What is the simplified value of $\frac{10! + 11! + 12!}{10! + 11!}$?

Answer:

10,341

Step-by-step explanation:

[tex]S_{n}=\frac{n}{2} (a_1}+a_{n})\\S_{54}=\frac{54}{2} (6+377)=27 \times 383=10,341[/tex]

Answer:

[tex]\boxed{x^2+y^2 = 49}[/tex]

Step-by-step explanation:

First, we'll find the length of the radius using distance formula and the coordinates (0,0) and (7,0)

Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

R = [tex]\sqrt{(7-0)^2+(0-0)^2}[/tex]

R = [tex]\sqrt{7^2}[/tex]

Radius = 7 units

Now, Equation of circle:

[tex](x-a)^2+(y-b)^2 = R^2[/tex]

Where (a,b) = (0,0) So, a = 0, b = 0 and R = 7 units

=> [tex](x-0)^2+(y-0)^2 = (7)^2[/tex]

=> [tex]x^2+y^2 = 49[/tex]

This is the required equation of the circle.

Answer:

x^2 + y^2 = 49

Step-by-step explanation:

We can write the equation of a circle as

( x-h) ^2 + ( y-k) ^2 = r^2

where ( h,k) is the center and r is the radius

The radius is the distance from the center to a point on the circle

(0,0) to (7,0) is 7 units

so the the radius is 7

( x-0) ^2 + ( y-0) ^2 = 7^2

x^2 + y^2 = 49

Answer:

x=(2+ √-32)/2 or x=(2- √-32)/2

Step-by-step explanation:

x^2 - 2x = -9

x^2 - 2x + 9 =0

x = 2± (√(-2)^2 - 4*1*9)/2*1

Use the quadratic formula in the expression using a=1, b= -2, c=9

x = 2±√4-36 /2

x = 2+√4-36 or x = 2 - √4 - 32 /2

x = (2+√-32) /2 or x=( 2 - √-32 )/2

The solution for the given quadratic equation are (2+i5.7)/2 or (2-i5.7)/2.

The given quadratic equation is x²-2x=-9.

Quadratic formula is the simplest way to find the roots of a quadratic equation.

The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.

By comparing x²-2x+9=0 with ax² + bx + c = 0, we get a=1, b=-2 and c=9

Substitute a=1, b=-2 and c=9 in the quadratic formula, we get

x = [2±√(-2)²-4×1×9)]/2×1

= [2±√4-36]/2

= (2±i5.7)/2

x = (2+i5.7)/2 or (2-i5.7)/2

Therefore, the solution for the given quadratic equation are (2+i5.7)/2 or (2-i5.7)/2.

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Answer:

Step-by-step explanation:

[tex] \frac{x - 1}{x + 5} \times \frac{x + 1}{x - 5} [/tex]

To multiply the fraction, multiply the numerators and denominators separately

[tex] \frac{(x - 1) \times (x + 1)}{(x + 5) \times (x - 5)} [/tex]

Using [tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex] simplify the product

[tex] = \frac{ {x}^{2} - 1 }{ {x}^{2} - 25 } [/tex]

Hope this helps..

Best regards!!

Answer:

b.  y = |x+4| - 10

Step-by-step explanation:

When you see a v-shaped graph, it could very well relate to an absolute-value function.

The value of the absolute value function has the vertex at x= -4, meaning that it has a minimum value when x=-4, which means that the absolute value function is of the form |x+4|  giving a zero when x= -4.

Also, the minimum of the function occurs at y = -10, meaning that the function has been translated by -10.

Therefore the function is

y = |x+4| - 10

Answer:

B

Step-by-step explanation:

EDGE unit review

Answer:

D) [tex]x+5\leq -4[/tex]

Step-by-step explanation:

We solve each of the inequalities

Option A

[tex]x+6<-8\\x<-8-6\\x<-14[/tex]

Option B

[tex]x+4\geq -6[/tex]

[tex]x\geq -6-4\\x\geq-10[/tex]

Option C

[tex]x-3>-10\\x>-10+3\\x>-7[/tex]

Option D

[tex]x+5\leq -4[/tex]

[tex]x\leq -4-5\\x\leq -9[/tex]

Therefore, only option D has -12 in its solution set.

Hey there! I'm happy to help!

First, we need to rotate our points 180° about the origin. To find the coordinates after such a rotation, we simply find the negative version of each number in the ordered pair, which can be written as (x,y)⇒(-x,-y).

Let's convert this below

A: (1,1)⇒(-1,-1)

B: (5,4)⇒(-5,-4)

C: (7,1)⇒(-7,-1)

D: (3,-2)⇒(-3,2)

Now, we need to translate these new points five units to the right and one unit down. This means we will add 5 to our x-value and subtract 1 from our y-value. This will look like (x,y)⇒(x+5,y-1). Let's do this below.

