what fraction of prism's volume will be filled by th sand

Answer:

The answer to your problem is, radian measure of angle AOB is π /3 radian

Step-by-step explanation:

How to find the length of an arc:

Arc Length (L) = θ × r

θ being the radian measure of the angle and r is the radius of the circle

From what is give;

L = 2π/9 yards, r = 2 feet = 2/3 yard

Using the formula, L = θ x r

Then concluding to:

2π/9 = θ × 2/3

θ  = (2π × 3) / (9×2) 

θ  = π /3 radian

Thus the answer to your problem is, radian measure of angle AOB is π /3 radian

Answer:

15.58

Step-by-step explanation:

1. Arrange n number of data points in ascending order: x1, x2, x3, ... xn

2. Calculate the rank r for the percentile p you want to find: r = (p/100) * (n - 1) + 1

3. If r is an integer then the data value at location r, xr, is the percentile p: p = xr

4. If r is not an integer, p is interpolated using ri, the integer part of r, and rf, the fractional part of r:

p = xri + rf * (xri+1 - xri)

Answer:

--------------------------------------

Permutation equation:

Combination equation:

--------------------------------------

This situation is a permutation because the order in which the candidates are selected for each position matters.

The number of possibilities for the board is:

This situation is also a permutation because the order in which the players are assigned to each position matters.

The number of ways the coach can arrange the team is:

This situation is a combination because the order in which Amy chooses the places to travel does not matter.

The number of possible trip choices is:

The answer responses are:

1) Permutation; 6720 possibilities;

2) Permutation; 95040 ways;

3) Combination; 35 choices.

The Permutation equation: nPr = n!/(n - r)!

1. This situation is a permutation, since the order in which the members are selected for each position matters. The number of different possibilities for the board can be calculated as follows:

8P5 = 8!/(8-5)! = 8 x 7 x 6 x 5 x 4 = 6,720

Therefore, there are 6,720 different possibilities for the Executive Board.

2. This situation is also a permutation, since the order in which the players are selected for each position matters. The number of different ways the coach can arrange the team can be calculated as follows:

12P5 = 12!/(12-5)! = 12 x 11 x 10 x 9 x 8 = 95,040

Therefore, there are 95,040 different ways the coach can arrange the team.

3. This situation is a combination, since the order in which the places are selected does not matter. The number of possible trip choices for Amy can be calculated as follows:

7C3 = 7!/(3!(7-3)!) = 35

Therefore, there are 35 possible trip choices for Amy.

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Answer:

A or B

Step-by-step explanation:

Bob has A or B type blood. This is because his father is an universal blood donor which means he has blood type O and Bob’s mom is an universal blood receiver which means she has blood type AB.

Two possibilities of the blood type that Bob can have are A or B.

Blood group is the group designated to the blood of each individual depending upon the specific antigens present.

The 4 groups are A, B, O and AB.

Here, given that,

Bob's father is an universal blood donor and his mother an universal blood receiver.

We know that, group O is the universal donor and group AB is the universal blood receiver.

Possibilities for the group of children are either A or B.

Hence the possibilities of the group that Bob can have are either A or B.

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The expression for when you translate the graph of y=|2x|−1 is

y= |2x-2|-1. i.e. d) One unit to the right: y = |2(x - 1)| - 1 y = |2x - 2| - 1.

We have,

Expression in mathematics is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division. A function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

We are given that;

y = |2x|−1

Now,

To write the expression for when you translate the graph of y = |2x| - 1, we need to use the rules for vertical and horizontal shifts. The rules are:

To shift the graph up or down by k units, add or subtract k to the original function.

To shift the graph left or right by h units, add or subtract h to the input variable.

Using these rules, we can write the expressions for each translation as follows:

a) One unit up: y = |2x| - 1 + 1 y = |2x|

b) One unit down: y = |2x| - 1 - 1 y = |2x| - 2

c) One unit to the left: y = |2(x + 1)| - 1 y = |2x + 2| - 1

d) One unit to the right: y = |2(x - 1)| - 1 y = |2x - 2| - 1

Therefore, by the expression the answer will be y = |2x - 2| - 1.

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Using the area formula for rectangle, we can find the height of the rectangle to be 8m.

