Use the discriminant to determine the number of real solutions for each quadratic equation. Do not solve.

The closest option is (d) 12.054 to 15.946.

To find the confidence interval for the mean of a normal population, we use the formula:

CI = x ± z* (σ/√n)

where x is the sample mean, z* is the critical value from the standard normal distribution corresponding to the desired confidence level (80% in this case), σ is the population standard deviation (unknown), and n is the sample size.

Since the population standard deviation is unknown, we can estimate it using the sample standard deviation:

s = √[ Σ(xi - x)² / (n - 1) ]

where xi is the ith observation, x is the sample mean, and n is the sample size.

Plugging in the values from the sample, we get:

x = (10 + 12 + 18 + 16) / 4 = 14

s = √[ (10-14)² + (12-14)² + (18-14)² + (16-14)² / 3 ] = 2.94

To find the critical value, we look it up from a standard normal distribution table or use a calculator. For an 80% confidence interval, the critical value is approximately 1.282.

Plugging in all the values, we get:

CI = 14 ± 1.282 * (2.94 / √4) = 14 ± 1.4952

Therefore, the 80% confidence interval for the mean is:

CI = (14 - 1.4952, 14 + 1.4952) = (12.5048, 15.4952)

The closest option is (d) 12.054 to 15.946.

To learn more about sample standard deviation visit:

https://brainly.com/question/24277447

#SPJ11

The firm's total revenue is $104,000, its total cost is $156,000, and its profit (or loss) is -$52,000.

Finding the profit-maximizing output.
According to the information provided,

The MR (market price)  $400.

Locating the point where the MC curve intersects with the MR curve at a price of $400.

Let's assume the quantity at this intersection = 260 (since 205 and 365 are not mentioned as intersecting points).

Total revenue

= Price × Quantity
= $400 × 260
= $104,000

Total cost

= ATC × Quantity
=$600 × 260
= $156,000

Profit

= Total revenue - Total cost
= $104,000 - $156,000
= -$52,000

To learn more about revenue: https://brainly.com/question/16232387

#SPJ11

The y-intercept of equation 11 + 2t where t is the months after the birth of the baby is 11.

The equation 11 + 2t is modeled by the situation where the weight, in pounds, of a newborn baby after t months is stated.

An equation is represented by y = b + mx where b is the y-intercept and m is the slope of the graph. On comparing the given equation 11 + 2t by the standard equation we have 11 as the intercept and 2 as the slope.

We can interpret from the given context and the equation that the newborn baby is born with 11 pounds weight at birth and with every month there is an increase of 2 pounds in the weight of the newborn.

Learn more about Equation:

https://brainly.com/question/28732353

#SPJ4

The length of the missing sides of the two quadrilaterals are listed below:

In this problem we must determine the length of missing sides in two quadrilaterals, this can be done with the help of Pythagorean theorem and properties for special right triangles:

r = √(x² + y²)

45 - 90 - 45 right triangle

r = √2 · x = √2 · y

Where:

Now we proceed to determine the missing sides for each case:

a = √[(6 - 3)² + 4²]

a = √(3² + 4²)

a = √25

a = 5

Case 2

z = √[(22 - 4√2 - 15)² + 4²]

z = √[(7 - 4√2)² + 4²]

z = 4.219

To learn more on quadrilaterals: https://brainly.com/question/28335375

#SPJ1

The linear approximation of F at (Pi, 0) is [tex]-Pi^2cos^2(Pi).[/tex]

To discover the linear approximation of the given function at (Pi, 0), we need to first discover the partial derivatives of the function with respect to x and y evaluated at (Pi, zero).

