The last step in a proof contains the

Answer:

The simplified form of given factorial expression is (N+3)!.

Step-by-step explanation:

The given expression is

[tex]\frac{(N+4)!}{N+4}[/tex]

The n! is defined as

[tex]n!=n(n-1)(n-2)...3(2)(1)[/tex]

[tex]n!=n(n-1)![/tex]

The given expression can be written as

[tex]\frac{(N+4)!}{N+4}=\frac{(N+4)(N+4-1)!}{N+4}[/tex]

[tex]\frac{(N+4)!}{N+4}=\frac{(N+4)(N+3)!}{N+4}[/tex]

Cancel out the common factors.

[tex]\frac{(N+4)!}{N+4}=(N+3)![/tex]

Therefore the simplified form of given factorial expression is (N+3)!.

Based on the length of the bridge and the scale used, the length of the scale model is a. 5.1 cm.

This can be found as:

= Length of Bridge / Number of meters per centimeters

Solving gives:

= 28 / 5.5

= 5.09

= 5.1 cm

In conclusion, option A is correct.

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Answer:

Step-by-step explanation:

From the figure, it can be seen that CD is the perpendicular bisector of AB and also, we have:

(A) CD is the Perpendicular bisector of AB.

(B) If AB=10, then [tex]EB=\frac{AB}{2}=\frac{10}{2}=5[/tex]

(C) [tex]AE=\frac{1}{2}(AB)[/tex]

(D) E is the mid point of AB.

(E) [tex]{\angle}BED=90^{\circ}[/tex] (Because ED is  perpendicular to AB)

The bridge builder used the tangent function to calculate the width of the river. The equation tan(43) = width/90 was set up, and solving for width gives an answer of approximately 91.6 feet.

The question gives us a right triangle set up, where point A is where the builder starts, point B is where he walks to, and point C is directly across the river. We can use trigonometry, specifically the tangent function, to find the unknown side. In a right triangle, the tangent of an angle is equal to the ratio of the opposite side (the side across from the angle) to the adjacent side (the side next to the angle).

The angle (θ) in this case is 43 degrees, the side adjacent to the angle is the walk of 90 feet, and the side opposite the angle is the width of the river, which we'll call 'w'. So we get the equation: tan(43) = w/90. Solving for 'w' gives us the width of the river.

Therefore, w = 90 * tan(43), which calculates to approximately 91.6 feet. So the width of the river is approximately 91.6 feet.

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Answer:

A. r^n=a

B. a^1/n=r

Step-by-step explanation:

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The true statements about the equation [tex]\sqrt[n]a = r[/tex] are (a) r^n=a and (b) a^1/n=r

The equation is given as:

[tex]\sqrt[n]a = r[/tex]

Take the power of n on both sides of the equation

[tex](\sqrt[n]a)^n = r^n[/tex]

This gives

a = r^n

Rewrite as:

r^n = a

Also, we have:

[tex]\sqrt[n]a = r[/tex]

Apply the law of indices

a^1/n = r

Hence, the true statements about the equation [tex]\sqrt[n]a = r[/tex] are (a) r^n=a and (b) a^1/n=r

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Final answer:

To determine how many minutes each boy plays in a 36-minute gym period with 24 boys wanting to play basketball, with only 10 able to play at a time, each boy would play for 15 minutes.

Explanation:

To find out how many minutes each boy plays in a 36-minute gym period with 24 boys and 10 playing at a time:

Calculate the total time for 24 boys: 24 boys / 10 boys playing at a time = 2.4 sets.

Divide the gym period by the number of sets: 36 minutes / 2.4 sets = 15 minutes per set.

Answer:

Lisa score 575 points and Kate scored 325 points.

Step-by-step explanation:

We are given the following information:

Total score for Lisa and Kate is 900 and Lisa scored 250 more points than Kate.

Scores for Lisa and Kate can be expressed with the help of two equations:

[tex]L + K = 900\\L = K + 250 \Rightarrow L-K = 250[/tex]

Solving these equations we have:

[tex]L + K + L - K = 900 + 250\\2L = 1150\\L = 575\\K = 575 - 250 = 325[/tex]

Hence, Lisa score 575 points and Kate scored 325 points.

The graph of the equations is attached.

Answer:

This information defines his socioeconomic status.

Step-by-step explanation:

Jameel has a college degree, lives in a nice neighborhood, and earns more than $50,000 a year.

This information defines his socioeconomic status.

Socioeconomic status tells the social class of a person.It is measured in terms of education, income and occupation.

We can say that with high socioeconomic comes some privilege, power and control.

Answer:

The success would expect are 1200.    

Step-by-step explanation:

Given : If a binomial event has a probability of success of 0.2.

To find : How many successes would you expect out of 6000 trials?

Solution :

The probability of success p=0.2.

The number of trials is n=6000

The formula to find number of successes is

The mean (expected value) of number of successes is the multiple of success and number of trials,

[tex]M=np[/tex]

[tex]M=6000\times 0.2[/tex]

[tex]M=1200[/tex]

Therefore, The success would expect are 1200.

The coordinates of point of intersection is (3,4).

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y = 2x-2 -----(1)

3y+x = 15 -----(2)

Now, substitute equation (1) in equation (2), we get

3(2x-2)+x=15

6x-6+x=15

7x=21

x=3

and, y =2(3)-2

y= 4

Hence, the coordinates of point of intersection is (3,4).

