What type of counting problem is this? How many different sequences of 3 playing cards (from a single 52-card deck) exist?

Combination without repetition
Permutation without repetition
Permutation with repetition
Combination with repetition

Answer:

[tex](a)\ C(x) = 6312.50 + 8.75x[/tex]

[tex](b)\ R(x) = 34x[/tex]

[tex](c)\ P(x) = 6312.50 -25.25x[/tex]

[tex](d)\ Break\ Even = 250\ hours[/tex]

Step-by-step explanation:

Solving (a): The cost function.

Given

[tex]Cost = \$6312.50[/tex] --- cost of saxophone

[tex]Additional = \$8.75[/tex] per hour

The cost function is: sum of the cost of the saxophone and the extra cost per hour.

If an hour costs 8.75, then x hours will cost 8.75x

So, the cost function is:

[tex]C(x) = Cost + Additional[/tex]

[tex]C(x) = 6312.50 + 8.75x[/tex]

Solving (b): The revenue function

Given

[tex]Charges = \$34.00[/tex] per hour

The revenue function is the product of the unit charge by the number of hours.

If in an hour, she charges $34.00, then in x hours, she will cost 34x

So, the revenue function is:

[tex]R(x) = Charges * Hours[/tex]

[tex]R(x) = 34.00 * x[/tex]

[tex]R(x) = 34x[/tex]

Solving (c): The profit function

This is the difference between the cost function and the revenue function

i.e.

[tex]P(x) = C(x) - R(x)[/tex]

So, we have:

[tex]P(x) = 6312.50 + 8.75x - 34x[/tex]

[tex]P(x) = 6312.50 -25.25x[/tex]

Solving (d): The break even hours.

To do this, we simply equate the cost function and the revenue function, then solve for x

i.e.

[tex]C(x) =R(x)[/tex]

[tex]6312.50 + 8.75x = 34x[/tex]

Collect like terms

[tex]6312.50 =- 8.75x + 34x[/tex]

[tex]6312.50 = 25.25x[/tex]

Solve for x

[tex]x = \frac{6312.50}{25.25}[/tex]

[tex]x = 250[/tex]

Answer:

The coordinates of point R are (7,6), second option

Step-by-step explanation:

Coordinates of point R:

The coordinates of point R are , so (6,-7).

90° counterclockwise rule:

The rule for a rotation of 90º counterclockwise is given by:

(x,y) -> (-y,x)

What are the coordinates of point R?

(6,-7) -> (-(-7),6) = (7,6).

The coordinates of point R are (7,6), second option

Answer:

remember this rhyme

Step-by-step explanation:

hey diddle diddle,

the median in the middle

you add and divide for the mean

the mode is the one you see the most

and the range is the differences between.

for median put them in order and then it's the one in the middle

so what you have to do is you have to get all the numbers put them in least to greatest order and slowly you're going to mark one off on the side and then on the other side Mark went off and keep on doing that until you get into the middle and then that should be your median

x=14

Step-by-step explanation:

the answer is 14

I just added 8 with 6

:)

Answer:

035

Step-by-step explanation:

193

86

81

87

223

226

151

126

120

76

Y:

163

140

150

179

204

128

73

89

136

145

Using a correlation Coefficient calculator, the correlation Coefficient, r for the data = 0.127

The test statistic :

T = r² / √(1 - r²) / (n - 2)

Sample size, n = 10

Hence,

T = 0.127² / √(1 - 0.127²) / (10 - 2)

T = (0.016129 / 0.3506905)

T = 0.3506905

The value of the test statistic to 2 decimal places is 0.35

The minimum number of pieces dan requires to achieve his objective of constructing a bigger square is; 4 pieces

We are told that dan is trying to construct a bigger square with a smaller square. That all the smaller square-shaped pieces of paper have similar dimensions.

Length = 2x

Width = x

Length = 2x

Width = 2x

Thus, the minimum number of pieces dan will require to construct the bigger square is 4 squares.

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Answer:

49

Step-by-step explanation:

Convert the dot plot into numbers

40, 40, 40, 45, 45, 50, 55, 55, 60, 60

Add all together

40+40+40+45+45+50+55+55+60+60 =490

Divide by amount of numbers there are

Amount of numbers = 10 --> 490/10 = 49

Mean = 49

Answer:

D. trapezoid

Step-by-step explanation:

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

The expected values for each experiment are:

A) 3.4

B) 3.36

C) 3.33

If we have an experiment with the outcomes:

{x₁, x₂, ..., xₙ}

Each one with the correspondent probability:

{p₁, p₂, ..., pₙ}

Then the expected value of that experiment will be:

EV = x₁*p₁ + x₂*p₂ + ... + xₙ*pₙ

A) in this case we have 10 slips of paper, 8 of them with the number 3, and 2 of them with the number 5.

