Lin is comparing the graph of two functions g and f. The function g

is given by g(x) = f(x - 2). Lin thinks the graph of g will be the same as

the graph of f, translated to the left by 2. Do you agree with Lin? Explain

your reasoning.

The length of side x in simplest radical form with a rational denominator is 8√3

The given parameters are:

Triangle type = Equilateral triangle

Height (h) = 12

Missing side length = x

The missing side length, x is calculated using the following sine ratio

sin(60) = Height/Missing side length

This gives

sin(60) = 12/x

Make x the subject of the formula

So, we have

x = 12/sin(60)

Evaluate the quotient

So, we have

x = 12/(√3/2)

This gives

x = 24/√3

Rationalize

x = 24/√3 * √3/√3

Evaluate

x = 8√3

Hence, the length of side x in simplest radical form with a rational denominator is 8√3

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To make 7500 Blueberry pies, 9.375 hours will be required. So, it will take 9.4 hours to use 30,000 cups of blueberries.

Given that a commercial bakery bakes 800 blueberry pies in 1 hour of baking.

Each blueberry pie requires 4 cups of blueberries.

To find the number of hours taken to use 30,000 cups of blueberries, we need to use the formula mentioned below:

Let us first calculate the total number of blueberry pies that can be baked using 30,000 cups of blueberries:

Number of blueberry pies = 30,000/4 = 7,500 pies

Hence, 7500 pies require (7500/800) = 9.375 hours. Therefore, 30,000 cups of blueberries can be used to make 7500 blueberry pies in 9.375 hours. Rounding off the answer to the nearest tenth gives: 9.4 hours.

Applying the formula, the Number of blueberry pies = Number of cups of blueberries ÷ Cups of blueberries per blueberry pieNumber of blueberry pies = 30,000 cups of blueberries ÷ 4 cups per blueberry pieNumber of blueberry pies = 7500 blueberry pies

Therefore, to make 7500 blueberry pies, 9.375 hours will be required.

So, it will take 9.4 hours to use 30,000 cups of blueberries.

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The system of equations can be used to find the roots of the considered  equation is y = 4+x^2 and y= x^3 + 2 + x

We do same operations on both the sides so that equality of both expressions doesn't get disturbed. Solving equations generally means finding the values of the variables used in it for which the considered equation is true.

Sometimes we can find such value, and sometimes it is not possible at all, or sometimes, there are infinite number of solutions.

For the given case, we are given with the equation \(4+x^2 = x^3 + 2 + x\)

We can take two equations as:

\(y = 4+x^2 \\y= x^3 + 2 + x\)

And when we will try to solve this system of equation, we will end up substituting the value of y in terms of x, and therefore, ending up on the same equation \(4+x^2 = x^3 + 2 + x\)

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Answer:

D

y=4x^2

y=x^3+2x

Step-by-step explanation:

im trying to pass just like yall, Good luck to all

Solving the characteristic equation z² + 1 = 0 We get,\(z = ±i\)As the roots are imaginary and distinct, general solution is given as z(x) = c₁ cos x + c₂ sin x

The solution to the initial value problem Solution: We have z''(x) + z(x) = 4c7x .....(1)

We need to find the particular solution Now, let us assume the particular solution to be of the form z = ax + b Substituting the value of z in equation (1) and solving for a and b, we geta = -2/7 and b = 0Therefore, the general solution of the differential equation is

z(x) = c₁ cos x + c₂ sin x - 2/7

x Putting the initial conditions

z(0) = 0 and z'(0) = 0 in the above equation,

we get c₁ = 0 and c₂ = 0

Therefore, the solution to the initial value problem is z(x) = 0

Hence, option (a) is the correct solution.

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Answer:

-3/2 which is a

Step-by-step explanation: finding the exact value

The value (-15/8 + 1.5) ÷ (15 - \(14\frac{3}{4}\))  = -3/2,

Hence, Option A is correct.

The given expression is,

(-15/8 + 1.5) ÷ (15 - \(14\frac{3}{4}\))

Since we know,

Dividing two fractions is equivalent to multiplying the first fraction by its reciprocal. The first step in splitting fractions is to get the reciprocal of the second fraction (reverse the numerator and denominator). Then, multiply the numerators.

Here we have to find the value of the given expression is,

We can write it as,

⇒  (-15/8 + 1.5) ÷ (15 - 59/4)

⇒  (-15 + 12)/8  ÷ (60-59)/4

⇒  -3/8 ÷ 1/4

⇒  -3/8 x 4/1

⇒  -3/2

Hence,

(-15/8 + 1.5) ÷ (15 - \(14\frac{3}{4}\))  = -3/2

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The height is changing at a rate of 15 inches every minute.

We can use the derivative of the volume formula to derive an equation that links the rates of change of the cone's volume, radius, and height:

Cone volume formula: V = (1/3)r2h

Using derivative on both sides with regard to time, we arrive at:

dV/dt equals (1/3) * 2r * dr/dt * h plus (1/3) r2 * dh/dt.

where

We can enter the values supplied here as substitutes in this equation:

dV/dt = 43 in3 minutes.

Dr/Dt = 3 In/Minute

r = 1 in

V = 13 in³

For dh/dt, we can solve for:

43 = (1/3)π * 2(1) * 3 * h + (1/3)π(1)² * dh/dt

43 = 2πh + (1/3)π * dh/dt

129 = 6πh + π * dh/dt

dh/dt = (129 - 6πh) / π

We may now change h = (3V) / (r2) to obtain:

dh/dt is equal to (129 - 6 (3V)/(r2)) /

(129 - 18V/r2) / dh/dt

By substituting the V and r values that are supplied, we obtain:

dh/dt = (129 - 18(13)/(1²)) / π

dh/dt = about 15 in/min

As a result, the height is changing at a rate of 15 inches every minute.

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Answer:

50%

Step-by-step explanation:

We Know

There are 6 numbers on a die: 1, 2, 3, 4, 5,6

There are 3 even numbers.

What is the likelihood of rolling an even number on a die?

3/6 = 1/2 = 50%

So, there is a 50% chance of rolling an even number on a die.

Answer:

$0.29 cents

Step-by-step explanation:

6.88/24 = 0.28666666666 about 0.29

\(11. \: we \: know \: that \\ \frac{sum \: of \: all \: quantities}{number \: of \: quantities} = mean \\ => \frac{7 + 11 + 13 + 6 + 8 + x}{6} = 8 \\ = > \frac{45 + x}{6} = 8 \\ = > 45 + x = 8 \: \times 6 \\ = > 45 + x = 48 \\ = > x = 48 - 45 \\ = > x = 2 \\ \\ 12. we \: know \: that \\ \frac{sum \: of \: all \: quantities}{number \: of \: quantities} = mean \\ => \frac{2 + 5 + 1.3 + 2.2 + x}{5} = 1.8 \\ = > \frac{10.5 + x}{5} = 1.8 \\ = > 10.5 + x = 5 \times 1.8 \\ = > 10.5 + x = 9 \\ = > x = 9 - 10.5 \\ = > x = - 1.5 \\ \)\)

This is the answer.

Hope it helps!!

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

23

Step-by-step explanation:

To solve this question I have used some formula.

1. Formula to find the value of term

x + (term number - 1) × {(greater term number - smaller term number) ÷ (greater term containing value) - (smaller term containing value)}

2. Formula to find the value of x given in 1st formula

x = value containing by term - (term number - 1) × {(value containing by greater term - value containing smaller term) ÷ (6-4)}

Here greater term number means the value containing by the greater term. In this question greater term is 6 which contain a value in it that is 18. So, greater term number in this question is 18. So, smaller term number means the smaller term containing a value in it or the number containing by the greater term.

4th term = 8

To find the value of 7th term first we need to find the value of x.

              x = 8 - (4 - 1) × {(18 - 8) ÷ (6 - 4)}

              x = 8 - 3 × (10 ÷ 2)

              x = 8 - 3 × 5

              x = 8 - 15

              x = -7

Now, to check whether the value of x is -7, I have find the 4th term by replacing x with -7 in the 1st formula.

              = -7 + (4 - 1) × {(18 - 8)} ÷ (6 - 4)

              = -7 + 3 × (10 ÷ 2)

              = -7 + 3 × 5

              = -7 + 15

              = 8

Answer came 8 and its correct answer. So, the value of x is -7

I have also find the 6th term so you understand it more properly.

6th term = 18

              = -7 + (6 - 1) × [{(18 - 8)} ÷ (6 - 4)]

              = -7 + 5 × {(10 ÷ 2)}

              = -7 + 5 × 5

              = -7 + 25

              = 18

Answer of 6th term is also correct.

I think now you know how to find the 7th term.

7th term = -7 + (7 - 1) × {(18 - 8) ÷ (6 - 4)

              = -7 + 6 × (10 ÷ 2)

              = -7 + 6 × 5

              = -7 + 30

              = 23

If you think that I have made mistake anywhere or you did not understood my explanation than please ask me in comment or you can report this answer. But, before reporting please see carefully because, once any answer got reported you can't undo it.

Therefore, it will take approximately 1415.7 weeks for all of the chemical to evaporate.

To calculate the volume of a cone, we can use the formula:

\(Volume = (1/3) * π * r^2 * h\)

Given that the height (h) of the cone is 240 inches and the radius (r) is 150 inches, we can substitute these values into the formula:

\(Volume = (1/3) * 3.14 * 150^2 * 240\)

Simplifying the equation:

Volume = 3.14 * 22500 * 240

Volume ≈ 16988400 cubic inches

Now, we know that the liquid chemical evaporates at a rate of 12,000 cubic inches per week. To find out how many weeks it will take for all the chemical to evaporate, we can divide the total volume of the chemical by the evaporation rate:

Number of weeks = Volume / Evaporation rate

Number of weeks = 16988400 / 12000

Number of weeks ≈ 1415.7 weeks

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Answer:

Last option) 3

Step-by-step explanation:

For having no real solutions, discriminant of this equation must be be less than 0.

D=\(\sqrt{b^{2}-4ac }<0\)

b²-4ac<0

b²<4ac

b²/4a<c

c>b²/4a

c>\(\frac{(-4^{2} )}{8}\)

c>16/8

c>2

Answer:

t=-3

Step-by-step explanation:

2x²-4x-t=0

disc=b²-4ac=(-4)²-4×2×(-t)=16+8t

it has no solution if 16+8t<0

8t<-16

t<-2

so t=-3

2.

\(\sqrt{x-a} =x-4\\if a=2\\\sqrt{x-2} =x-4\\squaring\\x-2=x^2-8x+16\\x^2-9x+18=0\\\)

x²-6x-3x+18=0

x(x-6)-3(x-6)=0

(x-6)(x-3)=0

x=6,3

when x=6

√(6-2)=6-4

√4=2

2=2

when x=3

√(3-2)=3-4

√1=-1

1=-1

which is not true.

Hence x=3 is an extraneous solution.

x=6 is real solution.

Answer: 915

Step-by-step explanation:  trust me i'm extremely good at math

200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

The absolute difference between the predicted and actual values must be determined, added together, and divided by the total number of periods.

Forecasted values are as follows: 1,500 and 1,400

Values in actuality: 1,200 and 1,500

Absolute differences:

|1,500 - 1,200| = 300

|1,400 - 1,500| = 100

Now, we calculate the MAD:

MAD = (300 + 100) / 2 = 400 / 2 = 200

Therefore, 200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

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Answer:

7

Step-by-step explanation:

njshhtb jahhhdvjsjjbvgshh shhkakhgsv jjjjgfe

The arrival rate is found to be 30 emails per hour and the service rate is calculated to be 45 emails per hour.

It has been mentioned in the question that in every 2 minutes, customers send emails to a help desk of an online retailer, on an average, and the standard deviation of the inter-arrival time is also given to be 2 minutes. The online retailer has three employees for answering those emails.

It takes almost 4 minutes to write a response email to the customer, on average. The standard deviation (SD) of the service times is 2 minutes. This is a g/g/k type queue.

