Factor the following expressions completely. Show and check all work on your own paper.

x^4 - 16

thx so much I will give brainiest

If the average person can walk 9/10 miles in 1/3 hour and an athlete can jog 3 times that speed, the estimated distance that the athlete can jog in 2 hours is C. 15 to 20 miles.

The estimated distance can be computed as follows:

The distance an average person can walk in ¹/₃ hours = ⁹/₁₀ miles.

In 1 hour, the average person can 2.7 miles (⁹/₁₀ miles x ³/₁).

The athlete's comparable speed = 3 times of 2.7 miles in 1 hour = 8.1 miles.

Thus, in 2 hours, the athlete can walk 16.2 miles (8.1 x 2), which falls between 15 and 20 miles.

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Answer: 2/3

Step-by-step explanation: d/dy (y^n) =ny^n -1

Hopes this helps you I try

If side of square is (x-1) units, and the dimensions of rectangle are x units by (x-2) units, then

(a) the possible values are : all real number greater than 2,

(b) Square has a greater area than rectangle,

(c) The difference in area is 1 unit.

Part (a) : To be a valid square, the sides must have the same length. So, we equate expression for length of each side of square equal to each other and solve for x:

x - 1 = x - 1

0 = 0

This equation is true for any value of x, so the possible values of x are all real numbers.

To be a valid rectangle, the length and width must both be positive.

So, we equate the expressions for the length and width of the rectangle greater than 0 and solve for x:

x > 0 and x - 2 > 0

x > 2,

Therefore, the possible values of x are all real-numbers greater than 2.

Part(b) :

The side of square is = (x-1),

So, it's area is represented by : (x-1)² = x² - 2x + 1;

The rectangle's length is : (x) units,

The rectangle's width is : (x-2) units,

So, the area will be = x(x-2) = x² - 2x,

We see that, the area of the square has a greater area than the rectangle,

Part (c) :

The difference in both areas will be calculated as : Area of Square - Area of rectangle;

(x² - 2x + 1) - (x² - 2x) = 1 units.

Therefore, the difference is 1 units.

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The given question is incomplete, the complete question is

A square has sides that are (x-1) units long and a rectangle has a length of x units and a width of (x-2) units;

(a) What are the possible values of x?

(b) does the square or the rectangle have the greater area?

(c) What is the difference in the areas?

Katie outscored approximately 1.39% of the students in her section.

If Katie received a z-score of 2.2, this means that her score was 2.2 standard deviations above the mean of the exam scores for her section.

We can use a standard normal distribution table or calculator to find the percentage of scores that fall above a z-score of 2.2.

Using a standard normal distribution table, we can find the proportion of scores that fall below a z-score of 2.2, and then subtract this from 1 to find the proportion of scores that fall above a z-score of 2.2.

The table value for a z-score of 2.2 is approximately 0.9861, which means that approximately 98.61% of the scores fall below a z-score of 2.2. Therefore, approximately:

1 - 0.9861 = 0.0139, or 1.39%

of the scores fall above a z-score of 2.2.

This means that Katie outscored approximately 1.39% of the students in her section.

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Answer:

Step 2

Step-by-step explanation:

Let me know if you need an explanation! I gtg

and

Have a great day!!

The height of the pyramid is 10 units.

We have,

The formula for the volume of a triangular pyramid is V = (1/3)Bh,

where B is the area of the base and h is the height of the pyramid.

The base of the pyramid is a triangle with a base of 12 units and a height of 6 units, so its area is:

B = (1/2) x base x height

   = (1/2) x 12 x 6 = 36 square units.

We know that the volume of the pyramid is 120 cubic units, so we can plug in the values for B and V in the formula and solve for h:

V = (1/3) x B x h

120 = (1/3) * 36 * h

120 = 12h

h = 10 units

Therefore,

The height of the pyramid is 10 units.

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A triangular pyramid is a geometrical shape which has a triangular base and three triangular faces. It has a vertex common to all the three lateral faces of a triangular pyramid. The height of the pyramid is 10 units.

A volume is simply defined as the amount of space occupied by any three dimensional solid. These solids can be a cube, cuboid, a cylinder or a sphere. It is generally measured in cubic units.

