A sample of 92 one-year-old spotted flounder had a mean length of 123.47 millimeters with a sample standard deviation of 18.72 millimeters, and a sample of 138 two-year-old spotted flounder had a mean length of 129.96 millimeters with a sample standard deviation of 31.60 millimeters. Construct an 80% confidence interval for the mean length difference between two-year-old founder and one-year-old flounder. Let µ_1, denote the mean tength of two-year-old flounder and round the answers to at least two decimal places.
An 80% confidence interval for the mean length difference, in millimeters, between two-year-old founder and one-year old flounder is___<µ_1-µ_2<_____

The dependent variable is "f" in the given equation f = 0.73g + 16.8.

Values that differ in respect to one another are referred to as independent and dependent variables in mathematics. Because the dependent variable is reliant on the independent variable, it will change if the value of the independent variable does.

Given:

f = 0.73g + 16.8 .....(i)

The formula used to forecast a student's final exam grade, f, based on their current grade, g.

Because the independent variable "g" and the dependent variable "f" are interdependent, the dependent variable "f" will change if the independent variable "g" changes in value.

Thus, the dependent variable is "f" in the given equation f = 0.73g + 16.8.

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Answer:A normal QRS complex measures 0.06 to 0.12 seconds which is 1.5 to 3 small boxes on the EKG strip. When you measure the QRS complex you start by measuring at the END of the PR interval to the END of S-wave.

Step-by-step explanation:

The percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is  28.87%.

Given that the carrying capacity is directly proportional to the area, we can write:

C1 ∝ A1 = πr₁²

Since the carrying capacity is directly proportional to the area, we have:

C2 ∝ A2 = πr₂²

To find the percentage increase in diameter, we need to find the ratio of the increased area to the initial area and then express it as a percentage. Let's calculate this ratio:

(A2 - A1) / A1 = (πr₂² - πr₁²) / (πr₁²) = (r₂² - r₁²) / r₁²

We can also express the ratio of the increased carrying capacity to the initial carrying capacity:

(C2 - C1) / C1 = (60 - 36) / 36 = 24 / 36 = 2 / 3

Since the area and the carrying capacity are directly proportional, the ratios should be equal:

(r₂² - r₁²) / r₁² = 2 / 3

Now, let's substitute r = D/2 in the equation:

((D₂/2)² - (D₁/2)²) / (D₁/2)² = 2 / 3

(D₂² - D₁²) / D₁² = 2 / 3

Cross-multiplying:

3(D₂² - D₁²) = 2D₁²

3D₂² - 3D₁² = 2D₁²

3D₂² = 5D₁²

Dividing by D₁²:

3(D₂² / D₁²) = 5

(D₂² / D₁²) = 5 / 3

Taking the square root of both sides:

D₂ / D₁ = √(5/3)

To find the percentage increase in diameter, we subtract 1 from the ratio and express it as a percentage:

Percentage increase = (D₂ / D₁ - 1) × 100

Percentage increase = (√(5/3) - 1) × 100

Percentage increase = 28.87%

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y = -2x - 4

compare with y = mx + c

m = slope, c constant

so, slope m = -2

for graph,

y = - 2x - 4

put x = 0 so,the point is (0, -4)

y = -4

x = 1

y = -2(1) - 4

y = -2 - 4

y = -6 (1,60)

put x = 2 (2, -12)

y = -2(4) - 4

y = -8 -4

y = -12

NOw we can say that we point to draw, so now you draw the points on your graph, thank you

Answer:

x = 70

Step-by-step explanation:

The two angles are same side interior angles and same side interior angles add to 180

45+ (2x-5) = 180

Combine like terms

2x +40 = 180

Subtract 40 from each side

2x+40-40 =180-40

2x =140

Divide by 2

2x/2 = 140/2

x = 70

Answer:

x=70

Step-by-step explanation:

hope it helped! :)

have a nice day

The complementary event of randomly selecting an orange flower is selecting an orange, red, white, or purple flower (option C).

To identify the complementary event to selecting an orange flower, we must identify what other possibilities may occur if we do not select an orange flower at random.

In this case, picking an orange, red, white, or purple rose are still complementary events because they all have a probability of occurrence. In this case, the one that is most likely to occur is purple, orange, white and red due to the number of flowers of each color.

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Answer:

yes

Step-by-step explanation: if it goes through the orgin it is

the 95% confidence interval for the proportion of all dies that pass the probe is [0.513,0.616].

Sampling is frequently used to estimate the percentage of population that possesses a particular attribute, such as the percentage of all faulty goods which come off an assembly line or the percentage among all buyers that enter a store and make a purchase before leaving. The population proportion is indicated p, while the sample proportion is written p. Thus, if 43% of individuals visiting a business make a purchase before departing, p = 0.43; if 78 people enter the store and make a transaction, p=78/200=0.39.

The sample proportion is a random variable because it differs from sample to sample in ways that are impossible to anticipate in advance. When seen as a random variable, it will be represented by the letter P.

How to solve?

An article reported that in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 169 of these passed the probe.

So,p'=201/356=0.56460

The 95% confidence interval for the proportion of all dies that passed the probe will be,

p∈[p'±zα/2√p'(1−p')/n]

p∈[0.56460±1.96×√0.56460(1−0.56460)356]

p∈[0.513,0.616]

So the 95% confidence interval is [0.513,0.616].

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x = a number

12 + 4x = -8

Subtract 12 from both sides

4x = -20

Divide both sides by 4

x = -5

Answer:

Step-by-step explanation:

To find the inverse of a matrix, we need to put it in the reduced row echelon form (RREF) using elementary row operations. We can augment the given matrix with an identity matrix of the same size, and then apply the row operations to both matrices simultaneously until the left-hand side becomes an identity matrix. The right-hand side will then be the inverse of the original matrix.

Here are the steps:

[ 5 3 | 1 0 ]

[13 8 | 0 1 ]

R1/5 -> R1:

[ 1 3/5 | 1/5 0 ]

[13 8 | 0 1 ]

R2-13R1 -> R2:

[ 1 3/5 | 1/5 0 ]

[ 0 1/5 | -13 1 ]

R1-(3/5)R2 -> R1:

[ 1 0 | 26/5 -3/5 ]

[ 0 1 | -13 1/5 ]

So, the inverse matrix is:

[ 26/5 -3/5 ]

[-13 1/5 ]

The polygon tool to graph the dilated figure will be drawn below.

The collection includes all locations on the surface of the shape (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the curve of y = f. (x). As a result, the diagram of an equation is a particular instance of the graphs of functions.

It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

Graph the image of this figure after a dilation with a scale factor of 2 centered at the origin.

The polygon tool to graph the dilated figure will be drawn below.

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The number of rabbits on the farm is 575 and the number of chickens is 425.

Here we have to find the number of rabbits and the number of chickens on the farm.

Data given:

Total number of rabbits and chicken = 1000

Number of legs = 3150

Let x be the number of rabbits and y be the number of chickens.

So we have

x + y = 1000 -------(1)

4x + 2y = 3150

A rabbit has 4 legs and a chicken has 2 legs.

2x + y = 1575 ------(2)

Substrating equation (1) from (2) we have:

x = 575

Now put in equation (1) we have:

575 + y = 1000

y = 425

Therefore the number of rabbits is 575 and the number of chickens is 425.

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Using it's concept, the average rate of change is given as follows for the intervals:

a) -6 millions of dollars per year.

b) -18 millions of dollars per year.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

\(r = \frac{f(b) - f(a)}{b - a}\)

For item a, we have that:

Hence:

r = (366 - 372)/1 = -6 millions of dollars per year.

For item b, we have that:

Hence:

r = (318 - 372)/3 = -18 millions of dollars per year.

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Answer:

Line 1 and Line 2:  Parallel

Line 1 and Line 3: Perpendicular

Line 2 and Line 3: Perpendicular

Step-by-step explanation:

Put it into Desmos.

It really helps. Please tell me if this is wrong.

312 minutes the participant took to complete the marathon

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding.

According to the question,

The time taken by participant to complete a marathon in hours = 5.2 hours

1 hour contains 60 minutes

so, to change hours into minutes , we have to multiple hours into 60

Time taken  by participant to complete a marathon in minutes = 5.2 × 60

=> 312 minutes

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THIS IS THE COMPLETE QUESTION BELOW;

Complete the paragraph proof. Given: ∠ABR and ∠ACR are right angles AB ≅ BC BC ≅ AC Prove: bisects ∠BAC

It is given that ∠ABR and ∠ACR are right angles, AB ≅ BC and BC ≅ AC Since they contain right angles, △ABR and △ACR are right triangles. The right triangles share hypotenuse AR, and reflexive property justifies that AR ≅ AR. Since AB ≅ BC and BC ≅ AC, the transitive property justifies AB ≅ AC. Now, the hypotenuse and leg of right △ABR is congruent to the hypotenuse and the leg of right △ACR, so △ABR ≅ △ACR by the HL congruence postulate. Therefore, by CPCTC, and bisects ∠BAC by the definition of bisector.

Answer:

The answer is ∠BAR=∠CAR

Step-by-step explanation:

From the question, In the ΔABR and ΔACR , AB=AC=X

CHECK THE ATTACHMENT FOR DETAILED STEP BY STEP EXPLANATION:

Answer:

A) <BAR = <CAR

Step-by-step explanation:

Edge

Answer:

So first we need to get the perimeter formula. P = 2(w+l). We know P but we dont know w and h.

280/2 = 140. So now we know that 140 = w+l. We also know that the length is 4/3 times greater than the width (we used the ratio). To prove this 3*4/3 = 4, just like in ratio. So we have 2 equations

140 = w+l

l = 4/3w

Now we can plug into 140

140 = w+4/3w

So if you solve algebraicly you get

60 = w.

Now we can find that the length =

80 is the answer to length..

Now to prove answer 60+80 = 140.

So the answer is

The length of the rectangle is 80cm and the width is 60cm

The perimeter of the rectangle is given as 280cm and the ratio of the length to width is 3:4.

The formula of perimeter of rectangle is given as;

\(P=2(L+W)\)

This implies that

\(280=2(l + w)\\280=2l+2w\\l+w=140...equation(i)\)

But let's go back to our given ratio

3:4 = l:w

3l = 4w

make w the subject of formula

\(w = (3/4)l\)

Let's substitute this into equation (i)

\(l+w=140\\w=(3/4)l\\l+(3/4)l=140\\(7/4)l=140\)

solve for l

\(\frac{7}{4}l=140\\4*140 = 7l\\560=7l\\l= 560/7\\l=80\)

Since L = 80, let's substitute it into equation (i)

\(l+w = 140\\80+w = 140\\w = 140 - 80\\w = 60\)

From the calculations above, we have the following data

The length of the rectangle is 80cm and the width is 60cm

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Answer:triangles always equal 180 so subtract the variable inside the triangle.

Step-by-step explanation:

The equivalent equation to the (x² - 5)² - 3x² + 15 = -2 in form of 'm' is given by option c.  m² -3m + 2 = 0.

The equation is equal to,

(x² - 5)² - 3x² + 15 = -2

let the value of m be equals to x² - 5.

Simplify the equation we have,

⇒ ( x² - 5 )² - 3x² + 15 = -2

Take '3' common factor from the 3x² + 15 so that it get convert into x² - 5 we get,

⇒ ( x² - 5 )² - 3 (x² - 5 )  = -2

Now replace x² - 5 by m to get the equivalent equation,

⇒ ( m )² - 3 (m ) = -2

⇒ m² -3m + 2 = 0

Therefore, the equivalent equation to the given equation is written as option c.  m² -3m + 2 = 0.

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To estimate the mean IQ of all students with 99% confidence, we should use a confidence interval based on the t-distribution.

Given that we have a sample of 60 students with a mean IQ of 100.4 and a standard deviation of 5.2, we can use the t-distribution to construct a confidence interval for the population mean.

Since the population standard deviation is unknown and the sample size is relatively small, the t-distribution is appropriate for this scenario. With a desired confidence level of 99%, we would use the critical value associated with a 99% confidence level from the t-distribution.

By calculating the confidence interval using the sample mean, sample standard deviation, sample size, and the appropriate critical value from the t-distribution, we can estimate the mean IQ of all students with 99% confidence.

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\( c.\:{x}^{ - 4} \)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\( \frac{7 {x}^{4} }{7 {x}^{8} } \\ = \frac{ {x}^{4} }{ {x}^{8} } \\ = {x}^{4 - 8} \\ = {x}^{ - 4} \)

Note:-

\( {x}^{m} \times {x}^{n} = {x}^{m + n} \\ {x}^{m} \div {x}^{n} = {x}^{m - n} \)

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}\)

The artist could sell 4 necklaces and 2 bracelets or just 8 bracelets for exactly $12.

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

Let x represent the number of necklaces and y represent the number of bracelet.

Necklace cost $2.25 each, and bracelets cost $1.50 per each. The artist could sell exactly $12.00.​ Hence:

2.25x + 1.5y = 12

From the graph, the points (4,2) and (0, 8) satisfy this equation

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Answer:

7/12x+5

Step-by-step explanation:

The general solution to the given exact ODE is:

x²y + 4xy + (1/4)y⁴ - 8y - 2x³ = C

where C is an arbitrary constant.

To determine if the given ordinary differential equation (ODE) is exact, we need to check if it satisfies the condition for exactness:

∂M/∂y = ∂N/∂x

Let's evaluate the partial derivatives of the given equation:

∂M/∂y = 2x

∂N/∂x = 2x + 4

Since ∂M/∂y = ∂N/∂x, the equation satisfies the condition for exactness.

