Among 100 students who enrolled in both Math 101 and English 101, 30% of the students scored an A in Math 101, 35% of the students scored an A in English 101, and 20% of the students scored an A in both Math 101 and English 101. What percentage of the students scored an A in neither Math 101 nor English 101?

Answer:

[tex]AB =3 \sqrt{5} = 6.708203932...[/tex]

Step-by-step explanation:

[tex]A( - 1,6) \:,\: B(5,3)\\ AB = \sqrt{{(x1 - x2)}^{2} + {(y1 - y2)}^{2} } \\ AB = \sqrt{ {( - 1 - 5)}^{2} + {(6 - 3)}^{2} } \\ AB = \sqrt{ {( - 6)}^{2} + {(3)}^{2} } \\ AB = \sqrt{36 + 9} \\ AB = \sqrt{45} = 3 \sqrt{5} = 6.708203932...[/tex]

The distance between A and B to 3 significant figure is 6.71

The formula for calculating the distance between two points is expressed as:

[tex]D =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Given the coordinate points (-1, 6) and (5, 3)

Substitute the given coordinates into the formula;

[tex]D =\sqrt{5+1)^2+(3-6)^2}\\D =\sqrt{(6^2+(-3)^2}\\D=\sqrt{36+9}\\D=\sqrt{45}\\D= 6.71\\[/tex]

Hence the distance between A and B to 3 significant figure is 6.71

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Answer:

Step-by-step explanation:

You need to use synthetic division to do all of these.  The thing to remember with these is that when you start off with a certain degree polyomial, what you get on the bottom line after the division is called the depressed polynomial (NOT because it has to math all summer!) because it is a degree lesser than what you started.

a.  3I   1   3   -34   48

I'm going to do this one in its entirety so you get the idea of how to do it, then you'll be able to do it on your own.

First step is to bring down the first number after the bold line, 1.

3I   1    3    -34    48

   _____________

      1

then multiply it by the 3 and put it up under the 3.  Add those together:

3I    1    3    -34    48

           3

----------------------------

      1     6

Now I'm going to multiply the 6 by the 3 after the bold line and add:

3I    1     3     -34     48                                                                                                    

             3      18

_________________

      1      6     -16

Same process, I'm going to multiply the -16 by the 3 after the bold line and add:

3I      1      3      -34      48

                3       18     -48

___________________

        1       6      -16       0

That last zero tells me that x-3 is a factor of that polynomial, AND that the depressed polynomial is one degree lesser and those numbers there under that line represent the leading coefficients of the depressed polynomial:

[tex]x^2+6x-16=0[/tex]

Factoring that depressed polynomial will give you the remaining zeros.  Because this was originally a third degree polynomial, there are 3 zeros as solutions.  Factoring that depressed polynomial gives you the remaining zeros of x = -8 and x = 2

I am assuming that since you are doing synthetic division that you have already learned the quadratic formula.  You could use that or just "regular" factoring would do the trick on all of them.

Do the remaining problems like that one; all of them come out to a 0 as the last "number" under the line.

You got this!        

Answer

x^3-15x^2+75x-125

Answer:

C) 4,850

Step-by-step explanation:

                  No. of

LED bulbs : CFL bulbs : Total

       2        :        3         :    5

   5000     :     7500     : 12 500

Percentage of non-defective LED bulbs = 100% - 3% = 97%

No. of non-defective LED bulbs = 97% x 5000 = 4850

Hello! :D

Answer:

[tex]\boxed{m=18}\checkmark[/tex]

*The answer should have a positive sign.*

Step-by-step explanation:

First, you do is switch sides.

[tex]\frac{m}{2}-7=2[/tex]

Then, you add by 7 from both sides.

[tex]\frac{m}{2}-7+7=2+7[/tex]

Add numbers from left to right.

[tex]2+7=9[/tex]

[tex]\frac{m}{2}=9[/tex]

Multiply by 2 from both sides.

[tex]\frac{2m}{2}=9*2[/tex]

Finally, multiply numbers from left to right.

[tex]9*2=18[/tex]

m=18 is the correct answer.

I hope this helps you!

Have a wonderful day! :)

:D

-Charlie

Thanks!

Answer:

m= 18

Step-by-step explanation:

Move all terms not containing "m" to the right side of the equation.

m/2 - 7= 2

Add +7 to each side.

m/2 - 7 = 2

       +7   +7

Add 2 and 7.

m/2= 9

Multiply both sides of the equation by 2

m= 9 (2)

Simplify.

m= 18

Answer:

785

Step-by-step explanation:

(25 - 10)² + 10(14)(4)

= 225 + 560

= 785

Answer:

  16.5 ft by 25.5 ft

Step-by-step explanation:

Let w represent the width of the garden in feet. Then w+9 is the garden's length, and w(w+9) represents its area.

