t takes one person 2 hours to grade 1 exam and it takes another 4 hours to grade 1 exam. If both work together, how many exams they can grades in 8 hours

Answer:

x  = - 2 is confirmed to be the real solution of the equation.

Step-by-step explanation:

We are tasked with the following activities

Conjecture: How many solutions do [tex]x^3 - 5x^2 + 28 = 0[/tex]  have?

Find the real solution(s) of the equation.

Then use polynomial long division to find the other solution(s).

To start with the how many solutions that  [tex]x^3 - 5x^2 + 28 = 0[/tex]  have

suppose that -2 happens to be a root of the equation, we can easily replace x = - 2 in the given equation. Then , we will have :

[tex](-2)^3 - 5(-2)^2 + 28 = 0[/tex]

[tex]-8 - 5\times 4 + 28 = 0[/tex]

-8 - 20  + 28 = 0

-28 - 28 = 0

0 = 0

The equation resulted to 0 = 0 when x = -2 , as such -2 happens to be one root of the equation

So , as x = - 2

x + 2 = 0  

x  = - 2 is confirmed to be the real solution of the equation.

A picture showing the polynomial long division method used for solving the polynomial equation and other solution(s) can be found in the attached file below.

Answer:

C: infinitely many solutions

Step-by-step explanation:

Answer:

8x+5

Step-by-step explanation:

8-6=2

2× 4x= 8x

8x+5

Answer:

Step-by-step explanation:

Use PEMDAS rule :

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

Let's solve :

[tex] \sf{5 + 4 \times {(8 - 6)}^{2} }[/tex]

⇒[tex] \sf{5 + 4 \times {2}^{2} }[/tex]

⇒[tex] \sf{5 + 4 \times 4}[/tex]

⇒[tex] \sf{5 + 16}[/tex]

⇒[tex] \sf{21}[/tex]

Hope I helped!

Best regards!

Answer:

  see below

Step-by-step explanation:

The cube of something to the 1/3 power is the original something. The cube of a cube root of something is the original something. Since the cube of a cube root is the same as the cube of a 1/3 power, the 1/3 power is equivalent to the cube root.

The applicable rules of exponents are ...

  (a^b)^c = a^(bc)

Answer:

The point estimate = 0.507

Margin error of  a given confidence interval = 0.032

Step-by-step explanation:

The point estimate is calculated by using the sample statistics of a population.

Thus; point estimate can be expressed with the formula:

[tex]\overline x = \dfrac{\sum \limits ^n _{i=1} \ x _i}{n}[/tex]

Given that : 0.475 < p < 0.539

[tex]\overline x = \dfrac{0.475+0.539}{2}[/tex]

[tex]\overline x = \dfrac{1.014}{2}[/tex]

[tex]\overline x = 0.507[/tex]

The point estimate = 0.507

The margin of error  which shows  the percentage of points that the derived results would differ from that of the given population value can be calculated with the formula:

Margin error of  a given confidence interval = [tex]\mathtt{\dfrac{upper \ confidence \ limit - lower \ confidence \ limit }{2}}[/tex]

Margin error of  a given confidence interval =  [tex]\dfrac{0.539-0.475}{2}[/tex]

Margin error of  a given confidence interval = [tex]\dfrac{0.064}{2}[/tex]

Margin error of  a given confidence interval = [tex]0.032[/tex]

Answer:

325/3

Step-by-step explanation:

[tex]48+4^2+\frac{3}{5}\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:48=\frac{48\cdot \:5}{5}\\\\=\frac{48\cdot \:5}{5}+\frac{3}{5}\\\\\mathrm{Since\:the\:denominators\:are\:equal,\\\\\:combine\:the\:fractions}:\\\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{48\cdot \:5+3}{5}\\\\48\cdot \:5+3=243\\\\=4^2+\frac{243}{5}\\\\=16+\frac{243}{5}\\\\=\frac{16\cdot \:5}{5}+\frac{243}{5}\\\\=\frac{16\cdot \:5+243}{5}\\\\16\cdot \:5+243=323\\\\=\frac{323}{5}[/tex]

Complete Question

A biologist reports a confidence interval of (3.5,4.9) when estimating the mean height (in centimeters) of a sample of seedlings. What is the estimated margin of error and the sample mean?

