What kind of transformation is illustrated in this figure ?

To locate the z-score where 25% of the standard normal distribution is to the left, one checks a z-table for the area closest to 0.25, which approximately corresponds to a z-score of -0.675.

To find the z-score so that 25% of the standard normal curve lies to the left, we need to look up the corresponding area in a z-table. Since most z-tables represent the cumulative area to the left of a z-score, we must find the value closest to 0.25, the decimal equivalent of 25%. Upon checking a standard z-table, we find that the area closest to 0.25 corresponds to a z-score of approximately -0.675. Therefore, the z-score that has 25% of the area under the normal curve to its left is -0.675.

The rays VW and VZ don't necessarily have to go in opposite directions even though they have the same endpoint. Even though they are opposite arrays only if the angle is 180 degrees, they could still go in right angle directions or any angle of directions. Fi the points V, W, and Z and collinear and W and Z are on the side of point V, then they could also in fact be the same ray as well. Travelling is opposite directions yet starting at the same point is one of the characteristics of opposite rays. The first point in the name must be the endpoint and rays are always named with two points.

The probability that the sample mean is less than 74 is about 10.38%.

To solve the problem step-by-step, let's go through each calculation in detail:

1. Compute the Standard Error (SE):

  Given:

  - Population mean [tex](\(\mu\))[/tex] = 75

  - Population standard deviation [tex](\(\sigma\))[/tex] = 5

  - Sample size (n) = 40

  The standard error of the mean is calculated using the formula:

[tex]\[ \text{SE} = \frac{\sigma}{\sqrt{n}} \][/tex]

  Substituting the given values:

[tex]\[ \text{SE} = \frac{5}{\sqrt{40}} = \frac{5}{6.3246} \approx 0.791 \][/tex]

2. Compute the Z-score for a sample mean of 74:

  The Z-score is calculated using the formula:

[tex]\[ Z = \frac{X - \mu}{\text{SE}} \][/tex]

  Where:

  - (X) is the sample mean.

     Given (X = 74):

[tex]\[ Z = \frac{74 - 75}{0.791} = \frac{-1}{0.791} \approx -1.26 \][/tex]

3. Find the probability corresponding to the Z-score:

The Z-score of -1.26 corresponds to the cumulative probability from the standard normal distribution table.

A Z-score of -1.26 gives a cumulative probability (area under the curve to the left of the Z-score) of approximately 0.1038.

Therefore, the probability that the sample mean is less than 74 is about 10.38%.

The quotient of 75,120 divided by 16 is 4,695.

To find the quotient of 75,120 divided by 16, you can follow these steps:

So, the quotient of 75,120 divided by 16 is 4,695.

Answer:

  a.  5

  b.  545

  c.  0

Step-by-step explanation:

These are straightforward division problems, easily solved using your own memorized multiplication facts, or using a calculator.

a.  20 ÷ 4 = 5 means 5 × 4 = 20

b.  2725 ÷ 5 = 545 means 545 × 5 = 2725

c.  0 ÷ 5 = 0 means 0 × 5 = 0

_____

When using the Google calculator and standard keyboard symbols, you can use the slash (/) for "divided by" and the asterisk (*) for "times."

Since we are to complete the square, therefore I believe the correct given should be:

x ^ 2 – 11 x

Take note of the symbol ^ which denotes that 2 is an exponent of x.

The general form of a binomial equation is in the form of:

a x^2 + b x + c

Where in this case:

a = 1

b = -11

c = unknown

To complete the square, we have to find for the value of c. This is calculated using the formula:

c = (b / 2) ^ 2

c = (-11 / 2) ^ 2

c = 30.25

Therefore the complete equation is:

x ^ 2 – 11 x + 30.25

30.25 is correct but apex asks for a fraction so 121/4

Answer:

11/26

Step-by-step explanation: took the test

The distributive property is used to expand [tex](a + b)^2[/tex] and  [tex](a - b)^2[/tex], resulting in [tex]a^2 + 2ab + b^2[/tex]and  [tex]a^2 - 2ab + b^2[/tex]respectively. The product (a - b)(a + b) uses the distributive property to result in [tex]a^2 - b^2[/tex], showcasing how signs affect the final expressions.

The distributive property of multiplication over addition is essential when multiplying polynomials. Let's explore how this property is applied to the given expressions:

For  [tex](a + b)^2[/tex], we have to multiply (a + b) by itself. According to the distributive property, it becomes a² + 2ab + b².

Similarly, for  [tex](a -b)^2[/tex], distributing (a - b) with itself yields a² - 2ab + b².

Lastly, (a - b)(a + b) represents a difference of squares. By applying the distributive property, the middle terms cancel out, leaving us with a² - b².

The final products differ because of the signs in the original binomials. The squared terms result in a positive sign whether the original binomial had a plus or minus (per rules of multiplying signs), but the product of the mixed terms determines whether you have a sum or difference in the final expression, affecting the middle term.

