SAMPLE MEANS
1. Diego wants to know how many hours students in his high school spend watching television on school nights. He asks 30 randomly selected students how many hours they spent watching television last night. The results are shown in the table.
1 3 2 0 4 1 2 1 5 3
0 4 2 3 2 3 1 0 4 5
2 1 3 3 2 4 1 5 1 0


Part A: Find the sample mean of Diego's television data. Round your answer to the nearest tenth.


Part B: If Diego repeats the process with more random samples of 30 students and calculates the mean of each sample, should his set of sample means have a normal distribution? Explain.


Part C: The standard deviation, s, of Diego's sample of 30 students is 1.55 hours. Use the formula to find the standard error of the sampling distribution. Round your answer to the nearest hundredth.


Part D: Use the formula and table of critical values to find the 90% confidence interval for Diego's sample.
90% confidence interval =
(pic linked)


Part E: Explain what your result from Part D tells you about the average number of hours students at Diego's high school spend watching television on a school night.

The function is not one-to-one.

A one-to-one function, also known as an injective function, is a function where each element in the domain is uniquely mapped to a distinct element in the range. In other words, for every element in the domain, there exists only one corresponding element in the range, and no two elements in the domain can have the same image in the range.

To determine whether the given function is one-to-one, we need to check whether for any two distinct values of x, the function produces two distinct values of y.

We can rewrite the given function in the form:

y = 2(x + 1)² - 4

y = 2(x² + 2x + 1) - 4

y = 2x² + 4x - 2

To check whether the function is one-to-one, we can take two different values of x and check if the corresponding values of y are different.

Let's take x₁ = 1 and x₂ = 2.

When x = 1, y = 2(1 + 1)² - 4 = 8.

When x = 2, y = 2(2 + 1)² - 4 = 18.

Since y₁ = 8 and y₂= 18, and y₁ ≠ y₂, we can conclude that the function is not one-to-one.

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None of the statements A, B, C, or D can be true for function h. This is because the domain of h is from -3 to 11, which means that the function only exists for x values between -3 and 11.

The domain of a function is the set of all possible values of the independent variable or input for which the function is defined. It is the set of values over which the function is defined and takes real values. In simpler terms, it is the set of all possible x-values for which the function is defined.

In the given question,

None of the statements A, B, C, or D can be true for function h. This is because the domain of h is from -3 to 11, which means that the function only exists for x values between -3 and 11. Statement A refers to h(8) = 21, which is not consistent with the given value of h(8) = 19. Statement B refers to h(-3), which is not a valid value since the domain starts at -3. Statement C refers to h(13), which is also not a valid value since the domain ends at 11. Finally, statement D refers to h(2), which is not within the given domain.

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Answer:

1144 to base 9

Step-by-step explanation:

9 94 r 4

9 10 r 4

9 1 r 1

9 0 r 1

After this take an arrow from down to up

The true statements are

The value of f(–10) = 82

The graph of the function is a parabola.

The graph contains the point (20, –8).

A parabola is a type of conic section that is formed when a plane intersects a cone in such a way that the angle between the plane and the vertical axis of the cone is equal to the angle between the plane and a generator (a straight line passing through the vertex and the base of the cone).

The resulting shape is a symmetrical, U-shaped curve. The standard form of the parabola is a quadratic function.

Here we have

The quadratic function f(x) = x²/5 – 5x + 12

Now check each option as follows

1. The value of f(–10) = 82

To check this find f(-10) as follows

f(-10) =1/5 (-10)²– 5(-10) + 12 = 20 + 50 + 12 = 82

Hence, The value of f(–10) is equal to  82

2. The graph of the function is a parabola.

As we know the standard equation of a parabola is a quadratic function that is in the form of ax² + bx + c

Hence, the quadratic function represents a parabola

3. The graph of the function opens down.

In the given function f(x) = x²– 5x + 12, the coefficient of the x² term is 1. Since the coefficient of x² is positive, the parabola opens upwards.

Hence, The graph of the function opens down is false

4. The graph contains the point (20, –8).

To check this substitute the point in f(x)

=> –8 = 1/5(20)²– 5(20) + 12

=> –8 = 80 – 100 + 12

=> –8 = –8   [ Which is true ]

Hence, The graph contains the point (20, –8).

