Working simultaneously, four fudge machines complete a big order in 48 hours. All the machines at the fudge factory work at the same pace. If only one half of the machines are working, in how many hours will the order be complete?

a = 4 and b = 5 are the answers to the system of equations.

Let's square both sides of the first equation to eliminate the square root:

√a + b = 7

(√a + b)² = 7²

a + 2√ab + b² = 49

a + b² = 49 - 2√ab ---(1)

Now, let's square both sides of the second equation:

√b + a = 11

(√b + a)² = 11²

b + 2√ab + a² = 121

a² + b + 2√ab = 121 ---(2)

We can use equation (1) to substitute for √ab in equation (2):

a + b² = 49 - 2√ab

√ab = (49 - a - b²)/2

Substituting for √ab in equation (2), we get:

a² + b + 2(49 - a - b²)/2 = 121

Simplifying and rearranging, we get:

a² - a + b² - b - 36 = 0

(a - 1/2)² + (b - 1/2)² = 37.25

This is the equation of a circle centered at (1/2, 1/2) with a radius √37.25. We need to find the points where this circle intersects the line defined by equation (1).

Substituting b = 49 - a - 2√(a(49 - a))/2 into equation (1), we get:

a + (49 - a - 2√(a(49 - a)))² = 49 - 2√a(49 - a)

Simplifying and rearranging, we get:

4a³ - 294a² + 2421a - 5929 = 0

Using a numerical solver or the rational root theorem, we can find that one solution of this cubic equation is a = 4.

Substituting this value back into equation (1), we can solve for b:

4 + b² = 49 - 2√(4b)

b² + 2√(4b) - 45 = 0

Using the quadratic formula, we get:

b = 5

Therefore, the solutions of the system of equations are a = 4 and b = 5.

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Complete question:

√a+b=7 and √b +a = 11 If a and b are real numbers that satisfy the equation above, what is the value of a and b respectively?

Answer: right answer is 23

Step-by-step explanation:

A system of equation is 1680mi3hr = p−w×600×2hr -p + w  for a jet airliner travels 1680 miles in 3hours with a tail wind.

Let p be  the speed of the jet airliner

and w  be the speed of the tail wind

It takes the plane 3 hours to go 1680 miles when a jet airliner travels with a tail wind and and 3.5 hours to go 1680 miles against the wind.. So, using system of equations we get

1680mi3hr = p−w×600×2hr = p + w

Solving for the left sides we get:

200mph = p - w

300mph = p + w

Now solve for one variable in either equation, we use

200mph = p - w

Add w to both sides:

p = 200mph + w

Using the value of x, we can found the value of w using system of equations.

300mph = (200mph + w) + w

Combine like terms:

300mph = 200mph + 2w

Subtract 200mph on both sides:

100mph = 2w

On dividing by 2:

50mph = w

So the speed of the tail wind is 50mph.

Therefore, 200mph = p - 50mph

Add 50mph on both sides:

250mph = p

Hence, speed of jet airliner is 250mph.

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W = [(n - 1)S² / σ₀²] is a Wald statistic for testing H₀: σ = σ₀.

(a) To show that Z = n(X - μ₀) / σ is a Wald statistic for testing H₀: μ = μ₀, we need to demonstrate that it follows a standard normal distribution under the null hypothesis.

Given:

X₁, X₂, ..., Xₙ: Random sample from a normal population with mean μ and known variance σ².

H₀: μ = μ₀ (null hypothesis).

Z = n(X - μ₀) / σ (test statistic to be shown as a Wald statistic).

To begin, let's calculate the distribution of the sample mean X. Since the population is normal, we have:

X ~ N(μ, σ²/n),

where X follows a normal distribution with mean μ and variance σ²/n.

Now, let's standardize X using the known variance σ²:

Z = (X - μ₀) / (σ/√n).

Since X follows a normal distribution, the linear combination of X, namely (X - μ₀), also follows a normal distribution. Furthermore, since the variance is known, the denominator σ/√n is a constant.

Thus, Z follows a normal distribution with mean (μ - μ₀) and variance (σ²/n):

Z ~ N((μ - μ₀), (σ²/n)).

Now, let's standardize Z:

Z' = (Z - (μ - μ₀)) / (σ/√n).