Partial derivative of F with recognize to x:

∂F/∂x = -2sin(x)cos(x)

evaluated at (Pi, 0):

∂F/∂x(Pi, 0) = -2sin(Pi)cos(Pi) = 0

Partial derivative of F with recognize to y:

∂F/∂y = 1/(2√y)

evaluated at (Pi, 0):

∂F/∂y(Pi, 0) = 1/(2√0) = undefined

For the reason that partial derivative of F with respect to y is undefined at (Pi, 0), we can't use the multivariable Taylor collection to discover the linear approximation. as an alternative, we will use the formula for the linear approximation:

[tex]L(x,y) = f(a,b) + ∂f/∂x(a,b)(x-a) + ∂f/∂y(a,b)(y-b)[/tex]

Wherein (a,b) is the factor at which we want to find the linear approximation.

In this case, a = Pi and b = 0. So, the linear approximation is:

[tex]L(x,y) = F(Pi, 0) + ∂F/∂x(Pi, 0)(x - Pi)[/tex]

[tex]L(x,y) = sqrt(0) + (cos(Pi))^2(0 - Pi)[/tex]

[tex]L(x,y) = -Pi^2cos^2(Pi)[/tex]

Consequently, the linear approximation of F at (Pi, 0) is [tex]-Pi^2cos^2(Pi).[/tex]

Learn more about  linear approximation :-

https://brainly.com/question/28384323

#SPJ4

Answer:

Step-by-step explanation:

If I found the mean, the answer would be:

3+ 4+4+4+5+6+7+23= 56

56/ 8 = 7

If I found the average value using the median, the answer would be 4.5.

In this set of data, the anomaly is 23 as it is much higher than the other numbers.

The median is more accurate because it find the more ‘central’ number and is not affected as greatly with anomalies whereas the mean is affected greatly with anomalies as it raises the value significantly.

Therefore, the median is better to work out the average in this set of data.

:)

The surface area of a surface parametrized by a function f(s, t), we use the formula:

Surface Area = ∫∫ √[f_s(s,t)^2 + f_t(s,t)^2 + 1] ds dt

The formula above calculates the surface area by integrating the square root of the sum of the squares of the partial derivatives of f with respect to s and t, plus one, over the surface.

Essentially, the formula is finding the magnitude of the gradient of the surface, which gives the rate of change of the surface in all directions.

Surface Area = ∫∫ √[f_s(s,t)^2 + f_t(s,t)^2 + 1] ds dt

The surface area formula can be used to find the surface area of various types of surfaces, such as parametric surfaces, implicit surfaces, and surfaces of revolution.

However, the integration required to evaluate the formula can be quite challenging, especially for complex surfaces. In such cases, numerical methods may be used to approximate the surface area.

Learn more about Surface area:

brainly.com/question/29298005

#SPJ11

Answer: Answer below in pic

Step-by-step explanation:

:)

The value of b as shown from the steps below is -21.

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

Given the equation:

4(b + 5) = 3b - 1

Opening the parenthesis:

4b + 20 = 3b - 1

Subtracting 3b from both sides:

b + 20 = -1

Subtracting 20 from both sides:

b = -21

The value of b is -21.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Han's retirement account earns $247,163.25 in simple interest.

To find the simplest interest, we need to use the formula:

Simple Interest = Principal × Rate × Time

In this case, the Principal is $410,000 and the Rate is $15,785 per year. We don't know the time period, but we can solve for it using the formula:

Time = Simple Interest ÷ (Principal × Rate)

Plugging in the values, we get:

Time = $15,785 ÷ ($410,000 × 1) = 0.0385 years

Therefore, the simplest interest is:

Simple Interest = $410,000 × $15,785 × 0.0385 = $247,163.25

So Han's retirement account earns $247,163.25 in simple interest.

To learn more on Percentage click:

https://brainly.com/question/24159063

#SPJ1

A table that shows the length and width of at least 3 different rectangles is shown below.

All the rectangles have the same perimeter.

An equation to represent the relationship is x + y = 18.

The independent variable is length and the dependent variable is width.

A graph of the points is shown in the image below.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(x + y)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

36 = 2(x + y)

18 = x + y

Length       Width     Perimeter

10                   8              36

14                   4              36

15                   3              36

Read more on perimeter of a rectangle here: brainly.com/question/28695033

#SPJ1

P(x = a), is always zero because there are an infinite number of possible values within the given range

a. The specific characteristics of the discrete probability distribution function are:
1. It represents the probabilities of a finite number of distinct outcomes, where each outcome has a non-negative probability.
2. The sum of the probabilities of all possible outcomes is equal to 1.
3. The probability of a particular outcome, P(x = a), can be directly computed from the function.

b. Three characteristics of a binomial experiment are:
1. There are a fixed number of trials (n) conducted independently.
2. Each trial has only two possible outcomes, often referred to as "success" and "failure".
3. The probability of success (p) is constant for all trials.

c. For continuous probability distribution:
1. Outcomes: The outcomes are represented by continuous random variables that can take an infinite number of values within a specified range.
2. Graph and area under the graph: The graph of the continuous probability distribution is a curve, and the area under the curve represents the probabilities associated with the range of values. The total area under the curve is equal to 1.
3. P(x = a): For a continuous distribution, the probability of the random variable equaling a specific value, P(x = a), is always zero because there are an infinite number of possible values within the given range.

To know more about "Probability" refer here:

https://brainly.com/question/30034780#

#SPJ11

We can use the recurrence relation for Bessel functions on the terms involving J_(n+2)(x):

x^2J"n(x) = (n^2 - n)J_n(x) - xJ_(n+1)(x) + (n+2)x^2J_n(x) + 2nxJ_(n+2)(x) + (d/dx)^(n-2) [xJ_n(x) +

To prove the given identity, we will start with the following expression:

x^2J_(n+1)(x) = xJ_n(x) + xJ_(n+2)(x) (Recurrence relation for Bessel functions)

Now, let's differentiate both sides of the above equation n times with respect to x:

(d/dx)^n [x^2J_(n+1)(x)] = (d/dx)^n [xJ_n(x)] + (d/dx)^n [xJ_(n+2)(x)]

Using the Leibniz rule for differentiating products, we can expand each term on the right-hand side:

(d/dx)^n [x^2J_(n+1)(x)] = x(d/dx)^n [J_n(x)] + n(d/dx)^(n-1) [J_n(x)] + (d/dx)^(n-2) [J_n(x)] + x(d/dx)^n [J_(n+2)(x)] + 2n(d/dx)^(n-1) [J_(n+2)(x)] + (d/dx)^(n-2) [J_(n+2)(x)]

Now, we can use the recurrence relation for Bessel functions on the terms involving J_n(x) and J_(n+2)(x):

(d/dx)^n [x^2J_(n+1)(x)] = xJ_(n-1)(x) + nJ_(n-1)(x) + (d/dx)^(n-2) [J_n(x)] + xJ_(n+3)(x) + 2nJ_(n+3)(x) + (d/dx)^(n-2) [J_(n+2)(x)]

We can simplify the above expression using the following identity:

(d/dx)^n [xJ_n(x)] = xJ_(n-n)(x) + nJ_(n-1)(x)

Substituting this identity into the above equation, we get:

(d/dx)^n [x^2J_(n+1)(x)] = xJ_n(x) + nJ_n(x) - nJ_(n-1)(x) + xJ_(n+2)(x) + 2nJ_(n+2)(x) + (d/dx)^(n-2) [J_n(x) + J_(n+2)(x)]

Next, we can multiply both sides of this equation by x^2 and simplify using the identity:

(n+1)J_n(x) = xJ_(n+1)(x) + xJ_(n-1)(x)

Multiplying both sides by x and substituting the resulting expression into the previous equation, we obtain:

x^2J"n(x) = (n^2 - n)J_n(x) - xJ_(n+1)(x) + x^2J_(n+2)(x) + 2nxJ_(n+2)(x) + (d/dx)^(n-2) [xJ_n(x) + xJ_(n+2)(x)]