The equation used to calculate volume is:

V = (1/3)B

Base area:

B = (1/2) x base x height

= (1/2) x 12 x 6 = 36 square units

Volume:

V = (1/3) x B x h

120 = (1/3) * 36 * h

120 = 12h

h = 10 units

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Answer:

3 and a half would be greater than 3

Step-by-step explanation:

3 and a half would be 3.5 which is .5 more than just 3.

Answer: what do you need help with?

Step-by-step explanation:

Answer:

2.6

Step-by-step explanation:

13/5 is 2.6

I hope i am right but if not then i am so sorry

The only option that describes the given histogram is; D.) Numerical and univariate.

A histogram is defined as a graphical representation representing data points that are organized into user-specified ranges.

Now, we see that from the given histogram that it shows how much water is used in a household in a given day.

Since it is dealing with amount of water, then we can call this a numerical data set since it is only one and doesn't categorize anything.

Secondly, since it gives only one information which is the amount of water for each household, then we can call this a univariate data set.

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complete question:

The display shows how much water is used in a household in a given day. Which of the following describes this data set

A.) Categorical and bivariate

B.) Categorical and univariate

C.) Numerical and bivariate

D.) Numerical and univariate

Answer:

A. 25%

B. Candidate B

C. 60% of voters chose Candidate A and Candidate C

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve this problem, we can use the fact that the distance traveled by each wheel is proportional to its circumference, and the circumference of a circle is given by:

circumference = π x diameter

Using this formula, we can find the distance traveled by each wheel in one rotation, and then divide the total distance traveled by each wheel to find how many rotations each wheel made.

For the front wheels with a diameter of 35 inches, the circumference is:

circumference = π x 35

circumference ≈ 109.96 inches

In one mile, there are 5280 feet and 12 inches in a foot, so the distance traveled in one mile is:

distance in one mile = 5280 x 12 = 63360 inches

Therefore, the number of rotations made by the front wheels in one mile is:

rotations per mile = distance in one mile / circumference

rotations per mile ≈ 63360 / 109.96 ≈ 576.15

In 14 miles, the number of rotations made by the front wheels is:

rotations for front wheels = rotations per mile x 14

rotations for front wheels ≈ 576.15 x 14 ≈ 8066.10

For the rear wheels with a diameter of 56 inches, the circumference is:

circumference = π x 56

circumference ≈ 175.93 inches

Using the same calculation, the number of rotations made by the rear wheels in 14 miles is:

rotations for rear wheels = (distance in one mile / circumference) x 14

rotations for rear wheels ≈ (63360 / 175.93) x 14 ≈ 5068.21

The difference in the number of rotations made by the front wheels and the rear wheels is:

difference = rotations for front wheels - rotations for rear wheels

difference ≈ 8066.10 - 5068.21 ≈ 2997.89

Rounding the difference to the nearest whole number, we get:

difference ≈ 2998

Therefore, the front wheel rotated approximately 2998 more times than the rear wheel on this day.

The probability of selecting two bottles of Coca-Cola and a bottle of water is 0.1385.

The total number of ways to select 3 bottles out of 15 bottles is given by the combination formula:

C(15, 3) = (15!)/(3!12!) = 455

where C(n, r) denotes the number of combinations of r items out of n items.

The number of ways to select 2 bottles of Coca-Cola and 1 bottle of water is given by the product of the number of ways to select 2 bottles of Coca-Cola out of 7 bottles and the number of ways to select 1 bottle of water out of 3 bottles:

C(7, 2) * C(3, 1) = (7!)/(2!5!) * (3!)/(1!2!) = 21 * 3 = 63

Therefore, the probability of selecting 2 bottles of Coca-Cola and 1 bottle of water is:

63/455 = 0.1385 (rounded to 4 decimal places)

So the probability of selecting two bottles of Coca-Cola and a bottle of water is approximately 0.1385.

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The exact values of sin(θ), cos(θ), and tan(θ) are -4/5, -3/5 and 4/3 respectively.

