the given point is on the graph of y=​f(x). Find a point on the graph of y=​g(x).
​g(x)=​f(x−​1)+​3; ​(6​,15​)

Answers

Answer 1

The point (6, 15) on the graph of y = f(x) corresponds to the point (6, 18) on the graph of y = g(x).

What is graph?

A graph is a visual representation of data, usually depicted as a set of points or lines plotted on a coordinate plane or a series of bars or other shapes displayed in a bar chart or pie chart. Graphs are used to show relationships between variables, trends over time, or comparisons between different data sets.

According to question:

The problem asks us to find a point on the graph of y = g(x) given that (6, 15) is a point on the graph of y = f(x), and g(x) = f(x - 1) + 3.

To find a point on the graph of y = g(x), we need to substitute the given value of x = 6 into the formula for g(x):

g(6) = f(6 - 1) + 3

Simplifying the expression on the right-hand side, we have:

g(6) = f(5) + 3

Since (6, 15) is a point on the graph of y = f(x), we know that f(6) = 15.

g(6) = f(5) + 3

g(6) = 15 + 3

g(6) = 18

Therefore, the point (6, 15) on the graph of y = f(x) corresponds to the point (6, 18) on the graph of y = g(x).

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Related Questions

A psychologist theorized that people could hear better when they have just eaten a large meal. Twenty individuals were randomly assigned to eat either a large meal or a small meal. After eating the meal, their hearing was tested. Assuming hearing ability was measured on an interval scale and that the scores were normally distributed, the research hypothesis would be ________ and the most appropriate statistic for testing the research hypothesis would __________
A. non-directional; t-test for independent means
B. directional; t-test for independent means
C. non-directional; t-test for dependent means
D. directional; t-test for dependent means

Answers

The correct research hypothesis and distribution is directional, t-test for independent means.

What is the research hypothesis?

The research hypothesis that "people can hear better when they have just eaten a large meal" is a directional hypothesis because it predicts the direction of the effect (i.e., hearing ability will improve after a large meal).

The appropriate statistical test to use would be a t-test for independent means, which compares the means of two independent groups to determine if there is a statistically significant difference between them.

Therefore, the correct answer is B. Directional; t-test for independent means.

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(x^2-x-12)/(x+5)=x-6

Answers

There is no value of x that solves the proportion (x^2-x-12)/(x+5) = x-6.

How to solve the proportion?

The proportion for this problem is defined by the equation presented as follows:

(x^2-x-12)/(x+5) = x-6.

As the measures are proportional, we can apply cross multiplication, hence:

x² - x - 12 = (x + 5)(x - 6)

x² - x - 12 = x² - x - 30

-12 = -30.

-12 = -30 is a false statement, hence there is no value of x which can solve the proportion (x^2-x-12)/(x+5)=x-6 presented in this problem.

Missing Information

The problem asks for the value of x that solves the proportion (x^2-x-12)/(x+5) = x-6.

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FI;LL IN THE BLANK. An online retailer has determined that the average time for credit card transactions to be electronically approved K 1.6 seconds. (Round your answers to three decimal places.) (a) Use on exponential density function to find the probability that a customer warts less than a second for credit card approval. (b) Find the probability that a customer waits more than 3 seconds. ____ (c) What Is the minimum approval time for the slowest 5% of transactions? ____sec

Answers

(a) By using the exponential density function, the probability that a customer warts less than a second for credit card approval is 0.334

(b) The probability that a customer waits more than 3 seconds is 0.154

(c) The minimum approval time for the slowest 5% of transactions is 4.013 seconds

(a) To find the probability that a customer waits less than a second for credit card approval, we need to use the exponential density function:

f(x) = [tex]\lambda e^{-\lambda x}[/tex]

Where λ is the rate parameter, which in this case is the reciprocal of the mean approval time. So, λ = 1/1.6 = 0.625.

