Ben, Rob, Kelly, Carla and Manu organised a pizza party for their business group, They ordered one vegetarian, one cheese, and one Nutella pizza. After the party, three-fourths of vegetarian pizza, five-eights of cheese pizza, and 11/12 of
Nutella pizza are remaining. Once all guests left, they decided to split the pizza equally among themselves, what
fraction of the whole pizza does each person get?

Answer: a

Step-by-step explanation: I did the test

Answer:

The total cost is $6.25

Step-by-step explanation:

3/4 of 1 kilo of rect

4/5 of 1 kilo of square

3/5 of 1 kilo of flower

rect = 3 per kilo

square = 3 per kilo

flower = 3 per kilo

First rectangle beads:

3x = y where x is number of kilos and y is full cost

3(3/4) = y

9/4 = y = 2 1/4 = $2.25

Second square beads:

3x = y where x is number of kilos and y is full cost

3(4/5) = y

12/5 = y = 2 2/5 = $2.20

Third flower beads:

3(x) = y where x is number of kilos and y is full cost

3(3/5) = y

9/5 = y = 1 4/5 = $1.80

Add costs together

1.80 + 2.20 + 2.25 = 6.25

The total cost is $6.25

Solution:

Given:

The radius and tangent to a circle at the point of intersection are perpendicular to each other.

Hence, considering the right triangle;

Hence, the length of the missing side can be gotten using the Pythagorean theorem.

Therefore, to the nearest tenth, the length of the missing side is 6.3

​Future Value received at the end of  one year is 1065

Future Value received at the end of  two year is 1134.225

​Future Value received at the end of  three year is 1207.949

 discount rate of 6.5 percent

  present value of a $1,000

Present Value= \(\frac{FV}{(1+r)^{n} }\)

​where:

FV=Future Value

r=Rate of return

n=Number of periods

Future Value received at the end of  one year

Future Value= Present Value * \((1+r)^{n}\)

                      =  1000 * (1+ 6.5%)^1

                     =  1000* 1.065

                      = 1065

Future Value received at the end of  two year

Future Value= Present Value * \((1+r)^{n}\)

                      =  1000 * (1+ 6.5%)^2

                     =  1000* 1.065^2

                      = 1000 * 1.134225

                      = 1134.225

​Future Value received at the end of  three year

Future Value= Present Value * \((1+r)^{n}\)

                      =  1000 * (1+ 6.5%)^3

                     =  1000* 1.065^3

                      = 1000 * 1.207949

                      = 1207.949

​Future Value received at the end of  one year is 1065

Future Value received at the end of  two year is 1134.225

​Future Value received at the end of  three year is 1207.949

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

x+1/2=21/14

x = ?

Step 02:

14 (x + 1 ) = 2 * 21

14x + 14 = 42

14x = 42 - 14

x = 28 / 14

x = 2

The answer is:

The value of x is 2

Answer:

=-1/6

Step-by-step explanation:

-1/2 + (3/4 * 4/9)

3/4 * 4/9 = 12/36

12/36 simplify to 1/3

-1/2 + 1/3 = -1/6

The value of the system in which newton's law of motion is applicable is (a) 25 (b) 10 (c) if output is x , 4y -x-15 =0

What about newton's law of motion?

Newton's laws of motion are three fundamental laws in classical physics that describe the behavior of objects in motion. They were first presented by Sir Isaac Newton in his work "Philosophiee Naturalis Principia Mathematica" in 1687. The three laws are:

According to the given information:

a) When input is 10.

   output= 10×4 - 15 =25

b) From the question output is 25

  Because input* 4 -15= output. So (output +15) / 4= input

  so input =\((25+15)/4\) =10

c) if output is x. So y × 4 - 1 5 = x , 4y - x - 15 = 0

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The value of the system in which newton's law of motion is applicable is (a) 25 (b) 10 (c) if output is x , 4y -x-15 =0

What about newton's law of motion?

Newton's laws of motion are three fundamental laws in classical physics that describe the behavior of objects in motion. They were first presented by Sir Isaac Newton in his work "Philosophiee Naturalis Principal Mathematical" in 1687. The three laws are:

The Law of Inertia: An object at rest will remain at rest, and an object in motion will continue in a straight line with constant velocity, unless acted upon by an external force.

