How much material was required for each dresses of the same size if it took 5 1/2 yards for both ?

Given:

In triangle ABC, \(m\angle A=66^\circ, AB=5\text{ mi}\).

To find:

The angle of depression from point A to point C.

Solution:

According to angle sum property, the sum of all interior angles of a triangle is 180 degrees.

In triangle ABC,

\(m\angle A+m\angle B+m\angle C=180^\circ\)

\(66^\circ+90^\circ+m\angle C=180^\circ\)

\(156^\circ+m\angle C=180^\circ\)

\(m\angle C=180^\circ-156^\circ\)

\(m\angle C=24^\circ\)

We know that if a transversal line intersect the two parallel lines, then alternate interior angles are equal. So, the angle of depression from point A to point C is equal to the measure of angle C in triangle ABC.

Therefore, the angle of depression is 24 degrees.

The number of months Mark can have the phone is given by the equation

A = 11.4 months

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of months be represented as = A

Now , the equation is

Now , the total amount with Mark = $ 146.43

The initial amount for the smartphone = $ 33

The amount per month for 2GB is = $ 9.95

So , the amount for A months = $ 9.95 ( A )

So , the equation will be

Initial amount for the smartphone + the amount for A months = total amount with Mark

Substituting the values in the equation , we get

33 + 9.95 ( A ) = 146.43   be equation (1)

On simplifying the equation , we get

Subtracting 33 on both sides of the equation , we get

9.95 ( A ) = 113.43

Divide by 9.95 on both sides of the equation , we get

A = 11.4 months

Therefore , the value of A is 11.4 months

Hence , the number of months is 11.4 months

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Answer:

~60•the length of PQ . , the length of QR is 90• Tell me if I'm wrong . sorry if I got it wrong .~

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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1. Revised Net Operating Income = $66,760

2. Revised Net Operating Income  =$64,640

3. Revised Net Operating Income  =$52,

1. If the sales volume increases by 40 units:

So, New Sales = 8,700 units + 40 units = 8,740 units

and, New Contribution Margin =

= $14.00 x 8,740 units

= 122, 360

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 122360 - 55600

= 66,760.

2. If the sales volume decreases by 40 units:

New Sales = 8,700 units - 40 units = 8,660 units

New Contribution Margin

= 14 x 8660

= 121,240

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 65,640

3. If the sales volume is 7,700 units:

New Sales = 7,700 units

New Contribution Margin

= 14 x 7700

= 107,800

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 52, 200

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The amount of your tax refund is $1,414

To find the tax refund, we need to subtract the amount of federal taxes owed after deductions from the amount of federal taxes already paid.

Tax refund = Federal taxes paid - Federal taxes owed after deductions

Tax refund = $12,042 - $10,628

Tax refund = $1,414

Rounding to the nearest cent, the tax refund is $1,414.00.

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Answer:

A

Step-by-step explanation:

A

Answer:

Q9 -  Option 1---- A -  15.6 Square Units

Q10 --Option --- (B) RECTANGLE

Step-by-step explanation:

Q9 --

we know area of triangle  = 1/2 ab sin theta

Where theta is the angle included between sides A and side B

A  = 5.2

B = 7

theta  = 121 degrees

1/2 * 5.2 * 7 * sin 121 degrees = 15.6 Square Units

Conclusion

The area of the triangle is 15.6 Square Units

Option --- (B) RECTANGLE

Hope this helps!

The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.

Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:

the measure of angle Z is equal to 65°

the side EF corresponds to JK and side FG corresponds to KL, so:

8/20 = 11/x

x = (11 × 20)/8 {cross multiplication}

x = 27.5

the side EF corresponds to JK and EH corresponds to JM, so:

8/20 = y/30

y = (30 × 8)/20 {cross multiplication}

y = 12

Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

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Answer:

I think B 90

Step-by-step explanation:

Its a right angle

it's B because I look it up

Answer:

Step-by-step explanation:

There are an infinite amount of possibilities with the solution of (4,1).  As proof, plot the point (4,1) on a coordinate system.  Then, draw straight lines that pass through that point.  These lines can differ in slopes. They can be either be positive, negative, vertical, or horizontal.

x = 4

y = 1

x + y = 5

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Answer:

The percent increase in the average cost of a dozen oranges from October 2020 to October 2021 is approximately 225%.

Step-by-step explanation:

To find the percent increase in the average cost of a dozen oranges from October 2020 to 2021, we need to first calculate the difference in the average cost and then divide it by the original average cost, and finally multiply by 100 to get the percentage increase.

The difference in the average cost of a dozen oranges between October 2020 and October 2021 is:

$5.59 - $1.72 = $3.87

To calculate the percent increase, we need to divide the difference by the original average cost and multiply by 100:

Percent increase = (difference/original average cost) x 100

Percent increase = ($3.87/$1.72) x 100

Percent increase = 224.41%

Therefore, the percent increase in the average cost of a dozen oranges from October 2020 to October 2021 is approximately 224.41%.

Step by step (for more help understanding):

The problem states that the average cost of a dozen oranges was $1.72 in October 2020 and $5.59 in October 2021. We need to find the percent increase in the average cost from October 2020 to October 2021.

Step 1: Find the difference in the average cost

To find the difference in the average cost, we subtract the original average cost from the new average cost.

$5.59 - $1.72 = $3.87

This means that the average cost of a dozen oranges increased by $3.87 from October 2020 to October 2021.

Step 2: Find the ratio of the difference to the original cost

To find the percentage increase, we need to express the difference as a percentage of the original cost. We do this by dividing the difference by the original cost.

$3.87 / $1.72 = 2.25

This means that the new average cost is 2.25 times the original average cost.

Step 3: Convert the ratio to a percentage

To convert the ratio to a percentage, we multiply it by 100.

2.25 x 100 = 225%

Step 4: Round the percentage to one or two decimal places

Finally, we round the percentage to one or two decimal places, depending on the level of accuracy required.

The percent increase in the average cost of a dozen oranges from October 2020 to October 2021 is approximately 225%.

Hope this helps, If not I'm sorry. If you need more help, ask me! :]

Answer:

$609

Step-by-step explanation:

Answer:

A ≈ 102.56

Step-by-step explanation:

The quantity decays continuously at a rate of 0.75% per day, which means that the amount of the quantity remaining after a certain number of days can be calculated using the formula:

A = A0 * e^(-rt)

where:

A0 is the initial value of the quantity

r is the decay rate (expressed as a decimal)

t is the number of days

e is the mathematical constant e (approximately equal to 2.71828)

A is the value of the quantity after t days

Substituting the given values, we get:

A = 170 * e^(-0.0075 * 56)

Using a calculator, we get:

A ≈ 102.56

Therefore, the value of the quantity after 56 days, rounded to the nearest hundredth, is approximately 102.56.

Answer:

1/4

Step-by-step explanation:

First you add all of the marbles in the bag which is 16 marbles.  The fraction of red marbles to the total would be 4/16.  In the simplest form that is 1/4. You can also just do 4 divide by 16 which gives you 0.25 and in decimal form that is 1/4.

Answer:

The answer is D.

\(3x {}^{2} - 10x - 1 = 0\)

Step-by-step explanation:

\(x = \frac{5 + 2 \sqrt{7} }{3} \)

Divide each term of 5+2√7 by 3 to get 5/3 + 2/3√7.

\(x = \frac{5}{3} + \frac{2}{3} \sqrt{7} \)

\(x = \frac{2 \sqrt{7 + 5} }{3} \)

or

\(x = 3.43\)

The distance between Bloemfontein and Upington is a distance of 582 kilometers. The distance between two cities may vary depending on the route taken, traffic, and other factors. The distance between these two cities is measured in a straight line, which may not be the actual road distance.

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The sampling distribution  of the sample proportion is approximately normal when the sample size (n) is large and the population proportion (p) is close to 0.5.

This can be mathematically expressed as follows:

\(n*p > 10 and n*(1-p) > 10\)

To illustrate, let's say we are sampling from a population with a proportion of 0.3. For the sampling distribution to be approximately normal, the sample size (n) must be larger than 33.3 (n > 33.3). This is because \(33.3*0.3 = 10 and 33.3*0.7 = 23.3\).

In other words, the sample size (n) must be large enough so that the product of the sample size (n) and the population proportion (p) is greater than 10 and the product of the sample size (n) and the population proportion (1-p) is also greater than 10. This ensures that the sampling distribution of the sample proportion is approximately normal.

To sum up, the sampling distribution of the sample proportion is approximately normal when the sample size (n) is large and the population proportion (p) is close to 0.5.

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Answer:

Step-by-step explanation:

Solution

The first step is to simplify the top of the fraction. Subtract 5.6 - 2.7

The numerator (top) and denominator(bottom) are decimal fractions. They are 2.9 for the top and 2.9 for the bottom.

The whole expression reduces down to 1, which is an integer.

Note

You have choices. If you want exact answers you will have to list those choices.

Answer: 1

Answer:

96?

Step-by-step explanation:

The total number of blocks the first time in the day:

14 +34 = 48

Mutiply that by 2 to see how many blocks he does twice a day

48(2)= 96

To evaluate the limit of the function as x approaches 0, where f(x) = sin(x)/x, we can use L'Hôpital's rule.

According to L'Hôpital's rule, if we have an indeterminate form of the type 0/0 or ∞/∞, we can take the derivative of the numerator and denominator until we reach a determinate form.

Let's differentiate the numerator and denominator:

\(\begin{align}f(x) &= \frac{\sin(x)}{x} \\f'(x)&=\frac{d}{dx}(\sin(x)) \\ &= \cos(x)\end{align}\)

\(\begin{align}f(x) &= \frac{\sin(x)}{x} \\f'(x)&=\frac{d}{dx}(x) \\ &= 1\end{align}\)

Now we can evaluate the limit as x approaches 0 using the derivatives:

\(\begin{align}\lim_{x \to 0} f(x) &= \lim_{x \to 0} \frac{\sin(x)}{x} \\ &= \lim_{x \to 0} \frac{\cos(x)}{1} \quad \text{(using L'Hôpital's rule)} \\ &= \cos(0) \\ &= 1 \end{align}\)

Therefore, the limit of f(x) as x approaches 0 is 1.

53 years for the Population of the United States to reach 300 million people according to this model.

The recursive formula of the population of the United States is given by ao = an1.015a - 1

Let's solve this to get a formula that is not recursive.a0 = a0 givena1 = 1.015a0 - 1a2 = 1.015a1 - 1 = 1.015 (1.015a0 - 1) - 1 = 1.0152 a0 - 1.015 - 1a3 = 1.015a2 - 1 = 1.015(1.015²a0 - 1.015 - 1) - 1 = 1.015³ a0 - 1.015² - 1.015 - 1a4 = 1.015a3 - 1 = 1.015(1.015³a0 - 1.015² - 1.015 - 1) - 1 = 1.015⁴ a0 - 1.015³ - 1.015² - 1.015 - 1an = 1.015na0 - 1.015n-1 - 1.015n-2 - ... - 1.015 - 1We can rewrite this asan = a0(1.015)

where a0 is the population of the United States in 1910 (92.2 million people) .

Now, we need to write an exponential function to find the population of the United States as a function of time in years since 1910.P(t) = 92.2(1.015)

To find the number of years it takes for the population to reach 300 million people, we need to solve the equation92.2(1.015)t = 300

Dividing both sides by 92.2, we get1.015t = 3.2596

Taking the natural logarithm of both sides, we get ln(1.015) = ln(3.2596)t = ln(3.2596)/ln(1.015) ≈ 53.2

Therefore,  approximately 53 years for the population of the United States to reach 300 million people according to this model.

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Answer:

uhhhhhhh you have to figure out what x is then choose wether it is the other variable a dependent variable, and explanatory variable, or a response variable

Step-by-step explanation:

easy as that

Answer:

Step-by-step explanation:

1 and 4/10

Answer:

g(4) = 10

f⁻¹(11) = 1

h{g(4)} =

if h(x) = (10/x) – 3 = 7

if h(x) = 10/(x – 3) = 10/7

____________

f⁻¹(x) = (x - 4) / 7

Answer:

Toyin weighs 50 kg, which is 20 kg more than Amara.

Step-by-step explanation:

If Amara weighs 30 kg and the ratio of the weight of Amara to the weight of Toyin is 3:5, then we can set up a proportion:

3/5 = 30/x

where x is the weight of Toyin in kg.

To solve for x, we can cross-multiply:

3x = 150

x = 50

Therefore, Toyin weighs 50 kg, which is 20 kg more than Amara.

The value of angle ABE is 52°

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted by triangle ABC.

The interior angles of a triangle are the inside angles formed where two sides of the triangle meet.

The sum of interior angle in a triangle is 180°

Angle EBD = 180-(90+27)

= 180-117

= 63°

angle ABE + EBD = ABD

ABE = ABD - EBD

ABE = 115-63

= 52°

Therefore the value of angle ABE is 52°

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Answer:

43.6 has 3 significant figures.

Answer:

x = 32

Step-by-step explanation:

The profit function for this problem is given as follows:

P(x) = -0.5x³ + 100x² - 500x + 300.

The profit function is obtained as the subtraction of the revenue function by the cost function, as follows:

P(x) = R(x) - C(x).

The functions for this problem are given as follows:

Hence the profit function is given as follows:

P(x) = -0.5x³ + 600x² - 200x + 300 - 500x² - 300x

P(x) = -0.5x³ + 100x² - 500x + 300.

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