What is the maximum volume of a square pyramid that can fit into a cube with a side length of 30cm ?

The central angle is approximately 51.6 degrees.

To solve this problem, we can use the formula for arc length of a circle:

arc length = θ × r

where θ is the central angle in radians, and r is the radius of the circle.

We know that the arc length is 4.5 feet and the radius is 5 feet. So we can rearrange the formula to solve for θ:

θ = arc length / r

θ = 4.5 / 5

θ = 0.9 radians

To find the central angle in degrees, we can convert radians to degrees by multiplying by 180/π:

θ = 0.9 × (180/π)

θ ≈ 51.6 degrees

Therefore, the central angle is approximately 51.6 degrees.

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Using probability, we can find probability of the random variable, x falling in the shaded region as to be 5/8.

Probability is the ratio of favourable outcomes to all other potential outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The following formula can be used to determine an event's probability.

Positive Outcomes/Total Results = x/n = Probability(Event)

Let's look at a simple example to better understand probability. Imagine that we need to predict whether it will rain or not. The right response to this question is "Yes" or "No." Whether it rains or not is uncertain. Probability is used to predict the outcomes when tossing coins, rolling dice, or drawing cards from a deck of cards.

Here in the question,

Total region = 8.

Shaded region = 5

So, probability of falling in the shaded region = 5/8

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The circumference of the circle with a diameter of 10m is 31.4m, using 3.14 as the value of pi and including the correct unit in the answer.

The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter. Substituting the given value of the diameter, we get C = 3.14 x 10m = 31.4m as the circumference of the circle.

Since the value of pi is irrational, it cannot be expressed as a finite decimal or fraction, so we use an approximation, such as 3.14, to calculate the circumference. It is important to include the correct unit, which is meters in this case, in the answer to indicate the quantity being measured. Therefore, the circumference of the circle is 31.4m.

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The amount of levels left at the end is 105.

There is a total of 840 levels in the game.

On the first day she completes 1/6 of the total, so she completes:

840/6 = 140

The remaining is 840 - 140 = 700

Then she completes 1/4 of that, which is:

(1/4)*700 = 175

So now she has left 700 - 175 = 525

Then she completes 4/5, so she does:

(4/5)*525 = 420

The amount left is: 525 - 420 = 105

The correct option is B.

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Your chances of winning a raffle with one ticket out of 325 sold is approximately 0.31% or 1 in 325.

The probability of winning a raffle is determined by dividing the number of tickets you have by the total number of tickets sold. In this case, since there are 325 tickets sold and you have only one ticket, your chances of winning are 1 in 325, which is equivalent to a probability of approximately 0.31%.

This means that you have a very low chance of winning, but it's not impossible. However, the more tickets you have, the greater your chances of winning will be. It's important to remember that winning a raffle is a matter of luck and chance, and not a guaranteed outcome.

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Answer:

2*Ab    Or AC

Step-by-step explanation:

No detail in question

The area under the curve at the given points is 3.758 sq.units.

The area under the curve at the given points is calculated as follows;

y = -3/x ; (-7, -2)

To find the area under the curve y = -3/x between x = -7 and x = -2, we need to integrate the function from x = -7 to x = -2.

∫[-7,-2] (-3/x) dx

= [-3 ln|x|]_(-7)^(-2)

= [-3 ln|-2| - (-3 ln|-7|)]

= [-3 ln(2) + 3 ln(7)]

= 3 ln(7/2)

= 3.758 sq.units

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In the given question, if y, p and q vary jointly and p is 14 when y and q are equal to 2 and  p and y are equal to 7, we get q is equal to 14 using the  joint variation formula.

To solve this problem, we need to use the formula for joint variation, which states that y, p, and q vary jointly if there exists a constant k such that ypk = kq.

In this case, we know that when y=2 and q=2, p=14. So we can set up the equation: 2*14*k = 2kq

Simplifying this, we get: 28k = 2kq
Dividing both sides by 2k, we get: 14 = q
So when p=7 and y=7, we can use the same equation: 7*14*k = 7kq

Simplifying this, we get: 98k = 7kq
Dividing both sides by 7k, we get: q = 14

Therefore, when p and y are equal to 7, q is equal to 14.

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Answer:

5.09

Step-by-step explanation:

You eliminate the decimal by multiplying both sides by 10:

10(.25x+0.5)=10(0.61+0.14x)

Then you get your new equation and combine like terms:

25x+5=61+14x

-14x           -14x

11x+5=61

11x+5=61

    -5  -5

11x=61

Then finally you do 61/11 which gets you around 5.09 if you round to 2 decimal places.

Answer:

c

Step-by-step explanation:

a. The area of Priya's scalp is ≈ [tex]615.75 cm^2[/tex]. b. Priya has approximately 92,363 strands of hair on her head.

a. The area of Priya's scalp can be estimated using the formula for the area of a circle, which is A = π[tex]r^2[/tex] ,where r is the radius (half the diameter) of the circle. Since Priya's diameter is 28cm, her radius would be 14cm. So, the area of her scalp would be:

A = π[tex](14cm)^2[/tex]
A ≈[tex]615.75 cm^2[/tex]

b. To estimate how many strands of hair Priya has on her head, we can multiply the number of hairs per square cm by the total area of her scalp. So, if Priya has approximately 150 hairs per square cm and her scalp has an estimated area of 615.75 cm^2, then:

Total number of hairs ≈ [tex]150 hairs/cm^2 * 615.75 cm^2[/tex]
Total number of hairs ≈ 92,362.5 hairs

Therefore, we can estimate that Priya has approximately 92,363 strands of hair on her head.

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The 95% confidence interval for the U.S. Cesarean delivery rate for this year is approximately (0.3314, 0.4886) or 33.14% to 48.86%.

To estimate the U.S. Cesarean delivery rate for this year with 95% confidence using the provided information, we can construct a confidence interval for the population proportion.

Given:

Population proportion estimates from the NVS Report for 2011: p = 0.328 (32.8%)

Sample size: n = 100

Number of C-sections in the sample: x = 41

First, we need to check if a normal model is appropriate for the sample proportion. For this, we can verify if the sample size is sufficiently large and if both np and n(1-p) are greater than 10.

np = 100 * 0.328 = 32.8

n(1-p) = 100 * (1 - 0.328) ≈ 67.2

Since both np and n(1-p) are greater than 10, we can assume that the conditions for a normal model are met.

Now, we can calculate the confidence interval using the sample proportion and the critical value corresponding to a 95% confidence level.

Sample proportion (p-hat) = [tex]\frac{x }{ n}[/tex] =[tex]\frac{ 41 }{ 100 }[/tex]= 0.41

The critical value for a 95% confidence level can be obtained from a standard normal distribution or a Z-table. In this case, the critical value is approximately 1.96.

The margin of error (E) can be calculated as:

E = Z * [tex]\sqrt((\frac{p-hat * (1 - p-hat))} { n})[/tex]

E = 1.96 * [tex]\sqrt((\frac{0.41 * (1 - 0.41))}{ 100)}[/tex]

E ≈ 0.0786

Finally, we can construct the confidence interval by subtracting and adding the margin of error from the sample proportion.

Confidence interval = p-hat ± E

Confidence interval = 0.41 ± 0.0786

Therefore, the 95% confidence interval for the U.S. Cesarean delivery rate for this year is approximately (0.3314, 0.4886) or 33.14% to 48.86%.

Note: It's important to consider that this calculation assumes the sample is representative of the U.S. population and that the conditions for a normal model are satisfied. Additionally, the estimate from the NVS Report for 2011 is used as the population proportion.

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The number of bricks, rounded to the nearest whole number, needed to complete the wall is 3,456 bricks.

To determine the number of bricks needed to complete a wall, you will need to know the dimensions of the wall and the size of the bricks being used. Let's say the wall is 10 feet high and 20 feet long, and the bricks being used are standard-sized bricks measuring 2.25 inches by 3.75 inches.

First, you'll need to convert the wall's dimensions from feet to inches. The wall is 120 inches high (10 feet x 12 inches per foot) and 240 inches long (20 feet x 12 inches per foot).

Next, you'll need to determine the number of bricks needed for each row. Assuming a standard brick orientation, you'll need to divide the length of the wall (240 inches) by the length of the brick (3.75 inches). This gives you 64 bricks per row (240/3.75).

To determine the number of rows needed, divide the height of the wall (120 inches) by the height of the brick (2.25 inches). This gives you 53.3 rows. Since you can't have a fraction of a row, round up to 54 rows.

To determine the total number of bricks needed, multiply the number of bricks per row (64) by the number of rows (54). This gives you 3,456 bricks. Rounded to the nearest whole number, the wall will need approximately 3,456 bricks to complete.

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After the discount and the tax, the amount that Roger pays is $45.41

We know that Roger purchased a pair of pants for 34.50 and a new a new for 12.00 he had a 10% discount on his total purchased and paid 8.5% sales tax, then the total cost before the discount and tax is:

C = 12.00 + 34.50 = 46.50

Now we apply the discount and the tax (as factors in a product) to get:

C' = 46.50*(1 - 0.1)*(1 + 0.085) = 45.41

That is the amouint that Roger pays for the two items.

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Answer:

Step-by-step explanation:

cos²x =3sin²x                     subtract both sides by 3sin²x

cos²x - 3sin²x = 0               use identity  cos²x+sin²x=1  => cos²x = 1-sin²x

                                           substitute in

(1-sin²x)-3sin²x = 0             combine like terms

1-4sin²x=0                           factor using difference of squares rule

(1-2sin x)(1+2sin x)=0          set each equal to 0

(1-2sin x)=0                                        (1+2sin x)=0

-2sinx = -1                                               2sinx= -1

sinx=1/2                                                    sinx =-1/2

Think of the unit circle.  When is sin x = ±1/2

at [tex]\pi /6, 5\pi /6, 7\pi /6, 11\pi /6[/tex]

This is from 0<x<2[tex]\pi[/tex]

The probability that the outcome is all heads if at least one coin shows a head is 8/49.

To solve these problems, we'll use the basic principles of probability.

The probability of an event K (at least one head) can be calculated by subtracting the probability of the complement of K (no heads) from 1.

Since the coins can either show all heads or not, the complement of K is the event of no heads, which is denoted as T (tails for all coins). Therefore, we have:

P(K) = 1 - P(T)

Each coin toss is independent, and the probability of getting tails on a single toss is 1/2. Since there are three coins tossed independently, we multiply the probabilities together:

P(T) = ([tex]\frac{1}{2}[/tex]) * ([tex]\frac{1}{2}[/tex]) * ([tex]\frac{1}{2}[/tex]) = [tex]\frac{1}{8}[/tex]

Substituting this into the equation for P(K):

P(K) = 1 - P(T) = 1 - [tex]\frac{1}{8}[/tex] = [tex]\frac{7}{8}[/tex]

So, the probability of event K (at least one head) is [tex]\frac{7}{8}[/tex].

The probability that the outcome is all heads if at least one coin shows a head can be calculated using conditional probability. We want to find P(H | K), which represents the probability of event H (all heads) given event K (at least one head).

The formula for conditional probability is:

P(H | K) = [tex]\frac{P(H \∩ K) }{ P(K)}[/tex]

To find P(H∩K), we need to determine the probability of the intersection of events H and K (i.e., the probability of getting all heads and at least one head).

Since H is a subset of K (if all coins show heads, then at least one head is shown), we have:

P(H∩K) = P(H)

Therefore, P(H∩K) is the same as P(H). According to the problem, P(H) = [tex]\frac{1}{7}[/tex].

Now, substituting P(H∩K) = P(H) and P(K) = [tex]\frac{7}{8}[/tex] into the conditional probability formula:

P(H | K) = [tex]\frac{P(H\∩K) }{ P(K)}[/tex] = ([tex]\frac{1}{7}[/tex]) / ([tex]\frac{7}{8}[/tex]) = ([tex]\frac{1}{7}[/tex]) * ([tex]\frac{8}{7}[/tex]) = [tex]\frac{8}{49}[/tex]

So, the probability that the outcome is all heads if at least one coin shows a head is [tex]\frac{8}{49}[/tex].

To summarize:

P(K) = [tex]\frac{7}{8}[/tex]

P(H | K) = [tex]\frac{8}{49}[/tex]

P(H∩K) = [tex]\frac{1}{7}[/tex]

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Answer is the probability that 144 furnace repair bills have a mean cost between 264 dollars and 266 dollars is approximately 0.2881 or 28.81%

The distribution of the sample mean of furnace repair bills will also be normally distributed with a mean of 264 dollars and a standard deviation of 30/sqrt(144) = 2.5 dollars (by the Central Limit Theorem).

We need to find the probability that the sample mean falls between 264 and 266 dollars:

z1 = (264 - 264) / 2.5 = 0

z2 = (266 - 264) / 2.5 = 0.8

Using a standard normal distribution table or calculator, we can find the area under the curve between z1 and z2:

P(0 ≤ Z ≤ 0.8) = 0.2881

Therefore, the probability that 144 furnace repair bills have a mean cost between 264 dollars and 266 dollars is approximately 0.2881 or 28.81%.

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Answer:

12

Step-by-step explanation:

-3(b - 5) + 7a - (9 - a) ^6                   a = 7 and b = -4

-3(-4 - 5) + 7(7) - (9 - 7)^6

= -3(-9) + 49 - (2)^6

= 27 + 49 - (64)

= 27 + 49 - 64

= 76 - 64

= 12      

Answer :

Step-by-step explanation :

As We Know that Opposite sides of the Parallelogram are equal.

SO,

(i) YZ = XW (opposite sides)

=> 2b = b + 1

=> 2b - b = 1

=> b = 1

Since, YZ = 2b

=> YZ = 2 × 1

=> YZ = 2.

Also,

(ii) XY = WZ (opposite sides)

=> 3a - 4 = a + 2

=> 3a - a = 2 + 4

=> 2a = 6

=> a = 6/2

=> a = 3 .

Since, XY = 3a - 4

putting the value of a = 3.

=> 3(3) - 4

=> 9 - 4

=> 5

XY = 5.

Therefore, Option D is the required answer.

In both cases, the inequality holds true. The inequality is 415 + d ≥ 500.  

Part A:
To write an inequality that represents the situation, we can use the following format: money raised so far + additional money needed ≥ goal. In this case, the money raised so far is $415, and the goal is $500. Let d represent the additional money needed. So the inequality would be:

415 + d ≥ 500

Part B:

The inequality 415 + d ≥ 500 has infinitely many solutions, as there are countless values of d that can satisfy the inequality. This is because as long as the total amount raised is equal to or greater than $500, the student council meets its goal. For example, if d is 85, then the council would exactly meet its goal (415 + 85 = 500). If d is 100, the council would exceed its goal (415 + 100 = 515). In both cases, the inequality holds true.

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The length should be less than or equal to 6 meters in order to have a plot with the maximum area allowed (45 square meters) when the width is 7.5 meters.

To find the length that will give a plot with the maximum area allowed, we can use the formula for the area of a rectangle:

Area = Length × Width

The width is given as 7.5 meters, and the area should not exceed 45 square meters.

Let's denote the length as L.

We want to maximize the area, so we need to find the value of L that satisfies the condition Area ≤ 45 and gives the largest possible area.

Substituting the given values into the area formula, we have:

Area = L × 7.5

Since the area should not exceed 45 square meters, we can write the inequality:

L × 7.5 ≤ 45

To find the maximum value of L, we can divide both sides of the inequality by 7.5:

L ≤ 45 / 7.5

Simplifying the right side:

L ≤ 6

Therefore, the length should be less than or equal to 6 meters in order to have a plot with the maximum area allowed (45 square meters) when the width is 7.5 meters.

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In the given line plot, the data represents the amount of water, in cups, that Harold, Rhonda, and Brad added to each of 14 beakers in their science class.

A line plot is a way to represent data that involves marking a number line for each data point and placing an “X” above the number that represents the value of that data point.

The line plot shows that most of the beakers were filled with either 1 or 2 cups of water. Specifically, there are 5 beakers with 1 cup of water and 6 beakers with 2 cups of water. There are also 2 beakers with 3 cups of water and 1 beaker with 4 cups of water.

The line plot provides a visual representation of the data that allows the viewer to quickly understand the distribution of the data. By seeing that most of the data is clustered around 1 and 2 cups of water, one can infer that the students were likely instructed to add a specific amount of water to each beaker. However, the presence of a few outliers, such as the beaker with 4 cups of water, suggests that some of the students may have made errors in their measurements or not followed the instructions closely.

Overall, the line plot provides a quick and easy way to visualize the distribution of the data and identify any outliers or patterns in the data. It is a useful tool for representing small to medium-sized datasets and is commonly used in education, research, and data analysis.

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Answer:

if this is study island than the answer is:

All of the beakers with more than  of a cup of water added to them were filled by Harold. Harold added a total of

4

cup(s) of water to his beakers.

All of the beakers with exactly  of a cup of water added to them were filled by Rhonda. Rhonda added a total of

15/8 or 1 7/8

cup(s) of water to her beakers.

Brad filled the rest of the beakers. Brad added a total of

13/8 or 1 5/8

cup(s) of water to his beakers.

Step-by-step explanation:

The completed equation is:

2 + 7 = a - 2

a = 11.

We are given the following equation:

2 + b = a - 2

We need to select the correct number from the drop-down menu to complete the equation.

From the first drop-down menu, we select 7.

2 + 7 = 9

From the second drop-down menu, we select 2.

2 + b = 9 - 2

2 + b = 7

Subtracting 2 from both sides, we get:

b = 5

Therefore, from the third drop-down menu, we select 5.

So, the completed equation is:

2 + 7 = 5 - 2

9 = 3

This is not a true statement, so there must be an error in one of our selections. Upon closer inspection, we can see that the correct number to select from the first drop-down menu is 5, not 7.

2 + 5 = 7

Now, substituting 5 for b in the original equation, we get:

2 + 5 = a - 2

7 + 2 = a

a = 9

Therefore, from the third drop-down menu, we select 9.

So, the completed equation is:

2 + 5 = 9 - 2

7 = 7

This is a true statement, so we have selected the correct numbers to complete the equation.

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The theoretical probability is: 12.5%. After 100 trials, the experimental probability is of: 20%. After 400 trials, the experimental probability is of: 11%. After more trials, the experimental probability is closer to the theoretical probability.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The dice has eight sides, hence the theoretical probability of rolling a six is given as follows:

1/8 = 0.125 = 12.5%.

(eight sides, each of them is equally as likely).

The experimental probabilities are obtained considering the trials, hence:

The more trials, the closer the experimental probability should be to the theoretical probability.

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The measure of in quadrilateral GERA ∠GAR = 102° , ∠TAR = 23°, ∠GAN = 55° , m AG = 110° , m RE = 110° , m GE = 94°

∠REG = 78° , m AR = 46

The sum of the opposite angle of the quadrilateral is equal to 180°

∠REG + ∠GAR = 180°

∠GAR = 180 - ∠REG

∠GAR = 180 - 78

∠GAR = 102°

The tangent chord angle is half the intercept arc

∠TAR = 1/2 m AR

∠TAR = 1/2 ×46

∠TAR = 23°

The sum of straight angles is 180

m ∠GAN = 180 - (m ∠TAR + m ∠GAR )

m ∠GAN =  180 - (23 + 120)

m ∠GAN = 55°

The tangent chord angle is half the intercept arc

m AG = 2 m ∠GAN

m AG = 2(55)

m AG = 110°

as EG = GA

m RE = m GA

m RE = 110°

Complete angle sum = 360°

m GE = 360 - (m AG + m AR + m RE)

m GE = 360 - (110 + 46 + 110 )

m GE = 94°

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Step-by-step explanation:

Looks as though it has been cropped.....picture is only a PART of the original...it has been 'cut off'  or 'cropped' on both sides .

Given that 0 < p < 1 for X~B(5,p) and P(X=3) = P(X=4), so the value of p is 2/3.

We know that X~B(5,p) and P(X=3) = P(X=4).

Using the probability mass function of a binomial distribution, we can write:
P(X=3) = (5 choose 3) * p³ * (1-p)²
P(X=4) = (5 choose 4) * p⁴ * (1-p)¹

Since P(X=3) = P(X=4), we can set these two expressions equal to each other and simplify:
(5 choose 3) * p^3 * (1-p)² = (5 choose 4) * p⁴ * (1-p)¹
10p^3(1-p)^2 = 5p^4(1-p)

Dividing both sides by [tex]p^{3(1-p)[/tex] and simplifying, we get:
10(1-p) = 5p
10 - 10p = 5p
10 = 15p
p = 2/3

Therefore, the value of p is 2/3, given that 0 < p < 1.

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The scale factor is 7/5 or 1.4.

In order to determine the scale factor, we need to compare the corresponding sides of two similar figures. Let's begin by drawing a diagram to represent the given information:

         M ------- N

        /             \

       /               \

      A ---------------- C

       <-----25cm----->

   <-----20cm-----> <-----35cm----->

From the diagram, we see that triangle AMC is similar to triangle CNC, since they share angle C and have proportional sides:

Scale factor = corresponding side length in triangle CNC / corresponding side length in triangle AMC

We can calculate the scale factor by comparing the lengths of the corresponding sides:

Scale factor = NC / AM

Scale factor = 35 cm / 25 cm

Scale factor = 7 / 5

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The volume of the cone is 57 cubic inches. To find the volume of the cone, we use the formula: V = (1/3)π[tex]r^{2}[/tex]h, where r is the radius of the cone, h is the height of the cone, and π is approximately 3.14.

Given that the radius of the cone is 3 inches and the height is 6 inches, we can substitute these values into the formula and solve for V: V = (1/3)π([tex]3^{2}[/tex])(6), V = (1/3)π(9)(6), V = (1/3)(3.14)(54), V = 56.52 cubic inches

Rounding to the nearest whole number, the volume of the cone is 57 cubic inches.

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