Answer:
Expected value=77 people
Standard error=0.0040
Step-by-step explanation:
-Given the proportion is, p=0.67
-The expected value can be calculated as:
[tex]Expected \ Value=np\\\\=120\times 0.637\\\\=76.44\approx 77[/tex]
#The standard deviation is calculated as:
[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\=\sqrt{\frac{0.637(1-0.637)}{120}}\\\\=0.0439[/tex]
#We use this calculated standard deviation to calculate the standard error:
[tex]SE=\frac{\sigma_p}{\sqrt{n}}\\\\=\frac{0.0439}{\sqrt{120}}\\\\=0.0040[/tex]
Hence, the sample has an expected value of approximately 77 people and a standard error of 0.0040
A ship's sonar locates a treasure chest at a 12° angle of depression. A diver is lowered 40 meters to the ocean floor. How far (to the nearest meters) does the diver need to swim along the ocean floor to get the treasure chest?
To find the distance the diver needs to swim along the ocean floor to reach the treasure chest, we can use trigonometry. By using the angle of depression and the depth the diver is lowered, we can calculate the hypotenuse of the right triangle formed, which represents the distance the diver needs to swim. The diver needs to swim approximately 199 meters along the ocean floor to reach the treasure chest.
Explanation:To find the distance the diver needs to swim along the ocean floor, we can use trigonometry. Let's consider the right triangle formed by the diver, the treasure chest, and the ship's sonar. The angle of depression is 12°, and the diver is lowered 40 meters. We need to find the hypotenuse of the triangle, which represents the distance the diver needs to swim.
Using the angle of depression and the opposite side of the triangle (the depth the diver is lowered), we can set up the following trigonometric equation:
tan(12°) = opposite/hypotenuse
Substituting the values:
tan(12°) = 40/hypotenuse
Solving for the hypotenuse, we get:
hypotenuse = 40/tan(12°)
Calculating this value gives us approximately 199.20 meters. Therefore, the diver needs to swim approximately 199 meters along the ocean floor to reach the treasure chest.
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A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator descends 6 feet per second. The elevator for the miners descends 16 feet per second. One day, the equipment elevator begins to descend. After 20 seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 17 seconds? At that time, which elevator is deeper?
29 is 6 more than k.
Solve for k.
Make an equation for k.
Answer:
23
Step-by-step explanation:
29 minus 6 equals 23
Answer:
k = 23
29 = k + 6
Step-by-step explanation:
29 = k + 6
k = 29 - 6
k = 23
If M(-2,8) is reflected in the y-axis what are the coordinates of M , the image M
Answer:
If it was reflected over the y-axis, the x variable would be inverted, causing the coords to be M(2,8)
The ages of the winners of a cycling tournament are approximately bell-shaped. The mean age is 27.2 years, with a standard deviation of 3.5 years. The winner in one recent year was 23 years old.
(a) Transform the age to a z-score.
(b) Interpret the results.
(c) Determine whether the age is unusual.
Part(a): The value of the Z-score is -1.2
Part(b): The age of the winner is -1.2 standard deviation from the mean.
Part(c): Yes, the age is unusual.
Given,
[tex]\mu =27.2\\\sigma = 3.5[/tex]
Winner age, X = 23
Part(a):
The formula for the Z-score is,
[tex]Z=\frac{x-\mu }{\sigma } \\=\frac{23-27.2}{3.5}\\=-1.2[/tex]
Part(b): The age of the winner is -1.2 standard deviation from the mean which is equal to its Z-score value.
Part(c): Yes, the age is unusual.
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To calculate the z-score, subtract the mean age from the winner's age and divide by the standard deviation, resulting in -1.2. This indicates the winner is 1.2 standard deviations younger than the mean age. Since the z-score is not beyond -2, the age is not considered unusual.
The question requires us to calculate a z-score and interpret the results regarding a recent cycling tournament winner's age in context of a normal distribution.
Calculating the z-score
To calculate the z-score:
Subtract the mean age from the winner's age.
Divide by the standard deviation.
In our case:
The winner's age = 23 years
The mean age = 27.2 years
The standard deviation = 3.5 years
Thus, z = (23 - 27.2) / 3.5 = -1.2
Interpretation
This z-score means the winner's age was 1.2 standard deviations to the left of the mean. In other words, the winner is younger than the average.
Determining Unusual Age
If we consider ages that lie more than 2 standard deviations from the mean as unusual (which corresponds to roughly the outer 5% of data in a normal distribution), then a z-score of -1.2 does not qualify as unusual, since it is not beyond the 2 standard deviation threshold.
A wheel with a diameter of 25 in. is in a puddle of water 8.1 in. deep. What is the width of the wheel, AB, at the surface of the water?
Answer:
AB = 23.4 inches
Step-by-step explanation:
If the diameter of the wheel is 25 inches, we have that its radius is 25/2 = 12.5 inches.
If we draw a radius to the bottom of the wheel and a radius to point A, we have a triangle where we can use Pythagoras' formula:
(see image attached for better understanding)
r^2 = (r-8.1)^2 + (AB/2)^2
12.5^2 = 4.4^2 + AB^2/4
156.25 = 19.36 + AB^2/4
AB^2/4 = 136.89
AB^2 = 547.56
AB = 23.4 inches
*click image*
Hello! I’m currently in need of help on a assignment thank you so much if you help out I really appreciate you and your hard work and effort!!
Also if you can please show work! I don’t really want to get the answers incorrect sorry!
Answer:
142
Step-by-step explanation:
[tex]\frac{x+18}{5}=32[/tex]
Multiplying both sides by 5, you get:
x+18=160
Now, you can subtract 18 from both sides to get:
x=142
Hope this helps! Comment if this wasn't clear enough, or you need more explanation.
Answer: x=142
Step-by-step explanation:
x+18 / 5 = 32
first multiply both sides by 5
x + 18 = 160
then subtract 18 from both sides
x=142
MARK USES 3/8 OF a box he uses to make enough to make enough for one person. Write and solve an equation to find p, how much of the box for 2 people. Use a drawing as needed.
Answer:
p = x * (3/8)
Where p is the amount of a box and x is the number of people.
For x=2 -> p = 2 * (3/8) = 3/4
Step-by-step explanation:
If Mark uses 3/8 of a box to make enough for one person, we can find the amount required (p) to be enough for 'x' people using a rule of three:
3/8 of a box -> 1 person
p -> 'x' people
(3/8)/p = 1/x
p/(3/8) = x
p = x * (3/8)
If we want the amount for 2 people, we use x = 2 in the equation:
p = 2 * (3/8) = 3/4
So Mark will need 3/4 of a box.
At the end of summer, Spencer's favorite toy store had a huge sale. Spencer picked out a remote–control car on sale for 20% off the original price of $79.99. He also picked out a robot for 25% off the original price of $99.99. How much money did Spencer save?
Answer:
he saved $40
Step-by-step explanation:
The required money saved by spencer at the end of the summer sale is $40.98.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
Spencer picked out a remote–control car on sale for 20% off the original price of $79.99.
He also picked out a robot for 25% off the original price of $99.99.
Money saved by spencer = 0.2 × 79.99 + 0.25 × 99.99
= 15.99 + 24.99
= $40.98
Thus, the required money saved by spencer at the end of the summer sale is $40.98.
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solve the equation!
5(n-2)=45
what is n?
Answer:
The answer is n = 11
Explanation:
Divide both sides by 5
Move the constant to the right
Then add the numbers.
Answer:
n is 11
Step-by-step explanation:
because when you work backwards 45 divided by 5 is 9 so then 9 + 2 is 11 and that is N
Which expression correctly represents "twice the sum of four and a number"?
Answer:
2(4+x)
Step-by-step explanation:
"Twice the sum of" tells us it will be the equation times two
"the sum of four and a number" is easy, thats 4 + x
The second number is x because the number is not specified so we need a place holder, x in this case, to tell us that the number is not given.
All this put together = twice the sum of four and a number, or 2(4+x)
The expression for "twice the sum of four and a number" is represented by 2(x + 4) or 2 * (x + 4), signifying that you first sum the number with four and then double the result.
Explanation:The expression that correctly represents "twice the sum of four and a number" is 2(x + 4) or 2 * (x + 4), where x is the variable representing the unknown number. To arrive at this expression, you first find the sum of four and the number (x + 4) and then multiply the result by two to get twice this sum.
In this context, the word 'twice' is similar to triple as in triple the amount of money being three times as much. This operation is an example of simple addition, much like when two numbers are added in any order, such as 2 + 3 or 3 + 2, which illustrates the commutative property of addition.
x + x + 3y how do I simplify?
Answer:
2x + 3y
Step-by-step explanation:
Question 11: Please help. What is the equation of the line that is parallel to y−5=−13(x+2) and passes through the point (6,−1)?
The equation will be in slope-intercept form.
Answer:
Step-by-step explanation:
Assume that you have two distinct and nonvertical lines, ℓ 1 {\ell _1} ℓ1 and ℓ 2 {\ell _2} ℓ2 in Slope-Intercept Form. They are parallel lines if their slopes are equal or the same. They are perpendicular lines if their slopes are opposite reciprocals of each other, or the product of their slopes equals −1.
Answer is y= -1
The equation will be y = -1/3x + 1 in slope-intercept form.
What is the equation of a line?The general equation of a line is y = mx + c
where m is the slope of the line and c is the intercept.
A linear equation is defined as an equation in which the highest power of the variable is always one.
First, we need to determine the slope of the given line.
To do this, we convert the equation to the slope/intercept form:
y − 5 = -1/3(x+2)
y = -1/3x -2/3 + 5
y = -1/3x - 13/3
So the slope of the given line is -13.
The line passes through the point (6,−1)
Now we can use the point-slope form of a line to create the equation of the new line:
(y + 1) = (-1/3) (x - 6)
y = -1/3x + 2 -1
y = -1/3x + 1
Hence, the equation will be y = -1/3x + 1 in slope-intercept form.
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hi what is the four time pi?
Answer:
12.5663706144 or just 12.57.Step-by-step explanation:
4 x pi = 12.57
EstimatePi is approx. equal to 3.14
4 x 3 = 12
A rectangle is 2 inches wide, and more than 2 inches long. It so happens that this rectangle can be divided, by a single cut, into a 2-inch square and a small rectangle that has exactly the same shape as the large rectangle. What is the length of the large rectangle
Answer:
6 in.
Step-by-step explanation:
The Length of the large rectangle is 2 units.
It is required to find the length of the large rectangle.
What is rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.
Given:
A rectangle is 2 inches wide, and more than 2 inches long.
According to given question we have,
Ratio of width to length of known rectangle is 2:4 this simplifies to 1:2
The smaller similar rectangle will have the same ratio. .i.e. 1:2
Since the width is 1 then the length will be 2.
.This can also be looked at another way. the second value in the ratio is
2:1 of the first value in the ratio and the first value is 1:2 of the second value.
So, Length of the large rectangle is 2 units.
Width of the large rectangle is 1 units.
Therefore, the Length of the large rectangle is 2 units.
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A bowling-ball maker starts with an 8.5-inch-diameter resin sphere and drills 3 cylindrical finger holes in it. Each hole is 1 inch in diameter and 3.5 inches deep. Which is the best estimate of the volume of resin in the finished ball?
Answer:
313.3084 in3
Step-by-step explanation:
To find the final volume of the finished ball, we need to find the volume of the whole sphere and then decrease it by the volume of the three holes.
The volume of the sphere is given by this formula:
V = (4/3)*pi*r^3
Where r is the radius. In our case, the radius is 8.5 / 2 = 4.25 in, so the volume is:
V1 = (4/3)*pi*4.25^3 = 321.5551 in3
The volume of each cilindrical hole can be calculated as:
V = pi*r^2*h
Where r is the radius and h is the height. We have that the radius is 1/2 = 0.5 inches and the height is 3.5 inches, so:
V2 = pi*0.5^2*3.5 = 2.7489 in3
So the final volume is:
V = V1 - 3*V2 = 321.5551 - 3*2.7489 = 313.3084 in3
Answer:
313.313inches³
Step-by-step explanation:
A bowling ball is spherical in shape hence,
The Formula used to calculate the volume of sphere is
= 4/3 πr³
For the question, we were given diameter.
Diameter of the bowling ball = 8.5 inches
Radius = Diameter ÷ 2
Radius = 8.5 inches ÷ 2
Radius = 4.25 inches
Hence,
Volume of a Sphere =
4/3πr³
= 4/3 × π ÷ 4.25
= 321.55509806inches³
Approximately = 321.56inches³
From the question we can see that the bowling ball has 3 cylindrical holes in it
With a diameter of 1 inch and a depth of 3.5inches
Hence we find the volume of these holes
Volume of a cylinder = πr²h
Diameter = 1 inch,
Radius = Diameter /2 = 1/2 inches
Height(Depth) = 3.5 inches
Volume of the cylindrical holes = π ×(1/2) ² × 3.5
Volumes = 2.749inches³
Since we have 3 holes ,
Volumes of the 3 holes = 2.749inches³ × 3
= 8.247inches³
The Volume of the total Spherical bowling ball
= Volume of the total bowling ball without holes - Volume of the cylindrical holes on the bowling ball
= 321.56inches³ - 8.247inches³
= 313.313inches³
Hence, the best estimate of the volume of resin in the finished ball = 313.313inches³
According to Jax's pedometer, he walked 12.783 miles on Monday, 17.2 miles on
Wednesday and 9.87 miles on Friday. How far did Jax walk on Monday, Wednesday
and Friday?
please help me
39.853
Step-by-step explanation:
He walked 39.853 miles on Monday, Wednesday
and Friday.
I need help with summation notation. Look at picture
Answer:
[tex]=18[/tex]
Step-by-step explanation:
[tex]\sum _{j=1}^33j[/tex]
Apply the constant multiplication rule:
[tex]=3\cdot \sum _{j=1}^3j[/tex]
[tex]\sum _{j=1}^3j[/tex]
Apply sum formula:
[tex]=\frac{1}{2}\cdot \:3\left(3+1\right)[/tex]
[tex]\frac{1}{2}\cdot \:3\left(3+1\right)[/tex]
[tex]=3\cdot \:4\cdot \frac{1}{2}\\[/tex]
[tex]=\frac{1\cdot \:3\cdot \:4}{2}[/tex]
[tex]=\frac{12}{2}[/tex]
[tex]=6[/tex]
[tex]=3\cdot \:6[/tex]
[tex]=18[/tex]
Which polynomial correctly combines the like term and express the given polynomial in standard form
Answer: c) [tex]3x^4-13y^4+x^3y+9xy^3-8x^2y^2[/tex]
Step-by-step explanation:
[tex]9xy^3-4y^4-10x^2y^2+x^3y+3x^4+2x^2y^2-9y^4[/tex]
Let's rearrange from the 4th power to 1.
[tex]3x^4-4y^4-9y^4+x^3y+9xy^3-10x^2y^2+2x^2y^2[/tex]
Combine like terms (check if they have the same variable raised to the same power.
[tex]3x^4+(-4y^4-9y^4)+x^3y+9xy^3+(-10x^2y^2+2x^2y^2)[/tex]
[tex]3x^4+(-13y^4)+x^3y+9xy^3+(-8x^2y^2)[/tex]
[tex]3x^4-13y^4+x^3y+9xy^3-8x^2y^2[/tex]
Let the random variable X represent the winnings at one play of game A. The mean, H. Of X is known to be -$0.42 and its standard deviation, o, is $0.26. Let the random variable Y represent the winnings at one play of game B. The mean, , of Y is known to be -$0.42 and its standard deviation, o, is $0.21. You have decided to play one of these two games just once. At which game are you more likely to make a profit (i.E., to not lose money)? Explain your thinking.
Answer:
345
Step-by-step explanation:
i know it not
Answer:
565$
Step-by-step explanation:
Y because he got more money
Amul is trying to find the volume of the cylinder. What
was Amul's error?
Amul should have squared pi.
Amul should not have multiplied by pi.
Amul should have squared the radius, not the
height
Amul did not make an error.
Answer:
c its the right answer
Step-by-step explanation: i just took it and got it right
Answer:
its C!!
Step-by-step explanation:
A class of 28 students can complete 896 math problems in one day how many problems does each student complete
Answer:
32
Step-by-step explanation:
Assuming they all complete it at the same rate,
896/28 = 32
Paco is trying to win a bear at carnival .The bear cost 30 tickets . Paco paid $5 for $10 tokens to use to play games . So far he's won 15 tickets and used 7 tokens for different games.How many more tickets does he need to win the bear.What unit should accompany the answer to this problem
Answer: 15 tickets
Step-by-step explanation:
given that the cost of the bear = 30 tickets
He has paid $5 for 10 tokens to use to play games . And So far he's won 15 tickets and used 7 tokens for different games. Since he has won 15 tickets, then
He needs to will 30 -15 = 15 tickets
The best unit for the answer is ticket
There are two traffic lights on Broadway. The probability of being stopped at the first light is
40%. The probability of being stopped at the second light is 70%.
Answer:
Most people found the probability of just stopping at the first light and the probability of just stopping at the second light and added them together. I'm just going to show another valid way to solve this problem. You can solve these kinds of problems whichever way you prefer.
There are three possibilities we need to consider:
Being stopped at both lights
Being stopped at neither light
Being stopped at exactly one light
The sum of the probabilities of all of the events has to be 1 because there is a 100% chance that one of these possibilities has to occur, so the probability of being stopped at exactly one light is 1 minus the probability of being stopped at both lights minus the probability of being stopped at neither.
