The gradient of every point on the curve C with equation y = f(x), satisfies

dy/dx = 3x2 – 4x + k, where k is a constant. The points P (0, -3) and Q (2,7) both lie on C. find the equation for C.

The average reading time for the entire book club each day is 55 minutes

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

The weighted average of the numbers is calculated as

Average = Product of numbers and weights/Sum of weights

So, we have

Average = (10 * 65 + 5 * 35)/15

Evaluate

Average = 55

Hence, the weighted average is 55

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We would expect the spinners to land on the same number approximately 2 times in 10 spins.

Based on the given probabilities, we know that the probability of the red spinner and blue spinner landing on the same number is 21%, and the probability of them landing on different numbers is 79%. We can use this information to calculate the expected number of times the spinners would land on the same number in 10 spins.

If we assume that the probability of the spinners landing on the same number is constant across all 10 spins, then we can model the number of times they land on the same number as a binomial distribution with n=10 (number of trials) and p=0.21 (probability of success).

Using the formula for expected value of a binomial distribution, we can calculate the expected number of times the spinners would land on the same number in 10 spins as:

E(X) = np = 100.21 = 2.1

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Complete question is:

The outcome of spinning 2 spinners 100 times is shown as.

Events                                            Actual outcomes                  Probability

P(red spinner = blue spinner)                  21                                            21%

P(not red spinner = blue spinner)          79                                            79%

How many times would you expect these spinners to land on the same number in 10 spins?

The function rule for the graph is -2 ≤ x ≤ 1 , where x is the domain

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is plotted on the graph

The values of the output represents the range of the function and the domain of the function is the input

So , the x values ranges from [ -2 , 1 ]

Hence , the function rule is domain ranges from -2 ≤ x ≤ 1

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The probability of observing an income between $70,000 and $90,000 for engineers at this computer company is 0.6217, or about 62.17%.

To solve this problem, we need to standardize the given income range using the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can do this by using the formula:

z = (x - μ) / σ

where x is the income, μ is the mean income, and σ is the standard deviation.

For the lower bound of $70,000, we have:

z₁ = (70,000 - 83,422) / 8,278 = -1.62

For the upper bound of $90,000, we have:

z₂ = (90,000 - 83,422) / 8,278 = 0.79

We can now find the probability of observing an income between $70,000 and $90,000 by calculating the area under the standard normal curve between z₁ and z₂.

We can use a standard normal distribution table or a calculator to find this probability, which turns out to be approximately 0.6217. This means that about 62.17% of engineers at this company earn an income within this range.

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Complete question is:

The salaries of engineers at a computer company are normally distributed with mean $83,422 and standard deviation $8,278. What is the probability of observing an income between $70,000 and $90,000?

Answer:yes, it’s a function, domain is all real # range all real #

Step-by-step explanation:

Answer:

We can solve this problem using the following steps:

1. **Calculate the probability of being in each group.**

The probability of being in the binge drinking group is 44%.

The probability of being in the moderate drinking group is 37%.

The probability of being in the abstain group is 9%.

2. **Calculate the probability of being in the accident group.**

The probability of being in the accident group is 17% + 9% = 26%.

3. **Calculate the probability of being in the abstain group and having an accident.**

The probability of being in the abstain group and having an accident is the probability of being in the abstain group multiplied by the probability of having an accident, given that you are in the abstain group.

The probability of being in the abstain group is 9%.

The probability of having an accident, given that you are in the abstain group, is the probability of being in the accident group and being in the abstain group, divided by the probability of being in the abstain group.

The probability of being in the accident group and being in the abstain group is 9%.

The probability of being in the abstain group is 9%.

Therefore, the probability of having an accident, given that you are in the abstain group, is 9% / 9% = 1.

4. **Calculate the probability of having an accident and being in the abstain group.**

The probability of having an accident and being in the abstain group is the probability of being in the abstain group and having an accident.

The probability of being in the abstain group is 9%.

The probability of having an accident, given that you are in the abstain group, is 1.

Therefore, the probability of having an accident and being in the abstain group is 9% * 1 = 9%.

**Answer:**

The probability of having an accident and being in the abstain group is 9%.

The range of the given linear function; f(t) = 2t + 1 given its domain (1, 2, 3, 5) is; (3, 5, 7, 11).

It follows from the task content that the range of the given function is to be determined given its domain as defined by the set; (1, 2, 3, 5).

Therefore;

At t = 1; f(1) = 2(1) + 1 = 3.

At t = 2; f(2) = 2(2) + 1 = 5.

At t = 2; f(3) = 2(3) + 1 = 7.

At t = 5; f(5) = 2(5) + 1 = 11.

Ultimately, the range of the given function as required is given by the set; (3, 5, 7, 11).

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Answer:

The graph appears to be a cosine function that has been shifted π units to the left and vertically reflected.

Option (d) represents this transformation:

f(x) = -4 cos(x + π)

Therefore, the answer is (d).

Step-by-step explanation:

The antiderivative of the function is t³/3 i + ln |cos(t)| j.

option C.

The antiderivative of the function is calculated as follows;

r = t²i + tan(t)j

tan(t) = sin(t)/cos(t)

Substituting sin(t)/cos(t) for tan(t) in the given function;

r = t²i + (sin(t)/cos(t))j

The antiderivative of sin(t)/cos(t) with respect to t is calculated as;

u = cos(t)

du = -sin(t)dt

∫ (sin(t)/cos(t)) dt = -∫ du/u

= -ln |u| + C

= -ln |cos(t)| + C

The antiderivative of t² is calculated as;

∫ t² dt = t³/3 + C

Add the two equations, to obtain the antiderivative;

∫ r dt = t³/3 i + ln |cos(t)| j

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By analyzing the end behavior of the function we can see that the correct options are A and D.

Here we have the exponential function:

[tex]F(x) = 2^x[/tex]

This is an exponential growth, this means that as x increases also does the function, then the end behavior of the function is:

as x → ∞, f(x) → ∞

And when x is a really large negative number, the function tends to zero, then we have:

as x →-∞, f(x) → 0

Then the correct options are A and D.

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The values of the arc length and angles are:

HE = 62

HD = 118

DG = 62

EG = 118

∠DEG + ∠HGE = 62

We have,

The central angle is equal to the intercepted arc length.

So,

62° = HE

And,

∠A = HD

∠A + 62 = 180

∠A = 180 - 62

∠A = 118

HD = 118

And,

DG = ∠M (say)

∠A + 118 = 180

∠M = 180 - 118

∠M = 62

DG = 62

And,

∠A is opposite to ∠N (say)

So,

∠A = ∠N = 118

∠A = EG

EG = 118

And,

From the definition of the exterior angle.

∠DEG + ∠HGE = 62 ______(1)

Also,

The sum of the three angles in AEG = 180

∠EAG + ∠DEG + ∠HGE = 180

∠EAG = 180 - 62 = 118

So,

∠DEG + ∠HGE = 180 - 118

∠DEG + ∠HGE = 62 _______(2)

Thus,

HE = 62

HD = 118

DG = 62

EG = 118

∠DEG + ∠HGE = 62

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The percentage of the data that falls within 2 standard deviations of the mean is  B. 68%

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

Percentage = 2 standard deviations

As a general rule:

The percentage of the data that falls within 2 standard deviations of the mean is 68%

This means that the correct option is (b) 68%

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Answer:

Step-by-step explanation:

m

2

−2m−8

Factor the expression by grouping. First, the expression needs to be rewritten as m

2

+am+bm−8. To find a and b, set up a system to be solved.

a+b=−2

ab=1(−8)=−8

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product −8.

1,−8

2,−4

Calculate the sum for each pair.

1−8=−7

2−4=−2

The solution is the pair that gives sum −2.

a=−4

b=2

Rewrite m

2

−2m−8 as (m

2

−4m)+(2m−8).

(m

2

−4m)+(2m−8)

Factor out m in the first and 2 in the second group.

m(m−4)+2(m−4)

Factor out common term m−4 by using distributive property.

(m−4)(m+2)

It will take approximately 4 years for the amount in Dillon's bank account to grow to $2,000.

We use the formula for simple interest to solve this problem;

I = P × r × t

where;

I = the interest earned

P = the initial principal (balance) = $1,766

r = the interest rate (as a decimal) = 3.2% = 0.032

t = the time (in years) we need to find

We know that the interest earned is the difference between the final amount (balance + interest) and the initial principal (balance), so we can write;

Interest = Final Amount - Initial Principal

Plugging in the values, we get;

I = $2,000 - $1,766

I = $234

Now we can substitute the values of I, P, and r into the simple interest formula and solve for t;

234 = 1766 × 0.032 × t

Dividing both sides of the equation by (1766 * 0.032) to isolate t:

t = 234 / (1766 × 0.032)

t ≈ 4.19

So, it will take approximately 4.19 years for the amount in Dillon's bank account to grow to $2,000. Since time cannot be in decimal years, we round to the nearest whole year:

t ≈ 4

Therefore, it will take 4 years for the amount in Dillon's bank account to grow to $2,000.

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There are 5 sheets of paper will she need to complete 10 problems.

We have to given that;'

Kendra is doing her math homework. For each problem, she uses 1/2 of a sheet of paper.

Hence, For complete 10 problems, number of sheets are,

⇒ 1/2 of 10

⇒ 1/2 x 10

⇒ 5

Thus, There are 5 sheets of paper will she need to complete 10 problems.

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The simplified expression for the difference in the area of circle A and B is 12π/(x+2)²

A circle is simply a round shape that has no corners or line segments. The area of a circle is expressed as;

A = πr²

The circumference of a circle = 2πr

for circle A;

8π/x+2 = 2πr

r = 8π/x+2 × 1/2π

r = 4/x+2

area = πr² = (4/x+2)²π

for circle B

4π/x+2 = 2πr

r = 4π/x+2 × 1/2π

r = 2/2x+2

area =( 2/2x+2)²π

difference = (4/x+2)²π - ( 2/x+2)²π

= π/(x+2)²( 4²-2²)

= π/(x+2)²(16-4)

= 12π/(x+2)²

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The testable question can be Which sprouts faster, a moist lima bean or a dry lima bean?

We have,

June laces a lima bean inside a damp paper towel, then places it in a baggie.

June takes another lima bean and places it in a dry paper towel and puts it in a baggie.

The Experiment is related to moisture because one damp and one dry towel is used.

So, the testable question can be

Which sprouts faster, a moist lima bean or a dry lima bean?

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Answer:

t = 6.8

Explanation:

We know that A is at 1, B is at 10, so that is where we place those two.

First, we need to know what 2/3 of 10 is because the distance between A and B is 10.

Solving 2/3 of 10:

_____________________

- Divide 10 by the denominator, 3

         10 ÷ 3 = 3.3333......

- Multiply 3.3333..... by 2

         3.3333..... x 2 = 6.6666666666667

            or about 6.8 if we round up, which is prefered in these scenarios

Now that we know what 2/3 of 10 is, we can use that number as where to put it on the number line.

So t = 6.8

Hope this helps :)

4 things can be selected from a total of 9 without replacement in 126 times without replacement.

Combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of selection does not matter.

How to determine this

To calculate the combination without replacement

nCr = n!/r!(n-r)!

9C4= 9!/4!(9-4)!

= 9!/4!(5!)

= 9*8*7*6*5*4*3*2*1/4*3*2*1*5*4*3*2*1

= 362880/24*120

= 362880/2880

= 126

Therefore, it can be combined in 126 times

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The Vector form is v = 11i + 0j.

We have,

P₁ =(-6,5), P2 = (5,5)

If we have the point p1 and p2 then the vector form p1 -> p2 is

v = p2 - p1

v = [ p(2x) - p(1x)) i + [ p (2y) - p(1y)] j

v = (5 - (-6)) i + (5 - 5)j

v = 11i + 0j

v = 11 i

Thus, the vector form is v = 11i + 0j.

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The distribution of the numbers of siblings is best described as skewed to the right so, the median will be a more appropriate measure of the center than the mean

If data is positively skewed - which means that the tail of the distribution leans towards higher values - the median will often be a superior indicator for ascertaining the center than the mean.

This advantage can be attributed to the fact that the median outright ignores extreme values, unlike the median which may become influenced by them and thus pulled towards the extremes of the overall set. Since it is simply the middle value obtained upon sorting the data, its sensitivity to conspicuous outliers is more limited.

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The vertices of the feasible region is (4, 3)

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

x + y ≤ 7

x - 2y ≤ -2

x ≥ 0

y ≥ 0

Express as equations

So, we have

x + y = 7

x - 2y = -2

Subtract the equations

3y = 9

So, we have

y = 3

Next, we have

x + 3 = 7

This gives

x = 4

Hence, the vertex of the feasible region is (4, 3)

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A graph of triangle ABC is shown below.

A graph of triangle A'B'C, the image of ΔABC after a translation right 1, down 3 is shown below.

A graph of triangle A"B"C", the image of ΔABC after a dilation of 2 is shown below.

ΔA"B"C" does not represent a rigid motion because the pre-image and the image are not congruent.

By translating the pre-image triangle ABC vertically down 3 units and horizontally right 1 unit, the coordinates of the image of triangle A'B'C'D' include the following:

(x, y)                               →                  (x + 1, y - 3)

Coordinate A = (2, 3)   →    Coordinate A' = (2 + 1, 3 - 3) = (3, 0)

Coordinate B = (4, 0)   →    Coordinate B' = (4 + 1, 0 - 3) = (5, -3)

Coordinate C = (5, 4)   →     Coordinate C' = (5 + 1, 4 - 3) = (6, 1)

By applying a dilation with a scale factor of 2 centered at the origin, we have:

Coordinate A = (2, 3)   →    Coordinate A" = (4, 6)

Coordinate B = (4, 0)   →    Coordinate B" = (8, 0)

Coordinate C = (5, 4)   →     Coordinate C" = (10, 8)

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Answer:

second option

Step-by-step explanation:

the volume of a cone is calculated as

[tex]\frac{1}{3}[/tex] πr²h

the volume of a sphere is calculated as

[tex]\frac{4}{3}[/tex] πr³

then the volume of a hemisphere is

[tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3}[/tex] πr³ = [tex]\frac{2}{3}[/tex] πr³

then the volume (V) of the composite solid is

V = [tex]\frac{1}{3}[/tex] πr²h + [tex]\frac{2}{3}[/tex] πr³

It will take 5 seconds for the object to hit the ground

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

-16r^2 + 400 = 0

So, we have

- 16r^2 = -400

Divide by -16

This gives

r^2 = 25

Take the square root of both sides

r = 5

Hence, the number of seconds is 5

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The area of the parallelogram can be found using the formula A = base × height:

A = 6 cm × 10 cm

A = 60 cm²

The area of a triangle is given by the formula A = 1/2 × base × height. We know the height is 5 cm and the area is also 60 cm² (since it is equal to the parallelogram). So, we can solve for the base:

60 cm² = 1/2 × base × 5 cm

Dividing both sides by 1/2 × 5 cm gives:

base = 24 cm

Therefore, the base of the triangle is 24 centimeters.

Answer:

24cm

Step-by-step explanation:

The match of the given words as per the definition of the terms related to data set is as follow.

1 → g

2 →c

3 → b

4 → d

5 → f

6 → a

7 → e

The description of the each word as per the definition is ,

Mean represents the average of the data.

1→g

Spread represents the similarity or variability of  the set of observed values of the data.

2→c

Center represents the middle value of the data set.

3→ b

Shape represents the values of the data set when plotted on the graph.

4 → d.

Median represents the middle value of the data set after arranging in ascending or descending order.

5 →f

Distribution represents measure of all the values of the data set spread.

6→a

variability represents the set of such values which satisfies the statistical question or relation.

7 → e.

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Answer:

X can be any number greater than -2 and less than or equal to 1/4.

Step-by-step explanation:

To solve for x in the inequality 3x + 1 ≤ 2 - x < 18 + 7x, we will first isolate the variable x on one side of the inequality.

3x + 1 ≤ 2 - x

Adding x to both sides, we get:

4x + 1 ≤ 2

Subtracting 1 from both sides, we get:

4x ≤ 1

Dividing both sides by 4, we get:

x ≤ 1/4

Next, we solve the second inequality:

2 - x < 18 + 7x

Adding x to both sides, we get:

2 < 18 + 8x

Subtracting 18 from both sides, we get:

-16 < 8x

Dividing both sides by 8, we get:

-2 < x

Therefore, the solution to the inequality 3x + 1 ≤ 2 - x < 18 + 7x is:

-2 < x ≤ 1/4

This means that x can be any number greater than -2 and less than or equal to 1/4.

that would be 5 pieces of cardboard needed