In a simple random sample of 180 households, the sample mean number of personal computers was 2.58. Assume the population standard deviation is 0.48.Construct a 98% confidence interval for the mean number of personal computers. Round the answers to two decimal places, if necessary.

Answer:

5

Step-by-step explanation:

Answer:

odd numbers divisible by 5 such as 5,15,25,35,45,55 and so on

Theorem: If m and n are integers such that m|n, then m|(5n³ - 2n² + 3n).

Proof: Let n = km, where k is an integer. Then we can rewrite (5n³ - 2n² + 3n) as follows:

5n³ - 2n² + 3n = 5(km)³ - 2(km)² + 3(km)

= 5k³m³ - 2k²m² + 3km

= km(5k²m² - 2km + 3)

Since m|n, we know that n = km is divisible by m. Therefore, we can write km as m times some integer, which we'll call p. Thus, we have:

5n³ - 2n² + 3n = m(5k²p² - 2kp + 3)

Since (5k²p² - 2kp + 3) is also an integer, we have shown that m is a factor of (5n³ - 2n² + 3n). Therefore, if m and n are integers such that m|n, then m|(5n³ - 2n² + 3n).

To prove this theorem, we need to show that if m is a factor of n, then m is also a factor of (5n³ - 2n² + 3n). We start by assuming that n is equal to km, where k is some integer. This is equivalent to saying that m divides n.

We then substitute km for n in the expression (5n³ - 2n² + 3n) and simplify the expression to get 5k²m³ - 2k²m² + km. We notice that this expression has a factor of m, since the last term km contains m.

To show that m is a factor of the entire expression, we need to write (5k²m² - 2km + 3) as an integer. We do this by factoring out the m from the expression and writing it as m(5k²p² - 2kp + 3), where p is some integer. Since (5k²p² - 2kp + 3) is also an integer, we have shown that m is a factor of (5n³ - 2n² + 3n).

Therefore, if m and n are integers such that m|n, then m|(5n³ - 2n² + 3n).

To know more about factor  click on below link:

https://brainly.com/question/2058395#

#SPJ11

Answer:

12 is a rational number because it can be expressed as the quotient of two integers: 12 ÷ 1.

12 belongs to the sets of natural numbers, integer numbers, rational numbers, and real numbers.

First, we can see that it is a whole number, so it is an integer number.

Also, all positive integers are natural numbers, so 12 is also a whole number.

Now, we also can rewrite 12 as:

12 = 12/1

So it is a quotient between two integer numbers, thus, 12 is also a rational number.

Finally, the trivial answer, 12 belongs to the set of the real numbers (the set that contains all the numbers).

Concluding:

12 belongs to the sets of whole numbers, integer numbers, rational numbers, and real numbers.

If you want to learn more about sets of numbers:

https://brainly.com/question/20118982

#SPJ1

The learning rate in gradient descent determines the step size and should be not too small or too large, as it can cause the algorithm to converge slowly or overshoot the minimum; adjusting the value of the learning rate can fix the problem, but the optimal value depends on the problem and data set.

According to the given information:

When running gradient descent,

The learning rate α determines the step size taken in each iteration toward the optimal solution.

If α is too small, the algorithm will take small steps and will converge slowly, or may even get stuck in a local minimum.

If α is too large, the algorithm may overshoot the minimum and diverge, or bounce back and forth without converging.

In the scenario described, the learning rate α of 0.5 appears too large, causing J(θ) to increase over time.

This suggests that the algorithm is not converging and is overshooting the minimum.

To fix this,
The value of α can be adjusted by reducing it to a smaller value,

Such as 0.1 or 0.01.

This should allow the algorithm to take smaller steps towards the minimum and eventually converge to a lower value of J(θ).

To learn more about statistics visit:

https://brainly.com/question/30765535

#SPJ4

Answer:

I think it is 671

Step-by-step explanation:

The 2 sides are the same length because of those dashes on them so 61 + 61 = 122.

144 - 122 = 22 which is the base

Area is  "Base times height divided by two"

The height is 61

so the area is (22 x 61) / 2

22 x 61 = 1,342

1,342 divided by 2 is 671

I think this is right, im sorry if it is wrong.

Answer:

7/20

0.35

35%

Step-by-step explanation:

12 year olds: 40%

12 year olds: 25%

11 year olds: 100% - 40% - 25% = 35%

35% = 35/100 = 7/20

35% = 0.35

35% = 35%

(a) No, Sarah would not be able to consume 3 snacks and movies because she has a limited weekly income of $50, and she spends it all on snacks and movies. If she were to consume 3 snacks and movies, the total cost would be $45 ($15 for 3 snacks and $30 for 3 movie tickets), which would exceed her weekly income of $50.

(b) To maximize utility, Sarah should allocate her income between snacks and movies in such a way that the marginal utility per dollar spent on each good is equal. We can calculate the marginal utility per dollar for each good by dividing the marginal utility of the good by its price.

For snacks, the marginal utility per dollar is:

MU_snacks / P_snacks = 10 / 5 = 2

For movies, the marginal utility per dollar is:

MU_movies / P_movies = 15 / 10 = 1.5

Since the marginal utility per dollar spent on snacks is greater than the marginal utility per dollar spent on movies, Sarah should consume more snacks and fewer movies to maximize her utility.

To find the optimal combination of snacks and movies, we can use the budget constraint:

P_snacks * Q_snacks + P_movies * Q_movies = Income

Substituting the given values, we get:

5Q_snacks + 10Q_movies = 50

We can rearrange this equation to get:

Q_movies = (50 - 5Q_snacks) / 10

Now, we can maximize utility by setting the marginal utility per dollar spent on snacks equal to the marginal utility per dollar spent on movies:

MU_snacks / P_snacks = MU_movies / P_movies

10 / 5 = MU_movies / 10

MU_movies = 15

From the table, we can see that Sarah gets a marginal utility of 15 from the first movie and a marginal utility of 5 from the second movie. Therefore, Sarah should consume one movie and 7 snacks to maximize her utility.

(c) The total utility Sarah will receive from consuming one movie and 7 snacks is:

MU_snacks * Q_snacks + MU_movies * Q_movies

= 10 * 7 + 15 * 1

= 105

Therefore, Sarah will receive a total utility of 105 utils.

(d) If Sarah's income increases to $60, her budget constraint will shift outward. The marginal utility per dollar spent on movies will decrease because the price of movies has stayed the same while her income has increased. Sarah will be able to buy more movies without giving up any snacks, so her consumption of movies will increase, while her consumption of snacks will stay the same.

(e) To determine whether Sarah would be better off buying two more snacks or one more movie ticket, we need to compare the marginal utility per dollar spent on each good.

For two more snacks: MU(2 snacks) / (2 x P(snacks)) = [(20 + 15) / (2 x 5)] = 3 utils per dollar spent

For one more movie: MU(movie) / P(movie) = (20 / 10) = 2 utils per dollar spent

Since the marginal utility per dollar spent on two more snacks is higher than that of one more movie ticket, Sarah will be better off buying two more snacks.

Visit here to learn more about marginal utility brainly.com/question/14149928

#SPJ11

Answer:

A

Step-by-step explanation:

the zero is significant

7540

Answer:

it is given , angle 2 , angle 3 , converse alternate exterior angles theorem

Step-by-step explanation:

We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because  it is given . We see that angle 2 is congruent to  angle 3  by the alternate interior angles theorem. Therefore, angle 1 is congruent to angle 2 by the transitive property. So, we can conclude that lines p and q are parallel by the converse alternate exterior angles theorem .

Answer:

✔ it is given

✔ angle 2

✔ angle 3

✔ converse alternate exterior angles theorem

Answer:

My best answer is 8x^6y^8

Step-by-step explanation:

Answer:

The value of V is  double of Q is

D)  V = 2Q

Step-by-step explanation:

A)

  The value of V is the square of Q

        V = Q²

B)

The value of V is the addition '2' of Q

       V = Q+2

C)

The value of V is the divided 'Q' by'2'

  V = Q/2

D)

The value of V is  double of Q is in notation

V = 2Q

Answer:

X intercept is (3,0)

Y intercept is (0,-10)

Step-by-step explanation:

The X intercept is where the line crosses the X axis

The Y intercept is where the line crosses the Y axis

Hope this helps.

False. A probability distribution for a discrete variable is not exclusive, collectively exhaustive list of numerical outcomes for that variable and the probability of occurrence associated with each outcome.

A probability distribution for a discrete variable is a list of all possible values that the variable can take on, along with the probability of each value occurring. The values must be collectively exhaustive (meaning they include all possible outcomes) and mutually exclusive (meaning that each outcome cannot occur at the same time as any other outcome). However, the numerical outcomes do not have to be exclusive, as they can have the same probability of occurring. For example, a coin toss has two possible outcomes (heads and tails) with equal probability, and a dice roll has six possible outcomes with equal probability. These probabilities can be represented using a probability distribution.

For more questions like Probability visit the link below:

https://brainly.com/question/16925724

#SPJ11

Answer:

The answer for your question is 15

Answer:

The Least common multiple of 5 and 3 is 15

Answer:14 dvd’s

Step-by-step explanation:

Answer:

the blank is -1/5

brainliest please?

When something decreases by 15.7%, the growth factor is about 1.182 and when something decreases by 0.12%, the growth factor is about 1.00012.

In math, what is the definition of multiplying?

Multiplication is a mathematical process that shows the amount of times a number has been added to itself. It is represented by the multiplication symbols (x) or (*). Division is a mathematical process that shows how many equal amounts add up to a given quantity.

If something decreases by 15.7%, the increase in the factor is 100 / (100 - 15.7) Equals 1.182.

As a result, when something decreases by 15.7%, the growth factor is about 1.182.

When something falls by 0.12%, the expansion factor is 100 / (100 - 0.12) = 1.00012.

As a result, when something decreases by 0.12%, the growth factor is about 1.00012.

To know more about Multiplying visit:

brainly.com/question/23536361

#SPJ1

Answer:

(8x-7)(8x+7)

Step-by-step explanation:

64x²-49

(8x)²-7²

(8x+7)(8x-7) (using a²-b²=(a+b)(a-b)

Or

(8x-7)(8+7)

Answer:

(0,-5)

Step-by-step explanation:

Terminal minus initial. (3-3, -7+2) = (0,-5)

A statement which best describes the graph of y ≥ -x² + 8x - 2 include the following: B. The vertex is at (4, 14). The parabola is a solid line that opens down. Shading is above the parabola.

Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, we can logically deduce that the graph is a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).

By critically observing the graph of the given quadratic function, we can logically deduce that the solutions (roots) and vertex are as follows;

x = 0.258, y = 0.

x = 7.742, y = 0.

Vertex = (4, 14).

Read more on quadratic functions here: brainly.com/question/2272989

#SPJ1

Answer:

If you mean the angle at X... 70°

Step-by-step explanation:

Answer:

36 square units

Step-by-step explanation:

The figure is made up of a rectangle above with length 6 and width 4.

The bottom part is a triangle with a base of 6 and a height of 4.

total area = area of rectangle + area of triangle

total area = LW + bh/2

total area = 6 × 4 + 6 × 4/2

total area = 24 + 12

total area = 36

Answer:

36 square units

Step-by-step explanation:

We can split the given figure into two familiar figure by drawing a line segment as shown in the attached figure

This splits the composite figure into a rectangle at the top and an inverted triangle at the bottom

The rectangle has a length(horizontal portion) of 6 units and a width(vertical portion) of 4 units

Area of rectangle = length x width = 6 x 4 = 24 square units

The triangle has a base of 6 units and a height of 4 units

Area of rectangle = 1/2 x base x height = 1/2 x 6 x 4 = 1/2 x 24 = 12 square units

Area of figure = 24 + 12 = 36 square units

The value of p is 2.

The value of q is 14

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Two functions:

f(x) = 3x + p

g(x) = px + 4

Now,

f(g(x)) = 6x + 9

This means,

3(g(x)) + p = 6x + q

Substituting g(x) = px + 4.

3(px + 4) + p = 6x + q

3px + 12 + p = 6x + q

3px + (p - q) = 6x - 12

This means,

3p = 6

p = 2

p - q = -12

2 - q = -12

q = 2 + 12

q = 14

Thus,

p is 2 and q is 14.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ2

The probability of choosing sausage and onion by Rosa's mom from the given 8 different toppings as per given condition is equal to

(1/ ⁸C₂).

As given in the question,

Total number of different toppings = 8

Number of different toppings choose by Rosa's mom randomly = 2

Possibility of choosing sausage and onion (any one) = 1

Total number of outcomes = ⁸C₂

Number of favorable outcomes = 1

Probability of choosing sausage and onion ( exactly ) one topping

= ( Number of favorable outcomes ) / ( Total number of outcomes )

= ( 1/⁸C₂ )

Therefore, the probability when Rosa's mom chooses sausage and onion out of 8 toppings is equal to ( 1/⁸C₂ ).

The above question is incomplete, the complete question is:

A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings

below:

Pepperoni ,Sausage, Chicken ,  Green pepper , Mushroom ,Pineapple, Ham, Onion

Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 2 different toppings.

What is the probability that Rosa's mom chooses sausage and onion?

Learn more about probability here

brainly.com/question/11234923

#SPJ4

Answer:

1/8c^2

Step-by-step explanation:

Khan Acadmey

Given:

\(\begin{aligned}&x^2+y^2=16 \\&z=x y\end{aligned}\)

Express 16 as \(4^{2}\): \(x^2+y^2=16\)

\(x^2+y^2=4^2\\x^2+y^2=4^2 \times 1\)

Trignometry,

\(\cos ^2(t)+\sin ^2(t)=1\)

Now, substitute \(\cos ^2(t)+\sin ^2(t)\) for 1:

\(\begin{aligned}&x^2+y^2=4^2 \times 1 \\&x^2+y^2=4^2 \times\left[\cos ^2(t)+\sin ^2(t)\right]\end{aligned}\\x^2+y^2=4^2 \times \cos ^2(t)+4^2 \times \sin ^2(t)\)

Law of indicates:
\(\begin{aligned}&x^2+y^2=[4 \times \cos (t)]^2+[4 \times \sin (t)]^2 \\&x^2+y^2=[4 \cos (t)]^2+[4 \sin (t)]^2\end{aligned}\\x^2=[4 \cos (t)]^2 \text { and } y^2=[4 \sin (t)]^2\)

Taking positive square roots as follows:

\(x=4 \cos (t), y=4 \sin (t)\)

Recall that, z = xy.

Now, we have:

\(\begin{aligned}&z=4 \cos (t) \times 4 \sin (t) \\&z=16 \cos (t) \cdot \sin (t)\end{aligned}\)

Now, substitute the values:
\(r(t)=x_t i+y_t j+z_t k\)

So, the vector r(t) is: \(r(t)=(4 \cos (t)) i+(4 \sin (t)) i+(16 \cos (t) \cdot \sin (t)) i\)

Therefore, the vector function r(t) is written as: \(r(t)=x_t i+y_t j+z_t k\)

Know more about vector functions here:

https://brainly.com/question/14895420

#SPJ4

To solve the inequality -6x < 36, we need to isolate x on one side of the inequality sign. We can do this by dividing both sides of the inequality by -6, remembering to reverse the inequality sign because we are dividing by a negative number:

-6x < 36

x > -6

Therefore, the solution set for the inequality is {x | x > -6}.

Answer:

-2/3

Step-by-step explanation:

Rise= -2

Run= 3

-2/3

Answer:

0 - 1 - 2 - 3 - 4 - 5

2 - 22.1 - 32.4 - 32.9 - 23.6 - 4.5

Step-by-step explanation:

The function is:

Calculating the value of H for each value of t from 0 to 5

Correct answer choice is the 3rd one or C

Yes the graph of the function represents a linear piecewise function of x.

From the graph we can see that the function can be broken down into 3 distinct parts.

Let us take the first part of the graph which represents the function:

For values of x ranging from negative infinity to 0, the value of y is 2 .

So the function is of the form y = 2.

Now for the second slanting part of the function.

The function passes through the points (0,2) and (2,-2)

Slope of the line = (-2-2)/(2-0) = -2

Equation of the line :

y-2 = -2(x)

or, y + 2x = 2.

Now for the third part of the function is y = -2 for all x>2

Hence the piecewise function can be represented as for the domain of x:

     {2 , x < -2 }

y = {2-2x , -2 ≤ x ≤ 2}

     {-2 , x > 2}

Hence all parts are linear so the function is linear in nature.

To learn more about function visit:

https://brainly.com/question/21107621

#SPJ9