PLZ HELP! I am stuck on his question.
The ages of two exercise groups at a local fitness center are listed below.
Group A: 37 36 32 41 42 36 44 45
Group B: 26 40 38 36 42 40 40 36
Which statement about the data is true?
The mean age is the same for both groups
The range of ages is greater in Group A than in Group B
The mode of the ages for both groups is 36
The median age is the same for both groups

The probability that you and your friend both have the same two numbers is approximately 0.4823, or about 48.23%.

If you and your friend each roll two dice, there are two possible cases:

You both roll doubles (i.e., both dice show the same number).

You both roll non-doubles (i.e., the two dice show different numbers).

Let's calculate the probability of each case separately:

The probability of rolling doubles on one die is 1/6, since there are six possible outcomes (1, 2, 3, 4, 5, or 6) and only one of them will result in doubles. The probability of rolling doubles on both dice is the product of the probabilities of rolling doubles on each die, which is (1/6) * (1/6) = 1/36. Therefore, the probability that you and your friend both roll doubles is (1/36) * (1/36) = 1/1296.

The probability of rolling non-doubles on one die is 5/6, since there are five possible outcomes (2, 3, 4, 5, or 6) that will result in non-doubles, out of a total of six possible outcomes. The probability of rolling non-doubles on both dice is the product of the probabilities of rolling non-doubles on each die, which is (5/6) * (5/6) = 25/36. Therefore, the probability that you and your friend both roll non-doubles is (25/36) * (25/36) = 625/1296.

Therefore, the overall probability that you and your friend both have the same two numbers is the sum of the probabilities of the two cases:

1/1296 + 625/1296

= 626/1296

= 0.4823 (rounded to four decimal places)

So, the probability that you and your friend both have the same two numbers is approximately 0.4823, or about 48.23%.

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The value of x for the given quadratic expression is x = 5 ± √11.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is 3(x-5)²=33. The value of x will be calculated as,

3(x-5)²=33

(x - 5 )² = 11

(x - 5 )  = ±√11

x = 5 ± √11

Therefore, the value of x for the given quadratic expression is x = 5 ± √11.

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The probability of all five people are still living is 0.1317.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability (Event) = Favorable Outcomes/Total Outcomes = x/n

Let us check simple application of probability to understand it better. Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.

As per the given data,

Probability of a person living in these conditions for 30 years or more\($=p=2 / 3$\)

Total number of samples\($=n=5$\)

Let \($X$\) be the number of people living.

\($X \sim \\) Binomial \((n=5, p=2 / 3)$\)

Probability mass function of \($X$\)  :

\($$P(X=x)=\left(\begin{array}{l}n \\x\end{array}\right) p^x(1-p)^{n-x}$$\)

a) Probability that all five people are still living:

\($$P(X=5)=\left(\begin{array}{l}5 \\5\end{array}\right)\left(\frac{2}{3}\right)^5\left(1-\frac{2}{3}\right)^{5-5}=0.1317$$\)

b) Probability that at least three people are still living:

\($$P(X=5)=\left(\begin{array}{l}5 \\5\end{array}\right)\left(\frac{2}{3}\right)^5\left(1-\frac{2}{3}\right)^{5-5}=0.1317$$\)\($$\begin{aligned}& P(X \geq 3)=P(X=3)+P(X=4)+P(X=5)=\left(\begin{array}{l}5 \\3\end{array}\right)\left(\frac{2}{3}\right)^3\left(1-\frac{2}{3}\right)^{5-3}+ \\& \left(\begin{array}{l}5 \\4\end{array}\right)\left(\frac{2}{3}\right)^4\left(1-\frac{2}{3}\right)^{5-4}+\left(\begin{array}{l}5 \\5\end{array}\right)\left(\frac{2}{3}\right)^5\left(1-\frac{2}{3}\right)^{5-5} \\& =0.7902 \\&\end{aligned}$$\) c) Probability that exactly two people are still living:

\($$P(X=2)=\left(\begin{array}{l}5 \\2\end{array}\right)\left(\frac{2}{3}\right)^2\left(1-\frac{2}{3}\right)^{5-2}=0.1646$$\)

Therefore, the probability of all five people are still living is 0.1317.

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Answer:

2(a)=20t

Step-by-step explanation:

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At the instant when the diameter of the dam is 20 m and the water level is 6 m, the rate at which the volume of water in the dam is changing is approximately 8.948 cubic meters per hour.

To determine the rate at which the volume is changing, we need to use the given formula and calculate the derivatives with respect to time. Let's denote the volume as V, the diameter as d, and the water level as h. The formula for the volume of water in the dam is V = 2πh^2(3d - 3h).

We are given that the water level is increasing at a rate of 0.06 m/hr, which means dh/dt = 0.06 m/hr. Additionally, the diameter is increasing at a rate of 0.25 m/hr, which gives us dd/dt = 0.25 m/hr.

We need to find dV/dt, the rate at which the volume is changing. To do this, we can apply the chain rule of differentiation. Taking the derivative of V with respect to time, we have:

dV/dt = (dV/dd) * (dd/dt) + (dV/dh) * (dh/dt)

Now, let's calculate the partial derivatives. Taking the derivative of V with respect to d, we get:

dV/dd = 2πh^2(3 - 3h)

And taking the derivative of V with respect to h, we get:

dV/dh = 2πh(6d - 6h)

Substituting the given values of d = 20 m and h = 6 m into the expressions for dV/dd and dV/dh, we can evaluate these partial derivatives. Plugging in the rates of change dh/dt = 0.06 m/hr and dd/dt = 0.25 m/hr, we can now calculate dV/dt:

dV/dt = (2π(6^2)(3(20) - 3(6)) * 0.25 + (2π(6)(6(20) - 6(6)) * 0.06

Simplifying this expression yields dV/dt ≈ 8.948 cubic meters per hour. Therefore, the rate at which the volume is changing at the instant when d = 20 m and h = 6 m is approximately 8.948 cubic meters per hour.

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Answer: one point only.

Step-by-step explanation:

Since the length of the sides of the square is 9 cm, taking a point outside the square which is equidistant from point B and C will never give exact 6 cm from A.

The only way to achieve this is by taking a equidistant point inside.

You can achieve exactly 6 cm from point A from point between B and C

But can only achieve a single point if it has to be equidistant from point B and C.

Answer:

the height is 6ft

Step-by-step explanation:

2 x 3 = 6ft

The probability of Jack taking 2 red candies is 3/28.

What do you mean by a union in probability?
The letter "U" (union) stands for "or." Specifically, P(AB) represents the probability of that event A or event B occurring. The sample points that are present in both event A and event B must be counted in order to determine P(AUB).

The new probability set made up of all the elements from both sets is created when two sets are joined. When two sets intersect, a new set is created that includes every element from both sets.

Solution Explained:

Given in the question,

A bag contains 3 red and 5 green candies.

Total possibilities is 3 + 5 = 8  

Jack takes a candy at random and eats it  

A/Q there are 3 red candies out of 8, the probability is given by,

P(R) = 3/8

Now there are 2 red candies out of 7, so the probability is given by,

P(R') = 2/7

The probability of both events is given by,

P(2R) = P(R) × P (R') = 3/8 × 2/7 = 3/28

Therefore, the probability of Tim taking 2 red candies is P(2R) = 3/28

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Answer:

the first option

Step-by-step explanation:

to find a set of ordered pairs that are not a function you would want to look at all the x-intercepts and find the order that has more than one number repeating itself like 1 in the first option

Answer:

B would be the answer to the problem

Step-by-step explanation:

HERE,

a+b=30

a^2+b^2=740

we know that,

\(\tt{(a+b)^2=a^2+b^2+2ab }\)

according to the question,

\(\tt{ (30)^2=740+2ab }\)

\(\tt{900=740+2ab }\)

\(\tt{ 2ab=900-740 }\)

\(\tt{ ab=\dfrac{160}{2} }\)

\(\tt{ab=80 }\)

#quality answer

the value of ab is 80

Answer:

Solution given:

(a+b)=30....(1)

a²+b²=740......(2)

squaring equation 1:

we have;

formula:

(a+b)²=a²+b²+2ab

use this formula:

(a+b)²=30²

a²+b²+2ab=30²

Substituting value of a²+b²=740

740+2ab=30²

take constant term on one side.

2ab=30²-740

subtract :30²-740

2ab=160

divide both side by 2

2ab/2=160/2

we get:

ab=80

the value of ab is 80

Answer:

printer A-  36/1.5

printer B-  114/3

printer C-  115/5

first, multiply 1.5 x 10, 3 x 5, and 5 x3

you should get 15 for each.

once you have the denominators all done, multiply the numerators by the value you multiplied the denominator by and you should have your answer.

so all in all, printer B prints the fastest

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If a matrix is diagonalizable then it is invertible is False.

