In how many ways can the seven members of a students’ council pose in a line for a yearbook photograph if the chair and vice-chair must be side by side?

The distance between the points (-3, -2) and (-6, 5) is 7.62 units.

We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

d = √( (x₁ - x₂)² + (y₂ - y₁)²)

So here, the distance between (-3, -2) and (-6, 5) will be:

d = √( (-3 + 6)² + (-2 - 5)²)

d = √( 58) = 7.62

The distance between the points  X(−3,−2) and Y(−6,5) is 7.62 units.

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a. The real annual interest rate is 1.6%

b. He made $14871 after 25 years in account.

What is the interest rate?

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate. The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.

Here, we have

Given: A taxpayer who pays 22%  in taxes each year has these two accounts. Account 1: $10000 is placed in a tax-deferred account that pays 2.1%  interest compounded annually for 25 years. Account 2:  $10000 is placed in a taxable account that pays 3.1%  interest compounded annually for 25 years.

b. His real annual interest rate is the interest rate decreased by the product of the interest rate and the tax rate.

Actual annual interest rate = 2.1% - (22% × 2.1%)

= 1.6%

Hence, the real annual interest rate is 1.6%

c. P = $10000 , n= 25, r = 1.6%

Compound interest = p(1+(r/100))ⁿ

= 10000(1+(1.6/100))²⁵

= $14871

Hence, he made $14871 after 25 years in account.

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Answer: az-bz+3b²-6ab+3a²

Step-by-step explanation: math whay

45 kg of one nut and 45 kg of another nut should be mixed in order to get 60 kg of a mixture worth $4.80kg.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

One nut = x kg

Cost = $5

Other nuts = y kg

Cost = $4.20

Now,

From the given statement we can make two equations.

x + y = 60

x = 60 - y

Substituting here,

5x + 4.20y = 4.80

5 (60 - y) + 4.20y = 4.80 x 60

300 - 5y + 4.20y = 288

300 - 288 = 5y - 4.20y

12 = 0.8y

y = 12/0.8

y = 15

Now,

x = 60 - 15

x = 45

Thus,

45 kg of one nut and 45 kg of another nut.

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Answer:

13/40

Step-by-step explanation:

Total No of pupils = 40

No of pupils who play the flute = 15

No of pupils who play the Piano = 7

No of pupils who play both = 5

Total No of pupils who can play the atleast one instrument = 15+5+7= 27

No one pupils who play neither instrument = 40 - 27 = 13

Probability of a pupil being chosen at random who plays neither instrument = No of Pupils who play neither instrument/ Total No of pupils = 13/40

Therefore the answer will be 13/40

An equation in standard form of a line that has a slope of 4 and passes through the point (-4, -4) is y = 4x + 12.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-4, -4), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-4) = 4(x - (-4))

y + 4 = 4(x + 4)

y + 4 = 4x + 16

y = 4x + 16 - 4

y = 4x + 12

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a) The new production rate is 1008 items per week.

b) The new unit cost is $63.

A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.

a) The new production rate can be calculated by increasing the old production rate of 900 items per week by 12%.

New production rate = 900 items/week + 12% of 900 items/week

New production rate = 900 items/week + (12/100) x 900 items/week

New production rate = 900 items/week + 108 items/week

New production rate = 1008 items/week

So, the new production rate is 1008 items per week.

b) The new unit cost can be calculated by reducing the old unit cost of $75 by 16%.

New unit cost = $75 - 16% of $75

New unit cost = $75 - (16/100) x $75

New unit cost = $75 - $12

New unit cost = $63

So, the new unit cost is $63.

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The question seems incomplete, the missing part has been below:

A factory produces 900 items per week at a unit cost of $75 new equipment is installed that increases productivity by 12% and reduces the unit cost by 16%.

a) What is the new production rate?

b) What is the new unit cost?

Answer:

See below

Step-by-step explanation:

What is margin of error?

Since it is impossible to predict results of a statistical survey on a sample population  with 100% accuracy, scientists often include an error in estimation along with the calculated proportion

This margin of error tells you how many percentage points your results will differ from the real population value

Answer:26

Step-by-step explanation: Base one plus Base 2 divided by 2

Answer:

Step-by-step explanation:

We know that

[tex]sin^2a+cos^2a = 1[/tex],
so if we rearrange that and solve for [tex]cosa[/tex] then we get
[tex]cosa[/tex] = ± [tex]\sqrt{1-sin^2a}[/tex]

Answer:

x= 8

Step-by-step explanation:

17x+14+4x-2= 180

21x= 168

x= 8

Answer:

brainliest plss

Step-by-step explanation:

The Least Common Multiple (LCM) of 60 and 72 is 360

Answer:8750

Step-by-step explanation:

I did 5000 times .25(1/4 as a decimal) which equals 1250. Then 1250 times 3(year) equals 3750. 5000 plus 3750 is 8750

The point at which the graphs of the equations would intersect is given as follows:

(-2, -1).

The point at which the two functions would intersect is the solution to the system of equations in this problem.

The equations are given as follows:

Multiplying the first equation by 2, we have that:

Adding the two equations, the solution for y is obtained as follows:

-3y = 3

3y = -3

y = -1.

Hence the solution for x is obtained as follows:

3x - 4(-1) = -2

3x + 4 = -2

3x = -6

x = -2.

Hence the point is:

(-2, -1).

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By applying the relative frequency concept, we make this table to represent the relative frequency of the problem:

                                Lunch order

                  Sandwich      Pasta      Total

Volleyball        27%            21%        49%

Swimming       37%            14%         51%

Total                64%            36%       100%

Relative frequency is a percentage number that states the amount of data in a certain group.

Relative frequency is given by the number of desired outcomes, also called frequency, divided by the number of total outcomes.

We already have the following information:

                                        Lunch order

                        Sandwich       Pasta         Total

Volleyball              19                15               34

Swimming             26               10               36

Total                      45               25              70

Now we want to find the relative frequency and put it into the following table:

                                                            Lunch order

                            Sandwich                      Pasta                        Total

Volleyball     19/70*100% = 27%     15/70*100% = 21%    34/70*100% = 49%

Swimming    26/70*100% = 37%    10/70*100% = 14%    36/70*100% = 51%

Total             45/70*100% = 64%    25/70*100% = 36%  70/70*100% = 100%

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Based on the given ratio, the number of teachers at Still Bay Middle School, who have earned their master's degrees, is 18.

The ratio is the relative size of a value compared to another.

Ratios are depicted as percentages, fractions, or decimals, to show that they are fractional values, representing a portion of a whole.

The ratio of teachers who have earned their master's = 3/5

The total number of teachers at the school = 30

The number of teachers with masters = 18 (30 x 3/5)

The number of teachers without masters = 2/5 (1 - 3/5)

= 12 (30 x 2/5)

Thus, since 3 out of 5 teachers at Still Bay Middle School have earned their master's degrees, the number is 18 if there are 30 teachers at the school.

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The system of equations will be:-

6y=4x-18

9y=6x-27

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

For a system to have an infinite number of solutions, the slopes and y-intercepts of the slope must be the same.

We have that one of the equations of the system is 3y = 2x – 9.

We generate another equation that has the same slope and y-intercept by just multiplying through by a non-zero constant.

Let us multiply by 2.

2(3y = 2x – 9)---->6y=4x-18

Or multiply through by 4 to get:

3(3y = 2x – 9)----->9y=6x-27

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Answer:

I don't know the answer.

Step-by-step explanation:

Sorry. ;(

As per unitary method Lower Yosemite Falls is 292.5 feet tall.

The unitary method is a mathematical problem-solving technique that involves using known information to find unknown information.

Let x be the height of the Middle Cascades Falls. The height of the Lower Yosemite Falls is 355 feet shorter than x, so the equation is:

Lower Yosemite Falls = x - 355

The height of the Upper Yosemite Falls is 80 feet more than twice the height of the Middle Cascades Falls, so the equation is:

Upper Yosemite Falls = 2x + 80

The total height of all three falls is 2425 feet, so we can add the heights of each fall to find the equation:

Lower Yosemite Falls + Middle Cascades Falls + Upper Yosemite Falls = 2425

Substituting in our previous equations:

x - 355 + x + 2x + 80 = 2425

Simplifying:

4x = 2425 + 355 - 80

4x = 2590

Dividing both sides by 4:

x = 647.5

So, the height of the Middle Cascades Falls is 647.5 feet. To find the height of the Lower Yosemite Falls, we substitute x back into the first equation:

Lower Yosemite Falls = x - 355

Lower Yosemite Falls = 647.5 - 355

Lower Yosemite Falls = 292.5 feet

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The mean of the scores is given as follows:

88.3.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.

Considering the absolute frequencies in the table, the sum of all the observations is given as follows:

1 x 75 + 9 x 80 + 3 x 85 + 2 x 90 + 2 x 95 + 7 x 100 = 2120.

The number of students is given as follows:

1 + 9 + 3 + 2 + 2 + 7 = 24.

Hence the mean is obtained as follows:

2120/24 = 88.3.

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The percentage of American women with shoe sizes between 3.48 and 12.6 is somewhere between 68% and 95%.

The empirical rule states that for a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

In this case, we want to find the percentage of American women with shoe sizes between 3.48 and 12.6. To use the empirical rule, we need to convert these values to standard deviations away from the mean. We can do this by subtracting the mean and dividing by the standard deviation:

3.48 - 8.04 = -4.56

-4.56 / 1.52 = -3.00

12.6 - 8.04 = 4.56

4.56 / 1.52 = 2.99

So we want to find the percentage of American women with shoe sizes that are between -3 standard deviations and +2.99 standard deviations from the mean.

According to the empirical rule, about 68% of the data falls within one standard deviation of the mean, so we can estimate that about 68% of the data falls within -1 and +1 standard deviations from the mean. The percentage between -2 and +2 standard deviations from the mean would be about 95%, and between -3 and +3 standard deviations from the mean would be about 99.7%.

Since our range of shoe sizes is partially contained within each of these ranges, we can estimate that the percentage of American women with shoe sizes between 3.48 and 12.6 is somewhere between 68% and 95%.

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Answer:

Fraction: 47/15

Mixed number: 3 2/15

Step-by-step explanation:

Hope it helps! =D

A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

If we know that percentages are parts of 100, we can simply set the denominator as 100, and keep the numerator the same.

Converting this into a mixed number will look like this:

Therefore, the percentage 940% written as a mixed number is [tex]9\frac{4}{10}[/tex].

After 10 years, the investment of £200 at 9% compound interest per annum would be worth approximately £432.97.

The amount of money that would be obtained after 10 years can be calculated using the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A = final amount

P = initial principal (£200)

r = interest rate (9%)

n = number of times compounded per year

t = number of years invested (10)

For an interest rate compounded annually, n = 1. Plugging in the values into the formula, we have:

A = £200 * (1 + 0.09/1)^(1 * 10)

A = £200 * (1.09)^10

A = £200 * 2.1669

A = £433.38

Therefore, £433.38 would be obtained after 10 years of investing £200 at 9% compound interest per annum.

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The volume of the cone is 60 ft³ when the base area is 12 ft² and the height is 6 ft.

Let the constant of variation be k. We know that the volume of a cone is given by the formula:

V = (1/3)πr²h

where r is the radius of the base and h is the height. Since the base area is given by πr², we can write:

V = (1/3)Bh

where B is the base area. From the given information, we know that:

12.5 = (1/3) * 15 * (2(1)/(2))

Solving for k, we get:

k = 12.5 / (15 * (2(1)/(2))) = (12.5 * 2) / 15 = 5/3

Now that we have found the variation constant, we can use it to find the volume when the base area is 12ft² and the height is 6ft:

V = (5/3) * 12 * 6 = 60 ft³

So the volume of the cone is 60 ft³ when the base area is 12 ft² and the height is 6 ft.

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Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

Joe can have four tacos for the cost of one burrito.

The cost of 4 burritos is 64%, which means the cost of 1 burrito is 16%.

The cost of 9 tacos is 36%, which means the cost of 1 taco is 4%.

1 taco Is 4%, 1 burrito = 16%

4 times 4 equals 16

Joe can get four tacos for the price of one burrito.

(Hope this helps!)

(Consider marking as the brainliest, so I can get to the next rank please :)

Answer:

it could be 20 and 20 or 0 and 40

The triangles are not similar.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles congruent to each other.

Therefore, for the triangles above to be similar the angles will be congruent and the sides will be a ratio of each other.

Therefore, the similarities statement for the two triangle can be represented as follows:

The triangles are not similar because the sides are not a ratio of each other.

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Answer:

16.8

Step-by-step explanation:

First, plug in the values given.

(0.7*15) - (2.1*3)
From there, it's simple math. Multiply what is in the parentheses first,

10.5 + 6.3

then add together the sums

16.8.

Answer:

 [tex]\frac{-1}{8}[/tex]

Step-by-step explanation:

[tex]\frac{-3/4}{6}=\frac{-0.75}{6}[/tex]

[tex]\frac{6}{-0.75}=-8[/tex]

[tex]\frac{-0.75}{6}=\frac{-1}{8}[/tex]

Answer:

Step-by-step explanation:

24x - 5 - 3 can be simplified by combining the constants (-5 and -3) into a single constant (-8):

24x - 5 - 3 = 24x - 8

Therefore, the simplified expression is 24x - 8.

Answer: 24x - 2

Step-by-step explanation:

You can't subtract the Coefficient and the Natural Number, so you can only do 24x - (5 - 3)

Which will end up as 24x - 2.