In a normal distribution, what proportion of people have a score between 60 and 70 when u = 40, and a = 157 Report your answer to the fourth decimal place. Answer: Question 19 Not yet answered Point out of so a question 19. TRUE or FALSE Jack has 1,000 books but will has 2,000 books. If the average number of books in a personal library is 1,400 with an SD of 400, then Jack and Jill have the same x-score. Select one: True False

The simplified expression of cos^2x sin^4x is cos^2x - 2cos^4x + cos^6x.

The expression cos^2x sin^4x can be simplified by using the trigonometric identity that states sin^2x + cos^2x = 1.

We can rewrite cos^2x sin^4x as cos^2x (sin^2x)^2. Then, using the trigonometric identity sin^2x + cos^2x = 1, we can substitute (1 - cos^2x) for sin^2x.

This gives us cos^2x (1 - cos^2x)^2, which can be expanded using the binomial theorem to give cos^2x (1 - 2cos^2x + cos^4x).

Finally, we can simplify this expression further by distributing the cos^2x term and collecting like terms to get cos^2x - 2cos^4x + cos^6x.

Therefore, the simplified expression of cos^2x sin^4x is cos^2x - 2cos^4x + cos^6x.

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Answer:

2560

Step-by-step explanation:

16×16×10 so the answer is 2560

Step-by-step explanation:

the correct answer is option a 6a-7

Using equivalent and fundamenta. angles, we find that:

a) \(\sin{\left(\frac{4\pi}{3}\right)} = \frac{\sqrt{3}}{2}\)

b) \(\cos{\left(\frac{11\pi}{3}\right)} = \frac{1}{2}\)

c) \(\sin{\left(-\frac{5\pi}{3}\right)} = -\frac{1}{2}\)

d) \(\cos{\left(-\frac{2\pi}{3}\right)} = -\frac{1}{2}\)

Item a:

\(\frac{4\pi}{3}\) is an angle in the third quadrant, as \(\pi < \frac{4\pi}{3} < \frac{3\pi}{2}\)

It's equivalent in the first quadrant is: \(\frac{4\pi}{3} - \pi = \frac{\pi}{3}\), which is a fundamental angle, which means that it's values of sine, cosine and tangent are known.

Sine in the third quadrant is negative, while in the first is positive, thus:

\(\sin{\left(\frac{4\pi}{3}\right)} = -\sin{\left(\frac{\pi}{3}\right)} = \frac{\sqrt{3}}{2}\)

Item b:

\(\frac{11\pi}{3} = 2\pi + \frac{5\pi}{3}\)

Thus, it is equivalent to an angle of \(\frac{5\pi}{3}\), which is in the fourth quadrant.

It's equivalent on the first quadrant is:

\(2\pi - \frac{5\pi}{3} = \frac{\pi}{3}\)

Cosine in the fourth quadrant is positive, just as in the first, thus:

\(\cos{\left(\frac{11\pi}{3}\right)} = \cos{\left(\frac{\pi}{3}\right)} = \frac{1}{2}\)

Item c:

\(2\pi - \frac{5\pi}{6} = \frac{7\pi}{6}\)

Which is a angle in the third quadrant.

It's equivalent in the first is:

\(\frac{7\pi}{6} - \pi = \frac{\pi}{6}\)

Sine in the third quadrant is negative, while in the first is positive, thus:

\(\sin{\left(-\frac{5\pi}{6}\right)} = \sin{\left(\frac{7\pi}{6}\right)} = -\sin{\left(\frac{\pi}{6}\right)} = -\frac{1}{2}\)

Item d:

\(2\pi - \frac{2\pi}{3} = \frac{4\pi}{3}\)

Which is in the third quadrant.

Cosine in the third quadrant is negative, while in the first is positive, thus:

\(\cos{\left(\frac{-2\pi}{3}\right)} = \cos{\left(\frac{4\pi}{3}\right)} = -\cos{\left(\frac{\pi}{3}\right)} = -\frac{1}{2}\)

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The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

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Using inferential statistics, it is found that the option that is best surveyed from the collected in the survey is given by:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

An inferential statistic is one that makes inference or predictions about a population based on a sample.

From the table, we have that cookies and cream is the most popular flavor, hence the correct option is:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

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Answer:

$10.44

Step-by-step explanation:

9(0.16)

1.44

9+1.44

10.44

Hope this helps

Btw I got .16 because in order to get a decimal you move the decimal place two to the left. And in this case the 16 has an imaginary decimal after it. Like so 16. So two to the left. .16

 74/5 milliliters of sand accumulate in the bag from time t=0 to time t=2.

Given that:

The rate at which sand is poured is r(t)

The function r(t) is defined as;

r(t) = 15t -\(2t^2\)

The accumulation in the bag from time t=0 to time t=2 is calculated as:

 r = \(\int_0^2 ( 15t -2t^2) dt\)

Using the limits:

    =\([\dfrac{15t^2}{2} - \dfrac{2t^3}{3}]_0^2\)

 =\(\dfrac{15(2) ^2}{2} - \dfrac{2(2)^3}{3} - (0-0)\)

\(30 - \dfrac{16}{3}\)

= \(\dfrac{74}{3}\)

  Thus, \(\dfrac{74}{3}\) milliliters of sand accumulate in the bag from time t=0 to time t=2.

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Answer:$2931.45

Step-by-step explanation:

The population of Nisos Isles is 19200 in 2050.

Let the number of people on the islands in 1998 be x, which triples every 25 years.

Therefore the population of the island in 2023 will be 3x, in 2048 will be 9x, and in 2050 will be 12x.

The total area of the Nisos Isles is 24900 square miles

.Queen Irene has decreed that there must be at least 1.5 square miles for every person living in the Isles.

Therefore, 1.5x = 24900 which implies that the current population in 1998 is:x = 16600We have to find the population of Nisos in the year 2050.Therefore, the population of Nisos in 2050 will be 12x = 12(16600) = 19200.

Summary: The population of Nisos Isles is 19200 in 2050.

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Step-by-step explanation:

Use the equation

\( \frac{x - x1}{y - y1} = m\)

So plug in the numbers

\( \frac{ 2 + 2}{3 - 4} = \frac{4}{ - 1} = - 4\)

So if y=mx+b and there is no intercept the equation would be

\(y = - 4x\)

A pyramid with a square base has a volume of 1682.64 cubic meters.

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter. The perimeter of a shape is the distance around its edge. A shape's perimeter is always computed by summing the lengths of each of its sides. The perimeter of a thing is the distance surrounding it. Your house, for example, has a fenced-in yard. The perimeter of the barrier is its length.

Here,

side=16.7 m

volume=1/3*16.7²*18.1

=1/3*5047.909

=1682.64 m³

The volume of a pyramid with a square base is 1682.64 m³.

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Answer:

Step-by-step explanation:

6 * 4500= 27000

Answer:

27,000 pounds.

Step-by-step explanation:

Answer:

Correct solution in steps

The error in the given solution was the first step: (5 - 2)

Given:

The equation is  

\(-0.4x+0.05y-1.25=0\)

Where, y is the total cost and x is the number of months.

To find:

The y-intercept of the line represented by this equation.

Solution:

We have,

\(-0.4x+0.05y-1.25=0\)

Isolate y variable.

\(0.05y=0.4x+1.25\)

Divide both sides by 0.05.

\(y=\dfrac{0.4x+1.25}{0.05}\)

\(y=\dfrac{0.4x}{0.05}+\dfrac{1.25}{0.05}\)

\(y=8x+25\)

Putting x=0, we get

\(y=8(0)+25\)

\(y=0+25\)

\(y=25\)

Therefore, the y-intercept of the given equation is 25 and the correct option is D.

39 subjects were tested in this simple one-way ANOVA.

The df for F distribution is (treatment df, error df)

Using given information

Treatment df = 7

Error df = 31

Total df= 7+31 = 38

Again, total df = N-1, N= number of subjects tested

Then, N-1 = 38

=> N= 39

One-way ANOVA is typically used when there is a single independent variable or factor and the goal is to see whether variation or different levels of that factor have a measurable effect on the dependent variable.

The t-test is a method of determining whether two populations are statistically different from each other, and ANOVA determines whether three or more populations are statistically different from each other.

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Answer:

d = 7

Step-by-step explanation:

The nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Give a₁₀ = 67 and a₁ = 4 , then

a₁ + 9d = 67

4 + 9d = 67 ( subtract 4 from both sides )

9d = 63 ( divide both sides by 9 )

d = 7

The volume of the remaining piece of ice cube is 6911.5 cubic cm

From the question, we have the following parameters that can be used in our computation:

The figure

Where, we have

Radius, r = 20/2  = 10 cm

Height, h = 33 cm

The volume of the remaining piece is calculated is

V = 2/3πr²h

Substitute the known values in the above equation, so, we have the following representation

V = 2/3 * 22/7 * 10² * 33

Evaluate

V = 6911.5

Hence, the volume of the remaining piece is 6911.5 cubic cm

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Answer:

Missing Value Is 4 .

Step-by-step explanation:

According To The Question, We Have

        Equation is 16+28 = X*(4+7)

        Solve the above Equation, We get 44=X*11 ⇔ X=4

Answer: A:4

explanation: just took the test and got 100

Step-by-step explanation:

The slope of 3 and -10.

If the slope is above 0, the line is increasing.

If the slope is at 0, it's a horizontal line or straight. Vertical If the run is 0.

If the slope is below 0, the line is decreasing.

3 is slanting upward, the slope is greater than 0 therefore the line is increasing.

-10 is slanting downward, the slope is less than 0 therefore the line is decreasing.

In summary, if the input graph G(V, E) has a negative weight cycle, there are no solutions to the single-source shortest path problem.

In the single-source shortest path problem, the goal is to find the shortest path from a given source vertex to all other vertices in a graph G(V, E), where V is the set of vertices and E is the set of edges.
If the input graph G(V, E) has a negative weight cycle, then there are no correct solutions to the single-source shortest path problem. This is because the presence of a negative weight cycle allows for a path with decreasing total weight, as you can continually traverse the cycle to reduce the path's weight. As a result, the shortest path is undefined in this case.

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Okay, here we have this:

Considering the provided information, we are going to calculate the requested probability, so we obtain the following:

Let us remember that in a 6-sided dice, the numbers it contains are (1,2,3,4,5,6), and of those 3 are odd, then we are going to substitute in the following formula of the simple probability of an event :

Probability of an event=Favorable Cases/Possible Cases

Probability of tossing an odd number with 6 sided number cube =3/6

Probability of tossing an odd number with 6 sided number cube =1/2

Finally we obtain that the probability of tossing an odd number with 6 sided number cube is 1/2.

Answer:

\(\frac{11}{20}\)     Eleven out of 20 guests order the signature dish

Step-by-step explanation:

55% of a population can also be expressed in math terms as :

\(\frac{55}{100} =\frac{11}{20}\)

when we reduce the fraction to lower terms.

That is: 11 out of 20 guests order the signature dish

Answer:

Step-by-step explanation:

True. Data Envelopment Analysis (DEA) is best used in an environment of low diverges and high complexity. In such situations, DEA can effectively analyze and compare the efficiency of decision-making units, even when dealing with multiple inputs and outputs.

Data Envelopment Analysis (DEA) is a method used to measure the efficiency of decision-making units. It works by analyzing a set of inputs and outputs to determine the relative efficiency of each unit. DEA is best suited for situations where there is low diverges among the units being analyzed, meaning they are all operating under similar conditions. Additionally, DEA is most effective in situations of high complexity, where there are multiple inputs and outputs that need to be considered. Therefore, the statement that DEA is best used in an environment of low divergence and high complexity is true.

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Answer:

Infinite

Step-by-step explanation:

Hope that this helps!

Answer:

Step-by-step explanation:

2 or 3 im not v sure tho

Let's say Dali's walking speed is x and his running speed is 3x.

In the morning, let's say the total distance is d. Therefore, Dali walks d/2 with speed x and runs d/2 with speed 3x. The time it takes for him to complete this distance is given by:

d/2x + d/2(3x) = 24

Simplifying this equation, we get:

d = 3x(8)

d = 24x

So, the total distance Dali covers in the morning is 24x.

After school, let's say the distance from school to home is d'. Therefore, Dali walks d'/2 with speed x and runs d'/2 with speed 3x. The time it takes for him to complete this distance is given by:

d'/2x + d'/2(3x) = ?

We don't know how much time it takes Dali to get home, so we'll leave the right-hand side of the equation blank for now.

Now, let's look at the ratios of Dali's walking and running speeds:

Walking speed : Running speed = x : 3x = 1 : 3

This means that for every 4 parts of the distance Dali covers, he walks one part and runs three parts. So, we can write:

d' = 4y, where y is the distance Dali walks

This also means that Dali spends one-fourth of the total time walking and three-fourths running. So, we can write:

d'/2x + d'/2(3x) = (1/4)t + (3/4)t, where t is the total time it takes Dali to get home

Simplifying this equation, we get:

2d' = 2t(x + 3x)

4y = 8tx

y = 2tx

Substituting this value of y in the equation d' = 4y, we get:

d' = 8tx

So, the total distance Dali covers in the afternoon is 8tx.

Now, we have two equations:

d = 24x

d' = 8tx

We need to simplify these equations further to find the value of t (the total time it takes Dali to get home).

From the first equation, we get:

x = d/24

Substituting this value of x in the second equation, we get:

d' = 8t(d/24)

d' = (1/3)dt

So, the total distance Dali covers in the afternoon is (1/3)dt.

Now, we can equate the two expressions we have for d':

d' = 8tx = (1/3)dt

Simplifying this equation, we get:

24x = t

Therefore, it takes Dali 24 minutes to get home.

algebra.............