How to find the indicated probability? Please show your work. Thanks!

Answer:

B.No. It describes the​ midrange, not the median.

Step-by-step explanation:

Further,

The range is the difference between the least and largest value of data. It measures skewness using all data points.

Mean is calculated as the ratio of the sum of all the observations to the total number of observations.

Median is the middle value of the data after arranging them in ascending order.

Answer:

  67 points

Step-by-step explanation:

To find the difference between the winning and losing scores, subtract the losing score from the winning score:

  50 -(-17) = 50 +17 = 67

The difference is 67 points.

Answer:

She needs 300 mililiters of Solution B so that the resulting mixture is a 12% alcohol

Step-by-step explanation:

In this problem you have to take into account that when you are talking about solutions you can't just add the porcentaje because each percentaje represent how many mililiters of the total of the solution are, in this case of alcohol.

So for solving this problem we are first going to establish the variables, because it si solved using a system of equations. In that way we are going to say that:

VT: represents the total volume of the resulting mixture of solution A and solution B at 12% of alcohol

VA: represent the mililiters of solution A, in the problem they say that this value it equals to 400 ml

VB: Represent the mililiters of solution B, that is what we need to find.

From now on, we are just going to use this variables but always keep in mind what does they represent.

VaT: Represent the total volume of alcohol in the resulting mixture solution at 12%

VaA: Represent the volume of alcohol in solution A

VaB: Represent the volume of alcohol in solution B

What comes next? we need to describe the equations from the information we have so that we create a system that can be solve after.

What can we first say about the total volume (VT)? That it is the result of the adition of solution A and B so we can state the following equation:

VT = VA + VB

As we know that VA equals to 400ml we can replace to get:

1) VT = 400ml + VB

But what happens with the other information we have? We now need to take into account the concentration of each solution, so as we can´t add the percentages of alcohol but we can add the volumes of alcohol in each solution we can say that:

2) VaT = VaA + VaB

Now we are going to start to reduce the number of variables changing does that we don't know for those that we do to solve the problem, starting first with the volumes of alcohol.

A porcentaje represents a part of the total volume so to know how much alcohol does each of the solutions has we must do rules of three so that we can leave all the variables in terms of VT, VA and VB:

- VT  → 100%

VaT → 12%

VaT = [tex]\frac{12.VT}{100}[/tex] = 0,12.VT

- VA  → 100% In this case we know that VA = 400

VaA → 6%

VaA = [tex]\frac{6x400}{100}[/tex]

VaA = [tex]\frac{6x4}{1}[/tex]

VaA=24ml

VaB  → 100%

VaB → 20%

VaB = [tex]\frac{20.VB}{100}[/tex] = 0,20.VB

Now we are going to replace this information in the equation number two to get the following expresion:

3) 0,12.VT = 24ml + 0.20VB

At this point we have a system of two equations (remember equation 1) with two variables VT and VB so we are going to do some algebra to clear the variables.

- Replace VT of equation 1 in equation 3

Remeber that VT = 400ml + VB so now we are going to put this information in equation 3) 0,12.VT = 24ml + 0.20VB to get:

4) 0,12 (400ml + VB) = 24ml + 0.20VB

- Use the distributive operation to solve the parentesis

0,12x400ml + 0.12.VB = 24ml + 0.20VB

5) 48ml + 0.12VB = 24ml + 0.20VB

- Organize the information in one side the ones with variables and in the other side just numbers:

0.12VB - 0.20VB = 24ml - 48ml

-0.08 VB = -24ml (do the operations)

As it is a minus in both sides we can divide it and cancel the sign to have:

0,08VB = 24 ml (to clear VB, we must divide in both sides by 0,08)

[tex]\frac{0,08.VB}{0,08} = \frac{24ml}{0.08}[/tex] after doing the division we get:

with this you already get the answer of how many mililiters of solution B does she use to get a resulting mixture of 12%.

To verficate we must do the following process:

VT = 300ml + 400ml = 700ml

The total volume of the solution is 700 ml of which 12% equals to:

VaT = 0,12. VT = 0,12(700ml) = 84 ml

VaA = 24ml (Volume of alcohol in solution A, we already calculated)

VaB = 0,20 VB = 0,20(300ml) = 60ml (Volume of alcohol in solution B)

VaT = VaA + VaB  (Prove the equation with the values we obtain)

84ml = 24ml + 60ml

84 ml = 84ml

As the equation is the same we have verificated our result.

Robyn needs to use 300 mL of Solution B to achieve a 12% alcohol solution when mixed with 400 mL of Solution A. This was calculated by setting up an equation based on the concentrations and solving for the quantity of Solution B.

To solve this problem, we need to find out how much Solution B (20% alcohol) Robyn needs to add to 400 mL of Solution A (6% alcohol) to get a 12% alcohol solution.

Step-by-Step Solution

First, let's set up the equation assuming she uses x milliliters of Solution B:

Since Solution A is 6% alcohol, in 400 mL of Solution A, there is:

Next, for Solution B, which is 20% alcohol, the amount of alcohol in x mL of Solution B is:

We need the resulting mixture to have a 12% concentration. The total volume of the mixture will be:

The total amount of alcohol in this mixture will be 12% of the total volume:

Simplify and solve for x:

So, Robyn needs to use 300 mL of Solution B.

Answer:

  1152 in²

Step-by-step explanation:

Barack can change the units using a suitable multiplier. It will have a numerator equal to its denominator, and will have units that cancel the square feet and give square inches:

  8 ft² × ((12 in)/(1 ft))² = 8×12×12 in² = 1192 in²

_____

12 in = 1 ft . . . so numerator is equal to denominator

Answer:

1) x = 6, y = -2 + 1/3x

2)

Step-by-step explanation:

1) x-3y=6

-3y=6-x, 6-x/-3y

y = -2 + 1/3x

x - 3(-2+1/3x) = 6

x - 6 + x = 6

2x =12

x = 6

2) x=3y+4

-3y = -x+4

y = -x/-3 +4/-3

y = 1/3x + -4/3

x = 3(1/3x + -4/3)

I am unsure about x on number two...

Answer:

  Multiply the number of cans by the volume of each: 12,000 oz.

Step-by-step explanation:

You find the total volume of more than one can by adding the volumes of the cans involved.

For 2 cans, the volume would be ...

  12 oz + 12 oz = 24 oz

__

When you consider adding numbers more than a couple of times, you start looking for ways to simplify the effort. Multiplication was invented for that purpose. Here, multiplying the volume of 1 can by 1000 is the same as adding the volumes of 1000 cans.

For 1000 cans with volume of 12 oz each, the volume of the total is ...

  1000 × 12 oz = 12,000 oz.

Answer:

  -11a +5

Step-by-step explanation:

(5a-6a-4) -(7a+3a-9) = a(5-6-7-3) -4+9 = -11a +5

Answer:

1)3/4 cups of pasta

2)4

Step-by-step explanation:

1) as malik I use half the cups better divide the initial amount 3/4 by 2

C=[tex]\frac{3}{2} .\frac{1}{2} =3/4[/tex]

2)

As Malik use 6 cups, and each plate needs 3/2 cups, we divide 6 by 3/2

C=[tex]\frac{ \frac{6}{1} }{ \frac{3}{2} }=\frac{6.2}{3} =\frac{12}{3} =4[/tex]

Answer:

when x= -7

h(-7) = (-7)^2 -5

= (-1)^2*(7)^2-5

= 1*49-5

= 49-5

=44

Therefore , h(-7)=5

Answer:

h(- 7) = 44

Step-by-step explanation:

To evaluate h(- 7) substitute x = - 7 into h(x), that is

h(- 7) = (- 7)² - 5 = 49 - 5 = 44

The survey design described is a statistical study on college student eating habits, specifically focusing on sweet potato consumption, to obtain quantitative data about behaviour patterns.