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The measure of the angle opposite to the shortest side is, 29.25°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The legs of a right triangle measure 14 and 25.

Now, We know that;

⇒ tan θ = Perpendicular / Base

⇒ tan θ = 14 / 25

⇒ θ = tan ⁻¹ (14/25)

⇒ θ = 29.25°

Thus, The measure of the angle opposite to the shortest side is, 29.25°

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Answer:

The power of 10 would be -5

Step-by-step explanation:

In scientific notation we write a very small or very large number as the product of a number from 0 to 9 and the exponent of 10,

For getting a number between 0 to 9 if the decimal shifted right side then the exponent of 10 is negative power of total shifting while if the decimal shifted left side then the exponent of 10 is positive power of total shifting.

Here, the number is,

0.000028

By the above explanation, we need to shift the decimal five time to the right so the exponent of 10 would be 5.

[tex]\implies 0.000028=2.8\times 10^{-5}[/tex]

Final answer:

Levers are classified based on the positions of the fulcrum, input force, and output force. First-class levers have the fulcrum in the middle, second-class levers have the load in the middle, and third-class levers have the effort in the middle. The Mechanical Advantage of a lever indicates how much the lever amplifies the input force.

Explanation:

The three classes of levers are differentiated by the positions of the fulcrum, input force, and output force. A first-class lever has the fulcrum placed between the input force and the output force. Examples would include a seesaw and a crowbar. A second-class lever has the output force between the input force and the fulcrum, with examples being a wheelbarrow and a nutcracker. Lastly, a third-class lever has the input force between the output force and the fulcrum, as seen in a pair of tweezers or a human arm when lifting a weight.

The Mechanical Advantage (MA) is a calculation that shows how much a lever amplifies the input force. It is given by the ratio of the distance from the fulcrum to the input force (effort arm) and the distance from the fulcrum to the output force (resistance arm). Levers are simple machines that utilize torque and the physical distances from their pivot point to achieve an output force that is greater or faster or travels a further distance than the input force.

Answer:

D. 99.9936%.

Step-by-step explanation:

We have been given that the length of a screw produced by a machine is normally distributed with a mean of 0.65 inches and a standard deviation of 0.01 inches.

To find the percent of screws that are between 0.61 and 0.69 inches, first of we will find z-score for our given raw scores using z-score formula.

[tex]z=\frac{x-\mu}{\sigma}[/tex], where,

[tex]z=\text{z-score}[/tex],

[tex]x=\text{Raw-score}[/tex],

[tex]\mu=\text{Mean}[/tex],

[tex]\sigma=\text{Standard deviation}[/tex].

Now let us find z-score corresponding to our given raw scores.

[tex]z=\frac{0.61-0.65}{0.01}[/tex]

[tex]z=\frac{-0.04}{0.01}[/tex]

[tex]z=-4[/tex]

Now let us find z-score for raw score 0.69.

[tex]z=\frac{0.69-0.65}{0.01}[/tex]

[tex]z=\frac{0.04}{0.01}[/tex]

[tex]z=4[/tex]

Now we will use formula to find the probability between two z-score as:

[tex]P(a<z<b)=P(z<b)-P(z<a)[/tex]

Upon substituting our given values in above formula we will get,

[tex]P(-4<z<4)=P(z<4)-P(z<-4)[/tex]

Using normal distribution table we will get,

[tex]P(-4<z<4)=0.99997-0.00003[/tex]

[tex]P(-4<z<4)=0.99994[/tex]

Now let us convert our answer into percent by multiplying 0.99994 by 100.

[tex]0.99994\times 100=99.994\%[/tex]

Therefore, 99.994% of screws are between 0.61 and 0.69 inches and option D is the correct choice.

128=8j; divide both sides by 8

j=16

Answer:

A) on Edge

Step-by-step explanation:

Took the test

Final answer:

The smallest number in the domain of the composite function f^o g,  is -8.

Explanation:

To find the smallest number that is in the domain of the composite function fo g, we need to consider the domains of the individual functions f(x) and g(x). First, since f(x) = √7x, f is only defined for x ≥ 0, as the square root function requires non-negative input. Secondly, g(x) = x+8 is defined for all real numbers, as it's a linear function.

However, the composite function f(g(x)) will also require that the output of g(x) be non-negative, because this output becomes the input for f(x). Thus, we need to find the smallest x such that g(x) is non-negative, which occurs when x+8 ≥ 0. Solving for x gives us x ≥ -8.

Hence, the smallest x in the domain of fo g is -8.

The answer is 1:18. I just took the statistics quiz and got it wrong due to the other person.

Since the plate is circular, therefore the area of the plate is jut equal to the area of a circle, so:

Area of plate = πr² = A

Taking the derivative:

dA / dr = 2πr                                                                           ---> 1

By the idea of partial differentiation, the equation can also take in the form of:
dA/dt = dA/dr x dr/dt                                                             ---> 2

Where we are given that:
change in radius over time = dr/dt = 0.02  cm/min
change in area with changing radius = dA/dr = 2πr              ---> from equation 1
at r = 40 
dA/dr = 2π(40) = 80π 

Substituting all the known values into equation 2:
dA/dt = (80π)(0.02)

dA/dt = 1.6π cm^2 /s = 5.03 cm^2/s