5. The graph contains the point (0, 0).

=>  0 = (0)²– 5(0) + 12

=>  0 = 12   [ which is not true ]

Hence, The graph doesn't contain the point (0, 0).

Therefore,

The true statements are

The value of f(–10) = 82

The graph of the function is a parabola.

The graph contains the point (20, –8).

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After the seventh time the vacuum is run over the carpet, approximately 94.757% of the original amount of dirt will be picked up.

A number can be expressed as a fraction of 100 using a percentage. When comparing amounts or expressing proportions, it is frequently represented using the symbol %. In numerous disciplines, including business, statistics, science, and daily life, percentages are frequently utilised. We frequently use percentages to indicate things like tax, discount, and interest rates as well as population growth rates. We divide a number by the total and multiply the result by 100 to get the percentage. For instance, we can claim that 40% of a class's students are female if there are 100 total students.

Given that, the vacuum picks up 80% of the dirt every time.

Thus, when the vaccum is run for the first time the dirt remaining is 20%.

Now, after second run we have:

20(80%) = 16%

Now, we see that a1 = 0.2 and the rate r = 0.8.

Thus, for seventh run we have:

[tex]a_7 = a_1 (r)^{7 -1}\\a_7 = 0.2 (0.8)^6\\a_7 = 0.0524[/tex]

Now, after seventh run we have:

100 - 5.24% = 94.757%

Therefore, after the seventh time the vacuum is run over the carpet, approximately 94.757% of the original amount of dirt will be picked up.

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Based on the information, EFH and GHF does not have to be congruent.

Congruents angles are presented in the figure below. Congruent angles are angles that have the same measure or size. When two angles are congruent, they look exactly the same, even if they are in different orientations.

The symbol used to represent congruence is an equals sign with a tilde above it, like this: ≅. For example, if angle A and angle B have the same measure, we can write it as:

angle A ≅ angle B

Congruent angles play an important role in geometry because they allow us to compare and analyze different shapes and figures. In particular, when two angles are congruent, we can use this fact to make conclusions about other angles and sides of a shape.

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In circle O shown, points E, F, G, and H lie on the circle asshown and chords FH and GE intersect at J. Based on thisinformation alone, which two angles below do not have tobe congruent?m(1) angle FJE and angle HJG(2) angle EFH and angle HGE(3) angle EFH and angle GHF(4) angle FEG and angle FHG

Answer:

Step-by-step explanation:

Similar triangles have the same shape but different sizes.

A is incorrect. We don't know the length of the sides, or if it is equilateral so we can't say that fg/lm=fh/ln

B is correct. FH and LN may be different sizes but they are similar

C is correct. Since the triangles are similar the angles are similar.

D is incorrect. The triangle is the same shape, not neccesarily the same size

E is correct. See C for explanation.

$36 is the 50 percentage of $72.

Let missing percentage be x.

A percentage in mathematics is a number or ratio that depicts a portion of 100. Per 100 is what "percentage" refers to. It is devoid of any units.

The equation will be,

Formula,

x% of 72 = 36

[tex]\frac{x}{100}[/tex] × 72 = 36

72x = 36(100)

72x = 3600

x = [tex]\frac{3600}{72}[/tex]

x = 50

$36 is the 50% of $72.

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The table shows a function that is decreasing over the interval (−2, 0) is option C: A 2-column table with 4 rows.  The first column is labeled x with entries negative 3, negative 2, negative 1, 0. The second column is labeled f of x with entries 2, 0, negative 10, negative 24.

The function is decreasing over the interval (-2, 0) because as the input x increases from -2 to 0, the output f(x) decreases. We can see this by looking at the values in the second column of the table:

When x = -2, f(x) = 0

When x = -1, f(x) = -10

When x = 0, f(x) = -24

Therefore, As x increases from -2 to 0, f(x) decreases from 0 to -24, which means the function is decreasing over the interval (-2, 0).

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we are given that CB is congruent to CA and that BE and AD are perpendicular

HOW TO SOLVE TRIANGLE?

