Which property is shown?

(c^4)^6 = c^24

Answer:

Step-by-step explanation:

it is given that Square contains a chord of of the circle equal to the radius thus from diagram

[tex]QR=chord =radius =R[/tex]

If Chord is equal to radius then triangle PQR is an equilateral Triangle

Thus [tex]QO=\frac{R}{2}=RO[/tex]

In triangle PQO applying Pythagoras theorem

[tex](PQ)^2=(PO)^2+(QO)^2[/tex]

[tex]PO=\sqrt{(PQ)^2-(QO)^2}[/tex]

[tex]PO=\sqrt{R^2-\frac{R^2}{4}}[/tex]

[tex]PO=\frac{\sqrt{3}}{2}R[/tex]

Thus length of Side of square [tex]=2PO=\sqrt{3}R[/tex]

Area of square[tex]=(\sqrt{3}R)^2=3R^2[/tex]

Area of Circle[tex]=\pi R^2[/tex]

Ratio of square to the circle[tex]=\frac{3R^2}{\pi R^2}=\frac{3}{\pi }[/tex]

Answer:

At time t = 0.408 sec diver will be at maximum height

Step-by-step explanation:

We have given equation of the height [tex]f(t)=-4.9t^2+4t+9[/tex]

We know that velocity is the rate of change of distance with respect to time

So [tex]v=\frac{df(t)}{dt}=\frac{df(-4.9t^2+4t+10)}{dt}=-9.8t+4+0=-9.8t+4[/tex]

At maximum height velocity will be zero

So [tex]-9.8t+4=0[/tex]

t = 0.408 sec

So at time t = 0.408 sec diver will be at maximum height

Answer:

The probability of given event = [tex]\frac{1}{15}[/tex]

Step-by-step explanation:

Ten slips of paper labeled from 1 to 10 are placed in a hat. The first slip of paper is not replaced before selecting the second slip of paper.

We have to find the probability of selecting a number less than 3 and then a number greater than 4.

Probability of an event = [tex]\frac{number of favourable events}{total number of events}[/tex]

The probability of selecting number less than 3 = [tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex]

The probability of selecting number greater than 4 = [tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex]

Total probability = [tex]\frac{1}{5}\times \frac{1}{3}[/tex] = [tex]\frac{1}{15}[/tex]

Answer with explanation:

A salesperson can use probability to get an idea of his business as using probability he can estimate his sale of the next month as well, based on the present and previous months sales.

It can help him sort issues or errors he is facing in his business as he will get a complete idea of his business using probability.

Moreover, he can forecast future sales by using a technique which involves assigning percentages or weighting benchmarks in sales cycle, so that he can estimate the expected revenue generated.

For example:

A supermarket sales person can assign probabilities to benchmarks in sale cycle as providing needs analysis (25 % probability), adding new product (50%Probability) , Remove a product ( 75 % probability), closing sale (100% Probability) . If these probabilities are large, then forecast model can be objective.

_____________________________________________________

So just like that by assigning probabilities to benchmarks, a sales person can forecast future sales

Answer:

Probability can be used to help a sales person forecast future sales best my showing the likelihood of a certain event occurring. The sales person can then plan around the events that are deemed to be the most likely to occur.

Explanation:

100%Attempt 1 Complete

Answer: b. $22.75

Step-by-step explanation:

Given : A large pizza with no toppings costs $14.00. A large pizza with 2 toppings costs $17.50.

Let x denotes the number of toppings and y be the cost of that pizza.

Then, [tex]y=mx+c[/tex] , m= cost per topping  and c= cost of pizza without any topping.

From the given information.

c= $14

Function of cost becomes = [tex]y=mx+14[/tex]

For x= 2 and y= 17.50, we have

[tex]17.50=m(2)+14[/tex]

tex]3.50=m(2)[/tex]  [Subtract 14 from both sides]

[tex]m=\$ 1.75[/tex]  [Divide both sides by 2]

For c= 14 and m =1.75  , our function becomes.

[tex]y=1.75x+14[/tex]

Now, for x= 5

[tex]y=1.75(5)+14=8.75+14=22.75[/tex]

Hence, the cost of a pizza with 5 toppings =  $22.75

The approximate height of the John Hancock replica is 2.33 meters.

Given that;

Willis Tower in Chicago is 1450 feet tall.

And, The John Hancock Center in Chicago is 1127 feet tall.

Let us assume that,

The approximate height of the John Hancock replica = x

Hence by using the definition of proportion, we get;

1450/3 = 1127/x

Cross multiplication,

1450x = 1127 × 3

x = 2.331

Round to the nearest hundredth;

x = 2.33

Thus, The approximate height of the John Hancock replica is 2.33 meters.

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Answer:

Option A - 10

Step-by-step explanation:

Given : There are 3 red chips and 2 blue chips. If they form a certain color pattern when arranged in a row, for example RBRRB.

To find : How many color patterns are possible?

Solution :

Total number of chips = 5

So, 5 chips can be arranged in 5! ways.

There are 3 red chips and 2 blue chips.

So, choosing 3 red chips in 3! ways

and choosing 2 blue chips in 2! ways.

As changing the places of similar chip will not create new pattern.

The total pattern is given by,

[tex]T=\frac{5!}{3!\times 2!}[/tex]

[tex]T=\frac{5\times 4\times 3!}{3!\times 2}[/tex]

[tex]T=10[/tex]

Therefore, color patterns are possible are 10.

Option A is correct.

Answer:

Step-by-step explanation:

1. Obviously, the figure is rotated CCW by 90°. If the center of rotation were the center of the figure, the image would be in the same quadrant as the pre-image. It is in the quadrant located 90° CCW from the original, so the center of rotation must not be the center of the image. That leaves one viable answer choice.

__

2. The line joining a point and its reflection is always perpendicular to (and bisected by) the line of reflection.

__

3. The theorem tells you a point on the perpendicular bisector is equidistant from the endpoints of the segment bisected. If the surveyor is to apply that theorem, he needs a point equidistant from the original two stakes.

__

4. The square has four (4) lines of symmetry: through the parallel side midpoints, and through opposite vertices. The corresponding lines would be ...

The appropriate choice is ...

  x + y = 4

Answer:

90k

Step-by-step explanation:

Taxable income is calculated by subtracting certain eligible deductions from gross income. In this scenario, a $10,000 investment in a 401k reduces the individual's taxable income from a $100,000 salary to $90,000.

When determining taxable income, it's important to subtract certain eligible deductions from the gross income. In this case, the individual earns a salary of $100,000 and invests $10,000 in a 401k plan. This investment is a pre-tax contribution, which means it lowers the amount of income that is subject to tax. Therefore, by investing $10,000 into a 401k, the individual's taxable income would be reduced to $90,000. So the correct answer is $90,000.

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Step-by-step explanation:

solve it through simultaneous equations

for fun guys : 10+6.5x=y

for game bank : 22+3.5x=y

10+6.5x=22+3.5x

3x=12

x=4

cost is same when game rentals =4

that cost= $36

For 4 games both the game stores charges the same, which is $36.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Fun Guys game rental store charges an annual fee of $10 plus $6.50 per game rented.

Let the number if games be x.

So, total cost =10+6.50x

The Game Bank charges an annual fee of $22 plus $3.50 per game.

So, total cost =22+3.50x

Game rentals will the cost be the same at both stores

Then, 10+6.50x=22+3.50x

6.50x-3.50x=22-10

3x=12

x=4

Total money fun Guys game rental store charges 10+6.50x=36

Therefore, the same money charged by both stores is $36.

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Answer:

The number of children attended the fair is 1520.

Step-by-step explanation:

We are given the following in the question:

Entry fee foe children = $1.50

Entry fee foe adult = $4.00

Total number of people in fair = 2200

Total money collected = $5000

Let x be the number of children and y be the number of adults in the fair.

Then, we can write the following equations:

[tex]x + y = 2200\\1.5x + 4y = 5000[/tex]

Solving the two equations, we have:

[tex]1.5x + 1.5y = 3300\\1.5x + 4y = 5000\\\Rightarrow 2.5y = 1700\\y = 680\\x = 2200-680 = 1520[/tex]

Thus, there were 1520 children and 680 adults in the fair.

