the probability that at least one of the events A and B occurs is 0.72.
What is probability ?
Probability is a measure of the likelihood of an event occurring. It is typically expressed as a decimal or fraction between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain.
The probability that event A occurs is 0.3 and the probability that event B does not occur is 0.4. To find the probability that at least one of the events A and B occurs, which states that the probability of an event occurring is equal to 1 minus the probability of it not occurring.
We can find the probability that neither event A nor event B occurs by multiplying the probability of event A not occurring (1-0.3 = 0.7) by the probability of event B not occurring (0.4). The probability that neither event A nor event B occurs is 0.7*0.4 = 0.28.
To find the probability that at least one of the events A and B occurs, we subtract the probability that neither event occurs from 1.
P(A or B) = 1 - P(neither A nor B) = 1 - 0.28 = 0.72
So the probability that at least one of the events A and B occurs is 0.72.
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*PLEASE HELP SOON* Use the laws of exponents to simplify the expression so that the base, x, appears once, and the exponent is positive.
Using the laws of exponential used to simplify the expression, we have; 1/x^2.
What is an exponential expression?When a given expression has an exponent, this implies that the degree of one of its variable is more than 1. So that the laws of exponent which is also law of indices can be used to determine the required simplification of the expression if required.
From the given question, we have;
x^3/ x^5
So that from the law of indices,
x^3/ x^5 = x^3 x^-5
= x^(3 - 5)
= x^-2
From the inverse law of exponent,
x^-2 = 1/ x^2
Using the law of exponents, the simplified form of the expression is 1/ x^2.
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Can someone please help me with this please?
Click on image for full view
Answer:
Obtuse and isosceles
Step-by-step explanation:
Cuz 2 sides and angles are equal and there is one obtuse angle
Answer:
obtuse and isoscelies
Step-by-step explanation:
120 is greater than 90 so obtuse
isoscelies means to sides of equal length and one of different length
2 sides are 3ft and one is 5ft
(8.6 x 10^-3)(8 x 10^-1)
Answer:
(8,6×10^-3) (8×10^-1)
=(0,0086). ( 0.8)
Please only give answers
The y-intercept of the line 11x + 10y = 2 is equal to 1/5.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
x and y represents the data points.m represents the slope of a line.c represents the y-intercept of a line.Based on the information provided about the line, it is represented by this equation;
11x + 10y = 2
By making "y" the subject of formula in the above equation, we have the following:
10y = -11x + 2
By dividing both sides of the equation by 10, we have the following:
y = -11x/10 + 2/10
y = -11x/10 + 1/5.
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need help algebra 2. write in rational exponent form
The rational exponent form is 5^3/5x. Option D
What is the rational exponent form?We know that a rational function would be the function that does not have the radical sign in it. We can see that we have the expression that have been written for us here as; 5√125x^5.
When we open up the radical we would have;
125^1/5 * 5^5/5
But we know that;
125 = 5^3
We now have;
5^3/5 * x
This becomes;
5^3/5x
Thus we are going to end up in the rational exponent form of the expression as 5^3/5x.
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Using a 3-4-5 right triangle and a 5-12-13 right triangle, John sets up the
proportion 3:4=5:12. Show that the proportion is incorrect. Explain what John
might have been thinking when he wrote the proportion.
ents
The proportion taken by John 3:4 = 5:12 is correct.
The term called proportion in math is defined as the values of the proportion that are close to each other when written in ratio form using a colon.
Here we know that the a 3-4-5 right triangle and a 5-12-13 right triangle are set by John.
And the taken proportion is written as,
=> 3:4 = 5:12
Here we have to use the Pythagoras theorem to verify this one, then we get,
=> 3² + 4² = 5²
=> 9 + 16 = 25
=> 25 = 25
Now, we have to take the other values and verify that one also,
=> 5² + 12² = 13²
=> 25 + 144 = 169
=> 169 = 169
Therefore the proportion is correct.
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Copy the figure and point P . Draw the image of the figure for a 180 rotation about P. Use prime notation to label the vertices of the image.
The solution is Option B.
The rotation of the line JK around the point P by 180° will be J'K'
What is Rotation?The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.
90° clockwise rotation: (x,y) becomes (y,-x)
90° counterclockwise rotation: (x,y) becomes (-y,x)
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
270° clockwise rotation: (x,y) becomes (-y,x)
270° counterclockwise rotation: (x,y) becomes (y,-x)
Given data ,
Let the rotation angle be represented as A
Now , the value of A is 180°
Let the points be represented as J and K
Let the rotated point be represented as J'K'
And , when a point is rotated by and angle 180° , the x and y coordinates of the point will become their additive inverse
For a 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
And , the figure which represents the coordinates of the point J' and K' is when K' is below and J' is above
Hence , the solution is Option B.
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suppose that someone made a graph of sat scores from 100 randomly selected students from the state of florida. standardized test scores like those for the sat are derived from the students' raw scores (number of questions answered correctly) and adjusted for slight differences in difficulties between versions. what shape would you expect the histogram of this data to be?
The shape of the histogram is expected to be symmetric.
A histogram is a graphical representation of the distribution of a dataset. It is an estimate of the probability distribution of a continuous variable. The histogram is plotted with bin ranges on the x-axis and the frequency (count) of data points that fall within each bin on the y-axis.
The shape of the histogram can give you a sense of the underlying distribution of the data, such as whether it is symmetric or skewed.
Standardized test scores, like the SAT, are typically designed to have a normal distribution, meaning that the majority of scores fall in the middle range, with fewer scores at the extremely high or low ends.
Additionally, because the data is being collected from a large and diverse population of students from one state, it is unlikely that there would be a significant skew in one direction or another.
However, some factors such as socioeconomic status, family background, school district, and student ethnicity may affect the distribution.
Therefore, The shape of the histogram is expected to be symmetric.
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Debra is seven years younger than her sister, Pam. The table represents the relationship. Which is the equation representing the relationship between their ages?
(x) (y)
9 2
11 4
13 6
15 8
1. y = x - 2
2. y = 7x
3. y = x + 7
4.y = x - 7
y = x + 2
Answer: y = x - 2
Step-by-step explanation:
The equation representing the relationship between the ages of Debra and Pam is y = x + 2. This is determined by analyzing the table provided, which shows the ages of Pam (x) and Debra (y) in years. From the table, we can see that for every 1 year increase in Pam's age, Debra's age also increases by 1 year. This is represented in the equation y = x + 2, where y (Debra's age) is equal to x (Pam's age) plus 2 years. This equation is supported by the data in the table, as all of the ordered pairs (x, y) in the table satisfy the equation y = x + 2.
A cube shaped fish tank holds 10 ft.³ of water. How much gravel is needed to cover the floor of the tank to a depth of 1 inch
The amount of gravel needed to cover the floor of the cube shaped tank to a depth of 1 inch is 0.38 ft^3.
What is volume?The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Various forms have various volumes.
Given that the fish tank is a cube that holds 10 ft^3 of water.
The volume of the cube is given by:
V = a³
Substituting the value of 10 in V we have:
a³ = 10
a = 2.15
Now, to gravel at the bottom of the tank will have the following dimensions as height will be 1 inch.
1 inch = 0.083
V = (a)(a)(a)
V = (2.15) (2.15) (0.083)
V = 0.38 ft^3
Hence, the amount of gravel needed to cover the floor of the tank to a depth of 1 inch is 0.38 ft^3.
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Point d is the center of the inscribed circle of abc. which step can you use to draw the inscribed circle of abc? a. draw arcs of equal lengths intersecting , , and in two points each. b. draw the perpendicular bisectors of , , and that pass through point d. c. label a point e on and draw a line joining e with d. d. draw a line through d that is perpendicular to one of the sides, , , or . e. draw one arc each on and , and find their point of intersection.
The step that can be used to draw an Inscribed Circle of A ABC is to draw the perpendicular bisectors of AB, BC, and AC that pass through point D
Inscribed Circle is a circle that touches each of the three sides of the triangle at exactly one point. Inscribed Circle is the largest circle that can be made in a triangle. The center of the Inscribed Circle is also the center of the triangle, that is, the point where the angle bisectors of the triangle meet.
Steps to draw an Inscribed Circle:
a. construct an angle bisector of each vertex (<ABC, <BAC, <ACB) of the triangle to determine the center of the triangle.
b. draw a line perpendicular to one side of the triangle that passes through its center.
c. draw an Inscribed Circle that passes through the point where the sides of the triangle intersect and the perpendicular from above.
As in the question, it was stated that the center of the Inscribed Circle is point D, so the step that can be used to draw an Inscribed Circle of A ABC is to draw the perpendicular bisectors of AB, BC, and AC that pass through point D
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If I bought a computer for $420. It had been reduced by 25%.
What was the original price of the computer before the reduction?
(If I could get an answer asap that would be great!)
Answer:
$560
Step-by-step explanation:
if 25% is the discount than the total of the item after the discount is .75x. So to find the original total we need the equation 420=.75x
first we need to isolate x so we divide both sides by .75, doing this will give us 560= x
to check our answer you need to multiply 560 by .75 (which I got by subtracting the discount, .25, from 1) which gives us our discounted total of $420
HELP I CANT FIGURE THIS OUT. Which math expression means "the difference of 150 and 99"?
• A. 150 • 99
• B. 150 - 99
O C. 150 - 99
• D. 150 + 99
Answer: C 150-99
Step-by-step explanation:
Solve using substitution. Y=1 -3x+4y=-20
Answer: We can start by solving for one variable in one of the equations and then substituting that value into the other equation.
Solve for y in the first equation: y = 1 - 3x
Substitute this value of y into the second equation: 4(1 - 3x) + 4x = -20
Solve for x: -4x = -24
x = 6
Substitute this value of x into the first equation to find the value of y: y = 1 - 3(6) = -17
So the solution is x = 6 and y = -17.
Step-by-step explanation:
A professional pool player claims that she sinks at least one ball in a pocket on 80% of her opening break shots. In a recent set of 20 games, she sunk at least one ball on her break shot in only 14 of the games. A simulation of 100 trials was conducted to see how unusual these most recent games are. A dotplot titled the professional pool player has number of games with at least one ball made on the break on the x-axis, and frequency on the y-axis. 10, 1; 12, 3; 13, 11; 14, 12; 15, 17; 16, 25; 17, 16; 18, 9; 19, 5; 20, 2. Based on the dotplot of the simulation results and the pool player’s last 20 games, which conclusion can be drawn?
There is about a 27% chance of her sinking at least one ball on her break 14 or fewer times in 20 games and no convincing evidence that her average is less than 80%.
Based on the dot plot of the simulation results, it appears that the player's true probability of sinking at least one ball on her break is not 80%. In the simulation, there were only 12 trials out of 100 where the player sank at least one ball on her break 14 or fewer times in 20 games. This corresponds to a probability of 12/100, or 12%.
Since the player's actual performance in the last 20 games (14 out of 20) is less likely to occur than what was observed in the simulation, we can get the conclusion that the player has a lower than 80% chance of sinking at least one ball during her break.
Therefore, the correct conclusion is, "there is about a 27% chance of her sinking at least one ball on her break 14 or fewer times in 20 games. This result is not unusual and there is no convincing evidence that her average is less than 80%."
The question is incomplete. The complete question is 'The player’s true probability of sinking at least one ball on her break is 27%. another 100 simulated trials would show a much different outcome; therefore, we cannot draw any conclusions. it is most likely that she would sink at least one ball during her break exactly 16 times. there is about a 27% chance of her sinking at least one ball on her break 14 or fewer times in 20 games. this result is not unusual and there is no convincing evidence that her average is less than 80%.'
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Answer:
d
Step-by-step explanation:
edge 2020
Answer Choices:
A: y=2x+4
B:
provide numerical measures of individuals. the measures can be added or​ subtracted, and provide meaningful results.
Quantitative variables provide numerical measures of individuals. The measurements yield useful results and can be added to or removed from.
A quantitative variable is one for which the data display amounts (e.g. height, weight, or age). A categorical variable is one where the data indicate categories. As was discussed in the chapter's section on variables, quantitative variables are those that are measured on a numeric scale.
Height, weight, reaction speed, subjective pain rating, temperature, and exam score are a few examples of quantitative variables.
A quantitative study works with numbers and data, whereas a qualitative study concentrates on words and meanings. Variables can be quantified, and hypotheses can be tested quantitatively. You can go more deeply into concepts and experiences by using qualitative research methods.
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1. Which method would be the simplest way to solve the system? y= 1/2x 2x+3y=28 A) graphing B) substitution C)elimination D) distributive 2.How many solutions does this system have?
Since the value of y can be known from equation 1, we can use the substitution method to solve the system of equations. By entering the value of y in equation 2, we can quickly get the value of x. So the option B is correct.
The system of equation are:
y = 1/2x...................(1)
2x + 3y = 28...................(2)
To solve the system of equation we use substitution method because the value of y is know from the equation 1. We can find easily the value of x by putting the value of y in equation 2.
Now putting the value of y in equation 2.
2x + 3(1/2x) = 28
2x + 3/2 x = 28
7/2 x = 28
Multiply by 2 on both side, we get
7x = 56
Divide by 7 on both side, we get
x = 8
Now putting the value of x in equation 1
y = 8/2 = 4
The solution of the system of equation is (8, 4).
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an unfair/biased die is considered as an even number is twice as likely to occur as an odd number, phenomena is called
The probability of an even number is twice as likely to occur as an odd number is 2/9 and 1/9 respectively.
Probability in math term is defined as a number that reflects the chance or likelihood that a particular event will occur.
Here we have given that an unfair/biased die is considered as an even number is twice as likely to occur as an odd number.
And here we need to find the probability of the event.
Here let us consider that probability of getting an even number = x and let probability of getting odd number = y
Then it can be written as
=> 3x+3y=1
Here we write it as because probability of getting even number or odd number = 1 since those two are the only possibilities.
Then we have to apply the value of x=2y (given)
Now, we have to solve these two, then we get,
=> x=2/9 and y=1/9
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Given the function g(x)=-x²+5x+14, determine the average rate of change of the function over the interval 1 ≤ x ≤ 9
the average rate of change of the function over the interval 1 ≤ x ≤ 9 is 3.75.
What is the average rate of change?It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
Given the function g(x)=-x²+5x+14, within the interval 1 ≤ x ≤ 9
At the lower interval x = 1
g(x) = -1 +5 + 14
g(x) = 18
At the lower interval x = 9
g(x) = -9²+5*9+14
g(x) = -22
The average change of the function will be expressed as:
Δy/Δx = (-22 - 8)/ (9-1)
Δy/Δx = -30/8
Δy/Δx = 3.75
therefore, the average rate of change of the function over the interval 1 ≤ x ≤ 9 is 3.75.
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45% as a fraction or a mixed number in simplest form
Answer:
[tex]\frac{9}{20}[/tex]
Step-by-step explanation:
45% = [tex]\frac{45}{100}[/tex]
[tex]\frac{45}{100}[/tex] ÷ [tex]\frac{5}{5}[/tex] = [tex]\frac{9}{20}[/tex]
Answer:45%=9/20 I hope this helps
Step-by-step explanation:
45%
By definition p%=p/100 which something like this
45/100
then you Cancel out the common factor 5
45/100 cancel these numbers out by 5
Then you will get your answer which is something like this
9/20
So 45%=9/20 as a fraction
a and b are parallel. Find the missing angles.
The missing angles are as calculated below. Fill them accordingly.
How to find the missing angles?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Check the attached image for labeling
a = 125° (vertically opposite angles are equal)
a + b = 180 (sum of angles on a line)
b = 180 - 125 = 55°
b + c = 90 (sum of angles in a triangle)
c = 90 - 55 = 35°
d = b (alternate angle)
d = 55°
e = 125° (alternate angle)
Fill in the missing angles accordingly
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If the hypotenuse of a 30°-60°-90° triangle is 8 cm, what is the measure of the longer leg of the triangle?
The measure of the longer leg of the triangle is given as follows:
6.93 cm.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.The longer leg is opposite to the angle of 60º, hence the sine relation is used to find the length, as follows:
sin(60º) = x/8
x = 8 x sine of 60 degrees
x = 6.93 cm.
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solve for side h with the given side and angle
Answer: 33.93 in
Step-by-step explanation:
we can see it is a right angle there. h is oppsite line of the right triangle and 70in is Hypotenuse. So, we can use the formula sin29 = h/70. Then sin29*70=h. h=33.93 in.
Your mother is very fond of collecting rare philodendron (an ornamental and
indoor plant). If she has a garden which measures 100 m2 (10 m by 10 m)
and each philodendron will occupy an estimated area of 0. 6 by 0. 6 m of the
garden, what is the maximum number of philodendron plants that will occupy
the whole area?
help me please
The maximum number of philodendron plants that will occupy the whole area is 256.
