Using the normal distribution and the central limit theorem, it is found that there is a:
a) 0.7054 = 70.54% probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months.b) 0.8869 = 88.69% probability that five randomly selected years will have an average precipitation greater than 18 inches for the first 7 months.Normal Probability Distribution
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
The mean is of 19.32 inches, hence [tex]\mu = 19.32[/tex].The standard deviation is of 2.44 inches, hence [tex]\sigma = 2.44[/tex].Item a:
The probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months is 1 subtracted by the p-value of Z when X = 18, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{18 - 19.32}{2.44}[/tex]
[tex]Z = -0.54[/tex]
[tex]Z = -0.54[/tex] has a p-value of 0.2946.
1 - 0.2946 = 0.7054.
0.7054 = 70.54% probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months.
Item b:
Now, we want the probability that five randomly selected years will have an average precipitation greater than 18 inches for the first 7 months, hence:
[tex]n = 5, s = \frac{2.44}{\sqrt{5}}[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{18 - 19.32}{\frac{2.44}{\sqrt{5}}}[/tex]
[tex]Z = -1.21[/tex]
[tex]Z = -1.21[/tex] has a p-value of 0.1131.
1 - 0.1131 = 0.8869.
0.8869 = 88.69% probability that five randomly selected years will have an average precipitation greater than 18 inches for the first 7 months.
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I NEED HELP I'M SOO LOST I'LL GIVE A BRAINLIEST TO THE BEST ANSWER
Contrast the tone of the following two passages. (First, determine the tone of each passage. Then determine how the tones differ. What is the tone of each? How do you know? How do the tones differ?)
Tone ONE
Envisioning paths where Russell’s discovery could lead him, Rosalind and I began grooming him for interviews with the local news and math journals. In our minds, Russell’s future was bright and without limitation, starting with a full scholarship to MIT or Northwestern.
Tone 2
I came home for brief visits, but these visits were too awkward without Rosalind. The house was profoundly still. Mommy stayed in her room. Russell didn’t talk, let alone look at me.
The first passage has a hopeful and ambitious tone, using optimistic language to express excitement for the future. The second passage has a melancholic and isolated tone, using somber phrases to convey discomfort and disconnection. These contrasting tones reflect a range of emotions in the narrative.
Explanation:To contrast the tone of two passages, we must first identify the attitude or mood present in each. In Tone ONE, the writer’s use of optimistic phrases such as "Envisioning paths," "grooming him for interviews," and "future was bright" convey a hopeful and ambitious tone. This tone suggests excitement for the future possibilities and success that lie ahead for Russell.
In contrast, Tone 2 uses phrases like "too awkward," "profoundly still," and "didn’t talk" which reveal a somber, isolated and possibly melancholic tone. It reflects the author’s feelings of discomfort, silence, and the lack of communication and connection with the family.
The two tones differ significantly, with the first being uplifted and forward-looking, while the second expresses a sense of disconnection and sadness, giving us a comprehensive view of the contrasting emotional landscapes in the same narrative context.
How many 10 are in 64785
Ow is the constant max_length declared inside a method with the value of 99.98?
Which expression is equivalent to 32⋅32⋅32⋅32 ?
32⋅4
(32)4
342
324
Answer: [tex]32^4[/tex].
Step-by-step explanation:
The given expression : [tex]32\cdot 32\cdot 32\cdot32[/tex]
Using the law of exponent :-
[tex]a\times\atimes....\times a (\text{ n times})=a^n[/tex]
Now, the given expression ,becomes
[tex]32\cdot 32\cdot 32\cdot32\text { (4 times)}=32^4[/tex]
Hence, the expression is equivalent to the given expression [tex]32\cdot 32\cdot 32\cdot32[/tex] is [tex]32^4[/tex].
Please be a good person and help me..I really need to get this right to boost my grade in math ((and boy do I need it!!))
Use the graph shown to fill in the blank.
When x = 1, then y = a0.
Solve for y 3y-9=6 show work
Rule that maps each preimage
A function is a rule that maps each preimage to a unique image.
Explanation:A rule that maps each preimage to a unique image is called a function. In mathematics, a function is a relation between a set of inputs (preimages) and a set of outputs (images) in which each input is associated with exactly one output.
For example, consider the function f(x) = 2x, where the input x is a preimage and the output 2x is the corresponding image. If we plug in x = 3, the preimage, we get f(3) = 2(3) = 6, the image.
Functions are commonly represented using algebraic expressions, tables, graphs, or diagrams. They are fundamental to many branches of mathematics and have applications in various fields. The phrase 'rule that maps each preimage' refers to the function or transformation that defines how to manipulate a preimage to obtain an image, either by applying a mathematical formula or by executing a geometric operation.
a. Find the value of a. b. Find the value of the marked angles.
