work out the value of 7a - 7b
when a-b=5

The area of the rectangle in mixed fraction form is 11(17/21) cm².

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

To find the area of the rectangle, we need to multiply the length and the breadth.

We can convert the mixed numbers to improper fractions and then multiply  -

Length = 2(2/7) cm = (7×2+2)/7 = 16/7 cm

Breadth = 5(1/6) cm = (6×5+1)/6 = 31/6 cm

The formula for area of rectangle is -

Area = Length × Breadth

Substitute the values in the equation -

= (16/7) cm × (31/6) cm

To simplify this product, we can first cancel a factor of 2 from the numerator of 16/7 and the denominator of 31/6 -

Area = (8/7) cm × (31/3) cm

Now we can multiply the numerators and denominators separately -

Area = (8 × 31) / (7 × 3) cm²

Area = 248/21 cm²

To write this as a mixed number, we can divide 248 by 21 -

248 ÷ 21 = 11 with a remainder of 17

So the area can be expressed as the mixed number -

11(17/21) cm²

Therefore, the area value is obtained as 11(17/21) cm².

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Answer:

The Circumference is 10π

Step-by-step explanation:

Use the equation [tex]C=2\sqrt{\pi A}[/tex] where A is the area.

Answer: The circumference of the circle is 10π.

Step-by-step explanation: The formula for the area of a circle is A = πr^2, where A represents area and r represents radius.

Given the area of the circle is 25π cm², we can start by evaluating the radius accordingly:

A = πr²

25π = πr²

25 = r²

r = 5

The radius of the circle is 5 cm.

Now, we can use the formula of circumference (C = 2πr) to evaluate the circumference of the circle:

C = 2πr

C = 2π(5)

C = 10π

Hence, the circumference of the circle is 10π.

Using the given exponential decay model for carbon-14, we found that the painting is approximately 10,521 years old.

What is meant by exponential functions?

A mathematical function called an exponential function is employed frequently in everyday life. It is generally used to find exponential decay or exponential growth. When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Throughout time, the rate of change quickens. As time goes on, the rate of increase accelerates. With exponential decay, the quantity initially falls very quickly and then gradually. Throughout time, the rate of change slows. As time goes on, change happens at a slower rate.

The exponential decay model for carbon-14 is given as:

[tex]A = A_0e^{(-0.000121t)}[/tex]

where,

A = Percentage remaining

A₀ = Initial amount

t = Time in years

Given,

A = 28% of A₀ = 0.28A₀

Substituting in the above exponential decay model,

[tex]A = A_0e^{(-0.000121t)}\\\\0.28A_0 = A_0e^{(-0.000121t)}\\\\0.28 = e^{(-0.000121t)}\\\\[/tex]

ln 0.28 = -0.000121t

-1.273 =  -0.000121t

t = 10,520.66 years = 10,521 years

Therefore using the given exponential decay model for carbon-14, we found that the painting is approximately 10,521 years old.

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The completely factorised form of the given polynomial as required to be determined is; Choice C; (y² + 3) (3y + 1).

As required in the task content; the given expression whose factorised form is to be determined is; 3y³ + y² + 9y + 3.

The completely factorised form can be determined as follows;

y² (3y + 1) + 3 (3y + 1).

Therefore, we have that;

(y² + 3) (3y + 1)

Ultimately, the completely factorised form of the given expression is; Choice C; (y² + 3) (3y + 1).

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The angle that is vertical to angle 3 is angle 1

Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.

This means that angles that are vertical are angle s that are opposite to each other. In the diagram above, angle 2 is opposite to angle 4 and angle 1 and angle 3.

Therefore all the angles will make a point. This means the sum of the angles is 360°.

angle 2 and angle 3 are adjascent to each other and angle 1 and 4 are adjascent to each other

Therefore the angle that is vertical to the angle 3 is angle 1

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As a result, the answer to the following question, Rectangle area minus inner rectangle area minus total area of little rectangles = 84 - 30 - 16 = 38 square inches.

An area is the size of a surface area. The surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a planar region or planar region refers to the area of a form or flat layer. The area of an item is the entire amount of space occupied by its planar (2-D) surface or form. Using a pencil, draw a square on a sheet of paper. A two-dimensional character. The area of a form on paper is the amount of space it occupies. Assume that the square is made up of smaller unit squares.

Rectangle area = length x breadth = 12 x 7 = 84 square inches

The size of the rectangle that makes up the space inside the letter E must then be subtracted:

5 × 6 = 30 square inches is the area of the inner rectangle.

A tiny rectangle's area 5 x 1 = 5 square inches = 1 = length x width

A tiny rectangle's area 5 x 1 = 5 square inches = 2 = length x width

A tiny rectangle's area 2 x 3 = 6 square inches = 3 = length x width

5 + 5 + 6 = 16 square inches is the total area of little rectangles.

Rectangle area minus inner rectangle area minus total area of little rectangles = 84 - 30 - 16 = 38 square inches

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The missing cοmpοnent in this study is  cοntrοl grοup

A methοd used in a cοntrοlled envirοnment tο find an unknοwn effect οr law, test οr establish a hypοthesis, οr prοvide an example οf an established law

In the scenariο described, individuals are chοsen at randοm tο participate in a new interventiοn, which appears tο be an example οf an experiment.

A cοntrοl grοup is a grοup οf participants whο are used fοr cοmparing anοther grοup tο in a test οr experiment. It is cοmpοsed οf participants whο dο nοt receive the experimental treatment.

In the given situatiοn an energy drink cοmpany claims that its prοduct increases students' memοry levels.

Tο suppοrt its claims, the cοmpany issues advertisements claiming that 8 οut οf 10 peοple (chοsen randοmly frοm acrοss the cοuntry) whο tried their prοduct repοrted imprοved memοry.

But they haven't cοmpοse a cοntrοl grοup tο cοmpare the results fοr test.

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Answer:

A. Control Group

Plato

To calculate the z-score for the new case count in Orange County, we use the formula:
z = (x - μ) / σ
where x is the value we are calculating the z-score for, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

Plugging in the values given in the question, we get:
z = (178 - 7.29) / 110.87
z = 170.71 / 110.87
z = 1.54
So the z-score for the new case count in Orange County is 1.54. This means that the new case count in Orange County is 1.54 standard deviations above the mean of the distribution.

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The area of the actual gym in the middle school is 20,400 square feet.

What is rectangle?

A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.

If the scale is 1 inch : 5 feet, then we can use this ratio to convert the dimensions of the gym in the drawing to their actual size.

The length of the gym in the actual middle school is:

34 inches x 5 feet/inch = 170 feet

The width of the gym in the actual middle school is:

24 inches x 5 feet/inch = 120 feet

The area of the gym in square feet is:

Area = length x width

Area = 170 feet x 120 feet

Area = 20,400 square feet

Therefore, the area of the actual gym in the middle school is 20,400 square feet.

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Answer:

one apple: 75 cents

one orange: 60 cents

Step-by-step explanation:

let x be price of one apple

let y be price of one orange

3x + 4y = 4.65

5x + 8y = 8.55

we can do elimination, substitution, or graphing.

this is elimination: (we're eliminating the x in this case to find y, and then use y to find x)

ORIGINAL EQUATIONS: (we're multiplying by 5 so we can eliminate x)

3x + 4y = 4.65

5x + 8y = 8.55

5(3x + 4y = 4.65) = 15x + 20y = 23.25

3(5x + 8y) = 8.55 = 15x + 24y = 25.65

(distribute, and then subtract to get one equation and eliminate x)

  15x + 20y = 23.25

-  15x + 24y = 25.65

------------------------------

  0    -    4y = - 2.4

so we got that, now we make it this:    -4y = -2.4

divide both sides by -4.

-4y = -2.4

-----    -----

-4          -4

y (orange variable) = 0.60

therefore, one orange cost 60 cents.

plug y (the 60 cents) back into one of the original equations (either works) and solve for x.

3x + 4y = 4.65

5x + 8y = 8.55

let's use this equation:  5x + 8y = 8.55

5x + 8(0.6) = 8.55

5x + 4.8 = 8.55

     -4.8      -4.8

5x = 3.75

----    ------

5        5

x = 0.75

therefore, one apple cost 75 cents.

(also, there was an easier number to multiple the equations by)

3x + 4y = 4.65

5x + 8y = 8.55

We could have multiplied (3x + 4y = 4.65) with 2, distributing and bringing it to 6x + 8y = 9.30

Then subtract 6x + 8y = 9.30 from 5x + 8y = 8.55, and you would have solved and gotten x just fine, then plugged x back in to find y)

sorry this answer is so long...good luck :))

Answer:

x=16.3

Step-by-step explanation:

sine: opposite side ÷ hypotenuse

sine(x)= 7 ÷ 25 = 0.28

sine^-1(0.28) = 16.3

x = 16.3

Answer:

16.3 rounded to the nearest tenth

Step-by-step explanation:

The formula for the sine rule is Sin A / a= Sin B / b = Sin C / c which is as, Sin V / v = Sin X / x = Sin S / s

Sin 90 / 25 = Sin X / 7, that is,

1 / 25 = Sin X / 7 (cross multiply)

Make Sin X the subject of the formula;

Sin X = 7 / 25

X = Sin^-1(7 / 25)

X = 16.26 = 16.3 rounded to the nearest tenth

The estimated copper production level in the year 2000 is 1066.5 million tons, and the estimated copper production level in 2024 is 1072.2 million tons.

In order to calculate the production level of copper in the year 2000, we can use the given equation: C = 0.5 * 1.033t.

To calculate the production level in 2000, we need to plug in 2000 for t. This gives us C = 0.5 * 1.033(2000) = 1066.5 million tons.

In order to estimate the production level of copper in 2024, we can use the known production level of 2023 and the given equation. We know that C = 0.5 * 1.033t. To calculate the production level in 2024, we need to plug in 2023 for t. This gives us C = 0.5 * 1.033(2023) = 1072.2 million tons. Therefore, the estimated production level of copper in 2024 is 1072.2 million tons.

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If babies weight increases by 8% over a month from birth to 4. 5 kg, the baby's weight at birth was approximately 4.17 kg.

To find out the weight at birth, we need to use the given information that the baby's weight increased by 8% over a month to reach 4.5 kg.

Let's start by setting up an equation. We can let x be the baby's weight at birth in kg. Then, we know that the baby's weight increased by 8% over a month, so the weight after one month would be:

x + 0.08x = 4.5 kg

Simplifying this equation by combining like terms, we get:

1.08x = 4.5 kg

To solve for x, we can divide both sides of the equation by 1.08:

x = 4.17 kg

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Answer:

Step-by-step explanation:

The total amount paid at the end of sixth month is S/78,000. So, the correct answer is (b).  Total amount paid at the end of the nth month is 24,000n + 9,000. So, the correct answer is (b). If the cooperative has already paid 50% of the price of the land by the end of the tenth month, the payment option did they choose is 20% down payment and fixed monthly payments of S/5,000. So, the correct option is (a).

For the first payment option, the down payment is 20% of S/240,000, which is S/48,000. The remaining balance is S/192,000, which is paid in fixed monthly payments of S/5,000. Therefore, at the end of the sixth month, the total amount paid is:

S/48,000 + 6 x S/5,000 = S/78,000

So, the answer is (b) S/78,000.

The amount of money paid at the end of the nth month for the second payment option is the sum of the down payment and the total monthly payments up to that month. The down payment is 10% of S/240,000, which is S/24,000. The total monthly payments up to the nth month is S/9,000 x n. Therefore, the expression for the total amount paid at the end of the nth month is:

S/24,000 + S/9,000 x n = (3S + 8n)/72

So, the answer is (b) 24,000n + 9,000.

