How many positive whole numbers less than 2016 have digit sum of 8?

a. If you can play the game for free, the expected value is zero since there is no cost and no prize for winning.

b. To calculate the expected value when it costs $3 to play, we need to first find the probability of winning.

There are 8 possible outcomes on the spinner, and only one of them results in a win, so the probability of winning is 1/8. The probability of losing is 7/8.

The expected value is the sum of the product of each outcome and its probability. Let X be the amount won. Then:

E(X) = (1/8)($100) + (7/8)(-$3)

= $12.50 - $2.63

= $9.87

So the expected value when it costs $3 to play is $9.87. Since the expected value is positive, you can expect to make a profit in the long run.

However, this does not mean that you will win every time you play, as the outcome of each individual game is still random.

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Answer: The distance between Star B and Star C can be found using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse (the longest side). In this case, the lengths of the two shorter sides are the distances from Star A to Star B (50 lightyears) and from Star A to Star C (120 lightyears).

So, we have:

(Star B to Star C)^2 = (Star A to Star B)^2 + (Star A to Star C)^2

(Star B to Star C)^2 = 50^2 + 120^2

(Star B to Star C)^2 = 2500 + 14400

(Star B to Star C)^2 = 16900

Taking the square root of both sides:

Star B to Star C = √16900

Star B to Star C = 129 lightyears

So, Star B and Star C are 129 lightyears apart.

Step-by-step explanation:

Answer:

4cm

Step-by-step explanation:

∵∆DEF ~ ∆ABC，AB/AC =2/3，

∴DE/DF=2/3.

∵DF=6cm，

∴DE=6*2/3=4cm.

Answer: B quadrant 2 or quadrant 3  

Step-by-step explanation:

The transformation that is used to transform the figure P to figure Q is described by (b) (x, y) → (x+5, y+3).

The Transformation of the "figure P" being translated 5 units to the right and 3 units up to create the "figure Q" is called as a type of "translation" in the coordinate plane.

When we shift a point (x, y) by "a" units to the right and "b" units up, the new coordinates become as ⇒  (x + a, y + b).

The coordinates of "figure P" is translated 5 units to the right and 3 units up, that means we will use the rule (x,y) → (x+5, y+3) to describe the transformation.

Therefore, the correct transformation used is  (b) (x, y) → (x+5, y+3).

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The given question is incomplete , the complete question is

A "figure P" was translated 5 units to the right and 3 units up to create "figure Q". Which rule describes this transformation ?

(a) (x, y) → (x-5, y-3)

(b) (x, y) → (x+5, y+3)

(c) (x, y) → (x-3, y-5)

(d) (x, y) → (x+3, y+5)

The correct answer is 178 bottles of water sold on Sunday.

Vendor is a person or a company that sells goods or services. The term is commonly used to refer to individuals who sell items at events, markets, or street stalls. Vendors may sell a variety of products, including food, drinks, clothing, accessories, and more

If the vendor sold 405 bottles of water on Saturday, and sold 127 fewer bottles on Sunday, then on Sunday she sold 405 - 127 = 278 bottles of water.

However, the question states that she actually sold 178 bottles of water on Sunday, so the number of bottles she sold on Sunday was incorrect.

The correct answer is 178 bottles of water sold on Sunday.

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The system of linear equations represented in the graph have (b) ne solution at (2, −1)

From the question, we have the following parameters that can be used in our computation:

The graph

The graph represents two linear functions

The point of intersection of the linear functions represent the solution

In this case, the linear functions intersect at (2, −1)

Hence, it has one solution at (2, −1)

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Answer:

I picked "d. Infinitely many solutions" but it turned out to be wrong lol, so I'm guessing the person above is correct.

Answer: 3/17 or 17.64%

Step-by-step explanation:

Just add everything (adds up to 17), then you put the color frequency number as the numerator of the fraction, then have the added up number as the denominator.

