Suppose we select one 2015 Spotify user at random
and record his or her age and whether his or her favorite music genre is pop.
(a) Draw a tree diagram to model this chance process.
(b) Find the probability that the person identifies his or her favorite music genre as pop.
(c) Suppose the chosen person identifies his or her favorite music genre as pop. What’s the probability
that he or she is aged 13–24?

Answer:

gotchu.

c = 36

Step-by-step explanation:

First add five to each side.

c/4 = 9

then you multiply by four:

c=36

Answer:

The answer to that question is 58

The expressions that have 3 as the greatest common factor are b + 3 + 6c, 27n + 66p, and 36 - 9j + 6k.

Thus,

b + 3 + 6c         - Yes

-30 - 24z           - No

27n + 66p         - Yes

36 - 9j + 6k       - Yes

From the question, we are to determine if 3 is the greatest common factor of the given expressions

b + 3 + 6c

3(b + 1 + 2c)

The greatest common factor is 3

-30 - 24z

6(-5 -4z)

The greatest common factor is not 3. The greatest common factor is 6

27n + 66p

3(9n + 22p)

The greatest common factor is 3

36 - 9j + 6k

3(12 - 3j + 2k)

Thus, The greatest common factor is 3

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We know that it took 18 hours to drive 666 miles. If we divide the distance by the hours (666 miles)/(18 hours)

We find that 666/18= 37 miles per hour . which means we travel 37 miles each hour.

So, we can estimate that driving 37 miles it will take 1 hour (the distance to Chicago).

Answer:

666/18=37miles/hour

it would take 1 hour to drive 37 miles

Answer:

2xy

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

intercept the x- intercept

Answer:

Step-by-step explain

x-intercept: 2.8 hours

y-intercept: 0.7 . . . . fraction of power remaining

Step-by-step explanation:

The equation is in slope-intercept form, so the y-intercept can be read directly: 0.7.

To find the x-intercept, set y=0 and solve for x:

0 = -0.25x +0.7

0.25x = 0.7 . . . . . add .25x

x = 2.8 . . . . . . . . . multiply by 4 (that is, the reciprocal of 0.25)

The x-intercept is 2.8; the y-intercept is 0.7.

Answer:

3.14159265359

Step-by-step explanation:

The required solution in interval notation is [−5,2].

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

Set of such values is called solution set to the considered equation or inequality.

Assuming we want to solve for x the result can vary.

We are given to find the solution to the following compound inequality in interval notation.

Inequality Form:

−5 ≤ x ≤ 2

Thus, the required solution in interval notation is [−5,2].

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An employee has a probability of 0.19706 to make between $70,000 and $80,000

Probability is the potential for an event to occur or occur, and it indicates the likelihood that a statement is true. It is a field of mathematics where the probabilities of experiments happening are computed. We can determine everything from the likelihood of getting heads or tails when tossing a coin to the likelihood of making a research error, for instance, using a probability. It's formula is = number of favorable outcomes/total number of outcomes

Let X be the annual salary of employees in a large company.

Given the mean salary is $65,000 and the standard deviation is $6,000, the probability of making between $70000 and 80000 can be calculated as:

\(P(70000 < X < 80000)\) = \(P(\frac{70000 - 65000}{6000} < z < \frac{80000 - 65000}{6000} )\)

\(P(0.833 < z < 2.5)\)

= 0.99379 - 0.79673 (from normal distribution table)

= 0.19706

Hence, the probability that an employee makes between $70,000 and $80,000 is 0.19706

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Answer: 5089.38

Step-by-step explanation:

Answer:

40ft per minute

Step-by-step explanation:

Just simply divide 5 into 200

The odds for the ball landing in an odd-numbered slot = 9/19

The odds against the ball landing in an odd-numbered slot = 10/19

From the 38 slots, the slots numbered 0 and 00 are even. Then the numbers from 1 to 36 has 18 odd and 18 even numbers.

So there are a total of 20 even numbers and 18 odd numbers.

The odd for the ball landing in an odd-numbered slot is the probability to get an odd slot from the 38 slots.

SO, P( odd slot) = Number of odd slots/ Total number of slots

                          = 18/38

                          = 9/19

The odds against the ball landing in an odd-numbered slot is the probability of getting an even numbered-slot out of the 38 slots.

