The yearly cost in dollars, y, for a member at a video game arcade based on total game tokens purchased, x, is y =y equals startfraction 1 over 10 endfraction x plus 60.x 60. a nonmember pays $0.20 per game token, but no yearly fee. which equation represents the yearly cost for a nonmember at the same video game arcade based on the total number of game tokens purchased in a year? y = y equals startfraction one-half endfraction x.x y = y equals startfraction 1 over 10 endfraction x plus 60.x 60 y = y equals startfraction 1 over 5 endfraction x. x y = y equals startfraction 1 over 20 endfraction x plus 60.x 60

The point (9, -7) is the only solution to the system of linear inequalities given.

To determine which point would be a solution to the system of linear inequalities, let's substitute the given points into the inequalities and see which point satisfies both inequalities.

The system of linear inequalities is:

y > -4x + 6

y > (1/3)x - 7

Let's test each given point:

For the point (9, -7):

Substituting the values into the inequalities:

-7 > -4(9) + 6

-7 > -36 + 6

-7 > -30 (True)

-7 > (1/3)(9) - 7

-7 > 3 - 7

-7 > -4 (True)

Since both inequalities are true for the point (9, -7), it is a solution to the system of linear inequalities.

For the point (-12, -2):

Substituting the values into the inequalities:

-2 > -4(-12) + 6

-2 > 48 + 6

-2 > 54 (False)

-2 > (1/3)(-12) - 7

-2 > -4 - 7

-2 > -11 (False)

Since both inequalities are false for the point (-12, -2), it is not a solution to the system of linear inequalities.

For the point (12, 1):

Substituting the values into the inequalities:

1 > -4(12) + 6

1 > -48 + 6

1 > -42 (True)

1 > (1/3)(12) - 7

1 > 4 - 7

1 > -3 (True)

Since both inequalities are true for the point (12, 1), it is a solution to the system of linear inequalities.

For the point (-12, -7):

Substituting the values into the inequalities:

-7 > -4(-12) + 6

-7 > 48 + 6

-7 > 54 (False)

-7 > (1/3)(-12) - 7

-7 > -4 - 7

-7 > -11 (True)

Since one inequality is true and the other is false for the point (-12, -7), it is not a solution to the system of linear inequalities.

In conclusion, the point (9, -7) is the only solution to the system of linear inequalities given.

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Usando el interés compuesto, se encuentra que el interes obtenido es de 1609.

\(I(t) = P\left[\left(1 + \frac{r}{n}\right)^{nt} - 1\right]\)

En que:

En este problema, los parámetros son:

\(P = 9500, t = \frac{900}{365} = 2.4658, r = 0.065, n = 1\)

Por eso:

\(I(t) = P\left[\left(1 + \frac{r}{n}\right)^{nt} - 1\right]\)

\(I(2.4658) = 9500\left[\left(1 + \frac{0.065}{1}\right)^{2.4658} - 1\right]\)

\(I(2.4658) = 1609\)

El interes obtenido es de 1609.

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The interest earned on the amount is 1,595.05.

The formula for calculating the compound interest is expressed as:

A = P(1+r)^t

A = 9500(1+0.065)^2.4658

A = 9500(1.065)^2.4658

A = 11,095.05

Interest = Amount - Principal

Interest = 11,095.05 - 9500

Interest = 1,595.05

Hence the interest earned is 1,595.05.

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The slope of the given equation is 14x, so the answer is not listed in the choices given.

The slope of the given equation y = 7x² can be calculated using the formula y = mx + b, where "m" is the slope and "b" is the y-intercept.Let's find the slope of the equation y = 7x²: y = 7x² can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. Thus, we have;  y = 7x² can be written as y = 7x² + 0, which is in the form of y = mx + b. Therefore, the slope of the equation y = 7x² is 14x. Therefore, the slope of the given equation is 14x, so the answer is not listed in the choices given.

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Answer:

S

Step-by-step explanation:

Answer: # 2

Step-by-step explanation:

Answer:

(4,5)

Step-by-step explanation:

Since you move right 4 from the origin, then your x value would increase by 4, and since you're moving 5 units up from the origin, then your y value would increase by 5

The Probability of winning based on the first two flips is:P(win) = P(X = 2) + P(X = 1) = 1/4 + 1/2 = 3/4The probability of winning is 3/4.

Jeremiah created a game where he flips a fair coin 3 times. Jeremiah wins the game if he flips heads at least 2 times. What are all the possible outcomes to win, based on the first two flips

The possible outcomes to win the game, based on the first two flips, are:

Head, Head (HH)Head, Tail (HT)Tail, Head (TH)The only possible outcome that does not lead to a win is Tail, Tail (TT).

What is the probability of winning, based on the first two flips

The probability of winning, based on the first two flips, can be calculated using the binomial distribution formula:P(X = k) = nCk * pk * (1-p)n-k

Where :n = 2 (since we are considering the first two flips)k = 2 or 1 (since we need at least 2 heads to win)P(head) = p = 1/2P(tail) = 1 - p = 1/2

Substituting the values in the formula:

P(X = 2) = 2C2 * (1/2)2 * (1/2)0 = 1 * 1/4 * 1 = 1/4P(X = 1) = 2C1 * (1/2)1 * (1/2)1 = 2 * 1/2 * 1/2 = 1/2

Therefore, the probability of winning based on the first two flips is:P(win) = P(X = 2) + P(X = 1) = 1/4 + 1/2 = 3/4The probability of winning is 3/4.

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Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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Answer: Median = 42

Mean = 43.8

Step-by-step explanation:

When we have a data set of n points {x₁, x₂, ..., xₙ}

The mean is written as:

(x₁ + ... + xₙ)/N

And the median will be the value in the middle of the data set.

So first, let's write our data set in order, from least to greatest.

{36, 36, 38, 40, 40, 40, 42, 42, 43, 45, 45, 48, 48, 70}

So we have 14 values.

The middle value will be at:

(n + 1)/2

(14 + 1)/2 = 7.5

Now, counting from the left, we have that the 7.5th value is 42. (the 7th value is 42, and the 8th value is 42)

So the median is 42.

Now the mean:

M = (36 + 36 +38 +40+40+40+ 42 +42 + 43 + 45 + 45 + 48 + 48 + 70)/14

M = 43.8

Therefore, we have shown that if the statement holds true for n = k, it also holds true for n = k+1. To prove the statement using induction, we will first show that it holds true for the base case, which is n = 1.

When n = 1, the left-hand side (LHS) of the equation is ∑i=1^1 i^3 = 1^3 = 1.
The right-hand side (RHS) of the equation is 4(1^2)(1+1)^2 = 4(1)(2)^2 = 4(1)(4) = 16. Since the LHS and RHS are not equal, the statement is false for n = 1.

Now, assume the statement holds true for n = k, where k is an arbitrary integer greater than or equal to 1. We need to prove that it also holds true for n = k+1. Using the assumption that the statement is true for n = k, we have: ∑i=1^k i^3 = 4k^2(k+1)^2.

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By the principle of mathematical induction, we can conclude that the statement is true for all integers n≥1.

To prove the statement using induction, we'll follow these steps:

Step 1: Base case
Let's start by verifying the statement for the base case, n = 1.
When n = 1, the left side of the equation becomes ∑i=1^1 i^3, which is equal to 1^3 = 1.
The right side of the equation becomes 4/1^2(1+1)^2, which simplifies to 4/4 = 1.
Since both sides are equal to 1, the statement holds true for the base case.

Step 2: Inductive hypothesis
Assume the statement is true for some arbitrary value k, i.e., ∑i=1^k i^3 = (4/k^2)(k+1)^2.

Step 3: Inductive step
Now we need to prove the statement for the next value, k+1.
We start with the left side of the equation:
∑i=1^(k+1) i^3 = ∑i=1^k i^3 + (k+1)^3 (by adding the (k+1)th term)
Using the inductive hypothesis, we can substitute the expression for ∑i=1^k i^3:
= (4/k^2)(k+1)^2 + (k+1)^3
= (k+1)^2[4/k^2 + (k+1)]
= (k+1)^2[(4+4k^2)/k^2]
= (k+1)^2(4(k^2+1)/k^2)
= 4(k+1)^2(k^2+1)/k^2

Now, let's simplify the right side of the equation:
(4/(k+1)^2)((k+1)+1)^2 = 4/(k+1)^2(k+2)^2 = 4(k+1)^2(k+2)^2/k^2

Comparing the left and right sides of the equation, we see they are equal.
Therefore, the statement holds for k+1.

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We are given that Mr. Tanaka needs to dig 24 holes to put up fence posts around his lawn and he has already dug 10 holes. We can find how many holes he has left to dig by subtracting the holes he has already dug from the total number of holes.

Therefore, the equation that can be used to find how many holes, h, Mr. Tanaka has left to dig is:24 - h = number of holes left to dig Since Mr. Tanaka has already dug 10 holes, we can substitute this value in the equation:24 - h = number of holes left to dig10 holes have already been dug so the number of holes left to dig is 24 - 10 = 14.Therefore, the correct equation is:24 - h = 14or h = 10.

Moreover, the other equation given in the options are incorrect. Thus, 24 - h = 14 or h = 10 Mr. Tanaka needs to dig 24 holes to put up fence posts around his lawn. He has already dug 10 holes. In order to find out how many holes, h, Mr. Tanaka has left to dig, we need to subtract the number of holes he has already dug from the total number of holes to be dug. This can be written as:24 - h = number of holes left to dig Since Mr. Tanaka has already dug 10 holes, we can substitute this value in the equation:24 - h = number of holes left to dig10 holes have already been dug so the number of holes left to dig is 24 - 10 = 14.Therefore, the correct equation is:24 - h = 14or h = 10.

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In a triangle one side that lies on an extended line segment,  statement about x is true, x = 62 because 147−85=62 and 85 + 62 = 147. So Option B is correct

In mathematics, the triangle is a type of polygon which has three sides and three vertices. the sum of all the interior angles of the triangle is 180°

Given that,

A triangle, which has one interior angle 85° and one exterior angle 147°

Another exterior angle x = ?

It is already known that,

Sum of complementary angles are 180

So,

⇒  Y + 147 = 180

⇒  Y  = 180 - 147

⇒  Y = 33

sum of all the interior angles of the triangle is 180°

X + Y + 85 = 180

X = 180 - 85 - 33

X = 62

Hence, the value of x is 62

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Yes, we can conclude that A = B. This is because the given conditions state that the union and intersection of A and C are equal to the union and intersection of B and C, respectively.

This implies that the elements in A and B are the same, as they share the same elements with C. Therefore, A and B are equivalent, and we can conclude that A = B. The given conditions also ensure that all the elements in A and B are contained within C, so they do not affect the equality of A and B. Overall, the given conditions provide enough information to conclude that A = B. Based on the given information, we cannot definitively conclude that A = B. Although the union and intersection of A and B with C are equal, this does not guarantee that A and B are identical sets. To prove A = B, we need to show that every element in A is also in B, and vice versa. Without additional information about the specific elements in sets A, B, and C, we cannot reach a conclusion about the equality of A and B. It's possible that they are equal, but the provided conditions are not sufficient to prove it.

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Answer:

Step-by-step explanation:

A=number Adult tickets;S=A+74= number Student tickets

Total tickets=adult tickets + student tickets

724=A+(A+74)

724=2A+74 Subtract 74 from each side

650=2A divide each side by 2

325=A ANSWER 1: There were 325 Adult tickets sold

Step-by-step explanation:

gof(x)= g(f(x))

gof(x)= g(4x-1)

gof(x)= (4x-1)²+7

gof(x)=16x²-8x+1+7

gof(x)=16x²-8x+8

r = 10/ sin (0) - cos (0)

Answer:

rsin(0) - rcos(0) = 10

Step-by-step explanation:

The question is to solve the differential equation x'=2(100-x)

or, dx/dt=200- 2x

or, ∫dx/(200-2x) = ∫dt.  Now, put 200-2x=z. Or, -2dx=dz.

substituting the variables, we get

-(1/2)∫dz/z= dt

or, -(1/2) ㏑z= t + ㏑c

or, ln z= -(2t+ 2*㏑c)

or, z= (1/c²)*exp(-2t) substituting the value of x in z and 1/c²=c1

x= (200- c1* exp(-2t))/2  putting c1/2=c2

or, x= 100- (c2*exp(-2t)).

x(0) =80 or, 100-80= c2 or, c2=20

so, x= 100- (20*exp(-2t))

now x(t)=40, or, 40=100- (20*exp(-2t))

or, 60/20= exp(-2t)

or, ㏑3=-2t

or, t= -0.54

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Answer:

A

Step-by-step explanation:

edge 2021

Answer:

It is A

Step-by-step explanation:

I got it right on the test Edge 2022.

Answer is A.

edited, this is the fixed ones.

Respuesta:

Edad de Claudia = 5 años

Edad de María = 5 * 3 = 15 años

Explicación paso a paso:

Dejar :

Edad de Claudia = x

Edad de María = 3x

En 5 años :

3x + 5 = 2 (x + 5)

3x + 5 = 2x + 10

3x - 2x = 10-5

x = 5

Edad de Claudia = 5 años

Edad de María = 5 * 3 = 15 años

Answer:

B) -x

Step-by-step explanation:

distribute the 2 to -3x to get 5x + (-6x)

combine terms to get -x

The probability that Serena does not serve an ace or a double fault is 0.6, when the probability of Serena serving an ace in tennis is 0.15, and the probability that she double faults is 0.25.

The formula of the favorable outcome over the total outcomes is used to describe probability. The likelihood of flipping a coin heads is one example. Given that there is only one head and two total sides, 50% of the time, a head will land up-side-down.

Given,

Serve tennis probability = 0.15

No ace probability = 1-0.15

No ace probability = 0.85

Double fault probability = 0.25

No double fault probability = 1-0.25 = 0.75

No double fault probability = 0.75

The probability of not receiving an Ace or Double Fault: is

= 0.75 ×0.85

= 0.6.

The probability that Serena does not serve an ace or a double fault is 0.6.

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Approximately 29% of players weighing greater than or equal to 172 pounds.

To determine the percentage of players weighing greater than or equal to 172 pounds:

The box plot given summarizes the weights of players in the high school football team where the :

minimum weight is 134 pounds,

maximum weight is 189 pounds,

the median weight is 159 pounds,

the first quartile (Q1) is 148 pounds, and

the third quartile (Q3) is 174 pounds

We need to find the upper fence and calculate the percentage of values greater than or equal to the upper fence.

Upper fence = Q3 + 1.5(IQR) where IQR is the interquartile range,

which is the difference between Q3 and Q1.

IQR = Q3 - Q1IQR = 174 - 148IQR = 26

Upper fence = 174 + 1.5(26)

Upper fence = 212

Percentage of players weighing greater than or equal to 172 pounds

Number of players weighing greater than or equal to 172 pounds

= 28 - 12 = 16 (from the box plot)

Percentage of players weighing greater than or equal to 172 pounds

= (number of players weighing greater than or equal to 172 pounds / total number of players) × 100

Percentage of players weighing greater than or equal to 172 pounds

= (16 / 28) × 100

Percentage of players weighing greater than or equal to 172 pounds = 57.1%

However, the upper fence is at 212 pounds, which is greater than the maximum weight of 189 pounds in the box plot.

Therefore, we cannot include any value greater than 189 pounds in our calculation of the percentage of players weighing greater than or equal to 172 pounds.

Thus, we need to count only the number of players whose weight is between 172 and 189 pounds (inclusive).

From the box plot, we know that 4 players weigh between 174 and 189 pounds, and 12 players weigh between 159 and 174 pounds.

Therefore, the total number of players weighing between 159 and 189 pounds is 4 + 12 = 16.

Out of these, 4 players weigh between 172 and 189 pounds (inclusive)

Therefore, the percentage of players weighing greater than or equal to 172 pounds is:

Percentage of players weighing greater than or equal to 172 pounds

= (number of players weighing between 172 and 189 pounds / total number of players) × 100

Percentage of players weighing greater than or equal to 172 pounds

= (4 / 28) × 100

Percentage of players weighing greater than or equal to 172 pounds

= 14.3%

Rounded to the nearest whole number, the percentage of players weighing greater than or equal to 172 pounds is approximately 29%

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Answer: False

Step-by-step explanation:

Researchers typically report the adjusted R-squared value in addition to the regular R-squared value, not because they lack confidence in the actual R-squared, but because the adjusted R-squared provides additional information about the goodness of fit of a statistical model. The regular R-squared value measures the proportion of the variance in the dependent variable that is explained by the independent variables in the model. However, it can be biased and increase as more predictors are added to the model, even if the additional predictors do not contribute significantly to the prediction.

The adjusted R-squared, on the other hand, takes into account the number of predictors in the model and penalizes the addition of irrelevant predictors. It provides a more conservative measure of the goodness of fit by adjusting for the number of predictors and the sample size. Researchers often use the adjusted R-squared to evaluate and compare different models with varying numbers of predictors or to assess the overall explanatory power of a model while considering its complexity.

In summary, researchers report the adjusted R-squared value to address the limitations of the regular R-squared and to provide a more accurate assessment of the model's goodness of fit.

Answer:

I'm sorry, because I can only answer questions number 5

Answer:

A yes

Step-by-step explanation:

Answer:

YES, because the points fall in a straight line when plotted on a graph.

Step-by-step explanation:

To graph these numbers we can take two of the points and put them into two point form and then convert that to slope intercept form.

(2,6) and (4,12)

(y-y1) = [(y2-y1)/(x2-x1)]*(x-x1)

y-6 = [(12-6)/(4-2)]*(x-2)

y = 3x+4

Answer:

24 ft

Step-by-step explanation:

so, we don't know anything else about the triangle ?

ok, let's see.

the area of a triangle is (a side length) × (the height from that side to the opposite corner) / 2

At = 24 = side × height / 2

48 = side × height = 10 × height

height = 48/10 = 4.8 = 24/5

let's say that the height on our known side splits this side into 2 parts, p and q (p+q = 10).

we can calculate the triangle side on the right hand side of our know side by calling it a and using Pythagoras :

a² = height² + q² = (4.8)² + q² = 23.04 + q²

as all sides have to be even integers, a² has to be an even square number larger than 23.04.

and because p+q = 10, we know q must be smaller than 10, and therefore q² smaller than 100.

the only candidates for a² are therefore 36 and 64 (6² and 8²).

in a similar way this applies to the left hand triangle side b tool.

b² = height² + p² = 23.04 + p²

with the same restrictions and possible solutions as a².

we have the possibilities that a = b = 6 or 8, or a = 6 and b = 8 (or vice versa).

let's rule out a=b :

a=b wound also mean p=q=5

then

a² = 23.04 + 5² = 23.04 + 25 = 48.04, which is not an even square integer. therefore, this assumption is wrong.

so, the only possible solution is a = 6 and b = 8 (or vice versa, but it did not matter which is which, as we only need the perimeter, which would be the same either way).

proof :

36 = 23.04 + 12.96 = 23.04 + q²

=> q = 3.6 ft

64 = 23.04 + 40.96 = 23.04 + p²

=> p = 6.4 ft

p+q = 3.6 + 6.4 = 10 ft

perfect, it fits, this is the correct solution

so, the perimeter of the triangle is

10 + 6 + 8 = 24 ft

Answer:

AG = 18

Step-by-step explanation:

The relationship of the segments created is one is 1/3 (shorter) and the other (longer) is 2/3 of the total length.

Lets make x represent AG.

So, 2/3 of x is 12

or

\(\frac{2}{3}\)x = 12

Multiply both sides by the reciprocal of \(\frac{2}{3}\) , which is \(\frac{3}{2}\).

( \(\frac{3}{2}\)) \(\frac{2}{3}\)x = 12 (\(\frac{3}{2}\))  (x is left alone, the fractions = 1 when multiplied)

x = 12 (\(\frac{3}{2}\))         ( 12 times 3 = 36, divided by 2 = 18)    

x = 18

The correct answer is given by option D which is "can be used to test joint hypothesis"

Given that,

f statistics computed using maximum likelihood estimators

How do you calculate the maximum likelihood ?

Finding estimators for various distributional parameters involves using data to do so. Using some observed data, the maximum likelihood estimation (MLE) technique is used to estimate the parameters of a given distribution. When a population is known to have a normal distribution but the mean and variance are unknown, for instance, MLE can be used to estimate the mean and variance using a small sample of the population by identifying specific mean and variance values that make the observation the most likely outcome to have occurred.

The correct answer is given as it can be used to test joint hypothesis.

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