The quantity of unit squares that can fit inside a rectangle is known as an area. The quantity of space occupied by a flat surface of a specific form is determined by its area. Each shape's area is specified as a "number of" square units and is based on the maximum number of unit squares that can fit inside it (square centimetres, square inches, square feet, etc.).

Area of the rectangle has been given = 52m².

Base of the rectangle has been given as = 6.5m.

Let height be = h

Area = b × h

⇒ 52 = 6.5 × h

⇒ h = 52/6.5

⇒ h = 8m.

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Answer: 21//2

Step-by-step explanation: 1 1/2 = 3/2

So it takes 3/2 hours to set up 1 comupter workstation.

If we want to find how many hours would it take to set up 7 computer workstation we would have to do 3/2 x 7 and get 21/2 or 20 1/2

The total cost of stay at Oceanview Hotel would be:

Total Cost = $45 x

The total cost of stay at Beachside Hotel would be:

Total Cost = $115 x

What is cost?

Cost is a term used in economics and business to refer to the total monetary expense incurred by a company or an individual in the production or purchase of goods and services.

The two given statements are about the total costs for staying at two different hotels. Let's break down what each of the statements mean:

"Oceanview Hotel changes their fee to $45": This means that the daily rate for staying at Oceanview Hotel is now $45. To find the total cost of staying at this hotel, we simply multiply the daily rate by the number of days stayed. This gives us the equation:

Total Cost = $45 x

where x is the number of days of stay.

"Beachside Hotel changes their daily rate to $115": This means that the daily rate for staying at Beachside Hotel is now $115. Again, we can find the total cost of staying at this hotel by multiplying the daily rate by the number of days stayed. This gives us the equation:

Total Cost = $115 x

where x is the number of days of stay.

So, these two equations give us the total costs for staying at Oceanview Hotel and Beachside Hotel respectively, given the new changes in their rates.

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Answer:

Diameter-3 inches

Circumference- 9.42 inches

Step-by-step explanation:

In order to get this, you must know that radius is 1/2 of diameter or diameter is 2 times the radius.

As such,

D-Diameter

R-Radius

R = 1.5

D = 2R--> FOR ANY CIRCLE

D = 2(1.5)

D = 3 inches

Now to find circumference you must understand the difference of formulas between the area of a circle and circumference of a circle.

Merely saying, the circumference of a circle is the perimeter of a circle and it is much different from finding the perimeter of other shapes.

The circumference formula is...

C - 2лr

As such,

C - 2(3.14)(1.5)

C - 9.42 inches

As such your answers are

Diameter - 3 inches

Circumference - 9.42 inches

Hope this helped!

The null and alternative hypothesis for a physician who check your blood pressure are as follows:

When a physician checks a patient's blood pressure, they may use a diagnostic threshold of 90 mmHg to diagnose hypertension. In statistical terms, the null hypothesis (H0) would be that the patient's blood pressure is less than or equal to 90 mmHg. The alternative hypothesis (H1) would be that the patient's blood pressure is greater than 90 mmHg.

The physician would then use various statistical tests, such as a t-test or a z-test, to determine whether the patient's blood pressure is statistically significantly different from the threshold of 90 mmHg. Based on the results of the test, the physician would either reject the null hypothesis in favor of the alternative hypothesis, indicating that the patient has hypertension, or fail to reject the null hypothesis, indicating that the patient's blood pressure is within the normal range.

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Answer:

point = ( -6, 2)

slope = -3

Step-by-step explanation:

point slope formula;

y - y1 = m ( x - x1) ,

where m= slope , (x1, y1) = the coordinates of a point

y - 2 = -3 ( x + 6)

a point the line passes through = (-6 , 2)

slope of the line = -3

Dish D has the density of clusters closest to 0.75 per square centimeter.

A substance's density is determined by how much mass there is per unit volume. It is typically expressed in units such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).

To find the density of clusters in each circular dish, we need to calculate the area of each dish and divide the number of clusters by that area.

The area of a circle is given by the formula A = πr², where r is the radius of the circle. In this case, we are given the diameter of each circular dish, which is 8 cm. Therefore, the radius of each dish is 4 cm.

