For 18-20, factor each of the following and show work.

18. 5x^4 - 25x

19. 4x^2 - 9

20. x^2+8x+12

Answer:

esarespuesta  ad 56

Step-by-step explanation:

Answer:

67 / 72

Step-by-step explanation:

3/8 + 5/9 = 27/72 + 40/72 = 67/72

Declan's reasoning does make sense. This is because 3/4 and 1/2 have the same denominator, and 3/4 is a larger fraction than 1/2.

Therefore, it is reasonable to assume that 3/4 is greater than 6/12 because 6/12 simplifies to 1/2. Simplifying fractions means dividing the numerator and denominator by the same number, in this case, 6 is divisible by 2, so we can reduce the fraction to 1/2.

So, Declan is correct in his reasoning that 3/4 is greater than 6/12. It is important to understand the relationship between fractions and their denominators to make such comparisons accurately.

3/4 = 9/12

1/2 = 6/12

6/12 = 6/12

Since 9/12 (which is equivalent to 3/4) is greater than 6/12 (which is equivalent to 1/2), we can say that 3/4 is indeed greater than 6/12.

Therefore, Declan's reasoning is correct.

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Set theory is a branch of mathematics that deals with the study of sets, which are collections of objects. A subset is a set that contains only elements that belong to a larger set, called the universal set. In this context, let S, T, X, and Y be subsets of some universal set.

Assuming that S [T X [Y, we can conclude that if a belongs to T, then a belongs to S or a belongs to X or a belongs to Y. This is because T is a subset of S [T X [Y, and any element in T must belong to at least one of these sets.

Assuming that S \T D, we can conclude that if a belongs to T, then a does not belong to S. This is because S \T is the set of elements that belong to S but not to T, and D is the empty set, meaning that there are no elements in the set. Therefore, if a belongs to T, it cannot belong to S \T, and so it must not belong to S.

Assuming that X S, we can use all three assumptions to prove that T Y. Suppose that a belongs to T. Then, using assumption (i), we know that a belongs to S or a belongs to X or a belongs to Y. But since a cannot belong to S (using assumption (ii)), we must have either a belongs to X or a belongs to Y. But since X is a subset of S (using assumption (iii)), we know that if a belongs to X, then a belongs to S. Therefore, we must have a belongs to Y. This holds for any element a in T, so we can conclude that T Y.

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The function of the town's population is an exponential growth

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

Initial population = 3800

Growth  rate = 2% every year

From the above, we understand that

There is a growth in the population by 2% every year

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

This means that the function is an exponential growth

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The length of the cube with a volume of 200³ is 200u.

The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes.

To find the length of a cube with a volume of 200³, we need to find the cube root of 200³. The cube root of a number is the number that, when multiplied by itself three times, gives the original number.

We can find the cube root of 200³ using a calculator or by simplifying the expression:

Cube root of 200³ = \((200^3)^{(1/3)\) = \(200^{(3/3)\) = 200¹ = 200

Therefore, the length of the cube with a volume of 200³ is 200 units.

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Answer:

y = 8x

Step-by-step explanation:

1. First, we need to know what slope-intercept form is. The slope-intercept form of any linear equation is y = mx + b, where y = y-coordinate, m = slope, x = x-coordinate, and b = y-intercept.

2. To find the slope, let's take the two points (0,0) and (10,80) and plug their values into this formula: \(\frac{y_2-y_1}{x_2-x_1}\)

3. Now that we know our slope, our equation should look like this so far: y = 8x + b.

4. Since b is the y-intercept, we can say that b = 0 because the line intersects with the y-axis at (0,0).

5. Therefore, we get an equation of y = 8x or y = 8x + 0.

Answer:

The y-intercept is 3.

Step-by-step explanation:

I had to use a graph but if you mark the point on the graph. The slope is 2 so you would go up 2 right 1. But you can also do it the opposite way, go down 2 left 1. I hope this helps!

The limit is: lim t → [infinity] t (t^2)/(9t - t^2) = 8

To find the limit of the expression as t approaches infinity, we can use the concept of asymptotes and dominant terms.

First, we can simplify the expression by factoring out t^2 from the numerator:

t^2(9 - 1)

Simplifying the expression further, we get:

8t^2 / t^2

which simplifies to:

8

Therefore, the limit of the expression as t approaches infinity is 8.

So, the answer is:

lim t → [infinity] t (t^2)/(9t - t^2) = 8

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The probability that a sample of 120 female graduates will = 0.8905

what is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

= |y -µ| ≥ 0.60

z = y -µ /σ√n

= 0.60/4.10√120

= 0.60/0.3742770

=1.60

Pr ( y -µy) ≤ 0.60 = P |z|≤1.60

=P ( -1.60≤ Z≤ -1.60)

=P (Z ≤ 1.60) -P ( Z≤ -1.60)

= 0.9452 - 0.0547 using z table

= 0.8905

Female graduates

mean = 27.83

sd = 4.10

sample = 120

µx = 27.83

σx = σ/√n

= 4.10/√120

a) P (X bar > 27.83)

= P (X bar -µx)/ σx > 27.83-27.83/4.10/√120

= P ( z > -1.60)

= 0.9452

For men

Mean=µ=37.39

Sd=σ=4.60 ,n=50

Probability that sample mean within $1.00 of the population mean

u-1=37.39-1=36.39

u+1=37.39+1=38.39

P = (36.39 <X bar < 38.39)

= P \(\frac{36.39-37.39 }{4.60/\sqrt{60} } < \frac{X bar - µ}{σ/\sqrt{n} } < \frac{39.39-37.39}{4.60/\sqrt{60} }\)

= P ( -1.6839 < Z <1.6839

= P ( -1.68 < Z <1.68)

= P (Z < 1.68) - P(Z < -1.68)

= 0.9535- 0.0465

= 0.9070

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The οnly sοlutiοn is sinθ = 0, θ = kπ, where k is any integer.

Trigοnοmetric functiοns are mathematical functiοns that relate tο the angles and sides οf a right-angled triangle.  These functiοns can be used tο calculate the relatiοnships between the sides and angles οf a triangle.

1a) Using inverse tangent functiοn,

θ = tan^{-1}(-2/3) ≈ -0.93 + kπ οr 2.21 + kπ, where k is any integer.

1b) Using cοsine functiοn,

\(2cos^{2}\theta - 1 = 0\)

\(cos^{2}\theta= 1/2\)

cοsθ = ±√(1/2) = ±1/√2

Sο, θ = π/4 + kπ/2 οr 3π/4 + kπ/2, where k is any integer.

1c) Rearranging the equatiοn, we get

\(sin^{2}\theta - 6sin\theta- 7 = 0\)

Using the quadratic fοrmula,

sinθ = [6 ± √(36 + 28)]/2 = 3 ± √19

Since -1 ≤ sinθ ≤ 1, the οnly sοlutiοn is

sinθ = 3 - √19

\(θ = sin^{(-1)(3 - \sqrt{19})} \approx 0.47 + 2k\pi\) οr π - 0.47 + 2kπ, where k is any integer.

1d) Factοring οut sinθ frοm the equatiοn, we get

sinθ(cοsθ - 7) = 0

Sο, either sinθ = 0 οr cοsθ = 7. Since -1 ≤ sinθ, cοsθ ≤ 1, the οnly sοlutiοn is

cοsθ = 7 has nο real sοlutiοn, sο the οnly sοlutiοn is

sinθ = 0

θ = kπ, where k is any integer.

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Answer: b.5.32

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

… = (3x² - 4) - (4x + 1)

… = 3x² - 4x - 5

The amount of money that Rob will have in five years is $412.50.

The savings account earns a simple interest. The amount of money she will have in 5 years is the sum of the amount that she deposited and the interest she has earned.

Value of the account in 5 years = amount deposited + interest

Interest = amount deposited x interest x number of years

= $330 x 0.05 x 5 = $82.50

Value of the account in 5 years =  $82.50 + $330 = $412.50

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Answer:

Monthly deposit= $323.78

Step-by-step explanation:

Giving the following information:

Future Value (FV)= 12,000*0.7= $8,400

Number of periods (n)= 2*12= 24

We weren't provided with the interest rate, suppose an annual interest rate of 8%.

Interest rate= 0.08/12= 0.00067

Now, to calculate the monthly deposit, we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

A= (8,400*0.0067) / [(1.0067^24) - 1]

A= $323.78

Answer:

\(team \: a \\ 8 \: in \: number \: with \: in \: 2hours \: \\ so \: in \: 1hour \frac{8}{2} = 4 \\ \\ team \: b \\ 5 \: in \: number \: in \: 1 \: hour \\ so \: b \: is \: fast \\ thank \: you\)

Answer:

Lil Kim and I will name Corbett 70 show are you okay give me $60 and I'll give you 5000 indicate 5060 and 60 cash cash cash cash me cash pay me if you don't care if you're paying me to buy tomorrow you know me you know me and you know when the worst of me man ke bachhe forget my even pay my money to move you will know me properly and see if the k-50 ktkk 5250 case I wanted to mow 50k ok ok ok ok this is Alia bhatt me 50k cash cash I will give you my cell number Mukesh number imma cash number okay let's let's control the day before we fight let's control the game before we fight let's do let's give me the money by tomorrow I'll tell you when I'm back at the work okay okay if we're at least you give me 16,000 or tomorrow and you are me 16 16 16 16 thousand 60 carat like this me and we don't do don't care just give me one clip I sleep sleep sleep and sleep well sleep well

A 95% confidence interval for the mean is (3193, 2607).

Confidence interval in simple words is the range of values that the specific parameter lies within.

Confidence interval for mean is found by the formula,

CI = Х ± t \(\frac{s}{\sqrt{n} }\)

where X is sample mean, s is the standard deviation and n is the sample size.

Sample mean = 2900

s = 1300

n = 55

Degree of freedom = n - 1 = 54

t value of degree of freedom 54 with the probability of exceeding the critical value as 1 - 95% = 5% = 0.05 is 1.674.

CI = 2900 ± (1.674)\(\frac{1300}{\sqrt{55} }\)

   = 2900 ± 293.44

   = (3193.44, 2606.56)

   = (3193, 2607)

Hence the confidence interval is (3193, 2607).

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Answer:

B

Step-by-step explanation:

The random circumstance in this case is whether or not a flight from one of the top 18 U.S. airlines arrives on time. Let's denote this random circumstance as "A." The associated probability, given that 77.6% of flights arrived on time, can be represented as P(A) = 0.776 or 77.6%.

Let's clarify the representation of the random circumstance and associated probability based on the given information.

The random circumstance in this case is whether or not a flight from one of the top 18 U.S. airlines arrives on time. Let's denote this random circumstance as event "A." The associated probability, given that 77.6% of flights arrived on time, can be represented as P(A) = 0.776 or 77.6%.

To explain in more detail, let's consider a large sample of domestic flights flown by the top 18 U.S. airlines in January of that certain year. Each flight in this sample can be seen as a random trial, where the outcome is whether the flight arrives on time or not.

In this context, event A represents the specific outcome of a flight arriving on time, and the complementary event, denoted as event "A'", represents the outcome of a flight being delayed or not arriving on time.

The given information states that 77.6% of domestic flights arrived on time. Therefore, the associated probability P(A) represents the probability of a flight from one of the top 18 U.S. airlines being on time, and it is equal to 0.776 or 77.6%.

It's important to note that this probability represents an average value based on historical data and may vary from month to month or between different airlines. Additionally, this probability assumes that each flight's on-time performance is independent of the others, which may not always hold true in practice.

Overall, the random circumstance "A" refers to a flight from one of the top 18 U.S. airlines arriving on time, and the associated probability P(A) represents the likelihood of this occurrence based on the given information.

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Answer:

I belive the answer is 3.

Step-by-step explanation:

35-2x4^2

35-2x16

35-32

3

Answer:

\(1225-140x^4+4x^8\)

Step-by-step explanation:

(35-2x^4)^2 is a form of \((a-b)^2=a^2+b^2-2ab\)

Applying this formula, we get 1225+4x^8-140x^4

Answer:

562.5

Step-by-step explanation:

hope this helps, trying to get more points so i can answer my question lol.

Answer:

(5x-1)(3x+2)

(if you don't want to do all of this you can use

Step-by-step explanation:

((3•5x2) +  7x) -  2

Factoring  15x2+7x-2

The first term is,  15x2  its coefficient is  15 .

The middle term is,  +7x  its coefficient is  7 .

The last term, "the constant", is  -2

Step-1 : Multiply the coefficient of the first term by the constant   15 • -2 = -30

Step-2 : Find two factors of  -30  whose sum equals the coefficient of the middle term, which is   7 .

     -30    +    1    =    -29

     -15    +    2    =    -13

     -10    +    3    =    -7

     -6    +    5    =    -1

     -5    +    6    =    1

     -3    +    10    =    7    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  10

                    15x2 - 3x + 10x - 2

Step-4 : Add up the first 2 terms, pulling out like factors :

                   3x • (5x-1)

             Add up the last 2 terms, pulling out common factors :

                   2 • (5x-1)

Step-5 : Add up the four terms of step 4 :

                   (3x+2)  •  (5x-1)

            Which is the desired factorization

Answer:

(5x-1)(3x+2)

Step-by-step explanation:

hope this helps!!

Answer:

Answer is C

Step-by-step explanation:

i.e (c x c x c x c) / (c x c x c) = c^1 = c

→\( {c}^{4} \div {c}^{3} \)

→\( \dfrac{ {c}^{4} }{ {c}^{3} } \)

→\( {c}^{4 - 3} \)

→\( {c}^{1} \)(c¹ and c is same thing)

________________________________

with regards!

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The probability that a student has a brother or a sister is: 92%

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

We are given the parameters as:

Percentage that have a brother = 75%

Percentage that have a sister = 82%

Percentage that have a brother and a sister = 65%

Thus:

P(Brother or Sister) = 0.75 + 0.82 - 0.65

P(Brother or Sister) = 0.92 = 92%

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The closest value to the volume of the water tower tank with a spherical tank diameter of 6 meters is 113.04 m3.

The volume of a sphere can be calculated using the formula V = (4/3)π\(r^{3}\), where V is the volume and r is the radius of the sphere. In this case, the diameter of the spherical tank is given as 6 meters, so the radius (r) is half of that, which is 3 meters.

Substituting the radius value into the formula, we have V = (4/3)π(\(3^{3}\)) = (4/3)π(27) ≈ 113.04 m3.

Among the given options, 113.04 m3 is the closest value to the volume of the water tower tank. It represents the approximate amount of water that the tank can hold.

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Answer:

f(x)=(x+2)^2+37

Step-by-step explanation:

Got it right on Khan :)

The quadratic function f(x) = x² + 4x + 41 is converted into square form is f(x) = (x + 2)² + 37.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

The quadratic function is given below.

f(x) = x² + 4x + 41.

The quadratic function is converted into square form by adding and subtracting the square of the half of the coefficient of x.

f(x) = x² + 4x + 41

Transform into square form. Then the quadratic function will be

f(x) = (x² + 4x + 4) + 41 – 4

f(x) = (x + 2)² + 37

The quadratic function f(x) = x² + 4x + 41 is converted into square form is f(x) = (x + 2)² + 37.

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\(m\angle E=\sin \dfrac{\sqrt{10}}{2\sqrt5}=\sin \dfrac{\sqrt2}{2}=45^{\circ}\)

The correct answer is  the formula for probability is equal to the number of times an event occurs divided by the number of attempts or chances for each outcome.

The formula for probability is equal to the number of times an event occurs divided by the number of attempts or chances for each outcome.

This means that the probability of a specific outcome is calculated by dividing the number of successful attempts by the total number of attempts. This is different from the number of possible outcomes, which represents the total number of different outcomes that could potentially occur.

So, to answer the multiple choice question, the formula for probability is equal to the number of times an event occurs divided by the number of attempts or chances for each outcome.

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