The surrounding walkway adds 8 feet to each dimension, so the total area of the garden with the walkway is ...

  (w+8)(w+9+8) = w^2 +25w +136

If we subtract the area of the garden itself, then the remaining area is that of the walkway:

  (w^2 +25w +136) - (w(w+9)) = 400

  16w + 136 = 400 . . .simplify

  16w = 264 . . . . . . . . subtract 136

  264/16 = w = 16.5 . . . . . width of the garden in feet

  w+9 = 25.5 . . . . . . . . . . .length of the garden in feet

Answer:

Monomial

Step-by-step explanation:

Let's look at the edfinitions of all three options.

Monomial: A polynomial with only one term is called a monomial.

Binomial: A polynomial with two terms is called a binomial.

Trinomial: A polynomial with three terms is called a trinomial.

So, according to the definition, the given polynomial is a monomial as it has only one term -2gh ..

The inverse of the function f(x) = x + 2 is found by swapping the variables and solving for y, resulting in f^-1(x) = x - 2.

The function f(x) = x + 2 is a simple linear function in Mathematics. The inverse of any function can be found by swapping the x and the y, and then solving for y. In this case, step-by-step, it would work like this:

So the inverse of the function f(x) = x + 2 is f^-1(x) = x - 2.

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The inverse of the function f(x) = x + 2 is found by switching the roles of x and y and solving for y, resulting in the inverse function h(x) = x - 2. None of the provided options is correct.

To determine the inverse of the function f(x) = x + 2, you need to first replace f(x) with y, resulting in the equation y = x + 2. Next, swap x and y to get x = y + 2. Solve for y to find the inverse function: y = x - 2. Therefore, none of the options provided is the correct inverse of the function f(x) = x + 2. The correct inverse is h(x) = x - 2.

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Answer:

Step-by-step explanation:

The zeros are where the graph crosses the x-axis (y=0). They are x=-2 and x=4.

The factors are the binomials that are zero when x has the value of a zero:

  y = (x +2)(x -4)

x = 30°.

The triangle drawn inside the circle is an equilateral and equiangular triangle which means that its three sides and its internal angles (that measure 60°) are equal.

To find x°:

First, we can see from the image that the tangent line to circle with arrows is formed a right angle, the angle of one side of the equilateral triangle, and the angle formed with the other side of the equilateral triangle, this three angles has to form 180° respect to the tangent line:

90° + 60° + y° = 180°

y° = 180° + 150°

y° = 30°

Second, the line in the right side of the equilateral triangle form an angle of 180°, so:

60° + z° = 180°

z° = 180° - 60°

z° = 120°

Finally, the triangle formed by this lines its internal angles are x°, y°, and z° and its sum is 180°, then:

x° + y° + z° = 180°

x° + 30° + 120° = 180°

x° + 150° = 180°

x° = 180° - 150°

x° = 30°  

Answer:

R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}

Select all numbers that are in the domain.

-3

-1

1

Select all numbers that are in the range.

-2

0

2

Have great day :)

Step-by-step explanation:

The -3, -1, and 1 are in the domain if the domain of the function as follows R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have domain of a function:

R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}

From the above relation, we can see:

-3 is in the domain.

-1 is in the domain.

1 is in the domain.

Thus, the -3, -1, and 1 are in the domain if the domain of the function as follows R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}

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Answer:

-6

Step-by-step explanation:

8,-6,-3,4,7 rearranged in ascending order produces -6, -3, 4, 7, 8.

-6 is the least of these scores (i. e., -6 is the lowest score).

Final answer:

Jack's least score from his last 5 card games is -6, as it is the smallest number in the set of his scores.

Explanation:

The question involves identifying the least score from a set of given numbers. To find the least score, Jack's scores from the last 5 card games are considered: 8, -6, -3, 4, 7.

Upon reviewing these numbers, it can be determined that -6 is the least because it is the smallest number and also it has a negative value, which makes it less than all the positive scores or any potential zero scores. Thus, the least of Jack’s scores is -6.

Check the picture below.

The elm is 21 m tall.

Both the triangles are the same.

To find the height, by similarity we get

17 / h = 51 / 63

h = 63 * 17 / 51 = 21

The answer is 21 m.

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar. Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.

