The probability of a less-than-ideal day (no free pizza and no sun) is 0.25
Let us define the events from the example.
Let event A: Sunny day for any given day
event B: Getting free pizza for any given day.
Now, we will translate the word problem into our symbols.
The probability of a sunny day is 80% i.e P(A)=0.8
The probability of free getting pizza is 30% i.e. P(B) = 0.3
The probability of free pizza and a sunny day is 35% .i.e P(A∩B) = 0.35
a)Complement means not happening an event i.e. event A’ : No sunny day for any given day event B’: Not getting day free pizza for any given.
Here dash ( ‘ ) complement.
The probability of a less-than-ideal day
(no free pizza and no sun) is
P(A'∩B') = P(A∪B)'... (De Morgan's Jaw)
De Morgan's law: (A∩B)'= A'∪B'
(A∪B)’ = A'∩B'
P(A'∩B') = 1-P(A∪B) (P(A) = 1-P(A)).
= 1-[P(A) + P(B)-P(A∩B)]
= 1-[0.8+0.3-0.35]
P(A'∩B') = 0·25
The probability of a less-than-ideal day (no free pizza and no sun) is 0.25.
b)To check whether free pizza and sun are independent events or not, let us see when two events are said to be independent.
Two events (A & b) are said to be independent if P(A∩B) = P(A)· P(B)
Let us check whether this property satisfies our case or not.
LHS = P(A∩B)=0.35
RHS= P(A) P(B)
= 0.8 x 0.3
RHS = 0.24.
LHS ≠ RHS
P(ANB) ≠ P(A). P(B) in our case.
Two events A and B are not independent in our case
Sun and free pizza are not independent events.
c)Probability of no free pizza on a sunny day is P(A∩B').
P(A∩B') = P(A) - P(A∩B) = 0.8 0.35
P(A∩B') = 0·45
The probability of no free pizza on a sunny day is 0.45
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− 5/7 . (−3) can someone write this in the simplest form
This data can best be modeled withwhich type of function?ху018,250118,730a. Linearb. QuadraticC. Exponential219,210319,690420,170
A linear function is a function in which we add multiple of a constant.
Given data:
We have
[tex]\begin{gathered} y=18,250+480(1)\text{ at x=0} \\ y=18,730=18,250+480(1)\text{ at x=1} \\ y=19,210=18,250+480(2)\text{ at x=2} \\ y=19,690=18,250+480(3)\text{ at x=3} \\ y=20,170=18,250+480(4)\text{ at x=4} \end{gathered}[/tex]Clearly, we have add multiples of 480 to 18,250.
So, the given function represents a linear function.
So, the correct option is (a).
Write a simplified expression for the right half of the equation that can be used to find the nth term in the sequence6,7,8 9,10
Adam plans to choose a video game from a section of the store where everything is 75% off. He writes the expression d−0.75d to find the sale price of the game if the original price is d dollars.
Rena correctly writes another expression, 0.25d, that will also find the sale price of the game if the original price is d dollars.
Drag each description to explain each part of both expressions.
Both Adam and Rena re both correct regarding the expression.
What is an expression?An expression simply means an illustration that can be used to represent a scenario or situation.
From the information, Adam writes the expression d−0.75d to find the sale price of the game if the original price is d dollars.
Rena correctly writes another expression, 0.25d, that will also find the sale price of the game if the original price is d dollars.
In this case, they are both correct. This can be illustrated as:
= 1 - 0.75d
= 0.25d
Note that the information was answered based on the information given.
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PLS HELP, 50 POINTS + BRAINLY FOR CORRECT ANSWER!!!
charlyn walks completely around the boundary of a square whose sides are each 55 km long. from any point on her path she can see exactly 11 km horizontally in all directions. what is the area of the region consisting of all points charlyn can see during her walk, expressed in square kilometers and rounded to the nearest whole number?
The area of the region consisting of all the points Charlyn can see during her walk is equal to, A = 4840 km.
Charlyn is walking around the boundary of square A, which is 55 km long, and she has a horizontal vision of 11 km.
So as she walks around the square of 55 km, let there be another square B which lies outside square A, which is created due to her 11 km field of vision.
length of sides of square B = 55+(2×11) which is equal to 77 km.
And as she walks around the square of 55 km, let there be yet another square C which lies inside square A, which is created due to her 11 km field of vision.
length of sides of square C = 55-(2×11) which is equal to 33 km.
The area that Charlyn can see throughout her walk is equal to,
A = Area of square B - Area of square C.
