b) Edward and Thomas share some money in the ratio 2:3 Thomas receives £243. How much does each Robert receive?​

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:

 [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]

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.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

Answer:26

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

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%.

Learn more about Empirical Rule Shoe Sizes here:

https://brainly.com/question/13478860

#SPJ4

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.

To learn more about the interest rate from the given link

https://brainly.com/question/25793394

#SPJ1

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.

Learn more about distance between points at:

https://brainly.com/question/7243416

#SPJ1

The pie chart for this problem is given by the image presented at the end of the answer.

A pie chart is constructed in pizza format, considering the percentages of each input data in the problem.

A percentage is calculated as the division of the number of desired outcomes by the number of total outcomes, and then multiplied by 100%.

The percentages for the data-set in this problem is given as follows:

More can be learned about pie charts at https://brainly.com/question/26851221

#SPJ1

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

To know more about an equation of the line follow

https://brainly.com/question/18831322

#SPJ1

The height of the wall is 3.10 meters

It is important to note the six types of trigonometric identities, they are;

From the information given, we have that;

θ = 15 degrees

Hypotenuse= 12 meters

Opposite side = top of the wall

Let's use the sine identity;

sin 15 = x/12

cross multiply

Find the value

0. 2588(12) = x

Multiply the values

x = 3.10 meter

Hence, the value is 3.10 meters

Learn about trigonometric identities on:

https://brainly.com/question/7331447

#SPJ1

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).

More can be learned about a system of equations at https://brainly.com/question/30374328

#SPJ1

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:

$36.55

Step-by-step explanation:

$33.75 x 2 = $67.50

$67.50 (two shirts) + $45.95 (pair of trousers) = $113.45 (the amount of money spent)

Subtract that from the budget of $150...

$150-$113.45= $36.55 left bro

Answer:

$36.55

Step-by-step explanation:

$33.75 x 2 = $67.50

$67.50 + $45.95 = $113.5

$150-$113.45= $36.55

The answer is $36.55

Hope this Helped! Have a GOOD DAY!!!!!

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%

To learn more about relative frequency, click here: https://brainly.com/question/26177128

#SPJ4

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.

Learn more about ratios at https://brainly.com/question/12024093

#SPJ1

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:

31.3 m/s

Step-by-step explanation:

v² = v₀² + 2aΔx

v² = 0 + 2(9.8 m/s²)(50 m)

v² = 980 m²/s²

v = √ 980 m²/s² = 31.3 m/s

Notes:  ball starts from rest, so v₀ = 0; ball is in free fall, so a = g = 9.8 m/s²; objects in free fall accelerate at the same rate, g, independent of mass.

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.

Learn more about Compound interest here brainly.com/question/29819517

#SPJ4

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:

55 x 9091 = 500,005

Step-by-step explanation:

This checks with a calculator

Based on their sharing ratio of 4:3, when Mike gets £ 75 less than Harvey, the total amount of money shared is $525.

The total amount being shared between Harvey and Mike is determined using the arithmetic of ratios.

Firstly, we determine the sum of ratios as 7.  Since Mike's share is 3/7, which is less by £75 than Harvey's share, which is 4/7, we find the difference as 1/7 and equate it to £75.

Proportionately, if 1/7 equals £75, the total sum being shared will be equal to $525 (£75 x 7/1)

Sharing ratio between Harvey and Mike = 4:3

Sum of ratios = 7

Let the amount Harvey gets = x

x = 4/7

Let the amount Mike gets = x - 75

x - 75 = 3/7

4/7 - 3/7 = 1/7

1/7 = £75

7 = £525 (£75 x 7/1)

Learn more about ratios and proportions at https://brainly.com/question/12024093

#SPJ1

Answer:

10 packages

Step-by-step explanation:

To find the number of 4 yard packages for the fencing, we need to find the perimeter of the fence.

Perimeter = 2*(20 + 40)

Perimeter = 2*60 = 120 feet

*It is important to note that the perimeter is in feet and the packages are in yards*

4 yards = 12 feet

120 / 12 = 10 packages

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.

Learn more about the area here: brainly.com/question/27683633

#SPJ4

Answer:

it could be 20 and 20 or 0 and 40

Answer:

x= 8

Step-by-step explanation:

17x+14+4x-2= 180

21x= 168

x= 8

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.

More can be learned about the mean of a data-set at brainly.com/question/1156334

#SPJ1

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

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

To know more about unitary method here.

https://brainly.com/question/28276953

#SPJ4

A polygon with the given area is given below.

Polygons are closed figures which has at least three set of line segments joined together.

The polygon with least number of sides is triangle.

We have to draw a triangle of area 15 unit².

Area of the triangle = [tex]\frac{1}{2}[/tex] × Base × Height

[tex]\frac{1}{2}[/tex] × Base × Height = 15

Base × Height = 30

Let base = 6 units, height = 5 units

We can draw a right triangle this way as shown below.

If we are starting from the point A(0, 0), a length of base of 6 units will be a line segment from A(0, 0) to B(6, 0).

If the height is 5 units, draw a line segment from B(6, 0) to C(6, 5).

Join A to C.

Hence the required triangle is shown below.

Learn more about Polygons here :

https://brainly.com/question/28276384

#SPJ1

The number of different ways that 7 guests can be seated is 720 and 5 guests can be seated is 24.

In mathematics, Placing the elements of a set into a certain sequence or order is known as permutation. In other terms, the process of permuting is reordering of the elements of a set if the set is already ordered.

In the case of a round table, the formula for the number of ways that 'n' elements can be arranged is (n - 1)!

Here we have

There are 7 guests and a round table.

By the given formula,  

No of different ways that 7 guests can be seated = (7 - 1)! = 6!

= 6 × 5 × 4 × 3 × 2 × 1  

= 720  

If they are only 5 people

No of different ways that 5 guests can be seated = (5 - 1)! = 4!

= 4 × 3 × 2 × 1  

= 24

Therefore,

The number of different ways that 7 guests can be seated is 720 and 5 guests can be seated is 24.

Learn more about Permutation problems at

https://brainly.com/question/2068687

#SPJ4