Simplify completely quantity x squared minus 100 over quantity x squared plus 2 x minus 120 divided quantity 6 x plus 60 over quantity x minus 2

Answer:

7/10

Step-by-step explanation:

[tex]1 - \frac{3}{10} \\ = \frac{10}{10} - \frac{3}{10 } \\ = \frac{7}{10} [/tex]

Step-by-step explanation:

To calculate the monthly payment for a mortgage, you can use the formula for a fixed-rate mortgage:

Monthly Payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

P = Loan amount (in this case, the home cost minus the down payment)

r = Monthly interest rate (annual rate divided by 12 and converted to decimal)

n = Total number of payments (number of years multiplied by 12)

Given:

Home cost = $600,000

Down payment = 40% of the home cost = 0.4 * $600,000 = $240,000

Loan amount = Home cost - Down payment = $600,000 - $240,000 = $360,000

Annual interest rate = 3.00%

Loan term = 30 years

First, calculate the monthly interest rate:

Monthly interest rate = (Annual interest rate / 100) / 12 = (3.00 / 100) / 12 = 0.0025

Next, calculate the total number of payments:

Total number of payments = Loan term * 12 = 30 * 12 = 360

Now, substitute the values into the formula:

Monthly Payment = ($360,000 * 0.0025 * (1 + 0.0025)^360) / ((1 + 0.0025)^360 - 1)

After performing the calculations, the monthly payment for this mortgage is approximately $1,520.06.

I hope I was helpful

For the function  [tex]A(t)=4000e^0^.^0^4^t[/tex] the value of A'(8) is $220 and the value of [tex]A'(t)=160e^0^.^0^4^t[/tex]

The given function is [tex]A(t)=4000e^0^.^0^4^t[/tex] gives the balance after t years.

The initial investment is 8000

4% is the compounded interest.

Now differentiate with respect to t

[tex]A'(t)=0.04(4000)e^0^.^0^4^t[/tex]

[tex]A'(t)=160e^0^.^0^4^t[/tex]

Now let us find the value of A'(8)

Plug in t as 8

[tex]A'(8)=160e^0^.^0^4^(^8^)[/tex]

A'(8)=220.3

Hence, the value of A'(8) is $220 and the value of [tex]A'(t)=160e^0^.^0^4^t[/tex]

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The equation shows that the point total in the 10th level is predicted to be 514.4.

The equation given is: y= 48.2x + 32.4

where y is the point total and x is the level.

In order to predict the point total in the 10th level, I will substitute x=10 into the equation:

y=48.2(10) + 32.4 = 482 + 32.4 = 514.4

Therefore, the point total in the 10th level is predicted to be 514.4.

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Answer:

27

Step-by-step explanation:

We can solve by using order of operations (PEMDAS), which shows us the order in which we're supposed to perform mathematical operations:

The / comes from the fact that you do these operations from left to right as multiplication and division have the same level of priority in an equation/operation.

Like multiplication/division, the / comes from the fact that you do these operations from left to right as addition and subtraction also have the same level of priority in an equation/operation.

Step 1:  Simplify inside the parentheses:

5 * 4 + (1 + 1) + 5

5 * 4 + 2 + 5

Step 2:  Multiply 5 and 4:

20 + 2 + 5

Step 3:  Add 20 and 2:

22 + 5

Step 4:  Add 22 and 5 to get your answer:

27

Thus, 5 *4 + (1 + 1) + 5 = 27

A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.

Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.

The equation would be 3 x + 2 = 14.

So we can solve for the equation to be :

3x + 2 - 2 = 14 - 2

3x = 12

3 x / 3 = 12 / 3

x = 4

In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.

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The prove of the statement is described below.

First of all ,

Labeling the given figure

And draw  a diagonal,

In the quadrilateral PQRS,

The side PQ is equal to the side RS.

Therefore,

PQ = RS

And also, the side PQ is parallel to the side RS.

Then,

PQ || RS.

Now, draw the diagonal PR.

We know that a parallelogram's diagonal divides the parallelogram into two congruent triangles.

By the rule of  Side-Angle-Side,

we can show that ∆ PQR ≅ ∆ RSP.

Therefore,

The side QR is parallel to PS

Then,

QR || PS.

Hence,

PQRS is a parallelogram.

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The triangles ABC and DBE are similar by the SAS similarity theorem

The measure of the side lengths AC is 16 units

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

The triangles ABC and DBE

These triangles have the following measures

This means that the triangles are similar by the SAS similarity theorem

Using the SAS similarity theorem, we have the following equation

(x + 1)/12 = (x + 5)/15

Cross multiply the equation

15x + 15 = 12x + 60

So, we have

3x = 45

Divide by 3

x = 15

This means that

x + 1 = 15 + 1 = 16

x + 5 = 15 + 5 = 20

Hence, the measure of the side lengths are 16 and 20 units

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The ball has traveled approximately 25.24 feet Horizontally.The correct answer is D. 25.2 ft.

The horizontal distance traveled by the soccer ball after 0.9 seconds, we can use the equation:

horizontal distance = initial velocity * time * cos(angle)

Substituting the given values:

initial velocity = 39 ft/s

time = 0.9 s

angle = 44°

horizontal distance = 39 ft/s * 0.9 s * cos(44°)

Calculating:

horizontal distance ≈ 39 ft/s * 0.9 s * 0.71934 ≈ 25.24 ft

Therefore, after 0.9 seconds, the ball has traveled approximately 25.24 feet horizontally.

The correct answer is D. 25.2 ft.

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Answer:

-----------------------

Quadratic equation has the form of:

Analyze the given equations and see which has the same form:

The z-score is calculated as z-score.

The score x = 33 is 1.5 standard deviations above the mean of 27.

To find the z-score for x = 33 in a normal distribution with a mean of 27 and a standard deviation of 4, we can use the formula for calculating the z-score:

z = (x - μ) / σ

where in this case, x = 33, μ = 27, and σ = 4. Plugging these values into the formula, we can calculate the z-score:

z = (33 - 27) / 4

z = 6 / 4

z = 1.5

The z-score for x = 33 is 1.5.

The z-score represents the number of standard deviations that a given value (x) is away from the mean (μ) in a normal distribution. It indicates how many standard deviations a data point is above or below the mean.

In this context, a z-score of 1.5 for x = 33 means that the value 33 is 1.5 standard deviations above the mean of 27.

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The number of ways to draw the socks in each case is given as follows:

a) 90 ways.

b) 48 ways.

c) 42 ways.

The Fundamental Counting Theorem states that if there are m ways for one trial and n ways for another trial, then there are m x n ways in which the two trials can happen simultaneously.

This can be extended to more than two trials, where the number of ways in which all the trials can happen simultaneously is the product of the number of outcomes of each individual trial, according to the equation presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For item a, we have that there are no restrictions, hence there are 10 options for the first sock and 9 for the second, hence:

10 x 9 = 90.

For item b, we need one of each, hence the possible combinations are:

Hence:

6 x 4 + 4 x 6 = 48.

For item c, we can take 6 then five(two blue) or 4 then 3(two white), hence:

6 x 5 + 4 x 3 = 42.

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Answer:

the distance between the cities is 21.75 miles.

Step-by-step explanation:

1 inch = 8.7 miles.

2.5 inches x 8.7 miles/inch = 21.75 miles

The value of function sin (π/4) is,

⇒ sin π/4 =  0.7071

We have to given that;

The expression is,

⇒ sin π/4

Now, We can simplify the expression as;

⇒ sin π/4

⇒ 1 / √2

⇒ 1 / 1.414

⇒ 0.7071

Thus, The value of function sin (π/4) is,

⇒ sin π/4 =  0.7071

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The value of function h (0) is,

h (0) = 10

And, The value of function h (4) is,

h (4) = 8

Given that;

The function is,

h (x) = { 3x - 4 , x < 0

       = {2x² - 3x + 10, 0 ≤ x < 4

       = { 2x , x≥ 4

Hence, The value of function h (0) is,

h (x) = 2x² - 3x + 10, 0 ≤ x < 4

h (0) = 2 (0) - 3 (0) + 10

h (0) = 10

The value of function h (4) is,

h (x) = 2x

h (4) = 2 (4)

h (4) = 8

Thus, The value of function h (0) is,

h (0) = 10

And, The value of function h (4) is,

h (4) = 8

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Answer:

Step-by-step explanation:

use gauth math it helps with maths

The probability that in a sample of 200 Americans, the proportion that uses CNN as their primary news source is at least 0.21 is 49.6%.

The probability is determined using the normal approximation to the binomial distribution.

Given that the sample size is large (n = 200) and the probability of success (p = 0.15) is not too close to 0 or 1, the mean (μ) and standard deviation (σ) of the binomial distribution, will be:

μ = n * p

μ = 200 * 0.15

μ = 30

σ = √(n * p * (1 - p))

σ = √(200 * 0.15 * (1 - 0.15))

σ ≈ 4.29

Then, the z-score corresponding to the proportion of 0.21 is:

z = (x - μ) / σ

z = (0.21 - 0.15) / 4.29

z ≈ 0.014

Using a calculator, the probability of a z-score of 0.014 is approximately 0.504.

Hence, the probability of obtaining a proportion at least 0.21, is:

Probability = 1 - 0.504

Probability ≈ 0.496

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The perpendicular height of the pyramid is  83.65 cm

To find the perpendicular height we can define a right triangle.

The perpendicular height is one leg, and the other leg will be half of the diagonal of the base.

The base is a square whose sidelength is 23cm, then the diagonal is:

D = √( (23cm)² + (23cm)²)

D = 32.527cm

Half of that is

D/2 =  32.527cm/2 = 16.26cm

Now, we know one side of the right triangle and the angle of 79°, for which the known cathetus is adjacent.

The perpendicular height is the opposite cathetus.

Then we can use the relation:

tan(79°) = H/16.26cm

Solving for H, the heigt, we will get.

H = tan(79°)*16.26cm = 83.65 cm

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I cannot solve that problem at the moment.

Step-by-step explanation:

But I will help you in the future

(17) The length of the arc is 39.27 in

(18) The length of the arc is 70.7 cm

(19) The area of the sector is 395.84 in²

(20) The area of the sector is 38.5 cm².

The area of each of the sector is calculated by using the following formula;

Area = πr² (θ/360)

Where;

The formula for length of arc is given as;

length of arc = 2πr (θ/360)

(17) The length of the arc is calculated as;

L = 2π (10 in) (225/360)

L = 39.27 in

(18) The length of the arc is calculated as;

L = 2π (15 cm) (270/360)

L = 70.7 cm

(19) The area of the sector is calculated as;

A = π(12)² (315/360)

A = 395.84 in²

(20) The area of the sector is calculated as;

A = π(7)² (90/360)

A = 38.5 cm²

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The function that represents the number of comic book as a function of the number of years, t is expressed as y = 30x or f(t) = 30t.

We can use the given data to create a linear equation of the form y = mx + b, where y represents the number of comic books and x represents the number of years.

To find the equation, we can use any two pairs of (x, y) values. Let's use the first and fourth years:

First year: (1, 30)

Fourth year: (4, 120)

The slope, m, of the line can be calculated using the formula:

m = change in y / change in x = (120 - 30) / (4 - 1)

m = 90 / 3

m = 30

The y-intercept, b, can be found by substituting one of the (x, y) values and the slope into the linear equation, y = mx + b:

30 = 30(1) + b

b = 0

Therefore, the equation that represents the number of comic books, y, as a function of the number of years, x, is:

y = 30x

or

f(t) = 30t [where t represents the number of years.]

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Answer:

A) Using Commutative property

Step-by-step explanation:

In step 1, it used distributive property when the number 5 is distributed inside of the equation in the parenthesis.

In Step 4, dividing both sides by 10 to further simplify the equation

In step 2, you combined like terms and it results to the equation in step 3

The z-scores for the observations 16, 11, 13, 22, 15, and 19 are approximately 0, -1.37, -0.82, 1.64, -0.27, and 0.82, respectively.

To compute the z-scores for each observation in the sample, we need to first calculate the mean and standard deviation of the data set.

Given the sample with observations: 16, 11, 13, 22, 15, and 19.

Calculate the mean (μ):

Add up all the observations and divide by the total number of observations.

Mean (μ) = (16 + 11 + 13 + 22 + 15 + 19) / 6 = 96 / 6 = 16.

Calculate the standard deviation (σ):

Subtract the mean from each observation.

Deviation = Observation - Mean

Square each deviation.

Squared Deviation = Deviation²

Calculate the average of the squared deviations.

Average Squared Deviation = (Squared Deviation1 + Squared Deviation2 + ... + Squared Deviation6) / 6

Take the square root of the average squared deviation.

