the graph of the function y = x^2 - x -2 is shown below. which of the following shows the correct key features of the graph

Answer:

to the right

Step-by-step explanation:

Answer:

Right.

Step-by-step explanation:

When the x coordinate is positive, you move right on the coordinate plane.

For reference, here are the other directions.

When the x coordinate is negative, you move left on the coordinate plane.

When the y coordinate is positive, you move up on the coordinate plane.

When the y coordinate is negative, you move down on the coordinate plane.

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

What is derivative?

The derivative of a function in calculus measures the function's sensitivity to changes in its input variable. Specifically, at a particular point, it represents the function's rate of change with respect to its input variable at that moment.

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

This limit represents the instantaneous rate of change or slope of the function at the point x = a. The difference quotient is the change in the function value divided by the change in the input variable (or the distance between two points on the graph of the function).

The derivative is a fundamental concept in calculus, and it has many applications in various fields of science, engineering, and economics. It allows us to calculate important quantities such as velocity, acceleration, and marginal cost, and it is used to optimize functions and solve many real-world problems.

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The margin of error is approximately 0.014 grams, rounded to three decimal places.

To construct a 98% confidence interval for the mean of repeated measurements of the weight, we can use the following formula:

CI = x ± z × (σ/√n)

Where:
x = mean result = 10.230 grams
σ = standard deviation of scale readings = 0.020 gram
n = number of repeated measurements = 40
z = z-score for 98% confidence interval = 2.326

Plugging in the values, we get:

CI = 10.230 ± 2.326×(0.020/√40)
CI = 10.230 ± 0.014
CI = (10.216, 10.244)

Therefore, the 98% confidence interval for the mean of repeated measurements of the weight is (10.216, 10.244) grams.

The margin of error is the difference between the upper and lower bounds of the confidence interval divided by 2, so:

Margin of error = (10.244 - 10.216)/2
Margin of error = 0.014

Thus, the margin of error is 0.014 grams.

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Answer:

24 yards = 72 feet

Step-by-step explanation:

3 feet per yard

24 x 3 = 72

If mark and Alexis work together on a particular truck, they can load all of the packages in 90 minutes.

It will take 90 minutes for both Mark and Alexis to load all of the products.

Given,

that Mark can load a truck with items in 120 minutes and Alexis can do the same in 240 minutes, the average time for the two of them is as follows:

Average = (120 + 240) ÷ 2

= 360 ÷ 2

= 180

In this case, the term "Average" refers to the value that should be used to represent the sample. By dividing the total number of values in a particular set by the sum of all the values in that set, the average is determined. also known as the arithmetic mean.

Since there were two parties engaged, our calculation is 180 ÷ 2 = 90.

Hence, in this case, it is concluded that the correct answer is option B. 90 minutes.

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It is not always possible for the hunter to ensure that the distance between her and the rabbit is at most 100 after $10⁹$ rounds. The distance between the hunter and the rabbit can increase by a factor of 2 in each round, making it impossible for the hunter to catch the rabbit in some scenarios.

It is not always possible for the hunter to ensure that the distance between her and the rabbit is at most 100 after $10⁹$ rounds, regardless of how the rabbit moves or what points are reported by the tracking device. This is because the distance between the hunter and the rabbit can increase by a factor of 2 in each round, which means that after $10⁹$ rounds, the distance between them could be as much as $2⁽¹⁰⁾⁹$ times the initial distance. This value could be much larger than 100, making it impossible for the hunter to catch the rabbit. Therefore, there are scenarios in which the hunter cannot catch the rabbit within $10⁹$ rounds.

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Answer: 1. Smaller than 8 SQUARE ft. 8 ft on one side and 7/8 ft one one side does NOT equal 8 square ft, it is less. It is actually 7ft. 2. 50,343 is the answer to the second question, so less than the number. Explanation: When you multiply a number by a fraction you get less than the number you started with.

Hope this helps

Answer:

7. Option 2 smaller than 8 sq.ft.

8. Less than 67.24

Step-by-step explanation:

7. the fraction 7/8 is proper, i.e. less than the unit, Any number multiplied by a proper fraction is less (reduced).

8. the same reason as the previous one, 3/4 is a proper fraction.

Hope this helps

Step-by-step explanation:

if you invest $20,000 with 6% compounded interest annually over the span of 5 years the interest would be $6,765 with a total of $26,765

Answer:

One solution

Step-by-step explanation:

3-2x=5-x+3+4x

3-2x=3x+8       Combine like terms

3-8-2x+2x=3x+2x+8-8         Minus or add terms to get x on one side by itself

-5=5x        Divide 5 to both sides to get x by itself

5    5      

x=-1           The 5 is cancelled out on the side with the x and then divide it on                       the side with -5

Answer:

A) D) F)

Step-by-step explanation:

A) Since the graph is 10x10, and there are 10 seasons, it makes sense for A) to be an option

D) There is a total of 50 values that will be on the verticle axis, which seems like a fair number when the highest value is 37

F) (Season 8, 30 average points per game)

The height of the cylinder is approximately 5.97 cm.

