This table shows the results of a survey that asked a group of people what time of day their favorite TV show aired. What time corresponds to the mode of this set of data? A. 8:00 P.M. B. 9:00 P.M. C. 10:00 P.M. D. 11:00 P.M.

Answer:

x=5

Step-by-step explanation:

Set the 2 equations equal to each other and solve for x.

11x-28=7x-8

add 28 to both sides (-8+28=20)

11x=7x+20

subtract 7x from both sides (11x-7x=4x)

4x=20

divide both sides by 4 to isolate x (20/4=5)

x=5

The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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Answer:

There are actually 20 occurrences of the digit "2" in the numbers {1,2,⋯,100}, though there are 19 numbers in the same range where the digit "2" appears.

Step-by-step explanation:

Hope this will be helpful for you.

(a) The correct answer is D. (b) \(\sigma\)\(\bar{X}\) = \(\sigma\)÷ \(\sqrt{n}\)= 4÷\(\sqrt{n}\) (c) The probability is:

P(\(\bar{X}\) \(\geq\) 46) = P(z \(\geq\) 81.437) ≈ 0 (rounded to four decimal places). (d) The correct answer is B.

(a) The correct answer is D. The sampling distribution of \(\bar{X}\) is approximately normal when the population is normally distributed and the sample size is large enough.

This is known as the Central Limit Theorem, which states that regardless of the shape of the population distribution, the sampling distribution of \(\bar{x}\)approaches a normal distribution as the sample size increases.

(b) Given that \(\mu\) = 4 and \(\sigma\) = 4, the mean (\(\mu\)\(\bar{X}\)) of the sampling distribution of \(\bar{X}\) is equal to the population mean, which is 4. The standard deviation (\(\sigma\)\(\bar{X}\)) of the sampling distribution of \(\bar{X}\) is equal to the population standard deviation divided by the square root of the sample size. Therefore:

\(\mu\)\(\bar{X}\)= \(\mu\) = 4

\(\sigma\)\(\bar{X}\) = \(\sigma\)÷\(\sqrt{n}\) = 4÷\(\sqrt{n}\)

(c) To find the probability of a simple random sample of 60 ten-gram portions resulting in a mean of at least 46 insect fragments, you need to calculate the z-score and find the corresponding probability using the standard normal distribution table or calculator. The formula to calculate the z-score is:

z = (\(\bar{X}\) - \(\mu\)) ÷ (\(\sigma\)÷\(\sqrt{n}\))

Given \(\bar{X}\) = 46, \(\mu\) = 4, σ = 4, and n = 60, the z-score is:

z = (46 - 4) ÷ (4÷\(\sqrt{60}\)) = 42 ÷ 0.5163977795 ≈ 81.437

Using the z-score, you can find the corresponding probability (P) using the standard normal distribution table or calculator. The probability is:

P(\(\bar{X}\) \(\geq\) 46) = P(z \(\geq\)81.437) ≈ 0 (rounded to four decimal places)

This result is considered very unusual because the probability is extremely small.

(d) The correct answer is B. Since the result is unusual (probability is small), it is reasonable to conclude that the population mean is higher than 4.

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Answer: 1kg

Step-by-step explanation:

Answer:

almost 4.5g

Step-by-step explanation:

Hope this is the answer you are looking for

The factored expression of the expression given as (a + b)^2 = 4 is (a + b + 2)(a + b - 2) = 0

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

(a + b)^2 = 4

Express 4 as 2^2

So, we have

(a + b)^2 = 2^2

Rewrite as

(a + b)^2 - 2^2 = 0

Apply the difference of two squares

So, we have

(a + b + 2)(a + b - 2) = 0

Hence, the equivalent expression of the expression given as (a + b)^2 = 4 when it is factored is (a + b + 2)(a + b - 2) = 0

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You did not clearly mention the second function. So, I am assuming you meant to say that the second function has the table values such as:

x           y

0           4

-2          2

So, I am solving the question based on this information table of the 2nd function, which anyways will clear your concept.

Answer:

We conclude that the rate of change of a function '1' is greater than the rate of change of function '2'.