A: (-1,-1)⇒(4,-2)

B: (-5,-4)⇒(0,-5)

C: (-7,-1)⇒(-2,-2)

D: (-3,2)⇒(2,1)

Therefore, this new parallelogram has coordinates of A'(4,-2), B'(0,-5), C'(-2,-2), and D'(2,1)

Now you know how to find the coordinates of translated figures! Have a wonderful day! :D

Answer:

[tex]x= \frac{5^{14}+3}{2}[/tex]

Step-by-step explanation:

The correct steps to solve the equation are:

[tex]14=log_5(2x-5)[/tex]

[tex]5^{14}=5^{log_5(2x-3)}[/tex]

Because [tex]a^{log_am}=m[/tex]

So, solving we get:

[tex]5^{14}=2x-3[/tex]

Sum 3 on every side:

[tex]5^{14}+3=2x-3+3\\5^{14}+3=2x[/tex]

Dividing by 2 into both sides:

[tex]\frac{5^{14}+3}{2}=\frac{2x}{2}\\\frac{5^{14}+3}{2}=x[/tex]

So, the answer is  [tex]x= \frac{5^{14}+3}{2}[/tex]

Answer: Step 2

Step-by-step explanation:

This is correct according to Edge 2021

Answer:  without trying each calculation individually,  6750 4-digit numbers are not divisible by 4

Step-by-step explanation:  From 1000 to 9999 there are 9000 4-digit numbers 9999 - 999 = 9000.

Eliminate all the odd numbers 9000/2 = 4500

Eliminate the even numbers divisible by 2 but not by 4. 4500/2 = 2250

9000 - 2250 = 6750.

Answer:

[tex]\mathbf{V = 1296 \pi }[/tex]

Step-by-step explanation:

Given that :

Find the volume of the region enclosed by the cylinder [tex]x^2 + y^2 =36[/tex] and the plane z = 0 and y + z = 36

From y + z = 36

z = 36 - y

The volume of the region can be represented by the equation:

[tex]V = \int\limits \int\limits_D(36-y)dA[/tex]

In this case;

D is the region given by [tex]x^2 + y^2 = 36[/tex]

Relating this to polar coordinates

x = rcosθ    y = rsinθ

x² + y² = r²

x² + y² = 36

r² = 36

r = [tex]\sqrt{36}[/tex]

r = 6

dA = rdrdθ

r → 0 to 6

θ to 0  to 2π

Therefore:

[tex]V = \int\limits^{2 \pi} _0 \int\limits ^6_0 (36-r sin \theta ) (rdrd \theta)[/tex]

[tex]V = \int\limits^{2 \pi} _0 \int\limits ^6_0 (36-r^2 sin \theta ) drd \theta[/tex]

[tex]V = \int\limits^{2 \pi} _0 [\dfrac{36r^2}{2}- \dfrac{r^3}{3}sin \theta]^6_0 \ d\theta[/tex]

[tex]V = \int\limits^{2 \pi} _0 [648- \dfrac{216}{3}sin \theta]d\theta[/tex]

[tex]V = \int\limits^{2 \pi} _0 [648+\dfrac{216}{3}cos \theta]d\theta[/tex]

[tex]V = [648+\dfrac{216}{3}cos \theta]^{2 \pi}_0[/tex]

[tex]V = [648(2 \pi -0)+\dfrac{216}{3}(1-1)][/tex]

[tex]V = [648(2 \pi )+\dfrac{216}{3}(0)][/tex]

[tex]V = 648(2 \pi )[/tex]

[tex]\mathbf{V = 1296 \pi }[/tex]

Answer:

1,-1,3,4

1,6,-2,-4

-4,6,-6,6

Step-by-step explanation:

I believe you just put in the values into the box. Watch the video to see how they did it to make sure it looks like how I did it.

Answer:

Answer E

Step-by-step explanation:

If you think about it, the origin is just (0,0). Now, think which one is the closest to that. (0,1/2), or answer E, should be your assumption.

Answer: You have the correct answer. It is y = 150x-50

Nice work on getting the correct answer. For anyone curious, the explanation is below.

=============================================

x = number of hours the stand is open

y = amount earned

(1,100) is from the fact the stand is open 1 hour and earns $100

(3,400) is due to the stand earning $400 after 3 hours.

Slope Formula

m = (y2 - y1)/(x2 - x1)

m = (400-100)/(3-1)

m = 300/2

m = 150 is the slope, and it is the amount earned per hour. It is the rate of change.