The Law of Acceleration: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, F = ma, where F is the net force, m is the mass of the object, and a is the acceleration.

The Law of Action-Reaction: For every action, there is an equal and opposite reaction. This means that when an object exerts a force on another object, the second object exerts an equal and opposite force back on the first object.

According to the given information:

a) When input is 10.

  output= 10×4 - 15 =25

b) From the question output is 25

 Because input* 4 -15= output. So (output +15) / 4= input

 so input = =10

c) if output is x. So y × 4 - 1 5 = x , 4y - x - 15 = 0

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Answer:

5c-9h

Step-by-step explanation:

1) 7c-4h-2c-5h

2) 5c-4h-5h

3) 5c-9h

Answer: 72

Step-by-step explanation:

12*6

Answer:

The answer to this is the last one, the on all the way at the bottom.

Step-by-step explanation:

This is because no 2 coordinates/points line up.

Answer:

$13.52

Step-by-step explanation:

Since we know the tax rate is 6%, we can multiply by 12.75*6/100 to get how much the tax would be added to the total. We get 0.765. And now we add 0.765 and 12.75 to get 13.515. Since it's asking to round to the nearest cent, we get $13.52

Answer:

0

Step-by-step explanation:

I am not sure you included the full question, but if it is a multiplication problem, the answer is 0.

The margin of error of a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report falls within the range of 0.222 to 0.378.

In other words, it represents the range within which the true population proportion is likely to fall.

To calculate the margin of error, we need to know the sample size, the proportion of managers in the sample who have caught salespeople cheating on an expense report, and the confidence level.

Assuming that we have a large enough sample size (at least 30) and that the sample proportion is not too close to 0 or 1.

we can use the following formula to calculate the margin of error:

Margin of error = z* (sqrt(p*(1-p)/n))

where z* is the z-score associated with the desired confidence level (in this case, 1.96 for 95% confidence).

p is the sample proportion, and n is the sample size.

For example, if we have a sample of 100 managers and 30% of them have caught salespeople cheating on an expense report.

The margin of error for a 95% confidence interval estimate would be:

Margin of error = 1.96* (sqrt(0.3*(1-0.3)/100)) = 0.078

This means that we can be 95% confident that the true population proportion of managers who have caught salespeople cheating on an expense report falls within the range of 0.222 to 0.378 (i.e., the sample proportion plus or minus the margin of error).

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Answer:

J.(4.1ft)

i hope i can help..

Answer:

the green and red one

Step-by-step explanation:

they're the same I'm pretty sure

Answer:

The Green and Red one

Step-by-step explanation:

They both have the same angles but their sides are different

the probability that the next customer that comes to the deli will order a ham sandwich is, 0.32

And,  the probability that the next customer that orders from the deli will NOT order a cheese sandwich is, 0.8

Given that;

The owner of a deli recorded the number of customers who ordered each of four sandwiches available.

Here, Total number of sandwiches = 160 + 100 + 180 + 60

= 500

Hence, the probability that the next customer that comes to the deli will order a ham sandwich is.,

⇒ 160 / 500

⇒ 16/50

⇒ 8/25

⇒ 0.32

And, the probability that the next customer that orders from the deli will NOT order a cheese sandwich is,

⇒ 1 - 100/500

⇒ 1 - 1/5

⇒ 4/5

⇒ 0.8

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Answer:

Diverges

There is no sum.

Step-by-step explanation:

A geometric series has a general formula of:

\(\sum ar^n\)

Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges, but if |r| > 1, than the series diverges.

In this problem, the initial term is a = 36, the ratio can be found by:

\(r = \frac{39.6}{36}=\frac{43.56}{39.6}\\ r=1.1\)

Since the ratio is r =1.1 and 1.1 > 1.0, the series diverges.

In a diverging series, it is not possible to determine the sum of infinite terms, since it would be infinite.

The geometric series diverges and the sum does not exists.

A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms .

A geometric series has a general formula of:

∑arⁿ

Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.

In this particular case, the initial term is a=36 and each term is multiplied by 1.1 to get the next term

Therefore r = 1.1 and as it is >1 therefore the series diverges.

The sum of a divergent series is not finite so the sum does not exists.

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1) The probability that a sitcom will have 25 or more minutes of programming is 0.125.

2) The probability that a sitcom will have between 21 and 25 minutes of programming is 1.000.

3) The probability that a sitcom will have more than 10 minutes of commercials (or other non-programming interruptions) is 0.250.

To solve this problem, we can use the probability density function of a uniform distribution

f(x) = 1/(b-a) for a <= x <= b

= 0 otherwise

where a and b are the endpoints of the interval.

Given that the programming time for sitcoms follows a uniform distribution from 18 to 26 minutes, we have

a = 18

b = 26

Therefore, the probability density function for the programming time is

f(x) = 1/8 for 18 <= x <= 26

= 0 otherwise

1) P(X >= 25) = ∫(25 to 26) f(x) dx

= ∫(25 to 26) 1/8 dx

= [x/8] from 25 to 26

= (26/8) - (25/8)

= 1/8

Therefore, the probability that a sitcom will have 25 or more minutes of programming is 0.125.

2) P(21 <= X <= 25) = ∫(21 to 25) f(x) dx

= ∫(21 to 25) 1/8 dx

= [x/8] from 21 to 25

= (25/8) - (21/8)

= 1

Therefore, the probability that a sitcom will have between 21 and 25 minutes of programming is 1.000.

3) Since the total running time of a sitcom is 30 minutes and the programming time is uniformly distributed between 18 and 26 minutes, the time for commercials and interruptions is:

T = 30 - X

where X is the programming time.

Therefore, the probability of having more than 10 minutes of commercials and interruptions is

P(T > 10) = P(30 - X > 10)

= P(X < 20)

Using the cumulative distribution function (CDF) of the uniform distribution, we get

F(x) = (x - a)/(b - a) for a <= x <= b

= 0 for x < a

= 1 for x >= b

Therefore

P(X < 20) = F(20)

= (20 - 18)/(26 - 18)

= 2/8

= 0.250

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Answer:

A & C

Step-by-step explanation:

You're looking for rational numbers that are also integers, but because (as the figure shows) ALL integers are already rational, you only have to worry about the integer part. An integer is a whole number, positive or negative. So, you need to simplify each element of each set (the numbers inside the curly braces) to see if they're whole.

A - The square root of 100 is just 10 or -10, divided by -2 is -5 or 5. 4, -2, 5, and -5 are all integers.

B - Wrong because 4/3 is not a whole number

C - 16/4 is just 4, and the square root of 49 is 7 or -7. 4, -6, 2, 7, & -7 are all integers.

D - Wrong because 27/2 is not a whole number

E - Wrong because 0.2 is not a whole number

Let me know if you need a more thorough explanation! (:

Answer :  8

Explanation : 4 × 2 = 8

◊ YusuCr ◊

Answer:

8

Step-by-step explanation: if your times it by two it would be 4x2 = 8 :)

Therefore, the second Taylor polynomial for the function \(f(x) = e^x * cos(x)\) about x₀ = 0 is p₂(x) = 1 + x.

To find the second Taylor polynomial for the function \(f(x) = e^x * cos(x)\) about x₀ = 0, we need to find the values of the function and its  derivatives at x₀ and then construct the polynomial.

Let's start by finding the first and second derivatives of f(x):

\(f'(x) = (e^x * cos(x))' \\= e^x * cos(x) - e^x * sin(x) \\= e^x * (cos(x) - sin(x)) \\f''(x) = (e^x * (cos(x) - sin(x)))' \\= e^x * (cos(x) - sin(x)) - e^x * (sin(x) + cos(x)) \\= e^x * (cos(x) - sin(x) - sin(x) - cos(x)) \\= -2e^x * sin(x) \\\)

Now, let's evaluate the function and its derivatives at x₀ = 0:

\(f(0) = e^0 * cos(0) \\= 1 * 1 \\= 1 \\f'(0) = e^0 * (cos(0) - sin(0)) \\= 1 * (1 - 0) \\= 1\\f''(0) = -2e^0 * sin(0) \\= -2 * 0 \\= 0\\\)

Now, we can construct the second Taylor polynomial using the values we obtained:

p₂(x) = f(x₀) + f'(x₀) * (x - x₀) + (f''(x₀) / 2!) * (x - x₀)²

p₂(x) = 1 + 1 * x + (0 / 2!) * x²

p₂(x) = 1 + x

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The second Taylor polynomial P2(x) for the function f(x) = e^x * cos(x) about x0 = 0 is P2(x) = 1 + x.

To find the second Taylor polynomial, denoted as P2(x), for the function f(x) = e^x * cos(x) about x0 = 0, we need to calculate the function's derivatives at x = 0 up to the second derivative.

First, let's find the derivatives:

f(x) = e^x * cos(x)

f'(x) = e^x * cos(x) - e^x * sin(x)

f''(x) = 2e^x * sin(x)

Now, we can evaluate the derivatives at x = 0:

f(0) = e^0 * cos(0) = 1 * 1 = 1

f'(0) = e^0 * cos(0) - e^0 * sin(0) = 1 * 1 - 1 * 0 = 1

f''(0) = 2e^0 * sin(0) = 2 * 0 = 0

Using the derivatives at x = 0, we can construct the second Taylor polynomial, which has the general form:

P2(x) = f(0) + f'(0) * x + (f''(0) / 2!) * x^2

Plugging in the values, we get:

P2(x) = 1 + 1 * x + (0 / 2!) * x^2

= 1 + x

Therefore, the second Taylor polynomial P2(x) for the function f(x) = e^x * cos(x) about x0 = 0 is P2(x) = 1 + x.

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The approximate 95% confidence interval for the proportion of coworkers who have received this year's flu vaccine is (0.339, 0.501). Based on this information, it is true that 95% of the coworkers fall within the interval (0.339, 0.501), and we can be 95% confident that the proportion of coworkers who have received the vaccine is between 33.9% and 50.1%. However, it is false to say that there is a 95% chance that a randomly selected coworker has received the vaccine or that there is a 42% chance for a randomly selected coworker to have received the vaccine.

The approximate 95% confidence interval for the proportion of coworkers who have received this year's flu vaccine is (0.339, 0.501). Based on this information, we can determine which of the following statements are true:

a) 95% of the coworkers fall in the interval (0.339, 0.501).

This statement is true. The 95% confidence interval represents the range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies. Therefore, we can say that 95% of the coworkers fall within the interval (0.339, 0.501).

b) We are 95% confident that the proportion of coworkers who have received this year's flu vaccine is between 33.9% and 50.1%.

This statement is true. The 95% confidence interval (0.339, 0.501) provides us with a range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies. Therefore, we can say that we are 95% confident that the proportion of coworkers who have received the vaccine is between 33.9% and 50.1%.

c) There is a 95% chance that a randomly selected coworker has received the vaccine.

This statement is false. The 95% confidence interval does not represent a probability or chance for an individual coworker. It provides a range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies. It does not give information about the likelihood of an individual coworker receiving the vaccine.

d) There is a 42% chance that a randomly selected coworker has received the vaccine.

This statement is false. The 42% represents the proportion of coworkers in the survey who have received the flu vaccine, but it does not represent the chance or probability for a randomly selected coworker to have received the vaccine. The 42% is a point estimate, not a probability.

e) We are 95% confident that between 33.9% and 50.1% of the samples will have a proportion near 42%.

This statement is false. The confidence interval (0.339, 0.501) does not directly provide information about the proportion of samples that will have a proportion near 42%. The confidence interval represents the range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies, but it does not specifically address the proportion of samples near 42%.

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Answer:

(1/4)n - 3

Step-by-step explanation:

In math, "of" means times so the first part of the expression is 1/4 times n. Then add minus 3 because it says she subtracted 3.

The error of Fatima is: C. She applied the exponent -2 to "4(-2) instead of only to "(-2).

An exponent in any expression is the letter or number on the right of a base in an expression.

In the evaluated expression shown, the base that the exponent "-2" applies to is "m", and does not include 4. If we substitute the value of m = -2, into the evaluated expression, the base that the exponent "-2" applies to is "-2" and does not include "4".

Therefore, Fatima's mistake is: C. She applied the exponent -2 to "4(-2) instead of only to "(-2).

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Answer:

\( \frac{ {x}^{ - 2} {y}^{ \frac{1}{2} } }{ \sqrt{36x {y}^{2} } } = \frac{ \sqrt{y} }{ {x}^{2} \sqrt{36x {y}^{2} } } = \frac{ \sqrt{y} }{6 {x}^{2}y \sqrt{x} } = \frac{1}{6 {x}^{ \frac{5}{2} } {y}^{ \frac{1}{2} } } = \frac{1}{6} {x}^{ - \frac{5}{2} } {y}^{ - \frac{1}{2} } \)

\( \frac{1}{6} \times - \frac{5}{2} \times - \frac{1}{2} = \frac{5}{24} \)

Answer:

For 10 visits, both gyms charge the same

Step-by-step explanation:

Equations

Gym memberships' costs are:

G1 = 100 + 2x

G2 = 12x

Where x is the number of visits to the gym.

We need to find the number of visits for which the charges for both gyms are the same. Thus equating the costs:

12x = 100 + 2x

Subtracting 2x:

10x = 100

Dividing by 10:

x =10

For 10 visits, both gyms charge the same

Answer:

To find the solution of the heat equation with the given boundary and initial conditions, we can use the method of separation of variables. Let's solve it step by step:

Step 1: Assume a separation of variables solution:

u(x, t) = X(x)T(t)

Step 2: Substitute the assumed solution into the heat equation:

X(x)T'(t) = 9X'''(x)T(t)

Step 3: Divide both sides of the equation by X(x)T(t):

T'(t) / T(t) = 9X'''(x) / X(x)

Step 4: Set both sides of the equation equal to a constant:

(1/T(t)) * T'(t) = (9/X(x)) * X'''(x) = -λ^2

Step 5: Solve the time-dependent equation:

T'(t) / T(t) = -λ^2

The solution to this ordinary differential equation for T(t) is:

T(t) = Ae^(-λ^2t)

Step 6: Solve the space-dependent equation:

X'''(x) = -λ^2X(x)

The general solution to this ordinary differential equation for X(x) is:

X(x) = B1e^(λx) + B2e^(-λx) + B3cos(λx) + B4sin(λx)

Step 7: Apply the boundary condition u(0, t) = 0:

X(0)T(t) = 0

B1 + B2 + B3 = 0

Step 8: Apply the boundary condition u(3, t) = 0:

X(3)T(t) = 0

B1e^(3λ) + B2e^(-3λ) + B3cos(3λ) + B4sin(3λ) = 0

Step 9: Apply the initial condition u(x, 0) = 5sin(7πx/3):

X(x)T(0) = 5sin(7πx/3)

(B1 + B2 + B3) * T(0) = 5sin(7πx/3)

Step 10: Since the boundary conditions lead to B1 + B2 + B3 = 0, we have:

B3 * T(0) = 5sin(7πx/3)

Step 11: Solve for B3 using the initial condition:

B3 = (5sin(7πx/3)) / T(0)

Step 12: Substitute B3 into the general solution for X(x):

X(x) = B1e^(λx) + B2e^(-λx) + (5sin(7πx/3)) / T(0) * sin(λx)

Step 13: Apply the boundary condition u(0, t) = 0:

X(0)T(t) = 0

B1 + B2 = 0

B1 = -B2

Step 14: Substitute B1 = -B2 into the general solution for X(x):

X(x) = -B2e^(λx) + B2e^(-λx) + (5sin(7πx/3)) / T(0) * sin(λx)

Step 15: Substitute T(t) = Ae^(-λ^2t) and simplify the solution:

u(x, t) = X(x)T(t)

u(x, t) = (-B2e^(λx) + B2e^(-λx) + (5sin(7πx

Answer:

B

Step-by-step explanation:

because if you multiply the denominators