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Answer:

  C)  ​7×10^8/(5×10^3)

Step-by-step explanation:

In cubic inches, the volume of a bucket of sand is ...

  (π/4)(20 in)²(15 in) = 1500π in³ ≈ 5×10^3 in³

__

The volume of the warehouse is

  (250 ft)(80 ft)(20 ft) = 400,000 ft³ = 4×10^5 ft³

The conversion to cubic inches is ...

  (4×10^5 ft³)(1728 in³/ft³) = 4×1.727×10^8 in³ ≈ 7×10^8 in³

Dividing the warehouse volume by the bucket volume gives the approximate number of buckets that will fit in the warehouse:

  (7×10^8)/(5×10^3) . . . . . matches choice C

Answer:

its one

Step-by-step explanation:

ape x legends

Answer:

The last choice availablle

Step-by-step explanation:

The way you can tell the points the function has in common with the x-axis (also known as the solutions, roots, or zeros of the functiion) you have to factor it to solve for x.  When you throw this into the quadratic formula you get that there is a negative under the square root sign, which is indicative of imaginary solutions.  Imaginary solutions do NOT cross the x-axis.  So the answer to your problem is the last choice.

Answer:

21 jk

Step-by-step explanation:

Evaluate the function

g(x) = 2x2 + 3x – 5 for the input values -2, 0, and 3.

This is tedious math work but necessary to sharpen your skills.

Let x = -2

g(-2) = 2(-2)^2 + 3(-2) – 5

g(-2) = 2(4) - 6 - 5

g(-2) = 8 - 11

g(-2) = -3

Now let x = 0 and repeat the process.

g(0) = 2(0)^2 + 3(0) - 5

g(0) = 0 + 0 - 5

g(0) = -5

Lastly, let x = 3.

g(3) = 2(3)^2 + 3(3) - 5

g(3) = 2(9) + 9 - 5

g(3) = 18 + 9 - 5

g(3) = 27 - 5

g(3) = 22

Did you follow through each step?

Answer:

-19

-5

-14

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Since the shape won't change, it won't deform, nothing will happen to the interior angle.

This figure is symmetric and not deformed, so the measure of the interior angle won't change no matter how many times you rotate it.

So the interior angle would still be 135º.

Correct answer D

Answer:

the answer is D on e2020

Step-by-step explanation:

Answer:

D. -5

Step-by-step explanation:

The denominator of the quotient is x+5. When the denominator is zero, the quotient is undefined. The denominator will be zero when x=-5.

14,776

/////////////////////////////////////////////////////////////

equation: 14494 + 282 = 14,776

(you convert the negative 282 to positive)

Add the highest elevation with the lowest elevation, to find the total difference. 14494 + 282 = 14,776. You convert the negative 282 to positive. The total difference in elevation between these two places is 14,776.

Answer:

I want to say that the answer is C.

Hope this helps!

Answer:

  7.5 ft

Step-by-step explanation:

The distance can be found using the Pythagorean theorem. The given distances form the legs of a right triangle, and the ending distance (d) between the players is its hypotenuse. The Pythagorean theorem tells you ...

  d² = (6 ft)² +(4.5 ft)² = 36 ft² +20.25 ft²

  d² = 56.25 ft² = (7.5 ft)² . . simplifying and rewriting as a square

  d = 7.5 ft . . . . . . . . . . . . . . . taking the positive square root

The ball must be passed a distance of 7.5 ft for it to reach between players.

_____

If you recognize the given numbers as having the ratio 3:4, then you may realize they are the legs of a 3-4-5 right triangle with a scale factor of 1.5. The distance between players will be 1.5×5 = 7.5 feet.

Answer:

[tex]\boxed{\text{7.5 ft}}[/tex]

Step-by-step explanation:

If the players are running perpendicular to each other, we have a right triangle, as in the diagram below.

We can apply Pythagoras' Theorem.

[tex]\begin{array}{rcl}a^{2} & = & b^{2} + c^{2}\\& = & 4.5^{2} + 6^{2}\\& = & 20.25 +36\\& = & 56.25\\a & = & \sqrt{56.25}\\& = & \mathbf{7.5}\\\end{array}\\\text{The distance between the two players will be } \boxed{\textbf{7.5 ft}}[/tex]

1. The four subintervals are [0, 2], [2, 5], [5, 6], and [6, 7]. Their respective right endpoints are 2, 5, 6, and 7. If [tex]C(t)[/tex] denotes the change in sea level [tex]t[/tex] years after 2010, then the total sea level rise over the course of 2010 to 2017 is

[tex]\displaystyle\int_0^7C(t)\,\mathrm dt[/tex]

approximated by the Riemann sum,

[tex]C(2)(2-0)+C(5)(5-2)+C(6)(6-5)+C(7)(7-6)\approx\boxed{20\,\mathrm{mm}}[/tex]

2. The sum represents the definite integral

[tex]\boxed{\displaystyle\int_1^4\sqrt x\,\mathrm dx}[/tex]

That is, we partition the interval [1, 4] into [tex]n[/tex] subintervals, each of width [tex]\dfrac{4-1}n=\dfrac3n[/tex]. Then we sample [tex]n[/tex] points in each subinterval, where [tex]1+\dfrac{3k}n[/tex] is the point used in the [tex]k[/tex]th subinterval, then take its square root.

3. The integral is trivial:

[tex]\displaystyle\int_1^4\sqrt x\,\mathrm dx=\frac23x^{3/2}\bigg|_{x=1}^{x=4}=\boxed{\frac{14}3}[/tex]

4. Using the fundamental properties of the definite integral, we have

[tex]\displaystyle\int_1^4f(x)\,\mathrm dx=e^4-e\implies2\int_1^4f(x)\,\mathrm dx=2e^4-2e[/tex]

[tex]\displaystyle\int_1^4(2f(x)-1)\,\mathrm dx=2e^4-2e-\int_1^4\mathrm dx=\boxed{2e^4-2e-3}[/tex]

5. First note that [tex]\sec x[/tex] is undefined at [tex]x=\dfrac\pi2[/tex], so the integral is improper. Recall that [tex](\tan x)'=\sec^2x[/tex]. Then

[tex]\displaystyle\int_0^{\pi/2}\sec^2\frac xk\,\mathrm dx=\lim_{t\to\pi/2^-}\int_0^t\sec^2\frac xk\,\mathrm dx[/tex]

[tex]=\displaystyle\lim_{t\to\pi/2^-}k\tan\frac xk\bigg|_{x=0}^{x=t}[/tex]

[tex]=\displaystyle k\lim_{t\to\pi/2^-}\tan\frac tk[/tex]

[tex]=k\tan\dfrac\pi{2k}[/tex]

Now,

[tex]k\tan\dfrac\pi{2k}=k\implies\tan\dfrac\pi{2k}=1[/tex]

[tex]\implies\dfrac\pi{2k}=\dfrac\pi4+n\pi[/tex]

[tex]\implies k=\dfrac2{1+4n}[/tex]

where [tex]n[/tex] is any integer.

We want to write the given function in the form ax^2 + bx + c = 0.

We foil the left side.

(2x - 1)(x + 5) =0

2x^2 + 10x - x - 5 = 0

2x^2 + 9x - 5 = 0

Can you see the value of "b"?

The b-value is the coefficient of x.

So, b = 9.

Done!

[tex]|\Omega|=5\cdot9=45\\|A|=3\cdot6=18\\\\P(A)=\dfrac{18}{45}=\dfrac{2}{5}[/tex]

Answer:

d. -4.4​

Step-by-step explanation:

We know that log (a/b) = log a - log b

Since log a = 1.2 and log b = 5.6 , we can substitute these values into the equation.

                        log (a/b)  =   1.2 - 5.6

                                       = -4.4

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=60\pi \end{cases}\implies 60\pi =2\pi r\implies \cfrac{\stackrel{30}{~~\begin{matrix} 60\pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} }{~~\begin{matrix} 2\pi\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }=r\implies 30=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r=30\\ \theta =140 \end{cases}\implies s=\cfrac{\pi (140)(30)}{180}\implies s=\cfrac{70\pi }{3} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill s\approx 73.30~\hfill[/tex]

Answer:

A = (1/2)(7 units)(5 units) = (35/2) units^2.

Step-by-step explanation:

Call AB "the base" and recognize that its length is 7 units.  Call BC "the height" and recognize that its length is 5 units.

Then apply the area-of-a-triangle formula A = (1/2)(base)(height):

A = (1/2)(7 units)(5 units) = (35/2) units^2.

The area of triangle ABC is A = (1/2)(7 units)(5 units) = (35/2) units^2.

Triangle's area is equal to 1/2 (b* h) square units.

where the triangle's base and height, respectively, are denoted by b and h.

Given

Call AB "the base" and recognize that its length is 7 units.  Call BC "the height" and recognize that its length is 5 units.

Then apply the area-of-a-triangle formula A = (1/2)(base)(height):

A = (1/2)(7 units)(5 units) = (35/2) units²

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