What is the value of y?

Answer:

B

Step-by-step explanation:

we need to find the probability that each of the 15 customers is able to purchase the type of drink they desire from a soft-drink machine that dispenses regular Coke and Diet Coke. The machine currently has 10 cans of each type, and 60% of all purchases are diet drinks.

To calculate the probability, we consider the number of customers who want a diet drink, denoted by x. For everyone to be satisfied, the number of customers wanting diet drinks (x) must be less than or equal to the number of available diet drinks (10), and the number of customers wanting regular Coke (15 - x) must be less than or equal to the number of available regular Coke cans (10).

We can calculate the probability by summing the probabilities for all possible values of x that satisfy the above conditions. In this case, x can range from 0 to 10, since there are a maximum of 10 diet drink cans available. For each value of x, we calculate the probability as (0.6)^x * (0.4)^(15-x), since the probability of a customer wanting a diet drink is 0.6 and the probability of wanting regular Coke is 0.4.

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Answer:

\($\frac{5}{8}$\)

Step-by-step explanation:

The true statement is (b) the random variable is x, the possible values are 0 to 3 and the values are numerical

The table is added as an attachment

From the attached image, we have:

Number of girls (x)          P(x)

0                                         0.125

1                                         0.375

2                                         0.375

3                                         0.125

In the above, the random variable is x, while P(x) represents its probabilities.

Also, the possible values are 0 to 3 as shown in the table.

0 to 3 are numerical digits, and the values are numerical

Hence, the true statement is (b)

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Answer:

The answer is

Step-by-step explanation:

The area of the flower bed is larger than 10 square feet.

Hope this helps....

Have a nice day!!!!

The solution of the given exponential equation is equal to option a. x = -2.

The exponential equation is equals to,

\(2^{3x}\) = \(4^{( x - 1 )}\)

Simplify the above equation we get,

⇒ \(2^{3x}\) =  \(4^{( x - 1 )}\)

⇒ \(2^{3x}\) = \(2^{2} ^{( x - 1 )}\)

⇒ \(2^{3x}\)= \(2^{2x-2}\)

⇒ \(2^{3x}\) = 2²ˣ × 2⁻²

Now rewrite the equation as,

\(2^{3x}\) = 2²ˣ × 2⁻²

Simplify further by using the fact that

\(2^{3x}\)= 8ˣ

and 2²ˣ =  4ˣ

This implies,

8ˣ = 4ˣ ×  2⁻²

Solve for x by taking the logarithm of both sides of the equation with base 2,

log₂(8ˣ) = log₂(4ˣ ×  2⁻²)

Using the laws of logarithms, simplify the right-hand side of the equation,

⇒ log₂(8ˣ) = log₂(4ˣ) + log₂( 2⁻²)

⇒ x log₂(8) = x log₂(4) - 2

⇒ 3x = 2x - 2

⇒ x = -2

Therefore, the only real solution to the exponential equation \(2^{3x}\) = \(4^{( x - 1 )}\) is option (a) x = -2.

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The above question is incomplete, the complete question is:

Solve the exponential equation.

2^(3x) = 4^(x-1 )

a) -2

b) -1

c)  0

Answer:

145

Step-by-step explanation:

Because what you want to do is add 260 to 182 then subtract from 587. I hope that helped! :)

Answer:

19

Step-by-step explanation:

30-26.39=3.61

3.61 divided by 0.19 = 19

hope this helps :)

Answer:

5x+3x=8x

8x = 32

x=32/8 = 4

boys are 4 x 5 = 20

girls are 4 x 3 = 12

Step-by-step explanation:

Add the ratios together: 5 + 3 = 8

Divide total students by 8:

32 / 8 = 4

Multiply each ratio by 4 to find the number of each:

Boys = 4 x 5 = 20

Girls = 3 x 4 = 12

There are 20 boys.

Answer: To find the common ratio of a geometric sequence, we divide any term in the sequence by the preceding term.

In this case, dividing each term by the preceding term gives:

9/6 = 3/2

(27/2)/9 = 3/2

(81/4)/(27/2) = 3/2

Since each division result in the same value, 3/2, we can conclude that the common ratio of the sequence is 3/2.

Therefore, the answer is:

R = 3/2

Step-by-step explanation:

In regression analysis , the error term ε is a random variable with expected value of 0.

What is regression analysis?

A set of statistical procedures known as regression analysis is used to estimate the relationships between a dependent variable and one or more independent variables.

Main Body:

In regression analysis, the model in the form is called regression model.

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as regression equation.

So the answer  to error term is 0.

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The probability that the artist chosen will be a painter or a photographer is 3/4

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

To solve this exercise the formula and the procedure that we have to use for probability is:

probability= (achieving success / possible outcomes)

Achieving success = 7 painters + 5 photographer = 12

Possible outcomes = 7 painters + 5 photographer + 4 sculptors = 16

Applying the formula to calculate the probability we get:

probability= (achieving success / possible outcomes)

probability= 12/16

Simplifying:

probability= 3/4

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The equation to determine the length and width of the rug is

28 = w² + 12w

Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.

What is a rectangle?

Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

We are given a rectangular rug with an area of 28 square feet.

Also, the rug is 12 feet longer than it is wide.

So,

Let 'l' be the length of the rug and 'w' be the width of the rug

As given, Length is 12 feet longer than its width

Therefore, l = w + 12

We know Area of rectangle = Length * Width and area is given to be 28 square feet.

So,

⇒28 = (w + 12)w

⇒28 = w² + 12w

Hence, the equation to determine the length and width of the rug is

28 = w² + 12w.

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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.

Create an equation to determine the length and the width of the rug.

Answer:

y=3x+10

Step-by-step explanation:

The formula for an equation in slope-intercept is y=mx+b. m is the slope and b is the y-intercept

The 3 is the slope because it says that you have to pay that amount per game so that is the rate. 10 is the y-int because it says that you have to pay a one-time fee and a y-intercept is just once and isn't a rate.

The average rate of change for this function for the interval from x = 1

to x = 3 will be 8. Therefore option B is correct.

Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:

\(\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}\)

where when

\(x = x_1, y = y_1\\and \\x = x_2, y = y_2\)

The average rate of change can be calculated as;

From x=1 to x=3,

y = 2 and y = 18

Therefore, based on the table, when:

\(x_1 = 1 y_1 = 2 \\and \\x_2 = 3, y_2 = 18\)

Then:

\(\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}\)

\(\text{Average rate} = \dfrac{18 - 2}{3-1}\\\\\text{Average rate} = \dfrac{16}{2}\\\\\text{Average rate} = 8\)

Therefore option B is correct.

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The grid that is shaded red and blue in ratio 1 : 2 is grid (c)

The complete question is in the image

The ratio is given as:

Red : Blue = 1 : 2

There are 12 squares in each grid.

This means that:

Red : Blue = 12 * 1/(1 + 2) : 12 * 2/(1 + 2)

Evaluate

Red : Blue = 4 : 8

The grid that has 4 red and 8 blue is (c)

Hence, the grid that is shaded red and blue in ratio 1 : 2 is grid (c)

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Answer: 1/216

Step-by-step explanation:

The ratio is 1/6 so the 7th term is 216 * (1/6) ^ (7 - 1) = 1/216

The given geometric sequence 216,36,6.. So, the 7th term of the given sequence would be 1/216.

Suppose the initial term of a geometric sequence is a

and the term by which we multiply the previous term to get the next term is r

Then the sequence would look like

\(a, ar, ar^2, ar^3, \cdots\)

Thus, the nth term of such sequence would be  \(T_n = ar^{n-1}\)

The given geometric sequence

216,36,6..

r = 1/6

a = 216

we need to find the 7th term

\(T_n = ar^{n-1}\\\\T_7 = 216 \times1/6^{7-1}\\\\T_7 = 216 \times1/6^{6}\\\\T_7 = 216 \times1/ 46656\\\\T_7 =1/ 216\)

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Answer:

Step-by-step explanation:

The length of a line segment or the distance between two points can be found by using the formula

\(d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ \)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

J(-4,2) and G(146,52)

The the length of the line segment joining the points is

\( |JG| = \sqrt{ ({ - 4 - 146})^{2} + ({2 - 52})^{2} } \\ = \sqrt{ ({ -150})^{2} + ({ -50})^{2} } \\ = \sqrt{22500 + 2500} \\ = \sqrt{25000} \\ = 50 \sqrt{10} \\ = 158.11388\)

We have the final answer as

Hope this helps you

There are 11 letters in the word mathematics. The probability of selecting the letter "e" first is 1/11, which is approximately 0.091 in decimal form when rounded to the nearest thousandth.

This is because there is only one "e" in the word mathematics, and we are selecting one letter out of the 11 total letters.

To find the probability that the first letter is "e" in the word "mathematics," follow these steps:

1. Count the total number of letters in the word: There are 11 letters in "mathematics."

2. Count the occurrences of the letter "e": There is 1 "e" in "mathematics."

3. Calculate the probability: Divide the occurrences of "e" by the total number of letters.

Probability = (Occurrences of "e") / (Total number of letters) = 1 / 11

In decimal form and rounded to the nearest thousandth, the probability that the first letter is "e" in the word "mathematics" when arranged randomly is approximately 0.091.

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Answer:

0.26

Solve it, it is very easy

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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Answer:

RS = 18 units

Step-by-step explanation:

the 2 red strokes through RM and MS indicate they are congruent, that is

RM = MS = 9 , then

RS = RM + MS = 9 + 9 = 18 units

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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Answer:

-

(x + is what you are looking for is the answer

The correct line of code that completes this operator which transforms a Point by dx and dy is shown below: Point operator+(int dx, int dy) { return Point(x_+dx,y_+dy);}Note that the function operator+ takes two arguments: an integer dx and an integer dy.

The function returns a point, which is created by adding dx to x and dy to y.The completed code is shown below:class Point { int x_{0}, y_{0};public: Point(int x, int y): x_{x}, y_{y} {} int x() const { return x_; } int y() const { return y_; }};Point operator+(int dx, int dy) { return Point(x_+dx,y_+dy);}Therefore, the correct answer is: `Point(x_+dx,y_+dy)`

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Answer:

y = -x - 1

Step-by-step explanation:

As per the given correlation, the appropriate null and alternative hypothesis for calculating number of goggles is

H0 : No linear relation

H1 : there is a relation

What is meant by correlation?

In math, correlation is referred as a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate).

And it is a common tool for describing simple relationships without making a statement about cause and effect.

Based on the given question, a group of scientist randomly selected 20 piknits from the sea-floor and measured their respective weights in grams.

And we also know that, they wanted to know if the weight of the piknits can be used to predict the number of gogles.

Here from the given information, the null hypothesis : H0 : There is no linear relationship between the weight of piknits and the number of goggles

And the Alternative hypothesis : Ha: There is a linear relationship between the weight of piknits and the number of gogles

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A total of 260 license plates can be made consisting of letters followed by digits.

The fundamental counting principle states that when you have two separate events, you can multiply the number of outcomes of each event to find the total number of outcomes.

In this problem, you are trying to find the number of license plates that can be made consisting of letters followed by digits. There are 26 letters in the English alphabet, and 10 digits (0-9).

Using the fundamental counting principle, we can multiply 26 by 10 to find the total number of outcomes, which is 260. Therefore, there are 260 different license plates that can be made consisting of letters followed by digits.

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Answer:

Step-by-step explanation:

Multiply the amount by 0.46 and subtract from the amount.

The difference between amount  and 0.46 * amount is the answer.