The exact values of sin(θ), cos(θ), and tan(θ) is calculated as follows;

sec(θ) = 1/cos(θ)

1/cos(θ) = -5/3

cos(θ) = -3/5

The value of sin (θ) is calculated as follows;

sin²(θ) + cos²(θ) = 1

sin²(θ) + (-3/5)² = 1

sin²(θ) + 9/25 = 1

sin²(θ) = 1 - 9/25

sin²(θ) = 16/25

sin(θ) = ±√(16/25)

sin(θ) = - 4/5

The value of tan(θ) is calculated as follows;

tan(θ) = sin(θ)/cos(θ)

tan(θ) = (-4/5)/(-3/5)

tan(θ)   = 4/3

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Answer:

b > -8

Step-by-step explanation:

Given inequality:

[tex]4b-3(2b-6) > 3-(5b+9)[/tex]

To solve for b, begin by expanding the brackets on the left side of the inequality:

[tex]4b-3 \cdot 2b -3 \cdot (-6) > 3-(5b+9)[/tex]

[tex]4b-6b +18 > 3-(5b+9)[/tex]

Distribute the negative sign inside the parentheses on the right side:

[tex]4b-6b +18 > 3-5b-9[/tex]

Combine like terms on both sides of the inequality:

[tex]-2b +18 > -5b-6[/tex]

Add 5b to both sides:

[tex]-2b +18 +5b > -5b-6+5b[/tex]

[tex]3b+18 > -6[/tex]

Subtract 18 from both sides:

[tex]3b+18-18 > -6-18[/tex]

[tex]3b > -24[/tex]

Divide both sides by 3 to isolate b:

[tex]\dfrac{3b}{3} > \dfrac{-24}{3}[/tex]

[tex]b > -8[/tex]

Therefore, the solution to the given inequality is:

[tex]\large\boxed{\boxed{b > -8}}[/tex]

Minimum sample size (n) = 15

To determine the minimum sample size required, we can use the formula:

n = (Zα/2 * σ / E)^2

Where:
- n is the minimum sample size
- Zα/2 is the z-score at the 95% confidence level, which is 1.96
- σ is the population standard deviation, which is given as 3.8
- E is the maximum error we can tolerate, which is 2 units in this case

Substituting the values, we get:

n = (1.96 * 3.8 / 2)^2
n = 27.44

Rounding up to the nearest whole number, we get a minimum sample size of 28.

Therefore, we need to sample at least 28 individuals from the normally distributed population to be 95% confident that the sample mean is within two units of the population mean, assuming a population standard deviation of 3.8.

To determine the minimum sample size required for a 95% confidence level, we'll need to use the following formula:

n = (Z * σ / E)^2

where:
- n is the minimum sample size
- Z is the Z-score corresponding to the desired confidence level (1.96 for a 95% confidence level)
- σ is the population standard deviation (3.8 in this case)
- E is the margin of error (2 units in this case)

Step 1: Identify the values
Z = 1.96 (from the 95% confidence level)
σ = 3.8
E = 2

Step 2: Plug the values into the formula
n = (1.96 * 3.8 / 2)^2

Step 3: Calculate the result
n = (7.528 / 2)^2
n = (3.764)^2
n ≈ 14.15

Since the sample size must be a whole number, round up to the nearest whole number to ensure the desired level of confidence is achieved.

Minimum sample size (n) = 15

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The circumference of circle be 60 in.

Give that,

Angle of sector = 60 degree

Arc length  = 10 inch

Arc length of circle = (Θ/360) x 2πr

Put the values

10 = (60/360)x2πr

⇒ r = 60/2π

Since circumference of circle = 2πr

Therefore,

circumference of the given circle = 2π x (60/2π)

                                                       = 60 in.

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At the grand opening, al's furniture store, there is offering spin wheel for discount. The probability that a customer gets a 10% or 20% discount is equals to the 0.75.

At the grand opening, al's furniture store, it offered a spin the wheel for a discount to its customers. The wheel is divided into 12 equal slices.

The percentage of discount awarded by 6 slices = 10%

The percentage of discount awarded by 3 slices = 20%

The percentage of discount awarded by 2 slices = 40%

The percentage of discount awarded by 1 slices

= 100%

We have to determine the probability that a customer gets a 10% or 20% discount. As we see all slices are independent to each other so events related to these also independent.