So the outcomes are:

{3, 5}

The probabilities are:

{8/10, 2/10}

Then the expected value is:

EV = 3*(8/10) + 5*(2/10) = 3.4

B) If we add another slip of paper with a number 3 on it, the new probabilities are:

{9/11, 2/11}

Then the new expected value is:

EV = 3*(9/11) + 5*(2/11) = 3.36

C) Finally, if we add 2 slips of paper with the number 3, now we will have a total of 12 slips of paper, then the new probabilities are:

{10/12, 2/12}

So the new expected value is:

EV = 3*(10/12) + 5*(2/12) = 3.33

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Answer:

19

Step-by-step explanation:

point y is 90

x is 3x - 5

w is 2x

so

3x - 5 + 2x = 90

5x - 5 = 90

5x = 95

x = 19

Answer:

x < 3

Step-by-step explanation:

3 + x-2/x-3 ≤ 4, x ≠ 3

3 + x-2/x-3 -4 ≤ 0

-1 + x-2/x-3 ≤ 0

-(x-3) + x-2/x-3 ≤ 0

1/x-3 ≤ 0

x-3 < 0

x < 3, x ≠ 3

x < 3

x<3 is the solution of the equation  3 + (x-2) / (x-3) ≤ 4.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The given equation can be rewritten as 3 + (x-2) / (x-3) ≤ 4.

To solve for x, we need to multiply both sides by (x-3)

3(x-3) + (x-2) ≤ 4(x-3).
3 + x-2/x-3 -4 ≤ 0

Solve the above equation.

-1 + x-2/x-3 ≤ 0

-(x-3) + x-2/x-3 ≤ 0

1/x-3 ≤ 0

x-3 < 0

x < 3

Hence, x<3 is the solution of the equation  3 + (x-2) / (x-3) ≤ 4.

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Sorry I over complicated the answer that i wrote, I think the answer is 18

Hi there!

[tex]\large\boxed{\text{ UVY} = 65^o, \text{ VYZ }= 65^o}[/tex]

We can begin by finding ∠VUY so we can solve for ∠UVY.

∠VUY is supplementary to ∠TUY, so:

180 = 144 + ∠VUY

∠VUY = 36°

In a triangle, angles sum up to 180°, so:

180 = 36° + 79° + m∠UVY

m∠UVY = 65°

Solve for m∠VYZ by comparing the angle to m∠UVY because the angles are alternating interior angles. Thus:

m∠UVY = m∠VYZ = 65°.

Answer:

8 meters

step-by-step explanation:

8 is in between 9 and 7

The graph of the equation x + 2 would be a straight line that starts at the point (-2, 0) and goes up 2 units on the y-axis. So, the line would pass through the point (0,2) and would be parallel to the x-axis.

The graph of the equation 3x when x is 2 would be a straight line that starts at the point (0,0) and goes up 6 units on the y-axis for each 1 unit on the x-axis. So, the line would pass through the point (2,6) and would have a slope of 3.

In mathematics, a diagram is a visual representation of mathematical concepts or ideas. Diagrams can take many forms, such as graphs, charts, illustrations, and figures, and can be used to help explain or understand mathematical concepts.

For example, a graph is a type of diagram that is used to represent the relationship between two variables. It is commonly used in algebra and calculus to show the relationship between an independent variable (x-axis) and a dependent variable (y-axis).

A chart is a type of diagram that is used to organize and present data. It is commonly used in statistics to show the distribution of data or to compare different sets of data.

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The total number of students in the student body is 110.

Percentage is the ratio of an amount expressed as a number out of 100. The sign that is used to represent percentage is %.

In order to convert a number to percentage, multiply the number by 100. Percentage is a measure of frequency.

In order to determine the total number of students in the student body, divide the number of students that watch TV everyday by the given percentage.

Number of students in the student body = number of students that watch TV everyday / percentage

88 / 80%

= 88 / 0.8 = 110

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Answer:

Probability = 1/5

Step-by-step explanation:

Total ways of arrangement for 10 students = 10 !

Ways to arrange 2 students consecutively & other 8 students =  9 ! x 2      

( As 9! to arrange 9 units, as 2 considered together ; &  2 for arranging 2 consecutive students - respectively )

So, Probability = Favourable outcomes / Total outcomes

= ( 2 x 9! ) / 10!  = ( 2 x 9 x 8 x ..... 2 x 1 ) / 10 x 9 x ....... 2 x 1)

= 2 / 10 = 1/5

Answer:

11.5

Step-by-step explanation:

[tex]14^{2} - 8^{2} = 132\\\sqrt{132}= 2\sqrt{33} = 11.48912529\\answer-is -11.5[/tex]

Answer:

11.48

Step-by-step explanation:

Pythagoras Therum

8^2 + x^2 = 14^2

64 +×^2 = 196

x^2 = 132

sqrt both sides

11.48

Answer:

- 18.377

Step-by-step explanation:

n1 = 17 ; xbar1 = 78.4 ; s1² = 90.3

n2 = 13 ; x2bar = 92 ; s2² = 107.8

Confidence interval :

(x1 - x2) ± Tcritical * sqrt[(sp²/n1 + sp²/n2)]

Pooled variance = Sp² = (df1*s1² + df2*s2²) ÷ (n1 + n2 - 2)

df = n - 1

Sp² = (16*90.3 + 12*107.8) / 28

Sp² = 97.8

Tcritical, 90%, df = n1 + n2 - 2 = 28 (1 - tail)

Tcritical = 1.313

(78.4-92)±1.313*sqrt[(sp²/n1 + sp²/n2)]

Margin of Error = Tcritical * sqrt[(sp²/n1 + sp²/n2)] Margin of Error = (1.313 * √(97.8/17 + 97.8/13)) = 4.7771473

Lower boundary :

(78.4-92) - 4.7771473

-13.6 - 4.7771473

= −18.3771473

= - 18.377

Summary of slope of parallel lines:

Parallel lines have equal slopes. The parallel lines are equally inclined with regard to the positive x-axis, and this is taken into account when calculating a line's slope.

If one line has a slope of m1, another line has a slope of m2, and both lines are parallel, then we get m1 = m2.

The coefficients for "x" and "y" in the equations that depict parallel lines are identical.

Ax + by + c2 = 0 is the line that is parallel to ax + by + c1 = 0. Observation reveals that the x and y coefficients in both equations are equivalent.

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Answer:

A.

Step-by-step explanation:

Answer:

The question doesn't make since so random guess

If you multiply $0.50 by 750 you get 375

If you multiply $0.25 by 750 you get 187.5

divide that by 85 and you get 2.2.

Step-by-step explanation:

Given:

The given digits are 1,2,3,4,5, and 6.

To find:

The number of 5-digit even numbers that can be formed by using the given digits (if repetition is allowed).

Solution:

To form an even number, we need multiples of 2 at ones place.

In the given digits 2,4,6 are even number. So, the possible ways for the ones place is 3.

We have six given digits and repetition is allowed. So, the number of possible ways for each of the remaining four places is 6.

Total number of ways to form a 5 digit even number is:

[tex]Total=6\times 6\times 6\times 6\times 3[/tex]

[tex]Total=3888[/tex]

Therefore, total 3888 five-digit even numbers can be formed by using the given digits if repetition is allowed.

On solving the provided question we can say that - the coordinates from the graphs will be P' = (0.0); Q' = (1,0); R' = (1,1); S' = (0,1)

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is r

A fixed point serves as the dilation's center.

Dk is used to represent dilation, where k is the scale factor.

Dk (x, y) = for a dilation centered on the origin (kx, ky)

Let's assume that you have a PQRS rectangle where

P = (0,0)

Q = (4,0)

R = (4,4)

S = (0,4)

You must multiply each coordinate by 1/4 to achieve the dilation of this PQRS to P'Q'R'S' with a scale factor of 1.

P' = (0.0)

Q' = (1,0)

R' = (1,1)

S' = (0,1)

You may plot both of these rectangles to see that they are the same size and are centered on the origin, but they have different shapes.

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On solving the inequality we know, Barrett should work 25 hours tutoring and 10 hours cutting grass to make $400.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality results from a lack of balance.

Solution:-

given,

z=hours of cutting grass

y=hours of tutoring

Two equation can be made using given condition

15z+10y=400

and

z+y=35

Solving both equation simultaneously,

we get

y=25

z=10

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The transformation is not isometric because the side lengths did not remain the same and hence option C is the correct answer.

An isometric transformation is one that keeps the angles and distances between the original and changed shapes the same. There are numerous techniques that can be used to alter any image in a plane.

The two figures are isometric only if they are congruent. In the given figure the angles remain the same however the lengths of the side are transformed as the figure is dilated.

Hence, the transformation is not isometric because the side lengths did not remain the same and hence option C is the correct answer.

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Answer:

6a. 0.02623

b. 0.5692

Thank you :)