Simplifying, we have:

Z' = [(X - μ₀) / (σ/√n)] - [(μ - μ₀) / (σ/√n)]

= Z - [(μ - μ₀) / (σ/√n)]

= Z - c,

where c = (μ - μ₀) / (σ/√n) is a constant.

Since Z follows a standard normal distribution (mean 0 and variance 1), Z' is also a standard normal random variable.

Hence, Z = n(X - μ₀) / σ is a Wald statistic for testing H₀: μ = μ₀.

(b) To find a Wald statistic for testing H₀: σ = σ₀, we need to use a similar approach.

Given:

X₁, X₂, ..., Xₙ: Random sample from a normal population with mean μ and unknown variance σ².

H₀: σ = σ₀ (null hypothesis).

We can use the sample variance S² as an estimator for σ².

The chi-square distribution can be used to estimate the distribution of (n - 1)S² / σ² under the null hypothesis.

Thus, a Wald statistic for testing H₀: σ = σ₀ can be defined as:

W = [(n - 1)S² / σ₀²],

where W follows a chi-square distribution with (n - 1) degrees of freedom under the null hypothesis.

Note that in this case, we are using the chi-square distribution instead of the standard normal distribution as in part (a) since the variance is unknown.

Therefore, W = [(n - 1)S² / σ₀²]  is a Wald statistic for testing H₀: σ = σ₀.

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Answer:

Hi could you specify the question, I don't see any question in here, else I'd answer it.

Step-by-step explanation:

Answer: 101

\(\leq 46,25+2b\leq 250\\\\=> 2b\leq 250-46,25=203,75\\\\<=> b\leq 203,75/2=101,876\)

but b is the number of new baseballs

=> \(b\leq 101\)

=> the team can purchase 101 baseballs

Step-by-step explanation:

Answer:

x= -16

Step-by-step explanation:

-3x-8/ 4 = 10

Here we can try to isolate x and so we have to first multiply 4 on each side.

-3x-8= 40

Then we can add the 8 to each side.

-3x= 48

Next, divide the -3 onto each side and we can get the answer!

x= -16

Answer: I think is A

Step-by-step explanation:

Answer:

Let's assume that Holly has x trophies. When you don't know the amount someone has you can always use x in your equation because later on in the calculation you'll figure it out anyways

Emma has 7 fewer trophies than Holly. So Emma has x - 7 trophies.

Together, they have 27 trophies. So we can write an equation:

x + (x-7) = 27

Simplifying and solving for x, we get:

2x - 7 = 27

2x = 34

x = 17

So Holly has 17 trophies, and Emma has 17 - 7 = 10 trophies in total!

The ratio for 3 feet / 1 yard will be 1:1 which is 1.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10.

It should be noted that 1 yard = 3 feet

Therefore, 3 feet / 1 yard will be:

= 3 feet / 3 feet

= 1/1

= 1

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Answer:

No

Step-by-step explanation:

To check if 2 expressions are equal to each other you can set them equal to each other. If, after you simplify, the equation is true, then they are equal. If it is not, then the expressions are not equal.

3(4x-2)=12x-2

12x-6=12x-2

12x=12x+4

0=4

The statement 0=4 is not true. This means that the expressions are not equal.

Money with Tom = ×

Money with Aaron = x + 8

Their sum = $20

This can be written as :

= x + x + 8 = 20

= 2x + 8 = 20

= 2x = 20 - 8 ( transposing +8 from LHS to RHS changes +8 to -8 ) .

= 2x = 12

= x = 12 ÷ 2 ( transposing ×2 from LHS to RHS changes ×2 to ÷2 ) .

= x = 6

Which means ,

Tom has = x = $6

Aaron has = x + 8 = $6 + $8 =

= $14

Therefore , Tom has = $6 and Aaron has = $14 .

The equation that represents the situation in which case the percent of successful free throws is 75% during the game is; ( 8 + x ) = 0.75 ( 15 + x ).

It follows from the task content that the equation which represents the situation in which case the percent of successful free throws rises to 75% is to be determined.

As evident in the task content; Initially, Shaq made 8 out of 15 free throws he attempted.

Therefore, let the number of consecutive free throws he has to make to raise the success rate to 75% be; x.

Therefore, it follows from percent proportion that;

( 8 + x ) / ( 15 + x ) = 75 / 100

The simplified equation which represents the required situation is therefore;

( 8 + x ) = 0.75 ( 15 + x ).

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We are going to calculate the area of paper neccesary to create the cone with 2 of radius, h=6 in

The area of the cone is:

We can find a using pitagoras:

The area is:

The answer is C.

The function is not a pdf because c is not defined.It is not bounded either.

a) f(x) = x3 / 4 for 0 < x < c(i) For f(x) to be a pdf, it must satisfy two conditions:It must be non-negative for all xIt must integrate to 1 between the limits of the random variable. That is,It is given that f(x) = x3 / 4 for 0 < x < c

For the above function, we have to find c.c = [4 / (c^4/4)](c^4/4) = 4

Now, the pdf is given by f(x) = x^3 / 4c = 4

(ii) The cdf is given by F(x) = P(X ≤ x)

The limits are from 0 to x. Hence we have

\(F(x) = ∫ f(x) dx = ∫ x^3 / 4c dx = [x^4 / (16c)] from 0 to x\)

Therefore,F(x) = x^4 / (16c)

(iii) The graph of the pdf and cdf can be sketched as below.(iv) Mean of the given pdf is given byμ =

∫x.f(x) dx = ∫0c x.x^3 / 4c dx = ∫0c x^4 / 4c dx= [x^5 / 20c] from 0 to c= c^4 / 80

Therefore,μ = c^4 / 80

Variance of the given pdf is given by

\(σ^2 = ∫(x - μ)^2 . f(x) dx = ∫0c (x - c^4 / 80)^2 . x^3 / 4c dx\)

On evaluating,

\(σ^2 = c^8 / 1280 - (c^4 / 16) + (3c^4 / 80) = c^8 / 1280 + (c^4 / 60)\)

b) f(x) = (3/16)x2 for -c < x < c

(i) For f(x) to be a pdf, it must satisfy two conditions:It must be non-negative for all xIt must integrate to 1 between the limits of the random variable. That is,It is given that f(x) = (3/16)x2 for -c < x < c

For the above function, we have to find c.∫(3/16)x2 dx = 1

Integrating within the limits, we get3/16 [x3 / 3] from -c to c = 1

On solving we getc3 = 16 / 3c = (16 / 3)1/3

Now, the pdf is given by f(x) = (3/16)x2 / c

(ii) The cdf is given by F(x) = P(X ≤ x)

The limits are from -c to x.

Hence we haveF(x) = ∫ f(x) dx = ∫ (3/16)x2 / c dx = [(x3 / 16c)] from -c to x

Therefore,F(x) = (x3 + c3) / 16c

(iii) The graph of the pdf and cdf can be sketched as below.

(iv) Mean of the given pdf is given byμ = ∫x.f(x) dx = ∫(-c)c x.(3/16)x2 / c dx = ∫(-c)c (3/16)x3 / c dx= 0

Therefore,μ = 0

Variance of the given pdf is given byσ^2 = ∫(x - μ)^2 . f(x) dx = ∫(-c)c (x - 0)^2 . (3/16)x2 / c dx

On evaluating,σ^2 = 3c4 / 80

Therefore,σ^2 = c4 / 26c) f(x) = c/student submitted image, transcription available belowfor 0 < x < 1.

Is this pdf bounded?(i) For f(x) to be a pdf, it must satisfy two conditions:It must be non-negative for all xIt must integrate to 1 between the limits of the random variable. That is,It is given that f(x) = c/student submitted image, transcription available belowfor 0 < x < 1Now, we have to find the value of c so that f(x) is a pdf.∫c/student submitted image, transcription available belowdx = 1Integrating within the limits, we getc [ln |x|] from 0 to 1 = 1On solving we getc = 1 / ln (1) = undefined

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The graph with all the solutions can be seen in the image at the end of the answer.

We want to solve the 3 quadratic equations and then graph them in a coordinate axis.

Remember that for a complex number z = a + bi, the real part a goes in the horizontal axis and the complex part b goes in the vertical axis.

a) We start with:

m² = 16

m = √16

m = ±4

b) x² = -9

x = ±√-9

x = ±3i

c) t² = -25

t = ±√-25

t = ±5i

The graph of all of these points can be seen in the image at the end.

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Answer:

y-5 = -2/3 (x+6)

Step-by-step explanation:

-2y = -3x -8

2y = 3x + 8

2/2 y = 3/2 x + 8/2

y = 3/2 x + 4

slope of a perpendicular line

- 2/3

y-5= -2/3(x-(-6)

y-5 = -2/3 (x+6)

It seems that you are referring to the exponential growth formula which is:

N(t) = N₀ * (1 + r)^t

Where:
N(t) is the number of individuals at time t
N₀ is the initial number of individuals (in this case, 25 alive in 1955)
r is the growth rate
t is the time period (in years)

In this problem, we have:
N₀ = 25 individuals (alive in 1955)
N(t) = 500 individuals (existed in 2013)
t = 2013 - 1955 = 58 years

We need to solve for r. To do that, rearrange the formula:

r = [(N(t) / N₀)^(1/t)] - 1

Plug in the given values:

r = [(500 / 25)^(1/58)] - 1

r ≈ 0.029

So, the answer is (d) 0.029.

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Answer: my soul will always be with you, its in banana fish and i cried

Step-by-step explanation:

Using Binary addition with 2's complement, the following answers are found for the given expressions:
a) 47 - 83 = 11011101 (2's complement) = -60
b) -16 - 131 =  10010011 (2's complement) = -146

a. To solve 47 - 83 using binary addition with 2's complement, we first convert the numbers to their binary representation:

47 = 00101111

83 = 01010011

Now, let's perform the subtraction using binary addition with 2's complement:

00101111 (47)

01010011 (83, 2's complement)

11011100 (2's complement of 83)
11011101 (2's complement result)

The result in binary is 11011101. To convert it back to decimal, we take the 2's complement and add 1:

= 11011101 (2's complement)

= -1

= 11011100

The decimal equivalent of the binary result is -60. Therefore, 47 - 83 = -60.

b)  To solve -16 - 131 using binary addition with 2's complement, we need to convert the numbers to their binary representation:

-16 = 11110000

-131 = 10000011

Since we are subtracting, we need to find the 2's complement of the second number (131).

2's complement of 131:

Step 1: Invert the bits: 10000011 -> 01111100

Step 2: Add 1 to the inverted bits: 01111100 + 1 = 01111101

Now, let's perform the subtraction using binary addition:

11110000 (-16)

01111101 (2's complement of 131)

1 01101101 (Overflow bit)

The result in binary is 101101101, but since we are using 8-bit representation, we consider the result modulo 2^8. Therefore, the final result is 01101101, which is equal to 109 in decimal.

However, since we were subtracting, the result should be negative. To obtain the negative value, we consider the overflow bit (leftmost bit) and perform the 2's complement on the result.

2's complement of 01101101:

Step 1: Invert the bits: 01101101 -> 10010010

Step 2: Add 1 to the inverted bits: 10010010 + 1 = 10010011

Therefore, -16 - 131 = -146.


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The amount of water at the end of the fourth hour is 27000 gallons.

Given that :

A water tank is emptied at a constant rate.

Let x be the amount of water at first.

Amount of water at the end of first hour = 36000 gallons

Amount of water after the sixth hour = 21000 gallons.

The relation will be linear since the rate is constant.

Rate = (21000-36000) / (6 - 1)

       = -3000

Amount of water after fourth hour = 36000 + (-3000×3)

                                                         = 27000 gallons

Hence the amount of water after the fourth hour is 27000 gallons.

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Answer:

Step-by-step explanation:

since EG bisects angle DEF

31 = x + 15

31 - 15 = x

x = 16 degree

6x - 4 = 56

6x = 56 + 4

x = 60/6

x = 10

Answer:

8. 16

9. 10

abcdefghijklmnopqrstyvwxyz

The probability that the person selected is older than 20 years old and watching the drama movie is 0.765.

We have,

The total number of people who watch drama.

= 12 + 20 + 19

= 51

The total number of people who is older than 20 years who watch drama.

= 20 + 19

= 39

Now,

The probability that the person selected is older than 20 years old and watching the drama movie.