Hence, P(even slot) = Number of even slots / Total number of slots

                                 = 20/38

                                 = 10/19

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Answer:

36 pi

Step-by-step explanation:

The radius is 6

A = pi r^2

A = pi 36

Answer:

Area of circle = 36 π square unit

Step-by-step explanation:

To calculate area of circle simplify formula area of circle . we have given radius of circle which is 6.

Area of circle = π × r²

where,

substitute the value

Area of circle = π × ( 6 ) ²

expand the exponent

Area of circle = π × 36

multiply

Area of circle = 36 π square unit

Answer:

Height and Base is 5 units, for 3:1 make the base and height 15 units, and for 50% make the base and height 2.5 units

Step-by-step explanation:

Count how many boxes the side length takes on both sides.

3:1 means your new shape is going to be three times as big, so multiply the height and base by 3.

50% of your original is half of 5, giving you 2.5 units for your base and height length.

The data in the accompanying table of 36 diamonds includes the price (in dollars), the weight (in carats), and the clarity grade of the diamonds. The diamonds have clarity grade either VS1 or VVS1. VVS1 diamonds are nearly flawless; VS1 have more visible (but still small) flaws. The results of the two-sample t-test to compare the prices of VS1 and VVS1 diamonds are as follows: Sample statistic, Two-sample t-statistic, P-value, Interpretation.

Sample statistic: The difference between the sample means of the two groups is x₁ - x₂ = -56.78 (rounded to two decimal places).

Two-sample t-statistic: The calculated t-value is -2.301 (rounded to three decimal places).

P-value: The p-value associated with the t-statistic is 0.0300 (rounded to four decimal places).

Interpretation: Based on the p-value, which is less than the commonly used significance level of 0.05, we can conclude that there is statistically significant evidence to suggest that there is a difference in prices between VS1 and VVS1 diamonds.

The negative value of the sample statistic indicates that, on average, VS1 diamonds have lower prices compared to VVS1 diamonds. This aligns with the definitions of the categories, as VVS1 diamonds are considered to have a higher clarity grade and are expected to command higher prices.

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The equation that represents the linear function is y = 2x.

A linear equation is in the form:

y = mx + b

Where y, x are variables, m is the rate of change and b is the y intercept.

Let us assume that from the table, we get the data with points (0, 0) and (2, 4). Hence:

\(y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{4-0}{2-0} (x-0)\\\\y=2x\)

The equation that represents the linear function is y = 2x.

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Answer:

Step-by-step explanation:

answer is -10

The probability of getting at least one nun in three spins of a dreidel is approximately 0.578

The probability is the ratio of number of favorable outcomes to the total number of outcomes

The probability of getting no nuns in a single spin is 3/4, since there are three non-nun letters (Gimel, Hei, Shin) and four total letters.

The probability of getting no nuns in three spins is then (3/4)^3, since the spins are independent and we can multiply probabilities of independent events.

So the probability of getting at least one nun in three spins is

= 1 - (3/4)^3

= 1 - 0.421875

= 0.578125

Therefore, the probability of getting at least one nun is 0.578

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The given question is incomplete, the complete question is:

A dreidel is a four-sided spinning top with the Hebrew letters nun, gimel, hei, and shin, one on each side. Each side is equally likely to come up in a single spin of the dreidel. Suppose you spin a dreidel three times. Calculate the probability of getting (a) at least one nun?

f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given f(x) and  g(x) two polynomial functions in the standard form of the polynomial,

According to Closure Property, when something is closed, the output will be the same as the input.

The polynomials f(x) and g(x) can be seen in the image.

On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.

Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.

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Complete question:

If Hanna is recovering hundreds of treasure chests from an ancient shipwreck. The ratio of chests recovered to time is always 3:1, since Hanna recovers 9 chests every 3 hours.

The table showing the number of treasure chests recovered by Hanna over time, assuming she can recover 9 chests every 3 hours:

Time (hours)     Number of Treasure Chests

3                              9

6                              18

9                              27

12                              36

15                              45

18                              54

21                              63

24                              72

27                              81

30                              90

33                              99

36                              108

39                              117

42                              126

45                              135

48                              144

51                              153

54                              162

57                              171

60                              180

As you can see, the ratio of chests recovered to time is always 3:1, since Hanna recovers 9 chests every 3 hours.

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The equation of the line through the points (0, 9) and (3, 0) is y = -3x + 9.

To find the equation of a line passing through two given points, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is one of the points on the line and m is the slope of the line.

First, we calculate the slope (m) using the formula: m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points. Substituting the values (0, 9) and (3, 0), we get m = (0 - 9)/(3 - 0) = -9/3 = -3.

Next, we choose one of the points, let's say (0, 9), and substitute its coordinates into the point-slope form: y - 9 = -3(x - 0).

Simplifying the equation, we get y - 9 = -3x, or rearranging it, y = -3x + 9.

Therefore, the equation of the line passing through the points (0, 9) and (3, 0) is y = -3x + 9.

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In statistical experiments, each time the experiment is repeated, a different outcome may occur. The correct answer is C.

Statistical experiments involve random processes, such as the random selection of individuals from a population, the random assignment of subjects to groups, or the random measurement of a variable.

The outcome of a statistical experiment is influenced by chance and is inherently uncertain, so it is not possible to guarantee that the same outcome will occur every time the experiment is repeated. Different outcomes may occur, even if the experimental conditions are kept constant, due to the random nature of the processes involved.

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The value of x in the given figure is 10.

In the given triangle,

∠ADC = ∠BDC =  90°

Hence the triangles ΔACD and ΔBCD are right-angle triangles. Thus we can apply Pythagoras' theorem in both triangles.

So in ΔACD,

CB² = BD² + DC²

And in ΔBCD,

CA² = AD²+ DC²

But, CA = 15 and CB = x + 5

So, (x + 5)² = BD² + DC²

15² = AD² + DC²

⇒225 = AD² + DC²

Here, BD = AD as given in the figure

Replacing BD with AD in the first equation we get,

(x + 5)² = AD² + DC²

Now, equate the values of AD² + DC² to obtain the value of x,

(x + 5)² = 225

⇒ x² + 25 + 10x = 225

⇒ x² + 10x - 200 = 0

⇒ x² + 20x - 10x - 200 = 0

⇒x(x + 20) - 10(x + 20) = 0

⇒(x + 20)(x - 10) = 0

Thus x = -20, 10

Hence the value of x is 10.

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Answer:

8 , 32 AND 14

Step-by-step explanation:

4x +3y =5 -------> eq (1)

2x -5y =9 -------> eq(2)

eq(2) * -2 --------> -4x +10y =-18 ------->eq(3)

eq(1) + eq(3) -----> 13y =13 ----> y=1 <>

then When you substitute y=1 into any equation

x=7

Answer:

x=2ln(2)/(2ln(2)-ln(3))

Step-by-step explanation:

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

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

(x-1)ln(4)=xln(3)

ln(4)x-ln(4)=xln(3)

ln(4)x=ln(3)x+2ln(2)

2ln(2)x-ln(3)x=2ln(2)

(2ln(2)-ln(3))x=2ln(2)

Therefore, x=2ln(2)/(2ln(2)-ln(3))

Answer:

4.819 =x

Step-by-step explanation:

4^(x-1) = 3^x

Take the log of each side

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

We know that log a^b = blog a

(x-1)  log 4 = x log (3)

Distribute

x log 4 -log 4 = x log 3

Subtract x log 4 from each side

x log 4 - x log 4 -log 4 = x log 3 - x log 4

- log 4 = x log 3 - x log 4

Factor out -x

- log 4 =- x ( log 4- log 3)

Divide by -1

log 4 = x (log 4 - log 3)

Divide each side by  (log 4 - log 3)

log 4 /  (log 4 - log 3) = x

4.81884167930641800 =x

Round to the nearest thousandth

4.819 =x

Zelma is 28 years old and her son is 10 years old. We brought this conclusion with the help of algebra.

Let x = son's age now

Then, x+18 = Zelma's age now

x-1 = son's age one year ago

x+17 = Zelma's age one year ago

x+17 = 3(x-1)

x+17 = 3x-3

   2x = 20

     x = 10

Algebra is the study of variables and the rules for manipulating these variables in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables as if they were numbers and is therefore essential in all applications of mathematics.

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