An arithmetic sequence calculator is a tool or program that can be used to find the terms of an arithmetic sequence, given the first term and the common difference. The "nth term" of an arithmetic sequence refers to the term in the sequence that is in the nth position.

An arithmetic sequence calculator is a tool or program that can be used to find the terms of an arithmetic sequence, given the first term and the common difference. The common difference is the value that is added to each term in the sequence to obtain the next term. Given these two values, the calculator can generate the entire sequence of terms. Some calculators may also be able to find the first term and common difference from a given set of terms, as well as other properties of an arithmetic sequence, such as the sum of the terms, the nth term, etc. The "nth term" of an arithmetic sequence refers to the term in the sequence that is in the nth position. In other words, it is the term that corresponds to the number n in the sequence. The nth term can be calculated using the formula for the nth term of an arithmetic sequence, which is given by: a_n = a_1 + (n-1)d. where a_1 is the first term of the sequence, d is the common difference, and n is the position of the term that we want to find. For example, if the first term of an arithmetic sequence is 3, and the common difference is 2, then the nth term can be found by plugging in the values of a_1, d, and n into the formula.

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Complete Question

What is Arithmetic sequences calculator and what is nth term?

The most likely explanation for the inconsistency between the first and second studies is that the initial findings were a false positive, meaning that the effect observed was not actually present in the population being studied.

In the given scenario, the researcher tested a new laparoscopic treatment for chronic shoulder dislocation and found statistically significant results compared to an older treatment. This means that the difference between the two treatments was not due to chance and is likely to be a real effect.

However, a replication study failed to show statistical significance, which means that the difference between the two treatments could have been due to chance. This can happen even if the sample sizes were sufficient in all four studies. A lack of statistical significance in a replication study indicates that the effect observed in the first study may not be as strong or consistent as previously thought.

The fact that the third and fourth studies produced the same effects as the second could be attributed to random variation or other factors such as study design, sample selection, or measurement methods.

Statistical significance is a crucial concept in research as it helps to establish the credibility of a study's findings. However, it is important to understand that statistical significance alone does not necessarily mean that the effect observed is meaningful or important in practical terms.

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The area of the composite figure is equal to 60.75 m² square metres.

The composite figure is made up of a triangle and two rectangles, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:

area of the triangle = 1/2 × 7.5 m × 3 m

area of the triangle = 1/2 × 22.5 m²

area of the triangle = 11.25 m²

area of smaller rectangle = 4.5 m × 3 m

area of smaller rectangle = 13.5 m²

area of the bigger rectangle = 12 m × 3 m

area of the bigger rectangle = 36 m²

total area of the composite figure = 11.25 m² + 13.5 m² + 36 m²

total area of the composite figure = 60.75 m²

Therefore, the area of the composite figure is equal to 60.75 m² square metres.

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a) The probability of a defect is  0.0668.

b. The process standard deviation can be reduced to  0.0062.

c. The advantage of reducing process variation is more efficient and reliable production process, as it reduces the need for inspection and rework.

Probability is the measure of the likelihood of an event occurring. It is used in various fields such as finance, engineering, and manufacturing to analyze and predict outcomes.

One company that utilizes probability in its production process is Motorola. In this scenario, Motorola uses the normal distribution, also known as the Gaussian distribution, to determine the probability of defects in their production process.

The normal distribution is a probability distribution that is symmetric and bell-shaped. It is characterized by its mean and standard deviation. The mean represents the center of the distribution, while the standard deviation represents the spread of the distribution.

a. To determine the probability of a defect, we need to find the area under the normal distribution curve to the left or right of ounces. This area represents the probability of a defect occurring. We can use a standard normal distribution table or a calculator to find this area. The probability of a defect to four decimal places is approximately 0.0668.

If the production run is for 100 items, then the expected number of defects would be 0.0668 x 100 = 6.68. Since we cannot have fractional defects, we would round this number to the nearest whole number, which is 7.

b. If the process standard deviation is reduced to, then the probability of a defect will decrease. This is because a smaller standard deviation means the distribution is less spread out, and therefore, fewer items will fall outside the control limits.

