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Answer:

x = - 3 , x = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

to find the x- intercepts let y = 0 , that is

(x + 3)(6x - 2) = 0

equate each factor to zero and solve for x

x + 3 = 0 ( subtract 3 from both sides )

x = - 3

6x - 2 = 0 ( add 2 to both sides )

6x = 2 ( divide both sides by 6 )

x = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

the x- intercepts are then x = - 2 and x = [tex]\frac{1}{3}[/tex]

The surface area and the volume of the rectangular prism are 280 and 300

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

The rectangular prism

The surface area is caculated as

Surface area = 2 * (10 * 5 + 10 * 6 + 5 * 6)

Evaluate

Surface area = 280

For the volume, we have

Volume = 10 * 5 * 6

Evaluate

Volume = 300

Hence, the surface area and the volume are 280 and 300

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Answer:

a. 5π cm

b. 144π in²

c. 6 ft

Step-by-step explanation:

a.

The circumference of a circle is given by:

Circumference pf circle= πd

where d is the diameter.

In this case, d = 5 cm,

Therefore, Circumference of circle = π*5=5π cm

b.

The area of a circle is given by:
Area of circle=πr²,

where r is the radius. In this case, the diameter is d = 24 in,

so, the radius is r = d/2 = 24/2=12in

Therefore, Area of circle=π*12²=144π in²

c.

The area of a circle is given by:

Area of circle=πr²,

where r is the radius. In this case, Area is 36π ft²

Now substituting value

36π=πr²

dividing both side by π, we get

36=r²

[tex]r=\sqrt{36}=6[/tex]

r=6 ft.

Therefore, Radius is 6 ft.

The numbers to complete the pythagorean triple in the equation (n² - 1)² + k² = (n² + 1)² are B. 35 and 37

A pythagorean triple is a set of 3 numbers that obey the pythagorean theorem.

Given the equation

(n² - 1)² + k² = (n² + 1)², we need to find the remaining numbers generated by the equation when k = 12. So, we proceed as follows/

Since we have the equation

(n² - 1)² + k² = (n² + 1)²

Subtracting (n² + 1)², from both sides, we have that

(n² - 1)² - (n² + 1)² + k² = (n² + 1)² - (n² + 1)²

(n² - 1)² - (n² + 1)² + k² = 0

Now, subtracting k from both sides, we have that

(n² - 1)² - (n² + 1)² + k² = 0

(n² - 1)² - (n² + 1)² + k² - k² = 0 - k²

(n² - 1)² - (n² + 1)² + 0 = - k²

(n² - 1)² - (n² + 1)² = - k²

Using the difference of two squares a² - b² = (a + b)(a - b)

(n² - 1)² - (n² + 1)² = - k²

(n² - 1 + n² + 1)[n² - 1 - (n² + 1)] = - k²

(n² + n² - 1 + 1)[n² - n² - 1 - 1)] = - k²

(2n² + 0)[0 - 2)] = - k²

(2n²)(- 2) = - k²

-4n² = - k²

4n² = k²

n² = k²/4

Taking square root of both sides, we have that

n = √(k²/4)

n = k/2

Since k = 12, we have that

n = 12/2

n = 6

So, the first number is (n² - 1) = (6² - 1)

= 36 - 1

= 35

The second number is (n² + 1) = (6² + 1)

= 36 + 1

= 37

So, the numbers are B. 35 and 37

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According to the Committee for the Study of the American Electorate, the four states with lower voter turnout in the 2004 presidential election compared to the 2000 election were Arkansas, Hawaii, Maryland, and Tennessee.

In the 2004 presidential election, voter turnout increased in most states compared to the 2000 election. However, Arkansas, Hawaii, Maryland, and Tennessee experienced a decrease in voter participation. This means that fewer eligible voters in these states cast their ballots in the 2004 election compared to the previous one.

The reasons behind the lower voter turnout in these states could vary and might be influenced by factors such as changes in voter registration laws, campaign strategies, voter demographics, or the overall political climate in each state during that particular election cycle.

It is worth noting that while voter turnout increased in most states, overall voter participation in the United States has been historically lower compared to some other democracies.

Efforts to increase voter engagement and turnout, such as expanding access to voting and improving voter education, continue to be important in ensuring that more eligible citizens exercise their right to vote and have their voices heard in the democratic process.

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In triangle PAD, using the Pythagorean theorem, we find AD = 5√2. Given that ∠PAQ's opposite side is PQ, which equals 3, we have sin∠PAQ = PQ/AQ = √2/10.

In square ABCD, we are given that points P and Q are on lines BC and CD respectively such that BP=4 and PC=1, DQ=4 and QC=1. Considering triangle PAD, it is a right triangle in the given square, and, using the Pythagorean theorem, we can find the hypotenuse AD as AD = √(5² + 5²) = 5√2. The same reasoning, AD = AQ.

Because ∠PAQ is the angle we are interested in finding the sine of, we know that sin∠PAQ = opposite/hypotenuse. In this case, the opposite side is PQ which we determine is 3 using the given distances (PC+QC). So, sin∠PAQ = PQ/AQ = 3/(5√2) = √2/10. Thus, the sine of angle PAQ is √2/10.

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The number we're looking for, which when added to 24/5 results in 9, is 21/5 or 4.2 in decimal form.

Let's solve the equation: 24/5 + x = 9, where x represents the unknown number we're trying to find.

To isolate x, we'll start by subtracting 24/5 from both sides of the equation:

x = 9 - 24/5

To add these two fractions, we need a common denominator. The denominator of 9 is 1, and the denominator of 24/5 is 5. To find a common denominator, we multiply 1 by 5:

x = (9 * 5)/5 - 24/5

This gives us:

x = 45/5 - 24/5

Now we can combine the fractions with the same denominator:

x = (45 - 24)/5

Simplifying the numerator:

x = 21/5

Therefore, the number we're looking for is 21/5. In decimal form, it can be written as 4.2.

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The equation (-14) + x = 14 is solved by adding 14 to both sides of the equation, resulting in x = 28. This means that 28 is the value of x that satisfies the equation and makes it true.

To solve the equation (-14) + x = 14, we need to isolate the variable x on one side of the equation. Let's go through the steps:

Step 1: Add 14 to both sides of the equation to eliminate the -14 on the left side.

(-14) + x + 14 = 14 + 14

x = 28

The solution to the equation (-14) + x = 14 is x = 28.

In this equation, we start with (-14) on the left side, and we want to determine the value of x that makes the equation true. To do that, we need to isolate x. By adding 14 to both sides of the equation, we cancel out the -14 on the left side, leaving us with just x. On the right side, 14 + 14 simplifies to 28.

Therefore, the solution to the equation is x = 28. This means that if we substitute 28 for x in the original equation, (-14) + 28 will indeed equal 14. Let's verify this:

(-14) + 28 = 14

14 = 14

The left side of the equation simplifies to 14, and the right side is also 14. Since both sides are equal, it confirms that x = 28 is the correct solution to the equation.

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The value of n is approximately -0.327.

To determine the value of n, we can substitute the given solution (x = 2.1) into the system of equations:

4x² - my = 10 ...(1)

mx² + ny = 20 ...(2)

Substituting x = 2.1 into equation (1), we get:

4(2.1)² - my = 10

8.4 - my = 10

-my = 10 - 8.4

-my = 1.6

Now, substituting x = 2.1 into equation (2), we get:

m(2.1)² + ny = 20

4.41m + ny = 20

Since we already have an expression for -my from equation (1), we can substitute it into equation (2):

4.41m + (-1.6) = 20

4.41m - 1.6 = 20

4.41m = 20 + 1.6

4.41m = 21.6

To solve for m, we divide both sides by 4.41:

m = 21.6 / 4.41

m ≈ 4.9

Now that we have the value of m, we can substitute it back into equation (1) to solve for n:

4(2.1)² - 4.9y = 10

8.4 - 4.9y = 10

-4.9y = 10 - 8.4

-4.9y = 1.6

Finally, to solve for y, we divide both sides by -4.9:

y = 1.6 / -4.9

y ≈ -0.327

Consequently, n has a value of roughly -0.327.

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Answer:

119in^2

Step-by-step explanation:

formula= 2(width×length+hight×length+hight×5

2×(5×8+3×8+3×5) = 119in^2

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are options 1 (x < 5) and 3 (–6x + 15 < 10 – 5x).

To determine the correct representations of the inequality –3(2x – 5) < 5(2 – x), let's simplify the expression and analyze the options:

First, we simplify the inequality:

–3(2x – 5) < 5(2 – x)

–6x + 15 < 10 – 5x

Now let's analyze the options:

x < 5: This option represents the solution to the inequality. It indicates that x must be less than 5 for the inequality to hold true.

–6x – 5 < 10 – x: This is not a correct representation of the inequality. The sign of the x-term on the right side of the inequality is incorrect.

–6x + 15 < 10 – 5x: This option represents the solution to the inequality. It correctly represents the simplified inequality we obtained earlier.

A number line from negative 3 to 3 in increments of 1, with an open circle at 5 and a bold line starting at 5 and pointing to the right: This representation does not accurately represent the solution to the inequality. The inequality is not satisfied at x = 5, so the circle should be closed.

A number line from negative 3 to 3 in increments of 1, with an open circle at negative 5 and a bold line starting at negative 5 and pointing to the left: This representation is not correct as it does not represent the solution to the inequality.

Therefore, choices 1 (x 5) and 3 (-6x + 15 10 - 5x) are the proper expressions of the inequality -3(2x - 5) 5(2 - x).

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The table of values for the equation y = 3/x can be completed as follows:

x | y

1 | 3/1 = 3

2 | 3/2 = 1.5

3 | 3/3 = 1

4 | 3/4 = 0.75

5 | 3/5 = 0.6

To complete the table of values for the equation y = 3/x, we substitute different values of x into the equation and calculate the corresponding values of y.

When x = 1:

Substitute x = 1 into the equation: y = 3/1 = 3

So, when x = 1, y = 3.

When x = 2:

Substitute x = 2 into the equation: y = 3/2 = 1.5

So, when x = 2, y = 1.5.

When x = 3:

Substitute x = 3 into the equation: y = 3/3 = 1

So, when x = 3, y = 1.

When x = 4:

Substitute x = 4 into the equation: y = 3/4 = 0.75

So, when x = 4, y = 0.75.

When x = 5:

Substitute x = 5 into the equation: y = 3/5 = 0.6

So, when x = 5, y = 0.6.

By substituting different values of x into the equation y = 3/x, we can complete the table of values as shown above.

Hence, the completed table of values for y = 3/x is:

x | y

1 | 3

2 | 1.5

3 | 1

4 | 0.75

5 | 0.6

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Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)

Gabby can get €23.73 for £21 when using the exchange rate of £1 = €1.13.

To calculate how many euros Gabby can get for £21, we need to use the exchange rate of £1 = €1.13.

To find the number of euros, we multiply the amount in pounds (£21) by the exchange rate (€1.13):

£21 * €1.13 = €23.73

Therefore, Gabby can get €23.73 for £21 when using the exchange rate of £1 = €1.13.

This means that for every pound exchanged, Gabby will receive €1.13. So, by multiplying the amount in pounds (£21) by the exchange rate (£1 = €1.13), we can determine the equivalent amount in euros.

It's important to note that exchange rates can fluctuate, and the rate provided here is just an example. When exchanging currency, it's always advisable to check the current exchange rates as they may vary. Additionally, some currency exchange services may charge fees or have different rates, so it's essential to consider those factors as well.

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Answer:

measure of arc JL = 55°

measure of angle PKJ = 27.5°

Answer:

A= 220.5ft

B= $2425.5

Step-by-step explanation:

A= 220.5ft

B= $2425.5

(3+9) + 13 correctly rewritten using the associative property and then correctly simplified is 13+(9+3) = 13 + 12 = 25.

1. Start with the expression (3+9) + 13.

2. According to the associative property of addition, we can group the numbers in any order without changing the result.

3. Rearrange the expression by grouping the numbers differently: (9+3) + 13.

4. Now simplify the grouped numbers: 9+3 = 12.

5. The expression becomes 12 + 13.

6. Finally, simplify the addition: 12 + 13 = 25.

Therefore, the correct rewritten expression using the associative property and the simplified result is 13+(9+3) = 13 + 12 = 25.

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The population at 4:00 P.M., 27 minutes earlier, is[tex]3^3[/tex] times the initial population P.

To determine the population of a bacteria culture 27 minutes earlier, we need to calculate the population growth from 4:00 P.M. to 4:27 P.M. given that the bacteria culture triples every 5 minutes.

