Standardized Test: You are trying to answer a multiple choice question on a standardized test. There are five choices. If you get the question right, you gain one point, and if you get it wrong, you lose 1/2point. Assume you have no idea what the right answer is, so you pick one of the choices at random. What is the expected value of the number of points you get? What is the expected value of the number of points you get? Round the answer to two decimal places. The expected value of the number of points you get is

Answer:

1. The slope of the graph is 3/1 or 3

2. The slope of the graph is 3/4

3. The slope of the points is 2

4. The slope of the points is Undefined

5. The slope of the graph is 1

6. The slope of the points is -1/4

Step-by-step explanation:

To find the slope of the graph you use rise over run

To find the slope of the points you use y2-y1 over x2-x1

Hope this is very helpful!!

Answer:

1. -1/3

2. 3/4

3. 2

4. -9/0

5. 1

6. -6/4

Step-by-step explanation:

1.  To find this numbers slope you have to go over and up (or down depending on where the line is going) You go over once and down three times to the next dot. This is why it is negative, because you go down

2. Same as number one you go over (Run) and up (Rise) . You go over 3 times and up 4. This makes it positive, since you are going up.

3.  Stick to this formula (y2-y1)

                                       (x2-x1)

-4-8

0-6     =-12/-6 =2

4. Same as 3

1-8

5-5     = -9/0

5.  Go over 1 and up 1 this will equal 1/1 which is just 1.

6.  

-2-4

-6-2   =-6/-8

This can be simplified down to -3/-4

For further explanation, look at the attachments

Hope this helps (:

According to the information given in the exercise:

• The cost of admission for couples is $12 and $7 for singles.

• On Friday the total amount of money for admissions was $2706.

• On Friday a total number of 268 people attended.

Knowing this, you can set up the following System of Equations, where "c" is the number of couples at the dance club on Friday night and "s" is the number of singles at the dance club on Friday night.

You can use the Elimination Method in order to find the value of "s":

1. Multiply the second equation by -12:

2. Add the equations:

3. Solve for "s":

Therefore, the answer is: There were 102 singles.

The measure of angle QRS in triangle QRS is found as 56.8 degrees.

An angle is  formed when two straight lines or rays meet at a common endpoint.

We know  that the sum of the angles in a triangle is  180 degrees.

In triangle QRS,  

angle RSQ = 48.2 degrees

angle SQR = 75 degrees.

48.2 + 75 + QRS  = 180 (sum of angles in a triangle)

123.2 + QRS  = 180

QRS  = 180 - 123.2

QRS  = 56.8

In conclusion, a triangle is described as a polygon with three edges and three vertices.

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Answer:

x = 180 - (66+70)

= 180-136

x= 44°

Given statement solution is :- It  would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.

Given:

Every 2 centimeters on the floor plan represents 1 meter of the house.

Dining Room:

On the floor plan, the dining room is 8 cm by 10 cm.

Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.

The area of the dining room is 4 meters * 5 meters = 20 square meters.

Bedroom:

On the floor plan, the bedroom is 6 cm by 10 cm.

Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.

The area of the bedroom is 3 meters * 5 meters = 15 square meters.

Now, let's calculate the costs.

Cost of Tile:

The cost of installing tile is $34 per square meter.

The area of the dining room is 20 square meters.

Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.

Cost of Carpet:

The cost of installing carpet is $21 per square meter.

The area of the bedroom is 15 square meters.

Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.

Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

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Answer:

SA=136

Step-by-step explanation:

6*2=12

12*2=24

7*2=14

14*2=28

6*7=42

42*2=84

84+28+24

136

Answer:

Step-by-step explanation:

A rectangular prism has six sides so the area is the sum of the side areas.

A=2(xy+xz+yz) where x,y,z are the dimensions, in this case

A=2(2(6)+2(7)+6(7))

A=2(12+14+42)

A=2(68)

A=136 ft^3

Answer:

Undefined

Step-by-step explanation:

m = (5 - 2) / (-4-(-4))

m= 3/0, so the slope is undefined

Answer:

78.54 cm

formula: A= pi x r^2

                        4

The rental car is getting approximately 37.56 miles per gallon.

