PLS HELP DUE TODAY i will give brailest if you show all work please help

She ran a total distance of 28 miles in 5 hours.

We can solve this problem by using the formula: distance = rate × time

First, we need to calculate the distance traveled during the first 3 hours at 6 mph. Using the formula, we have:

distance = rate × time

distance = 6 mph × 3 hours

distance = 18 miles

Next, we need to calculate the distance traveled during the last 2 hours at 5 mph. Using the same formula, we have:

distance = rate × time

distance = 5 mph × 2 hours

distance = 10 miles

Finally, we can add the distances traveled during the first 3 hours and the last 2 hours to get the total distance:

total distance = 18 miles + 10 miles

total distance = 28 miles

Therefore, the runner ran a total distance of 28 miles in 5 hours.

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When Steven combines the sacks into one large bag, the probability of drawing a "1" and a "B" without replacement reduces since the full number of balls increments, resulting in a little probability.

To decide on the off chance that the probability would alter when Steven combines the table tennis balls into one large bag, we ought to compare the probabilities sometime recently and after the combination.

In address 17, the probability of drawing a "1" and a "B" without substitution can be calculated utilizing the concept of conditional likelihood.

Let's expect the two-person sacks to be signified as Sack 1 and Pack 2, and they contain a add up to n balls each.

Sometime recently combining the packs:

The probability of drawing a "1" from Sack 1 is p(1) = 2/n (since there are 2 "1" balls in Pack 1).

The probability of drawing a "B" from Sack 2 is p(B) = 3/n (since there are 3 "B" balls in Sack 2).

Expecting the occasions of drawing a "1" and a "B" to be free, the likelihood of both occasions happening without replacement is given by the item of the person probabilities:

P(1 and B) = p(1) * p(B) = (2/n) * (3/n) = 6/n^2

After combining the bags:

When Steven combines the sacks into one expansive sack, the entire number of balls gets to be 2n (since each sack initially contained n balls).

The probability of drawing a "1" from the combined sack is presently p(1) = 2/(2n) = 1/n (since there are still 2 "1" balls).

The likelihood of drawing a "B" from the large bag is presently p(B) = 3/(2n) = 3/(2n) (since there are still 3 "B" balls).

Once more, accepting autonomy, the likelihood of both occasions happening without replacing the combined pack is given by:

P(1 and B) = p(1) * p(B) = (1/n) * (3/(2n)) = 3/(2n^2)

Comparing the probabilities:

P(1 and B) sometime recently combining packs: \(6/n^{2}\)

P(1 and B) after combining packs: \(3/(2n^{2})\)

Hence, the probability does alter when Steven combines the bags into one expansive pack. The probability of drawing a "1" and a "B" without substitution diminishes from \(6/n^{2} to 3/(2n^{2}).\)

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Answer:

Step-by-step explanation:

If the solutions are x = -3 and x = -1, then (x - 3) (x - 1) will give us our answer. Using the FOIL method,

(x - 3) (x - 1)

x^2 - x - 3x + 3

x^3 - 4x + 3 = 0

Your answer is 3

In summary, when the two new children (ages four and twelve) are added to the existing group, the mean age increases from 8 to 8, and the standard deviation changes from its original value to approximately 3.74.

To determine the effect of adding two children (ages four and twelve) to the existing group of five children (ages five, six, eight, nine, and twelve) on the mean and standard deviation of ages, we need to calculate the new values.

Let's calculate the mean first:

Calculate the sum of the ages of the initial five children:

5 + 6 + 8 + 9 + 12 = 40

Add the ages of the two new children:

40 + 4 + 12 = 56

Calculate the new mean by dividing the sum by the total number of children (5 initial + 2 new):

56 / 7 = 8

Therefore, the new mean age is 8.

Now let's calculate the standard deviation:

Calculate the squared difference between each age and the mean for the initial five children:

\((5 - 8)^2 + (6 - 8)^2 + (8 - 8)^2 + (9 - 8)^2 + (12 - 8)^2 = 54\)

Calculate the squared difference between each new age and the new mean:

\((4 - 8)^2 + (12 - 8)^2 = 80\)

Calculate the sum of the squared differences for the initial five children and the new children:

54 + 80 = 134

Divide the sum of squared differences by the total number of children (5 initial + 2 new) and take the square root:

√(134 / 7) ≈ 3.74

Therefore, the new standard deviation is approximately 3.74.

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Answer:

Opposite numbers are numbers that, when placed on a number line, are the exact same distance away from the 0, but on opposite sides/opposite directions

Answer:

Opposite number or additive inverse of any number (n) is a number which, if added to n, results in 0, the identity element of addition. The opposite number for n is written as −n. For example, −7 is opposite to 7, because with −7+7=0

You can say that the opposite number of a number, is the negative version of the positive number. This is what the opposite of 7 is or the opposite of -7.

Step Guide:

Step 1: Place your compass at W and extend it to X.

Step 2: Using the same length, place your compass at P and mark an arc.

Step 3: Using the straightedge, draw a line from P to meet the arc.

Step 4: Label the point of intersection of the line and the curve Q.

This gives segment PQ that is congruent to WX,

Answer:

it’s C. 0.02,0.2.1/2, 2 1/2

Answer:

Jacob got 18 votes.

Hope this helps :)

Seema left 6/11 of the book for reading over the weekend.

To calculate the part of the book left for reading during the weekend, we need to subtract the part of the book Seema read during the weekday from the total book.

If Seema reads 5/11 of the book during the weekday, then:

This means 6/11 of the book is left for reading during the weekend. It is important to note that the fraction of the book read during the weekday and the fraction left for reading during the weekend add up to the total book. This means that 11/11 of the book will be read by Seema in total.

This question should be written as:

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The correlation coefficient can take values between -1 and 1, inclusive. A correlation coefficient of -1 indicates negative correlation and 1  indicates positive correlation.

A correlation coefficient of -1 indicates a perfect negative correlation, meaning that as the values of one variable increase, the values of the other variable decrease. A correlation coefficient of 1 indicates a perfect positive correlation, meaning that as the values of one variable increase, the values of the other variable also increase.

A correlation coefficient of 0 indicates no correlation, meaning that there is no relationship between the two variables. Correlation coefficients can take any value between -1 and 1, inclusive, including fractional and decimal values.

Positive values indicate positive correlation, negative values indicate negative correlation, and values close to 0 indicate little or no correlation. The magnitude of the correlation coefficient indicates the strength of the relationship between the two variables.

The closer the coefficient is to 1 or -1, the stronger the relationship between the variables.

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The median of the given list of numbers is 87.

To find the median of a list of numbers, we arrange them in ascending order and identify the middle value.

If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

First, let's arrange the numbers in ascending order:

65.9, 68, 70, 74, 75, 78, 84, 86, 87, 90, 93, 93, 95, 96, 97, 380, 486, 680

There are 17 numbers in the list, which is an odd number. The middle number is the 9th number in the list, which is 87.

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To find the equation for line m, that is perpendicular to line k, we will take the steps below:

First, find the slope of line k from the graph given

To find the slope, locate the coordinates of any given 2 points from the line.

we have;

(4, 0) and (0, 3)

From the points above:

x₁= 4 y₁=0 x₂=0 y₂=3

slope = y₂-y₁ /x₂- x₁

substitute the values of the coordinate into the formula above

slope = 3 - 0 / 0 -4

= 3/ -4

= - 3/4

slopes of perpendicula equations are given by;

m₁m₂= -1

let m₁ be slope of k and m₂ be slope of m

(-3/4)m₂ = -1

multiply both-side of the equation by -4/3

m₂ = 4/3

The above is the slope of line M

Next, is to find the intercept of line M

y=mx + b

(a)  The joint PMF of S₁, S₂, ..., Sn is: P(S₁ = s₁, S₂ = s₂, ..., Sₙ = sₙ) =\((1 - p)^{(s_1 + s_2 + ... + s_n) } \times p^n\)

(b)  The random variables S₁,..., Sn are  independent.

(c)  the cumulative distribution function (CDF) of U is:

\(F(u) = (1 - \sum (1 - p)^{(k)} \timesp)^n\)

To compute the joint probability mass function (PMF) of S₁, S₂, ..., Sn, we need to consider the number of failures before each success.

(a) Joint probability mass function (PMF) of S₁, S₂, ..., Sn:

Let's first define the random variable S as the sequence of failures until the first success:

S = (S₁, S₂, ..., Sn)

Now, let's calculate the PMF of S:

P(S = (s₁, s₂, ..., sₙ))

Since the random variables X₁, X₂, ..., Xₙ are independent Bernoulli random variables with success probability p.

The probability of getting s failures before the first success is given by:

\(P(S_1 = s_1) = (1 - p)^{s_1} \times p\)

The probability of getting s₂ additional failures before the second success is:

\(P(S_2 = s_2) = (1 - p)^{s_2} \times p\)

\(P(S_3 = s_3) = (1 - p)^{s_3} \times p\)

And so on, until the probability of getting sₙ additional failures before the nth success:

\(P(S= s) = (1 - p)^{s} \times p\)

Now, since the random variables S₁, S₂, ..., Sn are independent, the joint PMF is the product of the individual probabilities:

P(S = (s₁, s₂, ..., sₙ)) = P(S₁ = s₁) × P(S₂ = s₂)×... × P(Sₙ = sₙ)

Therefore, the joint PMF of S₁, S₂, ..., Sn is:

P(S₁ = s₁, S₂ = s₂, ..., Sₙ = sₙ) =\((1 - p)^{(s_1 + s_2 + ... + s_n) } \times p^n\)

(b)

To determine whether the random variables S₁, S₂, ..., Sn are independent, we need to check if the joint PMF factorizes into the product of the individual PMFs.

Let's consider three random variables, S₁, S₂, and S₃:

P(S₁ = s₁, S₂ = s₂, S₃ = s₃) = P(S₁ = s₁) ×P(S₂ = s₂) × P(S₃ = s₃)

Using the joint PMF calculated in part (a), we can rewrite this as:

\((1 - p)^{(s_1 + s_2 + s_3)} p^3 = (1 - p)^{(s_1)} \times p \times (1 - p)^{(s_2)} \times p \times (1 - p)^{(s_3)}\times p\)

Simplifying, we have:

\((1 - p)^{(s_1 + s_2 + s_3)} p^3 = (1 - p)^{(s_1 + s_2 + s_3)} p^3\)

Since the equation holds true for any values of s₁, s₂, and s₃, we can conclude that the random variables S₁, S₂, and S₃ are indeed independent.

(c)

To compute the CDF of U, we need to determine the probability that U is less than or equal to a given value u.

CDF of U:

F(u) = P(U ≤ u) = 1 - P(U > u)

Since U represents the maximum value among S₁, S₂, ..., Sn, we have:

P(U > u) = P(S₁ > u, S₂ > u, ..., Sn > u)

Using the independence of S₁, S₂, ..., Sn, we can express this probability as:

P(U > u) = P(S₁ > u)×P(S₂ > u) × ...× P(Sn > u)

The probability that a single random variable Si is greater than u (where Si represents the number of failures between the (i-1)th and the ith success) is:

P(Si > u) = 1 - P(Si ≤ u) = 1 - ∑(k=0 to u) P(Si = k)

Using the PMF derived in part (a), we can calculate this probability:

\(P(Si > u) = 1 - \sum (1 - p)^(^k^) \times p\) (k=0 to u)

Finally, substituting this back into the expression for P(U > u), we have:

\(P(U > u) = (1 - \sum (1 - p)^{(k)} \timesp)^n\) (k=0 to u)

Therefore, the cumulative distribution function (CDF) of U is:

\(F(u) = (1 - \sum (1 - p)^{(k)} \timesp)^n\)

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The various equations are categorized into:

To determine which equations have one solution, infinitely many solutions, or no solution, simplify each equation and look for patterns.

1.  \(\frac{1}{2}y + 3.2y = 20\)

Combining like terms:

\(\frac{1}{2}y + 3.2y = 20\)

Simplifying:

3.7y = 20

Dividing both sides by 3.7:

\(y = \frac{20}{3.7}\)

Therefore, this equation has one solution.

