what is 35+25in GCF​

Answer:

b ≈ 9.5, c ≈ 14.7

Step-by-step explanation:

Using the Sine rule in Δ ABC, that is

\(\frac{a}{sinA}\) = \(\frac{b}{sinB}\) , substitute values

\(\frac{7}{sin23}\) = \(\frac{b}{sin32}\) ( cross- multiply )

b × sin23° = 7 × sin32° ( divide both sides by sin23° )

b = \(\frac{7sin32}{sin23}\) ≈ 9.5 ( to the nearest tenth )

Also

\(\frac{a}{sinA}\) = \(\frac{c}{sinC}\)

\(\frac{7}{sin23}\) = \(\frac{c}{sin125}\) ( cross- multiply )

c × sin23° = 7 × sin125° ( divide both sides by sin23° )

c = \(\frac{7sin125}{sin23}\) ≈ 14.7 ( to the nearest tenth )

Answer:

\(sum \: angle \: of \: a \: triangle \: = 180 \\ here \: 90 + x + y = 180 ....(1)\\ but \: given \: that \: x = \frac{y}{5} \\ y = 5x .....(2)\\ put \: (2) \: in \: (1) \\ = > 90 + x + 5x = 180 \\ 90 + 6x = 180 \\ 6x = 180 - 90 = 90 \\ 6x = 90 \\ x = \frac{90}{6} = 15 \: degree \\ angle \: for \: a \: stright \: \: line \: = 180 \\ x + unknown = 180 \\ 15 + unknown = 180 \\ unknown = 180 - 15 = 165 \: degree \\ thank \: you\)

Every problem has a solution .Lets solve it .

Here given that

\(\\ \sf\longmapsto x=\dfrac{y}{5}\)

\(\\ \sf\longmapsto y=5x\dots(1)\)

Now

As its a triangle

\(\\ \sf\longmapsto 90+x+y=180\)

\(\\ \sf\longmapsto 90+x+5x=180\)

\(\\ \sf\longmapsto 6x+90=180\)

\(\\ \sf\longmapsto 6x=180-90\)

\(\\ \sf\longmapsto 6x=90\)

\(\\ \sf\longmapsto x=\dfrac{90}{6}\)

\(\\ \sf\longmapsto x=15\)

We need not to find y

See the marked angle and x are supplementary angles hence there sum will be 180

\(\\ \sf\longmapsto x+15=180\)

\(\\ \sf\longmapsto x=180-15\)

\(\\ \sf\longmapsto x=165\)

The required angle is 165°.

1.1. Accumulated depreciation:

The accumulated depreciation for the machine bought on 1 July 2013 would be R150,000 as of 31 March 2016.

1.2. Machine realization:

The machine bought in 2013 was sold for R120,000 on 30 June 2015, resulting in a profit/loss on the sale of R10,000.

1.1. Accumulated Depreciation:

To calculate the accumulated depreciation, we need to determine the annual depreciation expense for each machine and then accumulate it over the years.

Machine bought on 1 July 2013:

Cost: R250,000

Depreciation rate: 20% per annum on cost

Depreciation expense for the year ended 31 March 2014: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2015: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2016: 20% of R250,000 = R50,000

Accumulated depreciation for the machine bought on 1 July 2013:

As of 31 March 2014: R50,000

As of 31 March 2015: R100,000

As of 31 March 2016: R150,000

1.2. Machine Realisation:

To record the sale of the machine bought in 2013, we need to adjust the machine's value and the accumulated depreciation.

Machine's original cost: R250,000

Accumulated depreciation as of 30 June 2015: R100,000

Net book value as of 30 June 2015:  

R250,000 - R100,000 = R150,000.

On 30 June 2015, the machine was sold for R120,000.

Realisation amount: R120,000

To record the sale:

Debit Cash: R120,000

Debit Accumulated Depreciation: R100,000

Credit Machine: R250,000

Credit Machine Realisation: R120,000

Credit Profit/Loss on Sale of Machine: R10,000 (difference between net book value and realisation amount).

These entries will reflect the appropriate balances in the ledger accounts and properly close off the accounts for the years ended 31 March 2016.

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If a sample consists of 600 test scores, 516 of them would be at or below the 86th percentile. If a sample consists of 600 test scores, 228 of them would be at or above the 62th percentile.

A percentile is a score that compares a specific score to the scores of the other members of a group. It displays the proportion of other scores that a given score outperformed. For instance, if you have a test score of 75 and are placed in the 85th percentile, it signifies that your score is greater than those of 85% of other test takers.

Given that,

In general, 70 % of the values in a data set lie at or below the 70th percentile.

20 % of the values in a data set lie at or above the 20th percentile.

Generally percentile defines the percentage of a data set that is below or at a value that is being considered.

Hence the percentage of the values of a data set that lies below or at the 16th percentile is  16%

Also  the values of a data set that lies below or at the 24th percentile is  24%

Given a sample of 600 test scores , the number of test scores that will be at or below the 86th percentile is 86% of  600 which is mathematically represented as:

K = \(\frac{86}{100}\) × 600

K = 516 test scores

Given a sample of 600 test scores , the number number of test scores that will be above  the 62 th percentile is (100 - 62 = 38 )% of  600 which is mathematically represented as:

a = \(\frac{38}{100}\) × 600

a = 228 test scores.

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A. x² - 200 gives the amount of money the interior designer will make decorating the house as a function of hours he works.

B. He will earn 1,875 if he works for 50 hours.

C. The difference quotient is equal to 2x.

The solution has been obtained by using functions.

What is a function?

Function is a kind of relation, or rule, that associates a single input with a single, predetermined output.

We are given two functions

f(x) = 49x² – 200

which represents the amount of money he earns per room decorated

g(x) = (1/7)x

which represents the number of rooms the interior designer decorates

A. The amount of money the interior designer will make decorating the house as a function of hours he works will be given by evaluating f(x) in g(x).

So,

f(g(x)) = 49((1/7)x)² – 200

f(g(x)) = x² - 200

B. Since, the house requires 50 hours of work, this means that x = 50.

Substituting this in f(g(x)) = x² - 200, we get

f(g(50)) = 50² - 200

f(g(50)) = 1,875

C. The difference quotient for the function is as follows

\(\lim_{h \to \ 0}\frac{f(x+h) -f(x)}{h}\)

\(\lim_{h \to \ 0}\frac{(x+h)^{2}-200-x^{2}+200}{h}\)

\(\lim_{h \to \ 0}\frac{x^{2} + 2xh + h^{2}-x^{2}}{h}\)

= 2x

Hence, x² - 200 gives the amount of money and he earns 1,875 if he works for 50 hours. The difference quotient is equal to 2x.

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The bar diagram representing 150% of the price 5 years ago would be a bar with a height of $4.50.

What is the percentage?

Percentage is a way to express a number as a fraction of 100. It is often used to describe the relationship between two quantities, or to express a rate or change in a quantity over time. The symbol for percent is "%".

For example, if a pizza is marked up by 20%, it means the price has increased by 20/100 or 1/5 of the original price. If a student scores 80% on a test, it means they got 80 out of 100 questions correct. If a stock's value increases by 10%, it means the value has gone up by 10/100 or 1/10 of the original value.

The current admission price is $3 + $3 * 50% = $3 + $1.50 = $4.50.

150% of the price 5 years ago is $3 * 150% = $3 * 1.5 = $4.50.

So, the bar diagram representing 150% of the price 5 years ago would be a bar with a height of $4.50.

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Answer:

the answer is option (B) 84 in².

Step-by-step explanation:

The surface area of a square pyramid can be calculated by finding the sum of the areas of the four triangular faces and the base.

The area of the base is given as 36 in². Since the base is a square, we can find the length of one side of the base by taking the square root of the area:

sqrt(36 in²) = 6 in

Therefore, the length of one side of the base is 6 in.

To find the area of one of the triangular faces, we can use the formula for the area of a triangle:

Area = 1/2 * base * height

In this case, the base is equal to the length of one side of the square base, or 6 in. The height is given as 4 in.

Area = 1/2 * 6 in * 4 in = 12 in²

So the area of one triangular face is 12 in².

The total surface area of the pyramid is:

Surface area = 4 * 12 in² + 36 in² = 84 in²

Therefore, the surface area of the pyramid is 84 in².

So the answer is option (B) 84 in².

Answer:

9x² + 6x -19

Step-by-step explanation:

= 33x³ + 6x - 9 - 33x³ + 9x² -10

= 33x³ - 33x³ + 9x² + 6x -10 -9

= 9x² + 6x -19

The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Using this formula, we can calculate the distances between each pair of consecutive points as follows:

Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards

Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards

Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards

Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards

Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.

The amount remaining after 50 years is approximately 45.5% of the Initial amount, A₀.

The given exponential function represents the amount A(t) (in grams) of cesium-137 remaining after t years:

A(t) = A₀ * (1/2)^(t/30)

We are asked to find the initial amount A₀ and the amount remaining after 50 years.

1. Initial amount:

The initial amount, A₀, is the amount of cesium-137 present at t = 0 years. To find A₀, we substitute t = 0 into the equation:

A(0) = A₀ * (1/2)^(0/30)

A(0) = A₀ * 1

Since anything raised to the power of zero is 1, we have A(0) = A₀ * 1, which simplifies to A(0) = A₀.

Therefore, the initial amount of the sample is A₀.

2. Amount after 50 years:

To find the amount remaining after 50 years, we substitute t = 50 into the equation:

A(50) = A₀ * (1/2)^(50/30)

Now we can calculate the amount using the given formula:

A(50) = A₀ * (1/2)^(5/3)

To round the answer to the nearest gram, we evaluate the expression and round the result to the nearest gram:

A(50) = A₀ * 0.455

A(50) ≈ A₀ * 0.455

Therefore, the amount remaining after 50 years is approximately 45.5% of the initial amount, A₀.

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The amount of money in account A is decreasing by 8% per year.

The account that recorded a greater percentage change in amount of money over the previous year is account B.

From the information, the amount f(x), in dollars, in account A after x years is represented by the function below:

f(x) = 9,628(0.92)x

Therefore, this shows a decrease and the percentage will be:

= 1 - 0.92

= 0.08

= 8%

The account that recorded a greater percentage change will be:

Account B = (8,972 - 8,074.80) / 8,972 × 100

= 10%

Therefore, B has a higher percentage.

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Answer:

The top-left box should be 4x, and the bottom-left box should be 2.50x.

Step-by-step explanation:

Because the cost from 2 hours to 6 hours is 4 dollars per hour, it is 4x.

Likewise, because the cost over 6 hours is 2.50 dollars per hour, the cost is 2.50x.

Everything else seems fine.

Hope this helps!

9514 1404 393

Answer:

  f(x) = {0, x≤ 1; 4(x -1), 1 < x ≤ 6; 2.5x +5, x > 6}

Step-by-step explanation:

The hourly rate gives you the slope of the function in the relevant interval. The added constant is chosen to make the function continuous.

That is, at 1 hour, the charge is zero, so the next segment (4x+b) must have a value of b that makes the charge for 1 hour be zero. That will be b=-4.

Likewise, for more than 6 hours, the charge will be (2.5x+b), where b is chosen to make this expression match the charge for 6 hours. We know the charge for 6 hours is 4(6) -4 = 20, so b must match ...

  2.5(6) +b = 20

  b = 20 -15 = 5

The segment from 1 to 6 hours is f(x) = 4x -4.

The segment for more than 6 hours is f(x) = 2.5x +5.

_____

Alternate solution

Since the charge is zero for the first hour, the first segment could be considered to be charging only for hours after the first. That is, an alternate expression for hours 1–6 could be 4(x -1). Likewise, we could say the expression for hours more than 6 is 2.5(x +2).

Answer:

You need 75 points.

Step-by-step explanation:

Giving the following information:

Total number of points= 510 + 100= 610 (100%)

Actual number of points= 493

First, we need to determine the number of points required to reach 93%:

Points required= 610*0.93

Points required= 567.3 = 568

Now, the points needed in the final exam:

Difference of points= 568 - 493

Difference of points= 75 points

You need 75 points.

Answer:

F

Step-by-step explanation:

Have a Great Day & Good Luck :)

Answer:

1. 4 Degrees Celsius

2. -3 Degrees Celsius

3. 6 Degrees Celsius

4. -1.5 Degrees Celsius

Step-by-step explanation:

Multiplication is the process of multiplying. The amount of cereal that John will eat in 15 days is 50 ounces.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Given that John eats 20 ounces of cereal every 6 days. Therefore, the amount of cereal that John eats every 6 days is,

Amount of cereal in a day = 20 ounces / 6 days

                                           = (20/6) ounces in a day

Now, the amount of cereal that John will eat in 15 days is,

Amount of cereal in 15 days = 15 days × (20/6) ounces in a day

                                               = 50 ounces

Hence, the amount of cereal that John will eat in 15 days is 50 ounces.

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Answer:

N = -2

Step-by-step explanation:

-12-8x is the answer your looking for :)

Answer:

JK is a line segment

Step-by-step explanation:

Answer:

20 and 40

Step-by-step explanation:

3x7 is 21 but thats only one too much it has to be 3 too much to go down one and be a factor

6x4 is 24 it has to be 6 too much to go down one to be a factor

20x1 and 40x1/2 are both factors unless your teacher doesn't include fractions, so just choose this for now and if you get it wrong ask your teacher because three and six arent

Answer: Total cost for 1 ride = $11. Total cost for 2 rides = $14. Total cost for 3 rides = $17. Total cost for 4 rides = $20. Total cost for 5 rides = $23

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solve for y:

\(2y-3x=10\\2y=3x+10\\y=\frac{3}{2} x+5\)

Therefore:

y = 3/2x + 5

m = 3/2

b = 5

Graph below courtesy of Desmos.

Answer: y = mx + b

Step-by-step explanation:

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

6666

Step-by-step explanation:

Answer:

840,000

Step-by-step explanation:

841,487 sice the ten thousands place is under the number five you round down to 840,000