Mathematics High School

## Answers

**Answer 1**

A line plot is a type of **graph** that displays data points as dots or markers connected by straight lines. The resultant **line plot **is given below.

What is a line plot:

A line plot, also known as a** dot plot,** is a simple way to display data that consists of a number of discrete points. It is a **one-dimensional** graph that uses dots or Xs to represent individual data points. Each dot or X represents a single data point, and the number of dots or X's at a given location on the line represents the **frequency** or count of that data point.

Here we have

Andy collects rocks and the lengths of the rocks

Rock 1 2 3 4 5 6

**length** (in) 2 7/8, 3 1/2, 2 7/8, 2 1/8, 2 1/8, 2 4/8

For simple calculations convert the given **fractions **into Improper fractions and then into decimal numbers

2 7/8 = 23/8 = 2.875

3 1/2 = 7/8 = 0.875

2 7/8 = 23/8 = 2.875

2 1/8 = 17/8 = 2.125

2 1/8 = 17/8 = 2.125

2 4/8 = 20/8 = 2.5

Now use the **coordinates** (1, 2.875) (2, 0.875) (3, 2.875) (4, 2.125) (5, 2.125) and (6, 2.5) to plot the line

Therefore,

A line plot is a type of **graph** that displays data points as dots or markers connected by straight lines. The resultant **line plot **is given below.

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## Related Questions

Please please help me!!

see the attached item for more information

### Answers

**Answer:**

Set your calculator to degree mode.

[tex] \tan(39) = \frac{12}{x} [/tex]

[tex]x \tan(39) = 12[/tex]

[tex]x = \frac{12}{ \tan(39) } = 14.818766[/tex]

So the area of this triangle is

(1/2)(14.818766)(12) = 88.91 (B)

Xe3-8xe2+18x-12 for this polynomial 2 is a zero

### Answers

Yes, 2 is a zero of the **polynomial **[tex]Xe3-8xe2+18x-12[/tex]

To determine if 2 is a zero of the polynomial [tex]Xe3-8xe2+18x-12[/tex], we can plug in 2 for x and see if the result is 0.

So, if we substitute x=2, we get:

[tex](2)^3 - 8(2)^2 + 18(2) - 12 = 0[/tex]

Simplifying this equation, we get:

8 - 32 + 36 - 12 = 0

This **equation **is true, which means that 2 is indeed a **zero **of the polynomial [tex]Xe3-8xe2+18x-12.[/tex]

Therefore, we can conclude that the polynomial can be **factored **as:

[tex](X-2)(X^2-6X+6)[/tex]

This means that the other two zeros of the polynomial are the solutions of the quadratic equation [tex]X^2-6X+6=0[/tex] which can be found using the quadratic formula.

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a survey reports that 67% of college students prefer to drink more coffee during the exams week. if we randomly select 80 college students and ask each whether they drink more coffee during exams week. what is the probability that at most 60 say that they drink coffee during exam week?

### Answers

From that 80 college students, the **probability **that at most 60 say that they drink coffee during exam week is **0.3085**

This is a binomial distribution problem in which we want to know the probability it is that at least 60 students out of 80 choose to drink coffee during test week.

Here, we have:

n = 80 (number of **trials**)

p = 0.67 (probability of **success **in each trial)

q = 1 - p = 0.33 (probability of **failure **in each trial)

x ≤ 60 (number of successes we want to find the probability for)

This probability may be calculated using the **binomial cumulative distribution function (CDF)**. The binomial CDF formula is as follows:

P(X ≤ k) = Σi=[tex]0^{K}[/tex] ([tex]_{n}C^{i} }[/tex]) * [tex]p^{i}[/tex] * ([tex](1-p)^{n-i}[/tex]

We can determine the chance of having 60 or fewer successes using this formula:

P(X ≤ 60) = Σi=[tex]0^{60}[/tex] ([tex]_{80} C^{i}[/tex]) * [tex]0.67^{i}[/tex] * [tex]0.33^{80-i}[/tex]

P(X ≤ 60) = **0.3085**

As a result, the probability that at least 60 college students claim they consume coffee during test week is 0.3085, or around **31%**. As a result,0.3085 is the correct answer.

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the in song the twelve days of christmas, my true love gave to me first 1 gift, then 2 gifts and 1 gift, then 3 gifts, 2 gifts and 1 gift, and so on. how many gifts did my true love give me all together during the twelve days?

### Answers

In a song the **twelve days** of **christmas**, my true love gave to me, then total number of possible gifts that my true love give me all together during the twelve days is equal to the 364.

We have There are twelve days of Christmas in a song and my true love gives me presents every day. We have to calculate **total number** of **gifts** my true love give me all together during the twelve days. Now, according to the song, on the first day of **Christmas** my true love gave me: a partridge on a pear tree 1 gift. On the second day of Christmas, my love really gave me: two doves and a gift. cake etc. Mathematically, gifts by true love are written as 1+2+3+... n gifts per day. Number of gifts **per day:** 1 to 1, 2 to 3, 3 to 6 and 4 to 10. The amount of mis N (N + 1) (N + 2) / 6. Number of parts This form is called **tetrahedral number**. Change the value N = 12, then N (N + 1) (N + 2) / 6

= 12 × 13 × 14 / 6

= 364

Hence, 364, the total number of gifts, almost one for each day of the year.

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how many ways are there to seat n couples around a circular table so that no couple sits together? (note: rotated seatings are considered to be the same, but reflected seatings are considered to be different.)

### Answers

Each couple can sit in two **different **seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.

Let's consider the **number **of ways to seat n couples around a circular table without any restrictions first.

Since there are 2 people in each couple, there are a total of 2n people. The number of ways to seat 2n people around a circular table is (2n-1)!/2n,

where we divide by 2n to account for rotations of the same seating arrangement.

Now, let's consider the restriction that no couple can sit together.

We can start by fixing one person in a couple, and then there are (2n-2) ways to seat the other person in that couple so that they don't sit together.

After that, we can fix another person and their partner, and there are (2n-4) ways to seat the remaining two people in their couple so that they don't sit together.

We can continue this **process **until all couples are seated.

Therefore, the total number of ways to seat n couples around a circular table so that no couple sits together is:

[tex](2n-2)(2n-4)(2n-6)...2 = 2^{n-1} * (n-1)![/tex]

We multiply by[tex]2^{n-1}[/tex] to account for the fact that each couple can sit in two different seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.

Note that reflected **seatings **are considered to be different, so we don't need to worry about dividing by 2 as we did in the unrestricted case.

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If a stock has a beta measure of 2.5, discuss what this means(be specific).

### Answers

The means of a stock that has a **beta measure** of 2.5 is 2.5%.

A beta measure of 2.5 indicates that the stock is 2.5 **times** as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

The beta measure is a **measure** of the volatility of a stock relative to the market.

If the market goes down by 1%, the stock is expected to go down by 2.5%.

Therefore,

The stock is considered to be more risky than the **average stock** in the market.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

Conversely, if the market goes down by 1%, the stock is expected to go down by 2.5%.

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the time it takes to cover the distance between two cities by car varies inversely with the speed of the car. the trip takes hours for a car moving at . how long does the trip take for a car moving at ?

### Answers

The time takes by car to cover the distance between two cities by car varies inversely with the **speed** of **car**. Total 5 **hours** will consume to complete the trip with a car moving at 40 mph.

Time is taken in traveling a particular distance is proportional to the distance traveled which means more distance covered in more time.

The speed of an object is defined as the 'distance traveled per unit time'. Formula is written as [tex]Speed(s ) = \frac{Distance(d)}{Time(t)}[/tex]

**Distance(d)** = Speed(r)×Time(t)Time(t) = Distance(d)/Speed(s)

Now, Speed of car (s) = 50 **miles per hour**

Car takes 4 hours to complete the trip. Let the distance travelled by car in 4 hour during the trip be 'x'. Applying the **speed formula, **[tex]50 mph = \frac{ x}{4 \: \: hours}[/tex]

=> x = 4 × 50 miles

=> x = 200 miles

Now, if the speed of car (s') = 40 mph in the trip. We have to determine the time taken by car to complete the trip with 40 mph speed. So, we know the speed of car and total distance travelled by car on trip. Using the **time** formula,[tex]time ( t') = \frac{distance (x) }{ speed( s')} [/tex]

=> [tex] time (t') = \frac{ 200 \: miles}{ 40 \: mph}[/tex]

= 5 hours.

Hence, required value of time is 5 hours.

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**Complete ****question ****:**** **

The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes four hours for a car moving at 50 mph. How long does the trip take for a car moving at 40 mph?

Practice & Problen In 8-13, complete each conversion. 2 8. 5 pt = C

### Answers

The value of 5 **pints** is equal to 10 cups.

A liquid measurement with a capacity of 1/8 of a gallon. If we recall, 8 ounces equals 1 cup and 2 cups (or 16 ounces) equals 1 pint. One pint is made up of 16 fluid ounces, which is also equivalent to 2 cups, 1/4 quart, and 1/8 gallon. Normally, there are 2 cups in 1 pint, however this might vary depending on the ingredients. A **pint** has two cups in it.

Two cups equal one **pint**. You must multiply the volume in pints by a factor of two to convert from pt to c.

Hence, 1 pt = 2c

Substitute the values;

Multiple both the sides by 5

5 * 1pt = 5* 2c

5pt = 10c

Therefore, The value of 5 **pints** is equal to 10 cups.

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The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.

circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent

Which of the following conclusions can we draw from the circle graph?

Together, Streetcar and Cable Car are the preferred transportation for 168 residents.

Together, Walk and Streetcar are the preferred transportation for 55 residents.

Bus is the preferred transportation for 45 residents.

Bicycle is the preferred transportation for 50 residents.

### Answers

The conclusion we can draw **graph** is: Together, Streetcar and Cable Car are the preferred transportation for 168 residents.

What is graph?

In mathematics, a graph is a **collection** of points (called vertices or nodes) connected by lines (called edges). Graphs are used to represent many kinds of relationships, such as social networks, road networks, electrical circuits, and chemical structures.

According to given information:

We can draw the following conclusions from the circle graph:

Together, Streetcar and Cable Car are the preferred transportation for 27% + 15% = 42% of the residents. To find the number of residents in this group, we can multiply 42% by the total sample size of 400:

0.42 x 400 = 168 residents.

Therefore, the conclusion we can draw is: Together, Streetcar and Cable Car are the preferred transportation for 168 residents.

We cannot conclude that Walk and Streetcar are the preferred transportation for 55 residents, as there is no overlap between the sections representing these modes of transportation on the **circle** graph.

We cannot conclude that Bus is the preferred transportation for 45 residents, as the Bus section represents only 10% of the total sample size, which corresponds to 0.10 x 400 = 40 residents.

We cannot conclude that Bicycle is the preferred transportation for 50 residents, as the Bicycle section represents only 8% of the total **sample** size, which corresponds to 0.08 x 400 = 32 residents.

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the resultant data are: forty mothers have taken the suspected drug during their pregnancies. of these mothers, 35 have delivered malformed infants. in addition, 10 other infants are born with malfunctions. the number of individuals who both did not take the drug and did not give birth to infants who were malformed was:

### Answers

No. of individuals **Suspected** drug and didn't give birth to in infants malformed is 10.

Number of **individuals **who did not take the drug and did not give birth to malformed infants.

subtract the number of individuals who took the drug and gave birth to malformed infants.

The total number of mothers, and then **subtract** the number of infants born with malfunctions.

Total number of mothers = 40

Number of** **mothers who gave birth to** malformed **infants after taking the drug = 35

Number of infants born with malfunctions = 10

the number of mothers who did not take the

drug = 40 - 35 = 5

The number of infants born without **malfunctions** = Total number of infants - Number of infants born with

malfunctions = (40 - 35) + 5 = 10

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Which of the following triangles is similar to the one shown below?

### Answers

Option C has the same **ratios **of sides as triangle ABC. Therefore, triangle DEF in option C is similar to triangle ABC.

Describe Triangles?

A triangle is a polygon with three sides and three angles. It is one of the most basic and important shapes in geometry. Triangles are classified based on the length of their sides and the size of their angles.

By side length, triangles can be classified as follows:

Scalene triangle: a triangle with all sides of different lengths

Isosceles triangle: a triangle with two sides of the same length

Equilateral triangle: a triangle with all sides of the same length

By angle size, triangles can be classified as follows:

Acute triangle: a triangle with all **angles **less than 90 degrees

Right triangle: a triangle with one angle exactly 90 degrees

Obtuse triangle: a triangle with one angle greater than 90 degrees

To determine whether two triangles are similar, we need to check if their corresponding angles are equal and their corresponding **sides **are in proportion.

Let's find the ratios of the sides of triangle ABC:

AB/AC = 7/8.5

AB/CA = 7/4

AC/CA = 8.5/4

Now let's compare these ratios to the ratios of the sides of each of the other triangles:

For option A:

DE/EF = 13/8

DE/FD = 13/17

EF/FD = 8/17

For option B:

DE/EF = 14/8

DE/FD = 14/16

EF/FD = 8/16

For option C:

DE/EF = 13/8

DE/FD = 13/17

EF/FD = 8/17

For option D:

DE/EF = 14/7

DE/FD = 14/17

EF/FD = 7/17

We see that only option C has the same ratios of sides as triangle ABC. Therefore, triangle DEF in option C is similar to triangle ABC.

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which linear optimization outcome is not possible? multiple optimal solutions are found a unique optimal solution is found solver requests to change a constraint there is an unbounded solution

### Answers

The option that **linear optimization **outcome is not possible is option (d) there is an** unbounded solution**

In linear optimization, a problem is said to be unbounded if there exists at least one** feasible solution** with an objective value that can be made infinitely large (or small) by increasing (or decreasing) the value of one or more decision variables without violating any of the problem's constraints. An unbounded solution is not a feasible or practical solution since it implies that there is no limit to how much the **objective function** can be improved.

On the other hand, it is possible to have multiple optimal solutions (a), a unique optimal solution (b), or have the solver request a change in a **constraint **(c) in linear optimization, depending on the specific problem and constraints.

Therefore, the correct option is (d) there is an unbounded solution

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your school wants to maximize their profit, P, from the sales of tickets, T, to the homecoming football game. They determine the function, P(t)=60t^2+420t-440 models the profit they can earn in hundreds of dollars in terms of price per ticket, in dollars.

### Answers

The **maximum profit** occurs at the **endpoint **t = 100, where the **profit **is $5551.20.

Maximum profit calculation

To maximize the **profit function** P(t) = 60t^2 + 420t - 440, we need to find the value of t that will give us the maximum profit.

One way to do this is to use **calculus**. We can take the derivative of P(t) with respect to t and set it equal to zero to find the critical points:

P'(t) = 120t + 420

Set P'(t) = 0 and solve for t:

120t + 420 = 0

t = -3.5

This gives us one critical point at t = -3.5. However, this value of t doesn't make sense in the context of the problem - we can't sell tickets at a negative price!

So we need to check the **endpoints **of the domain of the function, which is given by the constraint that t is greater than or equal to zero (we can't charge a negative price for tickets either).

When t = 0, P(0) = -440.

When t is very large, say t = 100, P(100) = 600000 - 44000 - 440 = 555120.

Therefore, the **maximum profit **occurs at the endpoint t = 100, where the profit is $5551.20.

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I will be given brainliest!!!!

### Answers

**Answer:2/3**

**Step-by-step explanation:**

its the only possible answer because it needs to have a scale factor below one as A'B'C'D' is smaller than ABCD

**Answer: 2/3**

**Step-by-step explanation:**

The corresponding side of AD is A'D'.

AD = 30

A'D' = 20

Scale factor = 2/3 because AD * 2/3 = A'D'

If I'm wrong, please tell me.

Simplify the factorial expressions,

### Answers

The** factorial expressions** after solving are as follows:

(A) 6! = 720

(B) 2!5! = 240

(C) 10!/7! = 720

**What are factorial expressions?**

The **product **of all positive integers less than or equal to n in mathematics is known as the factorial of a non-negative **integer**, indicated by the symbol n!.

Additionally, the factorial of n is equal to the sum of n and the subsequent smaller factorial:

For instance, According to the convention for an empty product, the value of 0! is 1.

