There are 10 people in a room. if each person shakes hands with exactly 3 other people, what is the total number of handshakes?

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 correct answer is b

F is a point which is greater than zero and F must be in the location of 1/11 and it can be determine by using arithmetic operations.

Given :

F partitions the directed line segment from D to E into a 5:6 ratio.

Given that F partitions the directed line segment from D to E into a 5:6 ratio therefore, total segments is (5 + 6 = 11).

From point D to E in the given line segment there are 9 units. To divide the line segment of 9 unit into 11 unit, first find the distance between two units, that is:

[tex]\dfrac{9}{11}=0.82[/tex]

[tex]0.82\times 5 = 4.1[/tex]

Now, it can be say that F is a point which is greater than zero and F must be in the location of 1/11.

For more information, refer the link given below:

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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.

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%.

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."

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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b. StartFraction x y Over p m EndFraction = 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]

The number of ways he can select his attire for the prom to look differently will be twenty-four (24).

A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.

Roger is renting a tuxedo for prom.

Once he has chosen his jacket, he must choose from three types of pants, four colors of vests, and two different styles of shoes.

Then the number of the ways he can select his attire for the prom will be

[tex]\rm Number \ of \ ways = ^3C_1 \times ^4C_1 \times ^2C_1 \\\\ Number \ of \ ways = 3 \times 4 \times 2\\\\Number \ of \ ways = 24[/tex]

More about the permutation and the combination link is given below.

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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.

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.

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:

Hi!

The correct answer is {56.35, 70.55, 81.2, 116.7} .

Step-by-step explanation:

The set {17, 21, 24, 34} represents the values of x.

If you replace each value in the equation:

Then you have the values {56.35, 70.55, 81.2, 116.7} .

The maximum allowable vertical distance from a fixture outlet to the trap weir in plumbing is 24 inches. This standard ensures proper drainage and the maintenance of a water seal, preventing sewer gases from entering a building.

The vertical distance from a fixture outlet to the trap weir, which is a critical aspect of plumbing design, should not be more than 24 inches. The fixture outlet is the point where water exits the fixture, and the trap weir is the peak point inside a P-trap, which maintains a water seal to prevent sewer gases from entering the building.

It's important to adhere to this standard to ensure proper drainage and maintain the water seal. If the distance is too great, it could lead to poor drainage and a loss of the trap seal due to siphoning, which would allow sewer gases to enter the home or building.

Answer:

The sum of the roots of the equation [tex]x^{2} + x = 2[/tex] is -1

Step-by-step explanation:

You have two options to find the sum of the roots,

[tex]x_{1,2} = \frac{-b\±\sqrt{b^{2}-4ac}}{2a} [/tex]

[tex]x^{2} + x - 2= [/tex] where:

a = 1

b = 1

c = -2

[tex]x_{1} = \frac{-1-\sqrt{1^{2}-4*1*-2}}{2*1}[/tex] = -2

[tex]x_{2} = \frac{-1+\sqrt{1^{2}-4*1*-2}}{2*1}[/tex] = 1

The sum of the roots is -2 + 1 = -1

    2. The second option is use the fact that a general quadratic equation is in the form of:

[tex]ax^{2}+bx+c=0[/tex]

if you divided by [tex]a[/tex] you get:

[tex]x^{2}+\frac{b}{a} x+\frac{c}{a} =0[/tex]

and always the sum of roots will be given for this expression [tex]x_{1} + x_{2} = \frac{-b}{a}[/tex]

Why this is true?

Because if we use the Quadratic Formula as follows:

[tex]x_{1} + x_{2} = \frac{-b+\sqrt{b^{2}-4ac}}{2*a} + \frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]

[tex]x_{1} + x_{2} = \frac{-2b+0}{2a}}[/tex]

[tex]x_{1} + x_{2} = \frac{-b}{a}[/tex]

In the case of this equation:

[tex]x_{1} + x_{2} = \frac{-1}{1} = -1[/tex]

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.