jingle bell jingle bell jingle bell rock​

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Work Shown:

F = future value

P = present value = 280

r = rate of inflation in decimal form = 0.08

t = elapsed time in years = 2

---------

F = P*(1+r)^t

F = 280*(1+0.08)^2

F = 326.592

F = 326.59

Let's check each of the

True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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Answer:

To simplify this expression, we need to combine like terms. To do that, we need to combine terms that have the same variables raised to the same powers.

First, we will combine the terms in the first set of parentheses:

(4m²n² + 6m²n)

We see that the terms have the same variables, m and n, and the same powers, 2 and 1, respectively. We can combine these terms by adding their coefficients:

(4m²n² + 6m²n) = (4 + 6)m²n = 10m²n

Next, we will combine the terms in the second set of parentheses:

(8m²n^ - 7m²n² - 13m²n)

In this case, we see that the first two terms have the same variables and powers, so we can combine them by adding their coefficients:

(8m²n^ - 7m²n² - 13m²n) = (8 - 7)m²n^ - 13m²n = m²n^ - 13m²n

We can then combine the remaining term with the first term in the expression:

m²n^ - 13m²n + 10m²n = m²n^ + (-13 + 10)m²n = m²n^ - 3m²n

Finally, we will combine the terms in the third set of parentheses:

(14m²n - 2m^n² + 9m²n)

In this case, we see that the first two terms have the same variable and power for the m variable, but the powers of the n variable are different. Since we cannot combine these terms, we will need to leave them as is. We can, however, combine the remaining term with one of the other terms:

(14m²n - 2m^n² + 9m²n) = 14m²n - 2m^n² + (9 + (-14))m²n = 14m²n - 2m^n² - 5m²n

We can then combine this expression with the previous one:

14m²n - 2m^n² - 5m²n + m²n^ - 3m²n = (14 - 1)m²n - 2m^n² - (5 - 3)m²n = 13m²n - 2m^n² - 2m²n

Finally, we have simplified the expression as much as possible:

(4m²n² + 6m²n) - (8m²n^ - 7m²n² - 13m²n) - (14m²n - 2m^n² + 9m²n) = 13m²n - 2m^n² - 2m²n

We can multiply each term in pattern A by 3 to obtain the corresponding term in pattern B. This consistent multiplication by 3 establishes the relationship between the terms in the two patterns.

To find the relationship between each pair of corresponding terms in patterns A and B, we need to identify the operation that transforms the terms in A into the corresponding terms in B.

Pattern A starts with the number 12 and subtracts 1 from each subsequent term to get the next term in the sequence:

12 - 1 = 11

11 - 1 = 10

10 - 1 = 9

9 - 1 = 8

Pattern B starts with the number 36 and subtracts 3 from each subsequent term to get the next term in the sequence:

36 - 3 = 33

33 - 3 = 30

30 - 3 = 27

27 - 3 = 24

By comparing the terms in patterns A and B, we can observe that each term in B is obtained by multiplying the corresponding term in A by a factor of 3.

For example:

12 (term in A) * 3 = 36 (term in B)

11 (term in A) * 3 = 33 (term in B)

10 (term in A) * 3 = 30 (term in B)

9 (term in A) * 3 = 27 (term in B)

8 (term in A) * 3 = 24 (term in B)

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Answer:

B) Yes

C) C = 3x + 25

Step-by-step explanation:

Given that:

Yearly charge = $25

Charge per visit = $3

The yearly cost will depend on the number of visits for the year :

B.) Cost can be represented by a linear function, as the graph it yields is a straight line graph having intercept and slope.

C.) C = mx + b

Where ;

b = intercept = yearly cost

m = slope or gradient = cost per visit

C = total cost

x = number of visits

Hence,

C = 3x + 25

Given the function

The inverse is given by

Replace f(x) with y:

Swap x with y:

Solve for y:

Factor

Answer:

the inverse of function f is, replace y with f^-1(x)

Domain of f^-1

These are the x-values of the function. First, Find undefined points

We have that x must be different from 4/7 therefore the domain is:

Answer:

in interval notation

Range of f^-1

These are the values and for which the function is defined. In this case, we have that given a function f and its inverse the domain of f becomes the range of f^-1. Therefore, we find the domain of the function f:

We have that x must be different from 5/7, so:

Combining the ranges

Answer:

the range in interval notation

The number of tickets which should be sold to $24 and $40 are 4500 and 1500 respectively.

Given, A 6000-seat theater has tickets for sale at $24 and $40.