The area of square B = Side² = 77² = 5929.
The area of square C = Side² = 33² = 1089.
A = 5929 - 1089.
A = 4840 km.
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Which of the following is NOT a misuse of statistics?Choose the correct answer below.A. Utilizing valid statistical methods and correct sampling techniquesB. Making conclusions about a population based on a voluntary response sampleC. Concluding that a variable causes another variable because they have some correlationD. Misleading graphs
Required:
We need to find the statement which is NOT a misuse of statistics.
Explanation:
Recall that misuse of statistics occurs when a statistical argument asserts a falsehood.
Utilizing valid statistical methods and correct sampling techniques is not a misuse of statistics.
Final answer:
A. Utilizing valid statistical methods and correct sampling techniques
What is the value of the the 9 in 194.6
The place value of 9 in 194.6 is tens or 90.
According to the question,
We have the following expression:
194.6
Now, we know that place value of any digit can be found easily. The place value of the digit at the right most corner (of a number without any decimal point) is unit, left to this digit we have place value of tens, then we have hundred, then thousand, ten thousand, etc.
Now, in this case, we have a decimal point. So, we will look at the last digit before the decimal point because it's place value is unit place. And the next left digit to this is tens.
Hence, the place value of 9 in 194.6 is tens.
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y=600(0.75)^x
growth or decay by what precent?
The function f(x) = 600(0.75)^x. is a decay function by 25%
How to graph the function?The equation of the function is given as
f(x) = 600(0.75)^x.
The above function is an exponential function
An exponential function is represented as
y = ab^x
When f(x) = 600(0.75)^x. and y = ab^x are compared, we have
b = 0.75
The value of b in this case is the factor
Also if b is less than 1, then the function is a decay function
0.75 is less than 1
So, the function represents a decay function
The decal percentage is then calculated as
Decay = 1 - b
So, we have
Decay = 1 - 0.75
Evaluate
Decay = 25%
Hence, the function is a decay function
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2. Evaluate the expression
4 (-1.2-4-4.75) +1+(-3)².
Answer:
-29.8
Step-by-step explanation:
4 (-1.2-4-4.75) +1+(-3)²
4 (-1.2-4-4.75) +1+(-3)²
4 (-9.95) +1+9
4 (-9.95) +1+9
-39.8 +1+9 = -29.8
2. Write three decimals that
have a sum of 114.056.
Three decimal that sum of 114.056 is 52.2+34.15+28.5.
What is decimal?
decimal is a term that describes the base-10 number system, probably of the most commonly used the number system. The decimal number system of consists of ten single-digit numbers.
We will represent this as 1.5 pizzas in decimal form. In this case, the dot stands in for the decimal point, the number before the dot, in this case "1," represents one whole pizza, and the number after the decimal point, or the fractional part, represents the other half of the pizza. You may have seen decimal numbers similar to these while grocery shopping, on a scale, or even during a baseball game.
Sol- we have to add three decimal that have a sum of 114.056 no parts are given here.
Let's take
X+Y+Z = 114.056
We need to add any particular number here
Let's put 52+34+28
Still we need .056 extra
So we have to add points here
52.2+34.15+28.5
So these are 3 decimal point.
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Jai left his house and drove to the store. He stopped and went inside. From there, he drove in the same direction until he got to the bank. He stopped and went inside the bank. Then he drove home. The graph below shows the number of blocks away from home Jai is xx minutes after he left his house, until he got back home. How many blocks is it from the store to the bank?
Considering the Graph and reading the distance blocks from the store to the bank we see a progression of 3blocks
This is further explained below.
What is the distance?Generally, There is a concept referred to as distance that may be used to quantify, either quantitatively or qualitatively, the distance that separates two items or sites.
When speaking about physics or using the phrase in everyday language, "distance" may either refer to a literal measurement or an estimate based on a number of other parameters.
Both meanings are appropriate when discussing or using the term.
The progression of existence and events that occur in what seems to be an unstoppable order beginning in the past, continuing through the present, and moving into the future is what we refer to as time.
Time may be broken down into three distinct parts: the past, the present, and the future.