A cylinder is a three-dimensional geometric shape that consists of two parallel, congruent circular bases and a curved lateral surface that connects the bases. The bases are perpendicular to the lateral surface, which means that the lateral surface forms a curved rectangle.

Given;

The circumference of the cylinder is 32π.

The lateral surface area of the cylinder is 750 cm².

Lateral surface area of a cylinder = 2πrh

Circumference of a cylinder = 2πr

We can use the circumference formula to find the radius of the cylinder:

2πr = 32π

r = 16

Now we can use the lateral surface area formula to find the height of the cylinder:

750 = 2π(16)(h)

750 = 32πh

h = 750/(32π)

h ≈ 5.97

As a result, the cylinder's height is around 5.97 cm.

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Answer:

Each term in Pattern A is equals to 6 times the value of corresponding term in Pattern B and subtract 12

Step-by-step explanation:

Given - Pattern A: start with 12 and add 12

             Pattern B: start with 4 and add 2

To find - Which statement best describes the relationship between the

              corresponding terms of Patter A and Pattern B.

Proof -

To find the relationship between the Pattern a and pattern B , firstly we have to find few terms of both the Patterns , so that we can see how the digits of both the Patterns are realted

Now,

For Pattern A :

1st digit = 12

2nd digit = 12 + 12 = 24

3rd digit = 24 + 12 = 36

4th term = 36 + 12 = 48

5th term = 48 + 12 = 60

.

.

.

and so on

Now,

For Pattern B :

1st digit = 4

2nd digit = 4 + 2 = 6

3rd digit = 6 + 2 = 8

4th term = 8 + 2 = 10

5th term = 10 + 2 = 12

∴ we get

Terms of Pattern A : 12, 24, 36, 48, 60, ....

Terms of Pattern B :  4, 6, 8, 10, 12, ....

As we can see that

4×6 - 12 = 12

6×6 - 12 = 24

8×6 - 12 = 36

10×6 - 12 = 48

12×6 - 12 = 60

.

.

The pattern is - Multiply by 6 in Pattern B and after that subtract by 12 , we get Pattern A.

Term in Pattern A = 6×corresponding term of Pattern B - 12

i.e. , we get

Each term in Pattern A is equals to 6 times the value of corresponding term in Pattern B and subtract 12

The standard deviation of a numerical data set measures the variability of the data. It is a widely used measure in statistics that helps to determine how spread out the values are within a given data set.

By calculating the standard deviation, we can better understand the range and distribution of values in the data set, as well as identify potential outliers. This measure is particularly important in fields such as finance, science, and engineering, where understanding the variability in data can be crucial for making informed decisions and predictions. So, the most appropriate term that makes the statement true is D: variability.

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So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

Answer:

n > -2

Step-by-step explanation:

7(1 - 2n) < 33 - n

7 - 14n < 33 - n

Subtract 7

-14n < 26 - n

Add n

-13n < 26

Divide by -13

n > -2

Answer:

n > -2

Step-by-step explanation:

Distribution property:

7 - 14n < 33 - n

Bring n over:

7 - 13n < 33

Bring 7 over:

-13n < 26

n > -2

Answer: I and III

Step-by-step explanation:

The origin is at (0,0).

When we look at the graph, we can see that the only visible x and y intercepts are at the origin, (0,0) (an x or y intercept is where the graph intersects the x or y axis). We also know that because the graph is going outwards, it will not have another x or y intercept. So, I is correct.

II would be incorrect because the maximum point would be WAY further up. The maximum point is the highest point the graph will reach.

III is correct because the origin is the lowest point, which means that the origin is the minimum point.

The variance of a distribution of means of samples of more than one is A) smaller than the original population variance.

When considering the distribution of means of samples, the central limit theorem states that as the sample size increases, the sampling distribution approaches a normal distribution regardless of the shape of the population distribution. Additionally, the standard error of the mean decreases as the sample size increases.

The variance of a population is denoted by σ^2.

The variance of the distribution of sample means, also known as the sampling distribution, is denoted by σ^2/N, where N is the sample size.

As the sample size (N) increases, the denominator increases, leading to a smaller value for the variance of the distribution of sample means (σ^2/N). Thus, the variance of the distribution of means of samples is smaller than the original population variance.

The variance of a distribution of means of samples of more than one is smaller than the original population variance. This is due to the central limit theorem and the decrease in standard error as the sample size increases.

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The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.

In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:

There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.

Two-way interactions:

There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.

These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:

There is 1 possible three-way interaction that can be tested in this design: AxBxC.

This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.

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30% of 42 is 12.6.

sorry if wrong.

hope it helps.

have a great day.

Answer:

30% of 42 is 12.6.

Step-by-step explanation:

Ok, so first you need to find the value of 1%. To do that, you divide 42 by 100. That gives you 0.42. So, 0.42 = 1%. TO find 30%, multiply the value of 1% by 30. That's 0.42 * 30, which gives you 12.6. Therefore, 30% of 42 is 12.6!

Luca picks his number first. then, craig picks a number from the remaining cards, these two events are Dependent.

Total number of cars are 25,

Luca picks randomly a card so probability is now 1/25 and total number of cars are now 24.

If craig have to pick then the probability of it becomes 1/24 as one card was already picked by the Luca,

So this indicated that these two events are Dependent.

In probability, dependent events are those whose occurrence influences the likelihood of occurrence of another event. Imagine there are 3 red and 6 green balls in a bag. One after the other, two balls are taken out of the bag.

Let A represent the first draw's red ball draw and B represent the second draw's green ball draw. If the first draw's ball is not put back in the bag, then A and B are dependent events because P(B) changes depending on whether the first draw's ball was red or green.

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Answer:

a = -4

Step-by-step explanation:

Solve for a:

-7 (3 a - 1) = 91

Divide both sides of -7 (3 a - 1) = 91 by -7:

(-7 (3 a - 1))/(-7) = 91/(-7)

(-7)/(-7) = 1:

3 a - 1 = 91/(-7)

The gcd of 91 and -7 is 7, so 91/(-7) = (7×13)/(7 (-1)) = 7/7×13/(-1) = 13/(-1):

3 a - 1 = 13/(-1)

Multiply numerator and denominator of 13/(-1) by -1:

3 a - 1 = -13

Add 1 to both sides:

3 a + (1 - 1) = 1 - 13

1 - 1 = 0:

3 a = 1 - 13

1 - 13 = -12:

3 a = -12

Divide both sides of 3 a = -12 by 3:

(3 a)/3 = (-12)/3

3/3 = 1:

a = (-12)/3

The gcd of -12 and 3 is 3, so (-12)/3 = (3 (-4))/(3×1) = 3/3×-4 = -4:

Answer: a = -4

Answer:

a = -4

Step-by-step explanation:

Step 1: Write out equation

-7(3a - 1) = 91

Step 2: Distribute -7

-21a + 7 = 91

Step 3: Subtract 7 on both sides

-21a = 84

Step 4: Divide both sides by -21

a = -4

Answer:

16 less than two times a number "x"

Answer:

he value of the integral ∫ y tan(x) dx is y sin(x) + C.

Step-by-step explanation:

Property 8 of integrals states that if we have an integral of the form ∫ f(x) g'(x) dx, it can be rewritten as ∫ f(x) dg(x), where g(x) is an antiderivative of g'(x).

In this case, we have the integral ∫ y tan(x) dx. By applying Property 8, we can rewrite it as ∫ y d(sin(x)).

Now, integrating with respect to y while treating sin(x) as a constant, we get:

∫ y d(sin(x)) = y sin(x) + C,

where C is the constant of integration.

So, using Property 8, the value of the integral ∫ y tan(x) dx is y sin(x) + C.

The mean and standard deviation of the population is 19.8 and 0.004 respectively.

Mean:

The mean is the simple mathematical average of a set of two or more numbers. The mean of a given set of numbers can be calculated in several ways, including the arithmetic mean, which uses the sum of the numbers in the range, and the geometric mean, which takes the mean product of a set. However, all major methods of calculating simple averages produce the same approximate result most of the time.

Standard Deviation:

In statistics, standard deviation is a measure of the amount of variation or distribution of a set of values.  A low standard deviation indicates that the values ​​tend to be close to the ensemble mean (also called the expected value), while a high standard deviation indicates that the values ​​are spread over a wider range.

Given that:

E(x) = μ = 19.8

var(x) = σ²/n = 0.2/50 = 0.004

from here can say that mean = 19.8 and

standard Deviation is 0.004.

Now,

295 -298 P(Bottle x < 295) =P(Z< ) =-1.00 =.15873

Thus, there is nearly a 16% probability that just 1 randomly selected

bottle contains < 295 ml.

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Answer: it is 2 ft

Step-by-step explanation:

because you have to do 12/3 and that equals 4 and then you have to do 4/2 and that equals 2

Answer:

it is 49 I took the test on edgenuity

Answer:

72 is your answer mate...

Answer:

3ab

Step-by-step explanation:

i hope you don't want to know how i did this :)