Find the arc length of a central angle of pi/6 in a circle whose radius is 10 inches.

Answer:

b

Step-by-step explanation:

B// 8pi x-24pi

Answer:

B

Step-by-step explanation:

Let [tex]r[/tex] be the radius of one sphere.

Since radius is r,  the height of the cylinder will be [tex]4r[/tex]

Also, the cylinder has the same radius as the sphere: [tex]r[/tex]

Plugging in the values we get: [tex]V=\pi (r)^{2}(4r)=4\pi r^3[/tex]

Ratio of volume of 1 sphere to volume of cylinder is:

[tex]\frac{\frac{4}{3}\pi r^3}{4\pi r^3}=\frac{\frac{4}{3}}{4}=\frac{4}{3}*\frac{1}{4}=\frac{1}{3}[/tex]

The ratio is 1:3

Answer choice B is right.

Answer:

[tex]x \leq 14.05[/tex]

Step-by-step explanation:

First, to find the boundary we need to find the amount of money left, simply subtract the spent amount from the total:

60 - 45.95 = 14.05

Seeing as this is the amount, she can spend any amount up to and including 14.05, so we need an equal to or smaller than sign:

Let x be the value of the object:

[tex]x \leq 14.05[/tex]

Which is the inequality!

Answer:

P ( blue ) =  1/4

P ( white ) =  5/12

P ( red ) = 1/3

P ( not red ) =  2/3

Step-by-step explanation:

To find the probability of a marble being chosen,  it is the number of that color over the total

We need to find the total number of marbles

4 red+ 5 white+3 blue = 12 marbles

P ( blue ) = 3 blue / 12 total = 3/12 = 1/4

P ( white ) = 5 white / 12 total = 5/12

P ( red ) = 4 red/ 12 total = 4/12 = 1/3

How man marbles are not red

total marbles - red marbles = 12-4 = 8

8 marbles are not red

P ( not red ) = 8 not red / 12 total = 8/12 = 2/3

Rectangle is the closed shaped polygon with 4 sides. Opposite sides of the rectangle are equal. when the length and the width of the sandbox are doubled the percent of change in the perimeter is 100 percent and the percent of change in the area is 300 percent.

Given-

The length of the sandbox is 10.

The width of the sandbox is 6.

a) The percent of change in the perimeter.

The perimeter of the rectangle is the twice of the sum of its side.The perimeter P of the sandbox is,

[tex]P =2\times (10+6)[/tex]

[tex]P =2\times (16)[/tex]

[tex]P=32[/tex]

When the length and the width of the sandbox are doubled the perimeter [tex]P_d[/tex] of the box is,

[tex]P_d=2\times(20+12)[/tex]

[tex]P_d=2\times(32)[/tex]

[tex]P_d=64[/tex]

Percentage [tex]\DeltaP[/tex][tex]\Delta P[/tex] change in the perimeter,

[tex]\Delta P=\dfrac{64-32}{32}\times 100[/tex]

[tex]\Delta P=100[/tex]

b) The percent of change in the area.

The area of the rectangle is the product of its side.The area A of the sandbox is,

[tex]A = (10\times6)[/tex]

[tex]A=60[/tex]

When the length and the width of the sandbox are doubled the area [tex]A_d[/tex] of the box is,

[tex]A_d=20\times12[/tex]

[tex]P_d=240[/tex]

Percentage [tex]\DeltaP[/tex][tex]\Delta A[/tex] change in the area,

[tex]\Delta A=\dfrac{240-60}{60}\times 100[/tex]

[tex]\Delta P=300[/tex]

Thus when the length and the width of the sandbox are doubled the percent of change in the perimeter is 100 percent and the percent of change in the area is 300 percent.

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Answer:

5y^3

Step-by-step explanation:

Find what is common to all the terms

5y^5 = 5 * y*y*y*y*y

35y^4 = 5*7*y*y*y*y

15y^3 = 3*5*y*y*y

The all have 5*y*y*y

So the  GCF is 5 y*y*y or 5y^3

Question:

line x + 2y = 0 is end side of angle θ

and cos θ < 0

Answer: sin θ = √5/5

Step-by-step explanation:

cos θ < 0 means x < 0

Line is y = -x/2, slope -1/2

Line intersects unit circle when x^2+y^2=1

x^2 + (-x/2)^2 = 1

x^2 + x^2/4 = 1

5x^2/4 = 1

x = -√(4/5) = -2√(1/5) = -2√5/5

y = √5/5

x^2 = 4/5, y^2 = 1/5

sin θ is y value at intersection of line and unit circle, √5/5

In this exercise we have to use the given equation and thus calculate the intersection value:

[tex]sin (\theta) = \sqrt{5/5}[/tex]

So knowing that you were informed:

Line x + 2y = 0 is end side of angle θ and  cos θ < 0 means x < 0.  Line is y = -x/2, slope -1/2 and the  Line intersects unit circle when :

[tex]x^2+y^2=1\\x^2 + (-x/2)^2 = 1\\x^2 + x^2/4 = 1\\5x^2/4 = 1\\x = -\sqrt{4/5} = -2\sqrt{1/5} = -2\sqrt{5/5}\\y = \sqrt{5/5}\\x^2 = 4/5, y^2 = 1/5[/tex]

[tex]sin(\theta)[/tex]  is y value at intersection of line and unit circle, [tex]\sqrt{5/5}[/tex]

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Answer:

The budget in 2010 is $4453.10915 billion

Step-by-step explanation:

We are given exponential function as

[tex]f(t)=39.4e^{0.0787932t}[/tex]

where t is the time in years since 1950

now, we can find time in 2010

t=2010-1950=60

now, we can plug t=60

and we get

[tex]f(60)=39.4e^{0.0787932\times 60}[/tex]

we get

[tex]f(60)=4453.10915[/tex]

So, the budget in 2010 is $4453.10915 billion

Answer:

0.1071

Step-by-step explanation:

Given

Total number of students=8

Boys=2

Girls=6

When we are picking a group from population we use combinations to calculate sample space and for event

So if a group of 5 has to be picked from 8 students

ⁿC_k=  n!/(k!)(n-k)!

C_(n,k)=  n!/(k!)(n-k)!

Here n=8 and k=5

C_8,5=  8!/(5!)(8-5)!

This will give us:  

C_8,5=56

And if we have to pick only girls:

C_6,5=  6!/(5!)(6-5)!

=6

The probability of picking all girls:

=6/56

=0.1071

The correct answer to this question would be 3/28

Answer:

A difference of squares has the following form [tex]a^2-b^2[/tex]. Any two perfect squares connected by subtraction can be factored.

It factors to (a+b)(a-b).

Step-by-step explanation:

A binomial is an expression with only terms where at least one is a term with a variable. When we can factor for difference of squares, we can have two variable terms or just one with a constant.

A difference of squares has the following form [tex]a^2-b^2[/tex]. Any two perfect squares connected by subtraction can be factored.

It factors to (a+b)(a-b).

Answer:

A. the graph flip over the x - axis...

Option b) the graph flips over the line y=x

When you multiply two function together, you will get a third function as the result,  and that third function as the result, and that third function will be the product of the two original functions . when we multiply the function by -1 ,it becomes y=-f(x)  . Then the coordinates becomes (x, -f(x))

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Answer:

∠A=40°

Step-by-step explanation:

Equation 1: ∠A+∠B+∠C=180°

Equation 2: ∠B/2+∠C/2+110°=180°

2(Equation 2): ∠B+∠C+220°=360°

                                 ∠B+∠C=140°

Equation 1 - 2(Equation 2): ∠A=40°

Therefore, ∠A=40°

Answer:

B

(x-2) is a factor since remainder is 0.

Step-by-step explanation:

We divide (x-2) into the polynomial [tex]-4x^4+6x^3+8x^2-6x-4[/tex] through long division or synthetic. We choose long division and look for what will multiply with (x-2) to make the polynomial [tex]-4x^4+6x^3+8x^2-6x-4[/tex] .

[tex](x-2)(-4x^3)=-4x^4+8x^3[/tex]

We subtract this from the original [tex]-4x^4-(-4x^4)+6x^3-(8x^3)+8x^2-6x-4[/tex].

This leaves [tex]-2x^3+8x^2-6x-4[/tex]. We repeat the step above.

[tex](x-2)(-2x^2)=-2x^3+4x^2[/tex].

We subtract this from [tex]-2x^3-(-2x^3)+8x^2-(4x^2)-6x-4=4x^2-6x-4[/tex]. We repeat the step above.

[tex](x-2)(4x)=4x^2-8x[/tex].

We subtract this from [tex]4x^2-(4x^2)-6x-(-8x)-4=2x-4[/tex]. We repeat the step above.

[tex](x-2)(2)=2x-4[/tex].

We subtract this from [tex]2x-(2x)-4-(4)=0[/tex]. There is no remainder. This means (x-2) is a factor.

The remainder R when the polynomial p(x) = -4x4 + 6x3 + 8x2 - 6x - 4 is divided by (x - 2) is 0, indicating that (x - 2) is indeed a factor of p(x).

To find the remainder R when the polynomial p(x) = -4x4 + 6x3 + 8x2 - 6x - 4 is divided by (x - 2), we can use the Remainder Theorem. The Remainder Theorem states that the remainder of the division of a polynomial p(x) by a linear term (x - a) is equal to p(a). Therefore, to find R, simply calculate p(2).

p(2) = -4(2)4 + 6(2)3 + 8(2)2 - 6(2) - 4

p(2) = -4(16) + 6(8) + 8(4) - 12 - 4

p(2) = -64 + 48 + 32 - 12 - 4

p(2) = 0

Since the remainder is 0, this means that (x - 2) is a factor of p(x).

The correct answer is therefore R = 0, and yes, (x - 2) is a factor of p(x).

The correct answer for dividing [tex](a^{2n} - a^n - 6) by (a^n + 8)[/tex] is indeed:

[tex](a^n - 9) + (-78)/(a^n + 8).[/tex]

Let's divide the given polynomials:

[tex]\frac{a^{2n -a^n -6}}{a^n +8}[/tex]

Here's the breakdown of the solution:

Factoring: We can factor the numerator [tex](a^{2n} - a^n - 6)[/tex] using difference of squares:

[tex](a^{2n} - a^n - 6) = (a^n)^2 - (a^n) - 6 = (a^n + 2)(a^n - 3)[/tex]

Division: Now, we can divide the factored numerator by the denominator:

[tex][(a^n + 2)(a^n - 3)] / (a^n + 8) = (a^n + 2) - [(a^n + 8) * (a^n - 3)] / (a^n + 8) = (a^n + 2) - (a^n - 3) = a^n - 9[/tex]

Remainder: Since the degree of the numerator is less than the degree of the denominator, we get a non-zero remainder.

This remainder is obtained by dividing the constant term (-6) in the numerator by the constant term (8) in the denominator, resulting in [tex]-78/(a^n + 8).[/tex]

Therefore, the final answer is [tex](a^n - 9) + (-78)/(a^n + 8)[/tex], with a quotient of [tex](a^n - 9)[/tex] and a non-zero remainder of [tex](-78)/(a^n + 8).[/tex]

Answer:

( 85 x 6 ) - 69 would equal 441

Step-by-step explanation:

You do 85 x 6 then - 69 (:

Answer:

441

Step-by-step explanation:

first do the

(85x6) you get 510

510-69

441

Answer:

12

Step-by-step explanation:

There are 6 for tails. Each is 2. 6 x 2 =12

Answer:

The game costs 32 dollars total, we know this because if you divid 32 by 4 its 8 and . if you multiply 8 times 3 its 24

Step-by-step explanation:

The total cost of the game is $32, calculated using the concept of fractions in mathematics where the given $24 was considered as three-fourths of the total game cost.

The subject of the question involves the concept of fractions in mathematics. Here the information provided states that $24, which Ivanna has saved, represents three-fourths (or 3/4) of the total cost of the game. To find out the total cost of the game, we will consider the $24 as three parts, and we need to find out the value of one part (or one-fourth). So, we divide $24 by 3, which gives us $8. This $8 is one-fourth of the total game cost. Now, to get the total cost, we will multiply this one-fourth value ($8) by 4. So, the total cost of the game is $8 * 4 = $32.

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Answer: 13 units

The x value goes from x = 21 to x = 9, which is an x distance of 12 units (21-9 = 12)

The y distance is 5 units (16-11 = 5)

We have a right triangle with legs of 12 and 5. The hypotenuse is x

Use the pythagorean theorem to find x

a^2 + b^2 = c^2

5^2 + 12^2 = x^2

25 + 144 = x^2

169 = x^2

x^2 = 169

x = sqrt(169)

x = 13

The hypotenuse of this right triangle is 13 units, so this is the distance between the two points.

Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0 or (0,y))

You know m = 2, so you can plug it into the equation

y = 2x + b

To find "b", plug in the point (3, -2) into the equation

y = 2x + b

-2 = 2(3) + b

-2 = 6 + b

-8 = b

y = 2x - 8

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the slope m = 2 and the point (3, -2) → x = 3 and y = -2.

Substitute:

[tex]-2=(2)(3)+b[/tex]

[tex]-2=6+b[/tex]      subtract 6 from both sides

[tex]-8=b\to b=-8[/tex]

Substitute to the equation y = mx + b:

Answer:

He will make 16.50 per hour after his raise.

Step-by-step explanation:

15 x .10 = 1.50

15.00 + 1.50 = 16.50

Since we are given that ABC is congruent to JKL, then AB has to be equal to JK

therefore --- [tex]14x+7=5x+34[/tex]

Subtract 7 from both sides

[tex]14x=5x+27[/tex]

Subtract 5x from each side

[tex]9x=27[/tex]

Divide 9 on each side

[tex]x=3[/tex]

Since, We are asked to find the length of AB and JK

plug in 3 for x

[tex]5(3)+34=15+34=49[/tex]

The point-slope form of line:

[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-5, -6) and (2, 8). Substitute:

[tex]m=\dfrac{8-(-6)}{2-(-5)}=\dfrac{8+6}{2+5}=\dfrac{14}{7}=2\\\\y-(-6)=2(x-(-5))\\\\\boxed{y+6=2(x+5)}[/tex]

The correct equation is 14 + n = 8n, option A is correct.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Let the number is n,

8 times of the number = 8n

According to the condition, The sum of 14 and number n is 8 times the number,

Implies that,

14 + n = 8n

The correct equation is 14 + n = 8n.

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Answer:

2/3 - 1/4

=> taking L.C.M of the denominators we get,

=> 8/12-3/12

=> 5/12 is left with her,, ;)

HOPE THIS HELPS YOU...;)

It's an arithmetic sequence:

[tex]a_1=4;\ a_2=10;\ a_3=16;\ a_4=22;\ ...[/tex]

The explicit rule:

[tex]a_n=a_1+(n-1)d[/tex]

[tex]d=a_{n+1}-a_n\to d=a_2-a_1=a_3-a_2=a_4-a_3=...[/tex]

[tex]d=10-4=16-10=22-16=6[/tex]

Substitute:

[tex]f(n)=4+(n-1)(6)=4+6n-6=6n-2[/tex]

The explicit rule for the arithmetic sequence 4, 10, 16, 22, ... is aₙ = 4 + (n - 1) x 6, where aₙ is the nth term of the sequence.

The given sequence is arithmetic, which means that it increases by the same amount each time. To find an explicit rule for the sequence, we should determine the common difference and use the formula for an arithmetic sequence, which is aₙ = a₁ + (n - 1)d, where an is the nth term, a1 is the first term, n is the number of the term in the sequence, and d is the common difference between terms.

In the sequence 4, 10, 16, 22, ..., the first term a1 is 4, and the common difference is 6 (since 10 - 4 = 16 - 10 = 22 - 16 = 6). Therefore, the explicit rule for the nth term of the sequence is aₙ = 4 + (n - 1) x 6.

Answer:

Warning:

I think that these are correct, but don't make this your official source :)

7. B

8. D

9. B

I hope this helps :)

Answer:

x > 5

Step-by-step explanation:

isolate x by subtracting 7 from both sides

x > 12 - 7

x > 5

f(x) = 2x^2 - 4x - 3; opens up; vertex: (1, -5); y-intercept: (0, -3)

g(x) = -x^2 + x + 1; opens down; vertex: (0.5, 1.25); y-intercept: (0, 1)

h(x) = -2x^2 + 3x - 1; opens down; vertex: (0.75, 0.125); y-intercept: (0, -1)

m(x) = x^2 - 9; opens up; vertex: (0, -9); y-intercept: (0, -9)

n(x) = -3x^2 + 7; opens down; vertex: (0, 7); y-intercept: (0, 7)

I have attached an image of the functions and their graphs.

Hope this helps!

Answer:

[tex]f(x) = -x^2 +x +1[/tex]

Step-by-step explanation:

Quadratic equation is in the form of

[tex]f(x)= ax^2+bx+c[/tex]

When the value of 'a' is positive then the graph opens up

When the value of 'a' is negative  then the graph opens down

When the graph opens up then the vertex is minimum.

When the graph opens down then the vertex is maximum.

y intercept is the value of 'c'

[tex]f(x) = 2x^2 - 4x - 3[/tex], a=2 the graph opens up

[tex]f(x) = -x^2 +x +1[/tex], a=-1 the graph opens down. So the vertex is maximum. Y intercept is +1. y intercept is positive.

[tex]f(x) = -2x^2 +3x - 1[/tex], a=-2 the graph opens down. So the vertex is maximum. Y intercept is -1. y intercept is negative.

[tex]f(x) = 2x^2 - 4x - 3[/tex], a=2 the graph opens up