Please help with this problem

Step-by-step explanation:

integral from 0 to 2pi of cos3x

(sin3x)/3 from 0 to 2 pi

sin 6pi /3 - sin 0 /3 = 0

Answer: 9500000

Step-by-step explanation: 95 × 100000 = 9500000

*Multiply the value by 100000*

After 5 days, the retailer starts making the money. The solution has been obtained by using the concept of break - even.

What is break - even?

The balance point known as "break-even" results in neither a profit nor a loss. Every value below the break-even mark represents a loss, whereas any value above it represents a gain.

We are given revenue function as R(x) = \(2x^3 + 11x^2 - 23x - 14\).

The cost function is given as C(x) = \(13x^2 + 11x + 16\).

The retailer will start earning only when the cost will be covered. This means that he will earn after when the R(x) = C(x).

So,

⇒ R(x) = C(x)

⇒ \(2x^3 + 11x^2 - 23x - 14\) = \(13x^2 + 11x + 16\)

⇒ \(2x^3\) = \(2x^2 + 34x + 30\)

⇒ \(x^3\) = \(x^2 + 17x + 15\)

⇒ \(x^3\) - \(x^2 - 17x - 15\) = 0

⇒ (x - 5) (x + 1) (x + 3) = 0

⇒ x = 5, -1, -3

Since, the days cannot be negative so, x = 5.

Hence, after 5 days, the retailer starts making the money.

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Question:

A popular video game retailer develops apps. The total revenue, in dollars per day, after x days can be modeled by the function R(x) = \(2x^3 + 11x^2 - 23x - 14\). The total cost, in dollars per day, after x days, can be modeled by the function C(x) = \(13x^2 + 11x + 16\). After how many days does the retailer start making money?

a. 1

b. 2

c. 5

d. 7

Both options a. A = 129.9° and b. A = 53.1° are correct.

To find the possible values for angle A in triangle ABC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Using the Law of Sines, we have sin(A)/a = sin(B)/b. Plugging in the given values, we get sin(A)/36 = sin(51°)/35.

To find the two possible values for angle A, we can solve the equation sin(A)/36 = sin(51°)/35. Taking the arcsine of both sides, we have A = arcsin((sin(51°)/35)*36).

Calculating this expression, we find two possible values for angle A:

A ≈ 53.1° (rounded to the nearest tenth)

A ≈ 129.9° (rounded to the nearest tenth)

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(D) If many random samples of size 15 are taken from this population, then 95% of the confidence intervals will contain the population mean.

The best interpretation of the 95% confidence interval (64.06, 66.96) for the population mean, based on a random sample of size 15, is choice (B). This interpretation correctly states that if many random samples of size 15 are taken from the same population, then 95% of the time the population mean will lie within the interval. In other words, we can be 95% confident that the true population mean falls within this range based on the sample data. It is important to note that this does not mean that 95% of the population measurements lie within the interval (choice A), nor does it mean that 95% of the sample means will lie within the interval (choice C) or that 95% of the confidence intervals will contain the population mean (choice D) or the sample mean (choice E). These options are incorrect because they either misinterpret or generalize the confidence interval beyond its intended scope. Therefore, the best interpretation is the one that accurately reflects the meaning and purpose of a confidence interval.
(D) If many random samples of size 15 are taken from this population, then 95% of the confidence intervals will contain the population mean.

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The number of hours it would take for the duckweed to grow to a mass triple the original size is 45 hours.

Given that ; The original mass of the duckweed population = 500 kg.

For it to have mass that will triple the original size then it will be

= ( 3* 500 kg)

= 1500 kg

Then we can substitute into the equation as ;

M(t)= 500• 3 t/45

500 * (3t/45) = 1500

3t/45 = 1500/500

3t/45 = 3

3t = (45 * 3)

3t = 135

t = 135 / 3

= 45

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The number of hours it would take for the duckweed to grow to a mass triple the original size is 45 hours.

How can the number of hours be calculated?

Given that ; The original mass of the duckweed population = 500 kg.

For it to have mass that will triple the original size then it will be

= ( 3* 500 kg)

= 1500 kg

Then we can substitute into the equation as ;

M(t)= 500• 3 t/45

500 * (3t/45) = 1500

3t/45 = 1500/500

3t/45 = 3

3t = (45 * 3)

3t = 135

t = 135 / 3

= 45

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Step-by-step explanation:

Use PEMDAS

\(\begin{array}{ccc}214.8-(4^2+3)\times4&\\214.8-(16+3)\times4&Evaluate\\214.8-19\times4&Add\\214.8-76&Multiply\\138.8&Subtract\end{array}\)

Answer: A $1,332.73

Step-by-step explanation:

The monthly payment if you put 3. 5% down is a. $1,332. 73.

