The probability that an individual will score of 50 or less is 0.06.
Given mean of 60 and standard deviation of 8.
We have to find the probability that individual will score 50or less.
Probability is the chance of happening an event among all the events possible. The probability lies between 0 and 1. The formula to calculate probability is as under:
Probability = number of items/total items.
We have to first find the z value from 50 to 60 which can be found as under:
z value=(50-60)/60
=-0.167
P value from 50 to 60 is 0.44
probability that the individual will score 50 or less is 0.5-0.44
=0.06
Hence the probability that the individual will score 50 or less is 0.06.
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What is the radius of a hemisphere with a volume of 4635 ft 3 , 4635 ft 3 , to the nearest tenth of a foot?
Step-by-step explanation:
Hemisphere Formulas in terms of radius r:
V = (2/3)πr.
Hereof, What is the radius of a hemisphere? As latter is 4πr2 , curved surface area of a hemisphere of radius r is 2πr2 . and hence total surface area of hemisphere is 2πr2+πr2=3πr2 . Hence, radius of hemisphere is 4 cm.
I'm not very good at solving these problems
1 atom of C has a mass of 12 amu (atomic mass unit).
1 atom of O has a mass of 16 amu.
1 molecule of CO₂ thus has a mass of 12 + 2×16 = 44 amu.
C thus makes up 12/44 ≈ 0.27 of the total mass of CO₂, while O makes up the remaining 32/44 ≈ 0.73.
Then in a 2 kg = 2000 g block of CO₂, carbon makes up about 12/44 × 2000 ≈ 545 g.
At what meter mark will Ario be when Miguel starts the race? Round to the nearest tenth.
x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1
A number line goes from 0 to 25. A line is drawn from 3 to 25. The point at 3 is labeled Start and the point at 25 is labeled End.
Miguel and his brother Ario are both standing 3 meters from one side of a 25-meter pool when they decide to race. Miguel offers Ario a head start. Miguel says he will start when the ratio of Ario’s completed meters to Ario’s remaining meters is 1:4.
4.4 meters
7.4 meters
17.6 meters
20.6 meters
The meter mark at which Ario wil be when Miguel starts the race is; 7.4 meters
How to calculate the distance?A ratio such as the ratio 1:4 shows the proportion of two factors. In this case, it shows the ratio between the completed meters vs the remaining meters.
To find the distance, we will have to determine how much 1:4 represents in the total distance.
Total distance = 25 meters - 3 metes = 22 meters
Thus; 22 * 1/ 5 = 22/5 = 4.4
However, we also know they are three meters behind the start.
Thus, the meter mark at which Ario will be when Miguel starts the race
4.4 + 3 =7.4 meters
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HELP ASAP
Given: ABCD is a parallelogram.
Prove: A is congruent to FCE.
Answer:
Step-by-step explanation:
C is equal to A. Because angle FCE is on the other side with C, it has to be equal to A
ABCD is a parallelogram (Given)
As opposite angles of a parallelogram are equal
<A=<BCD--(1)Also
<BCD=<FCE(Opposite angle)-(2)From (1) and (2)
<A is congruent to <FCE
una fracion reducicion a su minima expresion en igual a 1/8 . si la suma de sus terminos es 72. hallar la diferencia entre ellos
La diferencia entre el denominador y el númerador de la fracción es:
64 - 8 = 56.
¿Como encontrar la fracción?
Tendremos una fracción de la forma:
[tex]\frac{a}{b}[/tex]
Tal que:
[tex]\frac{a}{b} = \frac{1}{8}[/tex]
[tex]a + b = 72[/tex]
Eso es un sistema de ecuaciones
Primero, podemos reescribir la primer ecuación como:
[tex]8a = b[/tex]
Ahora podemos reemplazar "b" en la segunda ecuación por "8a", así obtenemos:
[tex]a + 8a = 72\\\\9a = 72\\\\a = 72/9 = 8[/tex]
Ahora podemos obtener el valor de b:
[tex]b = 8a = 8*8 = 64[/tex]
La diferencia entre a y b es:
[tex]b - a = 64 - 8 = 56[/tex]
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look at the pic below and please help.
Answer:
1) Equation's:
y = 500 + 15x y = 350 + 18x2) Number of guest and the charge:
Cost is same for both at 50 meals. The cost is $1250.Part 1
Turn sentences into equation's (Let 'y' be total cost and x per meal) :
(i) charges $500 and $15 per meal
y = 500 + 15x(ii) charges $350 and $18 per meal
y = 350 + 18xPart 2
y = y
500 + 15x = 350 + 18x
18x - 15x = 500 - 350
3x = 150
x = 150/3
x = 50
Charge at guest's 50 meal:
y = 500 + 15(50)
y = $1250
Point : (50, 1250)
Which set of systems of equations represents the solution to the graph?
an upward opening parabola decreasing from negative 3 comma 4 to a minimum at negative one comma zero and then increasing to 1 comma 4 and a downward opening parabola increasing from negative 2 comma negative 3 to a maximum at 0 comma 1 and then decreasing through the point 2 comma negative 3
The correct graph for the given sets of equation is given attached below.
Equation no 2 gives the perfect solution to the graph.
A parabola, is cross section cut out of the cone and represented by an equation [tex]Y=4ax^2[/tex]
Clearly, by property of the parabola, the curve of parabola should symmetric to its axis. From this property set of Equation (2) i.e. downward opening parabola increasing from negative 2 comma negative 3 to a maximum at 0 comma 1 and then decreasing through the point 2 comma negative 3 Holds the property of the parabola
Thus, the required solution for the sets of equation (2) is given in the attachment.
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4. A juice bottling company makes a variety pack
with 24 orange juices, 12 apple juices, and 8
grape juices. Describe the ratio of the juices to
one another (orange: apple: grape).
(A) 2:1:1
(B) 3:1:2
(C) 4:2:2
(D) 6:3:2
The ratio of orange juice to apple juice to grape juice is 6: 3 : 2
What is ratio?A ratio says how much of one thing there is compared to another thing.
Therefore, we are comparing the numbers of juice produce by a bottling company.
Hence,
number of orange juice = 24
number of apple juice = 12
number of grape juice = 8
Therefore, the ratio of orange juice to apple juice to grape juice is as follows:
ratio = 24 : 12 : 8
divide through by 4
ratio = 6: 3 : 2
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20 points. The length of a rectangular room is 4.5 m and it’s width is 9.6 m. Find the area of the room
Answer:
43.2 m square is ur answer .
Answer:
43.2 m^2
Step-by-step explanation:
The area of a rectangle is the width times the length.
Area = (9.6 m)*(4.5 m)
Area = 43.2 m^2
Create a list of steps, in order, that will solve the following equation. (x-5)^2=25(x−5) 2 =25left parenthesis, x, minus, 5, right parenthesis, squared, equals, 25 Solution steps:
The value of x in the equation (x - 5)² = 25 is 10.
How to solve an equation?(x - 5)² = 25
Take the square root of both sides
Therefore,
√(x - 5)² = √25
x - 5 = 5
add 5 to both sides
x - 5 + 5 = 5 + 5
x = 10
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Mass (kg)
45
61
57
78
68
Length (cm)
112
138
133
180
175
Which of the options is the most appropiate to suow data in the table?
Pictogram
Pie chart
Bar chart
Line Graph
Scatter Graph
Answer:
Line or scatter graph.
Step-by-step explanation:
I prefer line, although some of the points deviate a bit. But the line shows a definite relationship between mass and length.
See attached graph.
Kelly has 2 liters of milk in the refrigerator. she used 12 liters of milk in the morning with breakfast. she then used the same quantities of milk at both lunch and dinner, such that she used up all the milk. what quantity of milk did she use at dinner?
Kelly used a volume of [tex]\frac{3}{4}[/tex] liters of milk at dinner.
What is Volume?Each thing in 3-D takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity. Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank. The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.Given we have, Initial amount of milk is [tex]2[/tex] liters.
The amount of milk used in the morning is [tex]\frac{1}{2}[/tex] Liters.
Now, Milk left = [tex]2[/tex] liters- [tex]\frac{1}{2}[/tex] liter= [tex]\frac{3}{2}[/tex] liters
[tex]\frac{3}{2}[/tex] liters used in half:
[tex]\frac{1}{2} \frac{3}{2}[/tex] = [tex]\frac{3}{4}[/tex] liters.
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To estimate the number of bass in a lake, a biologist catches and tags 32 bass. several weeks later, the biologist catches a new sample of 55 bass and finds that 5 are tagged. how many bass are in the lake?
If the biologist catches and tags 32 bass and from sample of 55 he found only 5 tagged then there are 352 bas in the lake.
Given Biologist catches and tags 32 bass, when sample of 55 bass is taken then 5 are found tagged.
Population is basically number of living thing exists in a particular area.
Number of bass which are tagged in lake=32
Sample size=55
Number of bass found tagged=5
means percentage of tagged bas found is 5/32*100=1.6%
We have to calculate number of times 5 is multiplied to get 32 which is 6.4.
Number of bass in the lake=55*6.4
=352 basses.
Hence there are 352 basses in the lake if 5 are found tagged in a sample of 55.
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Find a cubic polynomial whose zeros are 1/2,1 and -3.
Answer:
2x³+3x²-8x+3
Step-by-step explanation:
So we know x=½,x=1 and x=-3
Then (2x-1)(x-1)(x+3) are the factors
(2x-1)[(x²+3x-x-3)]
(2x-1)[(x²+2x-3)]
2x³+4x²-6x-x²-2x+3
2x³+3x²-8x+3
6) Stacie was solving the triangle below. Can you find her mistake?
Stacie did the mistake that he put the value of base in place of perpendicular and vice versa.
The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°
Solution is supposed to be
[tex]tan_ (-1) (28/21) = 53.33[/tex]
Thus,Stacie did the mistake that he put the value of base in place of perpendicular and vice versa.
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Which set of data does not have a mode?
(A) 1, 2, 5, 6, 8
(B) 1, 3, 5, 5, 6
(D) 1, 1, 1, 2, 2
(C) 1, 5, 5, 5, 5
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\textbf{Which set of data does not have a mode?}[/tex]
[tex]\huge\textbf{The choices that you have provided:}[/tex]
[tex]\textbf{(A) 1, 2, 5, 6, 8}[/tex]
[tex]\textbf{(B) 1, 3, 5, 5, 6}[/tex]
[tex]\textbf{(C) 1, 5, 5, 5, 5}[/tex]
[tex]\textbf{(D) 1, 1, 1, 2, 2}[/tex]
[tex]\huge\textbf{Okay, so let's get the understanding}\\\\\huge\textbf{of the word mode is:}[/tex]
[tex]\large\textbf{The best way to understand what \boxed{\bf mode} it is known as}\\\\\large\textbf{the number you see MORE THAN once. }[/tex]
[tex]\huge\textbf{Now that we got that information out of}\\\\\huge\textbf{the way, we can answer your question by}\\\\\huge\textbf{doing process of elimination.}[/tex]
[tex]\huge\textsf{Option A.}[/tex]
[tex]\textbf{1, 2, 5, 6, 8}[/tex]
[tex]\large\textbf{None of the numbers r.e.p.e.a.t so this cann be your}\\\\\large\textbf{answer.}[/tex]
[tex]\huge\textsf{Option B.}[/tex]
[tex]\textbf{ 1, 3, 5, 5, 6}[/tex]
[tex]\large\textbf{1}\rightarrow\large\textbf{ is r.e.p.e.a.t.e.d once}\\\large\textbf{3}\rightarrow\large\textbf{ is r.e.p.e.a.t.e.d once}\\\large\textbf{5}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d twice}\\\large\textbf{6}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d once}[/tex]
[tex]\large\textbf{Just because majority of your numbers r.e.p.e.a.t.e.d}\\\\\large\textbf{once that doesn't mean it does have a mode rarely.}\\\\\\\\\\\large\textbf{So, Option B. isn't your answer because it has a mode.}[/tex]
[tex]\huge\textsf{Option C.}[/tex]
[tex]\textbf{ 1, 5, 5, 5, 5}[/tex]
[tex]\large\textbf{1}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d once}\\\large\textbf{5}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d four times}[/tex]
[tex]\large\textbf{Option C. isn't your answer because it has a mode.}[/tex]
[tex]\huge\textsf{Option D. }[/tex]
[tex]\textbf{1, 1, 1, 2, 2}[/tex]
[tex]\large\textbf{1}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d three times}\\\large\textbf{2}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d twice}[/tex]
[tex]\large\textbf{Just because we have like two modes, it still doesn't mean}\\\large\textbf{you don't have a mode. It 's kind of cool that you have more}\\\large\textbf{than once mode.}[/tex]
[tex]\large\textbf{Option D. isn't your answer because it has a mode though}\\\large\textbf{because it has like 2 sets of modes.}[/tex]
[tex]\huge\textsf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\textsf{Option\ A. 1, 2, 5, 6, 8}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A membership committee of three is formed from four eligible members. let the eligible members be represented by a, b, c, and d. the possible outcomes include s = {abc, abd, acd, bcd}. which statements about the situation are true? select three options.
The correct statements are:
There are four ways to choose the committee.
There are three ways to form the committee if person D must be on it.
If persons B and C must be on the committee, there are two ways to form the committee.
It is given that:
A membership committee of three is formed from four eligible members.
