The sum of two numbers is 16 and their product is 63

Answer:

C. $117.88

Step-by-step explanation:

$10.25 per hour

11.5 hours worked

$10.25 * 11.5 = $117.875

round $117.875 to $117.88

C. $117.88

If 0 = pi/ radians. Then the terminal point is (1, 0), and tanθ = 0.

Given the equation 0 = π /  radians.

To find the terminal point we need to use the below formula,θ = 2πn + α

Where,θ = Angle of Terminal Point = Number of revolutions

α = Remaining Angle Thus, here α = 0 radians = 2πn + 0n solving the above equation,

we get,n = 0, 1, 2, ... etc.

As the radian measure is given in the equation, we know that the angle is at the 3 o'clock position on the unit circle, which is also known as the standard position.

So, the terminal point is (1, 0).To find tanθ, we have to use the formula given as tanθ = y / x, where x and y are the coordinates of the terminal point.

Here, x = 1 and y = 0. Hence, tanθ = y / x = 0 / 1 = 0.

Therefore, the terminal point is (1, 0), and tanθ = 0.

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Answer:

  m = -5

Step-by-step explanation:

You want the solution to the equation 3m/(2m-5)-7/(3m+1)=3/2.

We like to work these in the form f(m) = 0. Subtracting 3/2 and using a common denominator, we have ...

  \(\dfrac{3m}{2m-5}-\dfrac{7}{3m+1}-\dfrac{3}{2}=0\\\\\\\dfrac{3m(3m+1)(2)-7(2m-5)(2)-3(2m-5)(3m+1)}{2(2m-5)(3m+1)}=0\\\\\\\dfrac{2(9m^2+3m)-2(14m-35)-3(6m^2-13m-5)}{2(2m-5)(3m+1)}=0\\\\\\\dfrac{(18-18)m^2+(6-28+39)m+70+15}{2(2m-5)(3m+1)}=0\\\\\\17m+85=0\\\\m=-5\)

The value of m that makes this true is -5.

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Step-by-step explanation:

the most common form of line equation is

y = ax + b

a is the slope of the line. it is expressed as the ratio

y coordinate change / x coordinate change

when going from one point to the other.

b is the y-intercept (the y value when x = 0).

once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and since for b.

for the slope a :

x changes by +5 (from -3 to 2)

y changes by -15 (from 10 to -5)

so, the slope is -15/+5 = -3

the equation looks now like

y = -3x + b

let's use the first point

10 = -3×-3 + b = 9 + b

1 = b

so, the equation is

y = -3x + 1

Answer:

the last one

Step-by-step explanation:

when something asks for product it means multiplication

to get 2 times -5, you move first to -5 then to -10

Answer:

27000 m

Step-by-step explanation:

1km = 1000 m

27km = 27 x 1000 = 27000 m

So, the answer is 27000 m

Answer:27 km in meters is 27000 m

Step-by-step explanation:

multiply the length by 1000!

It will take 15 days for Akash to complete the entire work if he is assisted by Sunil and Rakesh every third day.

To determine the number of days, we first represent the number of days to do a piece of work by each one of them in fractions as follows;

Fraction of work completed by Akash in 1 day = 1/20

Fraction of work completed by Sunil in 1 day = 1/30

Fraction of work completed by Rakesh in 1 day = 1/60

The total work done in 1 day can be given as;

Total work done by the three in one day = [(1/20) + (1/30) + (1/60)] = 1/10

Work done by Akash in two days = 2 × (1/20) = 2/20 = 1/10

The work done in three days (1 day of all three together + Work done by Akash in two days) = (1/10) + (1/10) = 1/5

Therefore; the total work done in 3 days = 1/5

At this rate, the total number of cycles required to finish the work =

(1) ÷ (1/5) = 5

Since each cycle has three days, the total number of days required to finish the work can be calculated as follows;

5 × 3 = 15 days

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The wonderful waffle cone holds more ice cream than super sundae cone.

In this question,

The ice cream cone is the shape of hemisphere at the top and cone shape at the bottom.

Volume of ice cream cone = volume of hemisphere + volume of cone

Volume of ice cream cone = \(\frac{2}{3}\pi r^{3} +\frac{1}{3} \pi r^{2} h\)

Volume of super sundae cone:

Radius of hemisphere = height of hemisphere = 0.5 in

Depth of the ice cream cone = 4 in

Volume of super sundae cone = \(\frac{2}{3}\pi (0.5)^{3} +\frac{1}{3} \pi (0.5)^{2} (4)\)

⇒ \(\frac{2}{3}(3.14)(0.125) +\frac{1}{3} (3.14)(0.25)(4)\)

⇒ 0.2616+1.0466

⇒ 1.3082 ≈ 1.31 cubic in.

Volume of wonderful waffle cone:

Radius of hemisphere = height of hemisphere = 0.9 in

Depth of the ice cream cone = 3 in

Volume of wonderful waffle cone = \(\frac{2}{3}\pi (0.9)^{3} +\frac{1}{3} \pi (0.9)^{2} (3)\)

⇒ \(\frac{2}{3}(3.14)(0.729) +\frac{1}{3} (3.14)(0.81)(3)\)

⇒ 1.526+2.5434

⇒ 4.0694 ≈ 4.07 cubic in.

Thus volume of wonderful waffle cone > volume of super sundae cone.

Hence we can conclude that the wonderful waffle cone holds more ice cream than super sundae cone.

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The factorization of the polynomial b³-1000 is (b-10)(b²+10b+100).

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The given expression is b³-1000.

Here, b³-1000=b³-10³

Using a³-b³=(a – b)(a² + ab + b²), we get

(b-10)(b²+10b+100)

Therefore, the factorization of the polynomial b³-1000 is (b-10)(b²+10b+100).

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As a result, the probability of landing on blue, yellow, or purple is 43/65, which may be decreased to 17/26.

Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. Probability is expressed as a number between 0 and 1, with 0 indicating that an event is impossible to occur and 1 indicating that an event is certain to occur. The probability of an event A, denoted by P(A), is calculated as the number of favorable outcomes for the event divided by the total number of possible outcomes. For example, if a fair six-sided die is rolled, the probability of rolling a 3 is 1/6 because there is only one favorable outcome (rolling a 3) out of the total 6 possible outcomes. Probabilities can be used to make predictions about the likelihood of future events and to make decisions under uncertainty. Probabilities can also be used to describe the distribution of random variables and to quantify the relationship between different events. Probability theory is widely used in many fields, such as statistics, engineering, finance, physics, and biology, among others.

Here,

The probability of landing on a particular color on the next spin is equal to the number of times that color was landed on divided by the total number of spins. To find the probability of landing on blue or yellow or purple, we need to add up the number of times each of these colors was landed on and divide that total by the total number of spins.

Blue: 20 spins

Yellow: 15 spins

Purple: 8 spins

Total: 20 + 15 + 8 = 43 spins

So the probability of landing on blue or yellow or purple is 43/65 which can be reduced to 17/26.

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Answer:

5. p (6) = -6

6. f (-9) = -3

7. g (-4) = 15

8. h (5) = 19

9. u answered already

10. p (-9) = 9

11. f (-11) = -5

12. g (1) = 0

13. h(-4) = -8

14. k (10) = 181

15. p (11) = 11

16. f(-8) = -2

17. g (-10) = 99

18. h (3) = 13

19. k (6) = 49

20. p (99) = -99

21. f(0) = 6

22. g (2) = 3

23. h(0) = 4

24. k(3) = 7

25. p(-1/2) = 1/2

26. f (0.4) = 6.4

27. g (1/2) = -3/4

28. h (-1.2) = 0.4

29. k (1/2) = -1/2

30. p (\(\sqrt{6}\)) = -\(\sqrt{6}\)

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A and B are independent events if the probability of getting a red convertible is 0.08

The given parameters are:

P(A) = 0.20

P(B) = 0.40

The events are independent, if

P(A and B) = P(A) * P(B)

So, we have:

P(A and B) = 0.20 * 0.40

Evaluate

P(A and B) = 0.08

Hence, A and B are independent events if the probability of getting a red convertible is 0.08

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Complete question

A video game randomly chooses your car color and type. The probability of getting a red car is 0.20, and the probability of getting a convertible is 0.40.

Event A = You get a red car.

Event B = You get a convertible.

A and B are independent events if _____.

A.The probability of getting a red car or a convertible is 0.60.

B.The probability of getting a red car or a convertible is 0.08.

C.The probability of getting a red convertible is 0

D.The probability of getting a red convertible is 0.08

Answer:

y=6/5x-8

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through (5, -2) and has the slope of 6/5

We can write the equation of the line in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept.

Since we are already given the slope of the line, we can immediately plug it into the equation:

y=6/5x+b

Now we need to find b

Since the equation passes through the point (5, -2), we can use it to solve for b

Substitute 5 as x and -2 as y:

-2=6/5(5)+b

Multiply

-2=6+b

Subtract 6 from both sides

-8=b

Substitute -8 as b.

y=6/5x-8

Hope this helps!

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.

Given information and corresponding atomic propositions:

We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:

r: Rabbits have been seen in the area.

b: Berries are ripe along the path.

w: Walking on the path is safe.

Now, let us formalize each of the given statements in terms of these atomic propositions:

a) Berries are ripe along the path, but rabbits have not been seen in the area.

b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.

c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.

d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.

e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.

The formalizations in terms of atomic propositions are:

a) b ∧ ¬r.b) ¬r ∧ w ∧

b.c) (b → w) ∧ (¬r → w).

d) ¬w ∧ ¬r ∧

b.e) (¬r ∧ ¬b) → w.b ∧

Berries are ripe along the path, but rabbits have not been seen in the area.

This is formalized by using the ∧(logical and) operator.

(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

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Answer:

first blank: 15

second blank: 90

Step-by-step explanation:

Obviously, sin and cos are related, but they are not the same thing. In order for them to be equal:

sin(____) = cos(75)

the angles have to add up to 90 (complementary)

What + 75 is 90?

Do a tiny calc:

90 - 75 is 15

The second question is stating the rule generically.

x + (90 - x) is 90

To evaluate the volume of the region D bounded by the paraboloids \(z=2x^{2} -2y^{2} -4\) and \(z=5-x^{2} -y^{2}\) in the first quadrant (x ≥ 0, y ≥ 0).

In cylindrical coordinates, we have:

x = r cos(θ)

y = r sin(θ)

z = z

The limits of integration for r, θ, and z can be determined by the intersection points of the two paraboloids.

Setting \(z=2x^{2} -2y^{2} -4\) equal toz=5-x^{2} -y^{2}, we can solve for the intersection points. The region D is bounded by the curves \(x^{2} +y^{2}=2\).

The limits for θ are from 0 to π/2, as we are considering the first quadrant (x ≥ 0, y ≥ 0).

The limits for r are from 0 to \(\sqrt{2}\), as the region is bounded by the curves \(x^{2} +y^{2}=2\).

The limits for z are from 5 -\(r^{2}\) to 2 - 4\(r^{2}\), representing the upper and lower surfaces of the region D.

Therefore, the correct choice is c. \(\int\limits^{\frac{\pi }{2} }_0\int\limits^{\sqrt{3} }_{_0} \int\limits^\(2-4r^{2} }} _{5-r^2}\) r dz dr dθ, which allows us to evaluate the volume of the region D.

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The complete question is:

Let D be the region bounded by the two paraboloids \(z=2x^{2} -2y^{2} -4\) and \(z=5-x^{2} -y^{2}\) where x ≥ 0 and y ≥ 0. Which of the following triple integral in cylindrical coordinates allows us to evaluate the volume of D?

a.  \(\int\limits^{\frac{\pi }{2} }_0\int\limits^{\sqrt{3} }_{_0} \int\limits^\(5-r^{2} }} _{2r^2-4}\) dz dr dθ

b. None of these.

c. \(\int\limits^{\frac{\pi }{2} }_0\int\limits^{\sqrt{3} }_{_0} \int\limits^\(2-4r^{2} }} _{5-r^2}\) rdz dr dθ

d. \(\int\limits^{\frac{\pi }{2} }_0\int\limits^{\sqrt{3} }_{_0} \int\limits^\(5-r^{2} }} _{2r^2-4}\) rdz dr dθ

The answers to each part is mentioned above.

Given is that Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. The first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.

Equation for tank {1} -

y = 175 - 25x

Equation for tank {2} -

y = 200 - 30x

For the solution we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5

and

y = 200 - 150

y = 50

For the same amount of water we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5 hours

In tank (1), there is : 175 - 25 x 5 = 50 gallons

In tank (2), there is : 200 - 30 x 5 = 50 gallons

Therefore, the answers to each part is mentioned above.

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Answer:

The slope of the lines is 1/3

Step-by-step explanation:

Since I can't graph it, I can make a table

x         y

8        5

2        3

From 5 to 3, you subtract 2 (this is for the y section)

From 8 to 2, you subtract 6 (this is for the x section)

Now all you have to do is divide y by x....

y/x = 2/6 = 1/3 (when simplified)

Hope this helped!

Answer:

631 and 51/1000

Step-by-step explanation:

Answer:

I got 147107

Step-by-step explanation:

If the subscriptions decrease by 8% each year then you would times 225000 by 0.08 then take the number you get from that and subtract it from 225000. And repeat until you get to the seventh year.

If the variable x2 has been omitted from the given regression equation, then the estimator obtained when b2 is omitted from the equation. The bias in b1 is positive if the following two conditions are met: The variable x1 and x2 are positively correlated i.e., x1 and x2 have the same sign (positive).

And, the variable x2 has a nonzero partial effect on the dependent variable y.The following is the given regression equation: y = b1x1 + b2x2 + u; where u is the error term. If we exclude the variable x2 from the regression equation, then the equation will become y = b1x1 + u. The estimator obtained when b2 is omitted from the regression equation will be an unbiased estimator because it meets the Gauss-Markov assumptions. So, the bias in b1 is positive only if the two above conditions hold true.

If the variable x2 has been omitted from the given regression equation, then the estimator obtained when b2 is omitted from the equation.

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The purpose of this test is to evaluate the effects of rotational acceleration on the semicircular ducts and dynamic equilibrium. This test is called Rotational Acceleration Test.

The purpose of the rotational acceleration test is to assess how the semicircular ducts and the body's dynamic equilibrium respond to rotational movements. The semicircular ducts are part of the vestibular system, which is responsible for detecting changes in head position and rotational movements.

During the test, the individual is subjected to controlled rotational acceleration, usually in a specially designed chair or device. The rotational acceleration induces a sense of spinning or movement, stimulating the semicircular ducts.

By observing the individual's responses, such as eye movements or changes in body posture, healthcare professionals can gather information about the functioning of the vestibular system and the body's ability to maintain balance.

This test is particularly useful in diagnosing disorders of the vestibular system, such as vestibular dysfunction, vertigo, or balance disorders. It helps healthcare providers determine the extent of the impairment and develop appropriate treatment plans or interventions to improve balance and reduce symptoms.

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Given:

The expressions are:

\((5x-3y)\) and \((8x+8y)\)

To find:

The difference of \((5x-3y)\) and \((8x+8y)\).

Solution:

Difference of \((5x-3y)\) and \((8x+8y)\) is written as:

\(Difference=(5x-3y)-(8x+8y)\)

On simplification, we get

\(Difference=5x-3y-8x-8y\)

\(Difference=(5x-8x)+(-3y-8y)\)

\(Difference=-3x-11y\)

Therefore, the difference of \((5x-3y)\) and \((8x+8y)\) is \(-3x-11y\).

It is False that by adding the number of inner loops , we get the total number of iterations.

A loop is defined as a segment of code that executes multiple times. Iteration refers to the process in which the code segment is executed once. One iteration refers to 1-time execution of a loop. A loop can undergo many iterations.

There are 3 types of iteration: tail-recursion, while loops, and for loops. We will use the task of reversing a list as an example to illustrate how different forms of iteration are related to each other and to recursion. A recursive implementation of reverse is given below.

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Answer:

The answer is A.

Step-by-step explanation:

The answer is A because if you divide the price by how many are sold it comes out to 14.75.

Answer: A

Step-by-step explanation:

1 book cost $14.75

2 books cost $29.50

3 books cost $44.25

4 books cost $59.00

5 books cost $73.75

6 books cost $88.50

7 books cost $103.25

Answer:

the median is 20 and the mean is 17

Step-by-step explanation:

(a) The set {(x1,x2)T|x1 + x2 = 0} is a subspace of R2.

To check whether the given set is a subspace of R2, we need to check whether it is closed under vector addition and scalar multiplication. Let u = (u1,u2)T and v = (v1,v2)T be two arbitrary vectors in the set, and let c be an arbitrary scalar. Then:

u + v = (u1 + v1, u2 + v2)

Since u1 + v1 + u2 + v2 = (u1 + u2) + (v1 + v2) = 0 + 0 = 0 (since u and v are in the set), we see that u + v is also in the set.

c*u = (c*u1, c*u2)

Since c*u1 + c*u2 = c*(u1 + u2) = c*0 = 0 (since u is in the set), we see that c*u is also in the set.

Therefore, the set {(x1,x2)T|x1 + x2 = 0} is a subspace of R2.

(b) It is not a subspace of R2

To check whether the given set is a subspace of R2, we need to check whether it is closed under vector addition and scalar multiplication.

Let u = (u1,u2)T and v = (v1,v2)T be two arbitrary vectors in the set, and let c be an arbitrary scalar. Then:

u + v = (u1 + v1, u2 + v2)

Since u21 = u22 and v21 = v22 (since u and v are in the set), we see that (u1 + v1)2 = (u2 + v2)2. Therefore, u + v is in the set.

c*u = (c*u1, c*u2)

Since u21 = u22 (since u is in the set), we see that (c*u1)2 = (c*u2)2. Therefore, c*u is in the set.

However, the set {(x1,x2)T|x21 = x22} is not a subspace of R2 because it does not contain the zero vector (0,0)T, which is required for any set to be a subspace.

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4x - 5y = -9

-4x + y = -7

Step 1

Eliminate variable x

Different sign eliminate x and add.

-5y + y = -9 + (-7)

- 4y = -9 - 7

- 4y = -16

y = -16/-4

y = 4

Step 2

Substitute y in any equation and find x.

-4x + y = -7

-4x + 4 = -7

-4x = -7 - 4

-4x = -11

x = -11/-4

x = 11/4

X = 11/4 Y = 4

A multiple regression equation that can be used to analyze the data for a two-factorial design with two levels for factor A and three levels for factor B can be written as:

Y = b0 + b1A + b2B + b3AB + e

where Y is the dependent variable, A is the independent variable for factor A, B is the independent variable for factor B, A*B is the interaction between A and B, and e is the error term.

The variables can be defined as follows:

Y: The dependent variable that is being measured in the study.

A: The independent variable representing factor A, which has two levels (A1 and A2).

B: The independent variable representing factor B, which has three levels (B1, B2, and B3).

A*B: The interaction term between factor A and factor B.

e: The error term that captures the variability in the dependent variable that is not explained by the independent variables.

This equation allows us to examine the main effects of both factors (A and B) as well as their interaction (A*B) on the dependent variable Y in a two-factorial design.

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