A)14; 94°
B)16; 106°
C)19; 124°
D)15; 100°
Answer:
D)15; 100°.
Step-by-step explanation:
Given : Verticle opposite angles (6a + 10) and (3a + 55).
To find : Find the value of a. b. Find the value of the marked angles.
Solution : We have given (6a + 10) and (3a + 55).
Verticle opposite angles are equal
Then
6a + 10 = 3a + 55
On subtracting both sides by 3a
6a - 3a + 10 = 55
3a + 10 = 55
On subtracting by 10 both sides.
3a = 55 -10.
3a = 45.
On dividing the 3 by both sides
a = 15°.
Then ,
6 (15) + 10.
90 + 10 = 100
b =100°.
Therefore, D)15; 100°.
If f(x) is the total number of bacteria present in a sample after x hours, which of the following statements best describes the meaning of f(2) = 12? (1 point)
the area of one of the smaller circles is 8 pi in2. find the area of the shaded region
the answer is D. 16 pi
Answer:
D.
Step-by-step explanation:
A piece of land is to be fenced and subdivided as shown so that each rectangle has the same dimensions. Express the total amount of fencing needed as an algebraic expression in x.
If two or more rectangles have the same dimensions is because they are congruent. In this way, they share two corresponding sides. Our first rectangle has the following sides:
L1 = x
L2 = 3x + 4
Therefore the second and third rectangles need to have the same sides. Therefore, we will have that the sides of the second one is also:
L1 = x
L2 = 3x + 4
and the sides of the third one is also:
L1 = x
L2 = 3x + 4
Therefore, the total amount of fencing needed is:
T = 3(3x + 4) + 4(x)
T = 9x + 12 + 4x
T = 13x + 12
Moreover, we can compute the area of the fence as follows:
A = [(3x + 4) + (3x + 4) + (3x + 4)]x = (3x + 3x + 3x + 4 + 4 + 4)x
A = (9x + 12)x
A = 9x² + 12x
The algebraic expression that expresses the total amount of fencing needed is 11X + 20.
CalculusGiven that a piece of land is to be fenced and subdivided as shown so that each rectangle has the same dimensions, to express the total amount of fencing needed as an algebraic expression in X, the following calculation must be performed:
3X + 4 = 6 wooden fence blocksEach rectangle has 3 blocks on each side and 6 blocks in front.Number of fronts = 3Number of sides = 4(3X + 4) x 3 + ((3X + 4) x 4) / 2 = Algebraic expression9X + 12 + (4X + 16) / 2 = Algebraic expression9X + 12 + 2X + 8 = Algebraic expression11X + 20 = Algebraic expressionTherefore, the algebraic expression that expresses the total amount of fencing needed is 11X + 20.
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12. What percent of 60 is 12? Show your work.
A clipboard costs 2.23. it costs 0.53 more than a notebook. lisa buys two clipboards and one notebook, and paid with a ten dollar bill. use a tape diagram with calculations to show her change
9 more than the quotient of negative 36 and negative 4
The sum of four consecutive even integers is 180. what is the smallest integer?
What is the area of a parallelogram whose vertices are A(−12, 2) , B(6, 2) , C(−2, −3) , and D(−20, −3) ? Enter your answer in the box.
Answer:
[tex]\boxed{90}\,\text{units$^2$}[/tex]
Step-by-step explanation:
The sides AB and CD are parallel to the x-axis and 5 units apart. The length of side AB is 6-(-12) = 18 units. The area is the product of these dimensions:
Area = (Base)(Height) = (18 units)(5 units) = 90 units²
A wooden board is leaning against a house. the base of the board is 10 ft from the base of the house and the base of the board forms a 35 degree angle with the ground
so what is the length of the wooden board?
3ax + 2b / c = 4d solve for x
Final answer:
To solve the equation 3ax + 2b / c = 4d for x, isolate x on one side of the equation by multiplying both sides by c, subtracting 2b, and dividing by 3a.
Explanation:
To solve the equation 3ax + 2b / c = 4d for x, we need to isolate x on one side of the equation. Here are the steps:
Multiply both sides of the equation by c to get rid of the denominator: 3ax + 2b = 4cd.Subtract 2b from both sides of the equation: 3ax = 4cd - 2b.Divide both sides of the equation by 3a to solve for x: x = (4cd - 2b) / (3a).Therefore, the solution for x is x = (4cd - 2b) / (3a).
Write each rational number as a terminating decimal.
1. 19/20
2. -1/8
3. 17/5
Thomas earns x dollars each week walking his neighbor’s dog. He also earns $10 allowance each week.
Which expression represents the amount of money Thomas has earned after 4 weeks?
Select each correct answer.
4x+10
4x⋅10x
4(x+10)
x+10+x+10+x+10+x+10
Answer:
option C and D
Step-by-step explanation:
Thomas earns x dollars each week walking his neighbor’s dog. He also earns $10 allowance each week.
we need to find how much Thomas has earned after 4 weeks
in 1 week , x dollars earned
Also $10 allowance each week.
So amount earned in 1 week is [tex]x+10[/tex]
To find the Amount earned in 4 weeks , multiply the expression by 4
amount of money Thomas has earned after 4 weeks is [tex]4(x+10)[/tex]
[tex]4(x+10)=4x+40=x+10+x+10+x+10+x+10[/tex]
option C and D
Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?
howdy!!
yr answer is
A. {–7, 1} !!!
help ma please
What are the steps for using a compass and straightedge to construct a line through point A that is parallel to line j?
A horizontal line j and a point A are drawn. The point A is below the horizontal line j.
Drag the steps and drop them in order from start to finish.
Place the point of the compass on point Q and open it to width QR .
Use the straightedge to draw a line k that passes through A and intersects line j. Label the point of intersection as point P.
Use the straightedge to draw AB←→.
Without changing the width of the compass opening, place the point of the compass on point A and draw an arc that intersects line k. Label the intersection as point S.
With the compass opening set to width QR , place the point of the compass on point S and draw an arc that intersects the arc that was drawn from point A. Label the intersection of the arcs as point B.
Place the point of the compass on point P and draw an arc that intersects lines j and k. Label the intersections as points Q and R.
Answer:
Step 1: Use the straightedge to draw a line k that passes through A and intersects line j. Label the point of intersection as point P. This is because you must have a point of intersection with the line before you can move forward.
Step 2: Place the point of the compass on point P and draw an arc that intersects lines j and k. Label the intersections as points Q and R. This will give us a compass width to move forward.
Step 3: Place the point of the compass on point Q and open it to width QR.
Step 4: Without changing the width of the compass opening, place the point of the compass on point A and draw an arc that intersects line k. Label the intersection as point S. This gives us the point to use to construct the second point of our parallel line.
Step 5: With the compass opening set to width QR , place the point of the compass on point S and draw an arc that intersects the arc that was drawn from point A. Label the intersection of the arcs as point B. This is the second point of our parallel line.
Step 6: Use the straightedge to draw AB←→.
The steps are shown below:
What is line segment?A line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between its endpoints.
Use the straightedge to draw a line k that passes through A and intersects line j. Label the point of intersection as point P. Place the point of the compass on point P and draw an arc that intersects lines j and k. Label the intersections as points Q and R. Place the point of the compass on point Q and open it to width QR. Without changing the width of the compass opening, place the point of the compass on point A and draw an arc that intersects line k. Label the intersection as point S. With the compass opening set to width QR , place the point of the compass on point S and draw an arc that intersects the arc that was drawn from point A. Label the intersection of the arcs as point B. Use the straightedge to draw AB←→.Learn more about line segment here:
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#SPJ4
1643 AD minus 582 BC
Answer:
2,225 years apart
Step-by-step explanation:
Judy has started walking briskly everyday. if, as a result, she burned 350 calories more per day than she consumes, how many days will it take her to lose 10 pounds
Express 3x + 4y = 24 in slope-intercept form.
What issues does a person "charged" with a crime typically have to deal with?
Triangle DEF is formed by the three squares P, Q, and R:
A right triangle DEF is shown. On the side DE of this triangle is a square. Inside the square is written Square P, and below it and inside the square is written Area equal to 64 square units. On the side EF of this triangle is another square. Inside the square is written Square Q, and below it and inside the square is written Area equal to 225 square units. On the side DF of this triangle is another square. Inside the square is written Square R, and below it and inside the square is written Area equal to 289 square units.
Which statement best explains the relationship between the sides of triangle DEF?
DE + EF = DF, because 64 + 225 = 289
(DE)2 + (EF)2 = (DF)2, because 172 + 82 = 152
(DE)2 + (EF)2 = (DF)2, because 64 + 225 = 289
DE + EF = DF because, 172 + 82 = 152
using the Pythagorean Theorem
a^2 + b^2 = C^2
so correct answer is:
(DE)2 + (EF)2 = (DF)2, because 64 + 225 = 289
Answer:
(DE)2 + (EF)2 = (DF)2, because 64 + 225 = 289
Step-by-step explanation:
Calculate the area of the irregular polygon shown below:
45 inches squared
50 inches squared
60 inches squared
85 inches squared
Tommy stands on a diving board that is 4 fee above the pools surface. He dives and touches the bottom of the pool, which is 12 feet below the pools surface. What is the total length of Tommy’s dive?
If three times the supp. of an angle is subtracted from seven times the comp. of the angle, the answer is the same a that obtained by trisecting a right angle. Find the supplement.