Factor the equation and show your work.
x^2 - 4

3 is the ways that she could do this

Let's first find the sum of each list:

List S: 3 + 5 + 8 + 11 + 13 + 14 = 54

List T: 2 + 5 + 6 + 10 + 12 + 13 = 48

The difference between the sums of the lists is 54 - 48 = 6.

two numbers must be half of 6, which is 3. In other words, we're looking for pairs of numbers where the number from List S is 3 greater than the number from List T.

Now we'll compare the numbers in the two lists to see which pairs meet this condition:

(3, 0): No match.

(5, 2): Match.

(8, 5): Match.

(11, 8): No match.

(13, 10): Match.

(14, 11): No match.

We found 3 pairs that meet the condition: (5, 2), (8, 5), and (13, 10). Therefore, there are 3 ways Jenny can swap the numbers to make the sums equal.

The correct answer is C, 3.

Read more on probability here:https://brainly.com/question/25870256

#SPJ1

The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

To know more about "standard normal distribution" refer here:

https://brainly.com/question/29509087#

#SPJ11

The solutions of linear equations are x = t and y = (3 - 5t)/2 for infinitely many solutions when k = 10.

The value of k for which the system of linear equations has infinitely many solutions, we need to find the condition under which the equations are dependent. Here are the equations:
1) 5x + 2y = 3
2) kx + 4y = 6
3) 20x + 8y = 12
First, let's express equation 1 in terms of y and make it match the form of equation 2:
y = (3 - 5x)/2
Now, substitute this expression into equation 2:
kx + 4((3 - 5x)/2) = 6
Simplify:
kx + 6 - 10x = 6
Now, let's express equation 3 in terms of y:
y = (12 - 20x)/8
Simplify:
y = (3 - 5x)/2
This is the same as the expression we found for equation 1, so the system is dependent.

To find the value of k, we'll set the simplified versions of equations 1 and 2 equal to each other:
kx - 10x = 0
Factor out x:
x(k - 10) = 0
For infinitely many solutions, k must be equal to 10. So, the system of equations becomes:
1) 5x + 2y = 3
2) 10x + 4y = 6
Now we can solve for the solutions in terms of the parameter t:
For this equation to be true, we must have k = 10. So, substituting k = 10 in the original equations, we have: 5x + 2y = 3 10x + 4y = 6 Dividing the second equation by 2, we get: 5x + 2y = 3

We can see that the two equations are identical, which means that any values of x and y that satisfy one equation will automatically satisfy the other equation. Therefore, the solutions to the system are given by: x = t y = (3-5t)/2 where t is any real number.
x = t
y = (3 - 5x)/2
y = (3 - 5t)/2
For similar question on linear equations:

https://brainly.com/question/29739212

#SPJ11

For example, we see that the value 3 appears twice in the data set, and that there is only one value of 34. The frequency chart provides a quick summary of the data that allows us to easily see which values are most common and how many times they occur.

A frequency chart is a way of organizing data by counting how often each value occurs. To create a frequency chart for this data set, we can follow these steps:

The completed frequency chart for this data set would look like this:

Note: Find the attached image for required table.

Learn more about Frequency chart at

brainly.com/question/14010049

#SPJ1

The probability that more than 12 but fewer than 20 of the 25 randomly selected UCF students have online access to library resources is about 57.0%.

To solve this problem, we can use the binomial distribution formula. Let's define:

- n = 25 (the number of randomly selected students)
- p = 0.6 (the probability that a UCF student has online access to library resources)
- x = the number of students who have online access to library resources

The formula for the probability of x successes in n trials with probability of success p is:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where (n choose x) is the binomial coefficient.

Now, we want to find the probability that more than 12 but fewer than 20 of the 25 randomly selected students have online access to library resources. We can calculate this by adding up the probabilities for x = 13, 14, ..., 19. In mathematical notation:

P(13 <= x <= 19) = ∑P(x), x=13 to 19

We can use a calculator or a spreadsheet program to calculate each term of the sum and add them up. The result is approximately 0.570, or 57.0%.

Therefore, the probability that more than 12 but fewer than 20 of the 25 randomly selected UCF students have online access to library resources is about 57.0%.

Learn more about probability here:

brainly.com/question/27342429

#SPJ11

The minimum side length or the value of {x} in the triangle as 35.

The given sides of a triangle are 17 and 19. From the triangle inequality, we can write that -

The sum of the two sides of a triangle is greater than the third side. So, we can write that -

17 + 19 > x

x < 36

Therefore, we will take the minimum side length of the triangle as 35.

To solve more questions on triangles, visit the link-

brainly.com/question/11805053

#SPJ1

Answer:

For this problem, you will need to use the pythagorean theorem which is  

So a and b are usually the sides that are NOT the hypotenuse, or in this case the long side that is not at a 90 degree angle.

You will start by plugging 12 into with (a) or (b) but not both. And then you will plug 17 in for (c). Make sure you square these values to solve the equation. Once you do that, it is basic algebra from there to solve for the missing variable. If you want to check to see if your answer is correct, then plug all the side numbers back into the equation. Also your answer should be between 12 and 17, or possibly one of those numbers.

Step-by-step explanation: I hope this helps!! God Bless you. Have a great day!!!!

Step-by-step explanation:

By taking the quotient between the two values, we will see that 17^6 is 289 times larger than 17^4

To find this we just need to take the quotient between the two expressions.

Remember that the quotient of two powers with the same base is:

[tex]\frac{x^n}{x^m} = x^{n - m}[/tex]

So here we need use that rule.

We will get the quotient:

[tex]\frac{17^6}{17^4} = 17^{6 - 4} = 17^2 \\\\17^2 = 289[/tex]

Then we can see that 17^6 is 289 times larger than 17^4

Learn more about powers at:

https://brainly.com/question/11569624

#SPJ1

Answer:

289 units

Step-by-step explanation:

To find out how many times larger 17^6 is than 17^4, we need to calculate the ratio of the two values. This can be done by dividing 17^6 by 17^4.

17^6/17^4 = (17^2)^3/17^4

Simplifying this, we get:

= 17^(2x3)/17^4

= 17^6/17^4

= 17^(6-4)

= 17^2

So, 17^6 is 289 times larger than 17^4 (17^2 = 289). This means that if 17^4 is represented by one unit, 17^6 would be represented by 289 units.

Answer: 1/12

Step-by-step explanation:

The probability of the first die roll showing a 5 is 1/6

The probability of getting an odd number is 3/6 or 1/2.

The we just multiply straight across:

1/2 x 1/6 = 1/12

Answer: To solve the equation, we need to simplify and isolate the variable (x) on one side of the equation.

Let's start by distributing the 3/2 on the left side:

3/2(x) - 3/2(5) - 3/2 = 9/2x

Simplifying:

3/2x - 15/2 - 3/2 = 9/2x

Combining the constants:

3/2x - 9/2 = 9/2x

Subtracting 3/2x from both sides:

-9/2 = 3/2x

Multiplying both sides by 2/3:

-3 = x

Therefore, the solution to the equation is x = -3.

The converse of the given true conditional statement is: "If a polygon is a rectangle, then it is a square." The correct option is B.

In a conditional statement of the form "If A, then B", A is called the hypothesis or the antecedent, and B is called the conclusion or the consequent. The converse of this conditional statement is "If B, then A."

To determine whether the converse is true or false, we need to examine whether all rectangles are squares. However, this is not true. While all squares are rectangles, not all rectangles are squares.

Thus, the correct option is B.

For more details regarding conditional statement, visit:

https://brainly.com/question/18152035

#SPJ1

Answer: Let's call the number of games that Lorelel plays "x".

The cost of playing x games would be:

4.25x

In addition to the cost of playing, Lorelel also has to pay a shoe rental fee of $9.59, regardless of how many games she plays.

So the total cost, C, of playing x games and renting shoes would be:

C = 4.25x + 9.59

For example, if Lorelel plays 3 games, the cost would be:

C = 4.25(3) + 9.59 = 21.34

If Lorelel plays 6 games, the cost would be:

C = 4.25(6) + 9.59 = 35.09

And so on, for any number of games she chooses to play.

The statement that shows the correct headings for the columns include the following: A. Column A = x, Column B = 5x + 8, Column C = y.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about the graph of this line, it can be modeled by this linear equation:

y = mx + c

y = 5x + 8

y = 5(1) + 8

y = 5 + 8

y = 13.

Read more on slope-intercept here: brainly.com/question/4074155

#SPJ1

The probability of getting 3 or fewer successes in 9 independent trials of a binomial probability experiment, where the probability of success in each trial is 0.3, is 0.143 (14.3%). This calculation assumes the trials are independent and the probability of success is constant for each trial.

To compute the probability of x successes in the n independent trials of the experiment, we can use the binomial probability formula:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where (n choose x) represents the number of ways to choose x items from a set of n items and is calculated as:

(n choose x) = n! / (x! * (n-x)!)

where n! represents the factorial of n, which is the product of all positive integers up to and including n.

Using this formula and the given parameters n=9, p=0.3, and x ≤ 3, we can calculate the probability of x successes as follows:

P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)

P(x = 0) = (9 choose 0) * 0.3^0 * (1-0.3)^(9-0) = 0.001

P(x = 1) = (9 choose 1) * 0.3^1 * (1-0.3)^(9-1) = 0.009

P(x = 2) = (9 choose 2) * 0.3^2 * (1-0.3)^(9-2) = 0.037

P(x = 3) = (9 choose 3) * 0.3^3 * (1-0.3)^(9-3) = 0.096

Therefore, the probability of x successes in the n independent trials of the experiment, where n=9 and p=0.3, and x ≤ 3, is:

P(x ≤ 3) = 0.001 + 0.009 + 0.037 + 0.096 = 0.143 (rounded to three decimal places)

So, the probability of x successes in the n independent trials of the experiment, where n=9 and p=0.3, and x ≤ 3, is 0.143 (rounded to three decimal places). This means that there is a 14.3% chance of getting 3 or fewer successes in the 9 independent trials of the experiment, where the probability of success in each trial is 0.3.

It is important to note that this calculation assumes that the trials are independent and that the probability of success is constant for each trial. If these assumptions are not met, the binomial probability formula may not be appropriate and other methods of probability calculation may need to be used.

Visit to know more about Probability:-

brainly.com/question/13604758

#SPJ11

The total area of Ruby-Rose paints will be 213 square feet. The Option B is correct.

In math, an area means the total space taken up by a flat surface or shape of an object.

The area of each wall is:

= 8 feet x 8 feet

= 64 square feet

The area of three walls:

= 3 x 64

= 192 square feet

The area of door is:

= 3 feet x 7 feet

= 21 square feet

The total area painted will equal:

= 192 + 21

= 213 square feet

Read more about area

brainly.com/question/2607596

#SPJ1

"B. either the null or the alternative hypothesis."

Learn more about  "hypothesis".

brainly.com/question/23056080

#SPJ11

This expression in the desired form X^A(B + Clog_D(x)):

f'(x) = x^2(3log6(x) + ln(6)) = x^2log6(x^3) = x^(2log6(x^3))

To find the derivative of the function f(x) = x^3 * log6(x), we can use the product rule and the chain rule.

Let's begin by applying the product rule:

f(x) = x^3 * log6(x)

f'(x) = (3x^2 * log6(x)) + (x^3 * 1/x * ln(6))

Simplifying the second term using the logarithmic identity loga(b^c) = c*loga(b), we get:

f'(x) = (3x^2 * log6(x)) + (x^2 * ln(6))

Finally, we can rewrite this expression in the desired form X^A(B + Clog_D(x)):

f'(x) = x^2(3log6(x) + ln(6)) = x^2log6(x^3) = x^(2log6(x^3))

Learn more about expression here

https://brainly.com/question/1859113

#SPJ11

Answer:

14cm

Step-by-step explanation:

l is length, h is height, and w is width.

We can construct the following equations:

l = 4h

volume = lwh

Given the length is 16cm, plugging the value into the first equation gives us a height of 4cm.

Based on the second equation, if we plug in the given length and volume values as well as our height value, we get:

896 = 16*4*w

w = 14cm.

