A square pyramid is sliced in such a way that the plane cuts in a direction perpendicular to the base but does not pass through the vertex, what is the resulting cross section?

Answer:

11 and 13

because prime number is the number which can be factorised by 1 or itself

Answer:

B. 11 and D. 13 because they are odd primes

The period of a sine function is the length of one complete cycle. For the function sin(2x), the period can be found by taking the standard period of sin(x), which is 2π, and dividing it by the coefficient of x, which is 2.

This gives a period of π. Therefore, sin(2x) completes one cycle (or oscillates) every π units. This means that the graph of sin(2x) will repeat itself every π units, with the maximum and minimum points occurring at intervals of π/2. It is important to note that the period of a function does not affect the amplitude or the phase shift of the function. These characteristics are determined by other factors in the equation.

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3xX

Step-by-step explanation:

The number is 7.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the number be x.

so,  2 less than 3 times a certain number is the same as 4 more than the product of 5 and 3

3x - 2 = 4+ 5(3)

3x- 2 = 4 + 15

3x- 2= 19

3x= 21

x= 21/3

x= 7

Hence, the number is 7.

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There are 30 elements in the array.

A collection of elements with the same data type stored in a line of memory is known as an array. As a result, adding an offset to a base value or the address in memory where the array's first member is stored makes it easier to establish each element's position. The base value, or index 0, serves as the offset, which is the difference between the two indices.

Given in question,

int[][][]x = new char[2][5][3]

No. of elements = 2x3x5

                        = 30

Hence, there are 30 elements in the array.

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When both groups are shifted to a situation in which they earn an alternative reward after being trained to navigate a runway for food, the group that received three food pellets will continue to perform the task at a high level while the group that received one food pellet will experience difficulty.

It is known that rats have a natural preference for higher rewards. As a result, the group that received three pellets will be more motivated to complete the task since they have already tasted a higher reward. Therefore, they will continue to perform at a high level in the new environment.

On the other hand, the group that received only one pellet may find it challenging to adapt to the new situation since they are now receiving a lower reward. As a result, they may struggle to complete the task, and their performance may decrease.

In conclusion, the group that received three pellets will perform better than the group that received one pellet when both groups are shifted to a situation in which they earn an alternative reward. This is because the rats have a natural preference for higher rewards.

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Answer:

cannot be factored

Step-by-step explanation:

I plugged into calculator

Answer:

D 150 ft is the length of 5 ft

The area of the shaded region round your answer to the nearest hundredth is 301.59 square units.

We are given that;

The radius of outer circle is 16 and inner circle is 8

Now,

we need to find the area of the outer circle. The formula for the area of a circle is A = pir2, where r is the radius. The radius of the outer circle is 16, so the area is A = pi162 = 256pi.

Next, we need to find the area of the inner circle. The radius of the inner circle is 8, so the area is A = pi*82 = 64pi.

Then, we need to subtract the area of the inner circle from the area of the outer circle. This gives us 256pi - 64pi = 192pi.

Finally, we need to divide the result by 2, since the shaded region is half of the area between the two circles. This gives us 192pi/2 = 96pi.

The final answer is 96pi square units. Rounding to the nearest hundredth, we get 301.59 square units.

Therefore, by the area answer will be 301.59 square units.

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Answer:

1) 20 Students    2) 5 Students 3) 11 Students

Step-by-step explanation:

1) Count how many numbers are there (not digits)

2) Count the number of 3's and 4's found

3) Count the number of times a number equal to or greater than 6 appears in the data range.

Answer:

0.0067 = 0.67% probability of selecting at least 3 defective fuses.

Step-by-step explanation:

For each fuse, there are only two possible outcomes. Either it is defective, or it is not. The probability of a fuse being defective is independent of any other fuse, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

A company manufactures fuses. The percentage of non-defective fuses is 95.4%.

This means that 100 - 95.4 = 4.6% = 0.046 are defective, which means that \(p = 0.046\)

A sample of 9 fuse was selected.

This means that \(n = 9\)

Calculate the probability of selecting at least 3 defective fuses.

This is:

\(P(X \geq 3) = 1 - P(X < 3)\)

In which

\(P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)\)

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{9,0}.(0.046)^{0}.(0.954)^{9} = 0.6545\)

\(P(X = 1) = C_{9,1}.(0.046)^{1}.(0.954)^{8} = 0.2840\)

\(P(X = 2) = C_{9,2}.(0.046)^{2}.(0.954)^{7} = 0.0548\)

Then

\(P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.6545 + 0.2840 + 0.0548 = 0.9933\)

\(P(X \geq 3) = 1 - P(X < 3) = 1 - 0.9933 = 0.0067\)

0.0067 = 0.67% probability of selecting at least 3 defective fuses.

Answer:

the scale factor is times 0.5

Explanation:

20 plus 10 is 30. Half of 20 is 10 so that is 0.5

It is also like that for the others

To calculate probability that children or their parents prefer hamburger, we need to find sum of the probabilities of two events. Therefore, the probability that children or their parents prefer hamburger is .83, or 83%.

The given table provides the probabilities for each of these events. By adding the probability that children prefer (.54) to the probability that parents prefer (.29), we obtain a total probability of .83.The table represents the probabilities of different preferences in the taste test.

To find the probability that either children or their parents prefer the hamburger, we sum the probabilities of these two events. According to the table, the probability that children prefer the hamburger is .54, and the probability that parents prefer the hamburger is .29. Adding these probabilities together, we get .54 + .29 = .83. Therefore, the probability that children or their parents prefer the hamburger is .83, or 83%.

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Given the following functions:

to find f(g(4)), we can start by finding g(4) first:

now that we know that g(4) = 8, we can calculate the composition f(g(4)):

Answer:

f(g(4) ) = 31

Step-by-step explanation:

evaluate g(4) then substitute the value obtained into f(x)

g(4) = \(\frac{4^2}{2}\) = \(\frac{16}{2}\) = 8 , then

f(8) = 3(8) + 7 = 24 + 7 = 31

To find the coordinates of the point on a circle with radius 16 corresponding to an angle of \frac{5\Pi}{9}, follow these steps:

1. Convert the angle to radians, if not already given. In this case, the angle is already given in radians as \frac{5\Pi}{9}.

2. Recall that the parametric equations for a circle with radius r and angle θ are:
x = r * cos(θ)
y = r * sin(θ)

3. Plug in the radius and angle into these equations:
x = 16 * cos(\frac{5\Pi}{9})
y = 16 * sin(\frac{5\Pi}{9})

4. Calculate the values of x and y, then round them to the nearest hundredth:
x ≈ 5.88
y ≈ 14.43

5. Write the coordinates as an ordered pair: (5.88, 14.43).

Therefore, the coordinates of the point on the circle with radius 16 corresponding to an angle of \frac{5\Pi}{9} are approximately (5.88, 14.43).

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The area between the curves x = 28 − 7y² and x = 7y² − 28 is 0.

By counting the number of squares on a piece of paper with grids (square shaped), and using basic formulas, it is possible to determine the area of shapes like quadrilaterals and circles, which are 2D shapes.

To find the area between the curves x = 28 − 7y² and x = 7y² − 28, we need to first find the points of intersection.

Setting the two equations equal to each other, we get:

28 - 7y² = 7y² - 28

Simplifying and solving for y, we get:

y = ±2

So, the two curves intersect at y = 2 and y = -2.

Next, we need to determine which curve is on top in each interval. To do this, we can evaluate the y-values for each curve at y = 0 and y = 2:

For x = 28 − 7y²:

- At y = 0, x = 28

- At y = 2, x = 0

For x = 7y² − 28:

- At y = 0, x = -28

- At y = 2, x = 28

So, the curve x = 28 − 7y² is on top for y between 0 and 2, and the curve x = 7y² − 28 is on top for y between -2 and 0.

Using the formula for finding the area between two curves, we can now calculate the total area:

A = ∫(-2)²[28 - 7y² - (7y² - 28)] dy + ∫02[(7y² - 28) - (28 - 7y²)] dy

Simplifying, we get:

A = 2∫02(14y² - 28) dy

A = 2[\(14y^{3/3\) - 28y]0²

A = 2(0 - 0)

A = 0

Therefore, the area between the curves x = 28 − 7y² and x = 7y² − 28 is 0.

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The mean time that a certain model of light bulb will last is ​hours is 900 hours and the required percentage of bulbs is 2.5%

Here,

x is the time that a certain bulb will last.

(in houses.

μ=900 hours;

σ=1200 hours.

The standardized value for a light bulbs lasts 1100 hours, is,

z=x-μ/σ

z=1100-900/100=2

We know, for a bell-shaped distance, Approximately,

68% of the data falls within M-uσ;

By rule (ii), here,

95% of the data falls within (μ-2σ,u+2σ)

(900-2x100,900+2x100)

(700,1100)

So (100-95=5%) falls outside of (700,1100)

Since, the distance is symmetric (i.e. bell-shaped); we find the percentage of bulbs that is expected lo lase longer than 1100 hours, is

5/2% =2.5%

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The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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Answer:

d 115.9

Step-by-step explanation:

The initial investment of Calvin must be increased by a factor of 115.927 % to equal Marquez's investment at any time. (Correct choice: D)

In this question we must apply the concept of compound interest to derive the initial investment to be done by Calvin. According to the statement, Calvin invests money five years later than Marquez.

To determine the initial investment to be deposited by Calvin such that his investment equals Marquez's investment at any time we resort to the following expression:

\(1500\cdot (1+0.03)^{t+5} = C_{C}\cdot (1+0.03)^{t}\)     (1)

Then, we simplify the required initial investment:

\(C_{C} = 1500\cdot (1+0.03)^{5}\)

\(C_{C} = 1738.911\)

And the increase factor is:

\(r_{C} = \frac{1738.911}{1500}\times 100\,\%\)

\(r_{C} = 115.927\,\%\)

The initial investment of Calvin must be increased by a factor of 115.927 % to equal Marquez's investment at any time. (Correct choice: D) \(\blacksquare\)

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Since the proposed side length of the square is between 6 and 7, we can assume that it is 6.5 hence, the lengths will be d = 6.5 and c = 9.19.

Here is what we were given:

Side length of square = 6 > x <7

A convenient assumption for this is 6.5

We also know that d and c and the base of two right triangles. where their hypotheses' are equal to the side lenght of the square = 6.5

we also know that the in between the line formed by D and C is a 90 degree angle.

Hence the sum of the other angle will be 45 degrees each.

This is  based on sum of angles in a triangle.

Hence,

c = b /sin(β)

= 6.5/sin (45)

= 6.5/0.70710678118

 c = 9.19

d = √c² - b²

 = √(9.19238815542512² - 6.52²)

= √42.25

d = 6.5

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The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
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Answer:

\(f(-1)=0\)

Step-by-step explanation:

You are given the set \(f(x) = {(-1,0),(-2,2),(-3,-1)}\).

All \(f(-1)\) means is to find the y value when x is at -1.

Look at your first set of parenthesis. Your very first x term is -1, and it has a y output of 0.

There's your answer.

The probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.

Given that Edward works as a waiter, where his monthly tip income is normally distributed with a mean of $2,000 and a standard deviation of $350.

The z score formula is given by;`z = (x - μ) / σ`

Where; x is the raw scoreμ the mean of the populationσ is the standard deviation of the population.

The probability that Edward’s monthly tip income exceeds $2,350 is to be found.`z = (x - μ) / σ``z = (2350 - 2000) / 350``z = 1`

The value of z is 1.

To find the area in the right tail, use the standard normal distribution table.

The table value for z = 1.0 is 0.8413.

Therefore, the probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.

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Answer:

Step-by-step explanation.

Answer:

d or c

Step-by-step explanation:

Answer:

5/33

Step-by-step explanation:

5/12 * 4/11 = 20/132 = 10/66 = 5/33

Answer: the missing part is 45

suppose:  the missing part is x

we use Thales theorem:

\(\frac{x}{18}=\frac{20}{8}\\\\=> x = \frac{20.18}{8}=45\)

Step-by-step explanation:

use thales theorem to solve this question

The partial derivatives of w are:

∂w/∂x = 4eˣ ln(y)

∂w/∂y = 4eˣ / y

We are given the following functions:

w = 4eˣ ln(y)

x = ln(t cos(s))

y = t sen(s)

We need to find the partial derivatives of w with respect to x and y.

Partial derivative of w with respect to x:

To find ∂w/∂x, we treat y as a constant and differentiate w with respect to x:

∂w/∂x = d/dx [4eˣ ln(y)] = 4eˣ ln(y)

Partial derivative of w with respect to y:

To find ∂w/∂y, we treat x as a constant and differentiate w with respect to y:

∂w/∂y = d/dy [4eˣ ln(y)] = 4eˣ / y

Therefore, the partial derivatives of w are:

∂w/∂x = 4eˣ ln(y)

∂w/∂y = 4eˣ / y

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