21.63²/√21.63² - 18²

c = 468/√468 - 324

c = 468/12

c = 39

Step 3: Now, we can solve for y, this way:

39 = 12 + y

y = 39 - 12

y = 27

The correct answer is D. 27

Answer:

NO

Step-by-step explanation:

A statistical question is a question that can be answered by collecting data that vary. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question.

TheThe figure that represents the total area of the figure is: B. 24.413 in².

Total area = 1/2 × 3.3×3.15 + 4.6×3.15  + 1/2×3× (6.3 - 3.15)

Total area =  5.1975 + 14.49  + 4.725

Total area = 24.4125in²

Total area = 24.413 in² (Approximately)

Therefore the correct option is B.

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We want to see if the given function represents a linear function.

We will see that yes, it does.

So we have the function:

y = f(x) = 30 + 5*x

And a general linear function is written as:

y = a*x + b

where a is the slope and b is the y-intercept.

Comparing these two, we can see that both have the same general shape, thus, our function is also a linear function.

A graph of our function also can be seen below, where it is evident that it is a line.

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Answer:

9 a.  This situation represents a linear function because the equation can be written in the form y =mx + b

9 b. The domain is discrete, because the number of extra services must be a whole number.

9c. graph 6 dots at : (0,30) ( 1 ,35 ) ( 2, 40) (3 , 45) (4, 50) (5 , 55)

Step-by-step explanation:

a. The given function is:

y = 30 + 5x

We know that,

The standard representation of the linear function is:

y = mx + c

Compare the given function with the standard representation

Hence, from the above,

We can conclude that the given situation represents a linear function

b. Find the domain of the function. Is the domain discrete or continuous? Explain.

Answer:

The given function is:

y = 30 + 5x

Where,

y is the amount in dollars

x is the cost of extra grooming services

From the above,

The maximum number of given extra grooming services is: 5

So,

We can use extra grooming service or not

Hence, from the above,

We can conclude that

The domain of the given function is: 0 ≤ x ≤ 5

Hence,

The domain of the given function is continuous

c. Graph the function using its domain.

Answer:

The given function is:

y = 30 + 5x

We know that,

The domain of the function is: 0 ≤ x ≤ 5

So,

y = 30 + 5(0) = 30

y = 30 + 5 (1) = 35

y = 30 + 5(2) = 40

y = 30 + 5 (3) = 45

y = 30 + 5 (4) = 50

y = 30 + 5 (5) = 55

False. The statement you described is not an equivalent form for a conditional statement. The process you mentioned, which is reversing and negating the antecedent and consequent, is known as forming the contrapositive of the statement.

A conditional statement has the form "If P, then Q," where P is the antecedent and Q is the consequent. The contrapositive is formed by negating both the antecedent and consequent, and reversing their order: "If not Q, then not P." The contrapositive is equivalent to the original conditional statement.

However, simply reversing the antecedent and consequent without negating them gives you the converse, which is "If Q, then P." The converse is not equivalent to the original conditional statement.

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The analysis of the graph, that has x-intercepts of (0, 2), and (0, 5), we get;

a. The function increases when x > 4

b. The function decreases when x < 4

c. The function is greater than zero when x < 3, and x > 5

d. The function is less than zero when 3 < x < 5

The location of a point where a function is increasing is where the slope of the function is larger than zero.

The description of the graph of the function are as follows;

The shape of the function  = Concave upwards

The coordinates of the vertex of the function = (4, -5)

The region where the function is decreasing is from -∞ to 4

The region where the function is decreasing is therefore; x < 4

At the vertex, (4, -5), the slope of the function is zero, therefore;

Therefore, the function is increasing where x > 4

The x-intercepts are at point (0, 3) and (0, 5)

Therefore, the function is greater than zero when x < 3, and when x > 5

The function is less than zero in the range 3 < x < 5

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Answer:

+60

Step-by-step explanation:

This is the answer because you multiply -15 x -4 =60

because negative and negative make positive and =60

Hope this helps:)

pls mark brainly

If a 600 room hotel generated the following room sales/ rates: 250 rooms sold at $195, 120 rooms sold at $165, 95 rooms sold at $770 and the occupancy suddenly increases to 100% and the ADR remains the same, then the RevPAR is $236.16.

To calculate the RevPAR, follow these steps:

Hence, none of the options provided are correct.

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Answer:

3(x-3)/4-1/2=2/3  

The least common denominator will be the least common multiple of 4,2,3 which is the product of the highest occurring primes of the numbers prime factorization...

Step-by-step explanation:

4=2*2, 2=2, 3=3, so the least common denominator is 2*2*3=12

Answer:

1. x =  80°

2. x = 95°

3. x =  -7

4. x = 32°

5. Yes, it is possible

Step-by-step explanation:

For questions 1, 2 and 3 we make use of the fact that the sum of the angles of a triangle = 180

Q1

Angle measures are 60, 40 and x
So 60 + 40 + x = 180
==> 100 + x = 180
==> x = 180 - 100 = 80°

Q2

Angles are 35, 50 and x
35 + 50 + x = 180

85 + x = 180

x = 180 - 85 = 95°

Q3
Angle measures are
76, 41 and (x + 70)

76 + 41 + x  + 70 = 180

187 + x = 180

x = 180 - 187

x = -7

Note: x is not an angle of the triangle, 70 + x is the third angle measure and that = 70 - 7 = 63°

Q4:

One leg of the triangle is extended creating an exterior angle of 122°

When an exterior angle is formed in this manner, it is equal to the sum of the two interior angles

The two interior angle measures are x° and 90°

So x + 90 = 122

x = 122-90 = 32°

Q5

One property of any triangle is that the sum of the lengths of any two sides must be greater than the length of the third side
Given three sides 85, 45, 45

45 + 45 = 90 > 85

45 + 85 = 130 > 45

So it is possible to have a triangle with lengths 85, 45 and 45

Answer:

$510 you get this answer by first rounding $849.75 to $850 and rounding 61.3% to 60% then multiply $850 and .6 to get your answer $510

Step-by-step explanation:

hello no explanation lol

The program that has to be modified serves as an example of how Python can generate random integers.

The random module will be used to create the random numbers from 1 to 10.

The modified program, which uses comments to clarify the program's lines, is as follows:

Here, the random module is imported.

import arbitrary

This produces random numbers.

A = Random.Random (1,10)

This produces a new random number.

B = Random.Random (1,10)

#This increases both integers by one.

response = a * b

This shows the program's outcome.

print the following: str(a) + "* " + str(b) + " = " + str(answer)

The sum of the two random numbers will be printed at the program's conclusion.

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Lisa bowling score is 100.

John bowling score is 282.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

Lisa and John are bowling.

Johns score is three times the difference of Lisa's score and 6.

The sum of their scores is 382.

Now, Let Lisa bowling score = x

Then, John bowling score = 3 (x - 6)

Since, The sum of their scores is 382.

Hence,

x + 3 ( x - 6 ) = 382

After solving,

x + 3x - 18 = 382

4x = 382 + 18

4x = 400

x = 100

Hence, Lisa bowling score = x = 100

And, John bowling score = 3 (x - 6)

                                       = 3 (100 - 6)

                                       = 3 × 94

                                       = 282

Therefore, Lisa bowling score is 100.

And, John bowling score is 282.

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                                            .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .        .

The measures in the circle given in the image above are calculated as:

1. m<PSQ = 130°;   2. m<AQS = 30°; 3. m(QR) = 100°; 4. m(PS) = 110°; 5. (RS) = 70°.

In order to find the measures in the circle shown, recall that according to the inscribed angle theorem, the measure of intercepted arc is equal to the central angle, but is twice the measure of the inscribed angle.

1. m<PSQ = m<PAQ

Substitute:

m<PSQ = 130°

2. Find m<PBQ:

m<PBQ = 1/2(m(PQ) + m(RS)) [based on the angles of intersecting chords theorem]

Substitute:

m<PBQ = 1/2(130 + 2(35))

m<PBQ = 100°

m<AQS = 180 - [m<BAQ + m<PBQ]

Substitute:

m<AQS = 180 - [(180 - 130) + 100]

m<AQS = 30°

3. m(QR) = m<QAR

Substitute:

m(QR) = 100°

4. m(PS) = 180 - m(RS)

Substitute:

m(PS) = 180 - 2(35)

m(PS) = 110°

5. m(RS) = 2(35)

m(RS) = 70°

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Answer:

-18.4 or also written as -18 2/5

Step-by-step explanation:

1. Substitute -6 in for x

h(-6) = 3(-6) - 2/5

2. Distribute the 3 and -6

h(-6) = -18 - 2/5

3. Subtract

h(-6) = -18.4 OR h(-6) = -18 2/5

Answer:

designing and building your own structure in tech :)

Step-by-step explanation:

Answer:

12 pieces can be cut

Step-by-step explanation:

5/8 yard per piece

5/8 = 0.625 yard

We have 7.5 yards total

7.5 / 0.625 = 12

Answer:

4/3

Step-by-step explanation:

If you use the slope formula you should get 4 over 3 (4/3)

The two events are dependent, and the indicated probability is 1÷36.

What is Probability ?

Probability is a measure of the likelihood or chance that a particular event or outcome will occur. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The two events, "the sum is greater than 9" and "the red cube shows a 5," are dependent because the outcome of one event (the red cube showing a 5) affects the probability of the other event (the sum being greater than 9).

If the red cube shows a 5, then the only way for the sum to be greater than 9 is if the white cube also shows a number greater than 4 (since the highest number on a standard number cube is 6). However, if the red cube does not show a 5, then it is impossible for the sum to be greater than 9, regardless of the outcome of the white cube.

Therefore, the outcome of the red cube affects the probability of the sum being greater than 9, making the two events dependent on each other.

To find the indicated probability, we need to consider the possible outcomes where the red cube shows a 5 and the sum is greater than 9. There is only one possible outcome in this case, which is the red cube showing a 5 and the white cube showing a 5.

The total number of possible outcomes when rolling two number cubes is 6 x 6 = 36, since each cube has 6 sides and each side is equally likely to occur.

So, the probability of the sum being greater than 9 and the red cube showing a 5 is 1 out of 36 possible outcomes, or 1÷36. This is the indicated probability in this case. Therefore, the probability of the two events occurring together is 1÷36, making them dependent on each other. So, the probability of the sum being greater than 9 and the red cube showing a 5 is 1÷36.

This is because there is only one possible outcome where both events occur (red cube shows a 5 and white cube shows a 5) out of 36 possible outcomes when rolling two number cubes. Hence, the two events are dependent and the indicated probability is 1÷36. So, the two events are dependent because the outcome of one event affects the probability of the other event occurring.

The indicated probability of the sum being greater than 9 and the red cube showing a 5 is 1÷36, as there is only one favorable outcome out of 36 possible outcomes when rolling two number cubes.

Therefore, the two events are dependent and the indicated probability is 1÷36. So, in conclusion, the two events "the sum is greater than 9" and "the red cube shows a 5" are dependent because the outcome of the red cube affects the probability of the sum being greater than 9. The indicated probability of the two events occurring together is 1÷36, as there is only one favorable outcome out of 36 possible outcomes.

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