The coordinates of Q will be (-2,-2/5)

The scale factor is a measure for similar figures, who look the same but have different scales or measures.

Scale factor = new dimension /old dimension

The trapezoid will under go a dilation about a scale factor of 2/5.

The original cordinate of Q is (-5,-1). With the dilation;

x cordinate of Q =

2/5 = x/-5

-10 = 5x

x = -2

y cordinate will be

2/5 = y/-1

-2 = 5y

y = -2/5

therefore the new cordinate of Q is ( -2,-2/5)

learn more about scale factor from

https://brainly.com/question/26855848

#SPJ1

To find the volume of the region between y = 4 - x^2 and y = 0 when revolved about the line y = -1, we'll use the method of cylindrical shells. This involves integrating the product of the shell's height, radius, and thickness over the range of x-values.

First, let's determine the intersection points of the two functions by setting them equal to each other:

4 - x^2 = 0
x^2 = 4
x = ±2

The region of interest lies between x = -2 and x = 2.

Next, consider a thin vertical strip of width dx at an arbitrary x-coordinate. When revolved about y = -1, this strip forms a cylindrical shell. The height of the shell is given by the difference in the y-values (y = 4 - x^2 and y = 0):

Height = 4 - x^2

The radius of the shell is the distance from the x-axis (where y = 0) to the line y = -1:

Radius = 1

Since the circumference of the shell is 2π * Radius, the volume of a single shell is:

dV = 2π * Radius * Height * dx = 2π * 1 * (4 - x^2) * dx

Now we need to integrate this expression over the x-range [-2, 2] to find the total volume:

Volume = ∫[-2, 2] 2π(4 - x^2)dx = 2π * ∫[-2, 2] (4 - x^2)dx

Solving the integral:

Volume = 2π * [4x - (1/3)x^3] evaluated from -2 to 2
Volume = 2π * [(4*2 - (1/3)*2^3) - (4*(-2) - (1/3)*(-2)^3)]
Volume = 2π * (8 - 8/3 + 8 + 8/3)
Volume = 2π * 16
Volume = 32π

So, the volume of the region between y = 4 - x^2 and y = 0, when revolved about the line y = -1, is 32π cubic units.

Learn more about volume here: brainly.com/question/6204273

#SPJ11

Answer: This is an example of empirical probability since it is based on the observed outcomes of an experiment. The fisherman used past experience to estimate the likelihood of catching a fish on his next trip.

The value of the binomial expansion of (x + 2)⁴ is,

⇒ x⁴ + 8x³ + 24x² + 32x + 16

We have to given that;

The expression is,

⇒ (x + 2)⁴

Use pascals triangle as;

We need to 5th row in pascals triangle because we have exponent 4 (1, 4,6,4,1)

[tex]x^{n-i} y^{i}[/tex] where i ranges from 0 to 4.

⇒ (x + 2)⁴

⇒ 1 × x⁴ × 2⁰ + 4 × x³ × 2¹ + 6 × x² × 2² + 4 × x¹ × 2³ + 1 × x⁰ × 2⁴

⇒ x⁴ + 8x³ + 24x² + 32x + 16

Thus, The value of the binomial expansion of (x + 2)⁴ is,

⇒ x⁴ + 8x³ + 24x² + 32x + 16

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ4

Answer:

C.) x^4+8x^3+24x^2+32x+16

Step-by-step explanation:

got it right on edg!

Null Hypothesis: The population mean is equal to 15. (H0: μ = 15)

Alternative Hypothesis: The population mean is not equal to 15. (HA: μ ≠ 15)

In hypothesis testing, the null hypothesis is assumed to be true until there is enough evidence to reject it. The alternative hypothesis is what the researcher wants to prove or find evidence for. In this case, the researcher wants to find out whether the population mean is different from 15 or not. If the sample data provides sufficient evidence to reject the null hypothesis, then the researcher can conclude that the population mean is different from 15. On the other hand, if the sample data does not provide enough evidence to reject the null hypothesis, then the researcher cannot conclude that the population mean is different from 15.

Learn more about  hypotheses

brainly.com/question/18064632

#SPJ11

Answer: D

Step-by-step explanation:

You could plug it in your calculator, just make sure your mode is in radians because there is a pi in your questions

When conducting hypothesis testing, a small p-value is an indication of strong evidence against the null hypothesis. A p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

A small p-value, typically less than 0.05, suggests that the observed data is unlikely to have occurred by chance alone and supports the alternative hypothesis. The implication of a small p-value is that the null hypothesis should be rejected, and the alternative hypothesis should be accepted. This indicates that the results are statistically significant, and the effect observed in the data is not due to chance.

Therefore, researchers can conclude that their intervention or treatment has a significant effect on the outcome of interest. In conclusion, small p-values play a crucial role in hypothesis testing, and they help researchers to make sound conclusions based on their data analysis.

Learn more about p-value here:

brainly.com/question/29537948

#SPJ11

Answer:

Step-by-step explanation:

area, perimeter, and volume are different measures used to quantify different properties of geometric shapes. Area measures the amount of space enclosed by a shape in two dimensions, perimeter measures the total length of the boundary of a shape in two dimensions, and volume measures the amount of space occupied by a shape in three dimensions.

a.one-way independent ANOVA

Choose inferential test based on data type and research design. One-way independent ANOVA for 3+ independent groups. Two-way independent ANOVA for 2 independent variables. Two-way repeated ANOVA for repeated measures at multiple time points from same group. Two-way mixed ANOVA for both independent groups and within-group repeated measures.

Inferential tests are statistical tools that are used to analyze data and draw conclusions about a population based on a sample. The choice of the inferential test depends on the type of data and the research design used.

One of the most commonly used inferential tests is the ANOVA (analysis of variance), which compares the means of two or more groups. The one-way independent ANOVA is used to compare means of three or more independent groups, while the two-way independent ANOVA is used to analyze data with two independent variables.

The two-way repeated ANOVA is used when data is collected at multiple time points from the same group, while the two-way mixed ANOVA is used when data is collected from both independent groups and within-group repeated measures.

Learn more about ANOVA (Analysis of Variance)

brainly.com/question/30399775

#SPJ11

The focus of a vertical parabola equation is at (3, 9).

We have,

To find the focus of a vertical parabola equation in the form of

(x - h)² = 4p (y - k)

The focus is located at the point $(h, k+p)$.

We can first rewrite it in the form (x - 3)² = 16 (y - 5).

This gives us h = 3, k = 5, and 4p = 16, so p =4.

Now,,

The focus is located at the point (3, 5+4) = (3, 9).

Thus,

The focus is at $(3, 9)$.

Learn more about parabola here:

https://brainly.com/question/21685473

#SPJ1

The circumference of the circle in terms of π whose radius is given would be = 63π. That is option D.

To calculate the circumference of a circle, the formula that should be used would be given below.

That is;

circumference of circle= 2πr

The radius = 31½

circumference = 2×π × 31½

= 2×π× 63/2

= 63π

Learn more about circle here:

https://brainly.com/question/26594685

#SPJ1

We can see here that the volume of the inside of the box = 12.8cm³

In order to find the volume of the inside of the box, we need to find the volume of the larger pentagonal prism and subtract the volume of the smaller pentagonal prism.

Volume of pentagonal prism = 1/4 × √[5(5 + 2√5)a²h]

Where:

h = height of the prism,

a = length of one of the sides of the pentagon

Volume of larger pentagonal prism, V1:

h = 9

a = 6

Substituting into the formula, we have:

V1 =  1/4 × √[5(5 + 2√5)×6²×9]

= 1/4 × √(5 × 9.47 × 36 × 9)

= 1/4 × 123.86 = 30.97cm³

Volume of smaller pentagonal prism, V2:

h = 7

a = 4

Substituting into the formula, we have:

V2 =  1/4 × √[5(5 + 2√5)× 4² × 7]

= 1/4 × √(5 × 9.47 × 16 × 7)

= 1/4 × 72.82

= 18.21cm³

Thus, volume of the inside of the box = V1 - V2 = 30.97cm³ - 18.21cm³

=  12.8cm³ (to the nearest tenth).

Learn more about prism on https://brainly.com/question/23766958

#SPJ1