We have total 12 slices. Since, 6 slices awarded for 10% discount i.e. chances of getting 10% discount is equal = 6/12

Similarly, 3 slices awarded for 20% discount i.e. chances of getting 20% discount is 3/12.

Hence chances of getting 10% or 20% discount is

= P( X = 20%) + P( X= 10%)

= 6/12 + 3/12

= 1/2 + 1/4

= 0.50 + 0.25

= 0.75

Hence, required value is 0.75.

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The cost of one watch is ₹4975. The answer we got was obtained by dividing the total amount for 36 watches by the number of watches

To find the price of one watch, we can divide the total fee of 36 watches by way of the quantity of number of watches:

Price of 1 watch = general cost of 36 watches / 36

We are given that the price of 36 watches is about ₹179100, so we can now do the replacement of this value in to the formulation:

Value of one watch Is = ₹179100 / 36

When we will Simplify this expression, we get:

Value of 1 watch = ₹4975

Therefore, the cost of one watch is ₹4975.

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Answer:

Starting with 4y - 12x + 8 = 0, we can isolate y by subtracting 12x and dividing by 4:

4y - 12x + 8 = 0

4y = 12x - 8

y = 3x - 2

Now we can see that the gradient (or slope) of the line is 3.

Step-by-step explanation:

use brain

Answer:

y = -3

x = 1

Step-by-step explanation:

To solve the system of equations using substitution, we need to isolate one variable in terms of the other in one of the equations and substitute this expression into the other equation. We can then solve for the remaining variable.

In this case, we are given two equations:6x - 9 = y

y = -3x

We can substitute the expression for y from the second equation into the first equation to get:

6x - 9 = -3x

Now we can solve for x:

6x + 3x = 9

9x = 9

x = 1

We can substitute this value of x back into one of the original equations to solve for y. Using the second equation, we have:

y = -3(1) = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

To verify the solution, we can substitute the values of x and y into the original equations and check if they are satisfied:

6x - 9 = y

6(1) - 9 = -3

-3 = -3

This equation is true, so x = 1 and y = -3 satisfy the first equation.

y = -3x

-3 = -3(1)

This equation is also true, so x = 1 and y = -3 satisfy the second equation.

Since x = 1 and y = -3 satisfy both equations, they are the solution to the system of equations using substitution.

The distance between the medic and the shelter is 626.3 feet.

A helicopter was hovering over a shelter and was 900 ft above the ground. A medic was on the ground and was looking up at an angle of 55 degrees to the helicopter.

The medic’s eyes were 5.5 feet off the ground when looking at this right angle of elevation.

This situation forms a right angle triangle. Therefore, the distance of the medic to the shelter can be found as follows:

Hence,

tan 55 = opposite / adjacent

tan 55 = 900 - 5.5 / a

cross multiply

a tan 55° = 894.5

divide both sides by tan 55°

a =  894.5 / 1.42814800674

a = 626.335645885

a = 626.3 feet

Hence,

distance between medic and shelter = 626.3 feet

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The speed of the tugboat without the current is 35 miles per hour, and the speed of the current is 15 miles per hour.


Let t be the speed of the tugboat without the current and c be the speed of the current.
Upstream, the tugboat moves against the current, so its speed is (t - c).
Downstream, the tugboat moves with the current, so its speed is (t + c).
The upstream distance is 200 miles in 10 hours, so the upstream speed is 200/10 = 20 miles per hour.
The downstream distance is also 200 miles, but it takes 4 hours, so the downstream speed is 200/4 = 50 miles per hour.
Now, we have two equations with two variables:
  a. t - c = 20
  b. t + c = 50
Solve these equations simultaneously:
  a. Add the two equations to eliminate the variable c: 2t = 70
  b. Divide both sides by 2 to get t: t = 35 miles per hour
  c. Substitute the value of t back into one of the equations (e.g., t - c = 20): 35 - c = 20
  d. Solve for c: c = 15 miles per hour

Hence, The speed of the tugboat without the current is 35 miles per hour, and the speed of the current is 15 miles per hour.

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a) The Sample size is calculated to be  4,272 U.S. adults and count is 897. (b) Sample proportion is 0.21 or 21%. (c)The sample proportion is an estimate of the population proportion.

The sample size is 4,272 U.S. adults, and the count of those who regularly wear a smart watch or fitness tracker is 897.

To calculate the sample proportion, we divide the count of those who regularly wear a smart watch or fitness tracker by the sample size:

sample proportion = count / sample size

sample proportion = 897 / 4,272

sample proportion = 0.21 or 21%

Therefore, the sample proportion of U.S. adults who regularly wear a smart watch or fitness tracker is 21%.

The population proportion is the proportion of all U.S. adults who regularly wear a smart watch or fitness tracker, while the sample proportion is the proportion of U.S. adults in the sample who regularly wear a smart watch or fitness tracker.

The relationship between the two proportions is that the sample proportion is an estimate of the population proportion. The sample proportion provides a rough idea of the proportion of all U.S. adults who regularly wear a smart watch or fitness tracker, but it may not be exactly the same as the population proportion due to sampling error.

To get a more accurate estimate of the population proportion, we would need to take a larger and more representative sample or survey the entire population.

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Answer:

Step-by-step explanation:

To determine if the table shows growth or decay, we can look at the coefficient of the exponential function y = 200(0.75)^t. The coefficient is 0.75, which is less than 1. This means that the value of the bike decreases over time, so the table shows decay.

To identify the annual percent increase or decrease in the value of the bike, we can compare the value of the bike after one year to its initial value. Plugging in t = 1 into the model, we get:

y = 200(0.75)^1

y = 150

So after one year, the value of the bike is $150. This represents a decrease of $50 from its initial value of $200. To find the percent decrease, we can use the formula:

percent decrease = (amount of decrease / initial value) x 100%

Plugging in the values, we get:

percent decrease = (50 / 200) x 100%

percent decrease = 25%

Therefore, the value of the bike decreases by 25% each year.

To estimate when the value of the bike will be $50, we can set y = 50 in the model and solve for t:

50 = 200(0.75)^t

0.25 = 0.75^t

log(0.25) = t log(0.75)

t = log(0.25) / log(0.75)

t ≈ 4.2

Therefore, the value of the bike will be $50 approximately 4.2 years after it was new.

It is not appropriate to compare two means at a time in the way described. This would inflate the overall Type I Error and is a 'Multiple Testing' problem. The one-way ANOVA controls for the Type I Error and should be used instead. Comparing multiple pairs of means using independent two-sample t-tests without adjusting for the multiple comparisons can lead to an increased probability of committing a Type I error.

When comparing three or more populations means within a set of quantitative data that is categorized according to one factor/treatment, it is appropriate to use a one-way ANOVA instead of multiple independent two-sample t-tests. The reason is that performing multiple t-tests increases the overall Type I error rate, which is the probability of falsely rejecting a true null hypothesis. This is known as the multiple testing problem, and it occurs when we conduct multiple hypothesis tests without controlling the overall error rate.

In contrast, the one-way ANOVA controls for the Type I error rate and tests the null hypothesis that all population means are equal. If the null hypothesis is rejected, then at least one population mean is significantly different from the others. We can then perform post-hoc tests, such as Tukey's HSD, to determine which population means are different.

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For cross products and the right hand rule, the order of the numbers does matter. For addition of vectors the order does not matter and for subtraction of vectors the order does matter.

For cross products and the right-hand rule, the order of the numbers does matter.

When you switch the order of the vectors in a cross product, you get the opposite (negative) of the original result. Mathematically, A x B = - (B x A). The right-hand rule is used to determine the direction of the resulting vector, and reversing the order changes the direction.

For addition and subtraction of vectors, the order does not matter for addition, as vector addition is commutative. That is, A + B = B + A.

However, the order does matter for subtraction, as vector subtraction is not commutative. In this case, A - B ≠ B - A.

To summarize:
1. For cross products and the right-hand rule, the order of the numbers matters.
2. For vector addition, the order does not matter.
3. For vector subtraction, the order does matter.

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