A matrix can be diagonalizable but not invertible. For example, the zero matrix (a matrix where all entries are 0) is diagonalizable but not invertible.

What is diagonalizable metrix?

A diagonalizable matrix is a square matrix that can be transformed into a diagonal matrix through a similarity transformation. In other words, a matrix A is diagonalizable if there exists an invertible matrix P and a diagonal matrix D such that A = PDP⁻¹.

Geometrically, diagonalizable matrices represent linear transformations that stretch or shrink the space along a set of independent directions, which are called eigenvectors. The diagonal entries of the diagonal matrix D correspond to the eigenvalues of A, which represent the scaling factors along these directions.

Not all matrices are diagonalizable. A matrix is diagonalizable if and only if it has a sufficient number of linearly independent eigenvectors. In particular, symmetric matrices are always diagonalizable, and non-diagonalizable matrices are often associated with non-invertible linear transformations or defective geometric structures.

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Complete question is: If a matrix is diagonalizable then it is invertible is False.

Answer:23

Step-by-step explanation:

Answer:

slope is 1/4

Step-by-step explanation:

Use rise over run

The slope of the line will be equal to 1/4.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope of the line is the ratio of the rise to the run of the line.

The formula to calculate the slope of the line is given as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the line is passing through points ( 0,6) and (8,8). The slope of the line is calculated below,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = (8 - 6 ) / ( 8 - 0)

Slope = 2 / 8

Slope = 1 / 4

Therefore, the slope of the line will be equal to 1/4.

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The solutions are given below,

(a) f(g(x)) = 2x² - 4x + 2

(b) g(f(x)) = 2x² - 1

(c) f(f(x)) = 8x⁴

To find f(g(x)), we substitute g(x) into the function f(x):

f(g(x)) = 2(g(x))²

f(g(x)) = 2(x-1)²

f(g(x)) = 2(x² - 2x + 1)

f(g(x)) = 2x² - 4x + 2

Therefore, f(g(x)) = 2x² - 4x + 2.

b. To find g(f(x)), we substitute f(x) into the function g(x):

g(f(x)) = f(x) - 1

g(f(x)) = 2x² - 1

Therefore, g(f(x)) = 2x² - 1.

c. To find f(f(x)), we substitute f(x) into the function f(x):

f(f(x)) = 2(f(x))²

f(f(x)) = 2(2x²)²

f(f(x)) = 2(4x⁴)

f(f(x)) = 8x⁴

Therefore, f(f(x)) = 8x⁴.

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Answer:11 kids were at the party

Step-by-step explanation:24 slices in all , 22 were eaten so that means 22 divided by 11 is 2 so there was 11 kids

Answer:

11 children

Step-by-step explanation:

First you have to do 8 times 3 to get the number of slices of pizza there were.

Then you have to divided that by 2. But remember, there are 2 slices left.

So, you have to take away one child to get the answer: 11 children

I feel bad for that last child. I hope this helped ;)

Answer:

A

Step-by-step explanation:

75÷ 15=5

Statistics computed for larger random samples tend to be less variable compared to statistics computed for smaller random samples.

This statement is based on the concept of the Central Limit Theorem (CLT) in statistics. According to the CLT, as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This means that the variability of the sample mean decreases as the sample size increases.

The variability of a statistic is commonly measured by its standard deviation or variance. When working with larger random samples, the individual observations have less impact on the overall variability of the statistic. As more data points are included in the sample, the effects of outliers or extreme values tend to diminish, resulting in a more stable and less variable estimate.

In practical terms, this implies that estimates or conclusions based on larger random samples are generally considered more reliable and accurate. Researchers and statisticians often strive to obtain larger sample sizes to reduce the variability of their results and increase the precision of their statistical inferences.

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Answer:

40 ft

Step-by-step explanation:

The maximum height of the ball is the y- coordinate of the vertex

Given a parabola in standard form then the x- coordinate of the vertex is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

h(t) = - 16t² + 48t + 4 ← is in standard form

with a = - 16, b = 48 , thus

\(x_{vertex}\) = - \(\frac{48}{-32}\) = 1.5

Substitute t = 1.5 into h(t) for max. height

h(1.5) = - 16(1.5)² + 48(1.5) + 4

         = - 36 + 72 + 4

          = 40

The proposed solution y = xr leads to r = -2 for the given differential equation.

