on a standard 6-sided die, what is the probability of rolling a 5?

a) Substituting in n = 2,

[tex]\frac{3(2)^{2}}{2}=6[/tex]

b) Substituting in n = 5,

[tex]\frac{3(5)^{2}}{2}=\frac{75}{2}[/tex]

c) Setting the nth term to be greater than 50,

[tex]\frac{3n^{2}}{2}>50 \\ \\ n^{2} >\frac{100}{3} \\ \\ n>\frac{10}{\sqrt{3}} \\ \\ \lceil n \rceil = 6[/tex]

Marry rate of investment is 4%.

Lets solve it through simple steps,

30% 0f $200,000 = $60,000

$200,000-$60,000 = $140,000

Rate 1.5%

Rate 4% = (140,000-x)

Interest earned = $4,350

1.5x+4(150,000-x)=4350*100

1.5x+600,000-4x=435,000

1.5x-4x=435,000-600,000

-2.5x=-165,000 /-2.5

x=66000

$ 66,000  1.5%

Balance = $74,000 at  4%

Hence the rate is 4%

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The mass of the same nickel which is 5 grams in milligrams is 5,000 milligram.

Weight of a nickel = 5 gram

Weight of same nickel in milligram = 5 grams × 1000

= 5,000 milligram

Therefore, the mass of the same nickel is 5,000 milligram

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The distance at which pumpkins are the same height.

What do you mean by X and Y coordinates?

The X and Y coordinates are an address that help locate a point in two dimensions of space. The coordinates (x, y) are used to represent any point in the coordinate plane. The x value indicates the point's position in regard to the x-axis, and the y value indicates its position in relation to the y-axis.

Both equations' graphs would be at an intersection, which would indicate that their x and y coordinates are identical. The same y coordinate would indicate being at the same height at that precise distance since y refers to the pumpkin's height.

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Answer:

D). the horizontal distance of the pumpkins from the launch site when their heights are the same

Step-by-step explanation:

I took the flipping test nickle

Answer:

11.  [tex]\frac{\sqrt{2} }{2}[/tex]

12. [tex]\sqrt{3}[/tex]

13. [tex]\frac{\sqrt{3} }{2}[/tex]

14. [tex]\frac{\sqrt{3} }{3}[/tex]

15. [tex]\sqrt{2}[/tex]

16. [tex]\frac{2\sqrt{3} }{3}[/tex]  

Step-by-step explanation:

Hope this helps

The response option that demonstrates why the three segments cannot be combined to form a triangle is AC + CB< AB.

According to the triangle inequality, the length of any two sides of a triangle added together must be longer than the length of the third side. Since a straight line is the shortest distance between two places, this conclusion follows. If the triangle isn't degenerate, the inequality is strict (meaning it has a non-zero area).

Since the length of any two sides of a triangle added together is longer than the length of the third side, it follows from the triangle inequalities theorem that this is the case.

As a result, the necessary inequality is AC + CB AB because the sum of sides AC + CB is less than AB.

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I understand that question you are looking for is:

Which inequality can be used to explain why these three segments cannot be used to construct a triangle?

A. AC + AB > CB

B. AC + CB < AB

C. AC + CB > AB

D. AC + AB < CB

The value of x is 7/2

The equation is given as:

x/3 - 3/4 = 5/12

Multiply through by 12

4x - 9 = 5

Add 9 to both sides

4x = 14

Divide by 4

x = 7/2

Hence, the value of x is 7/2

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Answer:

4

Step-by-step explanation:

[tex] {3}^{2} + {x}^{2} = {5}^{2} \\ \\ 9 + {x}^{2} = 25 \\ \\ {x}^{2} = 16 \\ \\ x = 4[/tex]

Answer: B

Step-by-step explanation:

The product of height and width is constant.

If we take the point (0.5,1), we get the product to be 0.5.

The value of f from the given expression is 3

Given the expression below

cos(22f-1) = sin(7f+4),

This can also be expressed

cos(22f-1) = cos(90-7f-4)

cos(22f-1) = cos(86-7f)

22f - 1 = 86 - 7f

Collect the like terms

22f+7f = 86 + 1

29f = 87

f = 3

Hence the value of f from the given expression is 3

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Answer:

I think that this answer is 22

Andy to get to Willie's house = 15 ways

Andy to get to Willie's house = 45 ways

From the information given, we have that from

Andy's house to Billy's  hometown = 3 roads

Billy's hometown to Willies house = 5 ways

To travel from Andy's house to Willies house, we should multiply the number of ways

= 3 × 5

= 15 ways

Dan's ranch to Andy's house = 1 road

To Willie's house = 2 roads

For Andy to get to Willie's house, we have;

= 3 × 15

= 45 ways

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Answer: the maximum is (-2,5 )and the equation for the axis of symmetry is  x = -2

Explanation if you want:

for the min and max:  when a quadratic has a maximum point, that is the largest point that it will ever be at.  When it has a minimum, that is the smallest.

for the axis of symmetry: basically, this is the line that splits the graph into two equal parts.

there u go

Step-by-step explanation:

z = (specific score - mean) / standard deviation

in our case

z = (105 - 101)/4.2 = 4/4.2 = 0.952380952... ≈ 0.95

as z-tables usually round the z-scores to hundredths.

The z-score of the normal distribution is 0.95.

A probability distribution which is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution.

It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution shows as a "bell curve" on a graph.

Z-score: A Z-score is just a metric that quantifies how closely a value relates to a mean of a set of values. Standard deviations from of the mean are used to measure Z-score.

A Z-score of zero means the data point is actually score is the same as the mean score.

The formula for z-score is-

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

Z = standard score

x  is observed value = 105

[tex]\mu[/tex] is mean of the sample 101.

[tex]\sigma[/tex] is standard deviation of the sample 4.2.

Substitute all the values in the z-score formula;

z = ( 105 - 101)/4.2

z = 0.9523..

z  = 0.95

Therefore, the z-score the given normal distribution is  0.95.

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The value of angle CFE in the diagram attached is 51 degrees.

An equation is an expression that shows the relationship between two or more numbers and variables.

From the diagram:

∠AFB = ∠CFD; ∠BFC = ∠DFE

Hence:

∠AFC = ∠CFE

∠AFD = ∠AFC + ∠CFD = ∠AFC + ∠AFB

90 = ∠AFC + 31

∠AFC = 51° = ∠CFE

The value of angle CFE in the diagram attached is 51 degrees.

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I got you, bro

Answer:

(x+4)(x+18)

Explanation

Let's factor x2+22x+72

x2+22x+72

The middle number is 22 and the last number is 72.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get 22

Multiply together to get 72

Can you think of the two numbers?

Try 4 and 18:

4+18 = 22

4*18 = 72

Fill in the blanks in

(x+_)(x+_)

with 4 and 18 to get...

(x+4)(x+18)

Answer:

(x+4)(x+18)

Answer:

(x+4)(x+18)

Step-by-step explanation:

Using the factorisation method :

We need 2 numbers that multiply to give +72 and add to give +22 :

To find these numbers we write out all the factors of 72 :

1, 72

2 , 36

3 , 24

4 , 18    ----> These must be the numbers as 4+18 = 22

Now we split +22x into +4x and +18x :

x² + 4x + 18x + 72

Factor the first 2 terms together and the last two terms :

x(x+4) + 18(x+4)

Keep 1 bracket and terms outside the brackets collect them into one:

(x+4)(x+18)

This is our final answer

Hope this helped and have a good day

The measure of n of the sector with the given area is: 100°

The area of a sector of a circle = ∅/360 × πr².

We are given that:

Area of the sector = 40π

Radius (r) = 12 units

∅ = n°

Plug in the values and solve for n

40π = n/360 × π(12²)

40π = n/360 × π144

Divide both sides by 144π

40π/144π = n/360 × 144π/144π

40/144 = n/360

40(360) = n(144)

14,400/144 = n

n = 100°

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The first equation is 5x² - 20x + 27 and the second equation will be y = 3x² + 6x + 15.

It should be noted that an equation simply means a formula that's used to express the equality of two expressions that are given in Mathematics.

It should be noted that before solving the equations, it's important to expand the functions that are squared and then solve accordingly. This will be illustrated below.

The first equation that's given is:

y = 5(x - 2)² + 7

= 5(x - 2)(x - 2) + 7

= 5(x² - 2x - 2x + 4) + 7

= 5(x² - 4x + 4) + 7

= 5x² - 20x + 20 + 7

= 5x² - 20x + 27

The second equation given is illustrated as:

y = 3(x + 1)² + 12

y = 3(x + 1)(x + 1) + 12

y = 3(x² + 2x + 1) + 12

y = 3x² + 6x + 3 + 12

y = 3x² + 6x + 15

In conclusion, writing the equations in form of y = ax² + bx + c will be y = 5x² - 20x + 27 and y = 3x² + 6x + 15.

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Answer:

0.0000000006

Step-by-step explanation:

0.6 * (0.1)^9 = 0.0000000006

Answer:

1. edge

2. cone

3. decompose

4. cubic units

5. cylinder

6. cube

7. composite figure

8. base

9. area

10. dimensions

Answer:

2/3 is the fraction of students who are boys.

Step-by-step explanation:

First of all, a fraction consists of two parts: The denominator and the numerator. The denominator is the whole, while the number is a part of the whole (and sometimes above).

1. Since in your question, there are 24 students in total in the class, the denominator will be 24.

2. You said that 16 of them are boys, so 16 is the numerator.

3. In a fraction, it will be 16/24.

4. 16/24 can be simplified into 2/3 since both 16 and 24 can be divided by 8.

So our final answer is 2/3.

Can send helicopter 3 but not helicopter 1 and 2.

What is distance formula?