To solve the exact ODE, we need to find a potential function ψ(x, y) such that its partial derivatives satisfy the equation:

∂ψ/∂x = M      and      ∂ψ/∂y = N

From the given ODE, we can determine ψ(x, y) by integrating M with respect to x and integrating N with respect to y. Let's perform these integrations:

ψ(x, y) = ∫ (2xy - 6x² + 4y) dx = x²y - 2x³ + 4xy + h(y)

ψ(x, y) = ∫ (x² + 4x + y³ − 8) dy = x²y + 4xy + (1/4)y⁴ - 8y + g(x)

In order for the equation to be exact, the expressions for ψ(x, y) obtained from integrating M with respect to x and N with respect to y must be equal. Therefore, we have:

x²y - 2x³ + 4xy + h(y) = x²y + 4xy + (1/4)y⁴ - 8y + g(x)

From this equation, we can conclude that:

h(y) = (1/4)y⁴ - 8y + C₁

g(x) = -2x³ + C₂

where C₁ and C₂ are constants of integration.

Finally, substituting h(y) and g(x) back into ψ(x, y), we obtain the potential function:

ψ(x, y) = x²y + 4xy + (1/4)y⁴ - 8y - 2x³

Therefore, the general solution to the given exact ODE is:

x²y + 4xy + (1/4)y⁴ - 8y - 2x³ = C

where C is an arbitrary constant.

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Answer:

hamburger

Step-by-step explanation:

9.24÷7=1.32

8.28÷6=1.38

the hamburger is lower than the hot dog

The food which has the lower unit price is hamburgers which costs $1.32 per unit.

Given that, at a restaurant 6 hot dogs cost $8.28 and 7 hamburgers cost $9.24.

A unit price is the price for one item or measurement, such as a pound, a kilogram, or a pint, which can be used to compare the same type of goods sold in varying weights and amounts. Multiple pricing is selling two or more of the same item at a price that is lower than the unit price of a single item.

Unit price of hot dogs = 8.28/6

= $1.38

Unit price of hamburgers = 9.24/7

= $1.32

Therefore, the food which has the lower unit price is hamburgers which costs $1.32 per unit.

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Answer:

1.5% of 4000 or 60

Step-by-step explanation:

Option (C) Yes, they are independent because P(California) is 0.55 and P(California | brand B) is 0.55 is the correct answer.

Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.

For the given situation,

Total number of people in Texas = 275

Total number of people in California = 150

Total number of people in California and preferring brand B = 54

Probability of people in California,

P(California) = Number of people in California / Total number of people

⇒ \(\frac{150}{275}\)

⇒ \(0.54545\) ≈ \(0.55\)

Probability of people in California and preferring brand B

P(California | brand B) = Number of people in California and preferred brand B / Number of people preferred brand B

⇒ \(\frac{54}{99}\)

⇒ \(0.54545\) ≈ \(0.55\)

In the data provided, each event is not dependent on other events.

Thus they are independent events.

Hence we can conclude that option (C) Yes, they are independent because P(California) is 0.55 and P(California | brand B) is 0.55 is the correct answer.

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Answer:

54

Step-by-step explanation:

First take

9 + 9 = 18

Then,

126 - 18 = 108

Then,

108 / 2 = 54

Which is the height

Hope this helps you. :)

Have a good day!

This formula counts for both height and width when you have the area.

John Barker's repair shop in Ontario is required to calculate the HST payable or refund for the first reporting period. The HST rate is 13% and the amount before HST sales is $150,000. The total HST collected from sales is $19,500 and the total ITCs are $19,790. The net HST payable/refund is $19,500 - $19,790 and the correct option is d) A refund of $5,980.

Given the following information for John Barker's repair shop in Ontario, we are required to calculate the HST payable or refund for the first reporting period. The HST rate for Ontario is 13%.Amount Before HST Sales $150,000 Equipment purchased $96,000 Supplies purchased $83,000 Wages paid $19,000 Rent paid $17,000Let's calculate the total HST collected from sales:

Total HST collected from Sales= HST Rate x Amount before HST Sales

Total HST collected from Sales= 13% x $150,000

Total HST collected from Sales= $19,500

Let's calculate the total ITCs for John Barker's repair shop:Input tax credits (ITCs) are the HST that a business pays on purchases made for the business. ITCs reduce the amount of HST payable. ITCs = (HST paid on eligible business purchases) - (HST paid on non-eligible business purchases)For John Barker's repair shop, all purchases are for business purposes. Hence, the ITCs are the total HST paid on purchases.

Total HST paid on purchases= HST rate x (equipment purchased + supplies purchased)

Total HST paid on purchases= 13% x ($96,000 + $83,000)

Total HST paid on purchases= $19,790

Let's calculate the net HST payable or refund:

Net HST payable/refund = Total HST collected from sales - Total ITCs

Net HST payable/refund = $19,500 - $19,790Net HST payable/refund

= -$290 Since the Net HST payable/refund is negative,

it implies that John Barker's repair shop is eligible for an HST refund. Hence, the correct option is d) A refund of $5,980.

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