6. The altitude of a rock climberthours after she begins her ascent up a mountain is modelled by the equation a(t) = −10t^2 + 60t, where the altitude,a(t), is measured in metres. a. Determine the altitude of the rock climber 2 hours after she begins her climb. b. Determine the altitude of the rock climber 3 hours after she begins her climb. c. Determine the average rate of change of the altitude of the rock climber between 2 and 3 hours after she begins her climb. d. Determine the instantaneous rate of change of the altitude of the rock climber 3 hours after she begins her climb. e. What is the significance of the instantaneous rate of change value found in part d)? Explain what this value tells us about the rock climber's travel at this poin.

The maximum that the company can expect for returned items is C. $5972.65

From the information, the average daily profit of an electronics store is $31,435 and the company estimates that 15% is lost each day to returns, with a margin of error of ±4%.

In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.

The maximum the company can expect for returned items will be:

= (15% + 4%) × Profit

= 19% × $31,435

= 0.19 × $31,435

= $5972.65

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The mean (μ) of a hypergeometric distribution is given by: 8.181

The standard deviation (σ) of a hypergeometric distribution is given by:

1.644

Here, we have,

To find the mean value and standard deviation of the number of projects not among the first 15 that are from the second section, we need to calculate the probabilities for different numbers of projects from the second section.

Let's denote:

N1: Number of students in the first section (25)

N2: Number of students in the second section (30)

N: Total number of projects graded (15)

To calculate the probability of exactly 10 projects being from the second section, we can use the hypergeometric distribution.

The formula for the hypergeometric distribution is:

P(X = k) = (C(N2, k) * C(N1, N - k)) / C(N1 + N2, N)

Where:

X is the random variable representing the number of projects from the second section among the first 15 graded projects.

C(a, b) is the binomial coefficient, also known as "a choose b."

Using this formula, we can calculate the probability for X = 10:

P(X = 10) = (C(30, 10) * C(25, 15 - 10)) / C(55, 15)

Next, we can calculate the mean and standard deviation.

The mean (μ) of a hypergeometric distribution is given by:

μ = N * (N2 / (N1 + N2))

  = 15 * (30 / (25 + 30) )

  = 8.181

The standard deviation (σ) of a hypergeometric distribution is given by:

σ = √(N * (N1 / (N1 + N2)) * (N2 / (N1 + N2)) * ((N1 + N2 - N) / (N1 + N2)) )

  = √(15 * (25 / (25 + 30)) * (30 / (25 + 30)) * (25+30 - 15 )/(25+30)) )

  = 1.644

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complete question:

An Instructor Who Taught Two Sections Of Engineering Statistics Last Term, The First With 25 Students And The Second With 30, Decided To Assign A Term Project. After All Projects Had Been Turned In, The Instructor Randomly Ordered Them Before Grading. Consider The First 15 Graded Projects. (A) What Is The Probability That Exactly 10 Of These Are From The

An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 30, decided to assign a term project. After all projects had been turned in, the instructor randomly ordered them before grading. Consider the first 15 graded projects.

what are the mean value and standard deviation of the number of projects not among these first 15 that are from the second section?

Answer:

4th option.

Step-by-step explanation:

You pay $9 and $__ for a total of $16.

$9 + $__ = $16.

9+__=16

Answer:

-3y (y^2+ 2y-2)

Step-by-step explanation:

i took the test and got this answer

a) True, P(A ∪ B) ≥ P(A).

b) False, If P(A ∪ B) = P(A) + P(B), then A and B are mutually exclusive.

c) True, If A and B are mutually exclusive events, then P(A | B) = 0.

d) False, P(A|B) ≠ P(B|A) for all events A and B.

Here, P(A ∪ B) denotes the probability of occurrence of either A or B. Now, if we talk about the probability of occurrence of either A or B, the maximum value of probability that can be attained is the probability of occurrence of A itself. Therefore, P(A ∪ B) ≥ P(A).

If P(A ∪ B) = P(A) + P(B), then it does not necessarily imply that the events A and B are mutually exclusive. This only suggests that the events A and B might be independent events.

If the events A and B are mutually exclusive, then it means that the occurrence of A excludes the possibility of occurrence of B and vice versa. Therefore, P(A | B) = 0.

If we are given two events A and B, then the conditional probability of A given that B has already occurred (i.e., P(A|B)) and the conditional probability of B given that A has already occurred (i.e., P(B|A)) may or may not be equal. Therefore, P(A|B) ≠ P(B|A) for all events A and B.

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Answer:

-35.626 < temperature < 733.928 . . . . degrees F

 (-35.626, 733.928)

Step-by-step explanation:

It is convenient to let a calculator evaluate the expression for converting °C to °F..

How this helps.

Given the fraction

The reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number). The negative reciprocal takes the negative of that number. Therefore:

Answer:

Step-by-step explanation:

2 + 3 × (8 + 53 ÷ 1)

we first work out the equation in the brackets

so...

(8 + 53 ÷ 1)

division comes first so we divide 53÷1 which is 1 so the equation looks like this:

(8+53)

we work this out and get

61

then we work the rest out

2 + 3 × 61

multiplication comes first so...

3×61= 183

and

2+ 183= 185

Therefore 2 + 3 × (8 + 53 ÷ 1)= 185

Hope this helped- have a good day bro cya)

\(\huge\text{Hey there!}\)

\(\large\boxed{\rm{2 + 3 \times (8 + 53 \div 1})}}\\\large\boxed{\rightarrow 2 + 3 \times (8 + 53)}\\\large\boxed{\rm{\rightarrow 2 + 3\times 61}}}\\\large\boxed{\rightarrow \rm{2 + 183}}\\\large\boxed{\rightarrow \rm{185}}\\\\\large\boxed{\text{Therefore, your answer is: 185}}\huge\checkmark\\\\\large\textsf{Good luck on your assignment \& enjoy your day!}\\\\\frak{Amphitrite1040:)}\)

A unit rate's component is always 1. To find the unit rate, divide the fraction by the fraction such that the denominator is equal to one.

The meaning of math units:

Of mathematics, a unit can be thought of as the right side point in a number or the number one. In this instance, the unit number in the number 6713 is 3. A unit is also a term that may be used to describe the common measurement units.

The dimensions of a unit:

The area of a unit as depicted on the subdivision or annexation map that created the unit is referred to as its size. The lot, tract, or parcel size divided by the number of dwellings is the unit size for two-family and multiple-family homes on a single unit.

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Step-by-step explanation:

\( = 1 - ( \frac{1}{6} + \frac{1}{5} )\)

\( = 1 - ( \frac{5}{30} + \frac{6}{30} )\)

\( = 1 - \frac{11}{30} \)

\( = \frac{30}{30} - \frac{11}{30} \)

\( = \frac{19}{30} \)

So, he keeps \( \frac{19}{30}\)

Answer:

Sanjeev kept 19/30 of his cake.

Step-by-step explanation:

So, if Sanjeev ate 1/6 of the cake there will be 5/6 of the cake left over.

He gave 1/5 of this 5/6 to his friend.

He did not give 1/5 of the entire cake, he gave 1/5 of the remainder of his cake, which was 5/6.

To solve this, we must first convert both fractions to the same denominator.

1/5 and 5/6 becomes 6/30 and 25/30

He gave away 6/30 of this 25/30

It is now clear that we must take away how much he gave away from the remainder of the cake.

25/30 subtract 6/30 becomes 19/30

We cannot simplify this.

Therefore, Sanjeev kept 19/30 of his cake.

Answer:

(a) (0.9240,  0.956)

(b) (0.6383, 0.7017)

Step-by-step explanation:

The number of internet users involved in the survey, n = 846

The percentage of the respondents that said the internet has been good thing for them personally, \(\hat p\) = 94%

(a) The confidence interval of a percentage is given as follows;

\(CI=\hat{p}\pm z\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\)

The z-value for 95% confidence interval = 1.96

We get;

\(CI=0.94\pm 1.96\times \sqrt{\dfrac{0.94 \times (1-0.94)}{846}} \approx 0.94 \pm 1.6003 \times 10^{-2}\)

CI = 0.9240 ≤ \(\hat p\) ≤ 0.956 = (0.9240,  0.956)

(b) The percentage of the internet users that said the internet has directly strengthened their relationship with their families, \(\hat p\) = 67% = 0.67

The 95% confidence interval is therefore;

\(CI=0.67\pm 1.96\times \sqrt{\dfrac{0.67 \times (1-0.67)}{846}} \approx 0.67 \pm 3.1686\times 10^{-2}\)

From which we have;

CI = 0.6383 ≤ \(\hat p\) ≤ 0.7017 = (0.6383, 0.7017)

The number of students with heights less than 163 cm should be expected is 12.

According to the statement

The mean of height is 175 cm

and  the standard deviation of height is 6 cm.

We use normal distribution here with formula

Z= X - μ /σ

Here X is 167.5 and μ is 175 and σ is 6 cm.

Substitute the values in it then

Z = 167.5 - 175 / 6

Z = -1.25

-1.25 have a p value 0.012

Out of 1000 students:

0.012 x 1000 = 12.

So, The number of students with heights less than 163 cm should be expected is 12.

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Answer:

If your answer choices are:

0.01d + 0.10p

0.10d + 0.01p

0.11dp

0.11d + p

A dime is 10% of a dollar and a penny is 1% of a dollar, or 0.10 and 0.01

Then 0.10d + 0.01p is the expression

Hope this helps!

The solutions to the quadratic equation f(x) = x² + 10x - 1 are x = -5 + √26 and x = -5 - √26

To solve the quadratic equation f(x) = x² + 10x - 1

we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For the given equation, a = 1, b = 10, and c = -1.

Substituting these values into the quadratic formula:

x = (-(10) ± √((10)² - 4(1)(-1))) / (2(1))

= (-10 ± √(100 + 4)) / 2

= (-10 ± √104) / 2

Simplifying further:

x = (-10 ± 2√26) / 2

= -5 ± √26

Therefore, the solutions to the quadratic equation f(x) = x² + 10x - 1 are:

x = -5 + √26 and x = -5 - √26

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Answer:

The answer is 13/4

Step-by-step explanation:

I divides and cross miltiplied.

Answer:

Step-by-step explanation:

The one that doesn't work with the other three is B. Nine cubed is huge compared to just plain 9 or 3^2. The other three each are equal to one another especially if you remove the brackets in D.

9 c^(2*3) * d^(3*3)

9 c^6 d^9

Answer:

1320

Step-by-step explanation:

12 x 11 x 10 = 1,320

The two numbers are 7 and 10 whose sum is 17 and whose difference is 3.

Two or more expressions with an Equal sign is called as Equation.

Given that the sum of two numbers is 17 and the difference of those same two numbers is 3.

We need to find those two numbers.

Let x and y are the two numbers.

Sum of two numbers is 17

x+y=17..(1)

Difference of two numbers is 3

x-y=3..(2)

From equation 1,

x=17-y

Now substitute this in equation 2.

17-y-y=3

17-2y=3

17-3=2y

14=2y

Divide both sides by 2

y=7

Now add y value in equation 1

x+7=17

Subtract 7 from both sides

x=10

Hence, the two numbers are 7 and 10.

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Answer:

As the ratio of the length of the arm of the old chair to the length of the arm of the new chair is 3/2, and the length of the old chair is 9 inches, hence the length of the arm of the new chair is 6 inches.

Let:

x = Amount of first brand

y = Amount of second brand

so:

where:

So:

so:

Answer:

44 mm of the first brand

176 mm of the second brand

Answer:

As x decreases, h increases (but never touches)

As x increases, h decreases (but never touches)

Step-by-step explanation:

If you graphed the exponential, you would be able to see that it is stuck in the 3rd quadrant.

Domain: (negative infinity, 1)

Range: (negative infinity, 0)

Answer: y =  ½x - 2

Step-by-step explanation:

Slope-intercept form: y = mx + b

y =  ½x + b

2 =  ½(8) + b

2 = 8/2 + b

2 = 4 + b

2 - 4 = b

b = -2

y =  ½x - 2

Answer:

To calculate measurements for both solids and liquids. An electrical engineer, for example, uses linear equations to solve problems involving voltage, current resistance.

Responder:

240 huevos

Explicación paso a paso:

Número de cajas de huevos = 4

Huevos por caja = 50

Total de huevos en caja = 50 * 4 = 200 huevos

Número de cajas = 3

Número de huevos por caja = 10

Total de huevos en caja = 10 * 4 = 40 huevos

Huevos totales = (huevos en caja + huevos en cartón)

Total = (200 + 40) = 240 huevos

A person leaves their home at noon walking toward a restaurant located 16 miles away If the person walks constantly at 2.5 miles per hour, the person arrive at the restaurant at 6:24 PM.

To determine the time it will take for the person to arrive at the restaurant, we can use the formula:

Time = Distance / Speed

Given:

Distance to the restaurant = 16 miles

Walking speed = 2.5 miles per hour

Substituting these values into the formula, we can calculate the time:

Time = 16 miles / 2.5 miles per hour

Time = 6.4 hours

Since we know the person leaves their home at noon, we can add the calculated time to noon to find the arrival time:

Arrival Time = Noon + 6.4 hours

To express the arrival time in a standard 12-hour clock format, we convert 6.4 hours into hours and minutes:

0.4 hours * 60 minutes/hour = 24 minutes

So, the person will arrive at the restaurant at approximately 6 hours and 24 minutes after noon.

Therefore, the person will arrive at the restaurant at approximately 6:24 PM.

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There are 4,782,905 strings with seven or more characters that can be formed from the letters in "evergreen".

What is a sequence?

A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).

The word "evergreen" has 9 letters. To find the number of strings with seven or more characters that can be formed from these letters, we need to count the total number of possible strings of length 7 or more, and then subtract the number of strings of length 6 or fewer.

The total number of possible strings of length 7 or more can be found by summing the number of strings of length 7, 8, 9, and so on. For each length, we can use the formula for counting the number of permutations with repetition:

\(n^r\)

where n is the number of distinct elements (in this case, 9 letters) and r is the length of the string. So the number of strings of length 7 or more is:

\(9^7 + 9^8 + 9^9 + ...\)

To subtract the number of strings of length 6 or fewer, we can sum the number of strings of length 1, 2, 3, 4, 5, or 6, and use the same formula:

\(9^1 + 9^2 + 9^3 + 9^4 + 9^5 + 9^6\)

Finally, we can subtract this sum from the first sum to get the total number of strings with seven or more characters:

\(9^7 + 9^8 + 9^9 + ... - (9^1 + 9^2 + 9^3 + 9^4 + 9^5 + 9^6)\)

This expression can be simplified using the formula for an infinite geometric series:

a/(1-r)

where a is the first term and r is the common ratio. In this case, a = 9⁷ and r = 1/9. So we get:

\(9^7/(1-1/9) - 9^1/(1-1/9)\)

= 4782969 - 9¹ * 8/9

= 4782969 - 64

= 4782905

Therefore, there are 4,782,905 strings with seven or more characters that can be formed from the letters in "evergreen".

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DNE in each coordinate of the ordered triplet are y is -7 , DNE ,y is-2.

1.) 2+3 = y + 12

Make y the formula's subject after adding the LHS.

5 = y + 12

Y = 5 - 12

Y = - 7

The answer to the equation is -7

2.) 2 + 13 = 1 +8

The equation cannot have a solution since there is no unknown variable and the sum of the numbers on the left hand side (LHS) does not equal the sum of the numbers on the right hand side (RHS).

3.) y - 7 = 2 - 11

RHS is added, and y is become the formula's subject.

Y - 7 = -9

Y = -9 + 7

Y = -2

The equation's answer is -2.

The complete question is:Solve the following system of equations. If there is no solution, write DNE in each coordinate of theordered triplet. If there are an infinite number of solution, write each coordinate in terms of z.2+3 = y + 12

2 + 13 = 1 +8

y - 7 = 2 - 11

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The equation for the contour of `f(x, y) = 2x^2` that goes through the point `(5, 2)` is `2x^2 = c = 50`.

The given function is given by `f(x, y) = 2x^2 y + 9x+ 15`

To find an equation for the contour of the given function, we can use the following steps:

Step 1: Replace `f(x, y)` with `c`

Step 2: Write the resulting equation as `y =` or `x =`

Step 3: Simplify the equation

Step 4: Write the equation in terms of `c` and simplify it.

Now let's solve the given problem.1. Find an equation for the contour of `f(x, y) = 2x^2 y + 9x+ 15`

First, let us replace `f(x, y)` with `c`.

Thus, `2x^2 y + 9x+ 15 = c`

This can be rewritten as `y = - 9/ (2x) - (15/ (2x^2)) + c/(2x^2)`

Hence, the equation for the contour of `f(x, y) = 2x^2 y + 9x+ 15` is `y = - 9/ (2x) - (15/ (2x^2)) + c/(2x^2)`2.

Find an equation for the contour of `f(x, y) = 2x^2` that goes through the point `(5, 2)`

The given function is `f(x, y) = 2x^2`.

If the equation has to pass through the point `(5, 2)`, then the value of `c` can be found using the given point.`f(5, 2) = 2(5)^2 = 50`

Thus, `c = 50`.

Hence, the equation for the contour of `f(x, y) = 2x^2` that goes through the point `(5, 2)` is `2x^2 = c = 50`.

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