Use m = 150 and (x,y) = (1,100) to find the value of b as shown below

y = mx+b

100 = 150(1) + b

100 = 150 + b

100-150 = b

-50 = b

b = -50 is the y intercept and it is the starting amount they earn. The negative earning indicates that they spent $50 to set up the stand, which is the cost of buying the food, equipment, etc.

So we have m = 150 as the slope and b =  -50 as the y intercept.

Therefore, y = mx+b turns into y = 150x-50.

-------

As a check, plugging in x = 1 should lead to y = 100

y = 150x-50

y = 150(1)-50

y = 150-50

y = 100 and indeed it does

The same should be the case with (3,400). Plug in x = 3 and we should get y = 400

y = 150x-50

y = 150(3)-50

y = 450-50

y = 400, we have confirmed the answer by showing that the line y = 150x-50 goes through the two points (1,100) and (3,400).

The equation for revenue earned from being opened for x hours will be y=150x-50 so it is absolutely correct.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Given,

$100 for 1 hour

So,

x = 1 and y = 100

And,

$400 for 3 hour

So,

x = 3 and y = 400

Now the slope of the linear equation is given by

m = difference in ys coordinate / difference in xs coordinate  

m = (400 - 300)/(3-1) = 150

So equation become

y = 150x + b

Now put (3,400) to find out b

400 = 150(3) + b

b = -50

So, equation

y = 150x - 50

Hence " The equation for revenue earned from being opened for x hours will be y=150x-50".

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Answer:

The Central Limit Theorem says that if the sample size is more than 30, the data follows a normal sampling distribution. Since the sample size is 180, and that is more than 30, a Normal sampling distribution can be used.

Since a normal sampling distribution can be used, we should FAIL TO REJECT the null hypothesis because p = 0.20, which is more than the significance level of α = 0.08. There is NOT sufficient evidence to suggest that the alternative hypothesis is true.

Hope this helps!

Answer:

h = 7 degrees

Step-by-step explanation:

To find h, we know that it is positive because it increases in value, not decreases:

h = 65 - 58

h = 7

Answer:

h = 7°F

Step-by-step explanation:

58 + h = 65

h = 65 - 58

h = 7

Check:

68 + 7 = 65

Answer:

C.

Step-by-step explanation:

It's the most reasonable answer.

Answer:

The Azimuths are 81 degrees, 6 degrees for Grid Azimuths and 269 degrees, 194 degrees for back Azimuths

Step-by-step explanation:

Stream = 89 degrees and Pond = 14 degrees

To Convert to grid Azimuth

G-M Azimuth of 89-8=81 degrees

G-M Azimuth of 14-8=6 degrees

To obtain the back Azimuth for the stream

89+180=269 degrees

To obtain the back Azimuth for the pond

14+180=194 degrees

Answer:

The least common multiple of $6!$ and $(4!)^2.$

is 6×4! or 144

Answer:

m = 7; n = 12

Step-by-step explanation:

"a regular n-sided polygon has 5 sides more than a

regular m-sided polygon"

n = m + 5

The sum of the measures of the interior angles is

180(n - 2) for the n-sided polygon and

180(m  2) for the m-sided polygon.

"If the sum of interior angles of the regular

n-sided polygon is twice that of the latter"

180(n - 2) = 2(180)(m - 2)

We have a system of equations with 2 equations.

n = m + 5

180(n - 2) = 2(180)(m - 2)

Simplify the second equation:

n - 2 = 2m - 4

n + 2 = 2m

Substitute m + 5 for n.

m + 5 + 2 = 2m

7 = m

m = 7

n = m + 5 = 7 + 5 = 12

Answer: m = 7; n = 12

Answer:

17.95+18x <= 40

Step-by-step explanation

<= less than or equal to0

Answer:

The maximum number of miles than Chloe can drive are:

122.5

Step-by-step explanation:

$1 = 100¢

18¢ = 18/100 = $0.18

17.95 + 0.18m = 40

m = maximum number of miles than  can drive

0.18m = 40 - 17.95

0.18m = 22.05

m = 22.05/0.18

m = 122.5

you can use the value of sin\

sin(theta) = 12/16

Now solve for theta, and do inverse sine

so theta would be 48.59037789 , or around 50 degrees

Answer:

Step-by-step explanation:

Since, it is a right triangle.

Perpendicular (p) = 12

hypotenuse ( h) = 16

now,

[tex]sin \: (x \: degree) = \frac{perpendicular}{hypotenuse} [/tex]

[tex]sin \: x \: = \frac{12}{16} [/tex]

[tex] x = {sin}^{ - 1} ( \frac{12}{16} )[/tex]

[tex]x = 48.59 \: degree[/tex]

hope this helps...

good luck on your assignment..

Answer:

-7/5

Step-by-step explanation:

We can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

   = ( -3 -4)/(8-3)

   = -7/5

Answer:

-7/5

Step-by-step explanation:

Hey there!

To find the slope of a line with 2 given points we'll use the following formula,

[tex]\frac{y^2-y^1}{x^2-x^2}[/tex]

-3 - 4 = -7

8 - 3 = 5

-7/5

Hope this helps :)

When you solve this equation using the quadratic formula, you will get [tex]x = \frac{-20\pm \sqrt{400-4k^2}}{2k}[/tex]. The only way for this number to be irrational is for [tex]\sqrt{400-4k^2}[/tex] to be irrational. The square root of any number that is not a perfect square is irrational*, so the solutions of the quadratic are rational if and only if [tex]400-4k^2[/tex] is a perfect square. We can factor out the 4 (which is already a perfect square), which means that [tex]100-k^2[/tex] must be a perfect square. This occurs exactly when k is equal to one of the following:[tex]\sqrt{100},\sqrt{99},\sqrt{96},\sqrt{91},\sqrt{84},\sqrt{75},\sqrt{64},\sqrt{51},\sqrt{36},\sqrt{19}, \sqrt{0}[/tex].

Of these, the only positive integer values of k are: [tex]\sqrt{100}, \sqrt{64}, \sqrt{36}[/tex], or simply 6, 8, and 10.

* This is quite simple to show: Take any rational number, a/b. Without loss of generality, we can assume that a/b is in reduced form, that is, a and b have no common factors. (a/b)^2 is a^2/b^2, and since a and b have no common factors, neither do a^2 and b^2. Therefore, a^2/b^2 cannot be an integer. In the event that a/b is an integer, b would equal 1, and this proof would not hold.

Answer:

60 ounces

Step-by-step explanation:

A certain mixture of paint contains 5 parts white paint for every 4 parts blue paint, that is, the white paint (w) to blue paint (b) ratio is 5:4. We can apply this ratio to different units such as ounces. This means that the mixture has 5 ounces of white paint to 4 ounces of blue paint. If a can of paint contains 75 ounces of white paint, the ounces of blue paint in the can are:

75 oz w × (4 oz b/5 oz w) = 60 oz b

Answer:

He stitched 1 shirt in 6 hours.

He can stitch 1/6 of a shirt in one hour

Step-by-step explanation:

Given Mike can stitch 7 shirts in 42 hours

No. of shirt stitch in one hour = total no of shirt stitch/total time taken

No. of shirt stitch in one hour = 7/42 = 1/6

Thus, he can stitch 1/6 of a shirt in one hour

Time taken to stitch 1 shirt = total time taken by him to stitch 7 shirts/ total no. of shirt stitch(i.e 7)  = 42/6 = 6 hours.

Thus, he stitched 1 shirt in 6 hours.

Answer:

He can stitch 1/6 of a shirt in one hour

Step-by-step explanation:

Because he stitched  7 shirts in 42 hours

42/7 = 6

so 6 hours per shirt

In one hour:

1/6

Answer:

6 2/9 miles per hour

Step-by-step explanation:

Take the miles and divide by the hours

4 2/3 ÷ 3/4

Change to an improper fraction

( 3*4+2)/3 ÷3/4

14/3 ÷3/4

Copy dot flip

14/3 * 4/3

56/9

Change back to a mixed number

9 goes into 56  6 times with 2 left over

6 2/9 miles per hour

Answer:

6 2/9 miles per hour

Step-by-step explanation:

Divide the miles by the hour.

4 2/3 ÷ 3/4

Reciprocal

4 2/3 × 4/3

Convert to improper fraction.

14/3 × 4/3

56/9

Convert to mixed fraction.

9 × 6 + 2

6 2/9

Answer:

The answer is:

The fourth option,

{s | s <90}

Step-by-step explanation:

yes

Answer:

[tex]\boxed{s|s<90}[/tex]

Step-by-step explanation:

1/3s-6<24

Add 6 on both sides.

1/3s<30

Multiply both sides by 3.

s<90

Answer:

the radius of the circle =7

Step-by-step explanation:

the function of a circle:(x – h)^2 + (y – k)^2 = r^2

center(0,0) because the center of a circle is at the origin (h,k)

a line intersect at (0,7)

(0-0)^+7-0)^2=r^2

r^2=49 , r=√49

radius r=7

Answer:

Step-by-step explanation:

The best first step to solve this is to just subtract 5/3 from both sides so it is easier to simplify.

Answer:

Subtract 5/3 to the other side

Step-by-step explanation:

Hey there!

Well the best first step is to -5/3 to both sides and move it to the right side.

-4x + 5/3 > 5/10

-5/3 to both sides

-4x > -7/6

Hope this helps :)