The probability that a customer waits less than a second can be calculated by integrating the density function from 0 to 1:

P(X < 1) = ∫[tex]0^1 \lambda e^{-\lambda x}[/tex] dx

P(X < 1) = [tex][-e^{-\lambda x}]0^1[/tex]

P(X < 1) = [tex]-e^{(-0.625)}[/tex] + 1

P(X < 1) = 0.334

Therefore, the probability that a customer waits less than a second for credit card approval is 0.334.

(b) To find the probability that a customer waits more than 3 seconds for credit card approval, we can use the same exponential density function and integrate from 3 to infinity:

P(X > 3) = ∫[tex]3^{\infty} \lambda e^{-\lambda x}[/tex] dx

P(X > 3) = [[tex]-e^{-\lambda x}[/tex])][tex]3^{\infty}[/tex]

P(X > 3) = [tex]e^{-1.875}[/tex]

P(X > 3) = 0.154

Therefore, the probability that a customer waits more than 3 seconds for credit card approval is 0.154.

(c) We can use the exponential distribution's inverse function to find this value:

P(X > x) = 0.05

[tex]e^{-\lambda x}[/tex] = 0.05

-xλ = ln(0.05)

x = ln(0.05)/(-λ)

x = ln(0.05)/(-0.625)

x = 4.013 seconds

Therefore, the minimum approval time for the slowest 5% of transactions is 4.013 seconds.

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PLEASE HELP YOU WILL BE BRAINIEST!!! Use the chart!!!!

Answers

Which outcome has a frequency closest to its expected frequency?
2

In a game of chance, players spin the pointer of a spinner with six equal-sized sections
I think 1

Find the potential inside and outside a sphere shell that carries a uniform surface charge $\sigma_0$, using results of Ex. 3.9

Answers

Inside the sphere, the potential is given by [tex]$V(r)=\frac{Q}{4\pi\epsilon_0r}$[/tex], where Q is the total charge enclosed within the sphere. Since the sphere shell has no charge inside, Q=0, and thus V(r)=0 inside the sphere.

Outside the sphere, the potential is given by

[tex]$V(r)=\frac{Q}{4\pi\epsilon_0r} + \frac{Q'}{4\pi\epsilon_0r'}$[/tex]

where Q is the total charge of the sphere shell, Q'= σ4πR²is the charge on an imaginary sphere of radius r'>R enclosing the sphere shell, and r is the distance from the center of the sphere. Using the result from Ex. 3.9, the potential outside the sphere becomes

[tex]$V(r)=\frac{Q}{4\pi\epsilon_0r} + \frac{\sigma_0 R^2}{2\epsilon_0 r}$[/tex]

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the area of a rectangle is 33.12cm². Given that one side of length is 4.6cm. Find the length of the other side​

Answers

Answer:

7.2 cm

----------------------------

Area of rectangle formula:

A = lw

Given:

A = 33.12 cm²,w = 4.6 cm.

Find the missing side length:

l = A/wl = 33.12/4.6l = 7.2 cm

Answer:

7.2cm

Step-by-step explanation:

We are here given that, the area of a rectangle is 33.12cm² and one of the side is 4.6cm .

We are interested in finding the length of the other side,

As we know that the area of rectangle is calculated using the formula,

Area = l * b

where l is the length and b is the breadth.

Now substitute the respective values,

33.12cm² = l * 4.6cm

l = 33.12cm²/4.6cm

l = 7.2 cm

Hence the value of second side is 7.2cm

xercise 1.3.4 in each case, either express y as a linear combination of a1, a2, and a3, or show that it is not such a linear combination. here:

Answers

Here, y can be expressed as a linear combination of a1, a2, and a3 is y = (-1/8) a1 + (9/4) a2 - (5/2) a3.

We can express y as a linear combination of a1, a2, and a3 if and only if y is a linear combination of the column vectors of the matrix A whose columns are a1, a2, and a3. We can write this as:

y = c1 a1 + c2 a2 + c3 a3

where c1, c2, and c3 are constants to be determined. We can solve for these constants by writing the system of equations in matrix form:

A [c1; c2; c3] = y

where [c1; c2; c3] is a column vector of the constants c1, c2, and c3. We can solve for [c1; c2; c3] by multiplying both sides by the inverse of A (assuming it exists):

[c1; c2; c3] = A^(-1) y

If A^(-1) exists, then y can be expressed as a linear combination of a1, a2, and a3. Otherwise, y cannot be expressed as a linear combination of a1, a2, and a3.

For y = [1 2 4 0], we have:

A = [-1 3 0 1; 3 1 2 0; 1 1 1 1]

We can compute the inverse of A using row reduction:

[A | I] = [-1 3 0 1 | 1 0 0;

3 1 2 0 | 0 1 0;

1 1 1 1 | 0 0 1]

[R2 - 3R1, R3 - R1] = [-1 3 0 1 | 1 0 0;

0 -8 2 -3 | -3 1 0;

0 -2 1 0 | -1 0 1]

[R2 / (-8), R3 + 2R2] = [1/8 -3/8 0 3/8 | 3/8 -1/8 0;

0 1 0 -1/4 | 3/4 -1/4 0;

0 0 1 -1/2 | 1/2 -1/2 1]

Therefore, A^(-1) = [1/8 -3/8 0 3/8;

0 1 0 -1/4;

0 0 1 -1/2;

0 0 0 0]

We can now compute [c1; c2; c3]:

[c1; c2; c3] = A^(-1) y = [1/8 -3/8 0 3/8;

0 1 0 -1/4;

0 0 1 -1/2;

0 0 0 0] [1; 2; 4; 0] = [-1/8; 9/4; -5/2; 0]

Therefore, y as a linear combination of a1, a2, and a3:

y = (-1/8) a1 + (9/4) a2 - (5/2) a3

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_____The given question is incomplete, the complete question is given below:

Exercise 1.3.4 in each case, either express y as a linear combination of a1 = [-1 3 0 1], a2 = [3 1 2 0], and a3= [1 1 1 1], or show that it is not such a linear combination. here: y = [1 2 4 0]

Tristan is going to invest $73,000 and leave it in an account for 18 years. Assuming
the interest is compounded continuously, what interest rate, to the nearest tenth of a
percent, would be required in order for Tristan to end up with $104,000?

Answers

Answer:

2%

Step-by-step explanation:

Given,P = $73000

A = $104000

T = 18 years, Compounded annually.

To find: r%

Soln: By formula, A = 73000*(1+r/100)^18

=> (104/73)^1/18 = (100+r)/100

=> 1.0198 = 100+r/100

=> 101.98 -100 = r

=> 1.98 = r

To the nearest percent, 2 = r

Hence, Rate of interest = 2%

What is the meaning of "complex numbers with absolute value 1 "?

Answers

Answer:

A complex number is said to have an absolute value of 1 if the magnitude of its real and imaginary parts together is equal to 1. Mathematically, |z| = (a²+b²)^½ = 1, where z is the complex number with real part ‘a’ and imaginary part ‘b’.

i need help i forgot how to do this

Answers

Step-by-step explanation:

For RIGHT triangles  :  sin ( angle) = opposite LEG / Hypotenuse

   so   sin B = 32 / 68 =  8 / 17

I am in my room (State 1). There is a 65% chance that I stay here and do my work like I am supposed to. There is a 35% chance I go get a snack and procrastinate (State 2). Once I have gone to get the snack, there is a 15% chance that I go back to work (go back to State 1), and there is an 85% chance that I get another snack and procrastinate further (stay in State 2).



Create a diagram and a transition matrix for this case.

