In 2014, the population of Ohio was 11.59 million people. One-hundred years earlier the population was 5.109 million people. Using scientific notation, how much did the population grow over the hundred-year span?

[tex]\\ \qquad\quad\sf\longmapsto ^nC_2=^nC_4[/tex]

[tex]\boxed{\sf ^nC_r=\dfrac{n!}{r!(n-r)!}}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{n!}{2!(n-2)!}=\dfrac{n!}{4!(n-4)!}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{2\times 1(n-2)!}=\dfrac{1}{4\times 3\times 2\times 1(n-4)(n-3)(n-2)!}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 2=24(n-4)(n-3)[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 2=24\left\{n(n-3)-4(n-3)\right\}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 2=24(n^2-3n-4n+12)[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 2=24(n^2-7n+12)[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 2=24n^2-168n+288[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 24n^2-168n=-286[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 24n^2-168n+286=0[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 12n^2-84n+143=0[/tex]

[tex]\\ \qquad\quad\bf\longmapsto n=\dfrac{7}{3}\pm \dfrac{1}{3}\sqrt{3}[/tex]

Answer:

n = 6

Step-by-step explanation:

There's a secret formula for this:

If nCx = nCy,

Then n = x + y.

Hence, for this question, n = 2 + 4 = 6

Answer:

see below

Step-by-step explanation:

Let r = amount of the 7% solution

y represent the amount of the 15 percent solution

.07r + .15 y = (r+y) .12

r+y = 20

y = 20-r

.07r + .15 (20-r) = (20) .12

0.07r+0.15(20-r)=2.4

.07r+ 3 - .15r = 2.4

-.08r = 2.4-3

-.08r = -.6

Divide by-.08

r =7.5 Liters of the 7%

y = 20-7.5

y = 12.5 L of 12%

Check

.07 *7.5 + .15 (12.5) =20*.12

.525+1.875=2.4

2.4=2.4

Answer:

A   and B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Since we know the measure of ∠B and the side opposite to ∠B and we want to find BC, which is adjacent to ∠B, we can use the tangent ratio. Recall that:

[tex]\displaystyle \tan\theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]

The angle is 54°, the opposite side measures 16 units, and the adjacent side is BC. Substitute:

[tex]\displaystyle \tan 54^\circ = \frac{16}{BC}[/tex]

Solve for BC. We can take the reciprocal of both sides:

[tex]\displaystyle \frac{1}{\tan 54^\circ} = \frac{BC}{16}[/tex]

Multiply:

[tex]\displaystyle BC = \frac{16}{\tan 54^\circ}[/tex]

Use a calculator. Hence:

[tex]\displaystyle BC \approx 11 .62\text{ units}[/tex]

BC measures approximately 11.62 units.

Our answer is B.

Answer:

10

Step-by-step explanation:

I used a calculator

Answer:

(a^3/b^7)^2 = (a^6/b^14)

Answer:

c(X)=R(X)

125x+18000=215x

18000=215x-125x

18000=90x (divede both sides by 90)

X=200

Step-by-step explanation:

If you like my answer than please mark me brainliest

[tex]\\ \sf\longmapsto 33M+3=9M+4[/tex]

[tex]\\ \sf\longmapsto 33M-9M=4-3[/tex]

[tex]\\ \sf\longmapsto (33-9)M=1[/tex]

[tex]\\ \sf\longmapsto 24M=1[/tex]

[tex]\\ \sf\longmapsto M=\dfrac{1}{24}[/tex]

Hey there! I'm happy to help!

Here is our equation.

[tex]2y-3x=10[/tex]

Let's add 3x to both sides.

[tex]2y=3x+10[/tex]

Divide both sides by 2.

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

Here is slope intercept form.

[tex]y=mx+b\\m=slope\\b=y-intercept[/tex]

So, we can just find those two things in the equation, and here are our answers.

[tex]y=\frac{3}{2}x+5\\m=\frac{3}{2}\\b=5[/tex]

The graph is down below. If our y-intercept is 5, then one of our points is (0,5). You can then plug a random x-value into the formula to find another point and then draw the line going through the two points.

[tex]y=\frac{3}{2}(2)+5\\y=3+5\\y=8\\(2,8)[/tex]

Have a wonderful day and keep on learning! :D

Answer:

Heyy mate... here's ur ans ;)

they asked us to apply pythagarus theorem becoz that theorem proves

that it is rectangle so lets get started

( p - perpendicular / b - base / h - hypotenuse )

a) =>

B = 8.1 m

P = 6.3 m

H = 10.15m

Now applying thm => H^2=p^2+b^2

(8.1)^2 + (6.3)^2 = (10.15)^2

65.61 + 39.69 = 103.02

so now LHS = 105.3 and RHS = 103.02 hence

LHS not equal to RHS

so is not rectangle

b) =>

B = 14.4

P = 5.2

H = 15.31

Now applying thm => H^2=p^2+b^2

(5.2)^2 + (14.4)^2 = (15.31)^2

27.04 + 207.36 = 234.39

LHS = 234.4 and RHS = 234.39

just taking approximation rhs is 234.4

hence

LHS = RHS

so it is a rectangle

please mark it brainliest <3

Answer:

a: 750 ml (three quarters)

b: 750 ml

Step-by-step explanation:

1/4 liter= 250ml

A) 250*3= 750ml

B) the same as A

Answer:

Answer B and C

Step-by-step explanation:

Z is the center of the circle passing through H,G,J:

HZ=85=ZG=ZJ ==> ZJ=85 : B is true

HK=KG=136/2=68: C is true.

The two options that are true are ZK = JL and ZL = JM.

The given information is that ZK, ZL, and ZM are perpendicular bisectors of AGHJ. This means that ZK, ZL, and ZM each bisect one of the sides of triangle AGHJ and form a right angle with that side.

In triangle AGJ, ZK is the perpendicular bisector of AG, so ZK = JL.

In triangle AHJ, ZL is the perpendicular bisector of AH, so ZL = JM.

The other two options are not true. ZK = GH is not true because ZK is the perpendicular bisector of AG, not GH. ZM = MG is not true because ZM is the perpendicular bisector of AH, not MG.

To learn more about perpendicular bisectors, here

https://brainly.com/question/24753075

#SPJ2

Answer:

m<2= 148.4

Step-by-step explanation:

A linear pair means that both angles add to 180.

m<2 = 4*m<1 +22

Together

m1 + m2 = 180

Put the value for m<2 into the above equation

m<1  + 4*m<1 + 22 = 180         Combine like terms\

5m<1 + 22 = 180                      Subtract 22

5m<1 = 180 - 22

5m<1 = 158                              Divide by 5

m<1 = 158/5

m<1 = 31.6

m<2 = 4*31.6 + 22

m<2 = 138.4

Answer:

Turn

Step-by-step explanation:

you could say that, "No matter which way you turn the image, it stays the same".

hope this helps :D

Step-by-step explanation:

4x + 19 + 3x = - 5

4x + 3x + 19 = - 5 collect the like terms

7x + 19 = - 5

7x = - 5 - 19 bring 19 to the right

7x/ 7x = - 24/ 7

x = - 3.4

I hope this answers your question

(625 • (a4)) + 22b4

54a4 + 22b4

Final result :

625a4 + 4b4

Answer:

3 large frames

Step-by-step explanation:

Let the large frames she bought be x in number and small frames be y in number.

ATQ, 17x+6y=141 and x+y=18. Solving it, we will get x=3 and y=15. So she bought 3 large frames

The perimeter of a triangle is the summation of the three sides of the triangle. Base on the assumed values, the length of side BD is 2.

For [tex]\triangle ACD[/tex], the sides are: AC, AD and CD

So, the perimeter is:

[tex]P_{\triangle ACD} = AC + AD + CD[/tex]

For [tex]\triangle ABD[/tex], the sides are: AB, AD and BD

So, the perimeter is:

[tex]P_{\triangle ABD} = AB + AD + BD[/tex]

The difference in the perimeters is:

[tex]P_{\triangle ACD} - P_{\triangle ABD} =1 + \sqrt 3[/tex]

So, we have:

[tex](AC + AD + CD) - ( AB + AD + BD) =1 + \sqrt 3[/tex]

Open brackets

[tex]AC + AD + CD - AB - AD - BD =1 + \sqrt 3[/tex]

Evaluate like terms

[tex]AC + CD - AB - BD =1 + \sqrt 3[/tex]

Make BD the subject

[tex]BD = AC + CD - AB - (1 + \sqrt 3)[/tex]

The solution cannot be completed because the side lengths of [tex]\triangle ACD[/tex] and [tex]\triangle ABD[/tex] are not given; so, I will assume the following values.

[tex]AC =2; CD = 1; AB = \sqrt 3[/tex]

[tex]BD = AC + CD - AB - (1 + \sqrt 3)[/tex] becomes

[tex]BD = 2 + 1 + \sqrt 3 - (1 + \sqrt 3)[/tex]

Open bracket

[tex]BD = 2 + 1 + \sqrt 3 - 1 - \sqrt 3[/tex]

Evaluate like terms

[tex]BD = 2[/tex]

Base on the assumed values, the length of side BD is 2.

Read more about perimeters at:

https://brainly.com/question/6465134

Answer:

3.1416

Step-by-step explanation:

A=pi*r^2, differentiate with respect to t both sides

dA/dt=2*pi*r*dr/dt

dA/dt=2*pi*5*(0.1)

dA/dt=pi=3.1416 cm^2/sec

Step-by-step explanation:

since the user is listed as beginner, I was wondering, if (while correct) the answer should be based on differentiation (rather advanced topic).

I thought originally this would be about sequences.

and I wondered about the start value.

in any case, here a different view.

the area of a circle is

Ac old = pi × r²

now, r is increasing by 0.1

Ac new = pi×(r+0.1)² = pi×(r² + 0.2r + 0.01) =

= pi×r² + pi×0.2r + pi×0.01 =

= Ac old + pi×0.2r + pi×0.01

so, the increase of the area is

pi×0.2r + pi×0.01

for r=5

pi×0.2×5 + pi×0.01

pi×1 + pi×0.01 = pi + p×0.01 = pi×(1 + 0.01) =

= pi×(1 + (radius change)²)

now, it depends on what your teacher wants to see here.

a "digital stair case" 0.1 by 0.1 increase/sequence approach ?

in this case you might also want to calculate the above with r=4.9 (as only with the last 0.1 step r reaches 5).

and either the r=4.9 (result a tiny bit less than pi) or r=5 (result a tiny bit larger than pi) is correct, of simply the value in the middle (practically pi).

or it was meant to be a continuous increase (not step by step).

in which case we need then to calculate the limit with "radius change" going to 0. which delivers pi as rate result (as with the differentiation).

Answer: a = 52/7

Step-by-step explanation:

remove the parentheses, move the constant to the right, calculate, then divide both sides

Answer:

The answer is, a = 52/7, or a = 7.42 in decimal form

Follow the steps below for better explanation:

Answer:

Median

Step-by-step explanation:

Using the median to measure central tendency, rather than the mean, is better for a skewed data set.

Since a skewed data set will have either very high or low extreme data points, the mean will be less representative and accurate when measuring central tendency.

Using the median will measure this better because it is not as vulnerable as the mean when there are extreme data points.

So, the answer is the median.

Answer:

1/4 cup each

Step-by-step explanation:

Take the amount of ice cream and divide by 3

3/4÷ 3

Copy dot flip

3/4 * 1/3

Rewriting

3/3 * 1/4

1/4 cup each

Answer:

the answer is 10

Step-by-step explanation:

900 ÷ 90

=> 10 [tex]\sf{}[/tex]

Answer:

The answer is 10.

Step-by-step explanation:

900/90=cut 0 of numerator and denominator then 90 divide by 9 is 10.

Answer:

M = (1,3) - 1 right, 3 up

A = (4,0) - 4 right, 0 up

T = (3,6) - 3 right, 6 up

H = (6,2) - 6 right, 2 up

Step-by-step explanation:

Remember, to write the ordered pair using the correct order (x,y) x means it moves either left or right and y moves up or down.

First identify the x-coordinate of a point on a graph. Start at (0,0) which is where the x and y axis meet. (Basically the center of the coordinate plane.)

Then move either left or right and count the number of spaces you move until you are under or over the coordinate. The number of spaces you counted it the x value.

Next, identify the y-coordinate of a point. Now move up or down and count the number of spaces until you meet the coordinate. The number of spaces you counted is the y value.

I tried my best to explain. Let me know if you are still confused.

Answer:

5n-7

simply like terms

Answer:

5n - 7

Step-by-step explanation:

n- 10 + 3 + 4n

n +  4n = 5n

-10 + 3 = -7

5n- 7

Answer:

it is 2 te he

Step-by-step explanation:

ONCE THE 5 6 = 7 10 .. ?% =1 x 7 =2 te he

Answer:

D

Step-by-step explanation:

Exponential functions always will end up being bigger than quadratic functions and since g(x) is probably the exponential it makes f(x) the quadratic because it is growing slower than the function g(x)

The function g(x) increases faster than the function f(x). Then the correct option is D.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The table below shows the values of f(x) and g(x) for different values of x.

One of the functions is a quadratic function, and the other is an exponential function.

The quadratic function f(x) will be

f(x) = ax² + bx + c

At x = 1, f(x) will be 3

a + b + c = 3 ...1

At x = 2, f(x) will be 6

4a + 2b + c = 6 ...2

At x = 3, f(x) will be 11

9a + 3b + c = 11 ...3

On solving equations 1, 2, and 3, we have

a = 1, b = 0, and c = 2

Then the quadratic function will be

f(x) = x² + 2

The exponential function g(x) will be given as

g(x) = abˣ

At x = 1, g(x) will be 3

ab = 3 ...4

At x = 2, g(x) will be 9

ab² = 9 ...5

From equations 4 and 5, we have

a = 1 and b = 3

Then the exponential function will be

[tex]\rm g(x) = 3^x[/tex]

More about the function link is given below.

https://brainly.com/question/5245372

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