Using the normal approximation to the binomial, there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.
What is the missing information?This problem is incomplete, but researching it on a search engine, it asks the probability that the sum of these Bernoulli variables is of less than 60.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The binomial distribution is a series of n Bernoulli trials with p probability of a success on each trial, hence the parameters for the binomial distribution are given as follows:
n = 100, p = 0.5.
The mean and the standard deviation are given by:
[tex]\mu = np = 100(0.5) = 50[/tex].[tex]\sigma = \sqrt{np(1-p)} = \sqrt{100(0.5)(0.5)} = 5[/tex]Using continuity correction, the probability that the sum is less than 60 is P(X < 59.5), which is the p-value of Z when X = 59.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (59.5 - 50)/5
Z = 1.9
Z = 1.9 has a p-value of 0.9713.
Hence there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.
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4|2x + 5|-7≤9
How would you solve this?
Answer:
- [tex]\frac{9}{2}[/tex] ≤ x ≤ - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
inequalities of the type | x | ≤ a , have solutions of the form
- a ≤ x ≤ a , then
4 | 2x + 5 | - 7 ≤ 9 ( add 7 to both sides )
4 | 2x + 5 | ≤ 16 ( divide both sides by 4 )
| 2x + 5 | ≤ 4 , so
- 4 ≤ 2x + 5 ≤ 4 ( subtract 5 from each interval )
- 9 ≤ 2x ≤ - 1 ( divide each interval by 2 )
- [tex]\frac{9}{2}[/tex] ≤ x ≤ - [tex]\frac{1}{2}[/tex]
diamond problem for -2 and -5
Step-by-step explanation:
if I understand you correctly, then let's call the missing numbers l, r (for left and right).
and
-2 = l × r
-5 = l + r
l = -r - 5
therefore,
-2 = (-r - 5) × r = -r² - 5r
that gives us the quadratic equation
-r² - 5r + 2 = 0
for the general solutions
x = (-b ± sqrt(b² - 4ac))/(2a)
we have here
a = -1
b = -5
c = 2
and x = r, of course
r = (5 ± sqrt(25 - 4×-1×2))/(2×-1) =
= (5 ± sqrt(25 + 8))/-2 = (5 ± sqrt(33))/-2
r1 = (5 + sqrt(33))/-2 = -5.372281323...
r2 = (5 - sqrt(33))/-2 = 0.372281323...
as l = -r - 5, we see that r1 = l2, and r2 = l1.
but these are the only solutions.
there are no integer number solutions.
A city park measures 7/8 mile wide by 3/4 mile long. What is the area of the park?
If f(x)=-2x+3then f(3)-f(4)
Sue's science class is competing to see who can build the tallest tower. Each group of students gets 10 newspapers and 2 meters of tape. Sue's group decides to roll up each of their newspapers. Then, they tape each roll with 125 millimeters of tape. How many meters of tape do they have left?
The amount of tape left in metres is 0.75 metres.
How to find the length of the tape left in metres?Each group of students gets 10 newspapers and 2 meters of tape.
This means the total length of tape for each group of student is as follows:
length of tape for each group = 2 metres
Sue's group decides to roll up each of their newspapers. Then, they tape each roll with 125 millimetres of tape.
Each roll of the 10 newspaper was taped with 125 mm tape.
Hence,
total taping = 125 × 10
total taping = 1250 mm
Let's convert from millimetres to metres.
Therefore,
1 mm = 0.001 m
1250 mm = ?
cross multiply
amount of taping done by Sue's group = 1.25 m
Therefore,
amount of meters of tape left = 2 - 1.25 = 0.75 metres
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How can you adjust both numbers and use compensation to find $7.99 + $19.99 mentally?
The adjustment of both numbers and using compensation to find $7.99 + $19.99 mentally is $27.98
How to calculate the value?It should be noted that compensation is the mental strategy in Mathematics used for addition by adjusting one of rte addends.
It should be noted that $7.99 is almost the same as $8. It should be noted that $19.99 is the same as $20. This is the compensation or the numbers.
Therefore, the addition of the numbers $7.99 + $19.99 will be:
= $7.99 + $19.99
= $27.98
In conclusion, the answer is $27.98.
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a line segment has (x1, y1) as one endpoint and (xm, ym) as its midpoint. find the other endpoint (x2, y2) of the line segment in terms of x1, y1, xm, and ym. use the result to find the coordinates of the endpoint (x2, y2) of each line segment with the given endpoint (x1, y1) and endpoint (xm, ym).
The coordinates are:
For the first line, coordinates are (3, 7).For the second line, the coordinates are (12, 0).What are coordinates?A coordinate system in geometry is a system that uses one or more numbers, or coordinates, to determine the position of points or other geometric elements on a manifold such as Euclidean space.To find the coordinates:
In Analytical Geometry, the midpoint of a line is calculated as the mean of two points, as follows:
[tex]$$x_m=\frac{x_1+x_2}{2}, y_m=\frac{y_1+y_2}{2}$$[/tex]
Each segment has two endpoints and two midpoints, which are as follows:
(1,-9), as well as its midpoint (2,-1)(-2,18), as well as its midpoint (5,9)We must be cautious not to add the wrong coordinates.
In the first line A:
[tex]$$\begin{aligned}&2=\frac{1+x_2}{2} \\&4=1+x_2 \\&4-1=-1+1+x_2 \\&x_2=3 \\&-1=\frac{y_2-9}{2} \\&-2=y_2-9 \\&+2-2=y_2-9+2 \\&y_2=-7\end{aligned}$$[/tex]
So (3,7) is the other endpoint where the segment begins (1,-9).
The endpoint of the second line b at (-2,18) and its midpoint (5,9).
[tex]$$\begin{aligned}&5=\frac{-2+x_2}{2} \\&10=-2+x_2 \\&+2+10=+2-2+x_2 \\&x_2=12 \\&9=\frac{18+y_2}{2} \\&18=18+y_2 \\&-18+18=-18+18+y_2 \\&y_2=0\end{aligned}$$[/tex]
So, (12,0) is the opposite endpoint.
Therefore, the coordinates are:
For the first line, coordinates are (3, 7).For the second line, the coordinates are (12, 0).Know more about coordinates here:
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The correct question is given below:
A line segment has (x1, y1) as one endpoint and (xm, ym) as its midpoint. Find the other endpoint (x2, y2) of the line segment in terms of x1, y1, xm, and ym. Use the result to find the coordinates of the endpoint of a line segment when the coordinates of the other endpoint and midpoint are, respectively, (1, −9), (2, −1) and (−2, 18), (5, 9).
In a recent year, 17.3% of all registered doctors were female. If there were 41,000 female registered doctors that year, what was the total number of registered doctors?
Round your answer to the nearest whole number. PLEASE HELP DUE IN 30 MINUTES!!!
The total number of registered doctors are estimated as 236,995.
What is meant by percentage?A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is one hundredth part; thus, 100 percent signifies the entire amount and 200 percent specifies twice this same given amount.
The concept of cumulative percentage (percentile) is widely used in statistics. For example, a student who achieves the 83rd percentile on an investigation has outperformed 83 percent of the students with and who a comparison is made. The likelihood of an event occurring can be expressed as a percentage. (or fraction).Now, as per the given question;
It says, from all the registered doctors 17.3% is female doctors.
Now, let use assume that the total number of registered doctors be 'x'.
Then, 17.3% of this x will give 41,000 female doctors.
So, the equation will form as;
17.3% of x = 41,000
Or, (17.3×x)/100 = 41,000
x = (41,000×100)/17.3
x = 236,994.21
x = 236995 (nearest whole number)
Therefore, the total number of the registered doctors are estimated as 236995.
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Does 44,555 and 45,555 round to 50,000?
45,555 does, but the other one doesn't.
94.
Scale: 1 in. = 3 ft
The diagram above shows a plan for a community garden. The plan is drawn on a grid made up of 1-inch squares. About how many square yards will be used to grow herbs?
Answer:
About 9 sq yd
Step-by-step explanation:
First, you know that 3ft. = 1 yd. That means each square is 1 sq yd. The length of the herb garden is 6 squares, while the width is about 1.5 squares. If you multiply those two to find the area, then you get about 9 square yards.
find the percentage if the denominators are not the factors of 100
Answer:
external factors that impact negatively on lifestyle choices namely.unsafe road use
#11 i Solve -14>w+3 or 3w > -27 Solution: or
The values of the inequalities will be:
1. -14>w+3 = w < -17
2. 3w > -27 = w > -9
How to explain the inequality?It should be noted that an inequality simply means the expression that illustrates that the variables aren't equal. This can be used by uinng less than, greater than, etc.
The inequalities will be:
-14>w+3
Collect like terms
-14 - 3 > w
-17 > w
w < -17
3w > -27
Divide both side by 3
3w/ 3 > -27/3
w > -9
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Correct to 2 decimal places, the volume of a solid cube is 3.37 m³. Calculate the upper bound for the surface area of the cube.
the upper bound for the surface area of the cube. is 14 m².
Volume of cube = 3.37 m³
We know the formula is:
V = a³ (where a is the side of the cube)
a³ = 3.37 m³
Cube rooting both the sides, we get that:
a = ∛3.37 m
Surface area will be:
A = 6 a²
A = 6 (∛3.37 m)²
A =6 (2.25 m²)
A = 13.5 m²
A ≈ 14 m²
Therefore, we get that, the upper bound for the surface area of the cube. is 14 m².
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Please help fast :(
Answer:
1/2
1/4
1/4
0/16
2 times
Step-by-step explanation:
THERE ARE 16 SQUARES TOTAL
8 triangles: 8/16 = 1/2
4 stars: 4/16 = 1/4
4 empty spaces: 4/16 = 1/4
0 circles = 0/16
8*1/4 is 2, so 2 times.
help please
0.1 - 4.37
Answer:
-4.27
Hope this helps.
Step-by-step explanation:
Because the negative number ( - 4.37 ) is bigger than 0.1, the answer is going to end up negative. You can swap sides on the equation to become - 4.37 + 0.1, in which case is 4.36 - 0.1 but you have to remember to add the negative sign afterward.
suppose you have an argument that has three premises, all of which are true, and a true conclusion. if so, then the argument must be
The conclusion might be accurate or inaccurate.
The conclusion could be true or false if an argument has some true premises and some false premises and is valid. You only know that the premises cannot both be true and the conclusion must be false because the argument is sound. But the incorrect premises already rule out the possibility of possessing this set of truth values (that is, you cannot have all true premises). As a result, the argument's validity is unaffected whether the conclusion is true or untrue. As a result, the conclusion of an argument that contains only false premises may or may not be true.
Can an argument have all true premises and a false conclusion?TRUE. A valid argument cannot, by definition, have a false conclusion and all true premises.
Therefore, a valid argument must have an erroneous premise if it has a false conclusion.
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.
Nickels: Someone offers to double the amount of money you have every
day for 1 month (30 days). You have 1 nickel. On the first day, you will
have 2 nickels worth $.10. On the second day, you will have 4 nickels
worth $.20. How much money will you have on the 30th day?
Answer: you will have $53,687,091.2 dollars once you reach the thirty-day milestone.
Step-by-step explanation:
Multiply 0.05 by 2 thirty times to get your answer.
0.05 * 2^30
0.05 * 1,073,741,824 = $53,687,091.2 or 10,737,418.24 nickels.
9x10^4 + 9x10^2 ??
add
Answer:
90900
Step-by-step explanation:
Answer:
9.09 x 10*4.