Answer:

The  margin of error is  [tex]E = 0.7[/tex]

The  sample mean is  [tex]\= x = 4.2[/tex]

Step-by-step explanation:

from the question we are told that

   The  upper limit is  [tex]k = 4.9[/tex]

    The  lower limit is  [tex]r = 3.5[/tex]

Generally the margin of error is mathematically represented as

      [tex]E = \frac{k - r}{ 2}[/tex]

      [tex]E = \frac{ 4.9 - 3.5 }{2}[/tex]

     [tex]E = 0.7[/tex]

Generally the sample mean is mathematically evaluated as

        [tex]\= x = k - E[/tex]

=>    [tex]\= x = 4.9 - 0.7[/tex]

=>    [tex]\= x = 4.2[/tex]

Answer:

[tex]m = 0.2[/tex]

Step-by-step explanation:

To solve this equation we're basically trying to isolate m on one side.

The equation is [tex]m^2=0.04[/tex].

If we want to make it [tex]m=x[/tex], we have to find the square root of both sides, as the square root of something squared is just that something.

[tex]\sqrt{m^2} = \sqrt{0.04}[/tex]

To find the square root of 0.04, we need to think "what number multiplied by itself get us 0.04?"

This number is 0.2.

So:

[tex]m = 0.2[/tex]

Hope this helped!

Answer:

The answer is

Step-by-step explanation:

To find the equation of a line given a point and slope we use the formula

where

m is the slope

( x1 , y1) is the point

From the question

Slope / m = - 2

The point is ( 10, - 9)

Substitute the values into the above formula

That's the final answer is

Hope this helps you

Answer:

C. [tex] z = 82 [/tex]

Step-by-step explanation:

To find z, find x first:

[tex] 105 = \frac{1}{2}(x + 120) [/tex] (angle of intersecting chord theorem)

Solve for x

[tex] 105*2 = \frac{1}{2}(x + 120)*2 [/tex]

[tex] 210 = x + 120 [/tex]

[tex] 210 - 120 = x + 120 - 120 [/tex]

[tex] 90 = x [/tex]

[tex] x = 90 [/tex]

Find z:

Full circle = 360°

Therefore,

[tex] x + z + 68 + 120 = 360 [/tex]

[tex] 90 + z + 68 + 120 = 360 [/tex]

[tex] z + 278 = 360 [/tex]

[tex] z + 278 - 278 = 360 - 278 [/tex]

[tex] z = 82 [/tex]

Answer:

plz give hlamberttx the brainliest!

Step-by-step explanation:

he saved my grade and helped me sooo much with this question. he is 100% correct i got an 100 on my usa test prep

Answer:

500 pa

Step-by-step explanation:

[tex]Force = 25N\\Area = 0.05m^2\\\\Pressure = \frac{Force}{Area}\\ \\Pressure = \frac{25}{0.05}\\\\ Pressure = 500 Pascals[/tex]

Answer:

A -3 − 4i C 13 + i

Step-by-step explanation:

We add the real part and the imaginary part separately.

Adding A and C will give us 10 - 3i:

-3 - 4i + 13 + i

= -3 + 13 - 4i + i

= 10 - 3i.

Answer:

it is this graph

Step-by-step explanation:

it is this graph

Answer:

B

Step-by-step explanation:

Answer:

-15 > -19

Step-by-step explanation:

-15 > -19

-15 is closer to 0 than -19 so it is greater than

Answer:

Is the number rational or irrational?

30‾‾‾√

rational

irrational

Step-by-step explanation: help ;-;

Option (3) the product of two irrational numbers is a rational number is a correct option.

"Rational numbers are numbers that can be expressed as a fraction or part of a whole number. It includes the integers, plus all fractions, or terminating decimals and repeating decimals".

"Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers".

For the given situation,

We need to analyze the all options.

Option 1:

The sum of a rational number and an irrational number is an irrational number.

Option 2:

The product of a rational number and an irrational number is an irrational number.

Option 3:

The product of two irrational numbers is a rational or an irrational number based on the numbers taken.

Option 4:

The sum of two irrational numbers is an irrational number.

Hence we can conclude option(3), the product of two irrational numbers is a rational number is a correct option.

Learn more about rational numbers here

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Answer:

Distance covered by Sean

= 540-x-y inches

Distance covered by Hannah =x

Step-by-step explanation:

Sean and Hannah are 540 inches apart and begin walking towards each other. Sean walks 2.6 times as fast as Hannah

Distance covered by Hannah =x

Distance between sean and Hannah= y

Distance covered by Sean= 540-x-y

Sean speed= (540-x-y)/t

Hannah speed= x/t

(540-x-y)/t /(x/t )= 2.6

(540-x-y)/x = 2.6

(540-x-y)= 2.6x

540 = 3.6x +y ...

Answer:

Step-by-step explanation:

See attachment

Answer:

yes

Step-by-step explanation:

Answer:

75°

Step-by-step explanation:

In a parallelogram, any two adjacent angles are supplementary. In other words, they total 180.

Angle D and Angle E are adjacent. Thus, they are supplementary. In other words:

[tex]\angle D +\angle E =180[/tex]

Substitute them for the equations:

[tex]7x+21+15+5x=180[/tex]

Combine like terms and add on the left:

[tex]12x+36=180[/tex]

Subtract 36 from both sides:

[tex]12x=144[/tex]

Divide both sides by 12:

[tex]x=12[/tex]

Thus, the value of x is 12.

Note that Angle D and Angle C are also adjacent. Thus, their angles also equal 180.

So:

[tex]\angle D+\angle C =180[/tex]

Substitute the equation for D:

[tex]7x+21+\angle C=180[/tex]

Plug in 12 for x:

[tex]7(12)+21+\angle C =180[/tex]

Simplify:

[tex]84+21+\angle C =180\\105+\angle C =180[/tex]

Subtract 105 from both sides:

[tex]\angle C =75\textdegree[/tex]

Thus, Angle C is 75 degrees.

Answer:

r = -7

Step-by-step explanation:

Solve for r:

8 r + 9 = -4 (3 - r) - 7

-4 (3 - r) = 4 r - 12:

8 r + 9 = 4 r - 12 - 7

Grouping like terms, 4 r - 12 - 7 = 4 r + (-7 - 12):

8 r + 9 = 4 r + (-7 - 12)

-7 - 12 = -19:

8 r + 9 = 4 r + -19

Subtract 4 r from both sides:

(8 r - 4 r) + 9 = (4 r - 4 r) - 19

8 r - 4 r = 4 r:

4 r + 9 = (4 r - 4 r) - 19

4 r - 4 r = 0:

4 r + 9 = -19

Subtract 9 from both sides:

4 r + (9 - 9) = -9 - 19

9 - 9 = 0:

4 r = -9 - 19

-9 - 19 = -28:

4 r = -28

Divide both sides of 4 r = -28 by 4:

(4 r)/4 = (-28)/4

4/4 = 1:

r = (-28)/4

The gcd of -28 and 4 is 4, so (-28)/4 = (4 (-7))/(4×1) = 4/4×-7 = -7:

Answer:  r = -7

Answer:

The  value is  [tex]Z = 6.299*10^{16} \ ways[/tex]

Step-by-step explanation:

From the question we are told that  

      The  number of countries is  n  =  12

Generally the number of way of selecting 3 from a block of 45  

        [tex]\left 45} \atop {}} \right.C _3 = \frac{ 45! }{ (45-3) ! 3!}[/tex]

       [tex]\left 45} \atop {}} \right.C _3 = 14190[/tex]

Generally the number of way of selecting 4 from a block of 57  

        [tex]\left 57} \atop {}} \right.C _3 = \frac{ 57! }{ (57-4) ! 4!}[/tex]

         [tex]\left 57} \atop {}} \right.C _3 = 395010[/tex]

Generally the number of way of selecting (12 - (4 + 3) = 5) from a block of 69

         [tex]\left 69} \atop {}} \right.C _5 = \frac{ 69! }{ (69-5) ! 5!}[/tex]

         [tex]\left 69} \atop {}} \right.C _3 = 11238513[/tex]

The ways of  selecting 12 countries in the United Nations  serve on a council is mathematically represented as

               [tex]Z = 14190 * 395010* 11238513[/tex]

               [tex]Z = 6.299*10^{16} \ ways[/tex]

Answer:

8.9 is the answer i just took the test

Answer:

5/6

Step-by-step explanation:

you must flip 3 over 5 and multiply

Answer:

Step-by-step explanation:

Parallel lines

Answer:

C' ( -10 , 4)

D' (-10 , 6)

E' (-8 , 6)

F' (-8 , 4)

Answer:

the answer is c: 44

hope it helps

:)

The value of m in the equation one-half m minus three-fourths n equals 16, when n equals 8 is 44.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

The equation form;

1/2m - 3/ 4n = 16

Substituting the value of n in the equation, we have;

½m - ¾n = 16

½m - (¾×8) = 16

½m - 6 = 16

½m = 16 + 6

½m = 22

m = 44

Hence, The value of m in the equation one-half m minus three-fourths n equals 16, when n equals 8 is 44.

Learn more about linear equations;

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Answer:

63/10 : 9/2

Step-by-step explanation:

6.3 is 6 and 3/10

we can turn that into an improper fraction so its 63/10

4.5 is 4 and 1/2

we can turn this into an improper fraction with is 9/2

so now its 63/10 : 9/2 as a ratio

Hope this helps. Good luck.

[tex] \frac{ \frac{19}{3}kg }{ \frac{9}{2}kg } [/tex]

Answer:

Step-by-step explanation:

4. when bases are equal ,powers are also equal.

x+4=3x-1

3x-x=4+1

2x=5

x=5/2=2.5