By substituting the proposed solution y = xr into the differential equation \(x^2y'' + 5xy' + 4y = 0\), we can find the value of r that satisfies the equation.

First, we differentiate y = xr twice to find the first and second derivatives.

\(y' = rx^(r-1)\)and \(y'' = r(r-1)x^(^r^-^2^).\)

Substituting these derivatives into the differential equation, we have:

\(x^2(r(r-1)x^(^r^-^2^)) + 5x(rx^(^r^-^1^)) + 4xr = 0\).

Simplifying the equation, we get:

\(r(r-1)x^r + 5rx^r + 4xr = 0\).

Factoring out the common term \(x^r\), we have:

\(x^r(r(r-1) + 5r + 4) = 0\).

For this equation to hold true for all x, the coefficient in front of \(x^r\) must be zero. Thus, we have:

r(r-1) + 5r + 4 = 0.

Simplifying the equation further, we get:

\(r^2 - r + 5r + 4 = 0,r^2 + 4r + 4 = 0,(r + 2)^2 = 0\).

From this equation, we find that r = -2. Therefore, the proposed solution y = xr leads to r = -2 as the solution for the given differential equation.

The proposed solution method for solving differential equations is based on the assumption that the solution can be expressed in a specific form. In this case, the proposed solution y = xr assumes that the solution is a power function of x. By substituting this solution and its derivatives into the differential equation, we can determine the value of r that satisfies the equation.

The process involves substituting the proposed solution and its derivatives into the differential equation, simplifying the equation, and identifying the condition under which the equation holds true. In this case, after simplifying the equation, we obtain a quadratic equation in terms of r. Solving this quadratic equation leads to the value r = -2, which satisfies the original differential equation.

The proposed solution method is a powerful technique used in solving linear homogeneous differential equations, where the equation can be expressed as a linear combination of the derivatives of the dependent variable with respect to the independent variable. By substituting the proposed solution, we can determine the values of the constants or exponents that satisfy the equation and find the general solution.

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The mean of the number of drivers expected not to be wearing seatbelts is approximately 4.35, the variance is approximately 15.62, and the standard deviation is approximately 3.95 and they expect to stop approximately 4.35 cars before finding a driver whose seatbelt is not buckled.

a. To find the mean, variance, and standard deviation of the number of drivers expected not to be wearing seatbelts, we can model the situation using a geometric distribution.

Let's define a random variable X that represents the number of cars stopped until the first driver without a seatbelt is found. The probability of a driver not wearing a seatbelt is given as p = 0.23.

The mean (μ) of a geometric distribution is given by μ = 1/p.
μ = 1/0.23 ≈ 4.35

The variance (σ^2) of a geometric distribution is given by σ^2 = q/p^2, where q = 1 - p.
σ^2 = (0.77)/(0.23^2) ≈ 15.62

The standard deviation (σ) is the square root of the variance.
σ = √(15.62) ≈ 3.95


b. The expected number of cars they expect to stop before finding a driver whose seatbelt is not buckled is equal to the reciprocal of the probability of success (finding a driver without a seatbelt) in one trial. In this case, the probability of success is p = 0.23.

Expected number of cars = 1/p = 1/0.23 ≈ 4.35

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Answer:

independent: b

dependent: p

Step-by-step explanation:

p = 2b

To find p, choose values for b, then do the calculation.

b is independent. You can choose any value for it.

p is dependent since its value depends on the value you chose for b.

The volume of the cylinder in cubic centimeters is 251.2 cm^3.

The volume of a cylinder is expressed as:

V = πr²h

V = base area * height

Given the following

Base area =  16π centimeters

Height = 5cm

Substitute into the formula to have:

V = 16(3.14) * 5

V = 251.2 cm^3

Hence the volume of the cylinder in cubic centimeters is 251.2 cm^3.

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Answer: -3

Step-by-step explanation: When you graph this that’s what you get

Answer:

-3

Step-by-step explanation:

the y intercept is when x is 0 on the graph. Since you know x has to be zero, you can substitute x for 0 in the equation:

y = -0.5x0 -3

Now you can ignore that first part of the equation because it equates to 0, and so you get:

y= 0 - 3

which equals:

y=-3

Part A: The reasonable domain for the growth function is d ≥ 0, allowing for positive days and future growth.

Part B: The y-intercept is 7, indicating the initial radius of the algae when the study began.

Part C: The average rate of change from d = 4 to d = 11 is approximately 0.55 mm/day, representing the daily increase in radius during that period.

Part A: To determine a reasonable domain to plot the growth function, we need to consider the context of the problem. The biologist's equation for the radius of the algae is given by f(d) = 7(1.06)^d, where d represents the number of days.

Since time (d) cannot be negative or non-existent, the domain for the growth function should be restricted to positive values.

Additionally, we can assume that the growth function is applicable within a reasonable range of days that align with the biologist's study. It's important to note that the given equation does not impose any upper limit on the number of days.

Based on the information given, a reasonable domain for the growth function would be d ≥ 0, meaning the number of days should be greater than or equal to zero.

This allows us to include the starting point of the study and extends the domain indefinitely into the future, accommodating any potential growth beyond the conclusion of the study.

Part B: The y-intercept of a function represents the value of the dependent variable (in this case, the radius of the algae) when the independent variable (days, d) is zero. In the given equation, f(d) = 7(1.06)^d, when d = 0, the equation becomes:

f(0) = 7(1.06)^0

f(0) = 7(1)

f(0) = 7

Therefore, the y-intercept of the graph of the function f(d) is 7. In the context of the problem, this means that when the biologist started her study (at d = 0), the radius of the algae was approximately 7 mm.

Part C: To calculate the average rate of change of the function f(d) from d = 4 to d = 11, we need to find the slope of the line connecting the two points on the graph.

Let's evaluate the function at d = 4 and d = 11:

f(4) = 7(1.06)^4

f(4) ≈ 7(1.26)

f(4) ≈ 8.82 mm

f(11) = 7(1.06)^11

f(11) ≈ 7(1.81)

f(11) ≈ 12.67 mm

The average rate of change (slope) between these two points is given by the difference in y-values divided by the difference in x-values:

Average rate of change = (change in y) / (change in x)

= (12.67 - 8.82) / (11 - 4)

= 3.85 / 7

≈ 0.55 mm/day

The average rate of change of the function f(d) from d = 4 to d = 11 is approximately 0.55 mm/day. This represents the average daily increase in the radius of the algae during the period from day 4 to day 11.

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The volume of the cylindrical construction pipe is approximately 1,371 cubic feet.

The volume of a cylinder is given by the formula  V = π\(r^2h\), where r is the radius of the cylinder, h is its height, and π (pi) is approximately 3.14.

Since the diameter of the pipe is given as 7 feet, the radius of the pipe is half of that, or 3.5 feet.

The height of the pipe is given as 35 feet.

Substituting these values into the formula for the volume of a cylinder:

V = π\(r^2h\)

\(V =\) \(3.14 × (3.5)^2 × 35\)

\(V ≈ 1371\)

Therefore, the volume of the cylindrical construction pipe is approximately 1,371 cubic feet.

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Answer:

- 2.2× (-2) ÷ (-1/4)×5

- 2.2× (-2) × (-4) ×5

4.4 × (-20)

-88

Step-by-step explanation:

Answer:

Step-by-step explanation:

For fraction division, multiply with the reciprocal of the fraction.

Reciprocal of (-1/4) = -4/1

-22 * (=2) ÷  (-1/4) * 5 = \(-22 * (-2) * \frac{-4}{1}*5\\\)

                                   \(= -22 * (-2) * (-4) * 5\\\\= - 880\)

The order of the colors is Red, blue, yellow

Chromatography is a laboratory technique used to separate and analyze mixtures of different compounds based on their physical and chemical properties. It involves passing a mixture through a stationary phase, which may be a solid or a liquid, and a mobile phase, which may be a liquid or a gas.

As the mixture passes through the stationary phase, the different compounds in the mixture interact with the stationary phase to varying degrees, causing them to separate. The mobile phase carries the separated components through the stationary phase, and the separated components are detected and analyzed using a detector, such as a spectrophotometer.

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The perimeter of the square is a rational number of meters. However, the product of a rational number and an irrational number is always irrational.

If the area of a square is 7 square meters, then each side of the square is √7 meters long. The perimeter of the square is simply the sum of the four sides, which is 4√7 meters.

To determine whether 4√7 is a rational or irrational number, we need to check if √7 is rational or irrational. Since √7 is not a perfect square, it cannot be expressed as a fraction of two integers. Therefore, √7 is an irrational number.

However, the product of a rational number and an irrational number is always irrational. Since 4 is a rational number and √7 is irrational, the product 4√7 is also an irrational number.

Therefore, the perimeter of the square is an irrational number of meters.

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