Select the correct answer.

This table represents value of a cubic polynomial function.

Based on the information in the table, which sentence best describes the interval [-2, 1]?
A. The function is increasing on the interval [-2, 1].
B. The function is both increasing and decreasing on the interval [-2, 1].
C. The function is decreasing on the interval [-2, 1].
D. The function is constant on the interval [-2, 1].

Step-by-step explanation:

For: x=-1

f(x)= -3*-1 -4 =-1

For: x=0

f(x)= -3*0-4 =-4

For: x=1

f(x)= -3*1 -4 =-7

Therefore, the range of f(x)= [-1, -4, -7]

Answer:

142

Step-by-step explanation:

∠P + ∠Q = 180

38 + ∠Q = 180

Subtract 38 from both sides

∠Q = 142 degrees

The equation of the linear function that fits the given data is y = 10x - 2.

To find the equation of a linear function in slope-intercept form, we need to determine the slope (m) and y-intercept (b).

m = (y2 - y1) / (x2 - x1)

(x1, y1) = (0, -2)

(x2, y2) = (4, 38)

m = (38 - (-2)) / (4 - 0)

= 40 / 4

= 10

y = mx + b

To find the y-intercept, we can use any point on the line. Let's use (0, -2):

-2 = 10(0) + b

b = -2

So,

y = 10x - 2

We can check that this equation satisfies all the given data points:

When x = 0, y = 10(0) - 2 = -2

When x = 1, y = 10(1) - 2 = 8

When x = 2, y = 10(2) - 2 = 18

When x = 3, y = 10(3) - 2 = 28

When x = 4, y = 10(4) - 2 = 38

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This is reflected in the data as the number of bacteria doubles every two hours, which is a characteristic of exponential growth.

Data that changes or grows at an exponential rate over time is referred to as exponential data. This indicates that the data changes quickly, either increasing or decreasing, and that the pace of change quickens over time. Exponential data frequently consists of numbers that rise steadily over time, with the rate of rise accelerating over time.

a.) exponential function would be the ideal option to model this data. An exponential curve is produced as the quantity of bacteria multiplies at an ever-increasingly rapid rate.

b. One way to determine which function is the best choice is to examine the rate of change of the data. In this case, we may calculate the average rate of change for each time period and see if it is constant. If the rate of change is constant, the data can be represented by a linear function. However, if the rate of change increases or decreases, an exponential or quadratic function might be a better fit.

From 0 to 2 hours: (25-10)/(2-0) = 7.5

From 2 to 4 hours: (50-25)/(4-2) = 12.5

From 4 to 6 hours: (100-50)/(6-4) = 25

c. The distance travelled by an automobile at a constant pace is an illustration of data that would be best characterised by a linear function. Imagine a car driving for four hours at a speed of 60 mph. Below is a list of the distance covered each hour:

After 1 hour: 60 miles

After 2 hours: 120 miles

After 3 hours: 180 miles

After 4 hours: 240 miles

In this case, the distance traveled is directly proportional to the time, so a linear function would be the best fit.

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To be 95% confident within a 4% margin of error, the programmer must survey at least 601 computers.

To estimate the percentage of computers that use a new operating system with a 95% confidence level and a 4% margin of error, you must first determine the required sample size. Here's a step-by-step explanation:
Identify the confidence level and margin of error: In this case, the confidence level is 95% and the margin of error is 4%.
Determine the standard value (Z-score) for the desired confidence level: For a 95% confidence level, the Z-score is 1.96. This value can be found using a Z-score table or an online calculator.
Use the formula for sample size calculation:
  n = (Z^2 * p * (1-p)) / E^2
  Where n is the required sample size, Z is the Z-score, p is the estimated proportion of computers using the new operating system, and E is the margin of error.
Since we do not have an estimate for the proportion (p), we will assume the worst-case scenario (p=0.5) to ensure the largest possible sample size:
  n = (1.96^2 * 0.5 * 0.5) / 0.04^2
Calculate the sample size:
  n ≈ (3.8416 * 0.25) / 0.0016
  n ≈ 0.9604 / 0.0016
  n ≈ 600.25
Round up to the nearest whole number: Since we cannot survey a fraction of a computer, we will round up to the next whole number, which is 601.

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The probabilities of rolling each number on the die are 1÷6, which is correctly represented by the branching probabilities from each die-rolling node.

What is an experiment ?

