The radius of a circle is 8 in. Find its area in terms of \piπ.

Answer:

6 gallons per minute

Step-by-step explanation:

54 gallons came out in 9 minutes

54/9 = 6

the rate is 6 gallons per minute

The profit for one small cake is approximately £0.3564.

To find the profit for one small cake, let's assign variables to represent the profits. Let's call the profit for one small cake "P_s," the profit for one medium cake "P_m," and the profit for one large cake "P_l."

Given information:

The ratio of small to medium to large cakes sold is 9:5:12.

The profit for one medium cake is three times the profit for one small cake.

The profit for one large cake is four times the profit for one small cake.

The total profit is £815.76.

We can set up equations based on the given information:

P_m = 3P_s (Profit for one medium cake is three times the profit for one small cake)

P_l = 4P_s (Profit for one large cake is four times the profit for one small cake)

Total profit = 286P_s + 286P_m + 286P_l = £815.76 (Total profit is the sum of profits for each cake sold)

Since we know the ratio of small, medium, and large cakes sold, we can express the number of each cake sold in terms of the ratio:

Let's assume the common ratio is "x," so we have:

Small cakes sold = 9x

Medium cakes sold = 5x

Large cakes sold = 12x

Now we can substitute these values into the total profit equation:

286P_s + 286P_m + 286P_l = £815.76

Substituting P_m = 3P_s and P_l = 4P_s:

286P_s + 286(3P_s) + 286(4P_s) = £815.76

Simplifying:

286P_s + 858P_s + 1144P_s = £815.76

2288P_s = £815.76

Dividing both sides by 2288:

P_s = £815.76 / 2288

P_s ≈ £0.3564

Therefore, the profit for one small cake is approximately £0.3564.

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As per the given correlation, the appropriate null and alternative hypothesis for calculating number of goggles is

H0 : No linear relation

H1 : there is a relation

What is meant by correlation?

In math, correlation is referred as a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate).

And it is a common tool for describing simple relationships without making a statement about cause and effect.

Based on the given question, a group of scientist randomly selected 20 piknits from the sea-floor and measured their respective weights in grams.

And we also know that, they wanted to know if the weight of the piknits can be used to predict the number of gogles.

Here from the given information, the null hypothesis : H0 : There is no linear relationship between the weight of piknits and the number of goggles

And the Alternative hypothesis : Ha: There is a linear relationship between the weight of piknits and the number of gogles

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Answer:

-7.3 = -7.3

Step-by-step explanation:

-2.2+(-3.7 + (-1.4)) = -7.3 || -2.2+(-3.7 + (-1.4)) = -7.3

So it will be -7.3=-7.3

Answer:

\(→(6.2 \times {10}^{ - 2} ) \times (2 \times {10}^{6} ) \\ = (6.2 \times 2) \times ( {10}^{ - 2} \times {10}^{6} ) \\ = 12.4 \times {10}^{( - 2 + 6)} \\ =12.4 \times {10}^{4} = \boxed{124000}✓\)

Answer:

124000

Step-by-step explanation:

The probability of at least one defective rivet in a seam requiring 27 rivets, assuming they are independently defective with the same probability, is approximately 68.3%.

To solve this problem, we can use the concept of probability and the binomial distribution.

The probability of a rivet being defective is denoted by "p". Since each rivet is defective independently of the others, the probability of a rivet not being defective (i.e., being good) is 1 - p.

The seam will need to be reworked if any of the 27 rivets is defective. Therefore, we want to calculate the probability that at least one rivet is defective.

The probability of at least one defective rivet can be found using the complement rule: subtracting the probability of no defective rivets from 1.

The probability of no defective rivets is given by (1 - p) raised to the power of 27 (since each rivet is independent).

So, the probability of at least one defective rivet is:

P(at least one defective rivet) = 1 - P(no defective rivets)

P(at least one defective rivet) = 1 - (1 - p)^27

Now, we can substitute any desired value for the probability of a defective rivet, "p," to calculate the probability of at least one defective rivet.

For example, if we assume a defective rivet probability of p = 0.05 (5%), the calculation would be as follows:

P(at least one defective rivet) = 1 - (1 - 0.05)^27

P(at least one defective rivet) ≈ 0.683

Therefore, with a 5% probability of a rivet being defective, the probability of at least one defective rivet in the seam is approximately 0.683 or 68.3%.

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Step-by-step explanation:

hope this helps, good night!!!!

Answer:

35

Step-by-step explanation:

20 + 15 = 35

BRAINLIEST PLEASE

The options which are true of the perpendicular bisector of AB are:

It meets Line AB at 90°

It passes through the midpoint of Line AB.

A perpendicular bisector is defined as a straight line or line segment cutting into two equally-sized portions at an exact 90-degree angle, intersecting the middle of the targeted line.

Some of the properties of a perpendicular bisector are:

- It divides a line segment or a line into two congruent segments.

- It divides the sides of a triangle into congruent parts.

- It makes an angle of 90° with the line that is being bisected.

- It intersects the line segment exactly at its midpoint.

Thus, the correct options are:

It meets Line AB at 90°

It passes through the midpoint of Line AB.

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Answer:

x = 48°

Step-by-step explanation:

The triangle on the left has 3 congruent sides and is equilateral with 3 congruent angles, each of 60°

The 3 angles on the base line sum to 180° , that is

60° + 54° + base = 180°

114° + base = 180° ( subtract 114° from both sides )

base = 66°

The triangle  on the right has 2 congruent sides and is isosceles with base angles congruent , both 66° , then

x = 180° - (66 + 66)° = 180° - 132° = 48°

Answer:

D hope this helps :)

Step-by-step explanation:

The velocity vector is given by () = (-5sin(10t), -4, 0). This represents the rate at which the position vector changes with respect to time in each direction

The velocity vector of the given path is determined by taking the derivative of the position vector with respect to time. In this case, we are given the position vector r(t) = (cos^2(5t), 8 - 4t, -7). The velocity vector is obtained by differentiating each component of the position vector with respect to time. The resulting velocity vector is written in the form (x-component, y-component, z-component).

To find the velocity vector, we need to take the derivative of the position vector with respect to time. Let's denote the position vector as r(t) = (x(t), y(t), z(t)). Taking the derivative of each component with respect to time gives us the following:

x'(t) = d/dt [cos^2(5t)] = -10cos(5t)sin(5t) = -5sin(10t),

y'(t) = d/dt [8 - 4t] = -4,

z'(t) = d/dt [-7] = 0.

Therefore, the velocity vector is given by () = (-5sin(10t), -4, 0). This represents the rate at which the position vector changes with respect to time in each direction. The x-component of the velocity vector is -5sin(10t), the y-component is -4, and the z-component is 0.

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Answer:

g(x) = - ( x^2)

Step-by-step explanation:

opposite of function f

Answer:

Step-by-step explanation:

Student G only involves in the band but Student B involves in the band and those who play piano. We can also assume that the instrument that Student B plays in the band is the piano.

The student of class B plays both pianos and they are in the band while a student of class G is in the band without knowing their role play as per the Venn diagram shown.

Given that,
The Venn diagram below provides a visual representation of the students in Mr. Griffin's class who participate in music programs after school. What does the diagram tell you about the musical involvement of Student B and Student G is to be determined

The Venn diagram is a mathematical representation of the system of scenarios.

Here,
There are 7 classes named A, B, C, D, E, F, and G in the Venn diagram
Where students of classes A and F are the proper piano players,
while, students of class B and D are both in the band and also they plays piano, and students of C, E, and G has no specified role play but they are part of the band,

Thus, the student of class B plays both pianos and they are in the band while a student of class G is in the band without knowing their role play.

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The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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Answer:

Step-by-step explanation:

48----------------100%

x------------------75%

x=36

Answer: A general solution of a differential equation is a solution that contains all possible solutions of the equation, including all arbitrary constants. It provides a general form of the solution that can be customized to fit the specific conditions of the problem.

For example, the general solution of a second-order linear homogeneous differential equation of the form

y'' + p(x)y' + q(x)y = 0

is a combination of two linearly independent functions, often represented by y = c1y1(x) + c2y2(x), where c1 and c2 are arbitrary constants and y1(x) and y2(x) are two linearly independent solutions of the differential equation.

The general solution represents the most general form of the solution that takes into account all possible solutions, including all arbitrary constants. To find a specific solution, one must apply initial or boundary conditions to determine the values of the arbitrary constants.

Step-by-step explanation:

Answer: Yes

Step-by-step explanation:

3/4 of 42 is (3/4)(42)=31.5, and 41 is greater than 31.5.

The components of the torque about the origin when the force acts in

(a) the positive x direction is 1.4N.

(b) the negative z direction is 2.21N.

What is constant force of magnitude?

The motion of a particle occurs on a plane and is influenced by a force of constant magnitude that is always perpendicular to the particle's velocity.

Given:

A particle is located at vector r = (0.54m)i + (-36m)j +(.85m)k constant force of magnitude 2.6 N acts on the particle.

We have to find the torque about positive x direction and negative z direction.

At  the positive x direction the torque is (T)

= the x component of position vector . F

= 0.54 x 2.6

= 1.4 N

At negative z direction Torque = - (z component of position vector).F

                                                   = .85 x 2.6

                                                   = 2.21 N

Hence,

The components of the torque about the origin when the force acts in

(a) the positive x direction is 1.4N.

(b) the negative z direction is 2.21N.

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The predicted quantity of balls in the first bin is (1/n)n.

Considering that,

There are the same number of balls and containers.

If so, then each container must always contain one ball. The probability of each ball landing in the first bin is (1/n)n.

For instance -

Three balls and three bins should be present. Next to each ball, place an A, B, and C. There are numbers 1, 2, and 3 on the containers. Ball A has a 1/3 chance of landing in bin 1. Although there is a 1/3 probability that ball B will drop in bin 1 and a 1/3 chance that ball C will do the same, both outcomes are possible. Therefore, bin 1 should be equal to 1/3 + 1/3 + 1/3. The rationale behind the projected values of bins 2 and 3 is identical.

According to the same logic, bins 2 and 3 should also have expected values of 1.

How probable is it that the first bin will receive all three balls?

In general, (1/n)n, which equals (1/3)3, or 1/3 x 1/3 x 1/3, equals 1/27.

Therefore, (1/n)n would be the expected number of balls in the first bin.

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Step-by-step explanation:

the process of finding out the variable value that makes the equation true is called 'solving' the equation. An equation is a statement that two quantities are equivalent. For exp/example:. x + 1 = 4 mean that when we add 1 to the unknown value, 'x', the answer is equal to 4 .

Answer:

Step-by-step explanation:

radius r=10/2=5 ft

h=6 ft.

volume of cone=1/3 πr²h=1/3×3.14×5²×6=157 cubic ft.

Answer:

.4

Step-by-step explanation:

.4 is the answer to the question