We can find out which payment option they chose by comparing the total amount paid up to the tenth month for each option to half of the price of the land.

For the first payment option, the down payment is S/48,000 and the total monthly payments up to the tenth month is

10 x S/5,000 = S/50,000.

Therefore, the total amount paid up to the tenth month is:

S/48,000 + S/50,000 x 10 = S/480,000/25

For the second payment option, the down payment is S/24,000 and the total monthly payments up to the tenth month is

10 x S/9,000 = S/9,000.

Therefore, the total amount paid up to the tenth month is:

S/24,000 + S/9,000 x 10 = S/24,000 + S/900

For the third payment option, there is no down payment, and the total monthly payments up to the tenth month is

10 x S/12,000 = S/1,200.

Therefore, the total amount paid up to the tenth month is:

S/1,200 x 10 = S/12,000

Comparing each total amount paid up to the tenth month to half of the price of the land (S/240,000 x 0.5 = S/120,000), we see that only the first payment option meets the condition, since:

S/480,000/25 < S/120,000

Therefore, the answer is (a) First.

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Answer:

Red I think maybe we should try hi friends I am new to this app

Answer: is there a Pic it would help

Step-by-step explanation:

Step-by-step explanation:

Her interest earned will be   p r t    

p = principal = amount of deposit = 1100 dollars

r = decimal  interest rate = .09

t = time in years = 3

$ 1100 * .09 * 3 = $ 297 .

Answer: To find the percentage of customers who chose the same meal, we need to divide the number of people who chose the same meal by the total number of customers, and then multiply by 100 to convert to a percentage:

percentage = (34 / 85) x 100

percentage = 40

Therefore, 40% of the customers chose the same meal.

Step-by-step explanation:

Answer:

Its 40%

Step-by-step explanation: you divide 85 by 34 to get your answer

Atul's father is wrong. The average amount is greater than Atul's allowance.

In order to determine if Atul is justified to ask for a raise in allowance, the mean of the data collected by Atul has to be determined.

Mean is the average of a set of numbers. It can be determined by adding the numbers together and dividing it by the total numbers in the dataset. Mean is a measure of central tendency.

Mean = sum of numbers / total numbers

(120 + 180 + 100 + 50 + 250 + 200 + 200 + 220 + 150 + 100 + 100 + 150 + 130 + 200 + 180 + 100 + 150 + 100 + 180 + 150+ 120 + 150+ 100 + 150 + 100 + 120 + 180 + 200 + 50) / 30 = 139.33

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Answer: Part A:

If Isabella's mother has a garden with an area of 10 2/3 square feet, and she plants peas in 1/4 of the garden, we can calculate the area used for planting peas by multiplying the garden area by 1/4:

Area used for planting peas = (10 2/3 square feet) x (1/4) = (32/3) x (1/4) = 8/3 square feet

Therefore, the area used for planting peas is 8/3 square feet.

Part B:

If Isabella's mother sells the peas and gets 3 dollars for each square foot, we can calculate how much money she made by multiplying the area used for planting peas by 3:

Money made = (8/3 square feet) x (3 dollars/square foot) = 8 dollars

Therefore, Isabella's mother made 8 dollars by selling the peas she planted in her garden.

Therefore, 21/28, which can be expressed as 3/4, represents the percentage of pupils who achieved their reading objective.

A figure can be expressed as a fraction of 100 using a percentage. "%" is used to represent it. In a variety of settings, including statistics, finance, and daily life, percentages are frequently used to indicate proportions, rates, or fractions. For instance, if a retailer gives a 20% discount on a $50 item, the discounted price would be $40, which is 80% of the original price. You can use the following method to determine a percentage:

(Part/Whole) x 100 Equals percentage where "whole" is the overall number and "part" is the quantity you are interested in.

given

We can use the ratio to determine the precise amount of illustrations Justin still needs to create:

40/100 = x/80

where x represents the amount of drawings Justin has already created. After finding x, we obtain:

x = (40/100) * 80 = 32

As a result, Justin has already created 32 drawings and still needs to create 48 more.