= 39/51

= 0.765

Thus,

The probability that the person selected is older than 20 years old and watching the drama movie is 0.765.

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Order from largest to smallest: 2.5 mL, 250μL, 0.025 mL, 2.5μL

Order from largest to smallest: 100μL, 0.015 mL, 250μL, 0.01 mL

To convert from μL to mL, divide by 1,000. Therefore, 1μL is equal to 0.001 mL or 1,000 μL is equal to 1 mL.To convert μL to mL, divide by 1,000. Thus, 2.5 mL is equal to 2,500 μL.To convert from μL to mL, divide by 1,000. Hence, 100μL is equal to 0.1 mL.To convert from μL to mL, divide by 1,000. Therefore, 250μL is equal to 0.25 mL.To convert from mL to μL, multiply by 1,000. So, 0.08 mL is equal to 80 μL.To convert from mL to μL, multiply by 1,000. Thus, 0.025 mL is equal to 25 μL.To convert from μL to mL, divide by 1,000. Hence, 2.5μL is equal to 0.0025 mL.To convert from mL to μL, multiply by 1,000. So, 0.01 mL is equal to 10 μL.To convert from mL to μL, multiply by 1,000. Thus, 0.015 mL is equal to 15 μL.

a. The volumes in order from largest to smallest are: 2.5 mL, 250μL, 0.025 mL, 2.5μL. This is determined by comparing the numerical values, with larger volumes being placed before smaller volumes.

b. The volumes in order from largest to smallest are: 100μL, 0.015 mL, 250μL, 0.01 mL. Again, this is determined by comparing the numerical values, with larger volumes placed before smaller volumes.

a. Setting the micropipette within its designated range is important to ensure accurate and precise volume measurements. Each micropipette has a specific volume range it can handle effectively, and using it within that range ensures reliable results.b. Using a micropipette with the appropriate tip is crucial for accurate volume transfer. Micropipette tips are designed to fit specific micropipette models, ensuring a secure and proper seal. Using the correct tip prevents leaks or inaccuracies in volume measurements.c. Holding a loaded micropipette in a vertical position helps prevent any air bubbles from being introduced into the sample or the pipette tip. This ensures accurate volume delivery and avoids any potential errors or contamination.d. Releasing the micropipette plunger slowly is necessary to ensure.

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Solving the question with the laws of combinatorics, specifically permutation problems.(a) 5,040 (b) 1,440. (c) 4,320.

(a) The word "mailbox" has 7 distinct letters. Therefore, the number of ways the letters can be arranged in a row is 7! = 5,040.

(b) If m and a must remain together (in order) as a unit, we can think of them as a single letter "ma". Now we have 6 letters to arrange in a row, which can be done in 6! ways. However, within the "ma" unit, the letters can be arranged in 2! ways. Therefore, the total number of arrangements is 6! × 2! = 1,440.

(c) If the letters ilb must remain together (in order) as a unit, we can think of them as a single letter "ilb". Now we have 5 letters to arrange in a row, which can be done in 5! ways. However, within the "ilb" unit, the letters can be arranged in 3! ways. Therefore, the total number of probable arrangements is 5! × 3! = 720 × 6 = 4,320.

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Step-by-step explanation:

my answer is in the image above

PN = LO

__________________________

(LO)^2 = (LN)^2 + (NO)^2

(LO)^2 = 6^2 + 8^2

(LO)^2 = 36 + 84

(LO)^2 = 100

LO = √100

LO = 10

__________________________

Thus :

PN = 10

Step-by-step explanation:

So, we can assume that LN and PO are equal in length and NO and LP are equal in length as well.  LO and PN are also equal.

We can see that PN is the hypotenus of either triangle NLP or NOP.  LO is the hypotenuse of LOP and LON, so those could be used to find the length as well.  I rather work with NOP, but any work.

We know that NO is 8 units long and LN is 6 units long.  Because LN = PO, PO = 6 units.

So, using the pythagorean theorem, the hypotenuse is:

8^2 + 6^2 = c^2

64 + 32 =c^2

sqrt(96)=c

c~9.8

I don't know how exact they want your answer.

c = 9.79795897113

Answer:

The answer is the picture down below. Hope this helps :)

Step-by-step explanation: