GAVIN WANTS TO HAVE HIS BIRTHDAY AT THE BOWLING ALLEY WITH A FEW OF HIS FRIENDS, BUT HE CAN SPEND NO MORE THAN $78. THE BOWLING ALLEY CHARGES A FLAT FEE OF $42 FOR A PRIVATE PARTY AND $4.50 PER PERSON FOR SHOE RENTALS AND UNLIMITED BOWLING.

Answer:

90°/• is the probability

The value of the expression x²+1/x²  is 18

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Given here: x²-4x=1

simplifying we get

x²-4x=1

Dividing both sides by x we get

x²/x-4x/x=1/x

x-4=1/x

x-1/x=4

Now squaring both sides we get

(x-1/x)²=4²

x²-2×x×1/x+1/x² =16

x²+1/x²=16+2

x²+1/x²=18

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Answer:

Step-by-step explanation:

The slope of the line passing through the points (0,2) and (6,6) can be found using the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (0, 2) and (x2, y2) = (6, 6)

slope = (6 - 2) / (6 - 0)

slope = 4 / 6

slope = 2/3

Therefore, the slope of the line is 2/3.

The probability that x is between 25 and 30 is 0.087.

The cumulative distribution function (CDF) of an exponential distribution with mean 25 is given by:

F(x) = 1 - exp(-x/25)

The probability that x is between 25 and 30 can be found by evaluating the CDF at x = 30 and x = 25 and subtracting the two values:

P(25 < x < 30) = F(30) - F(25) = (1 - exp(-30/25)) - (1 - exp(-25/25))

= (1 - exp(-1.2)) - (1 - exp(-1))

= 0.255 - 0.368

= 0.087

So, the probability that x is between 25 and 30 is 0.087.

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Answer: 50%

Step-by-step explanation: There is an equal chance of both events occurring so there is a half chance for it to occur or no.

Answer:

( 11 )y + ( 1 )z

Step-by-step explanation:

8y + 3y

5z - 4z

True, a simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.

What does standard deviation mean ?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.

                                Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

What does a simple random sample mean?

A subset of participants is randomly chosen from a population by the researcher using simple random sampling, a sort of probability sampling.

                          The probability of being chosen is the same for every person in the population. Then, data are gathered from as much of this randomly selected subgroup as possible.

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I'll do problem 8 to get you started.

Part (a)

To find the mean, we first add up the values

1.53+1.49+1.60+1.65+1.90+1.43 = 9.6

Then divide over 6 since this is the number of values in the set.

9.6/6 = 1.6

==================================================

Part (b)

The shortest boy is 1.43 meters tall. If he leaves the group, then we have these heights leftover

1.53, 1.49, 1.60, 1.65, 1.90

Adding them up gets us

1.53+1.49+1.60+1.65+1.90 = 8.17

Then divide by 5

8.17/5 = 1.634

Using percentages we can conclude that out of 800 people, 20% of the people who attended the football match were teenagers, 160.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.

If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.

A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction.

Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

So, we know that:

800 people attended the football game.

20% were teenagers.

Then, the number of teenagers was:

= 800/100*20

= 8*20

= 160

Therefore, using percentages we can conclude that out of 800 people 20% of the people who attended the football, match were teenagers, and 160 were.

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Point slope form is y - y1 = m ( x - x1 ), where m represents the slope, y1 represents the y value of the point, and x1 represents the x value of the point.

filling in the variables with the given information gives you

y - (-5) = -1 ( x - 1 ) which is also y + 5 = -1 ( x - 1)

Answer:

Step-by-step explanation:

7x + 19 = cost rent and electricity

2x - 7 = cost of rent only

cost of electricity only = (7x + 19) - (2x - 7) = 5x + 26

5x + 26 < 100

5x < 74

x < 74/5

x < $14.80

Using permutations and combinations, we know that a total of 60,060 different arrangements of flowers can be made in a row.

The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations.

When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination.

Examples of permutations include arranging persons, digits, numbers, alphabets, letters, and colors.

Examples of combinations include choosing the menu, the cuisine, the clothes, the subjects, and the team.

So, we have:

3 yellow, 4 red, and 6 blue flowers.

3 + 4 + 6 = 13

Now, the number of arrangements in the row will be:

= 13!/3!4!6!

= 6,22,70,20,800/6*24*720

= 6,22,70,20,800/1,03,680

= 60,060

Therefore, using permutations and combinations, we know that total of 60,060 different arrangements of flowers can be made in the row.

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Answer:

51 3/4 %

Step-by-step explanation:

The number 5 will be placed in the middle.

In order to make the sums across and down equal, we have to arrange the numbers in such a way that they balance each other out. We know that the middle number will be the average of the four numbers surrounding it.

So, if we place 2 and 8 on either side of the middle number, the sum of these two numbers is 10. To make the sum equal, we need two more numbers that add up to 10. The only two numbers that fit the criteria are 4 and 6.

Hence, the middle number will be the average of 4 and 6, which is 5. So, the answer is 5.

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--The given question is incomplete; the complete question is

"Place the numbers 2, 4, 5, 6, and 8 in the circles so that the sums across (horizontally) and down (vertically) are equal. Which number will you place in the middle?"--

Answer:

[tex]\mbox{\large \boxed{ 0.98}}[/tex]

Step-by-step explanation:

Cos H = ratio of the base to the length of the hypotenuse

In this triangle, the base = 40, hypotenuse = 41

cos H = 40/41 = 0.9756

To the nearest hundredth this would be 0.98

Answer:

x = 2.33

Step-by-step explanation:

3x - 4 = 3

3x = 7

x = 7/3

x = 2.33

The answers for questions G, H, K, and L are the same as questions C, D, K, and L, respectively, because the speed (65mi/h) remains constant.

A. 65 miles in one hour: If a car is traveling at 65 miles per hour (mi/h), then in one hour it will travel 65 miles.

B. 340,800 feet in one hour, 65 miles is equal to 5,280 x 65 = 340,800 feet.

C. 5,680 feet in one minute, 340,800 feet ÷ 60 = 5,680 feet in one minute.

D. 94.67 feet in one second, 5,680 feet ÷ 60 = 94.67 feet in one second.

E. 42 miles in one hour: If a car is traveling at 42 miles per hour, then in one hour it will travel 42 miles.

F. 221,760 feet in one hour, 42 miles is equal to 5,280 x 42 = 221,760 feet.

G. 5,680 feet in one minute.

H. 94.67 feet in one second.

I. x miles in one hour.

J. 5,280 x x feet in one hour:

K. (5,280 x x) ÷ 60 feet in one minute.

L. ((5,280 x x) ÷ 60) ÷ 60 feet in one second.

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There are 5,280 feet in a mile. Round answers to the nearest unit.

A. How many miles does a car traveling at 65mi/h go in one hour?

B. How many feet does a car traveling at 65mi/h go in one hour?

C. How many feet does a car traveling at 65mi/h go in one minute?

D. How many feet does a car traveling at 65mi/h go in one second?

E. How many miles does a car traveling at 42mi/h go in one hour?

F. How many feet does a car traveling at 42mi/h go in one hour?

G. How many feet does a car traveling at 65mi/h go in one minute?

H. How many feet does a car traveling at 65mi/h go in one second?

i. How many miles does a car traveling at x mi/h go in one hour?

J. How many feet does a car traveling at x mi/h go in one hour?

K. How many feet does a car traveling at x mi/h go in one minute?

L. How many feet does a car traveling at x mi/h go in one second?

Step-by-step explanation:

x = number of years after 2007.

x = 0 for 2007.

PC(x) is a function that calculates how many pounds of chicken the average adult will eat every year (x) after 2007 (up to 2012).

PC(x) = 0.8x + 52

0 <= x <= 5

in 2007 (x = 0) the average adult ate 52 pounds.

in every year after 2007 until 2012 0.8 pounds get added to the amount of the previous year.

so, in 2012 (x = 5) the average adult will eat

PC(5) = 0.8×5 + 52 = 4 + 52 = 56 pounds of chicken.

Answer:

12

Step-by-step explanation:

i hope this is right I suggest you double check

Answer:

450

Step-by-step explanation:

the speed of mass is 450

Answer:

Step-by-step explanation:

The distance across the lake is 190m. Rounding to the nearest hundredth of a meter, the answer is 190.00m.

We can use similar triangles to find the distance across the lake (DE). Since triangle CGF is similar to triangle CED, we can use ratios of the sides to find DE.

Let's call DE = x. Then, we have:

CE/FG = x/142.1

Solving for x, we have:

x = (CE * 142.1) / FG

CE = CF + FD = 130 + 60 = 190m

x = (190 * 142.1) / 142.1 = 190m

The distance across the lake is 190m. Rounding to the nearest hundredth of a meter, the answer is 190.00m.

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The complete question is :

To indirectly measure the distance across a lake, Dominic makes use of a couple landmarks at points D and E. She measures CF, FD, and FG as marked. Find the distance across the lake (DE), rounding your answer to the nearest hundredth of a meter.

There are 5040 ways to arrange these seven leaders in a row. There are 1440 ways to arrange these seven leaders in a row, so that the leader of japan and the leader of canada stand next to each other.

Using the multiplication principle, we multiply all the possible arrangements to determine the total number of configurations if we have seven individuals and want to know how many ways there are to place them in a row of seven seats. For instance, the first seat has seven alternatives, the second has six (as one has been taken), the third has five, the fourth has four, and so on.

So, these seven leaders in a row, so that the leader of japan and the leader of canada stand next to each other.

6! * 2! = 720 * 2 = 1440 .

To arrange these seven leaders in a row we just have to find,

7! = 7x6x5x4x3x2x1

= 5040

These two configurations are both permutations. Therefore, in the case, there are only two potential permutations.

It becomes more difficult if there are seven of us. The multiplication concept must be applied.

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The probability of a student being chosen at random and taking exactly one language class is 65%.

Probability is the likelihood or chance of an event happening. In this case, the event is a student taking exactly one language class.

First, we need to find the total number of students taking at least one language class. We have 28 students in the Spanish class, 26 students in the French class, and 16 in the German class. However, some students are taking multiple classes, so we need to subtract these students from the total. The 12 students taking both Spanish and French, 4 taking both Spanish and German, and 6 taking both French and German should only be counted once. In addition, the 2 students taking all three classes should also only be counted once.

So, the total number of students taking at least one language class is

=> 28 + 26 + 16 - 12 - 4 - 6 + 2 = 40 students.

To find the number of students taking Spanish only, we need to subtract the number of students taking both Spanish and French (12) and the number of students taking both Spanish and German (4) from the number of students taking Spanish (28).

So, the number of students taking Spanish only is

=> 28 - 12 - 4 = 12 students.

Similarly, the number of students taking French only is

=> 26 - 12 - 6 = 8 students

and the number of students taking German only is

=> 16 - 4 - 6 = 6 students.

Finally, to find the probability of a student being chosen at random and taking exactly one language class, we divide the number of students taking exactly one language class by the total number of students taking at least one language class.

So, the probability of a student taking exactly one language class is

=> (12 + 8 + 6) / 40 = 26 / 40 = 0.65 or 65%.

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Complete Question:

An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. The classes are open to any of the 100 students in the school. There are 28 students in the Spanish class, 26 students in the French class,, and 16 in the German class. There are 12 students that are in both Spanish and French, 4 that are in both Spanish and German, and 6 that are in both French and German. In addition, there are 2 students taking all 3 classes.

If a student is chosen randomly, what is the probability that he or she is taking exactly one language class?

Both BODMAS and PEMDAS are valid and in use in various parts of the globe. In the UK, BODMAS is frequently utilized, whereas in the US, PEMDAS is. Brackets, Order, Division, Multiplication, Addition, and Subtraction are all referred to as BODMAS.

The acronym PEMDAS, which stands for parenthesis, exponents, multiplication and division from left to right, as well as addition and subtraction from left to right, can be used to recall the order of operations. Start by using parenthesis first.

For the list of operations, we wish to create an expression.

9 to the second power raised then, determine the ratio between the outcome and z

First, raise 9 to the second power.

9 divided by two equals

Find the product of the result and z in step two.

Today, quotient refers to "division."

The outcome of step 1 is =[tex]9^2[/tex]

Therefore:

Indicator of and z

As a result, the statement that describes the specified order of operations is [tex]\frac{9^2}{z}[/tex]

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Answer:

Hi There! Here's your answer.

Keeping a healthy weight will lower your risk of stroke, according to the 95% confidence interval of (0.54, 0.62), which suggests that if the survey were conducted repeatedly, 95% of the intervals produced would represent the real population percentage of individual, who are aware of this.

In other words, there is a 95% confidence interval between 0.54 and 0.62 for the genuine population fraction of those who are aware of this knowledge.

It should not be assumed from this range that 95% of respondents indicated that they were aware of this knowledge.

Instead, it offers a range of numbers that, with a given level of certainty, are likely to include thee genuine population percentage.

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The slope is negative two thirds, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases two thirds of an inch every hour. The solution has been obtained by using the concept of slope.

What is a slope?

In mathematics, a line's slope is the ratio of the change in the y coordinate to the change in the x coordinate.

We are given that the graph of the line passes through (0,8) and (3,6) .

So,

Slope of the line = (6 - 8) ÷ (3 - 0) = -2/3

From this, we get the equation of line as

y - 6 = -2/3 (x - 3)

Now, for y-intercept, we need to put x = 0

So, we get

⇒y - 6 = -2/3 (-3)

⇒y - 6 = 2

⇒y = 8

Hence, the slope is negative two thirds, and the y-intercept is 8.

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The required error interval for y(probability of picking two green

apples) is  [1/4, 1/4].

The probability of picking two green apples can be calculated by multiplying the probability of picking a green apple on the first pick by the probability of picking another green apple on the second pick, given that the first pick was a green apple.

Let's call the number of green apples in the crate G, and the number of red apples in the crate R. Based on the given information, the ratio of green to red apples is 2:1, so we have G = 2R.

The probability of picking a green apple on the first pick is G/(G + R), and the probability of picking a green apple on the second pick, given that the first pick was a green apple, is (G-1)/(G + R - 1).

Therefore, the probability of picking two green apples is:

y = (G/(G + R)) * ((G-1)/(G + R - 1)) = (G/(G + R))²

Since we know that G = 2R, we can substitute that into the equation for y to get:

y = (2R/(2R + R))² = (2/(3R + R))² = (2/4R)² = 4/16 = 1/4

So the error interval for y is [1/4, 1/4].

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Answer:

-7/8

Step-by-step explanation:

slope = Δy/Δx = (-2 - 5) / (8 - 0) = -7/8