Consider two points (x1, y1) and (x2, y2) in the two-dimension, then the distance between these two points is given by,

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

We will solve given problem as shown below:

Let fire have coordinate F (-3,-5)

Let Helicopter 1 have coordinate H1(1,4)

Let Helicopter 2 have coordinate H2(-2,3)

Let Helicopter 1 have coordinate H3(4, -2)

A. Distance between helicopter 1 and fire

[tex]=\sqrt{(1-(-3))^2+(4-(-5))^2}[/tex]

[tex]=\sqrt{16+81}[/tex]

[tex]=\sqrt{97}=9.8[/tex]

No, cannot send helicopter 1

B. Distance between helicopter 2 and fire

[tex]=\sqrt{(-3-(-2))^2+(-5-3)^2}[/tex]

[tex]=\sqrt{1+64}[/tex]

[tex]=\sqrt{65}=8.06[/tex]

No, cannot send helicopter 2

Distance between helicopter 3 and fire

[tex]=\sqrt{(4-(-3))^2+(-2-(-5))^2}[/tex]

[tex]=\sqrt{49+9}[/tex]

[tex]=\sqrt{58}=7.6[/tex]

Yes, can send helicopter 3

Hence, can send helicopter 3 but not helicopter 1 and 2.

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Answer:

[tex]\sf 2^{(n+1)}[/tex]

Step-by-step explanation:

Explicit formula is used to represent all the terms of the geometric sequence using a single formula.

  [tex]\sf \boxed{\bf t_n=ar^{(n-1)}}[/tex]

Here, a is the first term.

r is the common ratio.

r = second term ÷ first term

4, 8,16,32,64,.....

    a = 4

    r = 8 ÷4 = 2

[tex]\sf t_n =4*2^{(n-1)}[/tex]

    [tex]\sf = 4*2^n * 2^{(-1)}\\\\ = 4*2^n*\dfrac{1}{2}\\\\ = 2*2^n[/tex]

   [tex]\sf = 2^{(n+1)}[/tex]

25,110.51 is the total amount accrued over the course of 4.5 years, principle plus interest, on a principal of 16,100.00.

We may employ the compound interest future value formula provided by:

[tex]A=P(1+r/n)^{nt}[/tex]

Where A is the final amount, P stands for the current value,

r=interest rate, n represents how many times interest is compounded annually, and t represents the number of years.

In this case,

P= 16100

r = 10%

t = 4 years and 6 months=4.5 years

n=4

So, A=[tex]16100(1+0.1/4)^{4*4.5}[/tex]

A= [tex]16100(1+0.025)^{18}[/tex]

A= 25110.51

So, 25,110.51 is the total amount accrued over the course of 4.5 years, principle plus interest, on a principal of 16,100.00 at a rate of 10 percent per year compounded four times each year.

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The interpretation of the point of intersection of the curves is (c) they give a solution to the equation 5x - x^2 = 3x - 0.5x^2

The graph of the two functions alongside their equations are the given parameters of this question

The functions are given as:

f(x) = 5x - x^2

g(x) = 3x - 0.5x^2

When the graphs of two curves or lines intersect on a coordinate plane, it means that the point of intersection represents where the graphs have equal value

In this case, it represents

f(x) = g(x)

Substitute the known values in the above equation

5x - x^2 = 3x - 0.5x^2

So, the interpretation of the point of intersection of the curves is (c) they give a solution to the equation 5x - x^2 = 3x - 0.5x^2

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The solution to the inequality is x > -3 or x < -13

The inequality is given as:

9|x + 8| > 45

Divide through  by 5

|x + 8| > 5

Split the inequality

x + 8 > 5 or x + 8 < -5

Solve for x

x > -3 or x < -13

Hence, the solution to the inequality is x > -3 or x < -13

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The linear function that goes through the points (2,-4) and (-4,2) is:

y = -x + 2.

A linear function is modeled by:

y = mx + b

In which:

A linear function going through the points (2,-4) and (-4,2) would intersect the parabola at these points, hence these points would be the solution for the system of equations.

The slope of the line is:

m = (-4 - 2)/(2 - (-4)) = -1.

The line goes through point (2,-4), that is, when x = 2, y = -4, which we use to find the y-intercept b.

y = -x + b

-4 = -2 + b

b = -2.

Hence the equation is:

y = -x + 2.

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Answer:

60 and 80.

Step-by-step explanation:

If the numbers are x and y:

x + y = 140

x - y = 20     Adding:

2x = 160

x = 80

So y =  140 - 80 = 60.

Answer:

80 and 60

Step-by-step explanation:

Expressing the Word Problem mathematically.

Let the first number be X.

Let the second number be Y.

From the question,

[tex]x + y = 140 - - - - - (1) \\ x - y = 20 - - - - - (2) \\ From \: equation \: (2) \\ x = 20 + y - - - - - - (3) \\ Substitute \: equation \: 3 \: into \: 1 \\ 20 + y + y = 140 \\ 20 + 2y = 140 \\ 2y = 140 - 20 \\ 2y = 120 \\ Dividing \: bothsides \: by \: 2 \\ \frac{2y}{2} = \frac{120}{2} \\ y = 60 \\ Substitute \: y \: into \: quation \: 3 \\ x = 20 + 60 \\ x = 80 \\ Therefore, \: x = 80 \: and \: y = 60[/tex]

The two numbers are 80 and 60