In science and statistics, an experiment is a controlled procedure designed to test a hypothesis or to investigate the effect of one or more factors or variables on an outcome of interest. The experiment involves manipulating one or more variables and observing the effect on one or more outcomes while controlling other factors that might influence the outcome(s).

Based on the image provided, the tree diagram appears to be correct for the described situation. The first event is drawing a card, which has two possible outcomes: "red" and "black." From each outcome of drawing a card, there are six possible outcomes of rolling a die: 1, 2, 3, 4, 5, and 6. The diagram correctly shows all of these possible outcomes and the probabilities of each outcome, assuming that the deck of cards is a standard deck with 26 red cards and 26 black cards, and the die is fair. The branching probabilities from the "drawing a red card" node are 26÷52 or 0.5, and the branching probabilities from the "drawing a black card" node are also 26÷52 or 0.5.

Therefore, The probabilities of rolling each number on the die are 1/6, which is correctly represented by the branching probabilities from each die-rolling node.

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1.143 x 10⁷ ft, or approximately 11.43 million feet is the length of the river.

To find the length of the river, we need to use the Pythagorean theorem, which states that the square of the length of the hypotenuse (the diagonal line connecting the two endpoints of a right triangle) is equal to the sum of the squares of the lengths of the other two sides.

Let's call the length of the southward flowing part of the river "a" and the length of the southeastward flowing part of the river "b". Then we have:

a = 1.1 x 10⁷ ft

b = 3.2 x 10⁶ ft

The length of the river is given by the hypotenuse of a right triangle with sides a and b. Therefore, we can calculate the length of the river, c, as follows:

c² = a² + b²

c² = (1.1 x 10⁷ ft)² + (3.2 x 10⁶ ft)²

c² = 1.21 x 10¹⁴ ft² + 1.024 x 10¹³ ft²

c² = 1.3104 x 10¹⁴ ft²

c = √(1.3104 x 10¹⁴ ft²)

c = 1.143 x 10⁷ ft

Therefore, the length of the river is 1.143 x 10⁷ ft, or approximately 11.43 million feet

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Answer:

Sure, I can help you with that. (a) His total wage for a basic week can be calculated as follows: Total wage for a basic week = Basic rate per hour x Number of hours worked in a basic week Total wage for a basic week = $16 x 40 Total wage for a basic week = $640 Therefore, his total wage for a basic week is $640. (b) His wage for a week in which he worked 47 hours can be calculated as follows: Wage for a week with overtime = (Basic rate per hour + Overtime rate per hour) x Number of overtime hours worked + Total wage for a basic week Overtime rate per hour = Basic rate per hour + $4 Overtime rate per hour = $16 + $4 Overtime rate per hour = $20 Wage for a week with overtime =$16

For the given information of standard deviation, the correct answer is option B) Between 65.5 inches and 75.5 inches.

What is standard deviation?

Standard deviation is a statistical measure that measures the amount of variation or dispersion of a set of data values from the mean. It tells how much the data deviates from the average of the data set.

We can use the z-score formula to solve this problem. If we assume a normal distribution, we can find the z-score associated with the 95th percentile (or 0.95 probability) using a standard normal distribution table or calculator. The z-score is approximately 1.96.

Then we can use the formula:

z = (x - μ) / σ

where z is the z-score, x is the height we want to find, μ is the mean height, and σ is the standard deviation.

Solving for x:

1.96 = (x - 70.5) / 2.5

Multiplying both sides by 2.5:

4.9 = x - 70.5

Adding 70.5 to both sides:

x = 75.4

So 95% of the men fall between 65.5 inches and 75.5 inches (option B).

Therefore, the correct answer is option B) Between 65.5 inches and 75.5 inches.

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The predicted sales for week 10 is 30.143.

Median is a measure οf central tendency that represents the middle value in a dataset when the values are arranged in οrder οf magnitude.

Tο remοve the aberrant values frοm the time series data, we can replace them with dummy values. We can use the mean οr median οf the remaining values in the series tο replace the aberrant values.

Using mean as the replacement value, we get:

Week 1 2 3 4 5 6 7

Sales 26 28 27 30 23 23 38

Now we can use a regression model to predict the sales for week 10. Let's assume a linear regression model:

Sales = a + b*Week

where a is the intercept and b is the slope of the regression line.