Answers

Answer:

Here is a diagram and transition matrix for this case:

Diagram:

        +---(0.65)---> State 1 (work)

        |

Start ---+

        |

        +---(0.35)---> State 2 (procrastinate)

                  |

                  +---(0.15)---> State 1 (work)

                  |

                  +---(0.85)---> State 2 (procrastinate)



Transition matrix:

         |  State 1  |  State 2  |

----------+-----------+-----------+

State 1   |   1.00    |   0.00    |

----------+-----------+-----------+

State 2   |   0.15    |   0.85    |

----------+-----------+-----------+


In the transition matrix, the rows represent the starting state and the columns represent the ending state. The entries in the matrix represent the probabilities of transitioning from the starting state to the ending state. For example, the entry in row 1 and column 2 (0.00) represents the probability of transitioning from State 1 to State 2, which is 0.00.

Question 8 of 10
Which of the following rational functions is graphed below?
A. F(x) = 1/4x
B. F(x) = 4/x
C. F(x) = 1/x+4
D. F(x) = 1/x-4

Answers

Option D, F(x) = 1/x-4, is the rational function that best fits the graph.

What are some examples and functions of reason?

Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. Since polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros of the denominator.

The graph features a vertical asymptote at x = 4 and a horizontal asymptote at y = 0, as can be seen by looking at it.

Option A, F(x) = 1/4x, has a horizontal asymptote at y = 0, but does not have a vertical asymptote at x = 4.

Option B, F(x) = 4/x, has a vertical asymptote at x = 0, but not at x = 4.

Option C, F(x) = 1/x+4, has a vertical asymptote at x = -4, but not at x = 4.

Option D, F(x) = 1/x-4, has a vertical asymptote at x = 4, and does not have any other vertical asymptotes.

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4) 6 out of the 80 dogs in a shelter were adopted yesterday. Express adopted rate as a percent.

Answers

Answer:

Step-by-step explanation:

To find the adoption rate as a percentage, we need to divide the number of dogs adopted by the total number of dogs in the shelter, then multiply by 100.

adoption rate = (dogs adopted / total dogs) * 100%

adoption rate = (6 / 80) * 100%

adoption rate = 0.075 * 100%

adoption rate = 7.5%

Therefore, the adoption rate as a percent is 7.5%.

Question 19 (2 points)
According to research conducted by the Department of Education, 80% of college
students took a mathematics course as part of their general education requirements.
If ten college students are selected at random, what is the probability at least one of
the ten has not taken a mathematics course?
0.0800
0.1073
0.7927
0.8000

Answers

Answer:

The probability that a single college student has not taken a mathematics course is 1 - 0.8 = 0.2.

The probability that all ten selected college students have taken a mathematics course is (0.8)^10 = 0.1074 (rounded to four decimal places).

Therefore, the probability that at least one of the ten selected college students has not taken a mathematics course is:

1 - 0.1074 = 0.8926 (rounded to four decimal places).

So the answer is 0.8926, which is closest to option C (0.7927).

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Find the center and radius of the circle whose equation is x^2+y^2+4y=32

Answers

Answer:

center: (0, -2)

radius: 6

Step-by-step explanation:

You have to "complete the square" this allows you to fold up the expressions and put the equation in a standard kinda of format where you can pick the center and radius right out of the equation.

see image.

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CPCTC can be used in proofs after triangles have been shown to be congruent.
A) True
B) False

Answers

Answer:

True.

Step-by-step explanation:

CPCTC is commonly used at or near the end of a proof, which asks the student to show that two angles or two sides are congruent. It means that once two triangles are proven to be congruent, then the three pairs of sides that correspond must be congruent and the three pairs of angles that correspond must be congruent.

NEED HELPPPP PLSSSS

DUE TOMORROW!!

Answers

8.The method that resulted in Garcia winning might not be fair to the other nominees because it does not account for their individual achievements or skill sets.

What is nominees ?

Nominees are individuals or organizations that have been selected or chosen from a given group to represent them in a certain process or event. Nominees are usually chosen for their proficiency, expertise, or reputation in a certain field or area. For example, in some elections, political parties nominate individuals to represent them in the election and these nominees are then voted upon by the public. Similarly, some organizations nominate a particular individual or group of individuals to represent them in awards or recognition ceremonies for their excellence and achievements.

It simply rewards the nominee with the most votes, regardless of their ability or accomplishments. This could lead to someone who is less qualified or experienced receiving the award, while the more deserving candidates are overlooked.

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Please answer the attached question

Answers

The values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

How are radicals solved?

Equations containing radicals can be made simpler by solving the resultant equation after squaring both sides of the equation to remove the radical. Nonetheless, caution must be exercised to guarantee that any solutions found are reliable and adhere to any variables' limitations.

The given equation is [tex](e - 2\sqrt{3} )^2[/tex] = f - 20√3.

Expanding the left side of the equation we have:

[tex](e - 2\sqrt{3} )^2[/tex] = (e - 2√3)(e - 2√3)

= [tex]e^2[/tex] - 2e√3 - 2e√3 + 12

= [tex]e^2[/tex] - 4e√3 + 12

Substituting back in the function

[tex]e^2[/tex] - 4e√3 + 12 = f - 20√3

[tex]e^2[/tex] - 4e√3 - f + 20√3 - 12 = 0

Using the quadratic formula:

e = [4√3 ± √(16*3 + 4(f - 20√3 + 12))] / 2

e = [4√3 ± √(4f - 64√3)] / 2

e = 2√3 ± √(f - 16√3)

Now for,

(e - 2√3)² = f - 20√3

(2√3 + √(f - 16√3) - 2√3)² = f - 20√3

f - 20√3 = f - 16√3

f = 4√3

Hence, the values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

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HELP ILL GIVE YOU ONE HUNDRED POINTS AND BE MARKED BRAINLIEST IF YOU HELP MME ITS DUE TODAY!!!!

Answers

Answer: Somewhere around 40%, write 0.4.

Step-by-step explanation:

I took all of the outcomes from the games got the. probabilities of winners and got 40%.

d. Two judges in a beauty contest rank the ten competitors in the following order.

Do d. Two judges in a beauty contest rank the ten competitors in the following order.

Do the two judges appear to agree in their standard? the two judges appear to agree in their standard?

Answers

The correlation coefficient is close to zero, we can conclude that the two judges do not appear to agree in their standards.

What is correlation and causation in statistics?

Nevertheless, a correlation between two variables does not always imply that a change in one variable is the reason for a change in the values of the other.

There is a causal link between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event. This concept is also known as cause and effect.

For the given ranks for two judges the difference between their ranks is:

d: 0.0 4.0 -2.0 1.0 -0.5 1.5 -1.0 -1.0 0.5 2.0

Squaring the given distance we have:

d²: 0.0 16.0 4.0 1.0 0.25 2.25 1.0 1.0 0.25 4.0

Σd² = 29.75

The Spearman's rank correlation coefficient is given as:

ρ = 1 - (6Σd²)/(n(n²-1))

ρ = 1 - (629.75)/(10(10²-1))

ρ ≈ 0.03

Since the correlation coefficient is close to zero, we can conclude that the two judges do not appear to agree in their standards.

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The complete question is:

The school cafeteria served 2,420 cups of milk in March and 1,660 cups of milk in April. How many quarts of milk did the cafeteria serve in those two months?
Solve on paper. Check your work on Zearn.
1 quart = 4 cups
The cafeteria served
total quarts of milk in March and April.

Answers

Hence, throughout March and April, the cafeteria served 1020 quarts of milk.

what is unitary method ?

The unitary method is a mathematical approach where issues are solved by determining a single unit rate. To relate various quantities to one another, proportions must be used. This approach is frequently employed in issues involving direct and inverse proportionality. In inverse proportionality, the product of the two quantities is constant, whereas in direct proportionality, the two numbers fluctuate in the same ratio.

given

We must first determine the total number of cups of milk served in both March and April in order to calculate the total number of quarts of milk served in both months.

4080 cups of milk totaled from 2420 + 1660 cups.

We can convert the total number of cups to quarts by dividing by 4 because 1 quart equals 4 cups:

4080 cups of milk divided by 4 equals 1020 quarts total.

Hence, throughout March and April, the cafeteria served 1020 quarts of milk.

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How do you solve this equation?

Answers

Solved  equation x=80 and z=2, y=40

What is Variables?

An element, feature, οr factοr that is liable tο vary οr change

If y varies directly as x and inversely as the square οf z, we can write the fοllοwing prοpοrtiοnality:

y ∝ x/z²

where ∝ denοtes prοpοrtiοnality cοnstant.

Tο find the value οf ∝, we can use the given values οf y, x, and z:

y = ∝ x/z²

28 = ∝ (63)/(3)²

∝ = 28 * (3)² / (63)

∝ = 4/3

Nοw we can use this value οf ∝ tο find y when x=80 and z=2:

y = ∝ x/z²

y = (4/3) * (80)/(2)²

y = 40

Therefοre, when x=80 and z=2, y=40.

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PLEASE HELP !!!! HELP!!label each equation is proportionality or non proportional Help

y=9/x

y=x-12

h=3d

f=1/3e

Answers

Answer:

y=9/x  => proportional

y = x - 12 ==> non-proportional

h = 3d ==> proportional

f = 1/3 e = proportional

Step-by-step explanation:

A proportional equation is of the general form

y = kx (directly proportional) or

y = k/x  (inversely proportional)

k is known as the constant of proportionality

y = 9/x ==> k = 9  proportional
y = x - 12  cannot be expressed as y = kx or y = k/x

h = 3d ==> k = 3  proportional

f = 1/3 e ==> k = 1/3   proportional

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Given the coordinates shown and given that SU = 10, what are the coordinates of U if STUV is a kite?

A) (10, 18)
B) (0, 28)
C) (18, 28)

Answers

The calculated coordinates of U if STUV is a kite is (10, 18)

Calculating the coordinates of U if STUV is a kite?

From the question, we have the following parameters that can be used in our computation:

The figute of a kite

Also, we have

S = (0, 18)

And the distance SU to be

SU = 10

If the quadrilateral STUV is a kite, then the coordinates S and U are on the same horizontal level (according to the figure)

So, we have

U = (0 + 10, 18)

Evaluate

U = (10, 18)

Hence, the coordinates of U if STUV is a kite is (10, 18)

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let be the space spanned by the two functions and . find the matrix of the linear transformation from into itself with respect to the basis .

Answers

When space is spanned by the two functions of linear transformation from into itself with respect to the basis we need to apply T to each basis vector vi to get the column vectors T(vi) = [T(vi)]B.

where [T(vi)]B is the coordinate vector of T(vi) with respect to the basis B. Arrange the column vectors [T(v1)]B, [T(v2)]B, ..., [T(vn)]B into a matrix. This matrix is the matrix of T with respect to the basis B.

In this case, you have two functions that span a vector space, so you need to specify the basis B. Once you have chosen the basis, you can apply the above steps to find the matrix of the linear transformation.

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Mason earns $8.10 per hour and worked 40 hours. Noah earns $10.80 per hour. How many hours would Noah need to work to equal Mason’s earnings over 40 hours?

Answers

Answer:

Noah would need to work 30 hours to equal Mason's earning for 40 hours

Step-by-step explanation:

Mason;

8.10 x 40 = 324

324 ÷ 10.80 = 30 hours.

Helping in the name of Jesus.

Answer:

30 hours

Step-by-step explanation:

40 times 8.10 is 324 and 324 divided by 10.8 is 30 hours

explain why a set in r5 ust be linearly independent when is linearly indedependent and v4 is not in span

Answers

A set in R⁵ must be linearly independent because of the dimensionality of the space.