Because the lights are independent, the probability of being stopped at both lights is just the probability of being stopped at the first light times the probability of being stopped at the second light. (0.4)(0.7) = 0.28
The probability of being stopped at neither is the probability of not being stopped at the first light, which is 1-0.4 or 0.6, times the probability of not being stopped at the second light, which is 1-0.7 or 0.3. (0.6)(0.3) = 0.18
The probability at being stopped at exactly one light is 1-0.18-0.28=.54 or 54%.
A line has a slope of Negative one-half and a y-intercept of –2.
Answer:
If you are asking for the equation, it is y= -(1/2)x -2
Ava's aquarium is 95% filled with water. The tank holds 1,120 gallons of water. Select the remaining number of gallons of water needed to fill the aquarium to the top.
Answer:
The answer to your question is 56 gal
Step-by-step explanation:
Data
Percent filled = 95%
Total water can hold = 1120 gal
remaining water = ?
Process
1.- Calculate the 95% of 1120 gal
1120 gal ------------------ 100%
x ------------------ 95%
x = (95 x 1120) / 100
x = 106400 / 100
x = 1064 gal
2.- Calculate the remaining water by subtracting the previuos value to the total capacity.
Remaining water = 1120 - 1064
= 56 gal
Answer:
sgdggggggggggggsdfgfgfg
Step-by-step explanation:
I don’t understand 1 2 and 3 please help
Answer:
1. 336 in3
2. 384 cm3
3. 336 m3
Step-by-step explanation:
im not positive but i think you just multiply the numbers and put the label as cubed
Suppose P(E) = 0.15, P(F) = 0.65, and P(F | E) = 0.82, compute the following:
P(E and F). P(E or F). P(E | F).
Answer:
P(E and F) = 0.123
P(E or F) = 0.677
P(E|F) = 0.189
Step-by-step explanation:
The formula for conditional probability is P(B|A) = P(A and B)/P(A)
The addition rule is P(A or B) = P(A) + P(B) - P(A and B)
∵ P(E) = 0.15
∵ P(F) = 0.65
∵ P(F|E) = 0.82
- Use the first rule above
∵ P(F|E) = P(E and F)/P(E)
- Substitute the values of P(F|E) and P(E) to find P(E and F)
∴ 0.82 = P(E and F)/0.15
- Multiply both sides by 0.15
∴ 0.123 = P(E and F)
- Switch the two sides
∴ P(E and F) = 0.123
Use the second rule to find P(E or F)
∵ P(E or F) = P(E) + P(F) - P(E and F)
∴ P(E or F) = 0.15 + 0.65 - 0.123
∴ P(E or F) = 0.677
Use the first rule to find P(E|F)
∵ P(E|F) = P(F and E)/P(F)
- P(F and E) is the same with P(E and F)
∴ P(E|F) = 0.123/0.65
∴ P(E|F) = 0.189
If n(U) = 360, n(A) = 240, n(B) = 160, find the maximum value of
n(AUB) and the minimum value of n(A n B). When will the value of
n(An B) be maximum and find its value.
Answer:
here is answer
Step-by-step explanation:
n(AUB) = n(A) + n(B) - n(AnB )
= 240 + 160 - n(A n B)
= 400 - n(AnB )
Since n(AnB) 20, so n(AUB) S 400
But n(U) = 360, so n(A U B)* 360
.. the maximum value of n(AUB) = 360.
When n(A U B) is maximum, n(AnB) will be minimum.
.. min. value of n(An B)
= n(A) + n(B) - Max, value of n(AUB)
= 240 - 160 - 360 = 40
Again, n(
A B) will be maximum when B C A.
..the max. value of n(
A B) = n(B) = 160
Alvin has a prism-like water tank whose base area is 0.9 square meters and height is 0.6 meters. He wants to buy guppy fish, and the pet store owner tells him to make sure their density in the tank isn't more than 5 fish per cubic meter. How many fish can Alvin get, at most?
Answer:
Alvin can't have more than 2 fishes on his tank.
Step-by-step explanation:
In order to calculate how many fish Alvin can have in his tank we first need to calculate the volume of the tank. A prism's volume is given by the following formula:
v = Abase*h
Therefore for Alvin's, we have:
v = 0.9*0.6 = 0.54 m³
Since he can't have more than 5 fish per cubic meter we can use a rule of three in a way that:
5 fish -> 1 m³
x fish -> 0.54 m³
5/x = 1/0.54
x = 0.54*5 = 2.7
Since he can't have a 0.7 fish and in order to mantain the density to the recommended level, he can't have more than 2 fishes.