To convert kilometers per liter (km/l) to miles per gallon (mpg), you can use the following conversion factor:

1 km/l ≈ 2.82475 mpg

Therefore, if your rental car is getting 13.3 km/l of gasoline, the equivalent value in miles per gallon would be:

13.3 km/l x 2.82475 mpg ≈ 37.56 mpg

So, your rental car is getting approximately 37.56 miles per gallon.

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The Amy has 42 books, Betty has 36 books, and Carol has 18 books.

Let's set up equations to represent the given information:

Let A represent the number of books Amy has.

Let B represent the number of books Betty has.

Let C represent the number of books Carol has.

Let's say Amy has x books.

Betty has 6 books less than Amy, so Betty has (x - 6) books.

Carol has half as many books as Betty, so Carol has (x - 6)/2 books.

According to the problem, the total number of books they have is 96.

So, we can write the equation:

x + (x - 6) + (x - 6)/2 = 96

To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:

2x + 2(x - 6) + (x - 6) = 192

2x + 2x - 12 + x - 6 = 192

5x - 18 = 192

5x = 210

x = 42

Amy has 42 books.

Betty has (42 - 6) = 36 books.

Carol has (36)/2 = 18 books.

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Answer:

x = 15

Step-by-step explanation:

The scale factor is 8:20, we need to set up a proportion

Setting up the proportion:

\( \frac{8}{20} = \frac{6}{x} \)

cross-multiply

8x = 120

x = 15 | Divide both sides by 8

Answer:

the measure of cord ab will be 4 unit.

because cord ab and cord cd are congruent

The shape of the graph of a function is the shape assumed by the graph of the function after the dataset generated by using the function is plotted on the coordinate plane. The shape in the graph of the question is a triangular shape.

A function is a direction used to map the values of an input variable of the function to the output variables.

The points in the attaches graph which are connected by lines are;

(0, 1.5), and (4.5, 0)

The joining of the above points in the attached graph, and the origin forms a triangular shape.

Details about the shape of the graph of a function

The graph of a function such as f(x) = -x² + 2·x + 3, is obtained by finding the values of the output values of the function, f(x) for each input value of the function, x as follows;

x     \({}\)             f(x)

0     \({}\)              3

1     \({}\)               4

2     \({}\)              3

3     \({}\)              0

4     \({}\)              -5

5     \({}\)              -12

6     \({}\)              -21

7     \({}\)              -32

8     \({}\)              -45

Please find attached the graph of the sample function created with MS Excel

The graph of the function f(x) = -x² + 2·x + 3 has the shape of a parabola, which is the shape of a quadratic function.

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By applying the concept of corresponding angles in similar triangles, we were able to establish the value of x as 25 in the given scenario.

In the given problem, we are provided with information about the angles in two similar triangles: triangle ABC and triangle STU. It is stated that angle UTS in triangle STU is 100 degrees, and since corresponding angles of similar triangles are congruent, we can conclude that angle STU is also 100 degrees.

Next, we examine angle BAC in triangle ABC, which is given as 4x. Using the same logic, we know that angle BAC is also congruent to angle STU. Therefore, we can equate the two angles:

angle BAC = angle STU

4x = 100

To find the value of x, we divide both sides of the equation by 4:

x = 100/4

x = 25

Hence, we determine that x is equal to 25. This method allows us to leverage the known information about one triangle to infer the measurements of corresponding angles in the other similar triangle.

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Answer:P=58

A=368

Step-by-step explanation:

I’m like 99% sure

Answer:

24.4 km

Step-by-step explanation:

\(\sqrt{14^2 + 20^2} = \sqrt{196 + 400} = \sqrt{596}\) = 24.413111 = 24.4 km

Using the concept of Pythagorean theorem, the distance between Closside and Farlisle is 24.4km

The Pythagorean theorem is a fundamental principle in geometry that relates the lengths of the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, the Pythagorean theorem can be expressed as:

c² = a² + b²

In this problem, we can substitute the values and solve the distance;

c² = 14² + 20²

c² = 596

c = 2√149

c = 24.4km

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The domain in interval notation is [-1, 3].

The domain in compound inequality is -1 ≤ x < 3.

The range in interval notation is [-5, 3].

The range in compound inequality is -5 < y ≤ 3.

