'Solve 4x- c= k for x.

The best interpretation of these data is that there is a direct relationship between number of hours studied and the score on the test.

The correlation coefficient r measures the strength and direction of a linear relationship between two variables. In this case, the positive value of r = .59 indicates a direct (or positive) relationship between number of hours studied and the score on the test. This means that as the number of hours studied increases, the score on the test tends to increase as well.

Therefore, we can conclude that more study leads to a higher score on the test.

Option 1 and 2 are correct interpretations, while options 3 and 4 are incorrect. Option 3 implies a negative correlation coefficient, while option 4 implies an inverse relationship between the variables, which is not the case here.

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The answer is explained in the photo I have linked.

Answer:

\(A_w=238x-2176\)

Step-by-step explanation:

From the question we are told that:

Length of pool \(L=34ft\)

Width of Pool \(W=x\).

Brick walkway Width \(W_b=4\)

Generally the expression for a Area of pool is mathematically given by

 \(A=L*W\)

 \(A=34*x\)

 \(A=34x\)

Generally the expression for a Area of pool + Walkway is mathematically given by

 \(A'=L'*B'\)

where

 \(L' =L+2(W_b)\)

 \(L' =34+2(4)\)

 \(L'=34+8\)

 \(L'=272\)

And

 \(W'=W+2(W_b)\)

 \(W' =x+2(4)\)

 \(W' =x+8\)

Therefore

 \(A'=L'*B'\)

 \(A'=(272)*(x+8)\)

 \(A'=272x+2176\)

Generally the expression for a Area of Walkway is mathematically given by

 \(A_w=Area\ of\ Pool+Walkway-Area\ of\ Pool\)

 \(A_w=A'-A\)

 \(A_w=272x+2176-34x\)

 \(A_w=238x-2176\)

Answer:

x=12

Step by step explanation:

Step by step explanation:Add 9 to both sides :

15 = 2x - 9

15 + 9 = 2x - 9 + 9

Simplify:

24 = 2x

Divide both sides to get the result:

24 = 2x

24/2 = (2x)/2

Result:

x=12

\(\boxed{\sf Answered \: By\: Subhash} \)

\(\boxed{\sf Good\: luck \: for \: your \:assignment} \)

Answer:

x=12

Step-by-step explanation:

\(15=2x-9\)

\(2x-9=15\)

\(2x-9+9=15+9\)

\(2x=24\)

\(\cfrac{2x}{2}=\cfrac{24}{2}\)

\(x=12\)

Answer:

-26x-15

Step-by-step explanation:

I'm positive this is the right answer

Answer:

Step-by-step explanation:

I guess you are simplifying the equation here.

by moving everything with the x to the left and the constants to the right,

we can get -26x-7x+7x+15

Here, -7x+7x can be cancelled out, therefore it would be -26x+15

Answer:

Segment Addition Postulate

The segment addition postulate in geometry is applicable on a line segment containing three collinear points. The segment addition postulate states that if there are two given points on a line segment A and C, then point B lies on the same line segment somewhere between A and C only if the sum of AB and BC is equal to AC.

Segment Addition Postulate Definition

The segment addition postulate states that if a line segment has two endpoints, A and C, a third point B lies somewhere on the line segment AC if and only if this equation AB + BC = AC is satisfied. Look at the image given below to have a better understanding of this postulate.

Answer:

A. y= -3x - 1

that's the answer of you substitute the figures in x into where x can be located in A

The concentrations of the other three tubes are 1500 ng/ml, 15000 ng/ml, and 150000 ng/ml, respectively.

In order to answer the question, we need to have more information about the dilution factor of the tubes. Assuming that all the tubes have the same dilution factor, we can use the formula:C1V1 = C2V2

Where,C1 = concentration of the initial solution,V1 = volume of the initial solution,C2 = concentration of the final solution,V2 = volume of the final solution

Given that the concentration of the first tube is 150 ng/ml, we can use the above formula to calculate the concentrations of the other three tubes, provided we know the dilution factor.

Let's assume that the dilution factor is 10, which means that the initial volume was diluted by a factor of 10 to obtain the final volume in each tube.

Using the formula,C1V1 = C2V2

For tube 1, C1 = 150 ng/ml, V1 = 1 ml (assuming initial volume is 1 ml), C2 = concentration of tube 2, V2 = 0.1 ml (assuming a dilution factor of 10)

Substituting the values,150 x 1 = C2 x 0.1C2 = 1500 ng/ml

Therefore, the concentration of tube 2 is 1500 ng/ml.

Repeating the same process for the other two tubes, we get:C3 = 15000 ng/mlC4 = 150000 ng/ml

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If the height of the toy box is changed from 4 yards to 8 yards, the volume of the box would double.