We can use the proportion to determine the percentage of pupils who achieved their reading objective:

75/100 = x/28

where x represents how many pupils achieved their reading objective. After finding x, we obtain:

x = (75/100) * 28 = 21

Therefore, 21/28, which can be expressed as 3/4, represents the percentage of pupils who achieved their reading objective.

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Answer:

144 in^3

Step-by-step explanation:

You need to separate the figure into the top and bottom rectangles

For the top, the volume = 12 x 4 x 1 = 48

For the bottom, the length is 12, the height is 5 - 1 = 4, the width is 2

so the volume is 12 x 4 x 2 = 96

The volume of the figure is 48 + 96 = 144 in^3

Answer:

Step-by-step explanation:

First we sould factor out the function:

y=x^2+5x-6

y=(x+6)(x-1)

Note: if you multiply out the factored equation, you will get your original equation.

Now, find what we need to plug in to make it equal 0.

If we plug in -6, then the (x+6) part equals 0. Since we are multiplying by 0, the whole thing equals 0.

If we plug in 1, then the (x-1) part equals 0. Since we are alo multiplying by 0 here, the function comes out to 0.

This means that at x=-6 and x=1 the function comes out to 0.

Answer:

6

Step-by-step explanation:

To find the hours of labor it took to repair the car, we need to subtract the cost of parts from the total cost and then divide the result by the cost per hour of labor.

So, $340 - $100 = $240 was spent on labor.

$240 ÷ $40 per hour = 6 hours of labor.

Therefore, the answer is OB. 6 hours.

The sοlutiοn οf the given prοblem οf interest cοmes οut tο be Reh will pay abοut $3,944 in interest fοr the duratiοn οf his lοan.

Tο calculate the simple interest rate, divide the amοunt by the cοst οf financing, the amοunt οf time left, and οther variables. The simple return strategy in marketing is principal student lοans hrs. This methοd is the mοst basic methοd fοr figuring οut invοlvement. The mοst typical methοd fοr calculating incοme is as a share οf the principal amοunt. Tο put this intο perspective, if he wants tο bοrrοw $100 frοm a single οf these friends .

Here,

a. The fοllοwing methοd can be used tο determine the mοnthly payment fοr a lοan:

=> The mοnthly payοut =  (P*r) / (1 - (1+r)(-n)).

We must first determine the entire lοan amοunt, including interest, that Reh must pay back. After 4.5 years οf interest accrual, the lοan sum is:

=>  [tex]9900 \times (1 + 0.0429/12)^{(12 \times 4.5)[/tex] = 12,723.97

The οverall debt balance is $12,723.97.

The numbers can then be entered intο the fοrmula as fοllοws:

=>  (12723.97*(0.0429/12)) / (1 - (1+(0.0429/12))(-12*10))

is the fοrmula fοr the mοnthly payοut.

Payment due each mοnth: $131.19 (rοunded tο the nearest dοllar)

Reh's mοnthly payment is therefοre $131, rοunded tο the clοsest dοllar.

b. The fοllοwing fοrmula can be used tο determine the tοtal interest charged οver the lοan's term:

=> tοtal interest = (mοnthly payment X n) - P .

There have been a tοtal οf:

=> 120 is equal tο ten years times οne year.

The entire interest paid is thus:

=> ($3,943.80) (tοtal mοnthly installments * n) - P

=> (131.19 * 120) - 9900 (rοunded tο the nearest dοllar)

Sο, rοunded tο the clοsest dοllar, Reh will pay abοut $3,944 in interest fοr the duratiοn οf his lοan.

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The critical value for a 0.05 level of significance is 1.96, so the calculated t-test statistic (-1.166) is lower than the critical value and therefore does not reject the null hypothesis.

The related samples t-test is used to determine if there is a statistically significant difference between the two sets of data. In this case, the t-test is used to determine if the students' grades have improved after receiving tutoring.

To calculate the t-test statistic, we need to first calculate the mean and standard deviation of the before and after data sets.

For the before data set, the mean is 2.56 and the standard deviation is 0.8. For the after data set, the mean is 3.22 and the standard deviation is 0.5.

We can then calculate the t-test statistic using the following formula:

t = (mean before - mean after) / (standard deviation before + standard deviation after / √n)

where n is the number of samples.

In this case, n = 5, so the t-test statistic is:

t = (2.56 - 3.22) / (0.8 + 0.5 / √5) = -1.166

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What describes the literature during the Goryeo dynasty is: b. It included books on history, sacred texts, and legends by both Buddhist and Confucian scholars.

Literature during the Goryeo dynasty (918-1392 CE) in Korea was characterized by a flourishing of literature in both Confucianism and Buddhism, which were the two dominant religions at the time.

The literature of this period included works on history, sacred texts, legends, and biographies written by scholars from both traditions. Poetry and drama also became popular during this time.

Therefore, we can state that: b. It included books on history, sacred texts, and legends by both Buddhist and Confucian scholars.

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A) Rounding to the nearest whole number, Anthony needs to scoop out 13 cups of water with this cup.

B) Rounding to the nearest whole number, Anthony needs to scoop out 3 cups of water with this cup.

The volume of the sink is given as 660 Pi inch cubed, which means the radius of the half-sphere sink is:

[tex]r = (3 \times 660 Pi / 4Pi)^{(1/3)} = 9 inches[/tex]

A) For the first cup with a diameter of 5 inches and a height of 8 inches, the volume of the cup is:

[tex]V = Pi \times r^2 \times h = Pi \times (2.5)^2 \times 8 = 50[/tex]Pi inch cubed

The number of scoops required to empty the sink can be found by dividing the volume of the sink by the volume of one scoop:

Number of scoops = 660 Pi / 50 Pi = 13.2

Rounding to the nearest whole number, Anthony needs to scoop out 13 cups of water with this cup.

B) For the second cup with a diameter of 10 inches and a height of 8 inches, the volume of the cup is:

[tex]V = Pi \times r^2 \times h = Pi \times (5)^2 \times 8 = 200[/tex] Pi inch cubed

The number of scoops required to empty the sink can be found by dividing the volume of the sink by the volume of one scoop:

Number of scoops = 660 Pi / 200 Pi = 3.3

Rounding to the nearest whole number, Anthony needs to scoop out 3 cups of water with this cup.

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Answer:

Step-by-step explanation:

Subtract -1 from both sides:

6x^2<=-1,

Divide by 6.
x^2<=-1/6

from here, no REAL value of x would make x^2 a negative number, but imaginary numbers can. This means that x belongs to C, which in this question means the 3rd option.

The solution set of the quadratic inequality 6x² +1≤0 is, ∅

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 6x² + 1 ≤ 0

Now, We can simplify as;

⇒6x² + 1 ≤ 0

⇒ 6x² ≤ - 1

⇒ x² ≤ - 1/6

Which is not possible.

Hence, The solution set of the quadratic inequality 6x² +1≤0 is, ∅

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The Curved surface area of the frustum is 60π.

In geometry, a frustum, is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting this solid.

The Curved surface area of the frustum is equal to the curved surface area of the large cone minus the curved surface area of the small cone.

The height of the large cone=√[tex]10^{2}[/tex]-[tex]8^{2}[/tex]

=√[tex]100-64[/tex]

=6cm

The height of small cone=6×(1/2)=3cm

(The little cone's height is equal to half that of the giant cone's height.)

The arc length of the small cone=10×1/2=5cm

The curved surface area of the frustum=π×8×10-π×r×5

=80π-5rπ

r=√[tex]5^{2}[/tex]-[tex]3^{2}[/tex]

=√25-9

=4cm

Hence, Curved surface area of the frustum is

= 80π-5×4×π

=80π-20π

=60π

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