The student in question is surveying to gather data on a particular behavioural pattern, in this case, the frequency of sweet potato consumption among college students. To achieve results that reflect the larger student body of the college, a random sample of 200 students is selected to answer the survey question. Completing the survey comprises the collection of quantitative data, which can later be analyzed statistically. Surveys are a common method in statistics to investigate various questions and hypotheses. For example, a survey similar to this might be performed to evaluate the number of movies students watch in a week or determine the daily average study time for freshmen students. The effectiveness of the survey method relies on a representative sample accurately reflecting the population of interest.

Answer:

[tex]2^{12}=4,096[/tex]

Step-by-step explanation:

You know that [tex]3x-y=12[/tex] and have to find

[tex]\dfrac{8^x}{2^y}[/tex]

Use the main properties of exponents:

1. [tex](a^m)^n=a^{m\cdot n}[/tex]

2. [tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex]

Note that

[tex]8=2^3,[/tex]

then

[tex]7^x=(2^3)^x=2^{3\cdot x}=2^{3x}[/tex]

Now

[tex]\dfrac{8^x}{2^y}=\dfrac{2^{3x}}{2^y}=2^{3x-y}[/tex]

Since [tex]3x-y=12,[/tex] then [tex]2^{3x-y}=2^{12}=4,096[/tex]

Final answer:

The value of the expression [tex]\(\frac{8^x}{2^y}\)[/tex] given the equation 3x - y = 12 is 4096, since 8 can be expressed as 2^3 and the properties of exponents allow us to simplify the expression to 2^12.

Explanation:

The question involves determining the value of a mathematical expression given a specific equation.

Given the equation 3x - y = 12, we want to find the value of [tex]\(\frac{8^x}{2^y}\)[/tex].

This can be done by recognizing that 8 is a power of 2, specifically 8 = 2^3.

Thus, [tex]\(8^x = (2^3)^x = 2^{3x}\)[/tex]. Substituting back into the original expression, we get [tex]\(\frac{2^{3x}}{2^y}\)[/tex].

Using the properties of exponents, when dividing terms with the same base, we subtract the exponents: [tex]\(2^{3x - y}\)[/tex].

Since we know 3x - y = 12, we substitute 12 in place of 3x - y, giving us 2^12.

Therefore, the answer is 2^{12}, or 4096.

In 12 days both geysers erupt on the same day again

The smallest number that is a multiple of each of two or more numbers.

Given:

A geyser Erupts every fourth day.

Another geyser erupts every sixth day.

so, to find how many days will both geysers erupt on the same day again

we have to find the LCM of 4 and 6

So, 4 = 2*2

6= 2*3

LCM (4, 6) =2*2*3 = 12

Hence,  12 days  both geysers erupt on the same day again.

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Answer:

Step-by-step explanation:

First you would multiply 12 by four since each person has to have a ticket ($48) next you would multiply 4.50 by two since they bought two buckets of popcorn ($9) then you would multiply 4.75 by four since they each bought their own drink ($15) then you would all three of those totals together to get the final cost of everything ($72)

Hoped that answered your question!

Answer:

$92.75

Step-by-step explanation:

Krystal and 4 friends were going to the movies.

Total person = 5

The cost of each ticket = $12.00

They bought 2 buckets of popcorn at $4.50 each

They all bought soda at $4.75 each.

Total money they spent = (12 × 5) + (4.50 × 2) + (4.75 × 5)

                                        = 60 + 9.00 + 23.75

                                        = $92.75

They spent $92.75 in total.

Answer: [tex]\dfrac{2}{5}[/tex]

Step-by-step explanation:

Given : The proportion of students have a dog : [tex]P(D)=\dfrac{45}{100}[/tex]

The proportion of students have a cat  : [tex]P(C)=\dfrac{30}{100}[/tex]

The proportion of students have  both a dog and a cat  : [tex]P(C\cap D)=\dfrac{18}{100}[/tex]

Now, the conditional probability that a student who has a dog also has a cat will be :-

[tex]P(C|D)=\dfrac{P(C\cap D)}{P(D)}\\\\\\\Rightarrow\ P(C|D)=\dfrac{\dfrac{18}{100}}{\dfrac{45}{100}}\\\\\\\Rightarrow\ P(C|D)=\dfrac{18}{45}=\dfrac{2}{5}[/tex]

Hence, the probability that a student who has a dog also has a cat = [tex]\dfrac{2}{5}[/tex]

Answer:

3/5

Step-by-step explanation: I just did the test and got it right. This was after I tried 2/5 and got it wrong.

Answer:

  r = 29

Step-by-step explanation:

We assume your diagram is showing ...

To find r, use the relationship between the side lengths of the triangle.

__

In a 30°-60°-90° triangle, the ratio of shortest to longest sides is 1 : 2. Therefore, we have ...

 CD/CA = r/(r+29) = 1/2

  2r = r +29 . . . . . . multiply by 2(r+29)

  r = 29 . . . . . . . . . .subtract r

_____

The knowledge of 30°-60°-90° triangle relationships can come from any of several sources. One such source is consideration of what happens when you cut an equilateral triangle along its altitude. (The short side is half the long side of the resulting 30-60-90 triangle.)

Another source is the sine ratio of the 30° angle (trigonometry). Sin(30°) = CD/CA = 1/2.

Answer:

a^4 - a^3 + a^2 - 2a - (2)/(a + 1)

The simplified form of (a⁷ - a⁴) ÷ (a³ + a²) is a³ - a⁴.

The given expression is: (a⁷ - a⁴) ÷ (a³ + a²)

To simplify it:

Factor out common terms: a⁴(a³ - 1) / a²(a + 1)

Cancel out common factors: a⁴(a³ - 1) / a²(a + 1) = a³ - a⁴

Therefore, the simplified form of (a⁷ - a⁴) ÷ (a³ + a²) is a³ - a⁴.

Answer: 90 Earth years.

Step-by-step explanation:

Analizing the information provided in the exercise, you need to find the Least Common Multiple (LCM) of the given numbers.

You can follow these steps:

1. You must descompose 6, 9, 15 and 18 into their prime factors:

[tex]6=2*3\\\\9=3*3=3^2\\\\15=3*5\\\\18=2*3*3=2*3^2[/tex]

2. Finally, you need to choose the commons and non commons with their greatest exponents and multiply them. Then you get:

[tex]L.C.M=2*3^2*5=2*9*5\\\\L.C.M=90[/tex]

Therefore, it will take 90 Earth years for them to all line up.

Answer:

As the x-values go to positive infinity, the function’s values go to positive infinity.

Step-by-step explanation:

With the information given you can plot a rough graph (see attachment)

As the x-values go to positive infinity, the function’s values go to positive infinity. -> True

As the x-values go to zero, the function’s values go to positive infinity. -> False, x = 0 is between a maximum and a minimum

As the x-values go to negative infinity, the function’s values are equal to zero. -> False x-values go to negative infinity, the function's values go to positive infinite

As the x-values go to negative infinity, the function’s values go to negative infinity. False x-values go to negative infinity, the function's values go to positive infinite

Answer: As the x-values go to positive infinity, the function’s values go to positive infinity.

Step-by-step explanation:

just did this

Did you ever get the answer for this?

Answer:

The order is Congruent, not congruent, not congruent, not congruent,congruent, not congruent

Step-by-step explanation:

-

Answers and explanations:

87. The domain of added functions includes the restrictions of both. So the range of the added function in this question is [-4, 3]

88. When finding the domain of a divided function we do the same as adding, but with an extra rule: g can't equal zero. So for this question the domain is (-4, 3)

89. To graph f + g you add the y-values for each x-value. I added a picture to help explain this one!

Answer:

87. [-4, 3]

88. (-4, 3)

89. See Attachment

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

*Notes:

Step 1: Define

Identify the domains of each function.

Domain of f(x): [-4, 3]

Domain of g(x): [-5, 5]

Step 2: Find 87.