The area of each dish is:

A = πr² = π(4 cm)² ≈ 50.27 cm²

Now, we can calculate the density of clusters in each dish:

Density in A = 53 clusters / 50.27 cm² ≈ 1.05 clusters/cm²

Density in B = 13 clusters / 50.27 cm² ≈ 0.26 clusters/cm²

Density in C = 151 clusters / 50.27 cm² ≈ 3.00 clusters/cm²

Density in D = 38 clusters / 50.27 cm² ≈ 0.76 clusters/cm²

Therefore, dish D has the density of clusters closest to 0.75 per square centimeter.

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The inversion point of (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0 is (6, 7).

To find the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0, we need to follow these steps:

Step 1: Write the equation of the given circle in standard form by completing the square for x and y: (x - 2)² + (y - 3)² = 16.

Step 2: Find the radius of the circle by taking the square root of the constant term: r = √16 = 4.

Step 3: Find the distance between the given point (4, 5) and the center of the circle (2, 3) using the distance formula: d = √[(4 - 2)² + (5 - 3)²] = √8.

Step 4: Use the formula for inversion point to find the coordinates of the inversion point (x', y'): (x', y') = (h + r²/d² * (x - h), k + r²/d² * (y - k)), where (h, k) is the center of the circle and r is the radius.

Plugging in the values, we get: (x', y') = (2 + 4²/8 * (4 - 2), 3 + 4²/8 * (5 - 3)) = (6, 7).

Therefore, the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0 is (6, 7).

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The diameter of the conductor with a cross-sectional area of 18,225 cmils is approximately 152.7 mils.

What is Diameter?

Diameter is a measurement of the size of a circle, defined as the distance between any two points on the circle passing through the center. It is the longest chord of a circle, and it bisects the circle into two equal halves.

To find the diameter in mils of a conductor with a cross-sectional area of 18,225 cmils, we can use the formula for the area of a circle:

A = π[tex]r^{2}[/tex]

where A is the cross-sectional area, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14159.

Convert the cross-sectional area from cmils to square inches:

A = 18,225 cmils = 18,225/1,000,000 sq. in. ≈ 0.018225 sq. in.

Solve for the radius of the circle:

A = π[tex]r^{2}[/tex]

[tex]r^{2}[/tex] = A/π

r = sqrt(A/π) ≈ 0.07635 inches

Convert the radius from inches to mils:

r = 0.07635 inches * 1000 mils/inch ≈ 76.35 mils

Find the diameter by doubling the radius:

diameter = 2 * r ≈ 152.7 mils

Therefore, the diameter of the conductor with a cross-sectional area of 18,225 cmils is approximately 152.7 mils.

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Answer:

x = 20

Step-by-step explanation:

You have pointed out the angles are supplementary, so they add to 180.

Add both angles to equal 180.

7x + x + 20 = 180

Combine like terms.

8x + 20 = 180

Subtract 20 from both sides.

8x = 160

Divide out the 8 to get x.

x = 20

The length of ML rounded to nearest tenth is 4.5.

From figure, KML is a right-angled triangle at M, with KM = 8 and KL = 9.2. Let ML = x be the length of the base.

Using Pythagorean theorem, we have:

KL² = KM² + ML²

Substituting the given values ML=x, KM = 8 and KL = 9.2, we have:

9.2² = 8² + x²

Simplifying the right-hand side, we get:

84.64 = 64 + x²

Subtracting 64 from both sides, we get:

20.64 = x²

Taking the square root of both sides, we get:

x ≈ 4.54

x=4.5 (rounded to nearest tenth)

Therefore, the length of ML is approximately 4.5.

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The triangles are similar by the sas similarity theorem.

The similarity theorem for tri angles states that if two triangles have the same shape, then their corresponding angles are equal and their corresponding sides are proportional.

More specifically, if we have two triangles, Triangle ABC and Triangle DEF, such that:

Angle A = Angle D

Angle B = Angle E

Angle C = Angle F

And also, their corresponding sides are proportional:

AB/DE = BC/EF = AC/DF

Then, we can say that Triangle ABC is similar to Triangle DEF. This means that these two triangles have the same shape and they are only different in size.

The similarity theorem is important in geometry, as it allows us to determine unknown side lengths or angle measures of similar triangles by using proportions. It is also useful in real-life situations where we need to determine the size of objects that are not directly measurable

To prove that two triangles are similar using the SAS (Side-Angle-Side) similarity theorem, you need to show that:

Two pairs of corresponding sides are proportional (have the same ratio).

The included angles (the angle between these two pairs of corresponding sides) are congruent.

So, for the SAS similarity theorem to apply, you need to have two triangles where two pairs of corresponding sides are proportional and the included angle between these sides is congruent. If these conditions are met, then the triangles are similar.

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Answer:  To determine the average rate of return for the investment, we need to calculate the net present value (NPV) of the investment using the given information.

The NPV can be calculated as follows:

NPV = -initial investment + (annual net cash flows / discount rate) x present value factor

We know the initial investment is $375,000 and the desired rate of return is 6%. The annual net cash flows are not given, but we can calculate them using the following formula:

Annual net cash flows = annual revenue - annual expenses

Without additional information about the revenue and expenses associated with the new machine, we cannot calculate the annual net cash flows or the NPV. Therefore, we cannot determine the acceptability of this investment or the average rate of return.

Step-by-step explanation: would really appreciate a thanks and brainliest :D

Answer:

Step-by-step explanation:

I looked at it like if I evened out the 2 shapes so that sat flush like in picture. I know all of the angles should =360 to go all the way around

So

120+120+2x+x=360

240+3x=360

3x=120

x=40

The conditional statement is solved and the following argument is invalid

Given data ,

Let the first statement be A

Now , (∀x)(∃y)(p(x, y) ⇒ r(x)):

This statement asserts that for every x, there exists a y such that if x is a factor of y, then x is prime. This is a valid statement, as it essentially says that there exists a prime factor for every integer x

Let the second statement be B

Now , (∀x)(∀y)(∀z)(¬q(x, y, z)): This statement asserts that for all x, y, and z, z is not the greatest common factor (GCF) of x and y. This is a generic statement and does not provide any specific information about the values of x, y, and z. It is not relevant to the conclusion of the argument.

Let the third statement be C

Now , (∃x)(∀y)(p(x, y) ∨ r(x)): This statement asserts that there exists an x such that for all y, either x is a factor of y or x is prime. This is also a valid statement, as it states that there exists an integer x that is either a factor of y or prime for all y.

According to the conclusion, there must exist an x and a z such that z is the GCF of x and y for any y. However, the premises merely state that x is a factor of y or that x is prime; they make no direct mention of the largest common factor between x and y.

Hence , the conclusion (y)(z)(x)q(x, y, z) is not supported by the argument. A stronger case for this conclusion would require more evidence or premises

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The solutions to the linear function are;

1. The soccer team makes more money per car ($8) than the French club ($5).

2. The graph that demonstrates Arnold's journey is graph 3

3. The graph that demonstrates Francisco's journey is graph 1

4. The graph that demonstrates Celia's journey is graph 2

To determine which group makes the most money per car, we can calculate the slope of the linear function representing the amount earned per car washed for both the French club and the soccer team. The slope of a linear function is the change in the dependent variable (y) divided by the change in the independent variable (x).

Let's calculate the slope for the soccer team. We can choose any two points to calculate the slope. Let's use the points (3, 24) and (6, 48):

Slope (m) = (change in y) / (change in x) = (48 - 24) / (6 - 3) = 24 / 3 = 8

The soccer team earns $8 per car washed.

We can choose any two points to calculate the slope for the French club. Let's use the points (2, 10) and (4, 20):

(20 - 10) / (4 - 2) = 10 / 2 = 5

The French club earns $5 per car washed

The above answer is dependent on the questions below;

The french club and soccer team are washing cars to earn money. The amount earned, (y) dollars for washind (x) cars is a linear function.  Which group makes the most money per car? explain

                                      French club

Number of cars (x)                       Amount earned (y)

2                                                         10

4                                                          20

6                                                          30

8                                                         40

10                                                         50

Soccer team

Number of cars (x)                       Amount earned (y)

3                                                      24

6                                                       48

9                                                      72

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Answer:

The mean length of time is 27 minutes.

Step-by-step explanation:

To find the mean, we have to first calculate x and fx.

(0+12)/2=6

(12+24)/2=18

(36+48)/2=42

(48+60)/2=54

Now we have x, and f

Calculate fx by multiplying:

6×11=66

18×25=450

30×23=690

42×15=630

54×6=324

The mean is the sum of fx/sum of f

(66+450+690+630+324)/(11+25+23+15+6)=27

Hope this helps!

Answer:

4 units²

Step-by-step explanation:

Calculate some vectors from the point (2,3).

Vector A = <1, 5>

Vector B = <-2, -2>

The area of the triangle is 1/2 * (the magnitude of the cross product of the vectors)

A × B = -2 + 10 = 8

the magnitude of 8 is 8.

Therefore 1/2 * 8 = 4

Answer:

4 units²

Step-by-step explanation:

The answers are expected values as seen below and the actual number of Type I errors may vary from one test to another. However, by choosing a smaller significance level, we can reduce the probability of committing a Type I error and increase the reliability of our hypothesis test.

If the null hypothesis is true, and we perform a hypothesis test with a significance level of α, then the probability of committing a Type I error (rejecting the null hypothesis when it is actually true) is α.

Therefore, if we repeat a hypothesis test 1,000 times, we would expect to commit a Type I error the following number of times for different values of α:

a = 0.05:

a = 0.01:

a = 0.001:

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The value of KL for the similar triangle ∆JKL is derived to be equal to 10.92

How to evaluate the for the value of x for the triangle ∆JKL

The triangles XYZ and JKL are similar, this implies that the length XY of the smaller triangle is similar to the length JK of the larger triangle

similarly, YZ is similar to KL so;

8.7/12.18 = 7.8/KL

KL = (7.8 × 12.18)/8.7 {cross multiplication}

KL = 95.004/8.7

KL = 10.92

Therefore, the value of KL for the similar triangle ∆JKL is derived to be equal to 10.92.

Answer: 58

Step-by-step explanation:

3^2 + 7^2 = 9 + 49

= 58

[tex]X^2 = 7^2 + 3^2 = 49+ 9[/tex]

[tex]X^2 = 58[/tex]

[tex]X = \sqrt{(58)}[/tex]

Therefore, the hypotenuse is approximately 7.62.

To find the coordinates of a' and b', you can solve the following system of equations:

a' = a + t

b' = b + t

A shape is translated when it is moved up, down, left or right without turning. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.

To find the coordinates of the translated image a' and b', you need to know the amount and direction of the translation.

If you know the horizontal and vertical distances between the original line ab and the translated line a'b, then you can find the coordinates of a' and b' using the following formulas:

a' = (a.x + h, a.y + v)

b' = (b.x + h, b.y + v)

where a.x and a.y are the coordinates of point a, b.x and b.y are the coordinates of point b, and h and v are the horizontal and vertical distances between the two lines.

Alternatively, you can use vector notation to represent the translation. If you represent the original line ab as the vector v = b - a, then the translated line a'b can be represented as the vector v' = b' - a'. The two vectors are related by the following equation:

v' = v + t

where t is the translation vector. The translation vector represents the horizontal and vertical distances between the two lines, and it can be written as:

t = (h, v)

To find the coordinates of a' and b', you can solve the following system of equations:

a' = a + t

b' = b + t

where a and b are the coordinates of points a and b, and t is the translation vector. This will give you the coordinates of a' and b' in terms of the original coordinates of a and b and the translation vector.

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The number of teenagers who gave data for the survey was 52 teenagers .

The number of teenagers who ate red meat at least once a week was 50 teenagers.

The percentage that ate red meat more than twice per week was 77 %.

The distribution can be described as normal.

The number of teenagers in the survey :

= ∑ ( Frequency of number of times meat eaten )

= 2 + 3 + 7 + 9 + 10 + 8 + 7 + 5 + 1

= 52 teenagers

Number of teenagers eating at least once a week :

= ( 52 total - 2 eating zero times )

= 50 teenagers

Percentage eating red meat more than twice :

= ( 52 total - 2 eating zero times - 3 eating once - 7 eating twice ) / 52 x 100 %

= 77 %

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