To fit the model, we can use the sales data for weeks 1-7:

Week 1 2 3 4 5 6 7

Sales 26 28 27 30 23 23 38

The least squares estimates for the model parameters are:

b = 1.6429

a = 14.7143

Using these parameter estimates, we can predict the sales for week 10:

Sales(10) = a + b10

= 14.7143 + 1.642910

= 30.143

Therefore, the predicted sales for week 10 is 30.143.

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To write f(x) = 5(x - 2)2 - 7 in standard form, we need to expand the squared term first:

f(x) = 5(x - 2)(x - 2) - 7

f(x) = 5(x2 - 4x + 4) - 7

f(x) = 5x2 - 20x + 13

Therefore, the standard form of f(x) = 5(x - 2)2 - 7 is f(x) = 5x2 - 20x + 13.

Answer: f(x)=5x2−20x+13

Step-by-step explanation:

Answer:

The formula for the volume of a sphere is:

V = (4/3)πr^3

where V is the volume and r is the radius of the sphere.

We are given that the volume of the sphere is 36π cm^3, so we can write:

36π = (4/3)πr^3

Simplifying:

r^3 = (36/4) * 3

r^3 = 27

r = 3

Therefore, the radius of the sphere is 3 cm.

The circumference of a great circle on a sphere is given by the formula:

C = 2πr

where r is the radius of the sphere.

So, the circumference of the great circle is:

C = 2π(3) = 6π

Therefore, the circumference of the great circle of the sphere is 6π cm.

we get a predicted number of 1111 people whose favorite snack will be pretzels or cookies at the reception.

The sample provides information about the favorite snack of a random sample of people, but we need to use this information to make a prediction about the whole population of 2600 people.

First, we can calculate the proportion of the sample who chose pretzels or cookies as their favorite snack:

proportion = (number of people who chose pretzels + number of people who chose cookies) / total number of people in the sample

proportion = (16 + 54) / (30 + 16 + 54 + 64)

proportion = 70 / 164

proportion ≈ 0.4268

Next, we can use this proportion to estimate the number of people who will choose pretzels or cookies as their favorite snack out of the whole population:

predicted number of people = proportion × total number of people in the population

predicted number of people = 0.4268 × 2600

predicted number of people ≈ 1110.8

Rounding to the nearest whole number, we get a predicted number of 1111 people whose favorite snack will be pretzels or cookies at the reception.

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The area of shaded part in the figures are

1. 7.07cm²

2. 19.54cm²

The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc.

The area of a sector is expressed as:

A= tetha/360 × πr²

Area of the shaded part = area of big sector - area of small sector.

1. area of big sector = 90/360 × 3.14 × 5²

= 7065/360

= 19.63cm²

area of small sector = 90/360 × 3.14 × 4²

= 12.56cm²

area of shaded part = 19.63 - 12.56

= 7.07cm²

2. Area of big sector = 40/360 × 3.14 × 9²

= 28.26cm²

area of small sector = 40/360 × 3.14 × 5²

= 8.72

area of shaded part = 28.26-8.72

= 19.54cm²

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a. The sample mean for sample 1 is 9.2, and the sample mean for sample 2 is 7.17.

b. The sample standard deviation for sample 1 is approximately 3.29, and the sample standard deviation for sample 2 is approximately 3.65.

c. The point estimate of the difference between the two population means is 2.03.

d. The 90% confidence interval estimate of the difference between the two population means is [-0.44, 4.50].

a. The sample mean for sample 1 is

(10 + 13 + 9 + 8 + 6) / 5 = 9.2

The sample mean for sample 2 is

(7 + 7 + 8 + 4 + 9 + 8) / 6 = 7.1667 ≈ 7.17

b. The sample standard deviation for sample 1 is:

√[((10-9.2)² + (13-9.2)² + (9-9.2)² + (8-9.2)² + (6-9.2)²) / (5-1)]

= √[10.8] ≈ 3.29

The sample standard deviation for sample 2 is

√[((7-7.17)² + (7-7.17)² + (8-7.17)² + (4-7.17)² + (9-7.17)² + (8-7.17)²) / (6-1)]

= √[13.33] ≈ 3.65

c. The point estimate of the difference between the two population means is:

9.2 - 7.17 = 2.03

d. To calculate the 90% confidence interval estimate of the difference between the two population means, we need to first calculate the standard error of the difference between the sample means:

s.e.(difference between sample means) = √[(s1²/n1) + (s2²/n2)]

= √[(3.29²/5) + (3.65²/6)]

= √[2.60]

≈ 1.61

Next, we can use the t-distribution with degrees of freedom equal to the smaller of n1-1 and n2-1 (in this case, 4) and a 90% confidence level to find the critical value, t*:

t* = 1.533 (from t-distribution table or calculator)

Finally, we can construct the confidence interval estimate:

9.2 - 7.17 ± (t* * s.e.(difference between sample means))

= 2.03 ± (1.533 * 1.61)

= 2.03 ± 2.47

= [ -0.44 , 4.50 ]

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In summary, the domain of the given function f(x) =[tex]3x^2 - 6x - 13[/tex] is all real numbers.

