a rectangle with diagonal of length 20cm has sides in the ratio of 2:1 .find the area of the rectangle and perimeter.

In linear equation, 3437.5  feet - lbs is the work done to haul the anchor .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Anchor  weighing = 100 lbs

   given 3  lb/ft

  the combined weight  = 3( 25 -y ) + 100

                                 = 175 - 3y

    the workdone on small solution is = (175 - 3y)Δy

                      w = ∫₀²⁵ (175 - 3y) dy

                        = 175[y]²⁵₀- 3/2[y²]²⁵₀

                       = 175 [ 25 - 0 ] - 3/2 [ 25²- 0²]

                       = 3437.5  feet - lbs

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Answer:

C

Step-by-step explanation:

Look at your Y-values. If you look at the constant difference for A. You will get a constant difference of 4 meaning its linear. B will give you a constant difference of 9 which also means that it is linear. D has a Constant difference of 1. However, C has no constant difference as the difference between each value changes, therefore meaning that it is not linear

ANSWER:

x = 4 or 12

STEP-BY-STEP EXPLANATION:

Finding the zero(s) of the function in a table is locating the point(s) when y = 0 .

Therefore, in this case the zeros occur when x = 4 and when x = 12.

The value of Social Security Tax = $ 244.28 & Medicare tax = $ 57.13.

Social Security Tax = $ 244.28

Medicare tax = $ 57.13

Now, let us understand what social security tax is.

In the United States, Social Security is the commonly used term for the federal Old-Age, Survivors, and Disability Insurance (OASDI) program and is administered by the Social Security Administration (SSA). The original Social Security Act was enacted in 1935, and the current version of the Act, as amended, encompasses several social welfare and social insurance programs.

Social Security is nearly universal, with 94 percent of individuals in paid employment in the United States working in covered employment.

The current tax rate for social security is 6.2% for the employer and 6.2% for the employee, or 12.4% total. The current rate for Medicare is 1.45% for the employer and 1.45% for the employee, or 2.9% total.

Using this information, we can find the taxes.

Social Security tax = Gross Pay x 6.2%

= 3820 x 0.062 = $236.84

Medicare tax = Gross Pay x 1.45%

= 3820 x 0.0145 = $55.39

Hence, the Social Security tax that Sebastian Wayne has to pay is $236.84, and the Medicare tax he has to pay is $55.39 per month, after earning a gross pay of $3,820.

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Answer:

Ratio of sandwiches with white bread and brown bread is 10:3. Of the white sandwiches 2/3 are vegetarian, of the sandwiches that are brown half are vegetarian. What fraction of the sandwiches are vegetarian?

Step-by-step explanation:

Givens

The ratio between white bread and brown bread is 10:3, that is, for every 10 white bread, there are 3 brown bread.

2/3 of white sandwiches are vegetarian.

1/2 of brown sandwiches are vegetarian.

We know that white bread is represented by 10, and brown bread is represents by 3. So, 2/3 of 10 are vegetarians, and 1/2 of 3 are vegetarians. The sum of them is

2/3 of 10 are vegetarians = \(\frac{2}{3} \times 10 = \frac{20}{3}\)

1/2 of 3 are vegetarians = \(\frac{1}{2} \times 3 = \frac{3}{2}\)

\(=\frac{20}{3}+\frac{3}{2}\\\\=\frac{40+9}{6}\\\\=\frac{49}{6}\)

Therefore, 49/6 represents all the sandwiches which are vegetarian.

Answer:

B

Step-by-step explanation:

25.4

The average time Janette to fold and put away all four items is 25.35 seconds. Then the correct option is C.

The mean of average is the ratio of the sum of observations and the number of observations.

Janette was timed by a store manager as she folded and stored a scarf, a shirt, a pair of trousers, and a jumper. Her time for the shirt was 26.1 seconds, the jumper 24.3 seconds, the trousers 32.8 seconds, and the scarf 18.2 seconds.

The average time Janette to fold and put away all four items will be given as,

Average = (26.1 + 24.3 + 32.8 + 18.2) / 4

Average = 101.4 / 4

Average = 25.35

The average time Janette to fold and put away all four items is 25.35 seconds. Then the correct option is C.

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Answer:

x=1

Step-by-step explanation:

Steps:

1: Step 1: Subtract 2 from both sides.

4x+2−2=6−2

4x=4

2: Step 2: Divide both sides by 4.

4x4=44x=1

Answer: x=1

Hope this helps.

Answer:

1

Step-by-step explanation:

Given expression:

4x+2=6

Bringing 2 to the other side, it becomes negative..

4x=6-2 = 4

4x=4

again 4 brought to rhs n divided..

x=4/4

x= 1

So the correct option is (a)

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

If the dimensions of stamp M are 76 times the dimensions of stamp P then the length of stamp P in inches will be 75/76.

Given that the width of stamp M is 43 inches, length is 75 inches and the dimensions of stamp M are 76 times the dimensions of stamp P.

We are required to find the length of stamp P in inches.

Suppose the length of stamp P be x.

According to question, the length of stamp will be 76x.So,

75=76x

x=75/76

Hence if the dimensions of stamp M are 76 times the dimensions of stamp P then the length of stamp P in inches will be 75/76.

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Answer:

the answer is A, 6/5

The correct option for generating values for this simulation is:

Use a random digit table to generate two-digit numbers, ignoring any besides 40 and 10. Use 40 for clothing, 40 for footwear, 10 for housewares, and 10 for athletic gear.

This method allows you to accurately simulate the store's sales split among the four areas, as it uses the correct percentages and generates random values within the appropriate range. The other options do not accurately reflect the store's sales split or use the correct percentages.

Answer:

it's A

Step-by-step explanation:

you start at 2, then subtract 4, and get -2, which is what you end with.

Answer:

x = -5

Step-by-step explanation:

If g(x) = 22 and g(x) = -4x + 2, then -4x + 2 = 22.

Isolate x.

-4x = 22 - 2

= -4x = 20

= x = 20 ÷ -4

= x = -5

No, this is not likely. The main reason is that the average height of a class of eighth-graders is typically reported in terms of feet or centimeters, not inches.

Without additional context or a comparison to known data about the heights of eighth-graders, it is not possible to determine whether the given average height and standard deviation are likely.

The given data "the average height of a class of eighth-graders is inches with a standard deviation of inches," doesn't seem likely, and it is difficult to come to any meaningful conclusions based on it.

The provided information, "the average height of a class of eighth-graders is inches with a standard deviation of inches," doesn't make sense. It is highly improbable that the height of eighth-graders can be less than one inch. This looks like a mistake in recording or reporting the data.

Although it is feasible that there can be a lot of variety in the height of eighth-graders, we cannot accept that the average height is fewer than 48 inches or 4 feet. Also, the standard deviation seems too low.

In the US, the average height of eighth-graders is usually about 63 inches (5 ft 3 in), with boys being somewhat taller and girls somewhat shorter.

Therefore, the given data "the average height of a class of eighth-graders is inches with a standard deviation of inches," doesn't seem likely, and it is difficult to come to any meaningful conclusions based on it.

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A. The equation to find the distance of the flowerbed from the hive is:  

x/20 +x/12 +900 = 1200, where x is the distance.

B.  The flowerbed is 2250 feet far from the hive.

Suppose, the distance of the flowerbed from the hive is x  feet.

The bee flies 20 feet per second directly to a flowerbed from its hive and flies directly back to the hive at 12 feet per second.

As, time = distance/speed

So, the time taken by the bee to reach the flowerbed x/20  seconds and the time taken to fly back to the hive = x/12  seconds.

The bee stays at the flowerbed for 15 minutes or (15×60)seconds or 900 seconds and it is away from the hive for a total of 20 minutes or (20×60)seconds or 1200 seconds.

So, the equation will be;

x/20+x/12 +900 = 1200

8x = 60 x 300

8x =18000

x = 18000/8

=2250

Therefore , the distance of the flowerbed from the hive is 2250 feet.

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Answer:

51/3

Step-by-step explanation:

Angles opposite congruent sides of a triangle are congruent.

\(x+17=4x-34 \\ \\ 17=3x-34 \\ \\ 51=3x \\ \\ x=51/3\)

In the case of the decimal 0.007, it can be written as the percent 0.7% and as the decimal 0.00007.

To write a decimal as a percent, you need to move the decimal point two places to the right and add the percent symbol (%).

For the decimal 0.007, moving the decimal point two places to the right gives us 0.7. Adding the percent symbol gives us 0.7%.

To write a percent as a decimal, you need to move the decimal point two places to the left and remove the percent symbol (%).

For example, to write 75% as a decimal, you move the decimal point two places to the left, giving us 0.75.

So, to summarize:

- Decimal to percent: Move the decimal point two places to the right and add the percent symbol.
- Percent to decimal: Move the decimal point two places to the left and remove the percent symbol.

In the case of the decimal 0.007, it can be written as the percent 0.7% and as the decimal 0.00007.

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The formula for the half-life of a substance that decays at a continuous rate is:        \(t _{1/2}\) = \(ln(2)\)/ λ where ln(2) is the natural logarithm of 2 (approximately 0.693) and λ is the decay constant. The half-life is 4.107 minutes

To find the decay constant, we can use the formula:

λ = \(\frac{ln(1/2)}{t _{1/2}}\)

where ln(1/2) is the natural logarithm of 1/2 (approximately -0.693) and t1/2 is the half-life.

λ = \(\frac{-.693}{t _{1/2}}\)

We know that the substance decays at a rate of 16% per minute, which means that after one minute, the remaining amount of the substance will be 84% of the original amount. This can be expressed as:

0.84 = e^(-λ)

Taking the natural logarithm of both sides, we get:

ln(0.84) = -λ

λ = -ln(0.84)

Substituting this value for λ in the formula for the half-life, we get:

\(t _{1/2}=\frac{ln2}{ln.84}\)

t1/2 = 4.107 minutes

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The Taylor approximation of degree three for 1+x around x=0 can be used to estimate 2. The error bound for this approximation can be calculated.

The Taylor approximation of degree three for 1+x around x=0 is given by:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3

To approximate 2 using this approximation, we substitute x=1:

f(1) = f(0) + f'(0)(1) + (f''(0)/2!)(1^2) + (f'''(0)/3!)(1^3)

The error bound is given by the absolute value of the remaining terms:

Error bound = |(f'''(0)/3!)(1^3)|

To determine the error bound, we need to know the value of f'''(0), which is the third derivative of f(x) evaluated at x=0. Without further information about the function, we cannot calculate the exact error bound.

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We may build up a proportion and solve for the scale model radius of Neptune using the ratio between the radii of the two planets and the known scale model radius of the Earth. The scale model of Neptune that is produced has a radius of around 9.7 cm.

We may take advantage of the fact that the ratio between the two planets' radii and the ratio between their respective scale model radii is the same. Let's name the Neptune scale model radius "r" Then, we may set up the ratio shown below:

Neptune's radius is equal to the product of Earth's radius and its scale model.

With the provided values, we may simplify and obtain:

24620 km / 6370 km equals 2.5 cm / r

We obtain the following when solving for "r":

r = (24620 km * 2.5 cm) / (6370 km)

r ≈ 9.7 cm

Therefore, a scale model of Neptune would have to be drawn with a radius of approximately 9.7 cm.

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Answer:

if u want step by step answers u need to give more points than that

Step-by-step explanation:

The profit-maximizing price and quantity for the monopolist are $350 and 150 units, respectively ,The expected return is greater than the initial investment And the producer surplus is $33,750, consumer surplus is $31,875, and firm profit is $37,500.

Ignoring the time value of money and discounting, the expected value of the lottery winnings each year is 2% × $1 million = $20,000, and this goes on for 10 years.

Thus, the expected value of the investment is 10 × $20,000 = $200,000.

Hence, the expected return is greater than the initial investment, and there is a condition under which the investment can be made.

The monopolist’s total cost can be represented as:

TC = 300 + 200Q + 3Q².

The demand function for the monopolist is given as:

Q = 500 - P,

which can be rearranged to derive the price function as:

P = 500 - Q.

From the total cost function, we can obtain the marginal cost (MC) as the derivative of TC with respect to Q, and it can be represented as follows:

MC = dTC/dQ = 200 + 6Q.

From the marginal cost, we can set the marginal revenue (MR) equal to MC to get the profit-maximising quantity as follows:

MR = dTR/dQ = P + Q(500 - P) = 500 - Q + 500Q - Q² = 1000Q - Q² - 500 = MC = 200 + 6Q.

Substituting P = 500 - Q in the above expression and rearranging yields the following:

Q = 150, and hence, P = $350.

Therefore, the profit-maximising price is $350, and the quantity is 150. We can verify that the solution is a maximum by computing the second-order condition, which is negative.

To calculate the producer surplus, we first need to obtain the area above the marginal cost and below the price.

Thus, we have:

PS = ∫ MC to QdQ

= ∫ (200 + 6Q) dQ from 0 to 150

= [200Q + 3Q²] from 0 to 150

= $33,750.

Similarly, the consumer surplus can be computed as the difference between the market value of the product and what the consumers paid for it. The area below the price line and above the demand curve yields the consumer surplus.

Thus, we have:

CS = ∫ P to QdQ

= ∫ (500 - Q) dQ from 0 to 150

= [(500 × Q) - (Q²/2)] from 0 to 150

= $31,875.

Finally, the firm profit can be obtained by multiplying the profit-maximizing quantity by the profit-maximizing price and subtracting the total cost.

Thus, we have:

Profit = TR - TC = Q × P - TC = (150 × $350) - (300 + 200 × 150 + 3 × 150²) = $37,500.

Hence, the producer surplus, consumer surplus, and firm profit are $33,750, $31,875, and $37,500, respectively.

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The probability of rolling less than three (P(x < 3)) when rolling the number cube 10 times is approximately 0.972, or 97.2%.

If a success is defined as getting a three on a six-sided number cube, we can calculate the probability of rolling less than three (P(x < 3)) when rolling the number cube 10 times.

To find this probability, we need to consider the complementary event, which is rolling a three or greater. The probability of rolling a three or greater on a single roll is 1 - P(x < 3).

The probability of rolling a three or greater on a single roll is 1 - (2/6) = 4/6 = 2/3.

Since rolling the number cube 10 times is independent, we can multiply the probabilities together. Therefore, the probability of rolling a three or greater on all 10 rolls is (2/3)^10.

To find P(x < 3), we take the complement of this probability:

P(x < 3) = 1 - P(x ≥ 3) = 1 - (2/3)^10 ≈ 1 - 0.028 ≈ 0.972.

Therefore, the probability of rolling less than three (P(x < 3)) when rolling the number cube 10 times is approximately 0.972, or 97.2%.

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Answer:1,2,4,6

Step-by-step explanation:

I just finished this assignment!!! Good luck and God bless.

Answer:bruh thats too much and its long

Step-by-step explanation:

Hausu

Answer:

c 23ft

Step-by-step explanation:

The ratio of the original heights of the two candles which are lighted at the same time is 3:4.

A ratio is a quantitative relationship between two or more quantities or values, expressing how many times one quantity is contained in or is equal to another quantity.

Let the original height of the first candle as h1 and the original height of the second candle as h2.

we have,

- In six hours, the first candle is extinguished.

- The second candle burns down in 8 hours.

- After 3 hours, both candles are equally high.

From this, we can deduce that after 3 hours, both candles have burned down to the same fraction of their original heights.

For the first candle:

Remaining height of the first candle = h1/2

For the second candle:

Remaining height of the second candle = (3/8) h2

Since both candles are equally high after 3 hours, we can set up the following equation:

h1/2 = (3/8) h2

h1/h2 = (3/8) 2

h1/h2 = 3/4

Therefore, the ratio of the original heights is 3:4.

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Answer:

Step-by-step explanation:

lim x -> +oo    -2x³ - 13x² + 8x + 52

x³ (-2 -13/x + 8/x² + 52/x³)

+oo³ (-2 - 13/+oo + 8/+oo² + 52/oo³)

+oo(-2 + 0 + 0 + 0)

-oo

lim x -> -oo    -2x³ - 13x² + 8x + 52

x³ (-2 -13/x + 8/x² + 52/x³)

-oo³ (-2 - 13/-oo + 8/-oo² + 52/-oo³)

-oo(-2 + 0 + 0 + 0)

+oo

The sample variance is the most accurate point estimate of the population variance sigmasquared.

The best point estimate of the population variance is the sample variance. This is because the sample variance is an unbiased estimator of the population variance, meaning that it is the most accurate estimate of the population variance. The sample variance is calculated by taking each individual data point, subtracting the sample mean, squaring the result, and then summing the results. The sample variance then is the sum of these squared differences divided by the number of data points minus one. This is a consistent estimator, meaning that it will always produce the same result even if the sample size is different. This is why the sample variance is the best point estimate for the population variance.

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Answer:

Step-by-step explanation:

Answer to Consider the area between the graphs x+6y=12 and x+4=y^2. ... This Can Be Computed As A Single Interval Where Alpha= Beta= And H(y)=

∠CFA ≅ ∠EDA (By Transitive Property of Congruence).

Given:

Three lines AD, CF, and BE are intersecting each other at the midpoint O.

To prove:

∠CFA ≅ ∠EDA

Proof:

Given that AD, CF, and BE intersect at the midpoint O.

By definition of a midpoint, OA ≅ OD, OB ≅ OE.

OA = OD and OB = OE.

Triangle OAD ≅ Triangle OBE (By Side-Side-Side congruence).

∠OAD ≅ ∠OBE (By Corresponding Parts of Congruent Triangles are Congruent).

∠CFA and ∠EDA are vertical angles.

∠OAD ≅ ∠CFA and ∠OBE ≅ ∠EDA (By Vertical Angles are Congruent).

Therefore, ∠CFA ≅ ∠EDA (By Transitive Property of Congruence).

Hence, it is proven that ∠CFA ≅ ∠EDA.

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