Step-by-step explanation:

Given the function 1

\(y = 2x + 6\)

Comparing the function with the slope-intercept form of the line equation of a linear function

where m is the rate of change or slope of the line

so

\(y = 2x + 6\)

rate of change = m = 2

Now, given the function 2

x           y

0           4

-2          2

Taking the slope of the two points in the table

(0 4), (-2, 2)

\(\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(0,\:4\right),\:\left(x_2,\:y_2\right)=\left(-2,\:2\right)\)

\(m=\frac{2-4}{-2-0}\)

\(m=1\)

So, the rate of change or slope of the function 2 is: m = 1

Hence, we observe that:

As the rate of change of a function '1' is greater than the rate of change of function 2.

i.e.

m = 2 > m = 1

Therefore, we conclude that the rate of change of a function '1' is greater than the rate of change of function '2'.

Factoring the sum or difference of cubes involves using specific formulas to simplify expressions.

The sum of cubes formula, a^3 + b^3 = (a + b)(a^2 - ab + b^2), and the difference of cubes formula, a^3 - b^3 = (a - b)(a^2 + ab + b^2), allow us to break down these expressions into more manageable factors.

To factor the sum or difference of cubes, you can use the following formulas:

Sum of Cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Cube difference: (a - b)(a - b)(a - b)(a - b)(a - b)

Sum of Cubes:

The sum of cubes formula states that the sum of two cubes, a^3 + b^3, can be factored into (a + b) multiplied by the quadratic expression a^2 - ab + b^2.

For example, let's factorize 8x^3 + 27:

We can identify a = 2x and b = 3, so using the sum of cubes formula:

8x^3 + 27 = (2x + 3)(4x^2 - 6x + 9)

Difference of Cubes:

The difference of cubes formula states that the difference between two cubes, a^3 - b^3, can be factored into (a - b) multiplied by the quadratic expression a^2 + ab + b^2.

For example, let's factorize 64y^3 - 125:

We can identify a = 4y and b = 5, so using the difference of cubes formula:

64y^3 - 125 = (4y - 5)(16y^2 + 20y + 25)

Factoring the sum or difference of cubes involves using specific formulas to simplify expressions. The sum of cubes formula, a^3 + b^3 = (a + b)(a^2 - ab + b^2), and the difference of cubes formula, a^3 - b^3 = (a - b)(a^2 + ab + b^2), allow us to break down these expressions into more manageable factors. Factoring such expressions can be useful in various algebraic calculations and simplifications.

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The relative rate of population change after seven years from now is a) 1.7 % (rounded off to 1 decimal place) b) Yes, the relative rate of population change will reach 2.3% in 19.21 years

The function for population t years from now is P(t)= 2+ 1.2e^(0.04t)

a) relative rate of change of population

= P'(t) / P(t)

= (0+1.2e^(0.04t) * 0.04 )/ ( 2+ 1.2e^(.04t) )

= 0.048 e ^(0.04t) / (2 + 1.2e^(0.04t) )

Relative rate of change of population 7 years from now

= 0.048 e ^(0.04 * 7) / (2+ 1.2e^(0.04*7))

=0.0177 = 0.177 * 100 = 1.7 % per year (rounded off to one decimal place

b) For the relative rate of change to reach 2.3 %

P'(t) / P(t) = 2.3 % = 0.023

⇒(0+1.2e^(0.04t) * 0.04 )/ ( 2+ 1.2e^(0.04t) ) = 0.023

⇒0.048e ^(0.04t) = 0.046 + 0.0267e^(0.04t)

⇒e ^(0.04t) = 0.958 + 0.556e ^(0.04t)

⇒e ^(0.04t) ( 1 - 0.556) = 0.958

⇒e ^(0.04t) ( 0.444) = 0.958

⇒e ^(0.04t) = 2.157

⇒0.04t = ln(2.157)           (applying ln on both sides)

⇒t = 19.21 years

The relative rate of population change is 2.3% in 19.21 years

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Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

Answer:

\(\frac{3}{7}\)

Step-by-step explanation:

Divide both sides of the equation by the same term

\(\frac{6}{14} =\frac{14m}{14}\)

Simplify

\(m=\frac{3}{7}\)

Answer:

m = \(\frac{3}{7}\)

Step-by-step explanation:

6 = 14m

Divide both sides by 14.

\(\frac{6}{14}\) = m

Reduce the fraction \(\frac{6}{14}\) to the lowest terms by extracting and canceling out 2.

\(\frac{3}{7}\) = m

Swap sides so that all variable terms are on the left-hand side.

m = \(\frac{3}{7}\)

Hope it helps and have a great day! =D

~sunshine~

A smaller level of significance or a larger sample size can reduce the risk of a Type I error, but may increase the risk of a Type II error, and vice versa.

Type I and Type II errors are two types of errors that can occur in hypothesis testing. In the context of the claim that "70% of applicants become", a Type I error occurs when we reject the null hypothesis (i.e., the claim that the true proportion is 70%) when it is actually true. This means that we conclude that the proportion of applicants who become something other than 70%, even though it is actually 70%. The probability of making a Type I error is denoted by the symbol alpha (α).

On the other hand, a Type II error occurs when we fail to reject the null hypothesis when it is actually false. In the context of the claim that "70% of applicants become", a Type II error occurs when we accept the null hypothesis (i.e., conclude that the true proportion is 70%) when it is actually false (i.e., the true proportion is different from 70%). The probability of making a Type II error is denoted by the symbol beta (β).

In other words, a Type I error is a false positive, where we reject the null hypothesis when we should not have, and a Type II error is a false negative, where we fail to reject the null hypothesis when we should have.

To minimize the risk of both Type I and Type II errors, it is important to carefully choose the level of significance (alpha) and the sample size. A smaller level of significance or a larger sample size can reduce the risk of a Type I error, but may increase the risk of a Type II error, and vice versa.

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A key requirement for the process of testing hypotheses in the scientific method is experimentation. A hypothesis is an idea or explanation for a phenomenon that is grounded in existing knowledge or observations, and the scientific method involves testing those hypotheses through experimentation.

The process of testing hypotheses requires the development of a testable hypothesis, the design of experiments to test the hypothesis, and the collection and analysis of data from those experiments to evaluate the hypothesis. The experiments must be designed carefully, with appropriate controls and variables to ensure that the results are reliable and valid. Scientists also need to communicate their findings to the scientific community, which involves publishing their results in scientific journals and presenting their work at conferences.

This helps to ensure that other scientists can replicate their experiments and validate their findings, which is a critical part of the scientific process. Ultimately, the process of testing hypotheses is essential for advancing scientific knowledge and understanding how the world works.

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Answer:

Answer: d) -310pi

Step-by-step explanation:

Instantaneous Rate of Change

Is the change in the rate of change of a function at a particular instant. It's the same as the derivative value at a specific point.

The surface area of a cylinder of radius r and height h is:

\(A=2\pi r^2+2\pi r h\)

We need to calculate the rate of change of the surface area of the cylinder at a specific moment where:

The radius is r=8 mm

The height is h=3 mm

The radius changes at r'=-9 mm/hr

The height changes at h'=+2 mm/hr

Find the derivative of A with respect to time:

\(A'=2\pi (r^2)'+2\pi (r h)'\)

\(A'=2\pi 2rr'+2\pi (r' h+rh')\)

Substituting the values:

\(A'=2\pi 2(8)(-9)+2\pi ((-9) (3)+(8)(2))\)

Calculating:

\(A'=-288\pi +2\pi (-27+16)\)

\(A'=-288\pi +2\pi (-11)\)

\(A'=-288\pi -22\pi\)

\(A'=-310\pi\)

Answer: d) -310pi

Answer:

-3

Step-by-step explanation:

Step 1: Solve (-2+(-1))^2/3 3

           1. -2+(-1) = -3

           2. (-3)^2 = 9

           3. 9/3 = 3

Step 2: Solve (-4)^2-17 -1

           1. 3/-1

Step 3: Simplify 3/-1 = -3. I hope this helped and please don't hesitate to reach out with more questions!

Answer:

Step-by-step explanation:

Perimeter of the rectangle = PQ + QR + RS + SP

                                      = b +l + b + l

                                      = 2b +2l

Again,  

ABCD is a rectangle. We know that the opposite sides of a rectangle are equal.

Perimeter of a Rectangle

AB = CD = 5 cm and BC = AD = 3 cm

So, the perimeter of the rectangle ABCD = AB + BC + CD + AD = 5 cm + 3 cm + 5 cm + 3 cm = 16 cm

It can be written as 5 cm + 5 cm + 3 cm + 3 cm

                       = (2 × 5) cm + (2 × 3) cm

                       = 2 (5 + 3) cm

                       = 2 × 8 cm

                       = 16 cm

We add length and breadth twice to find the perimeter of a rectangle.

Answer:

6x + 2 is your answer I THINK

The properties of the angles and sides of a triangle are as follows:

1. The sum of the three angles of any triangle is 180°

2. The longest side of a triangle is opposite the largest angle and the smallest side is opposite the smallest angle.

3. The sum of any two sides of a triangle is always greater than the third side.

These properties can be used to solve problems involving triangles by working out the angles or lengths of sides. For example, let's say we have a triangle with two sides of length 5 and 8, and we need to find the length of the third side. Using the third property listed above, we can set up the following equation:

5 + 8 > x

13 > x

Therefore, the length of the third side is greater than 13.

A triangle (of any kind) has a total angle of 180°. A triangle's two sides add up to a length bigger than its third side. In the same way, the length of the third side of a triangle's third side is shorter than the difference between its two sides.

Triangulus, which means "three-cornered" or "having three angles," is a Latin word with roots in tri-, "three," and angulus, "angle or corner."

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Answer:

$3941.57.

Step-by-step explanation:

Given,

Principal,P = $3,500

rate of interest,r = 2%

Time, n = 6 years

Now, the total amount Luca has to repay is:

\(A = P(1+\frac{r}{100})^n\)

A is the total amount.

\(A = 3500\times (1+\frac{2}{100})^6\\A = $3941.57\)

Hence, the total money he has to repay is $3941.57.

Answer:

3 < x

Step-by-step explanation:

Therefore the correct option is, P(Z < -1.75) where Z is a standard normal random variable.

To calculate the probability P(X > 17.5) for a normally-distributed random variable X with mean 14 and standard deviation 2, we can use the standardization process.

First, let's calculate the z-score for the value 17.5:

z = (X - μ) / σ = (17.5 - 14) / 2 = 3.5 / 2 = 1.75

Now, let's evaluate the given options:

P(X < 10.5) where X is described as above:

To calculate this probability, we can calculate the z-score for the value 10.5 using the same formula as above:

z = (X - μ) / σ = (10.5 - 14) / 2 = -3.5 / 2 = -1.75

P(Z > 1.75) where Z is a standard normal random variable:

This probability represents the area under the standard normal distribution curve to the right of z = 1.75.

P(Z < -1.75) where Z is a standard normal random variable:

This probability represents the area under the standard normal distribution curve to the left of z = -1.75.

P(Y < 1.25) where Y is normally distributed with mean 10 and standard deviation 5:

This option involves a different random variable Y with a different mean and standard deviation. We cannot directly compare it to the other options without additional information or calculations.

From the given options, the probabilities that are equal to P(X > 17.5) are:

P(Z < -1.75) where Z is a standard normal random variable.

Therefore, the correct option is:

P(Z < -1.75) where Z is a standard normal random variable.

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the correct choice is {0, 18}. These elements are unique to set C and do not appear in set A.

To find the set difference C - A, we need to remove all elements from A that are also present in C. Let's examine the sets:

C = {0, 6, 12, 18}

A = {2, 4, 6, 8, 10, 12}

We compare each element of A with the elements of C. If an element from A is found in C, we exclude it from the result. After the comparison, we find that the elements 2, 4, 8, 10 are not present in C.

Thus, the set difference C - A is {0, 18}, as these are the elements that remain in C after removing the common elements with A.

Therefore, the correct choice is {0, 18}. These elements are unique to set C and do not appear in set A.

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The coordinates of point S are (14,-10).

The coordinates represent the location of a point in the 2D coordinate plane with respect to the origin. A point's x-coordinate is its perpendicular distance from the y-axis as measured along the x-axis. A point's y-coordinate is the perpendicular distance from the x-axis measured along the y-axis.

Given, the coordinates of point T are (0,2).

The midpoint of ST is (7,-4).

Let, (a,b) be the coordinates of point S.

Then, (7,-4)= Then

\((\frac{0+a}{2},\frac{2+b}{2} )= \\7= \frac{a}{2} , -4= \frac{2+b}{2} \\a= 7*2= 14, 2+b= -8\\a=14, b= -10.\)

Hence, the coordinates of point S are (14,-10).

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Answer:

4/5=bc/8

Step-by-step explanation: