Evaluate the following integrals:

∫(x^3√(x^4+2)dx (Hint: by using the subsitution, u = x^4+2 )

Answer:

k=15/4

Step-by-step explanation:

so you have to do y=Kx and then find you constant witch would give you the answer witch the answer is above.

hope this helped you

Dan will need 360g of plain flour, 3 eggs, and 900ml of milk to make 12 pancakes.

To make 12 pancakes, Dan will need 360g of plain flour, 3 eggs, and 900ml of milk.

We can use proportions to figure out how much of each ingredient Dan will need. If 240g of plain flour, 2 eggs, and 600ml of milk are enough to make 8 pancakes, then we can set up the following ratios:

Plain flour: 240g/8 pancakes = x/12 pancakes

Eggs: 2/8 pancakes = y/12 pancakes

Milk: 600ml/8 pancakes = z/12 pancakes

Solving for x, y, and z in each of these ratios, we get x = 360g of plain flour, y = 3 eggs, and z = 900ml of milk. Therefore, Dan will need 360g of plain flour, 3 eggs, and 900ml of milk to make 12 pancakes.

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Out of the 20,000 athletes, 788 can be expected to test positive for drugs during the Olympics.

During the Olympics, all athletes must pass a mandatory drug test administered by the International Olympic Committee before they are permitted to compete. Assuming a 1% drug use rate among 20,000 athletes, we can expect about 200 athletes to actually use drugs (1% of 20,000). With a 97% accurate drug test, 3% of the test results will be inaccurate.
Out of the 200 athletes using drugs, 97% will test positive, which equals 194 athletes (0.97 * 200). However, there are also 19,800 athletes not using drugs (20,000 - 200). Out of these, 3% will falsely test positive, which equals 594 athletes (0.03 * 19,800).
Therefore, approximately 788 athletes (194 + 594) can be expected to test positive for drugs during the Olympics.

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approximately probability is 194 athletes can be expected to test positive for drugs out of a total of 20,000 athletes.

What is Probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability was introduced in mathematics to predict how likely events are to occur.

To determine the approximate number of athletes expected to test positive for drugs out of a total of 20,000 athletes, we can calculate it based on the given accuracy rate of the drug test and the rate of drug use among athletes.

The rate of drug use among athletes is given as 1 athlete per 100, which can also be expressed as a probability of 1/100 or 0.01. This means that the probability of an athlete using drugs is 0.01.

The accuracy rate of the drug test is stated as 97%, which can be expressed as a probability of 0.97. This means that the probability of a drug test correctly identifying an athlete who is using drugs is 0.97

Now, we can calculate the expected number of athletes who will test positive for drugs using these probabilities.

Expected number of athletes testing positive = Total number of athletes * Probability of drug use * Probability of accurate drug test result

Expected number of athletes testing positive = 20,000 * 0.01 * 0.97

Expected number of athletes testing positive = 200 * 0.97

Expected number of athletes testing positive ≈ 194

Therefore, approximately probability is 194 athletes can be expected to test positive for drugs out of a total of 20,000 athletes.

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Answer:

C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

When dividing exponents, you can subtract them from eachother.

So, x^2/x = x    y^3/y^-3=y^6     z^2/z^2 = z^0 = 1

Answer:

The "power rule" tells us that to raise a power to a power, just multiply the exponents. Here you see that 52 raised to the 3rd power is equal to 56. The quotient rule tells us that we can divide two powers with the same base by subtracting the exponents.

Step-by-step explanation:

sup

Answer:

67!

Step-by-step explanation:

A way to look at it is, since the number is 387, it can be broken into 6 parts. 50x6 is about 300. That leaves 87 to be left over. So it's safe to assume each number will be around 50-60, so I started to add up six consecutive numbers together until I reached my final set of numbers to reach 387.

My numbers were 62+63+64+65+66+67=387

I hope this makes sense!

The measure of the height of the right rectangular prism can be either 2 or 5 centimeters

To find the height of a right rectangular prism, we need to know the surface area of the prism. The surface area of a right rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

where l represents the length, w represents the width, and h represents the height of the prism.

In this case, we are given that the surface area is 310 square centimeters. We can set up the equation as follows:

310 = 2lw + 2lh + 2wh

Since we don't have specific values for the length, width, or height, we can't solve for each individually. However, we can find the relationship between the variables.

Let's assume the length, width, and height are positive integers. We can then factorize the surface area value of 310 to identify the possible combinations of the length, width, and height.

310 = 2 * 5 * 31

Here, we have various combinations of factors that can represent the length, width, and height:

Length = 5, Width = 31, Height = 2

Length = 31, Width = 5, Height = 2

Length = 2, Width = 31, Height = 5

Length = 31, Width = 2, Height = 5

Length = 5, Width = 2, Height = 31

Length = 2, Width = 5, Height = 31

Since the height is the value that we're interested in, we can conclude that the measure of the height of the prism can be either 2 or 5 centimeters, depending on the specific dimensions of the prism.

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The null hypothesis suggests that there is no dissimilarity in escape time among lizards from habitats that have been invaded and those from uninvaded habitats.

The alternative hypotheses is that lizards residing in environments that have been invaded will have a greater tendency to escape quickly as compared to those dwelling in uninvaded habitats.

The consequent p-value will demonstrate the level of statistical significance of the results.

The likelihood of obtaining the observed data, or a more extreme version of it, is denoted by the p-value when considering the null hypothesis.

When the p-value is below 0. 05, it signifies compelling evidence against the null hypothesis, implying that the variation in flee times observed is unlikely to be a random occurrence.

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(-6)x (y=3x+5)                                        22x=-2            x=-2/22

4x+6y=28                                                   y=3(-2/22)+5           y=52/11                    

-6y=-18x-30

4x+6y=28

eliminate

so -18x-30=0

     4x-28=0

    =-22x-2=0

*Mark Brainlist please that took me 7 minutes

Answer:3

Step-by-step explanation:

(-3/4)/(-2/8)=(-3/4)(-8/2)=(-3/4)(-4)=3

Renna cannot use the elevator because the elevator's mass limit is exceeded by the combined mass of Renna and her identical packages (620 kg)

Let the mass of one of the identical packages be represented by the letter m. Then, we are told that each of the packages has a mass of 37.4 kg. Therefore,m = 37.4 kgNow, to find the total mass of Renna and her identical packages, we multiply the mass of one of the identical packages by the total number of identical packages. Since Renna's load consists of identical packages, we can determine the total number of identical packages as follows:N = \frac{620}{m}where N represents the total number of identical packages.

So, N = \frac{620}{37.4} \approx 16.55. Since N must be a whole number, we round up to the nearest whole number to obtain N = 17.Therefore, the total mass of Renna and her identical packages is:total mass = Renna's mass + (mass of one package x total number of identical packages)= 620 + (37.4 x 17)≈ 1272.8 kgSince the mass limit for the elevator is 450 kg, it is not possible for Renna and her load of identical packages to use the elevator because their combined mass exceeds the maximum mass limit for the elevator. Renna cannot use the elevator because the elevator's mass limit is exceeded by the combined mass of Renna and her identical packages (620 kg).

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Answer:

67

Step-by-step explanation:

1. Find the common difference of the arithmetic sequence

2. Find the 3rd term of the arithmetic sequence using the arithmetic sequence formula

⭐What is an arithmetic sequence?

1. Substitute the first term into the arithmetic sequence formula

\(a_n = a_1 + d(n-1)\)

\(a_n = 40+d(n-1)\)

2. Substitute the 7th term into the equation to solve for d

\(a_7 = 40+d(7-1)\\a_7 = 40+d(6)\)

\(a_7 = 40 + 6d\\121 = 40 + 6d\)

\(81 = 6d\) . . . . . . . subtract 40 from both sides of the equation

\(13.5 = d\) . . . . . . divide both sides by 6 to isolate d

3. Substitute d back into our original equation

\(a_n = 40 +13.5(n-1)\)

4. Solve for the third term by substituting 3 for n

\(a_n = 40+13.5(n-1)\\a_3 = 40+13.5(3-1)\\a_3 = 40+13.5(2)\\a_3 = 40 + 27\\\)

∴ \(a_3 = 67\)

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The future value of $500 in 24 years, assuming an interest rate of 6 percent compounded semiannually, is $1,962.82.

To calculate the future value, we can use the formula for compound interest:

FV = PV * (1 + r/n)^(n*t)

Where:

FV = Future value

PV = Present value (initial investment)

r = Interest rate

n = Number of compounding periods per year

t = Number of years

In this case, the present value (PV) is $500, the interest rate (r) is 6 percent (or 0.06), the number of compounding periods per year (n) is 2 (semiannually), and the number of years (t) is 24.

Plugging these values into the formula, we get:

FV = $500 * (1 + 0.06/2)^(2*24)

     = $500 * (1 + 0.03)^(48)

     = $500 * (1.03)^(48)

     ≈ $1,962.82

Therefore, the future value of $500 after 24 years, compounded semiannually at an interest rate of 6 percent, is approximately $1,962.82.

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Answer: -1

Explanation: -3 + 5 = 2

2x + 2 = 0

x = -1

a)  The estimated interquartile range for the masses of the emperor penguins is 30 kg - 25 kg = 5 kg.

b) The median mass of the king penguins would be M kg, with Q1 being M - 3.5 kg and Q3 being M + 3.5 kg.

c) Without the specific value of M, we cannot make a direct comparison between the median masses of the two species. By comparing interquartile range  values, we can infer that the masses of the king penguins have a larger spread or variability within the interquartile range compared to the emperor penguins.

a) To estimate the interquartile range for the masses of the emperor penguins, we can use the cumulative frequency table provided. The median mass is given as 23 kg, which means that 50% of the emperor penguins have a mass of 23 kg or less. Since the cumulative frequency at this point is 20, we can infer that there are 20 emperor penguins with a mass of 23 kg or less.

b) Given that the interquartile range for the masses of the king penguins is 7 kg, we can apply a similar approach to estimate the median mass of the king penguins. Since the interquartile range represents the range between Q1 and Q3, which covers 50% of the data, the median will lie halfway between these quartiles.

c) To make comparisons between the masses of the emperor and king penguins, we can consider the following two aspects:

Overall, based on the available information, it is challenging to make specific comparisons between the masses of the two penguin species without knowing the exact values for the median mass of the

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Answer:

95800.77

Step-by-step explanation:

Answer:

95800.77

Step-by-step explanation:

Answer:

hi i think the answer shouldbe 34/43 as its out of 43 and there is 34 people on the internet. I think this should be write but it may  be wrong. if this is right please vote for brainliest. i hope my answer is right and this helps bye.

the general formula of a parabola is

we can replace the the points to find a,b and c

First (0,4)

Then (-5,1.5) and c=4

The equation to determine the length and width of the rug is

28 = w² + 12w

Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.

What is a rectangle?

Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

We are given a rectangular rug with an area of 28 square feet.

Also, the rug is 12 feet longer than it is wide.

So,

Let 'l' be the length of the rug and 'w' be the width of the rug

As given, Length is 12 feet longer than its width

Therefore, l = w + 12

We know Area of rectangle = Length * Width and area is given to be 28 square feet.

So,

⇒28 = (w + 12)w

⇒28 = w² + 12w

Hence, the equation to determine the length and width of the rug is

28 = w² + 12w.

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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.

Create an equation to determine the length and the width of the rug.

Answer:

x = 39

Step-by-step explanation:

let [180 - (31 + x)]   = 3rd angle inside triangle; simplified is '149 - x'

the (2x - 8) angle and '149 - x' angle are supplementary, thus add to 180

2x - 8 + (149 - x) = 180

2x + (-x) + (-8) + 149 = 180

x  + 141 = 180

x = 39

Answer: The correct answer would be Graph H.

Step-by-step explanation:

Answer:

top right

Step-by-step explanation:

600 per 10 hours is a rate of 60/hour.

You need a graph that has a slope of 60 and includes the point (1, 60).

Answer: top right

This can be derived using Chebyshev's inequality, as Chebyshev's inequality and the law of large numbers are different in nature.

Let M_n be the maximum of n independent U(0, 1) random variables.

To derive the exact expression for P(|M_n − 1| > ε), we need to follow the below steps:

First, we determine P(M_n ≤ 1-ε). The probability that all of the n variables are less than 1-ε is (1-ε)^n

So, P(M_n ≤ 1-ε) = (1-ε)^n

Similarly, we determine P(M_n ≥ 1+ε), which is equal to the probability that all the n variables are greater than 1+\epsilon

Hence, P(M_n ≥ 1+ε) = (1-ε)^n

Now we can write P(|M_n-1|>ε)=1-P(M_n≤1-ε)-P(M_n≥1+ε)

P(|M_n-1|>ε) = 1 - (1-ε)^n - (1+ε)^n.

Thus we have derived the exact expression for P(|M_n − 1| > ε) as P(|M_n-1|>ε) = 1 - (1-ε)^n - (1+ε)^n

Now, to show that $lim_{n\to\∞}$ P(|M_n - 1| > ε) = 0 , we can use Chebyshev's inequality which states that P(|X-\mu|>ε)≤{Var(X)/ε^2}

Chebyshev's inequality and the law of large numbers are different in nature as Chebyshev's inequality gives the upper bound for the probability of deviation of a random variable from its expected value. On the other hand, the law of large numbers provides information about how the sample mean approaches the population mean as the sample size increases.

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Answer: 11,500 grams

Step-by-step explanation: 920/8=115 115*100= 11,500

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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The cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is d(t) = 6cos(\(\pi\)t).

As long as its length is constant, a pendulum completes each swing (or oscillation) in precisely the same amount of time. Any particular pendulum oscillates for a fixed amount of time.

Calculation for the cosine function-

The given function is: cosine function, d = acos(bt).

As, the pendulum takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right.

The total time 't' by the pendulum is 2 sec.

Calculate the angular speed of the pendulum by-

ω = 2\(\pi\)f

   = 2\(\pi\)×(1/2)

ω = \(\pi\) which is 'b' value of the given function.

As given, the distance of the pendulum from the centre is half of the total distance.

a = 12/2

a = 6

Substitute the obtained values in the cosine function, d = acos(bt),

d(t) = 6cos(\(\pi\)t)

Therefore, the cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is  d(t) = 6cos(\(\pi\)t).

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The complete question is -

Starting at its rightmost position, it takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right. Write a cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds).

Answer:

a=6

The period is 2 seconds.

b=pi

t=0.5

d=4.243

Step-by-step explanation:

Answer:

7.5 MW

Step-by-step explanation:

The power generated from a falling water is a function of its height and volume. The power generated an be calculated using the formula:

Power (P) = Density(ρ) * volume flow rate(Q) * acceleration due to gravity(g) * height(h)

P = ρQgh

But Qh = Velocity(v) * volume(V).

Hence power = ρvgV

Given that ρ of water = 1000 kg/m³, v = 75 m/s, V = 10 m³, g = 10 m/s². Substituting:

P = ρvgV = 1000 * 75 * 10 * 10 = 7500000 W

P = 7.5 MW

Answer:

7

Step-by-step explanation:

x + 4y = 12

4y = -x + 12

Line G:

y = -1/4x + 3

Line H:

y = 4x + b

-5 = 4(-3) + b

-5 = -12 + b

7 = b

Answer:

9) u= -12

11) -18 over 2

Step-by-step explanation:

Hope this helps!!

Answer:

x would be -72 and 9 u would be -12

Step-by-step explanation: