What is the probability of pulling a blue marble out of a bag that has 16 red marbles, 24 blue marbles, 42 yellow marbles, and 64 green marbles?

The absolute value of change in the predicted value of dependent variable Y is 18.

Any variable whose value is influenced by an independent variable is said to be dependent. The thing that is measured or assessed in an experiment or mathematical equation is the dependent variable. The phrase "the outcome variable" is another name for the dependent variable.

Slope = b = -4

Intercept = a = -2.8

So, the equation of the regression line is

y  =  a + bx

y = -2.8 - 4x              ...Equation 1

Now suppose the value of x is changed by adding 4.5

i.e. put x = x + 4.5

So,

y = -2.8 - 4(x + 4.5)

y = -2.8 -4x - 18         ...Equation 2

Comparing 1 and 2 ,

We get the predicted value of dependent variable Y as 18

Therefore The absolute value of change in the predicted value of dependent variable Y is 18

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According to the calculations, the length of the enclosure is 100 meters, and the width is 50 meters.

To determine, using a linear system of inequalities, how long each side of the rectangle measures, the following calculation must be performed:

Length + width = Total fencing

Therefore, the length of the enclosure is 100 meters, and the width is 50 meters.

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3 (hight) × 8 (base) = 24

24 ÷ 2 = 12 (area of triangle)

12 × 2 = 24 (because there are 2 triangles)

5 × 7 = 35 (because length times width)

35 × 2 = 70 (because there are 2 rectangles)

8 × 7 = 56 (because of the base)

24 + 12 + 24 + 35 + 70 + 56 = 221

Answer: 3.9b−2.6

Step-by-step explanation: Hope this helps

Answer:

1.3b

Step-by-step explanation:

The equation is -2.6+3.9b. A negative number acts like subtraction, so we would subtract 2.6 from 3.9 to get 1.3. The b is still there, and we don't know what it is, so we simplify the equation to 1.3b.

Sorry, this explanation isn't the best. Hope it helped! :)

It is 45° because the sum of all the angles of a triangle is 180° so

\(75° +60° +x = 180° \\ x =180° - 75° -60° \\ x = 45°\)

The asymptotic distribution of \(\( \bar{X}_{n}^{2} \)\) can be determined using the Central Limit Theorem (CLT).

The CLT states that for a sequence of independent and identically distributed random variables with mean μ and variance σ^2, as n approaches infinity, the distribution of the sample mean \(\(\bar{X}_{n}\)\) converges to a normal distribution with mean μ and variance\(\(\frac{\sigma^2}{n}\)\)

In this case, we have \(\( \bar{X}_{n}^{2} \),\) which is the square of the sample mean. To find its asymptotic distribution, we can use the Delta Method. The Delta Method is a generalization of the CLT that allows us to find the asymptotic distribution of a function of a random variable.

Applying the Delta Method, we can express\(\( \bar{X}_{n}^{2} \)\)as a function of \(\(\bar{X}_{n}\): \( \bar{X}_{n}^{2} = g(\bar{X}_{n}) = (\bar{X}_{n})^{2} \).\)

Taking the derivative of g(x) with respect to x and evaluating it at the population mean μ, we have g'(x) = 2x, so g'(μ) = 2μ.

Using the Delta Method, the asymptotic distribution of\(\( \bar{X}_{n}^{2} \)\)is a chi-squared distribution with one degree of freedom (df=1) multiplied by \(\( (2\mu)^{2} \):\)

\(\( \bar{X}_{n}^{2} \) ~ \( \chi_{1}^{2} \) multiplied by \( (2\mu)^{2} \).\)

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Answer:

345 free throws

Step-by-step explanation:

To find the total number of free throws Caroline attempted, we can set up the equation: (total free throws) x 0.20 = 69 (missed free throws)

Solving for the total free throws:

(total free throws) = 69 / 0.20

(total free throws) = 345

So Caroline attempted 345 free throws in the season.

The name of the segment inside the large triangle is called the: 3. angle bisector.

The word "bisect" means to divide into two equal halves. Therefore, an angle bisector can be defined as a line segment that divides the an angle in a triangle into two parts that are of the same angle measure.

The image shows a triangle which has a segment that divides a vertex angle into equal parts. Thus, the segment can be named as an angle bisector.

A perpendicular bisector divides a segment into two equal halves at right angle, while a midsegment joins the middle points of two sides of a triangle. The median also, is a segment that joins a vertex of a triangle to the midpoint of the side that is opposite the angle.

Therefore, we can state that the name of the segment is: 3. angle bisector.

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Answer:

5.3

Step-by-step explanation:

a² + b² =² c²               the Pythagorean theorem

RQ² + RS² = QS²            Solve RS

6² + RS² = 8²

RS² = 64 -36

RS² = 28

RS = √28                  28 is slightly > 25   and since  √25 =5

RS = 5.3                    actually 5.2915  to a few more significant digits

Answer:

1) \(\sqrt{1225}+\sqrt{1024}=67\)

2)  \(\sqrt[3]{-1331}=-11\)

3) Evaluating \(2:p :: p:8\) we get \(p=\pm 4\)

4) \(x^3+y^2+z \ when \ x=3, y=-2, x=-6 \ we \ get \ \mathbf{25}\)

5) \(\frac{(-6)^4\times(-2)^3\times(3)^3}{(-6)^6}=-6\)

Step-by-step explanation:

1) \(\sqrt{1225}+\sqrt{1024}\)

Prime factors of 1225 : 5x5x7x7

Prime factors of 1024: 2x2x2x2x2x2x2x2x2x2

\(\sqrt{1225}+\sqrt{1024}\\=\sqrt{5\times5\times7\times7}+\sqrt{2\times2\times2\times2\times2\times2\times2\times2\times2\times2}\\=\sqrt{5^2\times7^2}+\sqrt{2^2\times2^2\times2^2\times2^2\times2^2}\\=5\times7+(2\times2\times2\times2\times2)\\=35+32\\=67\)

\(\sqrt{1225}+\sqrt{1024}=67\)

2) \(\sqrt[3]{-1331}\)

We know that \(\sqrt[n]{-x}=-\sqrt[n]{x} \ ( \ if \ n \ is \ odd)\)

Applying radical rule:

\(\sqrt[3]{-1331}\\=-\sqrt[3]{1331} \\=-\sqrt[3]{11\times\11\times11}\\=-\sqrt[3]{11^3} \\Using \ \sqrt[n]{x^n}=x \\=-11\)

So, \(\sqrt[3]{-1331}=-11\)

3) \(2:p :: p:8\)

It can be written as:

\(p*p=2*8\\p^2=16\\Taking \ square \ root \ on \ both \ sides\\\sqrt{p^2}=\sqrt{16}\\p=\pm 4\)

Evaluating \(2:p :: p:8\) we get \(p=\pm 4\)

4) \(x^3+y^2+z \ when \ x=3, y=-2, x=-6\)

Put value of x, y and z in equation and solve:

\(x^3+y^2+z \\=(3)^3+(-2)^2+(-6)\\=27+4-6\\=25\)

So, \(x^3+y^2+z \ when \ x=3, y=-2, x=-6 \ we \ get \ \mathbf{25}\)

5) \(\frac{(-6)^4\times(-2)^3\times(3)^3}{(-6)^6}\)

We know (-a)^n = (a)^n when n is even and (-a)^n = (-a)^n when n is odd

\(\frac{(-6)^4\times(-2)^3\times(3)^3}{(-6)^6}\\\\=\frac{1296\times-8\times 27}{46656}\\\\=\frac{-279936}{46656} \\\\=-6\)

So, \(\frac{(-6)^4\times(-2)^3\times(3)^3}{(-6)^6}=-6\)

The odds in favor of winning $5 or more is 3 : 13

The odds of winning $5 or more can be determined by finding the ratio of the total value of tickets that have a value of $5 or greater to the total value of tickets.

Total number  of the tickets that have a value of $5 or more = 25 + 5 = 30

Total number of ticket  = 25 + 5 + 100 = 130

Ratio : 30 : 130

3 ; 13

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On solving the given problem by help of mathematical operations, we got - After Ray poured 0.47L, he was left with 2.201L.

The term "operation" in mathematics refers to the process of calculating a value using operands and a math operator. For the given operands or numbers, the math operator's symbol has predetermined rules that must be followed.

In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Total amount of tea Ray has - 2.671L

Amount of tea Ray poured - 0.47

Therefore,

amount he was left with was  = 2.671- 0.47 = 2.201L

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Given functions f(x) = V1 and g(x) = 16 f 32, we can find f + g, f - g, 3g, and the domain of f + g. The results are: f + g = V1 + 16 f 32, f - g = V1 - 16 f + 32, 3g = 3(16 f 32), and the domain of f + g is the intersection of the domains of f and g.

To find f + g, we simply add the two functions together. In this case, f + g = V1 + 16 f 32.

For f - g, we subtract g from f. Therefore, f - g = V1 - 16 f + 32.

To find 3g, we multiply g by 3. Hence, 3g = 3(16 f 32) = 48 f - 96.

The domain of f + g is determined by the intersection of the domains of f and g. Since the domain of f is the set of all real numbers and the domain of g is also the set of all real numbers, the domain of f + g is also the set of all real numbers. This means that there are no restrictions on the values that x can take for the function f + g.

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The lateral faces of the given prism are rectangles and thus prove that it is a right prism, we need to have certain information about its properties and dimensions.

The term "right prism" means that the prism has rectangular bases that are perpendicular to the lateral faces or sides. This means that all the lateral faces must also be rectangles, as stated in the question.It also does not provide any angles or other measurements that can help us determine if the faces are rectangles or not.
We could make some assumptions based on the definition of a right prism and the fact that it is a commonly used shape in geometry and engineering. We could assume that the prism has right angles at all of its corners and that its lateral faces are parallel to each other.

The lateral faces of the prism are rectangles, its dimensions and properties. This could be provided through measurements or diagrams that show the shape and angles of the prism, or through mathematical calculations that demonstrate that the faces must be rectangles based on the given dimensions.

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Given the expression: (3.2+0.2)2+12​

To get the value of the expression, do the following:

1. add 3.2 and 0.2

2. multiply 3.4 by 2

3. add 6.8 and 12

So, the value of the expression = 18.8

The average retail price of Raymond's vehicle is $24,400.

What is Average Retail Price?

Average price is a measure of a range of prices. It is calculated by taking the sum of the values and dividing it by the number of prices being examined. The average price reduces the range into a single value, which can then be compared to any other point to determine if the value is higher or lower than what would be expected.

average retail value = $17,600

All the additions to the average retail value are;

$1,700 for 4-wheel drive

$475 for an entertainment system

$800 for a special trim package

$225 for power locks

$125 for a sliding rear window

$325 for a towing package

$250 for power windows

$3,125 for a diesel engine

$450 for less than expected mileage

Deductions

$675 for having a manual transmission

Average retail price = Average retail value + additions - deductions

Average retail price = $17,600 + ($1,700+$475+$800+$225+$125+$325+$250+$3,125+$450) - $675

Average retail price = $17,600 + $7,475 - $675

Average retail price = $24,400

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Answer:

x = 2af/cg.

Step-by-step explanation:

cx/2 = a f/g

Multiply through by 2g:

cgx = 2af

Divide both sides by cg:

x = 2af/cg.

The solution of the given equation for x is 2af/cg.

The given equation is cx/2 = a f/g.

We need to solve the given equation for x.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, cx/2 = a f/g

By multiplying 2g on both the side of the equation, we get

cgx = 2af

Divide both sides of the equation by cg.

That is, x = 2af/cg

Therefore, the solution of the given equation for x is 2af/cg.

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Answer:

325.6g

Step-by-step explanation:

weight of phone + weight of case

= 310 + 15.6

= 325.6g

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The ratios involved in the ROI formula are the net profit and the investment cost.

The ROI (Return on Investment) formula includes the following ratios:

Net Profit: The net profit represents the profit gained from an investment after deducting expenses, costs, and taxes.

Investment Cost: The investment cost refers to the total amount of money invested in a project, including initial capital, expenses, and any additional costs incurred.

The ROI formula is calculated by dividing the net profit by the investment cost and expressing it as a percentage.

ROI = (Net Profit / Investment Cost) * 100%

Therefore, the ratios involved in the ROI formula are the net profit and the investment cost.

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Ans: The value of f(t) is 10t/π.

The given signal is x(t)=3cos(−10t²+π/5)+4cos(10t²−π/7)

Let's use the following formula to convert x(t) into the standard sinusoidal form.

Acos(ωt2+φ).Acos(ωt2+φ)=Acosφcos(ωt2)−Asinφsin(ωt2)x(t)=3cos(−10t²+π/5)+4cos(10t²−π/7)x(t)=3cos(−10t²)cos(π/5)+3sin(−10t²)sin(π/5)+4cos(10t²)cos(π/7)−4sin(10t²)sin(π/7)x(t)=3cos(−10t²)cos(π/5)−3sin(10t²)sin(π/5)+4cos(10t²)cos(π/7)−4sin(10t²)sin(π/7)x(t)=(3cos(π/5))cos(10t²)+(−4sin(π/7))sin(10t²)+(−3sin(π/5))sin(10t²)+(4cos(π/7))cos(10t²)x(t) =3/2cos(10t²)+ 1/2cos(10t²−2π/7) −1/2cos(10t²+2π/5)+2sin(10t²−π/7)

Let's convert

x(t) into the standard sinusoidal form.

Acos(ωt2+φ).Here, A= 2√(13), φ=−π/7ω= 10Hzx(t)=3/2cos(10t²)+1/2cos(10t²−2π/7)−1/2cos(10t²+2π/5)+2sin(10t²−π/7)A= 2√(13)x(t)=2√(13)cos(10t²−π/7+π/2)x(t)=2√(13)cos(10t²−π/7)cos(π/2)−2√(13)sin(10t²−π/7)sin(π/2)x(t)=2√(13)sin(10t²−π/7)

Now, let's find the instantaneous frequency in Hz. An instantaneous frequency in Hz can be defined as the derivative of the phase φ with respect to time t.f(t)=1/2π dφ(t)/dtx(t)=Acos(ωt²+φ).

The derivative of the phase φ with respect to time t is given bydφ(t)/dt= 2ωtTherefore, the instantaneous frequency in Hz is given byf(t)=1/2π dφ(t)/dt=1/2π (2ωt)f(t)=ωt/πNow, let's substitute the value of ω and get the value of f(t).ω = 10 Hzf(t) = ωt/π = 10t/π

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The number 192 falls between the tens 190 and 200.

What is Number system?

A system for representing and expressing numbers is referred to as a number system. It is a system of guidelines, icons, and conventions for presenting and communicating numerical data. There are various number systems that differ according to the symbols used and the positional values given to each symbol.

The decimal system, usually referred to as the base-10 system, is the most widely used numbering scheme. Ten digits are used to express numbers in the decimal system: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Based on powers of 10, the position of each digit in a number affects that number's value. For instance, in the number 123, the digits 3 and 2 correspond to ones, tens, and hundreds, respectively.

Let us first contrast 192 with 190:

192 - 190 = 2

2 separates the numbers 192 and 190. We can infer that 192 is greater than the lower bound 190 because it is greater than 190.

Compare 192 to 200 next: 200 - 192 = 8

There are 8 decimal places between 200 and 192. We can infer that 192 is less than the upper bound of 200 because it is less than 200.

Combining the findings, we were able to demonstrate that 192 is higher than 190 and lower than 200. As a result, we can say that 192 is between tens 190 and 200.

Therefore the number 192 falls between the tens 190 and 200.

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To find the probability of event A (first card drawn is a club), event B (second card drawn is a club), and event C (third card drawn is red), we can use the Multiplication Rule for independent events.

Given that the events are independent, the probability of all three events occurring is the product of their individual probabilities.

Let's calculate the probability step by step:

1. Probability of event A: P(A) = Number of clubs / Total number of cards

  There are 13 clubs in a deck of 52 cards, so P(A) = 13/52 = 1/4.

2. Probability of event B: P(B) = Number of clubs (after one club is drawn) / Total number of remaining cards

  After one club is drawn, there are 12 clubs left out of 51 remaining cards, so P(B) = 12/51 = 4/17.

3. Probability of event C: P(C) = Number of red cards / Total number of remaining cards

  There are 26 red cards (diamonds and hearts) out of 50 remaining cards, so P(C) = 26/50 = 13/25

Now, using the Multiplication Rule:

P(A and B and C) = P(A) * P(B) * P(C) = (1/4) * (4/17) * (13/25) = 0.03117647059.

Rounding this result to four decimal places, we get approximately 0.0312.

Therefore, the probability that the first two cards drawn are clubs and the last card is red is approximately 0.0312.

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An interaction occurs when the effect of one factor (such as factor A) depends on the level of another factor (such as factor B). This means that the effect of factor A is not constant across all levels of factor B, and vice versa.

For example, consider a study examining the effects of a new drug on blood pressure in two different age groups: younger adults (age 18-35) and older adults (age 60 and above). The study also includes a placebo group. The researchers found that the new drug has a significantly larger effect on reducing blood pressure in older adults compared to younger adults and that the placebo has no effect on blood pressure in either age group.

In this case, there is an interaction between the factors of age and the new drug, because the effect of the drug on blood pressure depends on the age of the participants. It would not be appropriate to interpret the individual effects of the drug or age, because the relationship between these two factors is complex and cannot be accurately captured by examining the effects of each factor in isolation.

To properly understand the relationship between the two factors, it is necessary to examine the interaction between them. This may involve conducting further statistical analyses or creating plots to visualize the data. It is important to consider the interaction when interpreting the results of the study, as it can provide important insights into the underlying mechanisms and help inform decisions about treatment or interventions.

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There are 450 pieces of banana taffy in the jar because b = Total number of taffy pieces - Number of cherry taffy piecesb = 850 - 400b = 450.

The number of pieces of banana taffy in the jar can be found by solving the equation below:

Let b be the number of pieces of banana taffy in the jar.Number of pieces of cherry taffy = 400

Total number of pieces of taffy in the jar = 850

Number of pieces of banana taffy = Total number of pieces of taffy - Number of pieces of cherry taffy

Therefore,b = Total number of pieces of taffy - Number of pieces of cherry taffy b = 850 - 400b = 450Thus, there are 450 pieces of banana taffy in the jar.

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Answer the answer is a 15.81

Step-by-step explanation:

It can be concluded that the probability that all three students like pizza is more than 50% which implies that in a group of three students, it is more likely that all three will like pizza.

A school survey found that eight out of ten students like pizza. If three students are chosen at random with replacement, then we have to calculate the probability that all three students like pizza.

As given, P(likes pizza) = 8/10 = 0.8

We need to find the probability of three students liking pizza, which means the probability of an event happening thrice. This is a case of independent events with repetition.

Hence, the formula for independent events with repetition is used, which is: P(A and B and C) = P(A) × P(B) × P(C)

Where A, B and C are independent events. In this case, all three events are identical.

Hence, we have: P(A and A and A) = P(A)³ = (0.8)³ = 0.512

This implies that the probability that all three students like pizza is 0.512.

Therefore, if three students are chosen at random with replacement, the probability that all three students like pizza is 0.512 or 51.2%.

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Whave established that the series l~=l an - z converges uniformly for Re(z) ≤ c

What is uniformly?

The keyword "uniformly" refers to the concept of uniform convergence. In the context of the given question, it is stated that the series l~=l an - z converges uniformly for Re(z) ≤ c. Uniform convergence means that the convergence of the series is independent of the value of z within a certain range (Re(z) ≤ c in this case).

To show that the series l~=l an - z converges uniformly for Re(z) ≤ c, where an is a bounded sequence of complex numbers and we choose the principal branch of n - z, we need to demonstrate that for any ε > 0, there exists an N such that for all n > N and for all z with Re(z) ≤ c, the inequality |l~=l an - z| < ε holds.

Given that an is a bounded sequence, there exists an M > 0 such that |an| ≤ M for all n.

Let's consider the series l~=l an - z. We can write it as:

l~=l an - l z.

Now, since |an| ≤ M for all n, we have:

|an - z| ≤ |an| + |z| ≤ M + c.

By choosing N such that M + c < ε, we can ensure that for all n > N and for all z with Re(z) ≤ c, the inequality |an - z| < ε holds.

Now, using the triangle inequality, we have:

|l~=l an - z| ≤ |an - z|.

Since we have shown that |an - z| < ε for n > N and Re(z) ≤ c, it follows that |l~=l an - z| < ε for n > N and Re(z) ≤ c.

Therefore, we have established that the series l~=l an - z converges uniformly for Re(z) ≤ c.

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Answer:

4x -5

Step-by-step explanation:

3+2 (2x - 4)

Distribute

3 + 2*2x - 2*4

3+4x - 8

Combine like terms

4x +3-8

4x -5

Answer:

4x - 5

Step-by-step explanation:

3+ 2 (2x) + 2 (-4)

3+4x - 8

Answer:

Step-by-step explanation:

Use the formula:

Plug In:

22,411 ÷ 2 - 260

Solve:

Answer is L = 10,945.5 inches
explain: perimeter is all 4 sides added together

We know one side is 260
we know the perimeter is 22,411

260 + 260 + L + L = 22,411
combine like terms

520 + 2L = 22,411
subtract 520 from both sides to isolate 2L

2L = 21,891
divide both sides by 2 to isolate L

L = 10,945.5 inches

The height of the metal prism is 1/10 times the height of the tank.

The height h of the metal prism is calculated as follows;

Since the tank is half-filled with water, the height of the water in the tank is H/2.

let the height of the prism = h

Volume of the rectangular tank + volume of prism = total volume

1/2 x L x W x H + L x W x h = 3/5 x L x W x H

H/2  + h = 3H/5

h = 3H/5 - H/2

h = H/10

Therefore, the height of the metal prism is 1/10 times the height of the tank.

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