A Set of vectors in R⁵, the five-dimensional Euclidean space, must be linearly independent because of the dimensionality of the space.

The maximum number of linearly independent vectors in any set in R⁵ is 5 since any set with more than 5 vectors would necessarily contain a linearly dependent subset.

This is because any vector in R⁵ can be expressed as a linear combination of at most 5 linearly independent vectors, as the dimension of R⁵ is 5.

Therefore, any set with more than 5 vectors would have at least one vector that could be written as a linear combination of the other vectors in the set, making the set linearly dependent.

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The given question is incomplete, the complete question is

Explain why a set in R⁵ must be linearly independent.

-6(4p+5) > 34-8p HELP ASAP

Answers

Answer:

p < -4

Step-by-step explanation:

-6(4p+5) > 34 - 8p

-24p - 30 > 34 - 8p

-16p - 30 > 34

-16p > 64

p < -4

whats the radius of the button

Answers

Answer:

2.5

Step-by-step explanation:

diameter is 5 and the radius is half of the diameter so it is 2.5

hope this helps :)

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 385 grams and a standard deviation of 8 grams find the weight that corresponds to each event(use excel or appendix c to calculate the z value. Round your final answers to 2 decimal places)

URGENT

Answers

the weight that corresponds to each of the events are:

a) The weight is less than 380 grams: [tex]$P(X < 380)=0.266$[/tex].

b) The weight is between 375 and 395 grams: [tex]$P(375 < X < 395)=0.7887$[/tex].

c) The weight is greater than 400 grams: [tex]$P(X > 400)=0.0304$[/tex].

How to deal with Normal distribution?

Let X be the weight of a small Starbucks coffee. We are given that X is normally distributed with mean [tex]$\mu=385$[/tex] grams and standard deviation [tex]$\sigma=8$[/tex].

We want to find the weight that corresponds to each of the following events:

a) The weight is less than 380 grams.

b) The weight is between 375 and 395 grams.

c) The weight is greater than 400 grams.

To solve these problems, we first standardize the distribution by finding the corresponding z-scores using the formula:

[tex]$z=\frac{X-\mu}{\sigma}$$[/tex]

a) The weight is less than 380 grams.

We want to find P(X<380). We can find the z-score for X=380 as follows:

[tex]$z=\frac{380-385}{8}=-0.625$$[/tex]

Using a standard normal table or calculator, we find that the probability P(Z<-0.625)=0.266. Therefore,

[tex]$P(X < 380)=P\left(Z < -\frac{0.625}{1}\right)=0.266$$[/tex]

b) The weight is between 375 and 395 grams.

We want to find [tex]$P(375 < X < 395)$[/tex]. We can find the z-scores for X=375 and X=395 as follows:

[tex]$z_1=\frac{375-385}{8}=-1.25,\quad z_2=\frac{395-385}{8}=1.25$$[/tex]

Using a standard normal table or calculator, we find that the probability P(-1.25<Z<1.25)=0.7887. Therefore,

[tex]$P(375 < X < 395)=P\left(-1.25 < Z < 1.25\right)=0.7887$$[/tex]

c) The weight is greater than 400 grams.

We want to find P(X>400). We can find the z-score for X=400 as follows:

[tex]$z=\frac{400-385}{8}=1.875$$[/tex]

Using a standard normal table or calculator, we find that the probability P(Z>1.875)=0.0304. Therefore,

[tex]$P(X > 400)=P\left(Z > \frac{1.875}{1}\right)=0.0304$$[/tex]

Therefore, the weight that corresponds to each of the events are:

a) The weight is less than 380 grams: [tex]$P(X < 380)=0.266$[/tex].

b) The weight is between 375 and 395 grams: [tex]$P(375 < X < 395)=0.7887$[/tex].

c) The weight is greater than 400 grams: [tex]$P(X > 400)=0.0304$[/tex].

To know more about Normal distribution visit:

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