Standard Deviation (σ) = √(Average Squared Deviation)

Let's calculate each step:

Deviation1 = 16 - 16 = 0

Deviation2 = 11 - 16 = -5

Deviation3 = 13 - 16 = -3

Deviation4 = 22 - 16 = 6

Deviation5 = 15 - 16 = -1

Deviation6 = 19 - 16 = 3

Squared Deviation1 = 0² = 0

Squared Deviation2 = (-5)² = 25

Squared Deviation3 = (-3)² = 9

Squared Deviation4 = 6² = 36

Squared Deviation5 = (-1)² = 1

Squared Deviation6 = 3² = 9

Average Squared Deviation = (0 + 25 + 9 + 36 + 1 + 9) / 6 = 80 / 6 = 13.33

Standard Deviation (σ) = √13.33 ≈ 3.65

Now that we have the mean (μ = 16) and standard deviation (σ ≈ 3.65), we can calculate the z-score for each observation.

The z-score (Z) for an observation (X) is calculated using the formula:

Z = (X - μ) / σ

Let's calculate the z-scores for each observation:

Z1 = (16 - 16) / 3.65 = 0 / 3.65 = 0

Z2 = (11 - 16) / 3.65 = -5 / 3.65 ≈ -1.37

Z3 = (13 - 16) / 3.65 = -3 / 3.65 ≈ -0.82

Z4 = (22 - 16) / 3.65 = 6 / 3.65 ≈ 1.64

Z5 = (15 - 16) / 3.65 = -1 / 3.65 ≈ -0.27

Z6 = (19 - 16) / 3.65 = 3 / 3.65 ≈ 0.82

So, the z-scores for the observations 16, 11, 13, 22, 15, and 19 are approximately 0, -1.37, -0.82, 1.64, -0.27, and 0.82, respectively.

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The estimated population of the town in 2023 is 57,344.

(a) Let P be the population in t years after 2014.

Since the population doubles every year, we can use the formula :

P = P₀(2)ⁿ, where P₀ is the initial population in 2014.

We have P₀= 112, so the equation is P = 112(2)ⁿ.

(b) To find the population in 2023, we need to find t when t + 2014 = 2023.

So t = 2023 - 2014 = 9.

Substituting t = 9 into the equation from part (a), we get:

P = 112(2)⁹

P ≈ 57,344

Therefore, the estimated population of the town in 2023 is 57,344.

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The output of the program for the variable z is -22 or it returns an error if z = x - 25y

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

x = 1

x = 3

z = x - 25y

print(z)

The value of the variable y is not given

So, the program would return an error

However, if the complete program is as follows (removing the variable y)

x = 1

x = 3

z = x - 25

print(z)

Using the above as a guide, we have the following:

The final value of x is 3

So, we have

z = 3 - 25

Evaluate

z = -22

This means that the output of the program for z is -22

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(a). The statement can be translated into English as follows "Not exists x such that P(x) and Q(x), and for all y, if R(y) then P(y)." (b) The rewritten statement explicitly places the negation symbol "¬" only in front of the existential quantifier (∃x).  (c). This clarifies that the negation applies to the existence of x such that P(x) and Q(x).

a) Translation into English:

The statement can be translated into English as follows:

"Not exists x such that P(x) and Q(x), and for all y, if R(y) then P(y)."

b) Potential ambiguities in the translated statement:

Ambiguity in the scope of negation: The placement of the negation symbol "¬" might lead to ambiguity. It is not clear whether the negation applies only to the existential quantifier (∃x) or to the entire statement. Specifically, it is unclear if the negation applies to both conjuncts separately or to their conjunction as a whole.

Ambiguity in the scope of quantifiers: The scope of the quantifiers (∃x) and (∀y) is not explicitly defined. It is unclear which variables the quantifiers bind to and how they relate to the predicates P(x), Q(x), R(y), and P(y).

c) Rewritten statement to eliminate ambiguities while maintaining the original meaning:

To eliminate the ambiguities, we can rewrite the statement as follows:

(¬∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y))

The rewritten statement explicitly places the negation symbol "¬" only in front of the existential quantifier (∃x). This clarifies that the negation applies to the existence of x such that P(x) and Q(x). Additionally, parentheses are used to explicitly define the scope of the quantifiers (∃x) and (∀y), making it clear which variables they bind to.

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