The term area in math is defined as the region bounded by the shape of an object
Here we have given that your mother is very fond of collecting rare philodendron and here we have know that If she has a garden which measures 100 m² and each philodendron will occupy an estimated area of 0. 6 x 0. 6 m of the garden.
Here we have to 10 meters divided by 0.6 of a meter gives 16 philodendrons in one direction and the same number in the other direction.
Then the maximum number of plants is calculated as,
=> 16 x 16 = 256
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For the translation below, give the vertices of ABC
A' = (-1, 3)
B' = (-4, 0)
C' = (1, 6)
=======================================================
Reason:
The notation [tex]T_{ < -3, 5 > }[/tex] means "translate 3 units left, 5 units up".
Another way to write out this rule is [tex](\text{x},\text{y}) \to (\text{x}-3,\text{y}+5)[/tex]
-------------------
Let's apply that rule to the coordinates of point A.
[tex](\text{x},\text{y}) \to (\text{x}-3,\text{y}+5)\\\\(2,-2) \to (2-3,-2+5)\\\\(2,-2) \to (-1,3)\\\\[/tex]
Point A' is located at (-1, 3)
-------------------
Repeat for the coordinates of point B.
[tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+5)\\\\(-1,-5)\to(-1-3,-5+5)\\\\(-1,-5)\to(-4,0)\\\\[/tex]
Point B' is located at (-4, 0)
-------------------
Lastly do the same for point C.
[tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+5)\\\\(4,1)\to(4-3,1+5)\\\\(4,1)\to(1,6)\\\\[/tex]
Point C' is located at (1, 6)
The measures of the acute angles of a right triangle are (2x-3)^degree. What is the measure of the smallest angle in the triangle?
The required measure of the smallest angle in the triangle is 37°.
What is Right angled triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The sum of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
According to question:We know that one angle in right angled triangle is 90 degree and sum of other two angle is 90 degree.
So, acute angles are (2x -3) and (3x-7).
Then
(2x -3) + (3x-7) = 90
5x - 10 = 90
5x = 100
x = 20
Smallest angle = 2x - 3
= 2(20) - 3
= 40 - 3
= 37°
Thus, required Smallest angle is 37°
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Mr. Sato sells fish at a 60% markup. He pays $3.75 per pound for haddock one week. At what price per pound will he sell it?
Answer: $6
Step-by-step explanation:
60% of 3.75
3.75 * 0.60 = 2.25
2.25 + 3.75 = 6
Step-by-step explanation:
The answer is 2.25 because 60% of 3.75 is equal to 2.25
The smallest gecko on record is 0.8 inch long. Sarah's drawing has a scale factor of 1 inch to 0.1 inch. Which equation could be used to find g, the length of Sarah's drawing of the gecko?
The length of Sarah's drawing is given by the following equation:
0.1g = 0.8.
How to obtain the scale of the drawing?The scale of the drawing is obtained applying the proportions in the context of this problem.
The scale is defined as the division of the drawn length by the actual length.
Sarah's drawing has a scale factor of 1 inch to 0.1 inch, meaning that each inch she draws has an actual length of 0.1 inch.
The rule of three is defined as follows:
1 inch - 0.1 inches
g inches - 0.8 inches
Hence the equation is:
0.1g = 0.8.
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generally, all stakeholders agree that there is a problem and on what the problem is before beginning the dmaic process. state of true of false.1. true2. false
The given statement about the stake holders of DMAIC is false.
The term DMAIC stands for Define, Measure, Analyze, Improve, and Control and it represents the five phases that make the process,
Here we have given that generally, all stakeholders agree that there is a problem and on what the problem is before beginning the DMAIC process.
And we need to check whether the statement is true or not.
Here we know that in DMAIC process we have to follow the following steps they are listed as,
=> Define the problem
=> Improve activity
=> To determine opportunities for improvement
=> Identify the project goals
=> To analyze project goals and customer requirements.
Hence through this we have identified that the main purpose of DMAIC is to improve the effectiveness and efficiency of an organization's existing processes.
And here we have also know that DMAIC is a core data-driven improvement methodology of Six Sigma.
So, here the given statement is false.
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