Now, we can use the recurrence relation for Bessel functions on the terms involving J_(n+2)(x):

x^2J"n(x) = (n^2 - n)J_n(x) - xJ_(n+1)(x) + (n+2)x^2J_n(x) + 2nxJ_(n+2)(x) + (d/dx)^(n-2) [xJ_n(x) +

To learn more about differentiate visit:

https://brainly.com/question/31495179

#SPJ11

For the first question, we need to assign truth values to q, r, and s such that the pair of statements are not equivalent. For (a) sv(sq) and svq, we can assign q = True, r = False, and s = False. This makes sv(sq) True and svq False, thus showing that the two statements are not equivalent. For (b) (s19)►r and (-84-9)vr, we can assign q = False, r = True, and s = False. This makes (s19)►r False and (-84-9)vr True, thus showing that the two statements are not equivalent.

For the second question, we can construct the compound proposition as follows: (a∧b)∨(a∧c)∨(a∧d)∨(b∧c)∨(b∧d)∨(c∧d). This proposition is true precisely when at least two of the variables a, b, c, and d are true. We can see that this is the case because for the proposition to be true, at least two of the terms in the disjunction need to be true, each of which represents the case where at least two variables are true. For example, (a∧b) represents the case where both a and b are true, and (a∧c) represents the case where both a and c are true, and so on. Therefore, the given compound proposition satisfies the condition of being true precisely when at least two of the variables are true.

More on equivalent values: https://brainly.com/question/2972832

#SPJ11

The equation of the ellipse is 32(x + 7)² + 144(y + 9)² = 4608.

We have,

To determine the equation of an ellipse with a horizontal major axis, centered at the point (h,k), with a focus at (h + c, k) and a co-vertex at

(h, k + b), we can use the following formula:

(x - h)² / a² + (y - k)² / b² = 1

where:

h and k are the x- and y-coordinates of the center of the ellipse

a is the length of the semi-major axis (half of the length of the major axis)

b is the length of the semi-minor axis (half of the length of the minor axis)

c is the distance from the center of the ellipse to each focus

In this case,

The center of the ellipse is (-7, -9), the focus is (1, -9), and the co-vertex is (-7, -3).

The center of the ellipse is:

h = -7

k = -9

The distance between the center and the focus is:

c = 1 - (-7) = 8

The distance between the center and the co-vertex is:

b = 3 - (-9) = 12

Since the focus is to the right of the center, the major axis is horizontal, so the length of the semi-major axis is:

a = √(c² - b²) = √(8² - 12²) = 4 x √(2)

Now,

The equation of the ellipse is:

(x + 7)² / (4 x √(2))² + (y + 9)² / 12² = 1

Simplifying:

(x + 7)² / 32 + (y + 9)² / 144 = 1

Therefore,

The equation of the ellipse is:

32(x + 7)² + 144(y + 9)² = 4608

Learn mroe about ellipses here:

https://brainly.com/question/19507943

#SPJ1

The statement is false.

The projection of vector u onto vector v, denoted as proj_v u, is not necessarily a multiple of vector u.

In the case of vector projection, proj_v u is a scalar multiple of vector v, not vector u. It represents the component of vector u that lies in the direction of vector v.

This projection is obtained by taking the dot product of u and v, divided by the dot product of v and itself (which is equivalent to the magnitude of v squared), and then multiplying it by vector v. The resulting projection is parallel to vector v and can be scaled by a scalar factor, but it does not necessarily align with vector u.

Therefore, option c is the correct answer. Proj_v u is a multiple of vector v, not vector u.

Learn more about Vector:

brainly.com/question/24256726

#SPJ11

The parent functions that have negative y-values are those that are located below the x-axis.

These functions include the linear function with a negative slope, the quadratic function with a negative leading coefficient, the cubic function with a negative leading coefficient, and any other odd-degree polynomial function with a negative leading coefficient. Additionally, any exponential function with a negative base will also have negative y-values.

For example, the linear function y = -2x has a negative slope and will have negative y-values for any x values greater than zero. Similarly, the quadratic function y =

[tex]x^2[/tex]

will have negative y-values for all x values. The cubic function y =

[tex]-2x^3[/tex]

and the exponential function y = -

[tex]3^x[/tex]will also have negative y-values.

Any parent function that is located below the x-axis will have negative y-values. This can be determined by examining the equation of the function and its graphical representation.

Learn more about parent functions here:

https://brainly.com/question/17112852

#SPJ4

The coordinates of the vertices after the reflection across x = 1 are:

⇒ X'(2,-3),  W(1,0),  V'(2,1)

Now First, let's visualize the reflection across x = 1.

This means that all points will have the same x-coordinate but their y-coordinate will be mirrored across the line x = 1.

So, X(0,-3) will reflect to X'(2,-3),

Since, the distance between X and the line x = 1 is 1 unit,

and the y-coordinate of X' will be the same as that of X.

Similarly, W(1,0) will remain unchanged, as it lies on the line of reflection.

And, Lastly, V(4,1) will reflect to V'(2,1),

Since, the distance between V and the line x = 1 is 3 units, and the y-coordinate of V' will be the same as that of V.

Therefore, the coordinates of the vertices after the reflection across x = 1 are:

⇒ X'(2,-3),  W(1,0),  V'(2,1)

Learn more about the coordinate visit:

https://brainly.com/question/24394007

#SPJ1

Natalia's minimum hourly wage to support her family of 4 is $16.98.

The minimum hourly wage can be determined using some of the basic mathematical operations, including multiplication, addition, and division.

The estimated yearly income to support the first person = $18,946

The additional income required to support each additional person in the family = $4,437

The number of family members in Natalia's = 4

Natalia's work week hours = 38

The number of weeks per year = 50

Total work week hours per year = 1,900 hours (38 x 50)

First person's income = $18,946

Additional income for 3 = $13,211 ($4,437 x 3)

Total income = $32,257

Hourly wage = $16.98 ($32,257 ÷ 1,900)

Learn more about mathematical additions at bhttps://brainly.com/question/4721701.

#SPJ1

The best measure of variability for the data and the player which was more consistent include the following: B. Player B is the most consistent, with a range of 9.

In Mathematics and Statistics, interquartile range (IQR) of a data set and it is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):

Interquartile range (IQR) of Player A = Q₃ - Q₁

Interquartile range (IQR) of Player A = 4 - 1.5

Interquartile range (IQR) of Player A = 2.5.

Range of Player A = Highest number - Lowest number

Range of Player A = 8 - 1

Range of Player A = 7

Interquartile range (IQR) of Player B = Q₃ - Q₁

Interquartile range (IQR) of Player B = 5 - 1.5

Interquartile range (IQR) of Player B = 4.5.

Range of Player B = Highest number - Lowest number

Range of Player B = 10 - 1

Range of Player B = 9

Read more on range here: brainly.com/question/17083142

#SPJ1

The graph of g(x) is a V-shaped graph centered at x = -3, with the vertex at (-3, -2), and opening downward.

We have,

The graph of the function g(x) = -|x+3| - 2 can be obtained by first graphing the function f(x) = |x| and then transforming the graph.

The function f(x) = |x| is a V-shaped graph that passes through the origin and has a slope of 1 on either side of the origin.

The function -|x| is the reflection of f(x) about the x-axis and has the same shape, but opens downwards.

To obtain the graph of g(x) = -|x+3| - 2, we first shift the graph of -|x| three units to the left to get the graph of -|x+3|.

This means that the V-shape of the graph is centered at x = -3.

Then we shift the entire graph downward by 2 units to get the final graph of g(x).

Therefore,

The graph of g(x) is a V-shaped graph centered at x = -3, with the vertex at (-3, -2), and opening downward.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ1

The temperature of the object at time t = 70 is approximately 93.26 degrees.

To solve the problem, we can use the solution to the differential equation given by equation 2.15:

u(t) = [tex]Ce^[/tex](-kt) + A,

where C is a constant that we need to determine from the initial condition u(0) = 120. Substituting t = 0 and u(0) = 120 into the equation, we get:

120 = Ce^(-k*0) + A

120 = C + A

Next, we need to determine the value of C using the information that at t = 50, the temperature of the object is 100 degrees:

100 = Ce^(-k*50) + 90

10 = Ce^(-2.5)

Solving for C, we get:

C = 10/e^(-2.5)

C ≈ 14.868

Now we can use the value of C and equation 2.15 to find the temperature of the object at t = 70:

u(70) = 14.868e^(-0.05*70) + 90

u(70) ≈ 93.26 degrees

Therefore, the temperature of the object at time t = 70 is approximately 93.26 degrees.

To learn more about  temperature visit:

https://brainly.com/question/29768169

#SPJ11

The amount of feed the container can hold is 232 11/16 cubic inches. The correct option is the third option - two hundred thirty-two and eleven-sixteenths in3

From the question, we are to calculate how much feed the container can hold.

From the given information, the container is a rectangular prism

To calculate how much fed the container can hold, we will determine the volume of the rectangular prism

Volume of a rectangular prism is given by the formula

Volume = Length × Width × Height

Thus,

Volume of the container = 4 1/4 × 18 1/4 × 3

Volume of the container = 232 11/16 cubic inches

Hence,

The quantity of feed it can hold is 232 11/16 cubic inches

Learn more on Calculating volume here: https://brainly.com/question/5793407

#SPJ1

Answer:

45 2/3, or 45.666666..., rounded to the nearest tenth is 45.7.

The probability that the first card will be a club, the second card will be a black card, and the third card will be an ace is 1/104.

There are 13 clubs, 26 black cards (13 clubs and 13 spades), and 4 aces in a standard deck of cards. Since the cards are drawn with replacement, the probability of drawing a club on the first draw is 13/52 = 1/4. The probability of drawing a black card on the second draw is 26/52 = 1/2, and the probability of drawing an ace on the third draw is 4/52 = 1/13.

By the multiplication rule of probability, the probability of all three events occurring together is the product of their individual probabilities:

P(club, black, ace) = P(club) × P(black) × P(ace)

= (1/4) × (1/2) × (1/13)

= 1/104

Therefore, the probability that the first card will be a club, the second card will be a black card, and the third card will be an ace is 1/104.

Learn more about probability at https://brainly.com/question/4362589

#SPJ11

According to current fiscal policy theory, the best decision to help end a recession in the United States would be to increase government spending. This is based on the Keynesian theory that during a recession, there is a lack of aggregate demand in the economy, and government spending can help stimulate demand and encourage economic growth.

By increasing government spending on infrastructure, education, and other public services, it can create jobs, increase consumer spending, and boost economic activity. Additionally, the government can also implement tax cuts, which can give consumers more disposable income to spend and also stimulate demand.

However, it's important to note that the effectiveness of fiscal policy in ending a recession can be influenced by various factors such as the magnitude of the recession, the timing of the policy implementation, and the government's ability to finance the policy measures. Therefore, policymakers need to carefully consider all of these factors and adjust their decisions accordingly.
According to current fiscal policy theory, the best decision to help end a recession in the United States would involve implementing expansionary fiscal measures. This typically includes increasing government spending, cutting taxes, or a combination of both, which in turn stimulates economic activity and growth.

Expansionary fiscal policy works by injecting more money into the economy, which increases aggregate demand. This leads to higher levels of output and employment, eventually helping to alleviate the negative effects of a recession. Increased government spending can come in various forms, such as investments in infrastructure, public services, or direct financial assistance to individuals and businesses. Tax cuts provide more disposable income for consumers and lower costs for businesses, promoting spending and investment.

To implement these decisions, policymakers need to consider various factors, such as the severity of the recession, the level of public debt, and the effectiveness of specific fiscal measures in achieving the desired outcomes. It is essential to strike the right balance to avoid causing inflation or exacerbating long-term fiscal imbalances.

In conclusion, current fiscal policy theory suggests that the best decision to help end a recession in the United States involves implementing expansionary fiscal measures, such as increasing government spending and cutting taxes. These actions stimulate economic growth and alleviate the negative impacts of a recession, ultimately contributing to economic recovery.

Learn more about investments at : brainly.com/question/14682309

#SPJ11

To calculate the selling price of the house, we can use the formula for a mortgage:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Where:
M = monthly payment
P = principal (selling price)
i = interest rate per month (4.5%/12)
n = total number of payments (30 years x 12 months)

We know that the monthly payment is $811 and the total number of payments is 30 years x 12 months = 360 months. So we can solve for the principal:

$811 = P [ (0.045/12) (1 + 0.045/12)^360 ] / [ (1 + 0.045/12)^360 – 1]

$811 = P [ 0.00375 (1 + 0.00375)^360 ] / [ (1 + 0.00375)^360 – 1]

$811 = P [ 0.00375 (3.8113) ] / [ 3.8113 – 1]

$811 = P [ 0.014287 ]

P = $56,732.77

Therefore, the selling price of the house was $56,732.77.

To calculate the total interest paid over 30 years, we can use the formula:

Total interest = (monthly payment x total number of payments) - principal

Total interest = ($811 x 360) - $13,694

Total interest = $292,740 - $13,694

Total interest = $279,046

Therefore, they will pay a total of $279,046 in interest over 30 years.

Learn more about selling price: https://brainly.com/question/1153322

#SPJ11

Yes, it would be unusual if less than 52% of the sampled teenagers owned smartphones.

We are given the mean (μp) as 0.55 and the standard deviation (σp) as 0.0397. We need to find the probability of having less than 52% (0.52) of teenagers owning smartphones.

1) Calculate the z-score.
z = (x - μp) / σp
z = (0.52 - 0.55) / 0.0397
z ≈ -0.76

2) Find the probability associated with the z-score.
Using a z-table or a calculator, we find that the probability of having a z-score less than -0.76 is approximately 0.224. This means there is a 22.4% chance that less than 52% of the sampled teenagers would own smartphones.

Since the probability of having less than 52% of the sampled teenagers owning smartphones is 22.4%, it would be considered unusual, as the probability is relatively low.

To know more about probability visit:

https://brainly.com/question/31120123

#SPJ11

The standard deviation is approximately 1.50.

a) The random variable (X) is the number of left-handed people among the 25 randomly selected people.

b) The given numeric values with the correct symbols are:
n = 25 (sample size)
p = 0.1 (probability of being left-handed)

c) To compute the mean (µ), use the formula µ = n * p:
µ = 25 * 0.1 = 2.5

The correct interpretation of the mean is that on average, 2.5 people are expected to be left-handed in a sample of 25 randomly selected people.

d) To compute the standard deviation (σ), use the formula σ = √(n * p * (1 - p)):
σ = √(25 * 0.1 * (1 - 0.1))
σ = √(25 * 0.1 * 0.9)
σ = √(2.25)
σ ≈ 1.50 (rounded to 2 decimal places)

So, the standard deviation is approximately 1.50.

To learn more about standard deviation here:

https://brainly.com/question/23907081#

#SPJ11

4(3x + 2)4 12 + K (3x + 2) 6 + K is NOT a family of antiderivative of 2(3x + 2). The correct answer is Option b.

To find the antiderivative of 2(3x + 2), follow these steps:

1. Notice the function is 2(3x + 2).
2. Apply the power rule of integration, which states that ∫x^n dx = (x^(n+1))/(n+1) + C, where n ≠ -1.
3. In this case, n = 1, so the antiderivative is (2(3x + 2)^2)/(2) + C.
4. Simplify to obtain (3x + 2)^2 + C.

Option b doesn't match this result, so it is NOT a family of antiderivatives of 2(3x + 2).

Learn more about antiderivative:

https://brainly.com/question/12956882

#SPJ11