Therefore the arrival rate per hour is given by the following relation:

Arrival rate in 1 hr = No. of minutes in an hr / inter arrival time of email taken in minutes

Given here,

No. of minutes in an hour = 60 minutes

Inter arrival time of the email taken in minutes = 2 minutes

∴ Arrival rate in 1 hr = 60 / 2

                                = 30 emails / hr

Hence the arrival rate is 30 emails per hour.

Now for finding out the service rate we have the following formula:

Service rate = No. of minutes in an hr x No. of employes answering/ average time that is required to write response email

Given here,

No. of minutes in an hr = 60 minutes

No. of employes answering = 3

Average time that for writing response email = 2 minutes

∴ Service rate = 60 * 3 / 4

                       = 45 emails / hr

Hence the service rate is 45 emails per hour.

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A. A sample size of 62 should be taken for a 95% level of confidence.

B. The sample size of 107 should be taken for a 99% level of confidence.

a. To estimate the sample size needed to estimate the mean time a staff member spends with each patient, we can use the formula for sample size calculation:

n = (Z^2 * σ^2) / E^2

Where:

n = required sample size

Z = Z-score corresponding to the desired level of confidence

σ = population standard deviation

E = desired margin of error

For a 95% level of confidence:

Z = 1.96 (corresponding to a 95% confidence level)

E = 2 minutes

σ = 8 minutes (population standard deviation)

Substituting these values into the formula:

n = (1.96^2 * 8^2) / 2^2

n = (3.8416 * 64) / 4

n = 245.9904 / 4

n ≈ 61.4976

Since we can't have a fraction of a sample, we round up the sample size to the nearest whole number. Therefore, a sample size of 62 should be taken for a 95% level of confidence.

b. For a 99% level of confidence:

Z = 2.58 (corresponding to a 99% confidence level)

E = 2 minutes

σ = 8 minutes (population standard deviation)

Substituting these values into the formula:

n = (2.58^2 * 8^2) / 2^2

n = (6.6564 * 64) / 4

n = 426.0096 / 4

n ≈ 106.5024

Rounding up the sample size to the nearest whole number, a sample size of 107 should be taken for a 99% level of confidence.

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sin4π/3= sin(π+π/3) = - sinπ/3

cot4π/3=cot(π+π/3)= cotπ/3

OPTION C 4π/3

Answer:

You could compare the ounces or weight, the price per unit, or overall quality.

Step-by-step explanation:

You could use the ounce/weight to check which weighs more, or has more in it. Then figure out which is more reasonable. You could use the price per unit, and the ounce/weight because the price per unit/ price per ounce could be more expensive, or less expensive and make more sense to buy. Or you could just use overall quality. You can have an item with more in it, but have lower quality contents, when you could have a smaller amount with better quality contents, which might cost a little more.\

-Hope this helped

Hey there!

Use the slope formula:

\(\bold{\displaystyle\frac{y2-y1}{x2-x1}}\)

Where

y₂=-12

y₁=-6

x₂=11

x₁=8

Plug in the values:

\(\bold{\displaystyle\frac{-12-(-6)}{11-8}}\)

-12-(-6) is the same as -12+6:

\(\bold{\displaystyle\frac{-6}{3} =-2}\)

Hence, the slope of the line is

\(\boxed{\boxed{\bold{-2}}}\)

Hope everything is clear.

Let me know if you have any questions!

#NeverGiveUp

\(\text{A cheerful teenager :D}\)

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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Answer:1 1/2 gallons

Step-by-step explanation: there are 4 quarts in a gallon

Answer:

i don't know this one!

Step-by-step explanation:

sorry!

Answer:

D

Step-by-step explanation:

{ 0,2,4,6,8} is  the complement of the set.

What is natural number in math?

Is zero a natural number?

u = {0, 1, 2, 3, 4, 5, 6, 7, 8}

Odd number less than 8  = { 1,3,5,7 }

complement =  {0, 1, 2, 3, 4, 5, 6, 7, 8} -  { 1,3,5,7 }

                     = { 0,2,4,6,8}

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Answer:

look at the picture i have sent

Answer:

7 ft

Step-by-step explanation: