Need help ASAP on this adding polynomials

Answer:

14.72% probability that both professors get their grants funded

Step-by-step explanation:

Independent events:

If two events, A and B are independent, the probability of both happening is:

[tex]P(A \cap B) = P(A)*P(B)[/tex]

In this question:

Event A: Professor Jane is funded

Event B: Professor Joe is funded.

Professor Jane has a probability of 0.64 of being funded.

This means that [tex]P(A) = 0.64[/tex]

Professor Joe has probability 0.23 of being funded.

This means that [tex]P(B) = 0.23[/tex]

What is the probability that both professors get their grants funded

[tex]P(A \cap B) = P(A)*P(B) = 0.64*0.23 = 0.1472[/tex]

14.72% probability that both professors get their grants funded

The correct answer is 130 miles per hour

Explanation:

The speed refers to the rate of movement of a body, based on the distance and time of the movement. Additionally, the general formula to calculate the speed is to divide the distances by the time or s (speed) = d (distance) / t (time). Moreover, this factor is measured in units such as kilometers per hour or miles per hour.

In the case presented, we know the total distance was 390 miles and the total time was 3 hours. The formula and process are shown below.

Speed= [tex]\frac{d}{t}[/tex]

Speed = [tex]\frac{390 miles}{3 hours}[/tex]

Speed= 130 miles per hour

Therefore, the speed of the train in miles per hour is 130

Answer:

Option (B)

Step-by-step explanation:

If the probabilities of two events A and B are P(A) and P(B) then the conditional probability of an event that can be derived by the formula,

P(B | A) = [tex]\frac{P(A\cap B)}{P(A)}[/tex]

P(A ∩ B) = P(B|A) × P(A)

P(A ∩ B) = (0.8) × (0.4)

            = 0.32

Therefore, Option (B) will be the correct option.

Answer:

Option B is correct.

Step-by-step explanation:

Answer:

1675.52 cubic meters.

Step-by-step explanation:

First, we establish that the maximum amount of sand that can be stored in the structure is the volume of the conical structure.

[tex]\text{Volume of a Cone }= \frac{1}{3}\pi r^2 h$ where: \left\{\begin{array}{ll}$r=Base radius\\$h=height of the cone\\-----\\r=10m\\h=16m\end{array}\right[/tex]

Therefore:

[tex]\text{Volume of the structure}= \frac{1}{3}\pi \times 10^2 \times 16\\=\dfrac{1600\pi}{3} $ cubic meters\\\approx 1675.52$ m^3 $(correct to 2 d.p)[/tex]

The maximum amount of sand that can be stored in the structure is 1675.52 cubic meters.

Answer: C) (5,1)

Step-by-step explanation:

adding both equations, we get 2x = 10

which gives, x = 5

putting this value of x in first eq, we get

5 + y = 6

which gives y = 1

hence answer is (5,1)

Answer:

C. (5,1)

Step-by-step explanation:

Well first we need to single out y in the following equation,

x - y = 4

so,

-x to both sides -y = -x + 4

divide the - by everything y = x - 4.

Now that we have our two equations.

x + y = 6

y = x - 4

We can substitute the y in the x + y = 6 for x - 4

x + x - 4 = 6

2x - 4 = 6

Add the 4

2x = 10

Divide the 2

x = 5.

Now that we have the x we can plug it in for x in x + y = 6

5 + y = 6

-5 to both sides

y = 1

So the solution is (5,1)

For more proof look at the image below.

Answer:

$61.25

Step-by-step explanation:

To find the amount of discount, we can multiply the original price by 0.25, which will give us the value of 25% of the original price.

245(0.25) = 61.25

So, the amount of discount will be $61.25

Answer:

HT = 17

<T = 62°

<H = 28°

Step-by-step explanation:

1. Use the Pythagorean Theorem to find the length of the missing side.

a² + b² = c²

15² + 8² = c²

225 + 64 = c²

289 = c²

√289 = c

c = 17

The length of side HT is 17.

2. Use SOHCAHTOA to find the measure of <T. Since we know the measure of two sides, opposite (15) and adjacent (8), use the formula for tangent as tangent is opposite/adjacent.

Tangent = [tex]\frac{opposite}{adjacent}[/tex]  = [tex]\frac{15}{8}[/tex] = 1.875

Use the tan⁻¹ button on the calculator to find the value for <T.

tan⁻¹(1.875) = 61.9°

<T = 62°

3. To find the measure of <H, you can either add up the two angles and subtract from 180° or use SOHCAHTOA.

90° + 61.9° + x = 180°

151.9° + x = 180°

x = 28°

or

We know two sides: opposite (8) and adjacent (15). So, we will use tangent.

Tangent = [tex]\frac{opposite}{adjacent}[/tex] =  [tex]\frac{8}{15}[/tex] = 0.5333333333

Take the tan⁻¹ to get the measure of <H.

tan⁻¹(0.5333333333) = 28.07 = 28°

Hope this helps. Please give a thanks and mark as brainliest. :)

Answer:

12%.

Step-by-step explanation:

It is given that, after adding up all your expenses for the month you spent $465.36. your total budget for the month is $529.

Total budget = $529

Total expenditure = $465.36

Under budget = $529 - $465.36 = $63.64

We need to find the percentage of under budget.

[tex]\%=\dfrac{\text{Under budget}}{\text{Total budget}}\times 100[/tex]

[tex]\%=\dfrac{63.64}{529}\times 100[/tex]

[tex]\%=0.12030\times 100[/tex]

[tex]\%=12.030\%[/tex]

[tex]\%\approx 12\%[/tex]

Therefore, the required percentage is 12%.

Answer:

The number of people who voted in this election was 1.24 times the number who voted in the last election

Step-by-step explanation:

The multiplier for a increase of a% is 1 + a/100.

The multiplier for a decrease of b% is 1 - b/100.

In this question:

Up by about 24%, so we want the multiplier for a increase of 24%.

So

1 + (24/100) = 1 + 0.24 = 1.24

The number of people who voted in this election was 1.24 times the number who voted in the last election

Answer: 1 5/6, or 11/6, or 1.83333333

Step-by-step explanation:

[tex]\frac{6}{3} + -\frac{1}{6}[/tex]

6/3 is 2.

Thus, the answer is 2 - 1/6 or 1 5/6

Answer:

11/6

Step-by-step explanation:

First, we need to find a common denominator for the 2 fractions.

A common denominator for 3 and 6 is 6.

Let’s get the fraction 6/3 to a denominator of 6.

Multiply by 2/2

6/3 * 2/2

(6*2) / (3*2)

12/6

Now the fractions have common denominators and can be added.

12/6 + (-1/6)

When adding negative fractions, you can simply subtract.

12/6 - 1/6

Subtract across the numerator and leave the denominator as is

11/6

This fraction can be written as: 2 1/6, 11/6, or 1.83333

Answer:

42°

Step-by-step explanation:

This is right triangle and sum of 2 angles is 90°:

y+48°=90°

so y= 90°- 48°= 42°

Answer:

1/2

Step-by-step explanation:

The numbers 3 or odd are 1, 3, 5, and 7.

4 numbers out of 8.

4/8 = 1/2

P(3 or odd) = 1/2

Answer:

The perimeter of square is increasing by 3.76ft/min and then by 3.4 ft/min.

Step-by-step explanation:

Given that area of square is increasing at a rate of 16 sq ft/min.

Given that final perimeter is 36ft

Perimeter of a square = 4 [tex]\times[/tex] side = 36

So, side, a' = 9 ft

We know that area of a square is given by the formula:

[tex]A = side^2 = a^2[/tex] (If we let side = a units)

Change in area =

[tex]a'^2 - a^2\\\Rightarrow 9^2 - a^2 = 16\\\Rightarrow 81 - 16 = a^2\\\Rightarrow a = 8.06\ ft[/tex]

So, side got changed from 8.06ft to 9 ft.

So, perimeter when side was 8.06 ft:

[tex]4 \times 8.06 = 32.24\ ft[/tex]

Hence, increase in the perimeter when perimeter is 36 ft is = 36 - 32.24 = 3.76 ft

For finding Next increase:

area gets changed from 81 sq ft to 81+16 = 97 sq ft

So, new side = [tex]\sqrt{97}[/tex] ft = 9.85 ft

Next increase in perimeter = 4 (New side - Old side)

= 4 (9.85 - 9)

= 3.4 ft/min

Answer:

2.5

Step-by-step explanation:

the other persons answer is wrong

The number after rounding to the one significant figure is 4000.

The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation

Rounding off means a number is made simpler by keeping its value intact but closer to the next number

According to the given question we have an expression.

[tex]\frac{798}{8} (41)[/tex]

When we evaluate this expression we get

[tex]\frac{798}{8} (41)[/tex]

[tex]=99.75(41)[/tex]

[tex]= 4089.75[/tex]

Here, the first significant figure is 4 and the second one is 0 which is less than 5.

Hence, the number after rounding to the one significant figure is 4000.

Find out more information about rounding off here:

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Answer:

Domain stays the same while the range changes

Step-by-step explanation:

While reflecting cross x-axis, the x coordinates remains the same while the y-coordinate changes to its opposite.

=> x- coordinate = Domain

=> y-coordinate = Range

The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.

Domain is the set of values for which the given function is defined.Range is the set of all values which the given function can output.

When reflecting across the x-axis, the x coordinates remain constant, but the y coordinate changes to its inverse.

The Domain represent as x-coordinate and the range as y-coordinate

The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.

Hence, option C is correct.

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The answer is 41 because all of the them are in the 7 times table .so I deducted 2 from each one of them and 41 was not part

Answer:

  (x, y) = (-3, -5) or (1, 3)

Step-by-step explanation:

You can equate the expressions for y, then solve the resulting quadratic.

  -x^2 +4 = 2x +1

  4 = x^2 +2x +1 . . . . add x^2

  4 = (x +1)^2 . . . . . . . write as a square

  ±2 = x +1 . . . . . . . . . take the square root

  x = -1 ±2 = -3 or +1 . . . subtract 1

So, the solutions have x-values of -3 or +1. The corresponding y-values can be found from ...

  y = 2x +1

  y = 2(-3) +1 = -5   or   y = 2(1) +1 = 3

Solutions are ...

  (x, y) = (-3, -5) or (1, 3)

Answer:

6 bags

Step-by-step explanation:

3/4 = .75

4.5/.75 = 6 =

6 BAGS

Answer:

The answer is not "REMAINDER" it's "Quotient"

Step-by-step explanation:

Cancelling identical factors in the numerator and the denominator will give the quotient.

When dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the remainder.

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

Given that when dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the remainder.

A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is also known as the integer portion of a division, a fraction, or a ratio.

To know more about polynomials follow

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Answer:

Area of ring = 462 cm²

Perimeter of ring = 44 cm

Step-by-step explanation:

Given,

radius of inner ring = 7 cm

radius of outer ring = 14 cm

To find,

Area and perimeter of ring

Formula:

Area of circle = π Radius²

Perimeter of circle = 2π Radius

Area of inner ring =  π Radius²

⇒ [tex]\frac{22}{7}[/tex] × [tex]7^{2}[/tex]

⇒ 22 × 7

⇒ 154 cm²

Area of outer ring =  π Radius²

⇒ [tex]\frac{22}{7}[/tex] × [tex]14^{2}[/tex]

⇒ 22 × 14 × 2

⇒ 616 cm²

∴ Area of ring = 616 - 154 = 462 cm²

Perimeter of inner ring = 2π Radius

⇒  2 × [tex]\frac{22}{7}[/tex]  × 7

⇒  44 cm

Perimeter of outer ring = 2π Radius

⇒  2 × [tex]\frac{22}{7}[/tex]  × 14

⇒  88 cm

∴ Perimeter of ring = 88 - 44 = 44 cm

Answer:

they have lower interest rates and can be paid back with a lower out of pocket cost

Step-by-step explanation:

Student loans are issued as a kind of financial aid that assist students in their quest to acquire higher education. Private student loans are offered by the private-sector lenders. The alternative to this is a Federal loan.

Actually, private student loans are issued at a lower interest rate. Option of a fixed or variable interest rate may be offered on privately issued student loans. This offers a lower out of pocket cost, hence the answer.

Answer:

642 mm or 64.2 cm

Step-by-step explanation:

67cm-28mm

We need the same units

67 cm * 10 = 670 mm

670 mm - 28 mm

642 mm

We can convert back to cm by dividing by 10

64.2 cm

Answer:

642mm or 64.2 cm

Step-by-step explanation:

67 cm = 670mm

So, that's 670-28mm = 642mm

Answer:

  24/49

Step-by-step explanation:

Let's add the terms and see if there's a pattern

  [tex]\dfrac{1}{1\times 3}+\dfrac{1}{3\times 5}=\dfrac{5+1}{1\times 3\times 5}=\dfrac{2}{5}\quad\text{sum of 2 terms}\\\\\dfrac{2}{5}+\dfrac{1}{5\times 7}=\dfrac{14+1}{5\times7}=\dfrac{3}{7}\quad\text{sum of 3 terms}[/tex]

Suppose we say the sum of n terms is (n/(2n+1)), the next term in the series will be 1/((2n+1)(2n+3)) and adding that to the presumed sum gives ...

  [tex]\dfrac{n}{2n+1}+\dfrac{1}{(2n+1)(2n+3)}=\dfrac{n(2n+3)+1}{(2n+1)(2n+3)}=\dfrac{2n^2+3n+1}{(2n+1)(2n+3)}\\\\=\dfrac{(2n+1)(n+1)}{(2n+1)(2n+3)}=\dfrac{n+1}{2n+3}\text{ matches }\dfrac{(n+1)}{2(n+1)+1}[/tex]

Then it appears the sum of n terms is (n/(2n+1)). So, the sum of 24 terms is ...

  [tex]S_{24}=\dfrac{24}{2\times24+1}=\boxed{\dfrac{24}{49}}[/tex]

Answer:

The probability that the sample proportion will be greater than 13% is 0.99693.

Step-by-step explanation:

We are given that a large shipment of laser printers contained 18% defectives. A sample of size 340 is selected.

Let [tex]\hat p[/tex] = the sample proportion of defectives.

The z-score probability distribution for the sample proportion is given by;

                         Z  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }[/tex]  ~ N(0,1)

where, p = population proportion of defective laser printers = 18%

            n = sample size = 340

Now, the probability that the sample proportion will be greater than 13% is given by = P([tex]\hat p[/tex] > 0.13)

         P([tex]\hat p[/tex] > 0.13) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }[/tex] > [tex]\frac{0.13-0.18}{\sqrt{\frac{0.13(1-0.13)}{340}} }[/tex] ) = P(Z > -2.74) = P(Z < 2.74)

                                                                      = 0.99693

The above probability is calculated by looking at the value of x = 2.74 in the  table which has an area of 0.99693.

Answer:

The answer is 6 – 4i

Step-by-step explanation:

Complex values:

Have the following format: a + bi

In which a is the real part and b is the complex part.

Addition:

Suppose we are going to add two complex numbers. We add their real parts, and their complex parts separatly.

So

(–4 + i) + (10 – 5i) = (-4 + 10) + i(1-5) = 6 - 4i

The answer is 6 – 4i

Answer:

for the first question it is (9 + 4i) + (–1 – 7i)

and for the second one it is

6 – 4i

Answer:

The sample mean is 9.875 standard deviations from the mean of the distribution of sample

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation s, the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{s}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]X = 17.79, \mu = 17, s = 0.08[/tex]

How many standard deviations is the sample mean from the mean of the distribution of sample?

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{17.79 - 17}{0.08}[/tex]

[tex]Z = 9.875[/tex]

The sample mean is 9.875 standard deviations from the mean of the distribution of sample

Answer:

The question is incomplete, below is the complete question:

The volume of a flask has been determined to be 26.918 mL, and the mass of the flask has been determined to be 32.634g. The student then emptied the flask and dried it once again. To the empty flask, he added pieces of metal until the flask was about half full. He weighed the stoppered flask containing the metal and found that its mass was 100.356g. Next, he filled the flask containing the metal with water, stoppered it, reweighed it and obtained a total mass of 121.860g.

a.) Find the mass of the metal in the flask. (show work)

b.) Find the mass of water in the flask. (show work)

c.) Find the volume of water in the flask. (show work)

d.) Find the volume of metal in the flask (show work)

e.) Find the density of the metal. (show work)

Answers:

a.  mass of metal in the flask = 67.722g

b. mass of water in the flask = 21.504g

c. volume of water in the flask = 21.562mL

d.) volume of metal in the flask = 5.356mL

e.) density of the metal = 12.644g/mL

Step-by-step explanation:

a.) mass of metal in the flask = (mass of flask + metal) - mass of empty flask

= 100.356 - 32.634 = 67.722g

b.) mass of water in the flask = (mass of flask when filled with metal and water) - (mass of flask when filled with metal alone)

= 121.860 - 100.356 = 21.504g

c. volume of the water in the flask :

in order to calculate the volume of water in the flask, the density formula is used as follows:

density = mass ÷ volume

volume = mass ÷ density.

where:

Density of water = 0.9973 g/mL

Mass of water as calculated above = 21.504g

∴ volume of water = 21.504 ÷ 0.9973 = 21.562mL

d.) volume of the metal in the flask:

Next, to calculate the volume of the metal in the flask:

volume of flask = volume of metal + volume of water

∴ volume of metal = volume of flask - volume of water

where:

volume of flask = 26.918mL (given)

volume of water = 21.562mL (calculated above)

∴ volume of metal = 26.918 - 21.562 = 5.356mL

e.) density of the metal:

Density = mass ÷ volume

where:

mass of metal = 67.722g ; volume of metal = 5.356mL

∴ Density of metal = 67.722 ÷ 5.356 = 12.644g/mL

Answer:

The answer is "2nπ".

Step-by-step explanation:

Given:

[tex]4 \cos x= -\sin^2x+4.......(1)[/tex]

We know:

[tex]\Rightarrow \sin^2 x+\cos^2 x=1\\\\\Rightarrow \sin^2 x= 1 -\cos^2 x\\[/tex]

put the value of [tex]\sin^2 x[/tex] value in the above equation:

[tex]\Rightarrow 4 \cos x= - (1-\cos^2 x)+4\\\\\Rightarrow 4 \cos x= - 1+\cos^2 x+4\\\\\Rightarrow 4 \cos x= \cos^2 x+3\\\\\Rightarrow \cos^2 x-4 \cos x+3=0\\\\[/tex]

Let [tex]\cos x= A[/tex]

[tex]\Rightarrow A^2-4A+3=0 \\ \Rightarrow A^2-(3A+A)+3=0 \\\Rightarrow A^2-3A-A+3=0\\\Rightarrow A(A-3)-1(A-3)=0\\\Rightarrow (A-3)(A-1)=0 \\[/tex]

[tex]\Rightarrow A- 3=0 \ \ \ \ \ \ \ \ \ \ \ \Rightarrow A -1 =0 \\\\[/tex]

[tex]\Rightarrow A= 3\ \ \ \ \ \ \ \ \ \ \ \Rightarrow A =1 \\\\\Rightarrow \cos x = 3\ \ \ \ \ \ \ \Rightarrow \cos x =1\\\\\Rightarrow x = \cos^{-1} 3\ \ \ \ \ \ \ \Rightarrow \cos x =\cos 0\\\\\Rightarrow x = \cos^{-1} 3\ \ \ \ \ \ \ \Rightarrow x = 0\\\\[/tex]

The value of x is [tex]2n\pi\ \ \ _{where} \ \ \ \ \ \ \ n=1, 2, 3......[/tex]

[tex]\boxed{\bold{x=2 n \pi}}[/tex]

Answer:

Probability of successes or proportion 'p' =0.1818

                                              q = 0.8182

Given sample size 'n' =275

we will use binomial distribution

[tex]P(X=r) = n_{C_{r} } p^{r} q^{n-r}[/tex]

Step-by-step explanation:

Explanation:-

Given data number of students 'n' = 275

He asked a randomly selected 50 (of the 275) registered to select one of four reasons (convenience, liked his teaching style,needed it to graduate , or other)

Probability of successes or proportion

[tex]p = \frac{x}{n} = \frac{50}{275} = 0.1818[/tex]

conclusion:-

The experimental unit of interest to this problem

Probability of successes or proportion 'p' =0.1818

                                                     q = 1-p = 1- 0.1818 = 0.8182

Given sample size 'n' =275

we will use binomial distribution

[tex]P(X=r) = n_{C_{r} } p^{r} q^{n-r}[/tex]

Answer: The answer is 5/12 of her homework left.

Step-by-step explanation:

She first did 1/4 and then 1/3. Adding them together gives a total of 7/12 of it being completed. The part where it’s unfinished is 5/12, the answer.

Answer:

5/12

Step-by-step explanation:

Since we are adding fractions, we have to find the least common demoninator, which means the denominators (the bottom part of the fraction) are equal. To do this, we can take each denominator and multiply them together. 4x3=12, so the least common denominator is 12. We then multiply the numerator by however many we had to multiply the denominator. So to get to 12, 4 (the denominator) must be multiplied by 3, so 1 (the numerator) must be multiplied by 3, giving us 3/12. We do the same thing to the other fraction, so for 3 (the denominator), we multiply by 4, so 1 (the numerator) must be multiplied by 4, giving us 4/12. Then we add the two together and we get 7/12. We then have to subtract 7/12 from 12/12, giving us 5/12.