2. \(\frac{15}{2} + 2z - \frac{1}{4} = 4z + \frac{29}{4} - 2z\)

Combining like terms:

\(\frac{15}{2} + 2z - \frac{1}{4} = 4z + \frac{29}{4} - 2z\)

Simplifying:

\(\frac{15}{2} + z = z\)

Subtracting z from both sides:

\(\frac{15}{2} = 0\)

This is a contradiction since \(\frac{15}{2}\) cannot equal 0. Therefore, this equation has no solution.

3.  3z + 2.5 = 3.2 + 3z

Subtracting 3z from both sides:

2.5 = 3.2

This is a contradiction since 2.5 cannot equal 3.2. Therefore, this equation has no solution.

4.  \(1.1 + \frac{3}{4 } x + 2 = 3.1 + \frac{3}{4} x\)

Subtracting \(\frac{3}{4 } x\) from both sides and simplifying:

\(3.1 - 1.1 + 2 = \frac{3}{4} x\)

Simplifying:

4 = \(\frac{3}{4 } x\)

Multiplying both sides by \(\frac{4}{3}\) :

\(x = \frac{16}{3}\)

Therefore, this equation has one solution.

5.  4.5r = 3.2 + 4.5r

Subtracting 4.5r from both sides,:

0 = 3.2

This is a contradiction since 0 cannot equal 3.2. Therefore, this equation has no solution.

6.  \(2x + 4 = 3x + \frac{1}{2}\)

Subtracting 2x from both sides and simplifying:

\(4 = x + \frac{1}{2}\)

Subtracting 1/2 from both sides and simplifying:

\(\frac{7}{2} = x\)

Therefore, this equation has one solution.

In summary, the equations have the following number of solutions:

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Answer: 6, 4.5

Step-by-step explanation:

Hi!

I can help you with joy!

We are given 2 points: (-2, 3) and (5, 4), so we can easily calculate the slope of this line using this formula:

\(\displaystyle\frac{y2-y1}{x2-x1}\)

\(\displaystyle\frac{4-(-3)}{5-(-2)}\)

\(\displaystyle\frac{4+3}{5+2}\)

\(\displaystyle\frac{7}{7}\)

\(1\) (Answer)

I hope it helps!

Ask if you have any queries.

~Misty~

\(\bf{GracefulTeen\)

Enjoy your day!

Answer: see explanation

Step-by-step explanation:

Using x = 5, then

x² = 5² = 5 × 5 = 25

= 1 × 1 × 1 × 1 × 1 = 1

= 5

It takes approximately 26.56 seconds for the ferris wheel to make one revolution.

so, the correct option is: e) 26.56 seconds

Here, we have,

The ferris wheel makes one complete revolution when the distance of the person above the ground returns to the original value after completing a full circle.

This occurs when the sine function returns to its maximum value, which is 1.

Thus, we have the following equation:

20 * sin(π/30 * t) + 10 = 20

Solving for t,

we will get:

sin(π/30 * t) = 0.5

Taking the inverse sine of both sides:

(π/30 * t) = sin^-1(0.5)

Multiplying both sides by 30/π,

we will get the following:

t = (30/π) * sin^-1(0.5)

Now solving the value of t

We will get it as: t ≈ 26.56 seconds.

so, the correct option is: e) 26.56 seconds

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complete question:

the distance from the ground of a person riding on a ferris wheel can be modeled by the equation d equals 20 times the sine of the quantity pi over 30 times t end quantity plus 10 comma where d represents the distance, in feet, of the person above the ground after t seconds. how long will it take for the ferris wheel to make one revolution?

a) 10 seconds

b) 20 seconds

c) 30 seconds

d) 60 seconds

e) 26.56 seconds

When a set of eight cards were labeled with A, D, D, I, T, I, O, N. The sample space for choosing a card is

A sample space is a set or collection of potential outcomes from a random experiment.

The letter "S" stands for the sample space in a symbol. The term "events" refers to a subset of probable experiment results.

Depending on the experiment, a sample area could include a variety of results.

For the given problem, the sample space is A, D, D, I, T, I, O, N which is rearranged to be S = {A, D, D, I, I, N, O, T}

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we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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Answer:

each ticket = $27.75

Step-by-step explanation:

70.50-15=55.50

55.50÷2=27.75

Answer:$20.25

Step-by-step explanation:

Let x represent the price of a game ticket

The cost of a game ticket and a jersey is X + $15

The cost of a game ticket and a jersey for both Leo and Bonnie would be x + $15 multiplied by 2. 2(x + $15)

Together they paid $70.50

That is 2(x+$15) =$70.50

Open the bracket by multiplying by 2

2x + $30 =$70.50

2x= $70.50-$30 make 2x the subject

2x=$40.50

2x/2 = $40.50/2 Divide both sides by 2

x = $21.25

Hence the price of a game ticket as represented by x is $21.25

The probability that a cell phone user makes or receives less than 12 calls per day is 0.3971.

To find P(x < 12), we need to standardize the value of 12 using the formula: z = (x - μ) / σ where z = z-score, x = value of interest, μ = mean, and σ = standard deviation.

Substituting the values, we get:

z = (12 - 13.1) / 4.3

z = -0.25581

Using a calculator, we can find the probability that z is less than -0.25581, which is:

P(z < -0.25581) = 0.3971

P(z < -0.25581) = 39.71%.

Full question "Suppose the number of cell phone calls made or received per day by cell phone users follows a normal distribution with a mean of 13.1 and a standard deviation of 4.3. Find P (x <12)".

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Using probabilities P(A₁) = 0.40 , P(A₂) = 0.60, P(B|A₁) = 0.20, P(B|A₂) = 0.05,

a) No, A₁ , A₂ are not mutually exclusive because , their intersection probability is not a zero.

b) P(A₁∩ B) is 0.08 , P(A₂ ∩ B) is 0.03

c) P(B) = 0.09

d) Using Bayes' theorem P(A₁|B) is 0.89 , P(A₂|B) is 0.33 .

a. A₁ and A₂ are not mutually exclusive, as their intersection probability is non-zero (given as 0 in the problem statement).

b. We can compute P(A₁∩ B) and P(A₂∩ B) using the formula for conditional probability:

P(A₁∩ B) = P(B|A₁) * P(A₁) = 0.20 * 0.40 = 0.08

P(A₂ ∩ B) = P(B|A₂) * P(A₂) = 0.05 * 0.60 = 0.03

c. To compute P(B), we can use the law of total probability, which states that the probability of an event B can be calculated as the sum of the probabilities of B given each possible event in the sample space:

P(B) = P(B|A₁) * P(A₁) + P(B|A₂) * P(A₂) = 0.20 * 0.40 + 0.05 * 0.60 = 0.09

d. To compute P(A₁|B) and P(A₂|B), we can use Bayes' theorem:

P(A₁|B) = P(B|A₁) * P(A₁) / P(B) = 0.20 * 0.40 / 0.09 ≈ 0.89

P(A₂|B) = P(B|A₂) * P(A₂) / P(B) = 0.05 * 0.60 / 0.09 ≈ 0.33

Therefore, the probability that event A₁ occurred given that event B occurred is approximately 0.89, and the probability that event A₂ occurred given that event B occurred is approximately 0.33.

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The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Answer:

Step-by-step explanation:

an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?

Answer:

Width = 125 m

Length = 375 m.

Step-by-step explanation:

If the width = w then length l = 3w.

Perimeter = 2(w + l)

= 2(w + 3w)

2(w + 3w) = 1000

2 * 4w = 1000

w = 1000/8 = 125m

l = 3*125 = 375.

Step-by-step explanation:

width = x

length= 3x

perimeter of triangle =2( l + b)

1000 = 2( 3x + x )

1000÷ 2 = 4x

500=4x

x= 500÷ 4 = 125

width = 125

length = 125×3= 375

recheck by filling value

width= x = 125

length = 3x =375

perimeter = 2( l+ b)

= 2(375 + 125)

= 2× 500 = 1000

hence proved

hope it helps : )

Answer:

$133.20

Step-by-step explanation:

Since the amount of hours she worked isn't a whole number, we can first separate 18 and 1/2 and work the problem out one at a time.

1. Multiply 7.20 by 18 to get 129.60

2. Multiply 0.50 by 7.20 to get 3.60.

3. Add 129.60 and 3.60 together to get the answer, 133.20.