Determine the x-values for each function that overlap/intersect.

f(x) and g(x) have intersect from -4 to 3.

Domain f + g: [-4, 3]

Step 3: Find 88.

Determine the x-values for which g(x) = 0.

The function g(x) equals 0 at x = -4 and x = 3. Therefore, these x-values are excluded in the domain.

Domain of f/g: (-4, 3)

Step 4: Find 89.

To draw a graph of the f + g, we must combine the y-values for each x-value domain in a t-chart and plot by hand.

x   |   f(x)          x   |  g(x)          x   |  f + g

-4     5             -4     0             -4      5

-3     4             -3      1             -3      5

-2     3             -2     2             -2      5

-1      3             -1      2             -1       5

0      2             0       1             0       3

1        1              1       1              1       2

2      -1             2       1              2      0

3      -3             3      0             3      -3

Answer:

Step-by-step explanation:

1+|2+x|=9

1+|2+x| -1 =9-1

|2+x| = 8

2+x = 8 or 2+x = -8

x=6 or x= -10

Answer:

c

Step-by-step explanation:

i took the k12 test

Answer:

a. The dependent variable for this study is the "number of colds each individual experiences during the 3-month winter season" because it depends on the doses of vitamins and placebo.

b. The dependent variable is discrete because the number of colds is like 1,2,3,... so on.

c. The scale of measurement of the dependent variable is Ratio because the number of cold experiences can be 0.

Answer:

The required probability is : [tex]\frac{1}{15}[/tex]

Step-by-step explanation:

Three married couples have purchased theater tickets and are seated in a row consisting of just six seats.

First we will check the total arrangements that is 6! ways.

6! = [tex]6\times5\times4\times3\times2\times1=720[/tex]

Jim and Paula can sit at far left in 2 ways and the remaining 4 in 4! ways,.

So, probability will be = [tex]2\times\frac{4!}{6!}[/tex]

= [tex]2\times\frac{24}{720}[/tex]

= [tex]\frac{48}{720}[/tex]

= [tex]\frac{1}{15}[/tex]

Answer:

  35 years

Step-by-step explanation:

The proportion p that remains after y years is ...

  p = (1/2)^(y/5.27)

In order for 1/100 to remain (the level decays from 100 times to 1 times), we have ...

  .01 = .5^(y/5.27)

  log(0.01) = y/5.27·log(0.5) . . . take logs

  y = 5.27·log(0.01)/log(0.5) ≈ 35.01 ≈ 35 . . . . years

Given that the radioactive isotope cobalt-60 has a half-life of 5.27 years, it will take around 36.89 years for it to decay to a level that is safe for human habitation, assuming the initial level is 100 times the safe limit.

The subject of this question is the half-life of radioactive substances, specifically cobalt-60. The half-life is the time it takes for half of the radioactive atoms to decay. Cobalt-60 has a half-life of 5.27 years. This implies that 50% of the cobalt-60 will remain after 5.27 years, 25% will remain after 10.54 years (two half-lives), 12.5% will remain after 15.81 years (three half-lives), and so forth.

Understanding this concept, we can calculate when the region will be habitable. Currently, the radiation level is 100 times the acceptable limit. We need to determine how many half-lives it will take for the radiation level to reduce to 1% i.e., 1/100 of its original level. Since each half-life reduces the radiation by half, this is equivalent to finding when the cobalt-60 will be reduced to a fraction of 1/(2^n), where 'n' is the number of half-lives. Using n = 7 gives us 1/128, which is less than 1/100 (it will need to be less to be within safe levels).

So, it will take approximately 7 half-lives for the area to become safe for human habitation again. Since the half-life of cobalt-60 is 5.27 years, it will therefore take about 7 * 5.27 = 36.89 years for the region to become habitable once more.

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Answer:

See below.

Step-by-step explanation:

For the triangle to be a right triangle there must be a pair adjacent sides which are at right angles to each other - that is whose slope product = -1.

Slope of AB = (4-2)/(-6- -3) = -2/3.

Slope of BC = (8-4)/ (1 - - 6) =  2/7

Slope of AC =  (8-2) / (1 - -3) = 6/4 = 3/2.

Now 3/2 * -2/3 = -1 so sides AB and AC are at right angles and the 3 points are the vertices of a right triangle.

To confirm if the points A (-3, 2), B (-6, 4) and C (1, 8) are vertices of a right triangle, we use the Pythagorean theorem. After calculating the distances between each pair of points, we found that the square of the length of the longest side equals the sum of the squares of the lengths of the other two sides, proving that they form a right triangle.

To show that the points A (-3, 2), B (-6, 4), and C (1, 8) are vertices of a right triangle, we need to check if the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the lengths of the other two sides. This is known as the Pythagorean theorem. First, compute the distances between each pair of points using the distance formula:

AB = sqrt[(4-2)^2 + (-6-(-3))^2] = sqrt[2^2 + (-3)^2] = sqrt[4 + 9] = sqrt[13]

BC = sqrt[(8-4)^2 + (1-(-6))^2] = sqrt[4^2 + 7^2] = sqrt[16 + 49] = sqrt[65]

AC = sqrt[(8-2)^2 + (1-(-3))^2] = sqrt[6^2 + 4^2] = sqrt[36 + 16] = sqrt[52]

BC is the longest side, so we need to check if BC^2 = AB^2 + AC^2. Calculating, we find that 65 = 13 + 52, which is true. Therefore, points A, B, and C are vertices of a right triangle.

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To calculate the total area of two rectangular rooms, we multiply the length by the width of each room separately and then add the two results together. The formula used is Total Area = (width1 × length1) + (width2 × length2). This demonstrates a practical application of geometry in everyday situations.

The student's question is about calculating the total area of two rectangular rooms given their lengths and widths. To find the area of a rectangle, we multiply its length by its width. Therefore, to find the total area of both rooms, we calculate the area of each room separately and then add the two areas together. The formula for the total area of the two rooms would be:

Total Area = (width1 × length1) + (width2 × length2)

By inserting the specific values for width1, length1, width2, and length2 into this formula, we can calculate the exact total area covered by both rooms.

This approach utilizes basic principles of geometry to combine the areas of the two spaces, providing a clear example of how mathematical concepts are applied in practical situations like room measurements.

Answer:

The answer to your question is:

Step-by-step explanation:

1.-  1.09                                              In the table the order will be

2.- 0.99                                            1.- 6

3.- 0.919                                           2.- 10

4.- 0.66                                            3.- 7

5.- 0.647                                          4.- 11

6.- 0.394                                          5.- 5

7.-  0.298                                         6.- 4

8.- 0.256                                         7.- 9

9.- 0.23                                           8.- 8

10.- 0.136                                        9.- 1

11.- 0.112                                          10.- 2          11.- 3

The tension when the length is 0.3 meters and the number of vibrations is 12 is 40.96 Kg.

Given, that number of vibrations 'n' per second of a nylon guitar string varies directly with the square root of the tension 'T' and inversely with the length 'L' of the string.

Formulating the relation,

[tex]n \alpha \frac{\sqrt{T} }{L}[/tex]

[tex]n = K\frac{\sqrt{T} }{L}[/tex]

[tex]L \times n = K\sqrt{T}[/tex]

Substitute the values,

T = 256 Kg

n = 15

L = 0.6

[tex]0.6 \times 15 = K \times \sqrt{256}\\K = 9/16\\K = 0.5625\\[/tex]

Now when L = 0.3 and n = 12,

[tex]0.3 \times 12 = 0.5625 \times \sqrt{T}\\\sqrt{T} = 6.4\\ T = 40.96[/tex]

Therefore tension in the string is 40.96Kg .

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Answer:

  c.  7,999,999

Step-by-step explanation:

The number of possible phone numbers is the product of the number of possible digits in each position, less the excluded number:

  8·10·10 · 10·10·10·10 - 1 = 8,000,000 -1 = 7,999,999