1)
There are four ways to choose the committee.
This statement is true.
since we have to choose 3 members out of the 4 members so we can use the method of combination.
2)
There are three ways to form the committee if person D must be on it.
This statement is also true.
since D has to be in the committee, this means we have to choose 2 more people out of the three people to form the committee.
3)
If seven members are eligible next year, then there will be fewer combinations.
This statement is wrong.
Since we have to choose 3 members out of 7 members so the number of possible combinations will be:
i.e. there are 35 combinations possible.
4)
If persons B and C must be on the committee, there are two ways to form the committee.
if B and C have to be in the committee then we have to choose just one person out of the two people left.
Hence, the statement is true.
5)
If persons A and C must be on the committee, then there is only one way to form the committee.
If A and C have to be in the committee then as in last option we have to choose any one of the two person left.
so possible number of ways are 2.
Hence, the statement is false.
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How do the areas of the parallelograms compare? the area of parallelogram abcd is 4 square units greater than the area of parallelogram efgh. the area of parallelogram abcd is 2 square units greater than the area of parallelogram efgh. the area of parallelogram abcd is equal to the area of parallelogram efgh. the area of parallelogram abcd is 2 square units less than the area of parallelogram efgh.
option third "The area of parallelogram ABCD is equal to the area of parallelogram EFGH" is correct.
What is parallelogram?In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
The area of the parallelogram is:
A = b×h
Here b is the base length and h is the height
In ABCD parallelogram:
A = (3)×(3)
A = 9 square units
EFGH parallelogram:
a = (3)×(3)
A = 9 square units
The area of parallelogram ABCD is equal to the area of parallelogram EFGH.
Thus, option third "The area of parallelogram ABCD is equal to the area of parallelogram EFGH" is correct.
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Select the correct answer from each drop-down menu.
The slope of the line in the graph is [ ]. The y-intercept is [ ]. The equation of the line is y= [ ], and x is [ ]
BOX 1:
A. 2
B. 3
C. -2
D. -3
BOX 2:
A. -3
B. 3
C. 4
D. -4
BOX 3:
A. 2
B. 3
C. -2
D. -3
BOX 4:
A. -3
B. +3
C. +4
D. -4
For the linear function in the graph, we have that:
The slope is of 3.The y-intercept is of -4.The equation of the line is: y = 3x - 4.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The line goes through point (0,-4), hence:
The y-intercept is of -4.
The function also goes through point (2,2), hence the slope is:
m = (2 - (-4))/(2 - 0) = 6/2 = 3.
Then, the equation of the line is:
y = 3x - 4.
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In the diagram, the circle will be dilated by a scale factor of 3 about the origin. The points C, A, and B map to C', A', and B' after the dilation. What is the length of ? Use the distance formula to help you decide: . The graph shows a circle with three points, A is equal to (8, 15), B is equal to (12, 13), and C is equal to (8, 10). C is the center of the circle. A line is joining AC and BC A. 24 units B. 45 units C. 21 units D. 15 units E. 5 units Reset Next
The length of C'B' after dilation using a scale factor of 3 is: D. 15 units.
What is Dilation?Dilation is the reduction or enlargement of an image by a scale factor, whereby the original and new images are similar.
Applying the distance formula, we have:
BC = √[(8−12)² + (10−13)²]
BC = √(−4)² + (−3)²]
BC = √(16+9)
BC = √25
BC = 5 units
Applying the scale factor:
Length of C'B' = 3(5) = 15 units.
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Find an equation for the line that passes through the points (6,1) and (-4,3)
Answer: $$y=-2/3x+2$$
Explanation: Given that we have the slope and a point on the graph we can use the point slope formula to find the equation of the line.
A ′ B ′ C ′ triangle, A, prime, B, prime, C, prime is the image of △ A B C △ABCtriangle, A, B, C under a rotation about the origin, ( 0 , 0 ) (0,0)left parenthesis, 0, comma, 0, right parenthesis.
The angle of rotation of triangle ABC to A'B'C is 105°
How to illustrate the information?It should be noted that the rotation from ABC to A'B'C is in a clockwise direction.
Point B is also on the x axis and point B' is in the second quadrant.
In this case, the angle that depicts the second quadrant is 105°.
In conclusion, the correct option is D.
The complete question is:
Triangle A’ B’ C’ is the image of A B C under a rotation about the origin, (0,0)
Determine the angle of rotation
A. -105 degrees
B. -75 degrees
C. 75 degrees
D. 105 degrees
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Find the inverse of the function
y = log₂ (x-3)
Answer:
[tex]f^{-1}(x)=2^x+3[/tex]
Step-by-step explanation:
Given:
[tex]y=\log_2(x-3)[/tex]
To find the inverse of the given function, make x the subject.
[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies 2^y=x-3[/tex]
Add 3 to both sides:
[tex]\implies x=2^y+3[/tex]
Swap x for [tex]f^{-1}(x)[/tex] and y for x:
[tex]\implies f^{-1}(x)=2^x+3[/tex]
Consider the line y=3x-3.
Find the equation of the line that is perpendicular to this line and passes through the point (4, 5)
Find the equation of the line that is parallel to this line and passes through the point (4, 5).
Answer:
Perpendicular: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]
Parallel: [tex]y=3x-7[/tex]
Step-by-step explanation:
So when two lines are perpendicular, that means the the slope is the reciprocal with the opposite sign so: [tex]\frac{a}{b} \text{ has a slope perpendicular to } -\frac{b}{a}[/tex]. In this case we have the equation in slope-intercept form, so it's easy to determine the slope, it's 3. So that means the perpendicular line will have a slope of: [tex]-\frac{1}{3}[/tex]. Since you have a slope of 3/1 which becomes 1/3 and also an opposite sign. This gives you the equation: [tex]y=-\frac{1}{3}x+b[/tex]. We can solve for b, by plugging in a coordinate it passes through. This is given in the problem, with it being (4, 5) = (x, y). So plugging these values in as (x, y) gives you the equation: [tex]5=-\frac{1}{3}(4)+b\implies\frac{15}{3}=-\frac{4}{3}+b\implies\frac{19}{3}=b[/tex]. This gives you the complete equation: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]
So when two lines are parallel, that means they have the slope, and a different y-intercept. This is because if they had the same y-intercept, then the two lines would be the same exact line. We already know the slope, it's 3. So we have the general equation: [tex]y=3x+b\text{ where b}\ne-3[/tex]. The restriction on b, was explained on the previous sentence, if b=-3, then we have the same equation, which is not parallel, they would be the same line, meaning they would intersect at infinite points, which is completely different than two lines that never intersect. So now we can plug in the given point (4, 5) to solve for b. Plugging these coordinates in gives you: [tex]5=3(4)+b\implies5=12+b\implies-7=b[/tex]. This gives you the complete equation: [tex]y=3x-7[/tex]
Write a polynomial function with the real
zeros -3, 0, and 3.
[tex]f(x)=x(x-3)(x+3)[/tex]
Write and simplify an expression to represent the area. Then determine the area when x = 3
Answer:
5*8 = 40
Step-by-step explanation:
2(3) -1 = 5
3 +5 = 8
area = 5*8 = 40
Answer:
formula-Area=l×b
Step-by-step explanation:
Length (l)=2x-1
Breadth(b)=x+5
We know that,
Area(A)=l×b
=(2x-1)×(x+1)
=(2×3-1)×(3+1)
=5×4
=20cm*2*
Harry decided to buy some candy bars that
cost $2.19 each. He also bought a drink for
$3.55. Harry paid a total of $10.12. Write an
equation to find how many candy bars Harry
purchased.
A ratio is...
O where two numbers are written as a fraction in lowest terms.
O where two or more values are compared in lowest terms.
O when two numbers are written as a division problem.
O all of these.
Answer:
All of these definitions are correct.
Which type of parent function is f(x) = 1/x
Since it has a variable in the denominator, the function f(x) is a parent function classified as rational.
What are rational functions?Rational functions are functions that have the input variable, be it x, t, or any other, in the denominator.
The most simple example is given by:
[tex]f(x) = \frac{1}{x}[/tex].
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Answer: Reciprocal
Step-by-step explanation:
Reciprocal functions are functions that contain a constant numerator and x as its denominator. Its parent function is y = 1/x.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
Considering the given equation of the circle, the true statements are given as follows:
The radius of the circle is of 3 units.The center of the circle lies on the x-axis.The circle has the same radius as the circle with equation x² + y² = 9.What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The equation given is:
x2 + y² - 2x - 8 = 0.
Completing the squares, the equation is given as follows:
(x - 1)² + y² = 8 + 1
(x - 1)² + y² = 9.
Researching the problem on the internet, the true statements are:
The radius of the circle is of 3 units.The center of the circle lies on the x-axis([tex]y_0 = 0[/tex]).The circle has the same radius as the circle with equation x² + y² = 9.More can be learned about the equation of a circle at https://brainly.com/question/24307696
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