Which of the following represents the factorization of the binomial below?
49x2 - 81y2
A. (x-9y)7x-9y)
B. (7x+9yX(7x+9y)
C. (7x+y)(x-97)
D. (7x+9y)(7x-9y)

Answer:

x= 3/11

Step-by-step explanation:

Since you replace f(x) with 4,

4=-11x+7

-3=-11x

-3/-11=x

Answer:

51

Step-by-step explanation:

f(-4); f(x) = -11x + 7

f(x-4) = -11(-4) + 7

f(x-4) = 44 + 7

f(x-4) = 51

I basically just plugged -4 in for the value of the x's, and solved the equation.

The angle between the vectors a and b can be found using the dot product formula and the magnitude of the vectors. The dot product of two vectors a and b is given by the equation a · b = |a| |b| cos(theta), where |a| and |b| represent the magnitudes of vectors a and b, and theta is the angle between them.

In this case, vector a = i + 2j - 2k and vector b = 8i - 6k. The magnitudes of these vectors can be calculated as follows: |a| = sqrt(1^2 + 2^2 + (-2)^2) = sqrt(1 + 4 + 4) = sqrt(9) = 3, and |b| = sqrt(8^2 + 0^2 + (-6)^2) = sqrt(64 + 0 + 36) = sqrt(100) = 10.

Next, we can calculate the dot product of the vectors: a · b = (1)(8) + (2)(0) + (-2)(-6) = 8 + 0 + 12 = 20.

Substituting these values into the dot product formula, we have 20 = (3)(10) cos(theta).

Simplifying the equation, we get cos(theta) = 20 / (3)(10) = 20/30 = 2/3.

To find the angle theta, we can take the inverse cosine (or arccos) of 2/3: theta = arccos(2/3).

Approximating this angle to the nearest degree, we have theta ≈ 48 degrees.

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An IQ of 119 is more unusual because its corresponding z-score of 1.7 is further from 0 than the corresponding z-score of -1.2 for an IQ of 92.

The z-score of a data point is an indication of how many standard deviations the value is away from the mean. A z-score of 0 represents the mean, while negative z-scores are below the mean and positive z-scores are above the mean. To calculate the z-score of a given value, the formula is (X-μ)/σ, where X is the data point, μ is the population mean, and σ is the population standard deviation.In this case, the mean is 102 and the standard deviation is 10. The z-score of an IQ of 92 would be (-10-102)/10 = -1.2, while the z-score of an IQ of 119 would be (17-102)/10 = 1.7. Therefore, an IQ of 119 is more unusual because its corresponding z-score of 1.7 is further from 0 than the corresponding z-score of -1.2 for an IQ of 92.

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The probability of getting 3 heads in 5 trials with an unfair coin, where the probability of each head is 0.2, Using the binomial probability formula. The probability of 3 heads in 5 trials is approximately 0.0512, or 5.12%.

1. To find the probability of getting exactly 3 heads in 5 trials with an unfair coin, we can use the binomial probability formula. The formula is given by P(x) = (nCx) * (p^x) * ((1-p)^(n-x)), where P(x) represents the probability of getting x successes, nCx is the binomial coefficient, p is the probability of success, and (1-p) is the probability of failure.

2. In this case, we want to find P(3), where the probability of each head is 0.2, and the number of trials is 5. Therefore, substituting the values into the formula, we have P(3) = (5C3) * (0.2^3) * ((1-0.2)^(5-3)). Simplifying this expression, we get P(3) = 10 * 0.008 * 0.64 ≈ 0.0512, or 5.12%.

3. Therefore, the probability of obtaining exactly 3 heads in 5 trials with an unfair coin, where the probability of each head is 0.2, is approximately 0.0512, or 5.12%.

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The completed statements with regards to the compound interest of the amount in the account are;

If the account has a 5% interest rate and is compounded monthly, you have $101.655 million money after 2 years

If the account has a 5% interest rate compounded continuously, you would have $106.096 million money after 2 years

Compound interest is the interest calculated based on the initial amount and the accumulated interests accrued from the periods before the present.

The compound interest formula indicates that we get;

\(A = P\cdot (1 + \frac{r}{n}) ^{n\cdot t}\)

Where;

P = The principal amount invested = $92 million

r = The interest rate = 5% monthly

n = The number of times the interest is compounded per annum = 12

t = The number of years = 2 years

Therefore; \(A = 92\cdot (1 + \frac{0.05}{12}) ^{12\times 2}\approx 101.655\)

The amount in the account after 2 years is therefore about $101.655 million

The formula for the amount in the account if the principal is compounded continuously, we get;

A = \(P\cdot e^{(r\cdot t)}\)

Therefore, we get;

\(A = 96 \times e^{0.05 \times 2} \approx 106.096\)

The amount in the account after 2 years, compounded continuously therefore, is about $106.096 million

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The expression that represent the perimeter of the rectangle is 1458p⁹q⁶ + 6p³q².

A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

Therefore, the perimeter of the rectangle can be found as follows:

Therefore,

perimeter of the rectangle = 2(l + w) = 2l + 2w

where

Hence,

l = (9p³q²)³

w = 3p³q²

Therefore,

perimeter of the rectangle = 2((9p³q²)³) + 2(3p³q²)

perimeter of the rectangle = 2((9p³q²))(9p³q²))(9p³q²))) + 6p³q²

perimeter of the rectangle = 1458(p⁹q⁶) + 6p³q²

perimeter of the rectangle =  1458p⁹q⁶ + 6p³q²

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Answer:

A-B=x^2-x+1

Step-by-step explanation:

A-B=3x^2+5x-6+(-2x^2-6x+7)

 =3x^2+5x-6-2x^2-6x+7

 =x^2-x+1

The angle in the capital letter "L" measures 90°, making it a right angle.

A right angle is one that is exactly 90 degrees, or half of a straight angle. There is usually a quarter turn in it. The fundamental geometric forms, rectangle, and square, each have four angles that measure 90 degrees.

When two lines cross, and there is a 90-degree angle between them, the lines are said to be perpendicular. A few examples of 90-degree angles in real life include the angle between the hands of a clock at 3 o'clock, the angles between two neighboring sides of a rectangular door or window, etc.

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Answer:

F=2

Step-by-step explanation:

1.25f+2.75f=10-2

calculate like terms

4f=8

divide

F=2

Answer:

23.56 length units

Step-by-step explanation:

To calculate the perimeter of a triangle, we need to calculate the length of all the sides, then sum up the lengths.

To calculate each side, we take the differences of the coordinates of consecutive vertices, square, add, and take square-root (Pythagoras theorem).

Side 1: (3,-2), (5, -8)

difference in coordinates=(2,-6), length=sqrt(2^2+6^2) = sqrt(40)

Side 2: (5, -8), (-2,1)

difference in coordinates=(7,-9), length=sqrt(7^2+9^2) = sqrt(130)

Side 2: (-2,1), (3,-2)

difference in coordinates=(5,-3), length=sqrt(5^2+3^2) = sqrt(34)

Perimeter

= sum of sides

= sqrt(40)+sqrt(130)+sqrt(34)

= 6.32+11.40+5.83

= 23.56 approximately

Answer:

3

Step-by-step explanation:

If we use pythagoras theorem we know a^2+b^2=c^2

c being the hypoeneuse

so we half the 8 to get the dimensions of the right angle so the bottom side is 4cm and then we use the hypotenuese which is 5 and plug it in so

a^2+4^2=5^2

a^2+16=25

-16 from both sides

a^2=9

square root both sides

a=3

An equation for the plane tangent to the surface z = 6y cos(4x - 2y) at the point (2, 4, 24) is:

z - 24 = (∂z/∂x)(2, 4)(x - 2) + (∂z/∂y)(2, 4)(y - 4).

To find the equation of the plane

tangent

to the surface at a given point, we need to calculate the partial derivatives of z with respect to x and y, evaluate them at the point, and then use the point-normal form of the equation of a plane.

First, we find the partial derivatives of z with respect to x and y:

∂z/∂x = -24y sin(4x - 2y)

∂z/∂y = 6(4x - 4y) sin(4x - 2y)

Next, we substitute the coordinates of the given point (2, 4, 24) into the partial derivatives:

∂z/∂x (2, 4) = -24(4) sin(4(2) - 2(4)) = -96 sin(0) = 0

∂z/∂y (2, 4) = 6(4(2) - 4(4)) sin(4(2) - 2(4)) = -24 sin(0) = 0

Since both partial

derivatives

evaluate to 0 at the given point, the equation of the plane tangent to the surface at (2, 4, 24) simplifies to:

z - 24 = 0(x - 2) + 0(y - 4)

z - 24 = 0

z = 24

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After that, descriptive statistics like the 50th percentile should be computed, which is a measure of central tendency. Finally, graphs such as frequency histograms can be created, which are useful for displaying how often each score occurs in a distribution. Thus, option C, all of these, is the correct answer.

Upon being presented with data from 400 students responding to our online "Knowledge in Psychology" questionnaire, we should check for impossible scores and outliers, compute some descriptive statistics like the 50th percentile and create a graph such as a frequency histogram.The following steps need to be followed upon being presented with data from 400 students responding to our online "Knowledge in Psychology" questionnaire:Step 1: Check for impossible scores and outliersStep 2: Compute some descriptive statistics like the 50th percentileStep 3: Create a graph such as a frequency histogram When data is presented, the first step is to check for any impossible scores and outliers. This means removing scores that are too high or too low to be reasonable, and that could skew the results. After that, descriptive statistics like the 50th percentile should be computed, which is a measure of central tendency. Finally, graphs such as frequency histograms can be created, which are useful for displaying how often each score occurs in a distribution. Thus, option C, all of these, is the correct answer.

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Answer:

To find the perimeter of a polygon, we add up the lengths of all the sides. In this case, we have a quadrilateral with sides of length y+8, y+7, y+7, and y+8.

Perimeter = (y+8) + (y+7) + (y+7) + (y+8)

Simplifying by combining like terms, we get:

Perimeter = 4y + 30

Therefore, the perimeter of the quadrilateral is 4y + 30.

Answer:

4y + 30

Step-by-step explanation:

To find:-

Answer:-

Perimeter is simply the sum of all sides of any figure. Since here it is a quadrilateral, perimeter would be the sum of all four sides of it .

The four sides given to us are , y+7 , y+8 , y+7 and y+8. We can add them to find out the perimeter as ,

Perimeter = y+7 + y+8 + y+7 + y+8

Perimeter = 4y + 30

Hence the perimeter of the given figure is 4y+30 .

Answer:

9 laps

Step-by-step explanation:

75% of something is the same as three-fourths, or multiplying by 0.75

12 x 0.75 = 9

or you can divide by 4 and then multiply by three if you know what to separate the original number into

12/4 = 3     3 x 3 = 9

The work in process (WIP) for the grinding department involves inventory and costs associated with materials and conversion. The given information includes the inventory value on May 1st and the completed units transferred to the mixing department. The question seeks the inventory value for May 31st.

The work in process (WIP) in the grinding department represents the inventory and costs of products that are still being processed. In this case, the information provided includes the inventory value on May 1st, which is $93,100. This value represents the unfinished products in the grinding department at the beginning of the period.

Additionally, it is mentioned that a certain quantity of products was completed and transferred to the mixing department. However, the exact value or quantity of completed units is not provided. This transfer represents the movement of products from the grinding department to the next stage in the production process.

The question asks for the inventory value on May 31st, which is the end of the period. Unfortunately, the specific value for the inventory on that date is not given. To determine the inventory value on May 31st, more information is needed, such as the production and movement of units during the period, as well as any additional costs incurred. Without this information, it is not possible to provide a specific answer regarding the inventory value on May 31st.

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To determine the missing value in the Grinding Department's inventory for May 31, we need to consider the flow of costs and activities in the department.

Based on the information provided, we can break down the transactions as follows:

1. Beginning Inventory (May 1):

  - Debit: Inventory (May 1) = $93,100

2. Completed and Transferred to the Mixing Department:

  - Debit: Materials = $664,940

  - Debit: Conversion = $471,216

3. Ending Inventory (May 31):

  - Credit: Inventory (May 31) (missing value)

To find the missing value, we need to consider the concept of cost flow in the Grinding Department. The inventory at the beginning of the month (May 1) is debited, and the costs associated with completed units are transferred out of the department. The remaining cost should be credited to the ending inventory.

To determine the ending inventory, we need to subtract the costs incurred during the period (both materials and conversion) from the beginning inventory:

\[Inventory\ (May\ 31) = Beginning\ Inventory\ (May\ 1) - (Materials + Conversion)\]

\[Inventory\ (May\ 31) = $93,100 - ($664,940 + $471,216)\]

\[Inventory\ (May\ 31) = $93,100 - $1,136,156\]

\[Inventory\ (May\ 31) = -$1,043,056\]

The ending inventory is calculated to be -$1,043,056. However, a negative inventory value is not feasible, so it's likely there was an error or omission in the given information or calculations. Please double-check the provided figures to rectify any discrepancies.

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Answer: check the attached graph for the answer

Step-by-step explanation:  Please find the attached file for the solution

Using the given data on the number of live multiple-delivery births for women aged 15 to 54, we need to calculate probabilities related to the age groups of the mothers. The probability of a randomly selected multiple birth involving a mother aged 30 to 39 will be determined, as well as the probabilities of not being in the age range, being less than 45, and being at least 40. Finally, we need to interpret whether a multiple birth involving a mother aged at least 40 is unusual.

(a) To calculate the probability of a randomly selected multiple birth involving a mother aged 30 to 39, we sum the number of multiple births in that age group and divide it by the total number of multiple births for women aged 15 to 54.

P(30 to 39) = 2822 / (89 + 508 + 1631 + 2822 + 1855 + 374 + 119)

(b) To find the probability of a randomly selected multiple birth involving a mother who is not aged 30 to 39, we subtract the probability found in part (a) from 1.

P(not 30 to 39) = 1 - P(30 to 39)

(c) To determine the probability of a randomly selected multiple birth involving a mother aged less than 45, we sum the number of multiple births for age groups below 45 and divide it by the total number of multiple births for women aged 15 to 54.

P(less than 45) = (89 + 508 + 1631 + 2822 + 1855 + 374) / (89 + 508 + 1631 + 2822 + 1855 + 374 + 119)

(d) To find the probability of a randomly selected multiple birth involving a mother aged at least 40, we sum the number of multiple births for age groups 40-44 and 45-54, and divide it by the total number of multiple births for women aged 15 to 54.

P(at least 40) = (374 + 119) / (89 + 508 + 1631 + 2822 + 1855 + 374 + 119)

Interpretation: The answer to part (d) will determine whether a multiple birth involving a mother aged at least 40 is unusual. If the probability is less than 0.05, it can be considered unusual. Therefore, we need to compare the calculated probability to 0.05 and select the correct choice.

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The grooming cost for a 60-pound dog is the output $100 for the function f(x) define by 55 + 3(x - 45) and satisfying the rule for x > 45.

The function of a function rule is defined as the process that changes the input value to output.

The cost for 60 pounds dog will be determined by the rule for x > 45,

so we input the value 60 for x in the function defined as 55 + 3(x - 45);

55 + 3(60 - 45)

55 + 3(15)

55 + 45

100.

Therefore, the output $100 is the cost for a 60 pounds dog satisfying the rule for the function defined as 55 + 3(x - 45) for x > 45.

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Answer:

  9

Step-by-step explanation:

The time required by the ambulance is ...

  time = distance/speed

  time = (20 mi)/(40 mi/h) = 1/2 h = 30 minutes

The time required by the helicopter is ...

  trip time = takeoff time + route time + landing time

  = (3 min) + (15 mi)/(1 mi/min) +(3 min) = (3 + 15 + 3) min = 21 min

The difference in times is ...

  (30 min) -(21 min) = 9 min

The helicopter takes 9 fewer minutes for the trip.

Answer: The other team is extra information. 150 – 60 = 90

He got 90 yards running.

Step-by-step explanation:

Given that cot(0) = 4/3 and theta is in Quadrant I, what is sin(theta)?

we have that

If angle theta is in quadrant I , then the value of sin(theta) is positive

Remember that

tan(theta)=1/cot(theta)

so

tan(theta)=3/4

substitute in the expression above

is positive because is quadrant I

remember that

sec(theta)=1/cos(theta)

so

cos(theta)=4/5

tan(theta)=3/4

tan(theta)=sin(theta)/cos(theta)

substitute given values

3/4=sin(theta)/(4/5)

sin(theta)=(3/4)*(4/5)=3/5

the answer is

The value for x is 7π/6 and 11π/6.

sin2xsecx+2cosx=0

(2sinxcosx)(1/cosx)+2cosx=0

sinxcosx/cosx+2cosx=0

So,

2sinx+2cosx=0

2(sinx+cosx)=0

(2(sinx+cosx))²=0

4(sin²x+cos²x+2sinxcosx)=0

hence,

(sin²x+cos²x+2sinxcosx)/4=0/4

sin2x+cos2x+2sinxcosx=0

1+sin2x=0

sinx=−1/2

=7π/6 and 11π/6

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Given the following function:

f(x) = 3x - 3

Let's determine the value at f(-3),

This means that we will be replacing all x variables of f(x) by -3.

We get,

f(x) = 3x - 3

f(-3) = 3(-3) - 3

= -9 - 3

f(-3) = -12

Therefore, f(-3) = -12

Given the following function:

f(x) = 3x - 3

Let's determine the value at f(-3),

This means that we will be replacing all x variables of f(x) by -3.

We get,

f(x) = 3x - 3

f(-3) = 3(-3) - 3

= -9 - 3

f(-3) = -12

Therefore, f(-3) = -12

Answer:

169

Step-by-step explanation:

13² is equal to 13 × 13.

13 × 13 = 169

Answer:

169

Step-by-step explanation:

13 x 13 = 169

Answer:

= 30,550 rupee owed

Step-by-step explanation:

yr1 = 50000 x 0.10^1 = 5000

5000 - 10000 = 5000 credit from debt.

yr 2 = 50000 x 1.10^2 = 500 debit from debt = 5000-15000= 10,000 credit from debt

yr 3 = 50000 x 1.10^3 = 50 debit from debt

5000 + 500 = 15000 where 50,000 owed initially and yr1 and yr 2 paid in full interest of 5500 and we deduct this from his payment = 25000-5500 =

19500 paid of initial and nothing owed on interest.

50000-19500= 30,500 rupees owed + 50 rupee interest.

= 30,550 rupee owed

The amount he should pay at the end of the three years to settle the loan is; 41,550 Rupees

We are given;

Investment = 50000 rupees

Annual Interest Rate = 10% = 0.1

Since the interest is compounded annually, then number of times of compounding = 3

Thus;

Amount to pay after 3 years is;

A = 50000(1 + 0.1)³

A = 50000 × 1.1³

A = 66500 Rupees

Now, we are told that he has already paid 10000 rupees after one year and 15000 rupees after two years. Thus, amount he now owes to settle the loan = 66500 - (10000 + 15000) = 41,550 Rupees

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