The domain of a function is the set of all possible input values (x-values) for which the function is defined. In this case, the function f(x) is a quadratic function, which is given by [tex]f(x) = 3x^2 - 6x - 13.[/tex]

Quadratic functions are defined for all real numbers.

There are no restrictions on the input values of x for this function.

Therefore, the domain of f(x) is all real numbers.
To answer the student question, the correct option is "all real numbers."

The other options, "x ≥ 1," "x ≤ -6," and "x ≥ -13," do not apply in this case as there are no constraints on the values of x for a quadratic function.

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Answer:

To find A+3B, we need to first find A and B. A = 1 + r + 7r^2 B = 1 - r^2 Now we can substitute these expressions into A+3B: A+3B = (1 + r + 7r^2) + 3(1 - r^2) Simplifying this expression, we get: A+3B = 1 + r + 7r^2 + 3 - 3r^2 A+3B = 4 + r + 4r^2 So the expression that equals A+3B in standard form is 4 + r + 4r^2.

The described point iii is joint variation.

In the given question,

Three relationships are described.

They are:

i. The amount of fuel used on a trip increases as the size of the car increases and as the distance traveled increases.

ii. As the number of people helping mow a lawn increases, the time it takes to mow the lawn decreases.

iii. The cost of having a house painted increases as the size of the house increases.

Type of variation that describes each relationship:

Direct variation describes the relationship i between the amount of fuel used on a trip and the size of the car and distance traveled.

This is because the amount of fuel used is directly proportional to the size of the car and distance traveled. As the size of the car and distance traveled increases, the amount of fuel used also increases.

Hence,

i is direct variation.

Inverse variation describes the relationship

ii between the number of people helping mow a lawn and the time it takes to mow the lawn.

This is because the number of people helping is inversely proportional to the time it takes to mow the lawn.

As the number of people helping increases, the time it takes to mow the lawn decreases.

Hence, ii is inverse variation.Joint variation describes the relationship iii between the cost of having a house painted and the size of the house.

This is because the cost of having a house painted is jointly proportional to the size of the house. As the size of the house increases, the cost of having it painted also increases.

Hence, iii is joint variation.

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The two column proof is completed as follows

Statement                                               Reason

1. AB || CD                                           Given

2 Construct BE perpendicular to      Construction of side BE

CD  such that point E is on CD

3 Construct CF perpendicular to      Construction of side CF

AB such that point F is on AB

4 ∠ CFB = ∠ BEC = 90°                     All perpendicular angles measure 90°

5 CF = BE                                           Any point on one parallel line is the                          

                                                           same distance from the other line on        

                                                           a perpendicular transversal (1, 2, 3)

6. BC = BC                                         They are measures of the same            

                                                           segment.

7. Δ BCF ≅ Δ CBE                             SAS congruence (4, 6,5)

The SAS congruence theorem, also known as the Side-Angle-Side congruence theorem, states that if two triangles have two sides and the included angle of one triangle congruent to the corresponding parts of another triangle, then the triangles are congruent.

The equality of the included angle is by the alternate interior angles theorem.

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Answer:

[tex]x {}^{2} - 5[/tex]

Answer:

180 fr

Step-by-step explanation:

its too hard

Answer: it's 1

Step-by-step explanation:

The x in the numerator determines that the x is in absolute value, meaning only positive integers.

That wouldn't matter anyway, because since any value of x would have to be greater than 0 (meaning only positive values), and both x's are the same x, the equation would have to equal one.

For example, you could plug in 2 to both x's. 2/2 is 1.

Or you could plug in 289 to both x's, in which 289/289 is 1.

No matter what number, as long as it's positive, will be 1.

Step-by-step explanation:

if it is between 0 and pi/2 (90°), or between 3pi/2 (270°) and 2pi (360°).

for angle = 0, cos = 1. therefore, positive.

0 <= 5pi/12 <= pi/2. therefore, positive.

pi/2 <= 5pi/6 <= pi. therefore, negative.

pi/2 <= 3pi/4 <= pi. therefore, negative.

3pi/2 <= 5pi/3 <= 2pi. therefore, positive.

you do know how to compare fractions, right ?

you need to bring then to the same denominator by multiplying numerator and denominator by the same factor.

e.g. comparing 5pi/12 with pi/2.

to bring them both to .../12, we have to multiply pi/2 by 6/6.

so, we are comparing 5pi/12 and 6pi/12.

and we see, 5pi/12 is smaller.

the others work the same way.

3pi/6 <= 5pi/6 <= 6pi/6

2pi/4 <= 3pi/4 <= 4pi/4

9pi/6 <= 10pi/6 <= 12pi/6

now you see it clearly.

The minimum value of the function h(x) = log[(x - 5)² + 3] over the interval -5 < x < 5 is approximately log[3.000001].

The minimum value of the function h(x) = log[(x - 5)² + 3] over the interval -5 < x < 5 can be found through the following.

Recognize that the logarithm function is increasing.

Minimize the argument of the logarithm, i.e., (x - 5)² + 3.

Observe that (x - 5)² is always non-negative since it is a square of a real number.

The minimum value of (x - 5)² occurs when x = 5 (in this case, (x - 5)² = 0).

However, x cannot be equal to 5 because the interval is -5 < x < 5.

Since the interval is open, find the minimum value for (x - 5)² in this interval, which occurs when x is as close to 5 as possible within the given interval. This would be x = 4.999.

Substitute this value of x into the function:

h(x) = log[(4.999 - 5)² + 3] = log[0.001² + 3] ≈ log[3.000001].

Hence, the minimum value of the function h(x) = log[(x - 5)² + 3] over the interval -5 < x < 5 is approximately log[3.000001].

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The Classify each of the given sets of measurements is given below:

a) 52, 63, 65°: These measurements form a unique triangle. This is a right-angled triangle, also known as a Pythagorean triple.

b) 31°, 102°, 46°: These measurements do not form a triangle. The sum of the angles in a triangle is always 180°, but in this case, the sum is 179°, which is less than 180°.

c) 70.6°, 47.4°, 62°: These measurements do not form a unique triangle. There are multiple possible triangles that can be formed with these measurements.

d) 3 cm, 4 cm, 5 cm: These measurements form a unique triangle. This is another example of a Pythagorean triple.

e) 7.9 cm, 2.4 cm, 2.9 cm: These measurements do not form a triangle. The sum of the two smaller sides is less than the length of the largest side, which violates the triangle inequality.

f) 12% in, 6% in, 5% in: These measurements do not form a triangle. The sum of the two smaller sides is less than the length of the largest side, which violates the triangle inequality.

g) 124 mm, 432 mm, 385 mm: These measurements form a unique triangle.

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Answer:

x = 6.5

Step-by-step explanation:

-3 × ( 4x - 5 ) = 2 × ( 1 - 5x )     ------------->      (By multiplying each bracket times its coefficient)

= -12x + 15 = 2 - 10x      ------------->     (By subtracting "2" from each side)

= -12x + 13 = -10x       -------------> (By moving the "-10x" to the other side and the "13" to the right side different signs "-10x becomes +10x and 13 becomes -13")

= -12x + 10x = -13

= -2x = -13             ------------->   (Dividing by "-2")

then, x = 6.5

Have any questions? write in the comments

The function g(x) in the form a(x - h)² + k is g(x) = (x + 5)² + 0, where a = 1, h = -5, and k = 0.

What is the function?

Starting with the function f(x) = x², a translation 5 units left can be achieved by replacing x with (x + 5), since (x + 5) is 5 units to the left of x. Therefore, we have:

g(x) = f(x + 5)

g(x) = (x + 5)²

g(x) = x² + 10x + 25

This is the equation of the parabola obtained by translating the graph of y = x² five units to the left. We can write this equation in the desired form of a(x - h)² + k by completing the square:

g(x) = x² + 10x + 25

g(x) = 1(x² + 10x) + 25

g(x) = 1(x² + 10x + 25 - 25) + 25

g(x) = 1((x + 5)² - 25) + 25

g(x) = 1(x + 5)² - 1(25) + 25

g(x) = (x + 5)² + 0

Therefore, the function g(x) in the form a(x - h)² + k is g(x) = (x + 5)² + 0, where a = 1, h = -5, and k = 0.

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