So, solve as follows:

6!:

6*5*4*3*2*1 = 720

2!5!:

2*1 * 5*4*3*2*1 = 240

10!/7!

10*9*8*7*6*5*4*3*2*1/7*6*5*4*3*2*1 = 720

Therefore, the** factorial expressions** after solving are as follows:

(A) 6! = 720

(B) 2!5! = 240

(C) 10!/7! = 720

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a sample consists of n observations which are sorted into k frequency bins. what is the degrees of freedom for a chi-square goodness-of-fit test?

### Answers

For a **chi-square goodness-of-fit tes**t with n observations sorted into k frequency bins, the **degrees of freedom** are equal to (k - 1).

The degrees of freedom for a** chi-square goodness-of-fit test** in this scenario would be (k-1) since there are k frequency bins and the total frequency is fixed (n). The chi-square test compares the observed frequencies with the expected frequencies in each bin, and the difference between these frequencies is used to calculate the test statistic. The degrees of freedom determine the critical value of the test statistic and are based on the number of independent pieces of information used to estimate the expected frequencies.

Hi! I'd be happy to help you with your question. In a chi-square goodness-of-fit test, the degrees of freedom can be calculated using the given terms: **observations**, frequency, and chi-square. Here's the step-by-step explanation:

1. You have a sample consisting of n observations.

2. These observations are sorted into k **frequency **bins.

3. The chi-square goodness-of-fit test is used to determine how well the observed frequencies match the expected frequencies.

To calculate the degrees of freedom for this test, use the following formula:**Degrees of freedom** = (k - 1)

Where k is the number of frequency bins.

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The **degrees of freedom** (df) for a chi-square goodness-of-fit test in this scenario is k-1.

The **chi-square** goodness-of-fit test is used to test whether a set of observed frequencies fits a **theoretical distribution**.

The observed frequencies are sorted into k bins.

The test statistic is calculated by comparing the observed frequencies to the expected frequencies under the theoretical distribution, and summing the squared differences divided by the expected **frequencies**.

The degrees of freedom for the chi-square **goodness-of-fit** test is calculated as (k-1), where k is the number of frequency bins.

This is because once we have chosen the observed frequencies for k-1 of the bins, the frequency for the last bin is completely determined by the total number of observations and the frequencies in the other k-1 bins.

So, we only have (k-1) degrees of freedom to choose the observed frequencies independently.

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Please help me with this homework

### Answers

The **circumference **of a circle with a radius of 9 is 18π (or approximately 56.55) units.

What is the circumference of a circle?

The circumference of a circle can be calculated using the **formula**:

C = 2πr

where r is the radius of the **circle **and π (pi) is a mathematical constant approximately equal to 3.14.

Substituting r = 9 into the formula, we get:

C = 2π(9) = 18π

Therefore, the circumference of a circle with a **radius **of 9 is 18π (or approximately 56.55) units.

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I NEED HELP ON THIS ASAP!

### Answers

**f(x) = N * 4^x** is an exponential function that represents the number of new participants of the challenge as a function of the day number, x.

How do we calculate?

We define our variables:

N: the total number of participants on Day 1 (including Aliyah, Kim, and Reese)

r: the constant ratio by which the number of participants grows each day

x: the number of days since Day 1

r = 4.

There are **N participants **on Day 1. Each of the N participants contacts 4 new participants on Day 2, resulting in a total of **4N participants**.

Each of the 4N participants makes contact with 4 new participants on Day 3, resulting in a total of 4(4N) = 16N people. Since we can see that there are more participants every day, we can write:

f(x) = N * 4^x as an **exponential function** that represents the number of new participants of the challenge as a function of the day number, x.

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The function S(d) = √9.8d estimates the speed, S, in meters/second (m/s),

of a tsunami based on the ocean depth, d, in meters (m).

Determine the speed, in (m/s), of a tsunami at the depth of 2145 m. Round your

answer to the nearest thousandth.

### Answers

To find the speed of the tsunami at the depth of 2145 meters, you can use the given function:

S(d) = √(9.8 * d)

Plug in the value of d (2145 meters):

S(2145) = √(9.8 * 2145)S(2145) ≈ √(21001)**S(2145) ≈ 144.917**Rounded to the nearest thousandth, the speed of the tsunami at a depth of 2145 meters is approximately 144.917 m/s.