Statement Reason

BE and AD are perpendicular Perpendicular lines form angles

CB ≅ CA Given

∠BEC and ∠ADC are right angles Given

BC = AC Definition of congruent segments

∠BCE ≅ ∠ACD Corresponding parts of congruent triangles are congruent (CPCTC)

∠CEB ≅ ∠DCA Corresponding parts of congruent triangles are congruent (CPCTC)

∠A ≅ ∠B Vertical angles are congruent

ADC ≅ BEC ASA (angle-side-angle) postulate

In summary, we are given that CB is congruent to CA and that BE and AD are perpendicular. We also know that ∠BEC and ∠ADC are right angles. Using these facts, we can show that triangles ADC and BEC are congruent by showing that two pairs of corresponding angles and the included side are congruent. Specifically, we use the fact that ∠BCE ≅ ∠ACD and ∠CEB ≅ ∠DCA, along with the fact that BC = AC, to apply the CPCTC (corresponding parts of congruent triangles are congruent) to show that the two triangles are congruent by the ASA (angle-side-angle) postulate.

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Answer:

[tex]4\pi[/tex]

Step-by-step explanation:

the side of the square equals the diameter of the circle inscribed.

So side of the square a is 4! (a^2=16, a=4)

So the radius of the circle is 2!

The area of the circle is 4π!!!!! (πa^2)

Answer: 19,000 cents

Step-by-step explanation: The total amount of cents in the box can be found by multiplying the number of 50 cent pieces by 50.

So,

total amount of cents = 380 x 50

= 19,000 cents

Therefore, there are 19,000 cents in the box.

a.   the equation of the least-squares line is: y = -0.003x + 3884.658

b.  the estimated sales for a pizza chain having 4000 stores is  3754.658 million dollars.

c. the estimated number of stores for a pizza chain whose 2013 sales were 2000 million dollars is  295219.333.

We will use linear regression to obtain the least-squares line that fits the given data.

Let x be the number of stores and y be the sales in millions of dollars.

mean of x = (6326 + 4986 + 3890 + 3207)/4 = 4602.25

mean of y = (5700 + 3800 + 3025 + 2485)/4 = 3752.5

Σ((x - mean of x)(y - mean of y)) = (6326 - 4602.25)(5700 - 3752.5) + (4986 - 4602.25)(3800 - 3752.5) + (3890 - 4602.25)(3025 - 3752.5) + (3207 - 4602.25)(2485 - 3752.5) = -79470.75

calculating  the sum of the squared deviations of x from its mean:

Σ((x - mean of x)^2) = (6326 - 4602.25)^2 + (4986 - 4602.25)^2 + (3890 - 4602.25)^2 + (3207 - 4602.25)^2 = 25994899.5

finding the slope of the least-squares line:

slope = Σ((x - mean of x)(y - mean of y)) / Σ((x - mean of x)^2) = -79470.75 / 25994899.5 ≈ -0.003056

y-intercept = mean of y - slope * mean of x ≈ 3884.658

equation of the least-squares line is: y = -0.003x + 3884.658

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To make a table of values for g(x) = 3x², we can choose several values of x and plug them into the equation to get the corresponding values of g(x).

The table for g(x) is formulated as follows;

Let's choose some values of x:

To find the corresponding value of g(x), we simply plug each value of x into the equation and simplify:

For x = -2, g(x) = 3(-2)² = 3(4) = 12

For x = -1, g(x) = 3(-1)² = 3(1) = 3

For x = 0, g(x) = 3(0)² = 3(0) = 0

For x = 1, g(x) = 3(1)² = 3(1) = 3

For x = 2, g(x) = 3(2)² = 3(4) = 12

The table formed is in the image attached.

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The loan was for 4 years.

What is intrest?

Interest is a fee paid by a borrower of money to the lender as compensation for the use of the money over a certain period of time. It is usually expressed as a percentage of the amount borrowed or invested, and the percentage is called the interest rate. The borrower is expected to pay back the principal amount borrowed plus the interest within a specified period of time.

The formula for simple interest is:

I = P * r * t

where I is the interest paid, P is the principal (the amount borrowed), r is the annual interest rate (as a decimal), and t is the time period in years.

We know that Ryan borrowed $200 and paid $48 in interest, and the interest rate is 6%. Plugging these values into the formula, we get:

48 = 200 * 0.06 * t

Solving for t, we get:

t = 48 / (200 * 0.06)

t = 4

Therefore, the loan was for 4 years.

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Null hypothesis: The mean number of points scored by the taller team is not significantly different from the population mean of 72.

Alternative hypothesis: The mean number of points scored by the taller team is significantly greater than the population mean of 72.

Since the population variance is unknown, we will use a t-test. The degrees of freedom for this test will be 9 (n-1), where n is the sample size of the taller team (10).

Using an alpha level of 0.05 and 9 degrees of freedom, the critical t-value is 1.833.

To calculate the test statistic, we first need to find the sample mean and standard deviation of the taller team's scores. The sample mean is 82, and the sample standard deviation is 9.89. Using these values, we can calculate the t-value:

t = (82-72) / (9.89 / sqrt(10)) = 3.19

Since the calculated t-value (3.19) is greater than the critical t-value (1.833), we reject the null hypothesis and conclude that there is a significant difference between the mean number of points scored by the taller team and the population mean of 72. The coach can therefore conclude that having a taller team does result in a greater number of points scored.

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The 27 possible 3-digit numbers with repetition are: 222, 223, 224, 232, 233, 234, 242, 243, 244, 322, 323, 324, 332, 333, 334, 342, 343, 344, 422, 423, 424, 432, 433, 434, 442, 443, and 444.

The use of the same element repeatedly in a combination or permutation is referred to as repetition. You can use any of the numbers (1, 2, or 3) more than once to construct a 3-digit number, for instance, if you are asked to pick a 3-digit number using the digits 1, 2, and 3, with repetition permitted.

Without repetition, we can choose the first digit in 3 ways, the second digit in 2 ways (since we cannot repeat the first digit), and the third digit in 1 way (since we cannot repeat the first or second digit). This gives a total of 3 x 2 x 1 = 6 possible 3-digit numbers.

The 6 possible 3-digit numbers without repetition are: 234, 243, 324, 342, 423, and 432.

With repetition, we can choose each of the three digits in 3 ways (since we can repeat any of the three digits). This gives a total of 3 x 3 x 3 = 27 possible 3-digit numbers.

The 27 possible 3-digit numbers with repetition are: 222, 223, 224, 232, 233, 234, 242, 243, 244, 322, 323, 324, 332, 333, 334, 342, 343, 344, 422, 423, 424, 432, 433, 434, 442, 443, and 444.

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the probability of drawing one card from a standard deck of cards and choosing a "face card" is 3/13.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

There are 12 face cards in a standard deck of 52 cards (4 jacks, 4 queens, and 4 kings). So the probability of drawing a face card from a standard deck of cards is:

P(face card) = number of face cards / total number of cards

P(face card) = 12/52

Simplifying the fraction, we get:

P(face card) = 3/13

Therefore, the probability of drawing one card from a standard deck of cards and choosing a "face card" is 3/13.

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Answer:

Step-by-step explanation:

I think that the answer is ................................................................................................................................................Your adopted

I think the answer is 5/6 ohohohohohohohohohohohoh

Answer:

[tex]54\pi \: {cm}^{2} [/tex]

Step-by-step explanation:

Given:

A cone

r (radius) = 3 cm

l = 15 cm

Find: A (surface area) - ?

[tex]a(surface) = \pi {r}^{2} + \pi \times r \times l[/tex]

[tex]a(surface) = \pi \times {3}^{2} + \pi \times 3 \times 15 = 9\pi + 45\pi = 54\pi \: {cm}^{2} [/tex]

He can wear them in 5! orders in over 5 days. The solution has been obtained by using permutations.

What is permutation?

A permutation is a combination of objects arranged in a particular sequence. The elements of sets are arranged in a linear or sequential manner in this instance.

We are given that John has pairs of red, orange, yellow, blue, and green socks. Repetition is not allowed because John puts his socks in the wash at the end of the day.

From this we get,

On first day he has five choices but the nest day he is left with only 4 choices, then 3 choices and so on.

So,

5 * 4 * 3 * 2 * 1 = 5!

Hence, he can wear them in 5! orders in over 5 days.

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Answer:

B and C.

Step-by-step explanation:

To solve this problem, we need to set up a system of equations based on the given information. Let x be the amount of pretzels (in grams) and y be the amount of peanuts (in grams) that Howard needs to buy.

Then we have:x + y = 25 (since Howard needs 25 grams of trail mix in total)

1x + 3.5y = 45 (since the pretzels cost $1 per gram and the peanuts cost $3.50 per gram, and Howard has $45 to spend)

Therefore, the correct answer choices are:X+y=25 and X+3.5y=45, or B and C.

The probability that an individual man's step length is less than 2.3 feet is approximately 0.1587 or 15.87% (rounded to 4 decimal places).

Explain probability

Probability is a branch of mathematics concerned with measuring the likelihood or chance of events occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means it is certain. Probability theory is used in many fields, including statistics, economics, physics, and engineering, to analyze and make predictions based on uncertain events.

According to the given information

The standardized value, also known as the z-score, is given by:

z = (x - mu) / sigma

Substituting the given values, we get:

z = (2.3 - 2.7) / 0.4

z = -1

Now we need to find the probability that an individual man's step length is less than 2.3 feet, which is equivalent to finding the area under the standard normal distribution curve to the left of the z-score -1.

Using a standard normal distribution table or calculator, we can find that the area to the left of -1 is 0.1587.

Therefore, the probability that an individual man's step length is less than 2.3 feet is approximately 0.1587 or 15.87% (rounded to 4 decimal places).

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Answer:

Step-by-step explanation:

Account 1 name - CIBC Smart Account

Account 2 name - CIBC Everyday Chequing Account

Account 3 name - CIBC US$ Personal Account

Monthly Fee ($)

Account 1- $4.95 to $14.95 per month, depending on the account balance and number of transactions

Account 2- $3.90 to $14.95 per month, depending on the account balance and number of transactions

Account 3- $0 for a minimum balance of US$3,000, otherwise $4.95 per month

Answer:

6,000

Step-by-step explanation:

then answer is 6,00 becasue if there are 3 times as much then just do 2000x3=6000

Answer:

[tex]\huge\boxed{\sf Perimeter = 18\ units}[/tex]

Step-by-step explanation:

Here, the shape is made up of grids measuring 1 unit.

Let's count grids on each side.

AB = 5 units

BC = 2 units

CD = 2 units

DE = 2 units

EF = 3 units

FA = 4 units

Now,

Perimeter = sum of all sides

Perimeter = 5 + 2 + 2 + 2 + 3 + 4

[tex]\rule[225]{225}{2}[/tex]

the two correct representations of the inequality are: x < 5

How to solve the inequalities?

To solve the inequality –3(2x – 5) < 5(2 – x), we need to simplify it first:

–6x + 15 < 10 – 5x

Now, we can move all the x terms to one side and the constant terms to the other side:

–6x + 5x < 10 – 15

–x < –5

Finally, we need to remember that whenever we multiply or divide an inequality by a negative number, we need to reverse the inequality sign. In this case, we multiplied both sides by –1, so we need to flip the sign:

x > 5

Therefore, the two correct representations of the inequality are:

x < 5 (not x > 5 as mentioned above)

–6x + 15 < 10 – 5x

Option 2, –6x – 5 < 10 – x, is not correct because it doesn't represent the inequality we simplified. The correct representation of the inequality on a number line would be an open circle at x=5 with a bold line pointing to the right, indicating that all the values to the right of 5 satisfy the inequality. The number line from –3 to 3 in increments of 1 with an open circle at negative 5 and a bold line pointing to the left does not represent the inequality we just solved.

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In Linear equation, The volume of the solution is 100ml.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                       Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with power 1 variables are known as linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.

Let the volume of the solution be represented by x.

Therefore, we can form an equation based on the information given which will be

= 15% × x = 54

15/100 × x = 54.

0.15 × x = 54

0.15x = 54

x = 54/0.54

x = 100 ml

The volume of the solution is 100ml.

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