Answer:
The probability is [tex]P(x_1 \le X \le x_2 ) = 0.4332[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 400[/tex]
The standard deviation is [tex]\sigma = 10[/tex]
The considered values are [tex]x_1 = 400 \to x_2 = 415[/tex]
Given that the weight follows a normal distribution
i.e [tex]\approx X (\mu , \sigma )[/tex]
Now the probability of a weight between 415 pounds and the mean of 400 pounds is mathematically as
[tex]P(x_1 \le X \le x_2 ) = P(\frac{x_1 - \mu }{\sigma } \le \frac{X - \mu }{\sigma } \le \frac{x_2 - \mu }{\sigma } )[/tex]
So [tex]\frac{X - \mu }{\sigma }[/tex] is equal to Z (the standardized value of X )
Hence we have
[tex]P(x_1 \le X \le x_2 ) = P(\frac{x_1 - \mu }{\sigma } \le Z \le \frac{x_2 - \mu }{\sigma } )[/tex]
substituting values
[tex]P(x_1 \le X \le x_2 ) = P(\frac{400 - 400 }{10 } \le Z \le \frac{415 - 400}{415 } )[/tex]
[tex]P(x_1 \le X \le x_2 ) = P(0\le Z \le 1.5 )[/tex]
[tex]P(x_1 \le X \le x_2 ) = P( Z < 1.5) - P( Z < 0)[/tex]
From the standardized normal distribution table [tex]P( Z< 1.5) = 0.9332[/tex] and
[tex]P( Z < 0) = 0.5[/tex]
So
[tex]P(x_1 \le X \le x_2 ) = 0.9332 - 0.5[/tex]
[tex]P(x_1 \le X \le x_2 ) = 0.4332[/tex]
NOTE : This above values obtained from the standardized normal distribution table can also be obtained using the P(Z) calculator at (calculator dot net).
A swimming pool is circular with a 30-ft diameter. The depth is constant along east-west lines and increases linearly from 2 ft at the south end to 7 ft at the north end. Find the volume of water in the pool. (Round your answer to the nearest whole number.) ft3
Answer:
Volume of water in the pool is 3,182 ft^3
Step-by-step explanation:
In this question, what we want to calculate is the volume of water in the pool.
We proceed as follows;
diameter of pool = 30ft
depth: 2 to 7ft linearly
average depth = (2 + 7)/2 = 9/2 = 4.5 ft
Volume = area * average depth
V = pi * radius^2 * 4.5
where radius = diameter/2 = 30/2 = 15 ft
V = pi * 15^2 * 4.5
V = 22/7 * 225 * 4.5
V = 3,182.14 ft^3
which is 3,182 ft^3 to nearest whole number
The volume of water in the pool is; Volume = 3181 ft³
We are given;
Diameter of swimming Pool; d = 30 ft
Thus; radius; r = d/2 = 30/2 = 15 ft
We are told that the depth is constant along east-west lines and increases linearly from 2 ft at the south end to 7 ft at the north end.
Thus, average depth is;
h_avg = (2 + 7)/2
h_avg = 4.5 ft
Formula for area is; A = πr²
Thus;
A = π × 15²
A = 225π
Formula for volume here is;
Volume = Area × depth
Volume = 225π × 4.5
Volume = 3180.86 ft³
Approximating to a whole number gives;
Volume = 3181 ft³
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Find the indicated sum for each sequence. S9 of –9, 36, –144, 576, ... A –585 B –471,861 C 1,887,435 D –471,852
=====================================================
Explanation:
This is a geometric sequence because each new term is found by multiplying the last term by -4.
The common ratio is r = -4. The first term is a = -9. We want to sum up n = 9 terms.
Use the geometric nth partial sum formula below to plug in the terms mentioned
[tex]S_n = \frac{a*(1-r^n)}{1-r}\\\\S_9 = \frac{-9*(1-(-4)^9)}{1-(-4)}\\\\S_9 = \frac{-9*(1-(-262144))}{1+4}\\\\S_9 = \frac{-9*(1+262144)}{1+4}\\\\S_9 = \frac{-9*(262145)}{5}\\\\S_9 = \frac{-2359305}{5}\\\\S_9 = -471,861\\\\[/tex]
Answer:
-471,861
Step-by-step explanation:
. (08.03 LC) Determine the factors of x2 − 12x − 20. (5 points) (x − 2)(x + 10) (x − 10)(x + 2) (x − 5)(x + 4) Prime
Answer:
prime
Step-by-step explanation:
We're looking for 2 numbers with a sum of -12 and product of -20 but unfortunately there aren't any numbers that do so, therefore the answer is prime.