The function with the most x-intercepts in the image is g(x), which has four x-intercepts. The function f(x) has three x-intercepts, and the function h(x) has two x-intercepts.

The number of x-intercepts a function has is equal to the number of times the function crosses the x-axis. The x-axis is also known as the line y = 0, so any point where the function's graph touches the x-axis is a solution to the equation f(x) = 0.

g(x) crosses the x-axis four times, at approximately -10, 3/2, 2, and 15.

f(x) crosses the x-axis three times, at approximately -2, 1, and 12.

h(x) crosses the x-axis twice, at approximately -1 and 3.

Therefore, g(x) has the most x-intercepts because its graph intersects the x-axis the most times.

1.     Multiply the coefficients and round to the number of significant figures in the coefficient with the smallest number of significant figures.

2.     Add the exponents.

3.     Convert the result to scientific notation.

Answer:

Let's say that I have to multiply 2.5 x 10^3 and 6.23 x 10^5.

First, Let's multiply 10^3 and 10^5.

It would be 10^8.

next, let's multiply 2.5 and 6.23.

It is 15.575.

So, my answer is 15.575 x 10^8.

Answer:  B.  [tex]-7185024p^6q^5[/tex]

Step-by-step explanation:

The (r+1)th term in [tex](a+b)^n[/tex] is given by :

[tex]^nC_r(a)^{n-r}(b)^r[/tex]

The given binomial : [tex](2p - 3q)^{11}[/tex]

For the 6th term, we put r=6-1=5 , we get

[tex]^{11}C_5(2p)^{11-5}(-3q)^5\\\\=\dfrac{11!}{5!(11-5)!}(2p)^6(-243q^5)\\\\=-dfrac{11\times10\times9\times8\times7\times6!}{6!5!}(64p^6)(243q^5)\\\\=-462\times(64p^6)(243q^5)\\\\=-7185024p^6q^5[/tex]

Hence, the 6th term of the expansion of [tex](2p - 3q)^{11}[/tex] = [tex]-7185024p^6q^5[/tex]

Final answer:

Adam earned approximately a 28.03% interest rate on his $100 over 10 years to end up with $1649, as calculated using the formula A = Pert and taking the natural logarithm to solve for the interest rate.

Explanation:

To calculate the interest rate earned by Adam, we can use the given formula A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the original sum of money), r is the annual interest rate (in decimal), and t is the time the money is invested or borrowed for, in years. According to the question, Adam had a starting principal of $100 (P), which grew to $1649 (A) over 10 years (t).

Let's solve for the interest rate (r): A = Pert $1649 = $100e10r 16.49 = e10r To find r, we need to take the natural logarithm (ln) of both sides:

[tex]ln(16.49) = ln(e10r) ln(16.49) = 10r\\\\ Now divide both sides by 10 to isolate r:\\\(\dfrac{ln(16.49)}{10} = r\) \(r = \dfrac{ln(16.49)}{10}\)Now you just compute the value using a calculator:r ≈ \(\dfrac{2.803}{10}\) r ≈ 0.2803 or 28.03%\\[/tex]

Therefore, the interest rate that Adam earned was approximately 28.03%.

The key features of graphs of polynomials with higher degrees include the leading coefficient, end behavior, and turning points. These features can be used to sketch the graph of the polynomial function.

The key features that can be identified from graphs of polynomials with higher degrees include the leading coefficient, the end behavior, and the number and behavior of the turning points. The leading coefficient determines the orientation of the graph, whether it opens upwards or downwards. The end behavior of the graph shows how the function behaves as x approaches positive or negative infinity. The number and behavior of the turning points indicate the shape and direction of the graph.

These key features can be used to sketch the graph of the polynomial function by following these steps:

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Answer:

9.

Step-by-step explanation: To profit means to make more than originally spent. He Spent 4,000$ and needs to profit 1,400$. Bringing a total of 5,400$. 5,400 divided by 600$ equals 9 computers.

Answer: 60 inches

Step-by-step explanation:

Given: A frame in the shape of right triangle with the longest side = 87 inches

The height of the frame is labeled as 63 inches.

Let 'x' be the third side of the frame then by Pythagoras theorem of right triangle , we have

[tex]87^2=x^2+63^2\\\\\Righatrrow\ x^2=87^2-63^2\\\\\Rightarrow\ x^2=3600\\\\\Rightarrow\ x=\sqrt{3600}=60[/tex]

Hence, the length of the third side of the window frame = 60 inches.

Answer:x+7=2x+5-4x

x+7=-2x+5

The length of the hypotenuse of given right triangle is 9.2 units.

Given that, in a right triangle, the length of one leg is 6 units. The length of the other leg is 8 units.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Let the length of the hypotenuse be x.

Now, using Pythagoras theorem, we get

x²=6²+7²

⇒x²=36+49

⇒x²=85

⇒x=√85

⇒x=9.2 units

Therefore, the length of the hypotenuse of given right triangle is 9.2 units.

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