Answer:

Simon's Age = 47

Marcie's Age = 11

Step-by-step explanation:

The question is to find Simon's age and Marcie's age.

Let Simon's age be x and Marcie's age be y

Simon is 3 years more than 4 times marcie, so we can write:

x = 4y + 3

Also,

Sum of their ages is 58, so we can write:

x + y = 58

or x = 58 - y

Now, we substitute this into 1st equation and solve for y first:

[tex]x = 4y + 3\\58-y = 4y + 3\\58-3=4y+y\\55=5y\\y=\frac{55}{5}\\y=11[/tex]

We know

x = 58 - y

so,

x = 58 - 11

x = 47

So,

Simon's Age = 47

Marcie's Age = 11

Answer:

∠5 = 55°

Step-by-step explanation:

Since l and m are parallel lines, then ∠5 and ∠1 are same- side interior angles and are supplementary, thus

∠1 + ∠5 = 180°, that is

125° + ∠5 = 180° ( subtract 125° from both sides )

∠5 = 55°

Answer:

55 degrees.

Step-by-step explanation:

m < 2 = 180 - 125 = 55 degrees (adjacent angles).

m < 5 = m < 2 (alternate angles).

Therefore m < 5 = m < 2  = 55 degrees.

Answer: 11

Step-by-step explanation:

Formula to find the sample size using sample standard deviation (s) :

[tex]n= (\dfrac{z^*\cdot s}{E})^2[/tex] , where z* = critical z-value and E = Margin of error.

As per given , we have

E= 7

s= 14 minutes

We know that the critical value for 90% confidence interval = z*=1.645

Then, the required sample size = [tex]n= (\dfrac{(1.645)\cdot (14)}{7})^2[/tex]

[tex]n= (1.645\cdot 2)^2=(3.29)^2=10.8241\approx11[/tex]

Hence, the required sample size = 11

To estimate the mean length of time it takes for buses to arrive and unload students, a sample size of 29 is needed to assert with 90% confidence that the sample mean is off by, at most, 7 minutes.

To determine the sample size needed to estimate the mean length of time it takes for buses to arrive and unload students, we can use the formula:

n = (Z * σ / E)^2

Where n is the required sample size, Z is the z-score corresponding to the desired confidence level (1.645 for 90% confidence), σ is the standard deviation (14 minutes), and E is the maximum error allowed (7 minutes).

Substituting the values into the formula:

n = (1.645 * 14 / 7)^2 = 5.3229^2 = 28.27.

Rounding up to the nearest whole number, the sample size needed is 29.

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Answer:

125%

Step-by-step explanation:

In this kind of question, we could choose any arbitrary value for the length of the side of the square.

Let’s say the square is 10m in length, a 50% increase in the length means we add 5 to the original length making the new length to be 15m.

The area of a square is L^2

The former area is 10 * 10 = 100 while the new area is 15 * 15 = 225

The percentage increase is calculated as follows:

We simply subtract the old from the new to yield 225 - 100 = 125

The percentage increase would now be :

125/100 * 100 = 125%

Answer:

C

Step-by-step explanation:

Since there is no relationship between the two , there exists no correlation between them.

This is simply because the effect of one is not felt on the other

Answer:

The equation to determine the number of days Margo has owned the plant is [tex]5+2.5x=65[/tex].

Step-by-step explanation:

Given:

Actual length of the tree = 5 cm

Current length of the tree = 65 cm

Per day growth Rate of plant = 2.5 cm

Let number of days she owned the plant be 'x'

Now We can say that,

Current length of the tree is equal to sum of Actual length of the tree and Per day growth Rate of plant multiplied by number of days she owned the plant.

Farming the above sentence in equation form we get;

[tex]5+2.5x=65[/tex]

Hence the equation to determine the number of days Margo has owned the plant is [tex]5+2.5x=65[/tex].

Answer:

Step-by-step explanation:

total marbles=5+8+4+3=20

when he is drawing without replacing means red marble is drawn from 20 marbles.