Down payment=218,500 - (218.500×3.5%)

Down payment=218.500-7,647.5

Down payment=210,852.50

Time = 12×30=360 months

rate=6.5/1,200 = 0.005416667

Using the loan payment formula

Monthly payment = (Rate + [Rate / (((1 + rate)^months) -1)] × Principal

Let plug in the formula

Monthly payment = (0.005416667 + [0.005416667 / (((1.005416667)^360)-1)] × principal

Monthly payment = (0.005416667 + [0.005416667 / (((1.005416667)^360)-1)] ×principal

Monthly payment = 0.005416667 + [(0.005416667 / 6.9917988084 -1)] ×210,852.50

Monthly payment = 0.005416667 + [(0.005416667 / 5.9917988084)] × 210,852.50

Monthly payment = 0.005416667 + [(0.005416667 / 5.9917988084)] × 210,852.50

Monthly payment = (0.005416667 + 0.0009040135) × 210,852.50

Monthly payment = 0.0063206805× 210,852.50

Monthly payment = 1,332.73

Inconclusion the monthly payment if you put 3. 5% down is a. $1,332. 73.

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Answer:

C

Step-by-step explanation:

324 = 4 \((3)^{2x}\) ( divide both sides by 4 )

81 = \(3^{2x}\) , that is

\(3^{4}\) = \(3^{2x}\)

Since bases on both sides are equal, both 3, then equate exponents

4 = 2x ( divide both sides by 2 )

2 = x → C

The number of 1-point shot is 19 and the number of 2-point shot is 37.

At a basketball game, a team made 56 successful shots. They were a combination of 1- and 2-point shots. The team scored 93 points in all.

Therefore, the system of equation to find the number of each type of shot can be found as follows:

Hence,

let

x = number of 1- point shots

y = number of 2- point shots

Therefore,

x + y = 56

x + 2y = 93

subtract the equations'

y = 93 - 56

y = 37

Therefore,

x = 56 - 37

x = 19

Therefore,

number of 1-points shot = 19

number of 2-point shot = 37

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Answer:

B

Step-by-step explanation:

\( \sqrt[3]{x + 1} = 2\)

Let us cube both sides.

\( = > (\sqrt[3]{x + 1} ) ^{3} = {2}^{3} \)

Now, it will be only x + 1.

\( = > x + 1 = 8\)

Transpose 1 to the Right Hand Side.

\( = > x = 8 - 1\)

Now, subtract.

\( = > x = 7\)

Answer:

x = 7

Hope you could understand.

If you have any query, feel free to ask.

The total number of oranges present in the bag was 21.

For the stated question.

Let the total number of oranges in the bag be 'x'.

Total stale oranges = 7.

Thus,

Probability (first orange is stale) = Total stale oranges/ Total oranges.

Probability (first orange is stale) = 7/x

Probability (second orange is stale) = 6/(x - 1).

But, probability to pick two stale oranges is 2/21

7/x . 6/(x - 1) = 2/21

On solving,

x ² - x - 441 = 0

x = 21

Thus, the total number of oranges present in the bag was 21.

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In 77 times, the value of 1 3/5 is added with 1 3/5 to get 100 as the final value by solving the mathematical calculation.

To solve this problem, we can use a simple formula:

n = (target sum - initial sum) / increment

In this case, our target sum is 100, our initial sum is 1 3/5 or 8/5, and our increment is also 1 3/5 or 8/5. Substituting these values into the formula, we get:

n = (100 - 8/5) / 8/5

n = 625/8 - 8/5

n = 77.125

So we need to add 1 3/5 by 1 3/5 approximately 77 times to reach a sum of 100. We can confirm this by multiplying 77 by the increment and adding it to the initial sum:

77 x 8/5 = 123.2

123.2 + 8/5 = 100.0

Therefore, we have successfully reached a sum of 100 by adding 1 3/5 by 1 3/5 approximately 77 times.

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In order to calculate the expected revenue of a toll bridge during a particular daytime period, we need to know how many passenger cars and other vehicles are expected to pass through the bridge, as well as the toll charges for each type of vehicle.Let's say that X is the number of passenger cars and Y is the number of other vehicles. Then, we can use the following formula to calculate the expected revenue of the toll bridge:h\((X, Y) = 1.00X + 2.50Y\)This formula takes into account the toll charges for each type of vehicle and multiplies them by the number of vehicles that are expected to pass through the toll bridge during the daytime period.

For example, if we expect 100 passenger cars and 50 other vehicles to pass through the toll bridge during the daytime period, then the expected revenue of the toll bridge would be\(:h(100, 50) = 1.00(100) + 2.50(50) = 100 + 125 = $225\)

Therefore, the expected revenue of the toll bridge during the particular daytime period would be $225.

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There will be a $22.50 credit left on the card after Kala uses it for 15 minutes of calls.

We have,

The given function C(x) represents the credit remaining on a phone card after x minutes of use, where x is the number of minutes used and C(x) is the remaining credit in dollars.

C(x) = 25.50 - 0.20x

To find how much credit is left on the card after Kala uses it for 15 minutes of calls, we need to evaluate C(15).

C(15) = 25.50 - 0.20(15)

C(15) = 25.50 - 3

C(15) = 22.50

Therefore,

There will be a $22.50 credit left on the card after Kala uses it for 15 minutes of calls.

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Answer:

1. $11

2. $10.75

3. new median: 12

new mean: $11.75

The product $c_1 c_2$ in rectangular frame is \(\$10 e^{i(2\theta \pm \frac{pi}{3})}\$.\)

Let $c_1$ and $c_2$ be the two complex numbers that frame an even triangle with $3+2i$ and $6+i$.

The dispose of between two complex numbers $a$ and $b$ is given by $|b-a|$. Since the triangle is even, the wipe out someplace in the scope of $3+2i$ and $6+i$ ought to be equivalent to the underlying venture with to the kill among $3+2i$ and $c$, conjointly make back the underlying speculation with to the take out among $6+i$ and $c$.

So, we have the following conditions:

$|6 + i - (3 + 2i)| = |c - (3 + 2i)|$

$|6 + i - (3 + 2i)| = |c - (6 + i)|$

Tackling these conditions, we get:

$|3 - i| = |c - (3 + 2i)|$

$|3 - i| = |c - 6 - i|$

Presently, let's discover the esteem of $c$:

$|c - (3 + 2i)| = |3 - i|$

\(\$|c - (3 + 2i)| = \sqrt{(3-0)^{2} + (-1-0)^{2} = \sqrt{10}\$\)

So, \(\$c - (3 + 2i) = \pm \sqrt{10} e^{i\theta}\$\), where \(\$\theta\$\) is the point between the positive genuine hub and the line interfacing $3+2i$ and $c$?

Presently, let's discover the esteem of $c$ utilizing the moment condition:

$|c - (6 + i)| = |3 - i|$

\(\$|c - (6 + i)| = \sqrt{(3-0)^{2} + (-1-0)^{2} = \sqrt{10}\$\)

So, \(\$c - (6 + i) = \pm \sqrt{10} e^{i\theta'}\$\), where \(\$\theta'\$\) is the point between the positive genuine hub and the line interfacing $6+i$ and $c$?

Since the triangle is equilateral, $theta$  \(\$\theta'\$\) must vary by \(\$\pm\) \(\frac{\pi}{3}\$.\)

Presently, let's discover the item $c_1 c_2$:

$c_1 c_2 = (c - (3 + 2i))(c - (6 + i))$

$c_1 c_2 =\((\pm \sqrt{10} e^{i\theta})(\pm \sqrt{10} e^{i(\theta \pm \frac{\pi}{3})})\$\)

$c_1 c_2 = \(10 e^{i\theta} e^{i(\theta \pm \frac{\pi}{3})}\$\)

$c_1 c_2 = \(10 e^{i(2\theta \pm \frac{\pi}{3})}\$\)

So, the item $c_1 c_2$ in rectangular frame is \(\$10 e^{i(2\theta \pm \frac{\pi}{3})}\$.\)

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Answer:

A. About 1/3 of the people prefer pie without ice cream

Step-by-step explanation:

We know there were 80 people surveyed, so that's our denominator. Pie without ice cream is the bottom row. 15 + 12 = 27. 27/80 = 0.3375, which is 33.75% (multiply 0.3375 by 100), which is about 1/3.

B is wrong, because the blueberry pie numbers are not double the cherry pie numbers

C is wrong because cherry with ice cream is 24, blueberry without is 15

D is wrong because the ratio of blueberry to cherry is 44:36, and with ice cream to without is 53:27

Answer:

Molar Mass Molar mass is defined as the mass of one mole of representative particles of a substance. By looking at a periodic table, we can conclude that the molar mass of lithium is 6.94g, the molar mass of zinc is 65.38g, and the molar mass of gold is 196.97g. Each of these quantities contains 6.02 × 1023 atoms of that particular element.

Step-by-step explanation:

Hope this helps!!!

-BB

please mark me brainly

The interest rate for the savings account is 5% after 4 years, $20,000 deposited in a savings account with simple interest earned $800 in interest.

We can use the formula for simple interest to solve the problem:

Simple interest = (Principal * Rate * Time) / 100

where Principal is the initial amount deposited, Rate is the interest rate, and Time is the time period for which the interest is calculated.

We know that the Principal is $20,000 and the time period is 4 years. We are also given that the interest earned is $800. So we can plug in these values and solve for the interest rate:

$800 = (20,000 * Rate * 4) / 100

Multiplying both sides by 100 and dividing by 20,000 * 4, we get:

Rate = $800 / (20,000 * 4 / 100) = 0.05 or 5%

Therefore, the interest rate for the savings account is 5%.

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Answer:

Step-by-step explanation:

10x5=50

Answer:

50 cookies

Step-by-step explanation:

10 friends · 5 cookies each

10 · 5

50

(unless she needs some for herself as well...)

Answer:

We have this equation:

\(3(y+3)+7(2y-8)-(y-1)=0​\)

First, we do the parenthesis:

\(3y+9+14y-56-(y-1)=0\\\)

When there is a minus (-) in front of a parenthesis, all signs change inside it:

\(3y+9+14y-56-y+1)=0\\\)

Now we operate:

\(16y-46=0\)

We add 46 on both sides:

\(16y - 46 + 46 = 0 +46\)

\(16y = 46\)

And divide 16 on both sides:

\(\frac{16y}{16}=\frac{46}{16}\)

\(\bol{x = \frac{46}{16}}\) = \(\frac{23}{8}\)

Answer:

Step-by-step explanation:

3(y+3)+7(2y-8)-(y-1)=0​

3y + 9 + 14y - 56 - y + 1 = 0

16y - 46 = 0

16y - 46 + 46 = 0 + 46

16y = 46

16y/16 = 46/16

y = 23/8

Answer:

Step-by-step explanation:

that sucks

Answer:

Answer: 20025 gallons per hour

89 times 60= 5340 cups in one minute

5340 times 60= 320,400 cups in one hour

Convert 320,400 cups into gallons and you will get 20025.

Not positive if this is correct but it’s better than nothing lol

Answer:

47 years old.

Step-by-step explanation:

Let c represent each children, 'f' represent the father and 'm' represent the mother. We are given that:

\(4c=15*4=60\ years\\f=m+4\\\frac{4c+m+f}{6}=25\)

Replace the first two equations into the last to solve for 'f':

\(\frac{60+(f-4)+f}{6}=25 \\2f=(25*6)-60+4\\f=47\ years\)

The father is 47 years old.

The most appropriate units to describe the cost of the sandbox would indeed be dollars.

When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.

Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.

Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.

Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.

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When a high-value outlier is removed from a set of data, the standard deviation is expected to decrease. This is because the standard deviation is a measure of the dispersion or spread of the data.

An outlier is a value that lies far away from the other values in the data set, and its inclusion in the calculation of the standard deviation can significantly increase the value. By removing the outlier, the extreme value that contributed to the increased spread of the data is eliminated, resulting in a decrease in the standard deviation. The standard deviation measures the variability or dispersion of a set of data points from the mean. It is influenced by all the values in the data set, including outliers. An outlier is an observation that significantly differs from the other values in the data set. When a high-value outlier is removed, the standard deviation is expected to decrease. This is because the outlier has a large deviation from the mean, contributing to a higher spread in the data. By removing the outlier, we are essentially removing a value that is not representative of the overall pattern of the data. As a result, the remaining data points will have a smaller spread, and the standard deviation will decrease. To calculate the standard deviation after removing the outlier, you would simply recalculate it using the revised data set. The steps would be the same as calculating the standard deviation for any data set, but excluding the outlier from the calculation. This will give you a more accurate measure of the typical spread of the data without the influence of the outlier.

In conclusion, when a high-value outlier is removed from a data set, the standard deviation is expected to decrease. Removing the outlier eliminates the extreme value that contributed to the increased spread of the data, resulting in a more accurate measure of the typical variability of the remaining data points.

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Answer:

False, 82 inches is not greater than 5 feet and 10 inches

Step-by-step explanation:

1 feet = 12 inches

5x12=60+10=70

82 is greater than 70.

Answer: D

Step-by-step explanation:

Answer:

Step-by-step explanation:

The difference between the assets and the liabilities cannot be compared.