How many tickets should be sold at each price for a sellout performance to generate a total revenue of $168,000 = ?

first, assign variables:

X = # of $24 tickets,  Y = # or $40 tickets

write equations based on the data presented:

"6000 seat theater..."

   X + Y = 6000 ...equation 1

"total revenue of 168,000"

The revenue from each type of ticket is the cost times the number sold, so:

  24X + 40Y = 168,000 .....equation 2

from equation 1:

   X = 6000 - Y

substitute this into equation 2:   (replace X with 6000-Y)

   24 (6000 - Y) + 40Y = 168,000

expand:

144,000 -24Y + 40Y = 168,000

rearrange and simplify:

    16Y = 168,000 - 144,000

    y = 24000/16

     Y = 1500

from equation 1:

     X = 6000 - 1500

     X = 4500

hence the number of tickets for sale at $24 should be 4500.

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Answer:Portion put up on Wednesday =1/12

Step-by-step explanation:

Since we are dealing with fraction

Let the total fence = 1 whole

such that fence put up on Monday = 3/4

and fence he put p on Tuesday = 1/6

Since he put up the rest on Wednesday, To find the portion put up we have that

Portion put up on Wednesday =Total portion of fence - ( Portion put up on Monday and Tuesday)

=1- ( 3/4 + 1/6)

= 1-  18+ 4/ 24

=1- 22/24

= 2/24

Portion put up on Wednesday =1/12

Answer:

Step-by-step explanation:

Answer:

\(Probability = \frac{1}{969}\)

Step-by-step explanation:

Given

\(Members = 19\)

\(Selection = 3\)

Required

Determine the probability of selecting Jim, Bruce and Valerie

First, we need to calculate the possible number of selections.

This is calculated using combination formula:

\(Selection = ^nC_r\)

\(Selection = ^{19}C_3\)

\(Selection = \frac{19!}{(19-3)!3!}\)

\(Selection = \frac{19!}{16!3!}\)

\(Selection = \frac{19 * 18 * 17 * 16!}{16! * 3 * 2 * 1}\)

\(Selection = \frac{19 * 18 * 17}{3 * 2 * 1}\)

\(Selection = \frac{19 * 18 * 17}{6}\)

\(Selection = 969\)

Selection of Jim, Bruce and Valerie is only 1 selection of the 960 possible selection.

So:

\(Probability = \frac{1}{969}\)

The probability that Jim, Bruce, and Valerie are selected in any​ order is \(\rm P=\dfrac{1}{969}\) and this can be determined by using the given data.

Given :

Assume that Jim, Bruce, and Valerie are three of the 19 members of the​ class and that three of the class members will be chosen randomly to deliver their reports during the next class meeting.

In order to determine the probability that Jim, Bruce, and Valerie are selected in any​ order, first determine the total number of possible selections.

The total number of possible selections is given by:

\(\rm S = \; ^nC_r\)

\(\rm S = \; ^{19}C_3\)

\(\rm S = \dfrac{19!}{16! \times 3!}\)

S = 969

So, the probability that Jim, Bruce, and Valerie are selected in any​ order is:

\(\rm P=\dfrac{1}{969}\)

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Answer:

0.4459

Step-by-step explanation:

Let the random age variable, X = 4.5; mean,∪ = 4.8; standard deviation, α = 2.2

By comparing P ( 0≤ Z ≤ 4,8)

P(Z ≤ X - ∪/α) = P(Z ≤ 4.5 - 4.8/2.2) = P(Z ≤ - 0.136)

Using the table: P(0≤ Z ≤ 1) = 0.0541

P(Z > 1) = (0.5 - 0.0541) = 0.4459

∴ P(Z > 4.5) = 0.4459

The required sample standard deviation for the population mean of 20, a population standard deviation of 5, and a population size of 37 is equal to 0.8333 (rounded to four decimal places).

Population mean = 20

Population standard deviation  = 5

Population size = 37

Sample size = 36

The formula for the sample standard deviation is,

s = σ / √(n)

where s is the sample standard deviation,

σ is the population standard deviation,

And n is the sample size.

Plugging in the given values, we get:

s = 5 / √(36)

⇒ s = 5 / 6

⇒ s = 0.8333 (rounded to four decimal places)

Therefore, the sample standard deviation for the given data of population mean ,population standard deviation and population size is approximately 0.8333.

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

The smallest integer in the pair is -3

Step-by-step explanation:

One way to figure this out is by looking at if it is positive or negative. In this case, -3 has a negative sign, so it is smaller

Therefore, it is -3

Hope this helps :)

Answer:

−3.375

Step-by-step explanation:

Hope this helps :)

Answer:

\(\boldsymbol{-\dfrac{35}{8}}\)

or, in decimal
-4.375

Step-by-step explanation:

\(\textrm{The expression is }\rm -1\frac{1}{2}-\left(+3\frac{1}{2}\right)-\left(-5/8\right)\)

\(\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\\-1\dfrac{1}{2} = -\dfrac{1\cdot 2+1}{2} = -\dfrac{3}{2}\\\\\\+3\dfrac{1}{2} = +\dfrac{3\cdot 2+1}{2} = +\dfrac{7}{2} = \dfrac{7}{2}\)

\(\textrm{The expression is }\rm -1\frac{1}{2}-\left(+3\frac{1}{2}\right)-\left(-5/8\right)\\= -\dfrac{3}{2}-\left(\dfrac{7}{2}\right)-\dfrac{-5}{8}\\\\\\= -\dfrac{3}{2}-\dfrac{7}{2}\right)+\dfrac{5}{8}\\\\\\\)

The LCM of 2 and 8 is 8

Multiply each term by 8 and divide the result by 8

We get for numerator:
\(8\cdot\dfrac{-3}{2} - 8\cdot \dfrac{7}{2} + 8\cdot \dfrac{5}{8}\\\\= -12 - 28 + 5 = -35\\\)

Denominator is 8

So answer is
\(\boldsymbol{-\dfrac{35}{8}}\)

In decimal that would be -4.375

Choose whichever form you like

Answer:

YES!

Step-by-step explanation:

ratios are like fractions, and fractions are basically division problems. SO, if you divide 4 by 6 you get .66666666, and if you divide 8 by 12 you ALSO get .66666666, soooooo yes they are equivalent!

Ok, so

The point slope form of the line is given by the following formula:

Where

Is a point of the line, and m is the slope.

If we replace our values:

Slope = 7

Point = (-6, 1)

We obtain that the equation is:

To find the slope intercept form of the equation, we distribute in the brackets:

And the equation of our line in the slope intercept form will be:

y=7x+43

Answer:

Answer: P = The quantity S minus l times w all divided by 0.5 times h

Step-by-step explanation:

Hope this helps.

If Mira had spent the same total amount of time but an equal amount of time on each problem, each problem would have taken around 2.36 minutes.

In the given plot, Mira spent varying amounts of time on each of the 55 math problems. To find out how many minutes each problem would have taken if Mira had spent an equal amount of time on each problem, we need to calculate the total time she spent and divide it by the number of problems.

Looking at the plot, we can estimate the total time Mira spent by counting the dots above each tick mark and multiplying them by the corresponding time interval. Let's break it down step by step:

The tick marks on the plot are at 7, 7.5, 8, 8.5, 9, 9.5, and 10 minutes per problem.

There are 2 dots above the unlabeled tick mark between 8 and 8.5 minutes per problem. We can assume it represents 8.25 minutes.

There are 3 dots above the 9.5 minutes per problem tick mark.

Now, let's calculate the total time Mira spent:

(7 * 2) + (7.5 * 2) + (8 * 2) + (8.25 * 2) + (9 * 2) + (9.5 * 3) + (10 * 2) = 129.5 minutes.

Since Mira spent a total of 129.5 minutes on 55 problems, each problem would have taken approximately 2.36 minutes (rounded to two decimal places) if she had spent an equal amount of time on each problem.

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Answer:

5,2

Step-by-step explanation:

if you look for the point 5,2 its not there

hope this helps <3

Answer:

C. 5,2

Step-by-step explanation:

We can find out the ordered pairs that are marked in the picture first before finding the correct answer.

To write an ordered pair, we follow the format: (x, y).

Thus, the ordered pairs in the picture are:

(2, 5)

(2, 3)

(3, 2)

If we check from the options, the only ordered pair not in the picture is (5, 2) so that is the answer.

In a symmetric, unimodal distribution, about two-thirds of the observations are within one standard deviation of the mean. Option A is correct.

GIven that,
To determine the appropriate options that complete the statement "In a symmetric, unimodal distribution, about two-thirds of the observations are where".

The statistic is the study of mathematics that deal with relations between comprehensive data.

Here,
From the definition of symmetric and unimodal distribution,
At least one standard deviation of the mean is two-thirds of the observation.

Thus, In a symmetric, unimodal distribution, about two-thirds of the observations are within one standard deviation of the mean. Option A is correct.

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Step-by-step explanation:

Complex Number :- The number in the form of \(a + bi \) , where \( a\) is real part and \( bi\) is the imaginary part .

On comparison ,

\(\implies a = 7 \\\\\implies b = 2i \)

Answer:

6.8333333333 or 41/6

Step-by-step explanation:

Answer:

Dawn's Flowers earned a greater rate of return than Pop's Coffeeshop

Ren's initial investment in Dawn's Flowers was greater than her initial investment in Pop's Coffeeshop.

Step-by-step explanation:

31 + 6x + x + 16 = 180

7x + 47 = 180

7x = 180 - 47

x = 133/7

x = 19

a.The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b.  the probability is 0.1399.

c. the quarterback can expect to throw about 2.27 passes before completing one.

d. the probability is 0.1865.

e. the probability is 0.7349.

The possibility or chance of an event occurring is measured by probability. The expression is given as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. Compared to occurrences with a probability closer to 0, those with a probability closer to 1 are more likely to occur.

a. To construct a probability distribution table for the number of passes attempted before the quarterback has a completion, we can use the geometric probability distribution, which is given by:

P(X=k) = \((1-p)^{k-1}\)×p

where X is the number of attempts before the completion, p is the probability of completion on each attempt, and k is the number of attempts.

The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b. The probability that the quarterback throws 3 incomplete passes before he has a completion is given by:

P(X=3) = (1-0.44)³⁻¹× 0.44 × (1-0.44)⁰

= 0.56²×0.44

= 0.1399

Therefore, the probability is 0.1399.

c. The expected number of passes that the quarterback can throw before he completes a pass is given by the formula:

E(X) = 1/p

where p is the probability of completion on each attempt.

In this case, p = 0.44, so the expected number of passes is:

E(X) = 1/0.44

= 2.27

Therefore, the quarterback can expect to throw about 2.27 passes before completing one.

d. The probability that it takes more than 5 attempts before the quarterback completes a pass is given by:

P(X > 5) = 1 - P(X <= 5)

= 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

= 1 - [0.44 + (0.56 × 0.44) + (0.56² ×0.44) + (0.56³ × 0.44) + (0.56⁴×0.44)]

= 0.1865

Therefore, the probability is 0.1865.

e. If the quarterback throws 8 passes on the opening drive, the probability that he completes at least half of them is given by the binomial probability distribution, which is given by:

P(X ≥ 4) = 1 - P(X < 4)

where X is the number of completed passes and the probability of completion on each attempt is p = 0.44.

Using the binomial probability distribution table or calculator, we can find:

P(X≥4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

= 1 - [0.56⁸ + (8× 0.56⁷×0.44) + (28 × 0.56⁶ × 0.44²) + (56× 0.56⁵×0.44³)]

= 0.7349

Therefore, the probability is 0.7349.

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The velocity represented by vector AC of Michelle's canoe is approximately option C. 11.2 miles per hour.

To determine the velocity, represented by vector AC, of Michelle's canoe, use the concept of vector addition.

Break down the motion into its components:

1. Paddling due east at 10 miles per hour: This motion can be represented by a vector pointing in the positive x-direction with a magnitude of 10 mph.

2. Wind blowing due south at 5 miles per hour: This motion can be represented by a vector pointing in the negative y-direction with a magnitude of 5 mph.

To find the resultant velocity, add these two vectors. Using the Pythagorean theorem, calculate the magnitude of the resultant velocity:

AC² = AB² + BC²

AB (paddling east) = 10 mph

BC (wind blowing south) = -5 mph (negative sign due to opposite direction)

AC² = (10 mph)² + (-5 mph)²

AC² = 100 mph² + 25 mph²

AC² = 125 mph²

Taking the square root of both sides:

AC ≈ √(125) mph

AC ≈ 11.2 mph (rounded to the nearest tenth)

Therefore, the velocity represented by vector AC of Michelle's canoe is approximately 11.2 miles per hour.

The correct answer is option C: 11.2 miles per hour.

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Answer:

A = 228 tickets

Step-by-step explanation:

We need to set up a system of equation to find the number of adult tickets sold, where A represents the adult tickets and S represents the student tickets.

Because the number of adult and student tickets together equals 506, we have A + S = 506.

Because there are 56 more student tickets than adult tickets we have A + 56 = S

And the way the system is already set up allows us to use substitution.

Thus, we have:

\(A + S=506\\A+56 = S\\\\A+A+56 =506\\2A+56=506\\2A=456\\\\A=228\\228+56=S\\278=S\)

The number of student tickets was not necessary to find in this problem, but I found anyway just in case you wanted check the work or wanted to prove the validity of the values.