Blue marble is drawn from 19 marbles.

when he is drawing with replacing means he draws one red marble from 20 marbles.Then he replaces it and draws blue marble from 20 marbles also.

We have a better chance of drawing a red and then a blue marble without replacing the first marble.

It is the ratio that shows the likelihood of a particular event happening from when many other events could also happen.

The total number of marbles = 5 + 8 + 4 +3

= 20 marbles.

P( Drawing a red marble ) = 5/20

Now draw a blue marble:

Total marbles = 20

P( Drawing a blue marble ) = 8/20

Joint probability = 5/20 * 8/20

= 0.1

Total marbles = 19

P( Drawing a blue marble ) = 8/19

Joint probability = 5/20 * 8/19

= 0.105

This means that there is a higher probability of drawing a blue marble after a red marble without replacement.

Thus we have found that we have a better chance of drawing a red and then a blue marble without replacing the first marble.

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Step-by-step explanation:

Total number of trees = 300

Given that for every two pine trees there will be 3 maple trees.

Let 2t be the total number of pine trees.

Then total number of maple trees is 3t.

Total number of trees = 2 t + 3 t  = 5 t

That is

              5t = 300

                 t = 60

Total number of pine trees = 2t = 2 x 60 = 120

Total number of maple trees = 3t = 3 x 60 = 180

There are 120 pine trees and 180 maple trees.

Answer:

11 sections

Step-by-step explanation:

This problem is called the circle cutting or pancake cutting problem.

Let the number of cuts or divisions by straight line = n

With this information it is possible to calculate any number of pieces or section a circle will be divided into what straight lines are drawn (cut) across the circle.

When a straight line is drawn across the circle, it divides the circle into 2 sections or regions. The nth straight lines will divide the circle into n new sections or regions, so the progression is;

         f(1) = 2

         f(2) = 2 + f(1)

         f(3) = 3 + f(2)

         .

         .

         .

         f(n) = n + f(n-1)

Therefore,

         f(n) = n + [(n-1) + f(n-2)}

               = n + n-1 + ... + 2 + f(1)

               = f(1) + ∑[tex]_{i = 2}^{n}[/tex]i

               = [tex]2 + \frac{1}{2} (n + 2) (n - 1)[/tex]

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

When n = 4

              =  [tex]\frac{1}{2}(4^{2} + 4 + 2)[/tex]

              = 22/2

              = 11 sections

Answer:

It will take 80 minutes!

Step-by-step explanation:

From the table we see that in 5 minutes we get 325 copies.

This means in one minute we get [tex]$ \frac{325}{5} $[/tex] = 65 copies.

So, assume we get 5200 copies in 'x' minutes.

So, we form the equation.

i.e., 65x = 5200

⇒ x = 80

This means it would take 80 minutes to get 5200 copies.

Answer:

A. 67°

Step-by-step explanation:

Since AC is tangent to the circle, ∠C must be 90°.

You know all angles of a triangle should add up to 180°, so with A given as 23°, that leaves 180-90-23 = 67° for O.

Answer:

  1

Step-by-step explanation:

The centroid is the average of the coordinates of the three vertices. If you know two vertices (A and B) and the centroid (Q), then the third vertex (C) is ...

  C = 3Q -A -B

It has only one possible location.

Given the coordinates of two vertices and the centroid, the third vertex can be located by solving a system of linear equations derived from the centroid's coordinates. This results in only one possible location for the third vertex.

To find the number of possible locations for the third vertex of a triangle given two vertices and the centroid, we need to use the properties of the centroid. The centroid of a triangle is the point where the three medians intersect and it is located 1/3 of the way from each side towards the opposite vertex.

If we denote the vertices of the triangle as (x1, y1), (x2, y2), and (x3, y3), and the centroid as (Gx, Gy), the coordinates of the centroid can be calculated as:

Gx = (x1 + x2 + x3) / 3

Gy = (y1 + y2 + y3) / 3

Since we know the coordinates of the centroid (Gx, Gy) and two vertices (x1, y1), (x2, y2), we can set up the following system of equations:

Solving these equations for x3 and y3 gives:

x3 = 3Gx - x1 - x2

y3 = 3Gy - y1 - y2

Therefore, there is only one possible location for the third vertex given the two vertices and the centroid.

