You are playing a game that involves tossing a single die. If you roll a one, you win $50.
If you roll a 2, you win $25. If you roll anything else, you lose $15. What are you expected winnings?

The function type is Linear function.

What is Linear function?

The terms "linear function" in mathematics refer to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

From the given figure it is easily noticed that the function is increasing in nature for [tex]$x < 0$[/tex] and the function is constant in nature for [tex]$x > 0$[/tex] because the value of [tex]$\mathrm{y}$[/tex] remains unchanged for any value of [tex]$\mathrm{x}$[/tex], where [tex]$x \geq 0$[/tex].

The value of function is 3 at x=0.

The value of the function is always 3 for all [tex]$x \geq 0$[/tex]. So, f(x)=3 for [tex]x \geq 0$.[/tex]

The function is a straight line with intercepts (-3,0) and (0,3).

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Answer:

1. Given

2. Vertical Angles Theorem (1st Occurrence)

3. Vertical Angles Theorem (1st Occurrence)

4. Transitive Property of Congruence

5. Converse of the Alternate Interior Angles Theorem

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Transitive Property of Congruence

If one pair of angles is congruent to a third angle, then the first angle is congruent to the third angle.

Converse of the Alternate Interior Angles Theorem

If two lines are intersected by a transversal so that the alternate interior angles are congruent, then the lines are parallel.

[tex]\begin{array}{l|l}\vphantom{\dfrac12} \sf Statements & \sf Reasons \\\cline{1-2}\\1. \; \angle 2 \cong \angle 7 & 1.\; \sf Given\\\\2. \; \angle 2 \cong \angle 3 & 2.\; \sf Vertical\;Angles\;Theorem\;(1st\;Occurrence)\\\\3. \; \angle 6 \cong \angle 7 & 3.\;\sf Vertical\;Angles\;Theorem\;(2nd\;Occurrence)\\\\4. \; \angle 3 \cong \angle 6 & 4.\;\sf Transitive\;Property\;of\;Congruence\\\\5. \; a \parallel b & 5.\;\sf Converse\;of\;the\;Alternate\;Interior\;Angles\;Theorem\\\\ \end{array}[/tex]

From inspection of the given diagram, we can see that angles 2 and 3 are vertical angles, similarly angles 6 and 7 are vertical angles.  Therefore, the Vertical Angles Theorem applies.

According to the Transitive Property of Congruence,  if ∠2 ≅ ∠7 and ∠2 ≅ ∠3 and ∠6 ≅ ∠7 then ∠3 ≅ ∠6.

The two lines a and b are intersected by transversal [tex]\ell[/tex] so that the alternative interior angles 3 and 6 area congruent, then the lines a and b are parallel.  This is the Converse of the Alternate Interior Angles Theorem.

Answer:

x > –1/2

or x > –0.5

Step-by-step explanation:

2x + 8 > – 4x + 5

2x + 4x > 5 – 8

6x > –3

x > –3/6

x > –1/2

or x > –0.5

The value of the chi squared test statistic is 3.27

Chi square test means  a statistical test used to compare observed results with expected results.

Here we have given that Rachel recorded the number of calls she made at work during the week:

Monday: 18

Tuesday: 14

Wednesday: 24

Thursday: 16

And we need to find the chi squared test statistic

While looking into the given question, we have identified that, She expected to make 18 calls each day

Here when a test statistic is smaller than in a left tailed test we would reject H₀.

And if we go to the standard normal chart and use 1% or 0.01, we will search for the closest value to 1% as closely as possible.0.0099 corresponds with a z-score of 3.27

Therefore, option (c) is correct.

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There are 37 students in drama club and 27 students in yearbook club.

And the system of equations will be 1.x + 1.y = 64.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

Total number of students in drama club and yearbook club = 64,

Also, there is a yearbook club. Students in drama club has 10 more than yearbook club,

If x represents the number of students in the drama club and y represents the number of students in yearbook club.

According to given condition,

x+ y = 64        (1)

and x = y + 10

Substitute the value of x in equation (1),

y + 10 + y = 64

2y = 54

y = 27

And x = 27 + 10 = 37

The required system of equations,

1.x + 1.y = 64

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Answer:

(-3,6)

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] x + [tex]\frac{1}{4}[/tex] y = 1  Divide all the way through by 12 to clear the fraction

4x + 3y = 12  Add this to the second equation

2x -3y = -30

6x = -18   Divide both sides by 6

x = -3

Substitute -3 into either of the original equations to solve for y

4x + 3y = 12

4(-3) + 4y = 12

-12 + 4y = 12  Add 12 to both sides

4y = 24  Divide both sides by 4

y = 6

Answer:

Step-by-step explanation:

1) She can use the CUADRATIC FUNCTION for to solve

2) She can use factorization for to solve

3) She can use the ZERO method for to solve

The value of the expression in the scientific notation will be 6.4 × 10⁴. Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ [(8 × 10²) × (3.2 × 10⁵)] / (4 × 10³)

Simplify the expression, then we have

⇒ [(8 × 10²) × (3.2 × 10⁵)] / (4 × 10³)

⇒ [(25.6 × 10⁷)] / (4 × 10³)

⇒ 6.4 × 10⁷⁻³

⇒ 6.4 × 10⁴

The value of the expression in the scientific notation will be 6.4 × 10⁴. Then the correct option is D.

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a=34.697, only one triangle is formed.

And B=40°.7'

A≈77°.79'.So, option A is correct.

Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one.

Any three points determine a distinct triangle and a distinct plane in Euclidean geometry when they are non-collinear (i.e. a two-dimensional Euclidean space). To put it another way, each triangle is contained in a plane, and there is only one plane that includes that particular triangle. All triangles are contained in one plane if and only if all geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except as otherwise specified, the subject of this article is triangles in Euclidean geometry, more specifically, the Euclidean plane.

Given,

C​=61° 50, c​=31.2, b=23.6

Sine rule:

sin B/b=Sin C/c

sin B=b sin C/c

=(23.6 sin 61° 50)/31.2

sin B=0.65219

sin B=139.3

A+B+C=180

A=180-B-C

A=180-139.3-61.50

A= -20.8 which is not possible.

Because the angle must be positive.

sin B=sin 40.70

A+B+C=180

A=180-40.70-61.50

A=77.79'

sin A/a=sin C/c

a=c sin A/sin C

So, a=34.697

Only one triangle is formed

And B=40°.7'

A≈77°.79'

Hence, option A is correct.

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Null hypothesis: H₀: population mean, μ ≥ 36hours

Alternate hypothesis: H₁: population mean, μ < 36hours

Given that,

A maker of cell phones promises that the average battery life of its most recent cell phone model is at least 36 hours. To refute this assertion, you are required to create a hypothesis test.

We have to find

a. Describe the null and alternative hypotheses, then choose the one that best supports the claim.

b. Explain type I and type II mistakes for the claim's hypothesis test.

c. Describe if the hypothesis test has left-, right-, or two-tailed distributions.

d. Describe how to read a conclusion that rejects the null hypothesis. a. Describe how you should evaluate a choice that does not rule out the null hypothesis.

We know that,

a. Null hypothesis: H₀: population mean, μ ≥36hours

Alternate hypothesis: H₁: population mean, μ < 36hours

b. Type 1 error: is an error made when we reject the null hypothesis, when the null hypothesis is true. This happens the significance level % of time. In our example, a type 1 error would be made when the population mean is actually greater than 36 hours, but we conclude that the population mean is less than 36 hours.

Type 2 error: is an error made when we fail to reject the null hypothesis, when the null hypothesis is false. This is represented by beta. In our example, a type 2 error would be made when the population mean is actually less than 36 hours, but we conclude that the population mean is not less than 36 hours.

c. The test is left tailed since the area of rejection is on the left side (less than side).

d. We would interpret that at x% confidence level (generally 95%), we reject the claim that the population mean is greater than 36 hours. We would conclude that we have enough evidence from the sample that the population mean is significantly less than 36, and hasn't happened as a matter of chance.

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Answer is 0

Given:- arithmetic sequence 20,18,16,14,....

To find:- 11th term of given arithmetic sequence

Arithmetic Progression (AP) is  sequence of numbers in order, in which the difference between any two consecutive numbers is  constant value. It is also known as Arithmetic Sequence.

The 11th term of the A.P. can be found by a formula, a(n)=a(1)+(n-1)d , where n is the number of terms, a(1) is teh first term of A.P and d is difference between any two continuously terms.

Number of terms to be found = 11

therefore, a(11) = a(1)+(n-1)d  

d=a(2)-a(1)

d=18-20

d=-2

putting value of d in above equation,

a(11) = 20 + (11-1)(-2)

a(11) = 20 -  20

a(11) = 0

hence the 11th term of arithmetic sequence 20,18,16,14,.... is 0.

Answer:

the sinusoidal function that approximates the hours of daylight in Miami has an amplitude of approximately 1.44 hours.

Step-by-step explanation:

The amplitude of a sinusoidal function is half the difference between the maximum and minimum values of the function. In this case, the shortest day in Miami is 10 hours and 52 minutes long, and the longest day is 13 hours and 45 minutes long, so the difference between the maximum and minimum values is 2 hours and 53 minutes, which is equal to 173 minutes. Half of this is 86.5 minutes, which is the amplitude of the function.

To express this in hours, divide the amplitude in minutes by 60. This gives an amplitude of 86.5 / 60 = 1.44 hours.

So, the sinusoidal function that approximates the hours of daylight in Miami has an amplitude of approximately 1.44 hours.

Answer: i believe it is 14 too

Step-by-step explanation:

The following steps are used to set up a regression

Regression analysis is a set of statistical methods used for the estimation of relationships between a dependent variable and one or more independent variables. It can be utilized to assess the strength of the relationship between variables and for modeling the future relationship between them.

Here , first we identify which variable is independent and which is affect by this independent variable

Then , we plot the data to analyze the pattern between them

Then we find correlation between them after we will able to draw our conclusion about regression.

Therefore, the regression analyses are performed a couple of times to produce the best analysis results, including the test statistics and the predicted fitted regression.

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The confidence level is 60600<μ<3,524.786, assuming a standard deviation of $13,553 and the confidence level for estimating the population mean is 90%.

What do you mean by confidence level?

A confidence interval is a range of values that can contain the true value of the parameter being studied in statistics. It is created using observed data and calculated at a desired level of confidence.

The confidence level—for instance, a 95% confidence level—relates to the accuracy of the estimation process, not to the degree to which it is certain that the computed confidence interval contains the actual value of the parameter under investigation.

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By solving a linear equation, we will see that the distance is 479.98 miles.

We know:

The rental has a base cost of $49.95 plus $1.19 per mile.

There is also an extra cost of $3.89 per gallon of gas, and with one gallon they can travel 18 miles, then there is another extra cost of:

$3.89/18 per mile.

Then, if you travel x miles, the total cost is given by the linear equation:

C(x) = $49.95 + ($1.19 + $3.89/18)*x

We want to find the value of x, number of miles, such that the total cost is $724.85, then we need to solve:

$724.85 = $49.95 + ($1.19 + $3.89/18)*x

Let's solve that for x:

$724.85 -  $49.95 = ($1.19 + $3.89/18)*x

$674.90 = ($1.19 + $3.89/18)*x

$674.90/($1.19 + $3.89/18) = x

479.98 = x

So the distance is 479.98  miles.

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Answer: 19

Step-by-step explanation:

Answer:19

Step-by-step explanation: 10 add the 9

Answer: hope it helps

Step-by-step explanation:

2 1/2 + x = 5 1/3

(2 + 1/2) + x = (5 + 1/3)

6x = 17

x = 17/

6

= 2.83333333

x = 17/

6

≈ 2.833333

[tex] \huge \underline{ \boxed{ \tt Solution: }}[/tex]

[tex] \tt \pink{\large\dagger} \: \: \: \: \: \: 2\dfrac{1}{2} + x = 5\dfrac{1}{3} \\ \tt : \implies \dfrac{5}{2} + x = \dfrac{16}{3} \\ \tt : \implies x = \dfrac{16}{3} - \dfrac{5}{2} \\ \tt : \implies x = \dfrac{16 \times 2}{3 \times 2} - \dfrac{5 \times 3}{2 \times 3} \\ \tt : \implies x = \dfrac{32}{6} - \dfrac{15}{6} \\ \tt : \implies x = \dfrac{32 - 15}{6} \\ \tt : \implies x = \dfrac{17}{6} [/tex]

[tex] \tt \pink{ \star \: Hence \: the \: answer \: is \: \dfrac{17}{6}.}[/tex]

Answer:

30

Step-by-step explanation:

200 x .15   (1-.85 = .15)

30

The confidence interval for the given equation will be: 0.504.

What is confidence interval?

In frequency statistics, the confidence interval (CI) is the range of estimated values ​​for an unknown parameter. Confidence intervals are computed at the specified confidence level. A 95% confidence level is the most common, but other levels such as 90% and 99% are sometimes used. The confidence level represents the proportion of corresponding CIs over time that contain the true value of the parameter. For example, 95% of all intervals computed at the 95% level must contain the true value of the parameter.

Factors that affect the width of the CI include sample size, sample variability, and confidence level. All else being equal, a larger sample results in a narrower confidence interval, a more varied sample results in a wider confidence interval, and a higher confidence level results in a wider confidence interval.

Therefore, The confidence interval for the given equation will be: 0.504.

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Supplementary angles are two angles whose combined angle is 180 degrees. As shown below, the table of the proof that (1) is an addition to (3) can be completed.

Supplementary angles are two angles whose combined angle is 180 degrees. When a straight line crosses another line, two angles are created on either side of the initially imagined straight line. Two sets of additional angles make up those two-two angles. This implies that a straight line will be formed by the outside sides of any extra angles that are positioned next to one another.

For the demonstration that 1 is an addition to 3, the preceding table can be completed as shown below.

1) Line m in is parallel to line n;

2) ∠1 = ∠2  →  Corresponding angles

3) m∠1 = m∠2  →  Definition of Congruent angles

4) ∠2 and ∠3 for a linear pair  →  Adjacent angles on a straight line

5) ∠2 is supplementary to ∠3  →  Definition of linear pair

6) m∠2 + m∠3 = 180°  →  Definition of supplementary angles

7) m∠1 + m∠3 = 180°  →  Substitution Property

8) ∠1 is supplementary to ∠3

As a result, the table containing the proof that item 1 is an addition to item 3 can be completed as displayed above.

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The program for finding the two numbers in the array sum up to x is made.

Array A[n], x

Time Complexity:

As was covered in class, step one employs mergesort, which has an O(nlogn) complexity.

Since the worst-case scenario involves traversing through the full array, step three consumes O(n) time.

Total Running Time = O(nlogn + n) = O(nlogn)

Thus, the program for finding the two intergers in the array sum up to x is made.

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Answer:

16R = T or T = 16R

Step-by-step explanation:

R represents the unknown amount of rows and we know there are 16 boxes in each row.

This means to find the total number of boxes on display, you will have to times the number of rows by 16 as the clerk puts 16 boxes of cereal in each row

e.g, if there are 3 rows, then to find the total amount of cereal boxes, you would do 3 × 16 = 48

Since it's an expression, you need something to represent the total number so that can be represented by any letter ( I chose T ) — in most cases you can probably represent the total as x

Hence the expression should be 16R = T or T = 16R

...at least I think so

After using the quadratic equation the answer is [tex]\frac{2\left(x-3\right)}{x-2}+\frac{-x+4}{x-1}[/tex]

What is quadratic equation ?

Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

Square and quadrangle difficulties have a close relationship with quadratic equations (another name for rectangles). In actuality, the Latin word quadratus, which means square, is the root of the word quadratic.

Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).

[tex]\frac{2}{x-2} (x-3) = \frac{2(x-3)}{x-2} \\\\ \frac{2}{x-1} (3-x) = \frac{2(3-x)}{x-1} \\\\\frac{1}{1-x} (2-x) = \frac{2-x}{1-x} \\\\[/tex]

[tex]\frac{2\left(x-3\right)}{x-2}+\frac{2\left(3-x\right)}{x-1}+\frac{2-x}{1-x}[/tex]

[tex]\frac{2(3-x)}{x-1} + \frac{2-x}{1-x}[/tex]

[tex]\frac{2\left(x-3\right)}{x-2}+\frac{-x+4}{x-1}[/tex]

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Answer:

15

Step-by-step explanation:

25 / 15 = 1.666...

9 x 1.666.... = 15

Answer:

Step-by-step explanation:

375

if they are simiar than 15 from abc would have been the same length

Answer:

x <> -3, 8

Step-by-step explanation:

x² - 5x - 24 (the denominator of the fraction) must not be 0, because n/0 is not defined for any n.

since this is a quadratic equation, it must have 2 solutions.

therefore, the second answer must be right.

let's check.

a quadratic equation

ax² + bx + c = 0

has the solutions

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (5 ± sqrt((-5)² - 4×1×-24))/(2×1) =

= (5 ± sqrt(25 + 96))/2 = (5 ± sqrt(121))/2 =

= (5 ± 11)/2

x1 = (5 + 11)/2 = 16/2 = 8

x2 = (5 - 11)/2 = -6/2 = -3

correct.

Answer:

68%

Step-by-step explanation:

93 is 7 pts BELOW 100     this represents   -7 /15 = -.4666   Z-score

From Z-score table this  represents  .3192   ..or 31.92 % to the LEFT of the 93 ...... to the RIGHT is 100% - 31.92 %  = ~ 68%