Let's break down the time period into intervals of 5 minutes:

From 4:00 P.M. to 4:05 P.M., the population triples once.

From 4:05 P.M. to 4:10 P.M., the population triples again.

From 4:10 P.M. to 4:15 P.M., the population triples for the third time.

From 4:15 P.M. to 4:20 P.M., the population triples for the fourth time.

From 4:20 P.M. to 4:25 P.M., the population triples for the fifth time.

From 4:25 P.M. to 4:27 P.M., the population undergoes partial growth.

Since the population triples every 5 minutes, we can express the population at 4:27 P.M. as 3^5 times the initial population at 4:00 P.M.

Let's denote the initial population at 4:00 P.M. as P. Then, the population at 4:27 P.M. is [tex]3^5[/tex] * P.

To find the population 27 minutes earlier, we need to reverse the growth from 4:27 P.M. to 4:00 P.M. Since the population triples every 5 minutes, we need to divide the population at 4:27 P.M. by [tex]3^{(27/5).[/tex]

Therefore, the population at 4:00 P.M., 27 minutes earlier, can be calculated as:

Population at 4:00 P.M. = (Population at 4:27 P.M.) / [tex]3^{(27/5)[/tex]

[tex]= (3^{5} * P) / 3^{(27/5)\\\\\\\\= 3^{(25/5)} * P\\= 3^5 * P / 3^2\\= 3^3 * P[/tex]

Hence, the population at 4:00 P.M., 27 minutes earlier, is 3^3 times the initial population P.

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Answer:

f(2.5) = 100

Step-by-step explanation:

to evaluate f(2.5) substitute x = 2.5 into f(x)

f(2.5) = 16(2.5)² = 16 × 6.25 = 100

Answer:

The correct answer is A. As x increases, the rate of change of f(x) exceeds the rate of change of g(x)

Step-by-step explanation:

Han will have 2 liters (or 2000 milliliters) of sparkling juice after combining 1.5 liters of juice and 500 milliliters of sparkling water.

To make sparkling juice, Han mixes 1.5 liters of juice and 500 milliliters of sparkling water.

To add the quantities together, we need to convert the units to the same measurement. We can convert the liters to milliliters since 1 liter is equal to 1000 milliliters.

1.5 liters is equal to 1.5 x 1000 = 1500 milliliters.

Now we have 1500 milliliters of juice and 500 milliliters of sparkling water.

To find the total quantity of the sparkling juice, we add the volumes of juice and sparkling water together:

1500 milliliters + 500 milliliters = 2000 milliliters

Therefore, Han will have a total of 2000 milliliters (or 2 liters) of sparkling juice by mixing 1.5 liters of juice and 500 milliliters of sparkling water.

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The table that shows the same function as the given graph is: A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 5, 6, 7.

To determine which table shows the same function as the given graph, we need to find the values of y corresponding to the given values of x on the graph.

Point A: (0, 4)

Point B: (2, 5)

Let's check each table:

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries negative 8, negative 4, 0, 4.

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 0, 4, 0, 4.

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 5, 6, 7.

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 8, 12, 16.

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e^0 equals 1. e^infinity is undefined.

In mathematics, e^0 is equal to 1. This is because any number raised to the power of 0 is always equal to 1. The number e, which is approximately equal to 2.71828, follows this rule as well. So, when e is raised to the power of 0, the result is 1.

On the other hand, e^infinity is undefined. As the exponent approaches infinity, the value of e^infinity increases without bound. It does not converge to a specific number or approach any finite value.

In calculus and mathematical analysis, this is expressed by saying that the limit of e^x as x approaches infinity is equal to infinity.

The exponential function e^x is a fundamental mathematical concept with many applications in various fields such as physics, engineering, and finance.

Understanding the behavior of this function at different values of x, including 0 and infinity, is important for solving equations, modeling growth and decay processes, and studying the properties of exponential functions.

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The period of oscillation is 3 seconds

A Oscillation is the periodic change of a measure around a central value or between two or more states, usually in time.

The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle. It is measured in seconds

Oscillation can also be vibration or revolution or cycle.

Therefore, using the graph to determine the period. Then the wave particle made a complete oscillation at 3 second.

This means that the period of the particle is 3 seconds.

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Answer:

$3.3

Step-by-step explanation:

4x = 1.32

x = 0.33$ / ft

10x = 10 * 0.33 = 3.3$

The function that matches the graph is of the form:

4cos((pi x)/7) + 1

Graphs of trigonometric functions are graphs used in representing trigonometric functions.

From these graphs, some basic properties such as Amplitude, phase difference, period and vertical shift can be deduced.

From the given graph in the question, it can be seen that the graph crosses the y-axis at it's amplitude (highest point), so its easier to use the cosine relation.

To calculate the midline M:

Use the formula,

M = (maximum + minimum)/2

= (5 + -3)/2 = 2/2 = 1

Vertical shift: It can be seen from the graph that there is a vertical upward shift of 1 unit. C = 1

Amplitude: Maximum value - vertical shift is:

A = 5 - 1 = 4

Period = spacing between repeating patterns. There are 14 units between each peak (peak when x = -14, next peak when x = 0).

k = 2pi/Period;

So: k = 2pi/14 = pi/7

Therefore y = 4cos(pix/7) + 1 is the function that matches the given graph.

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The 90% confidence interval for the population variance (σ^2) is approximately [7.19, 20.19].

To construct a 90% confidence interval for the population variance (σ^2), given a sample size of 20 and a sample variance (s^2) of 12.5, we need to utilize the chi-square distribution.

The formula for constructing a confidence interval for the population variance is:

[ (n - 1)s^2 / χ^2_upper, (n - 1)s^2 / χ^2_lower ]

Where n is the sample size, s^2 is the sample variance, χ^2_upper is the upper critical value from the chi-square distribution, and χ^2_lower is the lower critical value from the chi-square distribution.

For a 90% confidence interval, we need to find the critical values from the chi-square distribution that correspond to the upper and lower tails of 5% each (since the confidence level is divided equally into two tails).

(a) Degrees of freedom:

The degrees of freedom (df) for the chi-square distribution is equal to n - 1. In this case, n = 20, so df = 20 - 1 = 19.

(b) Chi-square critical values:

We need to find the upper and lower critical values from the chi-square distribution table for df = 19 and a significance level of 0.05/2 = 0.025 (for each tail).

From the chi-square distribution table or using a statistical software, the upper critical value for a significance level of 0.025 and df = 19 is approximately 32.852. Similarly, the lower critical value is also approximately 8.907.

(c) Confidence interval calculation:

Substituting the values into the formula, we can construct the confidence interval:

[ (n - 1)s^2 / χ^2_upper, (n - 1)s^2 / χ^2_lower ]

[ (20 - 1) * 12.5 / 32.852, (20 - 1) * 12.5 / 8.907 ]

[ 19 * 12.5 / 32.852, 19 * 12.5 / 8.907 ]

[ 7.19, 20.19 ]

Therefore, the [7.19, 20.19] is roughly inside the 90% confidence interval for the population variance (2).

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Question

A simple random sample of size n is drawn from a population that is known to be normally distributed. The sample​ variance, s^2​, is determined to be 12.5.Complete parts​ (a) through​ (c).Construct a​ 90% confidence interval for

σ2 if the sample​ size, n, is 20.

Answer:

B :3

Step-by-step explanation:

good luck <3

Answer:

A critical number can have different meanings depending on the context. In mathematics, a critical number is a value of x where the derivative of a function is zero or undefined. It helps to find the maximum and minimum of a function. In business, a critical number is a metric that represents a weakness or vulnerability that needs to be addressed and corrected to improve the performance and security of the company

Step-by-step explanation:

The joint probability is found by multiplying the probability of event J by the probability of event K P(J and K) = P(J) * P(K) Option C.

When two events J and K are independent, it means that the occurrence or non-occurrence of one event does not affect the probability of the other event. In other words, the probability of event J happening is completely unrelated to the probability of event K happening.

The joint probability of two independent events J and K is the probability that both events J and K occur simultaneously. Since the events are independent, the probability of their intersection is equal to the product of their individual probabilities.

The joint probability is found by multiplying the probability of event J by the probability of event K.

This formula holds true for independent events because there is no interaction or dependency between the events. Each event has its own probability, and when they occur together, the joint probability is simply the product of their individual probabilities. Option C is correct.

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