To find the new probability of a defect, we would follow the same process as in part a. The probability of a defect to four decimal places is approximately 0.0062.

c. The advantage of reducing process variation is that it results in a larger distance between the mean and the control limits. This means that there is less chance of items falling outside the control limits, which in turn, reduces the probability of defects. This leads to a more efficient and reliable production process, as it reduces the need for inspection and rework. Additionally, it can lead to cost savings and improved customer satisfaction.

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The recursive rule for the geometric sequence 10, -80, 640, -5120, is a(1) = 10 (the first term) For n > 1, a(n) = -8*a(n-1) (each term is -8 times the previous term).

Recursive definitions of objects are those in which they are defined in terms of other objects of the same kind. The whole class of objects can then be built from a small set of initial values and a few of rules by utilising a recurrence relation of some sort. The most typical way to define the Fibonacci numbers is recursively.

geometric sequence 10, -80, 640, -5120

a(1) = 10 (the first term)

For n > 1, a(n) = -8*a(n-1) (each term is -8 times the previous term).

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The point (-1, 2) lies on the line 3x = 2x - 1.

The equation 3x = 2x - 1 can be simplified by subtracting 2x from both sides to get x = -1.

So the line passes through the point (-1, y) for any value of y.

To check which of the following points lie on the line, we can substitute the x and y coordinates of each point into the equation and see if it is true.

a) (0, -1)

3(0) = 2(0) - 1

0 = -1

This point does not lie on the line.

b) (-1, 2)

3(-1) = 2(-1) - 1

-3 = -3

This point does lie on the line.

c) (1, -4)

3(1) = 2(1) - 1

3 = 1

This point does not lie on the line.

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The length of PC and GC is 4.4 and 6.6 respectively.

What is centroid of a triangle?

A centroid of a triangle is defined as a equidistant from all the point present on the triangle. It is always lies on the interior of the triangle. The centroid divided the median in the ratio 2:1

Given ABC is the triangle.

In which G, H, J are the midpoints on AB, BC, AC sides respectively.

Then, AH, CG, BJ are the medians and they are intersect at the point P.

P is the centroid of the triangle.

Given, GP =2.2 we have  to find the PC and GC.

We know that the centroid divided the median in 2:1 ratios.

i.e., AP:PH = CP:PG = BP:PJ = 2:1

We know , GP = 2.2, then, [tex]\frac{CP}{PG} = \frac{2}{1}[/tex]

⇒CP= 2(2.2)= 4.4then, GC = GP+PC= 2.2 + 4.4= 6.6.

Hence, the length of PC and GC is 4.4 and 6.6 respectively.

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Answer:

So the polynomial function is

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

Step-by-step explanation:

A polynomial function of lowest degree in standard form with roots x = 1, 3, and 2i can be written as (x - 1), (x - 3), and (x - 2i),

From the above data we can get,

k(x) = (x - 1)(x - 3)(x - 2i)

After expanding the equation ,

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

So the polynomial function is

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

The one who types the fastest is Morgan. hence, the correct option is A.

An equation is defined as an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation , the instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We have been given that equation y=39x

Which models the total number of words Alexa can type, where y is the number of words typed and x is the time in minutes.

The data shows the relationship for Morgan.

Then we can conclude that Morgan types the fastest.

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Figure E has more area than Figure D. Figure E has an area of 26 square units, while Figure D has an area of 22 square units. The difference in area is 4 square units, which is the area of the 4 squares added to the bottom of Figure E.

If the side length of each square in the figures is doubled, the area of each square will be quadrupled since the area is proportional to the square of the length of the side.

In Figure D, each square has an area of 1 square unit, so if the side length is doubled, the area of each square will become 4 square units. Therefore, the total area of Figure D will be 15 x 4 = 60 square units.

In Figure E, each square also has an area of 1 square unit, so if the side length is doubled, the area of each square will become 4 square units. Therefore, the total area of Figure E will be 12.5 x 4 = 50 square units.

The new ratio of their areas would be:

New ratio of areas = (Area of Figure D) / (Area of Figure E) = 60 / 50 = 6/5

So the new ratio of their areas would be 6:5.

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The system of inequalities that will model the given scenerio are -

S + L < 30

13S + 18L ≥ 350

Equation modelling is the process of writing a given mathematical statement (or word problem) in the form of a mathematical equation for the correct analysis of the given problem (or situation).

Given is that Jordan's t-shirt business sells long sleeve shirts for $18 and short sleeve shirts for $13. He needs to make at least $350 to buy a new heat press machine.

Let {S} represent the short sleeves and {L} represents the long sleeves. So, we can model the equations as -

S + L < 30

13S + 18L ≥ 350

Therefore, the system of inequalities that will model the given scenerio are -

S + L < 30

13S + 18L ≥ 350

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For the given system of equations, no solution is possible.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Given:

The system of equations,

-18x + 2y = 8  {equation 1}

y = 9x + 4   {equation 2}

Substitute the value of y from equation 2 to equation 1,

we get,

-18x + 18x + 8 = 8

0 = 0

That means, the lines of the equation are parallel to each other.

Therefore, no solution is possible for the system.

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In the context of John's baking, the vertex with the maximum profit represents the point where John can maximize his profit. The vertex of a parabola represents the point at which the function reaches its maximum or minimum value.

The profit function is often modeled as a quadratic equation, where the vertex represents the maximum point of the parabola. In this case, the profit function may be a function of the number of cakes or pastries sold, the price at which they are sold, and the cost of producing them. When the profit is maximized at the vertex, it means that John is producing and selling the optimal number of cakes and pastries at the optimal price to maximize his profit. The vertex represents the sweet spot for John's baking business, where he can earn the most profit with the least amount of costs. Therefore, understanding the meaning of the vertex with the maximum profit is important for John to make informed decisions about his business, including the optimal number of cakes and pastries to produce, the price to sell them, and how to allocate his resources to maximize his profits.

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The appropriate methods are

y = x + 8 and y = 4x + 2 - Substitution method

2x + 6y = 18 and x + 5y = 13 - Elimination method  

y = 3x + 3 and y = x + 7  - Substitution method

4x + 7y = 10 and -3x + y = -1 - Elimination method  

In this approach, the equation in one variable is obtained by either adding or subtracting the equations. We can add the equation to delete a variable if its coefficients are the same and have the opposite sign from the other variables.

Similarly to this, we can subtract the equation to get the equation in one variable if the coefficients of one of the variables are the same and their signs are the same.

From the given options, the system of equations

2x + 6y = 18 and x + 5y = 13  

4x + 7y = 10 and -3x + y = -1    

Can be solved using the Elimination method  

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.

From the given options, the system of equations  

y = x + 8 and y = 4x + 2

y = 3x + 3 and y = x + 7

Can be solved by using the Substitution method

Therefore,

The appropriate methods are

y = x + 8 and y = 4x + 2 - Substitution method

2x + 6y = 18 and x + 5y = 13 - Elimination method  

y = 3x + 3 and y = x + 7  - Substitution method

4x + 7y = 10 and -3x + y = -1 - Elimination method  

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Answer:

Area of rectangle = [tex]\mbox{\large \boxed{\textrm{65 sq. inches}}}[/tex]

Step-by-step explanation:

Let square side = [tex]a[/tex]

Area of square   [tex]A = a^2[/tex]

Given [tex]A = 81[/tex]  and equating it to [tex]a^2[/tex]
[tex]a^2[/tex] [tex]= 81\;in^2[/tex]

[tex]a = \sqrt{81} = 9\;in[/tex]

Perimeter of square = [tex]4a = 4\cdot 9 = 36 \;in[/tex]

If [tex]l[/tex] = length of the rectangle and [tex]w[/tex] = width

Perimeter P of rectangle = [tex]2(l + w)\\[/tex]

Given perimeter of rectangle = perimeter of square we get
[tex]2(l + w) = 36\\\\l + w = 36/2\\\\l + w = 18[/tex]

Given

[tex]w = 5\\\\l + 5 = 18\\\\l = 18 - 5 = 13\\\\[/tex]

[tex]\\\\\textrm{Area of rectangle } = l \times w\\\\= 13 \times 5 \\\\= 65 \;sq.\;inches[/tex]

Answer:

14 bows

Step-by-step explanation:

.5 yards is need for one bow if you have 7 yards you have 14(.5) yards

easier way a half goes into 7, 14 times since 14 divide by two is 7

In 2020, Ramiro paid $4,537.22 for Social Security tax and $1,061.70 for Medicare tax

What is Percentage?

Percentage is a way of expressing a number as a fraction of 100. It represents a proportion or rate out of 100, and is often used to compare values or to express a change or growth.

Solution:

To find how much Ramiro paid for Social Security and Medicare taxes in 2020, we can follow these steps:

1. Calculate the amount of Ramiro's income that is subject to Social Security tax. In 2020, Social Security tax was only applied to the first $137,700 of income. Since Ramiro's income of $73,210 is less than $137,700, all of his income is subject to Social Security tax.

2. Calculate the amount of Social Security tax that Ramiro paid. Since Social Security tax was 6.2% of income in 2020, Ramiro paid:

3. Social Security tax = 0.062 x $73,210 = $4,537.22

1. Calculate the amount of Medicare tax that Ramiro paid. Medicare tax was 1.45% of all income, with no income limit. Therefore, Ramiro paid:

2. Medicare tax = 0.0145 x $73,210 = $1,061.70

Therefore, in 2020, Ramiro paid $4,537.22 for Social Security tax and $1,061.70 for Medicare tax, for a total of $5,598.92 in Social Security and Medicare taxes.

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Answer:

the answer is x=23.84 which is A

Step-by-step explanation:

using SOH CAH TOA

tan0 =opp/adj

where 0=40,opposite =20,adjacent =x

tan 40=20/x

0.8391=20/x

0.8391x=2

divide both sides by 0.8391

x=23.84

The required, we have proven that the sum of the measures of the angles in parallelogram ABCD is 360 degrees.

Given: ABCD is a parallelogram. To prove: mZA + mZB + mZC + mZD = 360 degrees

A parallelogram is a quadrilateral consisting of pairs of parallel sides.

Here,
The proof you provided is correct! Here's a step-by-step explanation of the proof:

By the definition of a parallelogram, AD // BC and AB/DC.

Using AD as a transversal, ZA and ZD are same-side interior angles, so they are supplementary (meaning their measures add up to 180 degrees).

Using side AB as a transversal, ZB and ZC are same-side interior angles, so they are supplementary as well.

By the definition of supplementary angles, mZA + mZD = 180 degrees and mZB + mZC = 180 degrees.
Adding the two equations together, we get:

mZA + mZD + mZB + mZC = 180 degrees + 180 degrees

Simplifying the right side of the equation, we get:

mZA + mZB + mZC + mZD = 360 degrees

Therefore, we have proven that the sum of the measures of the angles in parallelogram ABCD is 360 degrees.

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Answer: x is anything from the set {2, 3, 5, 7, 11}

This is the list of primes between 1 and 11. The value 1 is not prime.

Step-by-step explanation:

To find a percentage, it's the portion divided by the total. 100% represents the total between the children or adults respectively in the maintee and evening.

So, to answer, let's find the total of children and adults.

34+27 = 61 is the total for children.

38+46 = 84 is the total for adults.

Now, to find each percentage, take one of the numbers (Children-Maintee, Children-Evening) and divide it by the total we found.

34/61 = 0.557 or 55.7%

27/61 = 0.442 or 44.2%

I'm leaving it in fractional form in case you need a specific decimal answer.

As for adults, it's the same procedure.

38/84 = 0.452 or 45.2%

46/84 = 0.548 or 54.8%