Step-by-step explanation:
9x10^4 + 9x10^2
= 90000 + 900
= 90900
= 9.09 x 10*4.
The slope for a wheelchair ramp for a home has to be 1/2.
If the vertical distance from the ground to the door bottom is 3 ft, find the distance the ramp has to extend from the home in order to comply with the needed slope.
In order to comply with the required slope, the ramp must extend 36 ft from the house.
What do we mean by Distance?Distance is a mathematical or qualitative measure of the distance between two objects or points. Distance can refer to a physical length or an estimate based on other criteria in physics or everyday usage (e.g. "two counties over").So, to find the distance:
The formula of slope:
m = change in vertical height/change in horizontal heightVertical distance is now given as 3 ft.
To conform to the given slope, this means that:
1/12 = 3/xCross multiply:
x = 3 × 12x = 36 ftTherefore, in order to comply with the required slope, the ramp must extend 36 ft from the house.
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what is the distance between (-2.63, 7),(1.85,7)
The distance between the points is 4.48
What is the distance between the points?The coordinates of th points are given as:
(-2.63, 7) and (1.85,7)
The distance between the two points is calculated using
d = √(x2 - x1)^2 + (y2 -y1)^2
So, we have
d = √(-2.63 - 1.85)^2 + (7 - 7)^2
Evaluate
d = 4.48
Hence, the distance between the points is 4.48
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Consider the arithmetic sequence (87, 83, 79,75...)
A. Find common difference, d
B. Find explicit formula
Answer:
see explanation
Step-by-step explanation:
A
the common difference d of the arithmetic sequence is
d = a₂ - a₁ = 79 - 83 = - 4
B
the explicit formula of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 83 and d = - 4 , then
[tex]a_{n}[/tex] = 83 - 4(n - 1) = 83 - 4n + 4 = 87 - 4n
A restaurant had 9 days to sell 56 gallons of ice cream before it expired. How much should they sell each day?
5 gallons
5 gallons
6 6/4 gallons
6 6/4 gallons
6 1/2 gallons
6 1/2 gallons
6 2/9 gallons
Answer:
6 2/9
Step-by-step explanation:
56 divided by 9 is 6.22 and 2/9 is .22
Solve for x in the diagram below
The value of x will be 34°
Given that
(x+12)°+100°+x° are forming linear pair
Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles.
As mentioned, adjacent angles are angles that are next to each other. If you are sitting next to someone in class or on the bus, you could say that you are adjacent to them. More specifically, adjacent angles share a vertex and have a common side.
(x+12)°+100°+x°= 180°
⇒ x+ 12+ 100+x = 180°
⇒ 2x+112 = 180°
⇒ 2x = 180- 112
⇒ 2x = 68
⇒ x= 68/2
⇒ x= 34
For verification we will put value of x
(34+12)°+100°+34°
⇒ 46°+100°+34°
⇒146°+34°
⇒ 180°
So here we can see that by putting value of x we are getting the sum of 180°
Therefore value of x is 34
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Make x the subject of the formula
m=x+y/n
HELPPP
Answer: x=m-y/n
Step-by-step explanation:
The expression with x as the subject is x = mn - y.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
m = (x + y) / n
x as the subject means we have to solve for x.
Now,
m = (x + y) / n
Multiply both sides by n.
mn = x + y
Subtract y on both sides.
mn - y = x
x = mn - y
Thus,
x = mn - y.
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how many time does 13 go into 26
Answer:
2
Step-by-step explanation:
13+13=26
Answer:
Twice
Step-by-step explanation:
13+13=26
9. If AB= 25, AN= 2x-6, and NB = x + 7, find x, AN and NB.
2+
N
The value of x is equal to 8 and the values of AN and NB are 10 and 15 respectively.
The three points A, N and B are collinear, and N is between A and B. Collinear points are defined as set of those points which lie on the same line when plotted.
If A, N and B are collinear then,
AB = AN + NB
According to question, AB = 25, AN = 2x-6 and NB = x+7 thus,
25 = 2x-6 + x+7
25 = 3x + 1
24 = 3x
=> x = 24/3
=> x = 8
Now, AN = 2x-6 = 16-6 = 10
NB = x+7 = 8+7 = 15
Thus, the values of x, AN and NB are 8, 10 and 15 respectively.
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if asked to evaluate the following expression (5x+25) for x=3,5,-5,0 how many different substitutions will you make?
we did 4 different substitutions to evaluate the expression in 4 different values of x.
when x = 3 we get 40when x = 5 we get 50when x = -5 we get 0when x = 0 we get 25.How to evaluate an expression?
Here we have a linear expression that depends on the variable x, and can be written as:
(5x + 25)
And we want to evaluate this in some different values of x. This just means that we need to replace the value of x by different numbers.
First, let's use x = 3
This will give:
(5*3 + 25) = 15 + 25 = 40
Then we use x = 5
(5*5 + 25) = 25 + 25 = 50
Then we use x = -5
(5*-5 + 25) = -25 + 25 =0
Finally, we evaluate in x = 0.
(5*0 + 25) = 0 + 25 = 25
So we did 4 different substitutions to evaluate the expression in 4 different values of x.
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This list gives information about a video collection.
Study the list carefully. Then, use the drop-down menu to complete the statement
below about the list.
It
make sense to add the items on the inventory because these quantities
have meaning for the inventory.
The number 299
Romance:
74
Comedy: 123
Action: 102
Total: 299
CLEAR
be expressed using the same unit.
CHECK
Answer:
oh no I lost the Answer is was 18369
Answer:
Step-by-step explanation:
Bob fenced in his backyard. the perimeter of the yard is 22 feet, and the length of his yard is 5 feet. use the perimeter formula to find the width of the rectangular yard in inches: p = 2l 2w. (1 foot = 12 inches)
The width of yard in inches is 72 inches.
We are given the perimeter and length of yard. We are also given the perimeter of the rectangle, which is as follows -
P = 2l 2w
Rewriting this formula in simplified form, by taking 2 common from both the values -
P = 2×(l + w), where P refers to perimeter, l refers to length and w refers to width.
Now, keep the values in formula to find the width of rectangle -
22 = 2 × (5 + w)
Shifting 2 to other side of equation and performing division
5 + w = 22÷2
5 + w = 11
Shifting 5 to other side of equation and performing subtraction to find the value of width
w = 11 - 5
w = 6 feet
Now, we need the width in inches. We are given -
1 foot = 12 inches
So, 6 feet = 12 × 6
6 feet = 72 inches
Hence, the width of rectangular yard is 72 inches.
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Answer:
72in
Step-by-step explanation:
Solve two thirds times v plus 6 equals one third times v minus 2.
v equals negative eight thirds
v equals eight thirds
v = −24
v = 24
The value of v using the equation ( 2v/3 ) + 6 = ( v/3 ) - 2 is v = - 24.
Two-thirds of anything is an amount that is two out of three equal parts of it. Similarly, one-third of something is an amount that is one out of three equal parts of it.
Now, we have
Two-thirds times v plus 6 equals one-third times v minus 2.
Hence, when the above statement is expressed as an equation we get:
Two third of v + 6 = one third of v - 2
2/3 × v + 6 = 1/3 × v - 2
( 2v/3 ) + 6 = ( v/3 ) - 2
Adding 2 on both sides of the equation,
( 2v/3 ) + 6 + 2 = ( v/3 ) - 2 + 2
( 2v/3 ) + 8 = ( v/3 )
Subtracting 2v/3 from both sides of the equation,
2v/3 + 8 - 2v/3 = v/3 - 2v/3
8 = ( v - 2v )/3
- v/3 = 8/1
By cross multiplication,
- v × 1 = 8 × 3
- v = 24
Multiplying each side by - 1,
v = - 24
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