In Mathematics, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-1, 3] or -1 ≤ x < 3.

Range = [-5, 3] or -5 < y ≤ 3.

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Answer:

First, let's divide 1563 by 47, so

So, first, we select 2 numbers from 1563 because 47 has two numbers. However, 15 is lower than 47, so we need to select one number more and get 156.

Now, we need to find a number that multiplied to 47 is 156 or closer to 156. This number is 3 because 47 x 3 = 141. We subtract 141 from 156 to get 15.

Then, we take another move down the 3, and we work with 153. So, again, we need to find a number that multiplied to 47 is 153 or closer. This number is again 3 because 47 x 3 = 141.

Subtract 141 from 153 to get 12. Since 12 is lower than 47 and there are no more numbers to move down, the division is ended.

Now, let's multiply 67 x 78

In this case, we first multiply 8 x 7 = 56, we type 6 and write the 5 in another place. Then, 8 x 6 = 48. But we have 5, so we type 48 + 5 = 53.

Then, we multiply 7 x 7 = 49, so we type 9 one place to the left and let the 4 in another place. Now, multiply 7 x 6 = 42, but we write 42 + 4 = 46.

Finally, we need to add the numbers. So, the result is 5226.

Answer:it might be A

Answer: B I think...

Step-by-step explanation: Sorry if im wrong

Answer:

A

Step-by-step explanation:

Average rate per hour = 18 / 3 or 6

if we want to find how many miles the hot air balloon will travel in 3/4 of an hour we multiply average distance by time

So our answer = 3/4 * 6

3/4 * 6 = 4.5

Therefore in 3/4 hour the hot air balloon will have traveled 4.5 miles.

Answer is in the file atttached.            

Answer:

B) \(-\sqrt{64}\)

Step-by-step explanation:

A rational number, can be expressed as a fraction: \(\frac{a}{b}\) where a and b are both integers.

The square root of 64, can be simplified to 8, since 8 * 8 = 64.

So the expression: \(-\sqrt{64} = -8\), and 8 is a rational number, since it can be expressed as: \(\frac{8}{1}\)

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Using Pascal's triangle and the difference quotient formula, we expand (x + h)^2 and simplify the expression to (2hx + h^2) / h. As h approaches 0, the term h becomes negligible, and we are left with 2x, which represents the derivative of x^2.

To use Pascal's triangle to find x^2 using the difference quotient formula, we can follow these steps:

1. Write the second row of Pascal's triangle: 1, 1.

2. Use the coefficients in the row as the binomial coefficients for (x + h)^2. In this case, we have (1x + 1h)^2.

3. Expand (x + h)^2 using the binomial theorem: x^2 + 2hx + h^2.

4. Apply the difference quotient formula: f(x + h) - f(x) / h.

5. Substitute the expanded expression into the formula: [(x + h)^2 - x^2] / h.

6. Simplify the numerator: (x^2 + 2hx + h^2 - x^2) / h.

7. Cancel out the x^2 terms in the numerator: (2hx + h^2) / h.

8. Divide both terms in the numerator by h: 2x + h.

9. As h approaches 0, the term h becomes negligible, and we are left with the derivative of x^2, which is 2x.

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To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Answer:

3/7 x 8/3 = 8/7 = 1 1/7

Step-by-step explanation:

3/7 × 8/3

3 x 8

7 x 3

= 24/21

24 ÷ 3

21 ÷ 3

=8/7

= 1 1/7

By translation, the image of the triangle X is equivalent to the triangle E.

Herein we find the representation of a triangle, whose vertices are described below:

A(x, y) = (5, 5), B(x, y) = (5, 6), C(x, y) = (7, 5)

Whose image must be determined by a rigid transformation known as translation:

P'(x, y) = P(x, y) + T(x, y)

Where:

Now we proceed to determine the images of the vertices of the triangle:

A'(x, y) = (5, 5) + (4, - 3)

A'(x, y) = (9, 2)

B'(x, y) = (5, 6) + (4, - 3)

B'(x, y) = (9, 3)

C'(x, y) = (7, 5) + (4, - 3)

C'(x, y) = (11, 2)

Therefore, the triangle E is the image of the triangle X.

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