According to Masterfoods, the company that manufactures M&M's, 12% of peanut M&M's are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. (Round your answers to 4 decimal places where possible) a. Compute the probability that a randomly selected peanut M&M is not red. 0.88 b. Compute the probability that a randomly selected peanut M&M is green or orange. 0.38 C. Compute the probability that three randomly selected peanut M&M's are all yellow. 0.0034 d. If you randomly select six peanut M&M's, compute that probability that none of them are brown. e. If you randomly select six peanut M&M's, compute that probability that at least one of them is brown.

For the 3×3 matrices having  det(A)=−3 det(A)=−3, det(B)=7 the det(AB) is -21 ,det(3A) is -81 ,det(Aᵀ) is -3 , det(B-¹) is 1/7 and

To find the det(B²) is 49. values of det(AB), det(3A), det(Aᵀ), det(B-¹),

and det(B²) given that A and B are 3x3 matrices, det(A) = -3, and det(B) = 7.

1. det(AB):
Using the property of determinants, det(AB) = det(A) * det(B).

So, det(AB) = (-3) * (7) = -21.

2. det(3A):
For a 3x3 matrix, det(kA) = k³ * det(A) where k is a scalar. In this case, k = 3.

So, det(3A) = 3³ * (-3) = 27 * (-3) = -81.

3. det(Aᵀ):
The determinant of the transpose of a matrix is equal to the determinant of the original matrix.

So, det(Aᵀ) = det(A) = -3.

4. det(B-¹):
For the inverse of a matrix, det(B-¹) = 1 / det(B).

So, det(B-¹) = 1 / 7.

5. det(B²):
Using the property of determinants for powers, det(B²) = det(B) * det(B) = 7 * 7 = 49.

So, det(AB) = -21, det(3A) = -81, det(Aᵀ) = -3, det(B-¹) = 1/7, and det(B²) = 49.

To learn more about matrices and determinants : https://brainly.in/question/2179101

#SPJ11

The solution to the given system of equations is as follows:

(-1,-39) and (1,-1).

The equations that compose the system in this problem are given as follows:

We solve the system graphically, hence the solution is given by the point of intersection of the graphs of the two functions.

From the graph of the system given at the end of the answer, it is found that the solution to the system of equations is given as follows:

(-1,-39) and (1,-1).

More can be learned about a system of equations at brainly.com/question/30347294

#SPJ1

An exponential function is y = 0.5ˣ.

What is an exponential function?

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.

Here, we have

Given: (-2,4) & (1,0.5)

We have to find an exponential function.

An exponential function is in the general form

y = a(b)ˣ

We know the points  (-2,4) & (1,0.5)  so the following is true:

4 = a(b)⁻².....(1)

0.5 = ab.....(2)

From equation(1), we get

4 = a/b²

4b² = a

Now we put the value of a in equation(2) and we get

0.5 = b(4b²)

0.5/4 = b³

b = 0.5

If b = 0.5 then the value of a is:

0.5 = a(0.5)

a = 1

Giving us the equation:

y = 1(0.5)ˣ

y = 0.5ˣ

Hence, an exponential function is y = 0.5ˣ.

To learn more about the exponential function from the given link

https://brainly.com/question/2456547

#SPJ9

Check the picture below.

[tex]\cfrac{18}{11+x}=\cfrac{2}{x}\implies 18x=22+2x\implies 16x=22\implies x=\cfrac{22}{16}\implies x=\cfrac{11}{8}[/tex]

A square piece of cardboard with side length of 34 inches is needed to make the box.

Let the side of the square piece of cardboard be x inches.

After cutting out 7 inch squares from each corner, the dimensions of the base of the box will be (x-14) inches by (x-14) inches, and the height of the box will be 7 inches.

The volume of the box can be expressed as:

V = (x-14[tex])^2[/tex][tex]\times[/tex]7

We know that the box is to hold 2800 in3, so we can set up an equation:

(x-14[tex])^2[/tex][tex]\times[/tex] 7 = 2800

Simplifying and solving for x, we get:

(x-14[tex])^2[/tex] = 400

x-14 = ±20

x = 34 or x = 6

Since the cardboard cannot have a side length of less than 7+7=14 inches, the only valid solution is x=34 inches.