-4 ≤ x- 4 ≤ 0 graph the conjuntion ?? can someone help

### Answers

The **inequality ** is simplified as 0 ≤ x ≤ 4

Define inequality

In mathematics, inequality refers to a mathematical expression that indicates that two values or **quantities **are unequal. An inequality is represented by the symbols "<" (**less than**), ">" (**greater than**), "≤" (less than or equal to), or "≥" (greater than or equal to).

For example, the inequality "x > 5" means that the value of x is greater than 5, and the inequality "y ≤ 10" means that the value of y is less than or equal to 10.

To graph the** conjunction**, we first need to solve for x:

-4 ≤ x - 4 ≤ 0

Add 4 to all parts of the inequality:

0 ≤ x ≤ 4

Image of graph is attached below.

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select the correct answer. you are throwing darts at a dart board. you have a chance of striking the bull's-eye each time you throw. if you throw 3 times, what is the probability that you will strike the bull's-eye all 3 times?

### Answers

The probability of hitting the **bull's-eye** all three times when throwing darts can be calculated using the multiplication rule of probability as P(3 hits) = p x p x p = [tex]p^3[/tex],

where p is the probability of hitting the bull's-eye on each throw.

How to find the probability of striking the bull's-eye all 3 times?

When throwing darts at a dart board, the **probability** of striking the bull's-eye is affected by many factors, such as the player's skill, the distance from the board, the type of dart used, and so on.

However, assuming that the probability of hitting the bull's-eye is the same for each throw and independent of previous throws;

We can calculate the probability of hitting the bull's-eye all three times using the multiplication rule of probability.

Suppose the probability of hitting the bull's-eye on each throw is p. Then, the probability of missing the bull's-eye on each throw is 1 - p.

The probability of **hitting** the bull's-eye all three times can be calculated as follows:

P(3 hits) = p x p x p = [tex]p^3[/tex]

For example, if p = 0.05 (or 5%), then the probability of hitting the bull's-eye all three times would be:

P(3 hits) = 0.05 x 0.05 x 0.05 = 0.000125 or 0.0125%

This means that the chance of hitting the bull's-eye all three times is very low, and it would require a lot of skill and luck to achieve such a feat.

However, the probability of hitting the bull's-eye at least once in three throws would be much higher, and it would depend on the player's skill and consistency.

Overall, the probability of hitting the bull's-eye all three times is quite low, and it is more likely that a player will hit it once or twice or miss it altogether.

Nonetheless, the thrill of the game lies in the challenge and the **unpredictability** of each throw, making darts a popular game of skill and chance.

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Average movie prices in the United States are, in general, lower than in other countries. It would cost $78.40 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $74.05. How much does an average movie ticket cost in each of these countries?

### Answers

Solving the **equations **we get the average cost of movie tickets for **Japan is $17.42** and **Switzerland is $13.07.**

What is equation?

An equation is a mathematical statement which is made by two expressions connected by an equal sign. For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.

Let, the cost for 1 movie ticket in Japan = $x

the cost for 1 movie ticket in Switzerland = $y

It would cost $78.40 to buy three tickets in Japan plus two tickets in Switzerland.

So the first **equation **will be,

3x+2y= 78.40 ------------(1)

Three tickets in Switzerland plus two tickets in Japan would cost $74.05

From this the 2nd **equation **will be,

2x+3y= 74.05 --------------(2)

Multiplying **equation (1) **by 2 and multiplying **equation (2) ** by 3 we get,

6x+4y= 156.8 --------------(3)

6x+9y= 222.15 ------------(4)

**equation **(4)- (3) gives,

5y= 65.35

y= 13.07

putting this value in **equation (1) **we get,

x= (78.40- 2× 13.07)/ 3

= 17.42

Hence, the average cost of movie tickets for Japan is $17.42 and Switzerland is $13.07.

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the number of seconds it takes an individual to read a news story is normally distributed with a population standard deviation of 33 seconds and an unknown population mean. a random sample of 16 readers is taken and results in a sample mean of 334 seconds. what is the correct interpretation of the 99% confidence interval? select the correct answer below: we estimate with 99% confidence that the sample mean is between 313 and 355 seconds. we estimate with 99% confidence that the true population mean is between 313 and 355 seconds. we estimate that 99% of the readers read a news story between 313 and 355 seconds.

### Answers

The 99% **confidence interval** is, ( 314 , 358 )

Given that,

** sample mean** = x = 334

sample **standard deviation** = s = 33

sample size = n = 16

**Degrees of freedom** = df = n - 1 = 16-1 = 15

At 99% confidence level the t is ,

α = 1 - 99% = 1 - 0.99 = 0.01

α / 2 = 0.01 / 2 = 0.005

t_α /2,df = t0.005,15 = 2.9467

Margin of error = E = t_α/2,df * (s /√n)

= 2.9467 * (33 / √16)

**Margin of error** = E = 24

The 99% **confidence interval **estimate of the population mean is,

x - E <u< x + E

334 - 24 < u < 334 + 24

310 < u < 358

so, we get,

The 99% **confidence interval** is,

( 314 , 358 )

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I need a bit of help please

### Answers

The** slope** of the line in the **reduced form** is 4 / 7.

How to find the slope of a line?

The** slope** of a line is the change in the dependent variable with respect to the change in the **independent variable**.

Therefore,

slope = m = change in y / change in x

slope = m = y₂ - y₁ / x₂ - x₁

P = (2, 3)

Q = (9, 7)

x₁ = 2

x₂ = 9

y₁ = 3

y₂ = 7

Therefore,

**slope** = 7 - 3 / 9 - 2

slope = 4 / 7

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I need help with this question

### Answers

The **value** of C of is 49/4

What is completing the square?

**Completing** the **square** is a technique for converting a quadratic polynomial of the form to the form for some **values** of h and k. In other words, completing the **square** places a perfect square trinomial inside of a quadratic expression.

10k²+7k+C , to find the **value** of c that will make the expression a perfect **square** we divide b by 2 and **Square** it.

Since b = 7

therefore c =( b/2)²

c = (7/2)² = 49/4

therefore the **value** of C is 49/4.

The expression can now be written as;

10k²+7k +49/4

and it can be simplified as;

40k²+28k +49

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Hello solve this, what is 9 x 5/7

### Answers

Answer: 6 3/7

Step-by-step explanation:

9/1 x 5/7

If we multiply the numerators and denominators, we get 45/7 or 6 3/7 as a mixed number.

**Answer:**

[tex]\frac{45}{7}[/tex] or 6.4285

**Step-by-step explanation:**

First, multiply 9 and 5, which gives you 45.

9(5)=45

Then, divide 45 by 7.

45/7=6.4285

That gives you [tex]\frac{45}{7}[/tex] or 6.4285

Hope this helps!

The function g(x) is shown on the graph.

The graph shows an upward opening parabola with a vertex at negative 4 comma 3, a point at negative 6 comma 7, and a point at negative 2 comma 7.

What is the equation of g(x) in vertex form?

g(x) = (x − 4)2 − 3

g(x) = (x − 4)2 + 3

g(x) = (x + 4)2 − 3

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

### Answers

The equation of g(x) in **parabola** vertex form is g(x) = (x + 4)^2 + 3. Option (D) is the correct answer.

**Parabola calculation.**

Since the vertex of the** parabola** is at (-4, 3), we can write the equation of the parabola in vertex form as:

g(x) = a(x + 4)^2 + 3

where "a" is a constant that determines the shape of the parabola. Since the parabola opens upward, "a" must be positive.

We also know that the parabola passes through the points (-6, 7) and (-2, 7). Substituting these values into the equation above, we get:

7 = a(-6 + 4)^2 + 3

7 = 4a + 3

4a = 4

a = 1

Substituting "a = 1" into the equation above, we get:

g(x) = (x + 4)^2 + 3

Therefore, the equation of g(x) in vertex form is g(x) = (x + 4)^2 + 3. Option (D) is the correct answer.

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create an expression that is equivalent to 9(3× + 5 + ×) without using parentheses

### Answers

**Answer: After solving the given expression, the equivalent expression will be 36x + 45.**

**Step-by-step explanation: sorry if wrong**