Answer:
Prime
Step-by-step explanation:
which of the following is the correct graph of the linear equation below? y+3=-2/3(x-4)
Answer:
see details.
Step-by-step explanation:
Graphs from question not yet uploaded, so read attached graph to make a match.
In general, what would every child function have in common with the parent function f (x)= x?
Step-by-step explanation:
If f(x) =x, is the father function, then all it's child function would be equally inclined to x and y-axis respectively.
If f(x) =x, is the father function, then all its child functions would be equally inclined to the x and y-axis respectively.
How is each function in a family related to the parent function?Each family of capabilities has a determining feature. A discern function is the best function that also satisfies the definition of a certain sort of function. As an instance, whilst we think about the linear capabilities which make up our own family of capabilities, the parent feature could be y = x.
What key attributes are common among parent functions?Key commonplace points of linear determine features encompass the reality that the equation is y = x. Domain and variety are actual numbers. Slope, or fee of alternate, is steady.
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Find the probability of each event. A basketball player has a 50% chance of making each free throw. What is the probability that the player makes at least seven out of eight free throws?
Hey there! I'm happy to help!
We want to find the probability that the player makes at least seven out of eight free throws. First, we find the probability of them making seven free throws.
[tex]\frac{1}{2}^7=\frac{1}{128}[/tex]
Then, we find the probability of them making eight, which is another possibility that fits this.
[tex]\frac{1}{2}^8=\frac{1}{256}[/tex]
Now, we add the probability of these two events happening.
[tex]\frac{1}{128}+\frac{1}{256}=\frac{3}{256}[/tex]
Therefore, the probability that the player makes at least seven of eight free throws is 3/256 or about 1.17%
Have a wonderful day! :D
Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to approximate the sum of the series with an error of less than 0.0001.
Answer:
yeyyyaya
Step-by-step explanation:
can some one plz help me Find an equation in standard form for the ellipse with the vertical major axis of length 16 and minor axis of length 4.
One of the equations of ellipse is in a form of the lengths of its axes. If we have the length of its major axis as 2a and the length of its minor axis as 2b then, the values of a and b are,
2a = 16, a = 16/2 = 8
2b = 4, b = 4/2 = 2
Given that we have the major axis as vertical, the equation for ellipse is,
y²/a² + x²/b² = 1
Substituting,
y²/8² + x²/2² = 1
Simplifying,
y² + 16x² = 1
Answer: y² + 16x² = 1
Hope this helped and if it did please give me brainliest, it will help me a lot. :)
Have a good day!
9. Express 400cm3 as a fraction of 2 litres
in the lowest form. *
options
1/10
1/5
2/5
Answer:
[tex]\boxed{\red{\frac{1}{5} }}[/tex]
Step-by-step explanation:
[tex]400 {cm}^{3} = 400ml \\ 2l = 2000ml[/tex]
So, now we have to write 400cm^3 as a fraction of 2l
[tex] \frac{400}{2000} = \frac{4}{20} = \frac{1}{5} [/tex]
There are 4 red balls and 6 green balls in a bag.
You reach in the bag and take out 3 balls without looking.
What is the probability that all three of the balls you take out are red?
[tex]\frac{1}{30}[/tex]
Step-by-step explanation:From the question, in the bag there are;
4 red balls
6 green balls
10 balls in total.
Now, reaching in the bag and taking out 3 balls without looking, the probability that all three balls are red, can be analyzed as follows;
All three red means;
The first ball is red,
The second ball is red and;
The third ball is red.
i. First you take out a ball from a total of 10 balls. The probability P⁰(R) of having a red ball is given as;
P⁰(R) = [tex]\frac{possible-space}{total-space}[/tex]
Since there are 4 red balls, the possible-space is 4
Also, since there are a total of 10 balls, the total-space is 10
P⁰(R) = [tex]\frac{4}{10} = \frac{2}{5}[/tex]
ii. Secondly, you take out a ball from a remaining total of 9 balls. The probability P¹(R) of still having a red ball is given as;
P¹(R) = [tex]\frac{possible-space}{total-space}[/tex]
Since there are 3 red balls remaining, the possible-space is 3
Also, since there are a remaining total of 9 balls, the total-space is 9
P¹(R) = [tex]\frac{3}{9} = \frac{1}{3}[/tex]
iii. Thirdly, you take out a ball from a remaining total of 8 balls. The probability P²(R) of still having a red ball is given as;
P²(R) = [tex]\frac{possible-space}{total-space}[/tex]
Since there are 2 red balls remaining, the possible-space is 2
Also, since there are a remaining total of 8 balls, the total-space is 8
P²(R) = [tex]\frac{2}{8} = \frac{1}{4}[/tex]
Therefore, the probability P(R) of taking out three red balls without looking is given by the product of the probabilities described above. i.e
P(R) = P⁰(R) x P¹(R) x P²(R)
P(R) = [tex]\frac{2}{5} * \frac{1}{3} * \frac{1}{4} = \frac{1}{30}[/tex]
which formulas can be used to find the surface area of a regular pyramid where p is the perimeter of the base, s is the slant height, BA is the base area, and LA is the lateral area click all that apply options: A. SA= 1/2BA + 1/2ps B. SA= BA-LA C. SA= BA+LA D. SA= BA • LA E. SA= BA + 1/2ps
Answer:
C and E
Step-by-step explanation:
He got it on ap.ex
The area of the pyramid can be found using the formula SA = BA + LA and SA= BA + 1/2ps option (C) and (E) are correct.
What is a square pyramid?In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the center of the square.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a pyramid with a square base:
The perimeter of the base is p
The slant height is s.
The base area is BA
The lateral area is LA.
We can find the area of the pyramid as follows:
SA = BA + LA
SA= BA + 1/2ps
Thus, the area of the pyramid can be found using the formula SA = BA + LA and SA= BA + 1/2ps option (C) and (E) are correct.
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What the answer fast
Answer:
72
Step-by-step explanation:
36+36=72
4x + 12 = 20y Solve for x.
Answer:
x=5y-3
Step-by-step explanation:
[tex]4x+12=20y\\4x=20y-12\\x=\frac{20y-12}{4} \\x=\frac{20y}{4}- \frac{12}{4} \\x=5y-3[/tex]
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Factor completely and then place the factors in the proper location on the grid. 4y2 + 25y + 6
Answer:
(4y +1)(y +6)
Step-by-step explanation:
We can rewrite the middle term and factor by grouping.
4y^2 + 25y + 6 = (4y^2 +24y) +(y +6)
= 4y(y +6) +1(y +6)
= (4y +1)(y +6)
think about whether the diagram represents a function.
Step-by-step explanation:
im sorry but i need more info or a picture or something to actually anwser the question...
I need help with this quickly, it would be very much appreciated.
Answer:
complementary because 2 angles that add up to 90º is a complementary angle and x=9 :)
Step-by-step explanation:
90=46+5x-1
45=5x
x=9
Answer:
x = 9 Complementary
Step-by-step explanation:
The angles are compplementary cause the angle add up to 90°
Well to find x we need to make the following equation,
46 + (5x - 1) = 90
We need to simplify and combine like terms,
46 - 1 = 45
45 + 5x = 90
-45 to both sides
5x = 45
Divide 5 by both sides
x = 9
Thus,
x is 9.
Hope this helps :)
What are the positive and negative square roots of 1?
Answer:
Positive is 1
Negative is-1
Step-by-step explanation:
Solve: 5x=110. (Round to three decimal places.)
Hey there! Welcome to Brainly! I'm happy to help!
In equations, letters like x or y are called variables. They represent a number that we do not know yet, or they can almost be seen as a question mark in an equation. For example, 1+?=2. We know that this ? represents the number 1, and the same would go if you put a variable in there. If you have 1+x=2, you can figure out that x=1!
Our equation is 5x=110. When you see a number next to a variable, that number is called the coefficient. It is a number that multiplies a variable. So, our coefficient is 5. This means that five is multiplied by x to equal 110.
5·x=110
What if we don't know off the top of our heads what we multiply 5 by to get to 110? It was easy with 1+1=2, but this is trickier. Here's how to figure it out.
We want to get the x all by itself on one side of the equation. Then, we will see what x equals.
To do this, we use inverse operations. I will show you below with our 1+x=2 example.
1+x=2
We have a positive one plus an x equals two. We could visualize this like this.
+1+x=2
What we want to do is move the 1 to the other side of the equation so that x is by itself. So, what's the opposite of adding? Subtracting!
However, we don't just subtract the 1 from the left side, but we do it from the right side! You have to do the inverse operation on both sides to find the answer.
So, let's subtract 1 from both sides.
+1+x-1=2-1
x=1
We see that x equals 1, and if we plug this into the equation 1+x=2, we see that it is correct.
Now, with our problem, we need to divide, because that is the opposite of multiplication. We need to divide both sides by 5 to isolate the x. Let's do it!
5x÷5=110÷5
x=22
We see that 5×22 is equal to 110, so this is correct! Now you can solve for variables in equations!
Have a wonderful day!
The number of users on a website has grown exponentially since its launch. After 1 month, there were 120 users. After 4 months, there were 960 users. Find the exponential function that models the number of users x months after the website was launched. Write your answer in the form f(x)=a(b)x.
Answer:
f(x) = 60(2)ˣ
Step-by-step explanation:
f(x) = a(b)ˣ
After one month:
120 = a(b)¹
After four months:
960 = a(b)⁴
Divide the second equation by the first:
8 = b³
b = 2
Plug into either equation and find a.
120 = a(2)¹
a = 60
Therefore, f(x) = 60(2)ˣ.
Find the area under the standard normal curve between z=−0.89 and z=2.56. Round your answer to four decimal places, if necessary.
Answer:
0.8080
Step-by-step explanation:
A suitable probability calculator gives that area as 0.8080.
Thank you for the help!!
Answer:
B. 5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
You know that the empty barrel is 1/4 of the full barrel. Find 1/4 of 20 to get 0.25 x 20 = 5
In Sparrowtown, the use of landlines has been declining at a rate of 5% every year. If there are 20,000 landlines this year, how many will there be in 15 years? If necessary, round your answer to the nearest whole number.
Answer:
5,000
Step-by-step explanation:
If it decreases by 5% a year, it'll decrease by 75% in 15 years
i.e 1 year = 5%
15 years = x
Cross multiply
x = 75%
Therefore, since it decreases by 75%
100 - 75 x 20,000 = 5,000
100
Question 1 (10 points). (a) Explain the difference between linear and logistic regression. (Explain at least two differences and one similarity in detail). (b) Give an example of a modeling problem (ie, using X to predict Y, where X and Y are real life examples) for each type.
Answer:
(a) Linear regression is used to estimate dependent variable which is continuous by using a independent variable set. Logistic regression we predict the dependent variable which is categorical using a set of independent variables.
(b) Finding the relationship between the Number of doors in the house vs the number of openings. Suppose that the number of door is a dependent variable X and the number of openings is an independent variable Y.
Step-by-step explanation:
(a) Linear regression is used to estimate dependent variable which is continuous by using a independent variable set .whereas In the logistic regression we predict the dependent variable which is categorical using a set of independent variables. Linear regression is regression problem solving method while logistic regression is having use for solving the classification problem.
(b) Example: Finding the relationship between the Number of doors in the house vs the number of openings. Suppose that the number of door is a dependent variable X and the number of openings is an independent variable Y.
If I am to predict that increasing or reducing the X will have an effect on the input variable X or by how much we will make a regression to find the variance that define the relationship or strong relationship status between them. I will run the regression on any computing software and check the stats result to measure the relationship and plots.
What is the GIM of a strip mall with annual income of $547,500 and a value of $6,345,000?
Answer:
11.6Step-by-step explanation:
GIM means Gross Income Multiplier and it is a method used for valuating a property or an investment. It is expressed mathematically as the ratio of the property's value/sales price and its gross annual income.
GIM = Value of an investment/Gross annual income.
Given the annual income = $547,500 and Value = $6,345,000;
GIM = $6,345,000/$547,500
GIM = 11.589
GIM ≈ 11.6
Hence, the Gross Income Multiplier of the strip mall is approximately 11.6.
GIM has no units.
Which statement best explains the relationship between lines PQ and RS? They are parallel because their slopes are equal. They are parallel because their slopes are negative reciprocals. They are not parallel because their slopes are not equal. They are not parallel because their slopes are negative reciprocals.
Answer:
They are not parallel because their slopes are not equal
Step-by-step explanation:
From the diagram attached, The line PQ has point P at (-5, 3) and point Q at (5, 1).
For line RS, point R is at (-4, -2) and point S is at (0, -4).
Two lines AB and CD are said to be parallel to each other if they have the same slope, i.e if the slope of AB is m1 and the slope of CD is m2, m1 = m2. When two lines are parallel, they can never intersect.
The slope (m) of of a line given two points on the line is calculated using:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For line PQ has point P at (-5, 3) and point Q at (5, 1), the slope is given as:
[tex]m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{1-3}{5-(-5)}=-\frac{1}{5}\\[/tex]
For line RS, point R is at (-4, -2) and point S is at (0, -4), the slope is given as:
[tex]m_2=\frac{y_2-y_1}{x_2-x_1}=\frac{-4-(-2)}{0-(-2)}=-1[/tex]
Since the slope of PQ (-1/5) and the slope of line RS (-1) are not equal, therefore the lines are not parallel
Answer:
They are not parallel because their slopes are not equal.
Step-by-step explanation:
The first person to answer this was correct, please mark them brainliest.
What is the second step when evaluating the expression 49 + 63 ÷ (3 + 2 × 2) – 7? 63 ÷ 3 63 ÷ 7 2 × 2 3 + 4
ANSWER: Multiply and Divide from left to right
To do this question we must follow the rules of PEMDAS. The first step would be to evaluate the equation given to us in the parentheses. To solve that we would have to use PEMDAS once again which tells us to multiply 2 x 2 before we add 3, so we get 7. Now that there is no more Parentheses, our second step is to evaluate each Multiplication and Division expression from left to right. This would start by dividing 63 by 7 to get 9.
If y>0, which of these values of x is NOT in the domain of this equation? y=x2+7x
Answer:
[tex]\boxed{\sf \ \ \ [-7,0] \ \ \ }[/tex]
Step-by-step explanation:
Hello
[tex]y=x^2+7x=x(x+7) >0\\<=> x>0 \ and \ x+7 >0 \ \ or \ \ x<0 \ and \ x+7<0\\<=> x>0 \ \ or \ \ x<-7\\[/tex]
So values of x which is not in this domain is
[tex]-7\leq x\leq 0[/tex]
which is [-7,0]
hope this helps
Find the value of y........
Answer:
hope this is right y=74
Step-by-step explanation:
have not done this since two years ago so...
but anyway 148-180 = 32
32 is that angle
if this were a right triangle my answer would be different but 148/2 still completes this triangle and somewhat makes sense.
The correct answer is 90.
The table shows the cost, C, in dollars, to rent a car from Carl's Car Rentals. Determine the following: a) What is the fixed cost? b) What is the variable cost? c) Write an equation relating your answer from part (a) and part (b) [be sure to use the variables stated in the table]. d) What kind of variation is this relationship showing? e) Calculate the cost of renting a car for a day and driving a total of 800km.
Answer:
a) Fixed cost = $50
b) Total variable cost is $15, while variable cost per unit is $0.15.
c) C = 50 + d0.15
d) Direct variation
e) The cost of renting a car for a day and driving a total of 800km is $170,
Step-by-step explanation:
a) What is the fixed cost?
Fixed cost is a cost that does not change with the level of activity. Fixed is incurred whether there is an activity, or there is no activity at all, that is, when the activity is zero.
Since cost, C, is equal to $50 when distance, d (km), is equal to zero in the table, the fixed cost is therefore equal to $50, i.e.:
Fixed cost = $50
b) What is the variable cost?
Variable cost is a cost that changes as the level of activity changes. From the table, the variable cost can be obtained by deducting the fixed cost from the total cost. This can be calculated using any of the distance, d (km), in the table.
Using the distance of 100 as an example, the total variable cost can be obtained as follows:
Variable cost = Total Cost at 100 distance - Fixed cost = $65 - $50 = $15
Note that variable cost per distance at 100 distance can be obtained as follows:
Variable cost per distance = $15 / 100 = $0.15
c) Write an equation relating your answer from part (a) and part (b)
Since,
C = Cost
d = distance (km)
Fixed cost = $50
Variable cost per distance = $0.15
Therefore, suppressing the dollar sign for simplicity purpose, an equation relating the above can be given as follows:
C = 50 + d0.15 ............................................. (1)
d) What kind of variation is this relationship showing?
This is a direct variation.
Direct variation is a variation in which an increase in one variable will lead to an increase in another variable.
For example in equation (1), a increase in d which is multiplied by $0.15 will lead to an increase in C.
e) Calculate the cost of renting a car for a day and driving a total of 800km.
This implies that d = 800.
Substituting d = 800 into equation (1), we have:
C = 50 + (800 * 0.15) = 170
Therefore, the cost of renting a car for a day and driving a total of 800km is $170.
In how many ways can 13 people be divided into four groups with 3, 6, 2 and 2 people respectively?
Answer:
6227020800
Step-by-step explanation:
There are 13 ways to choose the first person in the first group, 12 ways to choose the second person in the first group and so on until we get 1 way to choose the second person in the last group so the answer is 13 * 12 * 11 * ... * 3 * 2 * 1 = 13! = 6227020800.