Therefore, a square piece of cardboard with side length of 34 inches is needed to make the box.

To learn more about  square piece  visit:  https://brainly.com/question/29983117

#SPJ11

Therefore, the volume of the soup can is 603.84 cubic centimeters when the diameter is 8 cm.

To characterise and simulate the physical, chemical, or physiological aspects of goods or materials including dispersed phases, mean particle sizes may be utilised. These mean diameters are represented by several notational schemes, which could lead to a lot of misunderstanding. This also holds true for their nomenclature.

The De Brouckere mean diameter, also known as volume-weighted mean diameter, volume moment mean diameter, or volume-weighted mean size, is the average of a particle size distribution weighted by volume.

The formula for the volume of a cylinder is V = [tex]pi*r^2h[/tex], where r is the radius and h is the height.

The diameter of the soup can is 8 cm, so the radius is half of that, or 4 cm. The height is 12 cm.

These values into the formula, we get:

V = π[tex](4 cm)^2(12 cm)[/tex]

V = 3.14 * [tex](16 cm^2)(12 cm)[/tex]

V = 603.84[tex]cm^3[/tex]

Learn more about diameter visit: brainly.com/question/28162977

#SPJ4

The number of text messages for which the costs will be the same is of:

50 messages.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

For each plan, the slope and the intercept are given as follows:

Hence the functions are given as follows:

The costs will be the same when:

A(x) = B(x)

Hence:

30 + 0.2x = 40

0.2x = 10

x = 100/2

x = 50 messages.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:

below

Step-by-step explanation:

Part A)

The radius of a circle is half of its diameter.

Therefore, the radius of the circle is:

radius = diameter/2 = 8cm/2 = 4cm

So, the radius of the circle is 4cm.

You can also find radius by just dividing the diameter in half, or by 2.

Part B)

The area of a circle can be found using the formula:

Area = πr^2

where π is the mathematical constant pi (approximated as 3.14), and r is the radius of the circle.

Substituting the values given in the question, we get:

Area = πr^2

= 3.14 × (4cm)^2

= 3.14 × 16cm^2

Therefore, the area of the circle is:Area = 50.24cm^2 (rounded to two decimal places)

So, the area of the circle with a diameter of 8cm is 50.24cm^2.

Answer: The answer to your question is 60%

Step-by-step explanation: The total number of marbles in Joseph's bag is:

2 (red) + 4 (green) + 10 (yellow) + 9 (purple) = 25

The probability of choosing one marble that is not yellow can be found by dividing the total number of marbles that are not yellow by the total number of marbles in the bag:

P(not yellow) = (2 red + 4 green + 9 purple) / 25

P(not yellow) = 15/25

P(not yellow) = 3/5

P(not yellow) = 0.6 or 60%

Therefore, the answer is 60%.

Answer:

60%

Step-by-step explanation:

Answer: The answer to your question is 60%

Step-by-step explanation: The total number of marbles in Joseph's bag is:

2 (red) + 4 (green) + 10 (yellow) + 9 (purple) = 25

The probability of choosing one marble that is not yellow can be found by dividing the total number of marbles that are not yellow by the total number of marbles in the bag:

P(not yellow) = (2 red + 4 green + 9 purple) / 25

P(not yellow) = 15/25

P(not yellow) = 3/5

P(not yellow) = 0.6 or 60%

Therefore, the answer is 60%.

The ladder should be about 10.44 feet long (rounded to the nearest hundredth of a foot) for Joseph to reach the window 10 feet above the ground when the ladder is 3 feet away from the wall.

To solve this problem, we'll use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): c² = a² + b².

In this case, the ladder acts as the hypotenuse, the distance from the wall to the ladder's base is one side (a = 3 feet), and the height of the window is the other side (b = 10 feet).

Using the Pythagorean theorem:
c² = (3)² + (10)²
c² = 9 + 100
c² = 109

Now, to find the length of the ladder, we'll take the square root of 109:
c ≈ √109
c ≈ 10.44

So, Joseph should use a ladder that is approximately 10.44 feet long, rounded to the nearest hundredth of a foot.

Learn more about Pythagorean theorem here: brainly.com/question/14930619

#SPJ11

The probability that the basketball player will make exactly 7 of her 10 free throws is approximately 0.226, or 22.6%.

We may utilize the binomial probability formula to resolve this issue:

P(X=k) = C(n,k) * p^k * (1-p)^(n-k)

where X is the number of made baskets from free throws, k is the number of made baskets we're looking for (k=7), n is the total number of attempts (n=10), p is the chance of success (p=0.65), and C(n,k) is the number of combinations of n things taken k at a time. (also known as the binomial coefficient).

When we enter the values, we obtain:

P(X=7) = C(10,7) * (0.65)⁷ * (1-0.65)³

We can calculate that C(10,7) = 120 using a calculator or a table. We thus have:

P(X=7) = 120 * (0.65)⁷ * (0.35)³

P(X=7) ≈ 0.226

Learn more about probability here:

brainly.com/question/30034780

#SPJ1

The sum of the series ∑∞ n = 1 an is equal to 5.

To find the sum of the series ∑∞ n = 1 an using the given partial sum formula sn = 5 − 8(0.8)ⁿ, we can use the concept of the limit.

First, let's find the general term of the series.

We can do this by taking the difference between consecutive partial sums:

sⁿ⁺¹ - sn = (5 - 8(0.8)ⁿ⁺¹) - (5 - 8(0.8)ⁿ)

= 5 - 5 - 8(0.8)ⁿ⁺¹ + 8(0.8)ⁿ

= 8(0.8)ⁿ(0.8 - 1)

Notice that we can simplify 0.8 - 1 as -0.2:

sn+1 - sn = -0.2 × 8(0.8)ⁿ

Now, let's take the limit as n approaches infinity:

lim (n→∞) (sn+1 - sn) = lim (n→∞) (-0.2 × 8(0.8)ⁿ)

Since 0.8 is less than 1, we can see that the term 8(0.8)ⁿ approaches zero as n approaches infinity:

lim (n→∞) 8(0.8)ⁿ = 0

Therefore, we have:

lim (n→∞) (sn+1 - sn) = lim (n→∞) (-0.2 × 8(0.8)ⁿ) = -0.2 × 0 = 0

The limit of (sn+1 - sn) as n approaches infinity is zero, indicating that the series converges to a finite sum.

To find the actual sum, we can calculate the limit of the partial sum formula as n approaches infinity:

lim (n→∞) sn = lim (n→∞) (5 − 8(0.8)ⁿ)

Since 0.8 is less than 1, we have:

lim (n→∞) (0.8)ⁿ = 0

Therefore, we have:

lim (n→∞) sn = lim (n→∞) (5 − 8(0.8)ⁿ) = 5 - 8 × 0 = 5

Hence, the sum of the series ∑∞ n = 1 an is equal to 5.

Learn more about partial sum click;

https://brainly.com/question/31900309

#SPJ12

In the C programming language, the standard library procedure for reading a 32-bit signed decimal integer from standard input is scanf(). In the Python programming language, the standard library is int(input()).

An example usage of scanf() to read a 32-bit signed decimal integer from standard input is:

#include <stdio.h>

int main() {

   int my_integer;

   scanf("%d", &my_integer);

   printf("The integer is %d\n", my_integer);

   return 0;

}

An example usage of int(input()) to read a 32-bit signed decimal integer from standard input is:

my_integer = int(input())

print("The integer is", my_integer)

Other programming languages may have different procedures for reading input.

To learn more about 32-bit signed integer click on,

https://brainly.com/question/16672724

#SPJ4

The equation has no genuine/real solutions [tex]$(\frac{3}{4}-\frac{5}{6})x^2$[/tex], but if working with complex numbers, [tex]$x = \pm\sqrt{60}i$[/tex].

What is x in the given equation, find it using complex number property?

We can begin by simplifying the left side of the equation to find x:

[tex]$(\frac{3}{4} - \frac{5}{6})x^2 = 5$[/tex]

To simplify the left side, we need to find a common denominator for 4 and 6, which is 12:

[tex]$(\frac{9}{12} - \frac{10}{12})x^2 = 5$[/tex]

Simplifying further:

[tex]$-\frac{1}{12}x^2 = 5$[/tex]

Multiplying both sides by -12:

[tex]$x^2 = -60$[/tex]

We can't take the square root of a negative number and get a real number, so there are no real solutions to this equation. If you're working with complex numbers, you could say:

[tex]$x = \pm\sqrt{60}i$[/tex]

where i is the imaginary unit.

The question is not complete; the full question will be -
[tex]$(\frac{3}{4}-\frac{5}{6})x^2 = 5$[/tex]  Find the x in the given equation using complex number property?

To learn more about complex numbers, visit: https://brainly.com/question/28654613

#SPJ1

The equation of the trend line in the scatter plot is y = (6/5)x - 12/5.

We can use the two-point form of the equation of a line to find the equation of the line that passes through the points (2, 0) and (7, 6).

The two-point form states that the equation of the line passing through two points (x1, y1) and (x2, y2) is given by:

y - y1 = (y2 - y1)/(x2 - x1) * (x - x1)

where m = (y2 - y1)/(x2 - x1) is the slope of the line.

In this case, we have:

x1 = 2, y1 = 0

x2 = 7, y2 = 6

So, the slope of the line is:

m = (y2 - y1)/(x2 - x1) = (6 - 0)/(7 - 2) = 6/5

Now, we can use either point to find the y-intercept (b) of the line. Let's use the first point (2, 0):

y - y1 = m(x - x1)

y - 0 = (6/5)(x - 2)

y = (6/5)x - 12/5

Therefore, the equation of the line passing through the points (2, 0) and (7, 6) is y = (6/5)x - 12/5.

Read more about scatter plot at

https://brainly.com/question/23202763

#SPJ1

Using L'Hopital's rule, the value of [tex]\lim_{x \to 3}[/tex] (x - 3)/(x^2-9) is 1/6 and this is verified using algebraic simplification

To find the limit using L'Hopital's rule, we differentiate both the numerator and denominator with respect to x.

[tex]\lim_{x \to 3}[/tex] (x - 3)/(x^2-9)

= [tex]\lim_{x \to 3}[/tex] [d/dx (x-3)]/[d/dx(x^2-9)]

= [tex]\lim_{x \to 3}[/tex] [1]/[2x]

Now, substituting x=3 in the above expression, we get:

= 1/6

To check our answer using an algebraic simplification, we factorize the denominator:

x^2-9 = (x-3)(x+3)

[tex]\lim_{x \to 3}[/tex] (x - 3)/(x^2-9)

= [tex]\lim_{x \to 3}[/tex] (x - 3)/[(x-3)(x+3)]

= [tex]\lim_{x \to 3}[/tex] [1]/[x+3]

Now, substituting x=3 in the above expression, we get:

= 1/6

Hence, both the methods give the same result, and the limit of the given expression is 1/6.

To learn more about limit click on,

https://brainly.com/question/30466115

#SPJ4

A two-step experiment consists of tossing a six-sided die and flipping a coin. The sample space for this experiment consists of all possible outcomes that could result from both steps. To find the number of elements in the sample space, we need to multiply the number of possible outcomes for each step.

The first step involves rolling a six-sided die, which has six possible outcomes. The second step involves flipping a coin, which has two possible outcomes. To find the total number of elements in the sample space, we need to multiply these two numbers together:

6 x 2 = 12

Therefore, the sample space for this two-step experiment consists of 12 elements, each representing a unique outcome that could result from rolling the die and flipping the coin. This could be represented in a tree diagram, where each branch represents a possible outcome at each step, and the endpoints of the branches represent the final outcomes in the sample space.

Learn more about experiment here:

https://brainly.com/question/11256472

#SPJ11

Answer:

25/15 = 15/x

25x = 225, so x = 9 and y = 16

z = √(20^2 - 16^2) = √(400 - 256) = √144

= 12

a) The distribution of the sample mean X is approximately normal distribution. So, first option is right answer.

b) The graph of probability density function is present in above figure. The mean and the variance of the sampling distribution is equals to the 8.25 in. and 0.0006 in. respectively.

c) The probability that the sample mean diameter for the 35 columns will be greater than 8 in. is equals to the 1.0000.

d) The probability that the sample mean diameter for the 35 columns will be between 8.2 and 8.4 in. is equals to the 0.9981.

We have a certain hurricane-prone areas of the United States, concrete columns used in construction must meet specific building codes. The minimum diameter for a cylindrical column = 8 in.

Mean diameter, μ = 8.25 in.

Standard deviation σ = 0.1 in.

Sample size, n = 35

a) As we see, sample size, n > 30, by centeral limit theorem, the distribution of the sample mean X is approximately is normal.

b) The graph of the probability density function, is present in above figure. That for a random variable, [tex]\bar X \tilde \: N ( \mu , \frac{\sigma}{\sqrt n} )[/tex]

\bar X ~ N ( \mu , \frac{\sigma}{\sqrt n} Now, mean of sampling distribution of mean is [tex]\mu_{\bar X} = 8.25 [/tex].

Variance is square of standard deviations. The variation is sampling distribution is [tex]\sigma²_{ \bar X } = \frac{ \sigma²}{n}[/tex]

= 0.15²/35 = 0.0006

c) Now, assume that population standard deviation, σₓ = 0.15 in.

The probability that the sample mean diameter for the 35 columns will be greater than 8 in., [tex]P ( \bar X> 8) = P ( \frac{\bar X - \mu_x }{\sigma_x} > \frac{ (8 - 8.25)}{0.15} )[/tex]

[tex]P ( \bar X> 8) = P ( z > -1.66) [/tex]

Using the normal distribution table value of P( z > - 1.66) is 1 .

d) The probability that the sample mean diameter for the 35 columns will be between 8.2 and 8.4 in., [tex]P (8.2 < \bar X < 8.4) [/tex]

= [tex]P ( \frac{(8.2 - 8.25)}{0.15} < \frac{\bar X - \mu_x}{\sigma_x} < \frac{8.4 - 8.25}{0.15}) [/tex]

= P( -2.9 < z < 8.82)

= P( z < 8.82) - P( z < - 2.9)

= 1.00 - 0.0019

= 0.9981

Hence, required probability value is 0.9981.

For more information about Normal distribution, refer:

https://brainly.com/question/4079902

#SPJ4

Complete question:

In certain hurricane-prone areas of the United States, concrete columns used in construction must meet specific building codes. The minimum diameter for a cylindrical column is 8 in. Suppose the mean diameter for all columns is 8.25 in., with a standard deviation of 0.1 in. A building inspector randomly selects 35 columns and measures the diameter of each. Suppose the population standard deviation is 0.15 in.

a) The distribution of the sample mean X is approximately

i) normal.

ii) O uniform.

iii)Poisson.

iv) exponential.

b) Carefully sketch a graph of the probability density function. Then enter the mean and the variance of the sampling distribution of X. (Use decimal notation. Give your answers to four decimal places if necessary.) mean: variance:

c) Suppose the population standard deviation is 0.15 in. What is the probability that the sample mean diameter for the 35 columns will be greater than 8 in.? (Use decimal notation. Use Table III. Give your answer to four decimal places if necessary.)

d) Suppose the population standard deviation is 0.15 in. What is the probability that the sample mean diameter for the 35 columns will be between 8.2 and 8.4 in.? (Use decimal notation. Use Table III. Give your answer to four decimal places.)

The number pattern that uses the rule "add 3" is:3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...In this pattern, each term is obtained by adding 3 to the previous term.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

A number pattern is a sequence of numbers that follows a certain rule or pattern. In this case, the rule is to "add 3" to each term to obtain the next term in the sequence.

The pattern starts with the number 3, and then we add 3 to get the next term, which is 6. Then we add 3 to 6 to get 9, and so on. Each term is found by adding 3 to the previous term.

The pattern continues indefinitely, producing an infinite sequence of numbers. The pattern is also known as an arithmetic sequence or arithmetic progression, because each term is obtained by adding a constant (in this case, 3) to the previous term.

So, the number pattern that uses the rule "add 3" is a sequence of numbers that starts with 3 and adds 3 to each term to obtain the next term in the sequence.

The number pattern that uses the rule "add 3" is:3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...In this pattern, each term is obtained by adding 3 to the previous term.

To learn more about arithmetic sequence from the given link:

https://brainly.com/question/15412619

#SPJ1

The length of the curve defined by y = 3x^(3/2) + 11 from x = 2 to x = 7 is 95.8

We can use the formula:
L = ∫[a,b] √[1 + (dy/dx)^2] dx

First, let's find dy/dx:

dy/dx = (9/2)x^(1/2)

Now, we can plug this into the arc length formula:

L = ∫[2,7] √[1 + (9/2)^2x dx]

L = ∫[2,7] √[1 + 81x^2/4] dx

This integral can be quite tricky to solve, so we can use a substitution. Let u = 9x/2:

du/dx = 9/2

dx = 2/9 du

Now, we can rewrite the integral in terms of u:

L = ∫[9,21] √[1 + u^2] (2/9) du

We can use a trigonometric substitution to solve this integral. Let u = tanθ:

du = sec^2θ dθ

Now, we can rewrite the integral again:

L = ∫[θ1,θ2] √[1 + tan^2θ] secθ dθ

L = ∫[θ1,θ2] sec^3θ dθ

Using a formula for the integral of sec^3θ, we get:

L = [1/2 secθ tanθ + 1/2 ln|secθ + tanθ|]θ1^θ2

Now, we just need to plug in the values for θ1 and θ2:

θ1 = tan^-1(9/2)

θ2 = tan^-1(21/2)

L = [1/2 secθ tanθ + 1/2 ln|secθ + tanθ|]tan^-1(9/2)^tan^-1(21/2)

L ≈ 95.8

Therefore, the length of the curve is approximately 95.8 units.

To find the length of the curve defined by y = 3x^(3/2) from x = 2 to x = 7, we can use the arc length formula for a curve:

Length = ∫[sqrt(1 + (dy/dx)^2)] dx from x = 2 to x = 7

Step 1: Calculate the derivative dy/dx:
y = 3x^(3/2)
dy/dx = (3/2) * 3x^(1/2)

Step 2: Square the derivative and add 1:
(dy/dx)^2 = (9/4)x + 1

Step 3: Calculate the square root of the sum:
sqrt(1 + (dy/dx)^2) = sqrt((9/4)x + 1)

Step 4: Evaluate the integral of the expression from x = 2 to x = 7:
Length = ∫[sqrt((9/4)x + 1)] dx from x = 2 to x = 7

This integral does not have a simple closed-form solution, so we would typically use a numerical method or calculator to solve it.

After using a numerical method, you will get an approximate value for the length of the curve.

Learn more about curve at: brainly.in/question/12142919  

#SPJ11

The volume of the solid is approximately 0.018 cubic units.

To find the volume of the solid, we need to use the method of cylindrical shells. First, we need to determine the height of the cylinder at a given value of x, which is given by the difference between the y-coordinates of the two curves at that point.

Using the identity given in the problem, we can rewrite cos²(7x) as (1/2) + (cos(14x)/2), so the height of the cylinder is (3 + cos(14x))/2.

Next, we need to determine the radius of the cylinder at a given value of x, which is the distance between x and the y-axis. Therefore, the radius is x.

Now, we can use the formula for the volume of a cylindrical shell:

V = 2π ∫[pi/14, 0] x(3 + cos(14x))/2 dx

Using integration by parts, we can find that this integral evaluates to approximately 0.018 cubic units.

Therefore, the volume of the solid obtained by rotating the region about the y-axis is approximately 0.018 cubic units.

To know more about volume of the solid, refer here:
https://brainly.com/question/23705404#
#SPJ11

The probability that the mean of your sample is greater than the mean number of hours per week worked by your parents is approximately   [tex]0.7802,[/tex]  as a decimal, rounded to [tex]4[/tex] decimal places.

To calculate the probability that the mean of your sample is greater than the mean number of hours per week worked by your parents, we can use the z-test for comparing means of two normal distributions.

Given data:

Mean number of hours worked by parents   [tex](\mu1) = 48.69[/tex] hours

Standard deviation of hours worked by parents (σ1) = 2.90 hours

Mean number of hours you study (μ2) = 48.17 hours

Standard deviation of hours you study (σ2) = 2.60 hours

Sample size (n) = 15

We can first calculate the standard error of the mean (SEM) for your sample using the formula:

[tex]SEM = \sigma2 / \sqrt(n)[/tex]

where σ2 is the standard deviation of the population (in this case, your study hours), and sqrt(n) is the square root of the sample size.

Plugging in the values:

[tex]SEM = 2.60 / \sqrt(15) \approx0.6728[/tex]

Next, we can calculate the z-score using the formula:

[tex]z = (x_1 - x_2) / SEM[/tex]

where [tex]x_1[/tex]  is the sample mean (mean number of hours you study) and   [tex]x_2[/tex] is the population mean (mean number of hours worked by your parents).

Plugging in the values:

x1 = 48.17

x2 = 48.69

SEM = 0.6728

[tex]z = (48.17 - 48.69) / 0.6728 \approx -0.7725[/tex]

Now, we can use a standard normal distribution table or a calculator to find the probability that a z-score is greater than -0.7725.

Using a standard normal distribution table or a calculator, we find that the probability that a z-score is greater than   [tex]-0.7725[/tex] is approximately [tex]0.7802[/tex].

Therefore, The probability that the mean of your sample is greater than the mean number of hours per week worked by your parents is approximately   [tex]0.7802,[/tex]  as a decimal, rounded to [tex]4[/tex] decimal places.

Learn more about decimal here:

https://brainly.com/question/30958821

#SPJ1

The total number of bit strings of length 10 over the alphabet {a,b} that have exactly four a's and start with bb or end with bb is 510.

To solve this problem, we can use the principle of multiplication and addition.

First, we need to find the number of bit strings of length 10 with exactly four a's. We can place the four a's in any of the 10 positions, so we have 10 choose 4 (or 10C4) ways to do this. For each of these arrangements, the remaining six positions must be filled with b's, so there is only one way to do this.

Therefore, there are 10C4 = 210 bit strings of length 10 with exactly four a's. Next, we need to count the number of bit strings that start with bb or end with bb.

For bit strings that start with bb, the remaining eight positions can be filled with any combination of a's and b's, so there are 2^8 = 256 such bit strings.

Similarly, for bit strings that end with bb, the first eight positions can be filled with any combination of a's and b's, so there are also 256 such bit strings.

However, we have counted the bit string bbbbbbbbb and bbbaaaaaaa twice (once for each case). Therefore, we need to subtract 2 from the total count.

Thus, the total number of bit strings of length 10 over the alphabet {a,b} that have exactly four a's and start with bb or end with bb is 256 + 256 - 2 = 510.

To learn more about strings click on,

https://brainly.com/question/31327778

#SPJ4

The given statement: Variability in a distribution that would be otherwise non-normal may tend towards normality with random sampling is TRUE.

Random sampling is a statistical technique that involves selecting a random sample from a population to make inferences about the population as a whole. The central limit theorem states that the sample mean of a sufficiently large sample size from any population with a finite variance will tend towards a normal distribution.

Therefore, if a distribution is non-normal but has a finite variance, random sampling can cause the variability in the sample means to tend towards normality. This is because the variability of the sample means decreases with increasing sample size due to the central limit theorem. In other words, the distribution of sample means becomes increasingly normal as the sample size increases.

This is important because many statistical methods assume normality, so random sampling can make these methods applicable to non-normal populations. However, it's important to note that there are some cases where random sampling may not be effective in making a non-normal distribution tend towards normality.

To know more about Variability in a distribution, refer here:
https://brainly.com/question/27376566#
#SPJ11

Answer:

<C = 54 degrees

b = 123.6

a = 72.6

Step-by-step explanation:

<C = 180 - 90 - 36 = 54 degrees

b = 100/sin54 = 123.6

a = sqrt (123.6^2 - 100^2) = 72.6

The equation of the vertical asymptote is:

x = 12

The correct option is the third one.

The vertical asymptote of the graph is at the line where the graph tends at positive infinite and negative infinite at the same time.

You can see that it happens in the right side of the graph.

You can see that it is a vertical asymptote, so it will be represented by a vertical line, these are of the form x =a.

By looking at the graph, you can see that it is located at x = 12, so that is the equation of the vertical line. The correct option is the third one.

Learn more about asymptotes at:

https://brainly.com/question/1851758

#SPJ1

The probability of randomly picking a nickel twice in a row from four nickels and eight dimes is 1/9.

Given that there are four nickels and eight dimes in your pocket, the total number of coins is twelve. If you randomly pick a coin and then return it to your pocket, there are still twelve coins in your pocket, and the probability of picking a nickel remains the same. Therefore, the probability of picking a nickel on the first draw is 4/12, which simplifies to 1/3.

Now, you pick another coin from the pocket, and again there are twelve coins. Since the first coin was returned to the pocket, the probability of picking a nickel on the second draw is also 4/12 or 1/3.

To calculate the probability of both events occurring together, we multiply the probability of the first event by the probability of the second event.

Thus, the probability of picking a nickel on the first draw AND picking a nickel on the second draw is (1/3) x (1/3) = 1/9.

To know more about probability here

https://brainly.com/question/11234923

#SPJ4

Answer:

b) x is about 5.4

c) x is about 21.27

Step-by-step explanation:

for b), you are given the measure of two angles (the right angle measuring 90 degrees and the 78 degree angle), and the length of one side. with these values, you can use the Law of Sines to find the length of a missing side.

to make this easier lets label all sides and angles of the triangle. the right angle can be A, the 78 degree angle can be B, and the last one is C. therefor the side between angles A and B is side c, the side between angles B and C is side a, and the side between angles A and C is side b.

the Law of Sines says that if ABC has sides a,b,c then a/sinA= b/sinB= c/sinC. we can use this to find the length of side c, which is the value of X we are looking for.

first find the measure of angle C. we are given two angles in the triangle, 90 and 78, and know the total angles must measure 180 so C=180-(90+78), C=12

since we have the measure of angle A and the length of side a, I will use this to set up the equation

[tex]\\\frac{a}{sinA} =\frac{c}{sinC} \\\\\frac{25.9}{sin90} =\frac{c}{sin12}[/tex]

solve for sin of 90 degrees and 12 degrees with calculator and then solve for c:

[tex]\frac{25.9}{1} =\frac{c}{0.21} \\\\25.9=\frac{c}{0.21} \\\\c=5.44[/tex]

so the length of side x is about 5.4

for c), you are given the length of two sides and the included angle, so you can use the Law of Cosines to solve.

again, lets label the angles and sides to make this easier. the right angle can be A, the angle to the right of A can be B, and the bottom angle can be C. therefore the side between A and B is side C, the side between B and C is side a, and the side between A and C is side b.

according to this labeling, we are trying to find side a to solve for x.

we can use the equation

[tex]a^{2} =b^{2} +c^{2} -2(b)(c)(cosA)[/tex]

we know side b=19.5 and side c=8.5 and angle A measures 90 degrees so fill in the values and solve for a:

[tex]a^{2} =19.5^{2} +8.5^{2} -2(19.5)(8.5)(cos90)\\\\a^{2} =380.25 +72.25-(331.5)(0)\\\\a^{2} =452.5\\a=21.27[/tex]

so side a is about 21.27 so that is the value of x.