The volume of a rectangular box can be calculated by multiplying its length, width, and height. In this case, the toy box initially has dimensions of 7 yards by 6 yards by 4 yards.

The initial volume of the toy box is:

Volume = Length * Width * Height

Volume = 7 yd * 6 yd * 4 yd

Volume = 168 cubic yards

When the height is changed to 8 yards, the new volume of the box would be: Volume = Length * Width * Height

Volume = 7 yd * 6 yd * 8 yd

Volume = 336 cubic yards

Comparing the initial volume (168 cubic yards) to the new volume (336 cubic yards), we can see that the volume of the box doubles when the height is changed from 4 yards to 8 yards.

This is because the volume of a rectangular box is directly proportional to its dimensions. When the height is doubled, the overall volume doubles as well.

This can be understood by considering that doubling the height effectively doubles the number of cubic units that can fit within the box, resulting in a doubled volume

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Answer:

Step-by-step explanation:

In the arithmetic sequence \(t_1\), \(t_2\), \(t_3\), ..., \(t_n\), \(t_1=23\) and \(t_n= t_{n-1} - 3\) for each n > 1. What is the value of n when \(t_n = -4\)?

A. -1

B. 7

C. 10

D. 14

E. 20

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E.

MGMAT 1 --> 530

MGMAT 2--> 640

MGMAT 3 ---> 610

GMAT ==> 730

Answer:

4 + 3(n-1)

Step-by-step explanation:

Sequences start from n=1,2,3....

In this case

4 + 3(1-1)= 4

4 + 3(2-1) =7

And continue the pattern

Therefore, the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM is approximately 0.1755, rounded to four decimal places.

To calculate the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM, we need to use the Poisson distribution formula. The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space. In this case, the mean (λ) is given as 5. The formula for the Poisson distribution is:

P(X = k) = (e*(-λ) * λ\(^k\)) / k!

Where:

P(X = k) is the probability of getting exactly k calls

e is the base of the natural logarithm (approximately 2.71828)

λ is the mean number of calls (given as 5)

k is the number of calls (in this case, 4)

k! is the factorial of k

Let's calculate the probability using the formula:

P(X = 4) = (e*(-5) * 5⁴) / 4!

P(X = 4) ≈ 0.1755

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Answer:

  18.8 inches

Step-by-step explanation:

You want the length of arc traveled by the tip of a 4" minute hand moving from 1:30 pm to 2:15 pm.

The time difference between 2:15 and 1:30 is 45 minutes, or 3/4 hour. The minute hand moves through an angle of 2π radians in 1 hour, so will move through an angle of (3/4)(2π) = 3/2π radians in 3/4 hour.

The length of an arc is given by the formula ...

  s = rθ

where r is the radius, and θ is the central angle in radians.

Here, we have r = 4 in, and θ = 3π/2. The arc length is ...

  s = (4 in)(3π/2) = 6π in ≈ 18.8496 in

The minute hand moves through an arc of about 18.8 inches from 1:30 to 2:15.

\(\left \{ {{2y-x=-9} \atop {y=2x-3}} \right. \iff \left \{ {{2(2x-3)-x=-9} \atop {y=2x-3}} \right. \iff \{ {{4x-6-x=-9} \atop {y=2x-3}} \right. \\\)

\(\{ {{3x=-9+6} \atop {y=2x-3}} \right. \iff \{ {{3x=-3} \atop {y=2x-3}} \right. \iff \{ {{x=-1} \atop {y=2x-3}} \right. \\\)

\(\{ {{x=-1} \atop {y=2(-1)-3}} \right \iff \{ {{x=-1} \atop {y=-2-3}} \right \implies \bf \{ {{x=-1} \atop {y=-5}}\)

\(\implies (x, \ y) = (-1, \ -5)\)

Answer:

The third triangle

Step-by-step explanation:

The Exterior Angle is the angle a side of a shape and a line extended from the side next to it.

So for example, the first picture shows an exterior angle because a line was extended and it forms an angle with the triangle's side.

The second picture is still an exterior angle because the angle is formed with an extended line and the triangle's side.

The third photo shows an angle formed between a random line and the triangle's side. This is not an exterior angle because the angle is not formed with any side's extension.

The fourth photo is an exterior angle because it shows the angle being formed with an extension of a line from the triangle and a side of the triangle.

Hope this helps! Feel free to ask any questions! :)

Answer:

C the third triangle. Hope this helps

Step-by-step explanation:

The given integral is ∫(0 / x² √(2² + 490)) dx. To solve this integral, we can make a substitution by letting x = 7tan(θ), where θ is between -π/8 and π/8. Then, dx = 2sec²(θ) dθ. The given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

Substituting these expressions in the integral, we have ∫(0 / (7tan(θ))² √(2² + 490))(2sec²(θ)) dθ. Simplifying further, we get ∫(0 / 49tan²(θ) √(4 + 490))(2sec²(θ)) dθ. Rearranging the expression under the square root, we have ∫(0 / 49sec²(θ) √(4(1 + 122.5tan²(θ))))(2sec²(θ)) dθ. This can be simplified to ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

In summary, the given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

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The given integral is ∫(0 / x² √(2² + 490)) dx. To solve this integral, we can make a substitution by letting x = 7tan(θ), where θ is between -π/8 and π/8. Then, dx = 2sec²(θ) dθ. The given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

Substituting these expressions in the integral, we have ∫(0 / (7tan(θ))² √(2² + 490))(2sec²(θ)) dθ. Simplifying further, we get ∫(0 / 49tan²(θ) √(4 + 490))(2sec²(θ)) dθ. Rearranging the expression under the square root, we have ∫(0 / 49sec²(θ) √(4(1 + 122.5tan²(θ))))(2sec²(θ)) dθ. This can be simplified to ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

In summary, the given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

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Actually Welcome to the concept of Radioactive decay.

So the left would be 30 grams.

Answer:

1256cm^2

Step-by-step explanation:

The area of a circle is πr^2.

The radius is half of the diameter, so it's 20 cm.

A=3.14*(20cm)^2

A=3.14*400cm^2

A=1256cm^2

The answer of the given question based on the assuming that the spins are independent, the pmf of x is P(x = k) = (2/3)^(k-1) * (1/3).

Probability is a measure of likelihood or chance that specific event will occur. It is  branch of mathematics that deals with study of random events and their associated outcomes.

In probability theory, events are typically represented as sets of possible outcomes, and probabilities are assigned to these events based on likelihood of their occurrence. The probability of  event is  number between 0 and 1, where 0 represents  impossible event and 1 represents certain event.

Let's denote the probability of getting a 3 on any given spin as p. Since the spinner only has three numbers, the probability of getting a 3 on any given spin is 1/3.

Now, let's consider the probability distribution of x, the number of spins until the first 3 occurs. The probability that x = 1 is simply the probability of getting a 3 on the first spin, which is p = 1/3.

The probability that x = 2 is the probability of not getting a 3 on the first spin (which is 2/3), multiplied by the probability of getting a 3 on the second spin (which is p = 1/3). So:

P(x = 2) = (2/3) * (1/3) = 2/9

Similarly, the probability that x = 3 is the probability of not getting a 3 on the first two spins (which is (2/3)^2), multiplied by the probability of getting a 3 on the third spin (which is p = 1/3). So:

P(x = 3) = (2/3)²* (1/3) = 4/27

In general, the probability that x = k (where k is a positive integer greater than or equal to 1) is the probability of not getting a 3 on the first k-1 spins (which is (2/3)^(k-1)), multiplied by the probability of getting a 3 on the kth spin (which is p = 1/3). So:

P(x = k) = (2/3)^(k-1) * (1/3)

This is the pmf (probability mass function) of x, the number of spins until the first 3 occurs.

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The answer of the given question based on the assuming that the spins are independent, the pmf of x is P(x = k) =\((2/3)^{k-1}\) × (1/3).

Probability is a measure of likelihood or chance that specific event will occur. It is  branch of mathematics that deals with study of random events and their associated outcomes.

In probability theory, events are typically represented as sets of possible outcomes, and probabilities are assigned to these events based on likelihood of their occurrence. The probability of  event is  number between 0 and 1, where 0 represents  impossible event and 1 represents certain event.

Let's denote the probability of getting a 3 on any given spin as p. Since the spinner only has three numbers, the probability of getting a 3 on any given spin is 1/3.

Now, let's consider the probability distribution of x, the number of spins until the first 3 occurs. The probability that x = 1 is simply the probability of getting a 3 on the first spin, which is p = 1/3.

The probability that x = 2 is the probability of not getting a 3 on the first spin (which is 2/3), multiplied by the probability of getting a 3 on the second spin (which is p = 1/3). So:

P(x = 2) = (2/3) × (1/3) = 2/9

Similarly, the probability that x = 3 is the probability of not getting a 3 on the first two spins (which is (2/3)^2), multiplied by the probability of getting a 3 on the third spin (which is p = 1/3). So:

P(x = 3) = (2/3)² × (1/3)

= 4/27

In general, the probability that x = k (where k is a positive integer greater than or equal to 1) is the probability of not getting a 3 on the first k-1 spins (which is  \((2/3)^{k-1}\)), multiplied by the probability of getting a 3 on the kth spin (which is p = 1/3). So:

P(x = k) = \((2/3)^{k-1}\) × (1/3).

This is the pmf (probability mass function) of x, the number of spins until the first 3 occurs.

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By repeatedly dividing the number by 2 and noting the remainders in each step, we can obtain the binary representation. The completed table will provide the binary digits, and combining them in reverse order will give the binary number.

We start by dividing 146 by 2 and noting the quotient and remainder. The quotient is obtained by dividing the number by 2, and the remainder is the modulo 2 of the number. In the table, we record the quotient in the "n div 2" column and the remainder in the "n mod 2" column. We repeat this process by dividing each subsequent quotient by 2 until the quotient becomes 0.

For the given example:

In the first row, we divide 146 by 2, resulting in a quotient of 73 and a remainder of 0.

In the second row, we divide 73 by 2, resulting in a quotient of 36 and a remainder of 1.

We continue this process until we reach a quotient of 0.

Once the table is completed, we read the remainders from bottom to top to obtain the binary digits. In this case, the binary representation of 146 is 10010010.

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Answer:

A

Step-by-step explanation:

This is because vertical angles are always congruent, they cross diagonally which makes them equal to each other.

When two perpendiculars line intersect the angles formed must be a right angle. Hence option b is correct.

The angle can be defined as the one line inclined over other line.

Here, When perpendicular lines intersect each other the angle formed between them is 90 degree. So the angles are right angles.

Thus, when two perpendiculars line intersect the angles formed must be a right angle.

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Answer:

-4

Step-by-step explanation:

Use PEMDAS

Answer:

-4

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

;-;

Answer:

the answer to your question is 9

Step-by-step explanation:

1+(1+1+1+1+1+1+1+1)=9

Answer:

246 in^2

Step-by-step explanation:

Given data

Length= 8 in

Width= 3 in

Height= 9 in

SA= 2( lw + wh + hl)

substitute

SA= 2(8*3+ 3*9+ 9*8)

SA= 2(24+ 27+72)

SA= 2(123)

SA= 246 in^2

Hence the SA is 246 in^2

The value beach according to the analogy will be 38 .

Given,

dad = 18

fish = 84

feed = 40

Here,

Analogy applied :

Determine the place value of the letters in each word.

dad = 4 + 1 + 4= 9

Now multiply the sum by 2.

dad = 9 *2 = 18

Similarly,

fish = 6 + 9 + 19 + 8 = 42

fish = 42 *2

fish = 84

Similarly,

feed = 6 + 5 + 5 + 4

feed = 20 *2 = 40

Finally,

beach = 2 + 5 + 1 + 3 + 8

beach = 19

beach = 19*2 = 38 .

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Due to availability of evidence we support the claim that the bags are underfilled, therefore we reject the null hypothesis, under the condition bag filling machine works correctly at the 443.0 gram setting.

The null hypothesis is that the bags are considered not underfilled and the other alternative hypothesis is that the bags are underfilled.

The level of significance is 0.05 which means that we have  to reject the null hypothesis if the p-value  < 0.05.
Given,
The sample size is 48 and the sample mean is 439 grams. Standard deviation = 25 grams.
The test statistic is evaluated
Z = (x'- μ) / (σ / √n)

Here,
x' = sample mean,
μ = hypothesized population mean,
σ = population standard deviation,
n = sample size.

Staging the values we get:

Z = (439 - 443) / (25 / √48)
= -2.45

The p-value can be calculated applying a Z-table.
Z = -2.45 is approximately 0.0071.

Since the p-value (0.0071) is less than the level of significance (0.05), we reject the null hypothesis.

Hence, there is enough proof to support the fact that the bags are underfilled.

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Answer: Profit: $240

Step-by-step explanation:

In order to find the profit you need to multiply $64 by 8 sweaters. After you multiply $64 by 8 sweaters, you get your answer as $512. Finally, you subtract $512 by $272 and get your final answer as $240.

Using the t-distribution, we have that the 95% confidence interval for the true mean number of pushups that can be done is (9, 21).

For this problem, we have the standard deviation for the sample, thus, the t-distribution is used.

First, we find the number of degrees of freedom, which is the one less than the sample size, thus df = 9.

Then, looking at the t-table or using a calculator, we find the critical value for a 95% confidence interval, with 9 df, thus t = 2.2622.

The margin of error is of:

\(M = t\frac{s}{n}\)

Then:

\(M = 2.2622\frac{9}{\sqrt{10}} = 6\)

The confidence interval is:

\(\overline{x} \pm M\)

Then

\(\overline{x} - M = 15 - 6 = 9\)

\(\overline{x} + M = 15 + 6 = 21\)

The confidence interval is (9, 21).

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