In this question, you're solving for d.

Solve for d:

5(-6 - 3d) = 3(8+7d)

Use the distributive property:

-30 - 15d = 3(8+7d)

-30 - 15d = 24 + 21d

Add 30 to both sides:

-15d = 54 + 21d

Subtract 21d from both sides

-36d = 54

Divide both sides by -36

d = -3/2

Answer:

d = -3/2 or -1.5

Answer:

d = -1.5

Step-by-step explanation:

5 (- 6 - 3d) = 3 (8 + 7d)

- 30 - 15d = 24 + 21d

- 15d - 21d = 24 + 30

- 36d = 54

- d = 54/36

- d = 1.5

d = -1.5

Answer:

Option C.

Step-by-step explanation:

Given information: In triangle ABC, ST║AC, SB=10 ft, BT=9 ft and CT=2.7 ft.

Triangle proportionality theorem: If a line segment parallel to a side of a triangle then the line segments divides the remaining sides proportionally.

Using triangle proportionality theorem we get

[tex]\dfrac{SA}{SB}=\dfrac{CT}{BT}[/tex]

[tex]\dfrac{SA}{10}=\dfrac{2.7}{9}[/tex]

On cross multiplication we get

[tex]9\times SA=2.7\times 10[/tex]

[tex]9SA=27[/tex]

Divide both sides by 9.

[tex]SA=3[/tex]

The length of SA is 3ft.

Therefore, the correct option is C.

Answer: C on edg.

Step-by-step explanation:

Answer:

612 feet

Step-by-step explanation:

LA is located at 330 feet ABOVE SEA LEVEL

Death Valley is located 282 feet BELOW SEA LEVEL

We let the sea level be at 0 (consider a number line).

So,

LA would be at +330 feet

and

Death Valley would be at -282 feet

The elevation change between the two would be the difference:

330 - (-282) = 330 + 282 = 612 feet

The difference in elevation = 612 feet

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.

3a+7=4a

a=7

2b=b+11

b=11

2.

y=101°

101+x=180

x=180-101=79°

3.

x+6=11

x=11-6=5

y-7=10

y=10+7=17

Answer:

It costs Lauren 14 dollars to ride 8 miles

Step-by-step explanation:

The equation for the price of the taxi ride is

y= 1.5x+2

where y is the price, and x is the number of miles driven. Lauren needs to ride 8 miles, so the price of her taxi ride is

y= 1.5*8 +2 =12+2=14

Answer:

Time for the object to get h(max)    s = 1.1875 sec

h (max)  = 1272.57 feet

Down time for the object to hit the ground   =  4.25 sec

Step-by-step explanation:

The relation

h(s)  =  -  16*s²  +  38* s  + 1250    (1)

Is equivalent to the equation for vertical shot

Δh = V(i)*t  -  1/2g*t²  (in this case we don´t have independent term since the shot is from ground level. We can see in (1), the independent term is 1250 feet ( the height of the empire state building), the starting point of the movement.

The description of the movement is:

V(s)  =  V(i)  - g*s     ⇒  V(s) = 38 - 32*s

At h(max)    V(s)  =  0      38/32  = s

So the maximum height is at  s = t = 1.1875 sec

The time for the object to pass for starting point is the same

t  =  1.1875 sec

h(max) is

h(max)  = - 16* (1.1875)² +  38 (1.1875) + 1250

h(max)  =  -  22,56  +  45.13  +  1250

h(max)  =  1272.57 feet

Time for the object to hit the ground is

h(s)  =  - 1250 feet

-1250  =  - 16 s² + 38*s  + 1250

-16s² +  38s  =  0

s ( -16s + 38 )  =  0

First solution for that second degree equation  is x = 0 which we dismiss

then  

( -16s + 38 )  =  0    ⇒ 16s   =  38     s  =  38/16

s =  2.375 sec    and  we have to add time between h (max) and to get to starting point  ( 1. 1875 sec)

total time is  = 2.375 + 1.875

Total time  =  4.25 sec