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Assume that each circle shown below represents one unit. Express the shaded amount as a single fraction and as a mixed number. One Fraction: Mixed Number: Submit Answer attempt
The shaded amount can be express as a single fraction and mixed fraction below
[tex]\begin{gathered} \text{each circle=1 unit} \\ 2\text{ circle= 2 unit} \\ \text{each circle was divided into 12 parts} \\ \text{the shaded parts in the 24 parts =14} \\ Therefore, \\ 1\frac{2}{12}=\frac{14}{12}=1\frac{1}{6} \end{gathered}[/tex]Solve the inequality
r/-3.2>7.6 for r
Answer:
> -24.32 I hope that help so it is a on your screen
Which of the following equations represents the line that passes through the point (4, 3) and has a slope of 1/2.
A) 2x-3y=-18
B)2x-3y=17
C)3x-2y=-17
D)3x-2y-18
The equation of the line in standard form is -1/2x + y = 1 or y = 1/2x + 1 in slope-intercept form.
(note: none of the option given is correct).
What is the Equation of a Line?In standard form, the equation of a line can be expressed as Ax + By = C, where x and y are coordinate of a point on the line, A, B, and C are integers.
This equation can be rewritten in slope-intercept form as y = mx + b, where b is the y-intercept and m is the slope.
Given:
Slope (m) = 1/2Point (x, y) = (4, 3)Substitute m = 1/2, x = 4, and y = 3 into y = mx + b to find b:
3 = 1/2(4) + b
3 = 2 + b
3 - 2 = b
1 = b
b = 1
Write the equation by substituting b = 1 and m = 1/2 into y = mx + b:
y = 1/2x + 1
Rewrite in standard form
- 1/2x + y = 1
Thus, none of the options is correct, The equation is: y = 1/2x + 1 in slope-intercept form or - 1/2x + y = 1 in standard form.
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Jeremiah keeps a record of how many pages he reads each day. He read 40% fewer pages today than yesterday. If he read 90 pages today, how many pages did he read yesterday?
Answer: 126
Step-by-step explanation:: 90 ÷ 10 = 9 (10%) 9 × 4 = 36 (40%) 90 + 36 = 126
What is the value of x?
Answer:
15
Step-by-step explanation:
Use the following two points to answer parts a -c . (2, 3) , (- 1, - 6) a. Find the slope of the line passing through the two pointsb . Write an equation of a line passing through the two points in point slope form . c . Rewrite the equation of the line in slope -intercept form .
sSlope means the inclination of the line
Intercept is the point where the line touches the Y axis.
x-4y=-2
Determine if the given ordered pair, (2, 1), satisfies the given equation.
O YES
O NO
Answer:
Yes.
Step-by-step explanation:
Replace x with 2 and y with 1 and see if the equation is true
x - 4y = -2
2 - 4(1) = -2
2 - 4 = -2
-2 = -2
The statement is true so the point is on the line.
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. tan 26° = ___
Answer:
0.49
Explanation:
Given the expression:
tan 26°
Evaluating using calculator
tan 26° = 0.4877
Hence the decimal rounded to the nearest hundredth is 0.49
Answer:
0.49 to nearest hundredth
Step-by-step explanation:
tan 26⁰ = 0.48773
Given segments AB and CD intersect at E.
A(1, 2), B(4, 5), C(2, 4), D(2, 1), E(2, 3)
What is the midpoint of cd?
Answer: (2, 5/2)
Step-by-step explanation:
CD=(2, 4),(2, 1)
((2+2)/2, (4+1)/2)=
(4/2, 5/2)=(2, 5/2)
a 13-ft ladder rests against a vertical wall. if the bottom of the ladder slides away at 1 ft/s, at what rate is the top of the ladder sliding down the wall when the bottom of the ladder is 5 ft from the wall? g
The given situation can be solved using the differential equation and the top of the ladder slides downward at 0.417 ft/s.
Let:
x be the distance from the bottom of the ladder to the base of the wall
y be the distance from the top of the ladder to the bottom of the wall
When the ladder is still, apply the Pythagorean Theorem,
x² + y² = 13²
5² + y² = 13²
y² = 169 - 25 = 144
y = 12 ft
When the ladder slides, apply the differential equation:
x² + y² = 13²
2x . dx/dt + 2y . dy/dt = 0
Substitute x = 5, dx/dt = 1, y = 12
2 . 5 . 1 + 2 . 12 . dy/dt = 0
24 dy/dt = -10
dy/dt = -5/12 = - 0.417 ft/s
The minus sign indicates that the ladder is sliding downward.
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Is the ordered pair a solution of the equation?
y = x + 16; (-1,-17)
a. yes
b. no
Answer:
b.
Step-by-step explanation:
No, because -1 is x and -17 is y. if You plug it in, it will look like this:
-17=-1+16
-1+16=15
15 is not equal to -17, so the answer is no, b.
Hope this helps!
Answer:
a.)yes. у=х+16
Answer:
(-1)
There are 125 people in a sport centre.
59 people use the gym.
70 people use the swimming pool.
55 people use the track.
25 people use the gym and the pool.
30 people use the pool and the track.
17 people use the gym and the track.
6 people use all three facilities.
A person is selected at random.
What is the probability that this person doesn't use any facility?
Probability that the person selected at random from the sport centre of 125 people is a fraction of 1/4 or 0.25.
Probability of an eventThe probability of an event is the fraction of the required number of outcome divided by the number of possible outcomes.
We shall determine the answer to the question as follows;
People in the sport centre = 125
People who used the 3 facilities = 6
People who accessed only gym = 59 - (6 + 11 + 19) = 26
People who accessed only track event = 55 - (6 + 11 + 24) = 14
People who accessed only swimming pool event = 70 - (6 + 19 + 24) = 21
People who accessed only gym and swimming pool events = 29 - 6 = 19
People who accessed only gym and track events = 17 - 6 = 11
People who accessed only swimming pool and track events = 30 - 6 = 24
Total number of people who accessed at least any one of the facilities = 121
The number of people who did not access any of the facility = 125 - 121 = 4, which is the number of possible outcomes for our required outcome.
Therefore, the probability that the person selected doesn't use any facility = 1/4
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Jim sits on a seesaw. If Jim weighs 100 pounds, what mass in kilograms does the person on the other side need to be for the seesaw to be balanced?
The weight of the other person has to be the same in order for the seesaw to be balanced, then the person on the other side weighs 100 pounds as well. Now, we know that:
[tex]1\text{ lb=}0.45\text{ kg}[/tex]Then to find the mass we just multiply the weight in pounds by 0.45:
[tex]100\cdot0.45=45[/tex]Therefore the other person has a mass of 45 kg.
The weight of the other person has to be the same in order for the seesaw to be balanced, then the person on the other side weighs 100 pounds as well. Now, we know that:
[tex]1\text{ lb=}0.45\text{ kg}[/tex]Then to find the mass we just multiply the weight in pounds by 0.45:
[tex]100\cdot0.45=45[/tex]Therefore the other person has a mass of 45 kg.
C)
to make the total value equal to 2. Re-write the statement 19 + 7 + 2 x 6 + 1 by including two pairs
of brackets
If you place brackets or parenthesis around the numbers 19+7 and 2*6+1. It would appear as follows: (19+7)/(2*6+1) = 26/13 = 2. It takes special parenthetical treatment to express the mathematical expression 19+7/26+1 to get a result of 2.
What is expression?An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being similar to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence.
Here,
y=19+7/2×6+1
becomes
y=(19+7)/(2×6+1)
y=26/(12+1)
y=26/13
y=2
If you enclose the numbers 19+7 and 2*6+1 in parenthesis or brackets. It would look like this: (19+7)/(2*6+1) = 26/13 = 2. The mathematical expression 19+7/26+1 must be expressed with special parenthetical treatment to yield the number 2.
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Provide an example and explain the steps to convert a fraction into a percent.
note: this is a multi-part question. once an answer is submitted, you will be unable to return to this part. 7 women and 7 men are on the faculty in the mathematics department at a school. how many ways are there to select a committee of five members of the department if at least one woman must be on the committee?
No. of ways of selecting the 5 member committee by combination= 1981
What are the number of ways of selecting the 5 member committee ?
No. of women faculty in the mathematics department = 7
No. of men faculty in the mathematics department = 7
Total number of faculty members = 14
Condition - at least one woman must be on the committee
No. of ways of selection = C (14, 5) - C (7, 5)
We know that combination C(n , r) = [tex]\frac{n!}{(n-r)!r!}[/tex]
Consider the total combination C (14, 5),
[tex]C (14, 5)=\frac{14!}{9!5!} \\\\=\frac{14 *13* 12 *11 *10 *9!}{9!* 5!} \\\\=\frac{14 *13* 12 *11 *10}{120} \\\\= \frac{240240}{120} \\\\= 2002[/tex]
Consider the combination of men C (7, 5) ,
[tex]C (7, 5)=\frac{7!}{2!5!} \\\\=\frac{7*6*5!}{2!* 5!} \\\\=\frac{7*6}{2} \\\\= 7*3\\\\=21[/tex]
No. of ways of selection = C (14, 5) - C (7, 5)
= 2002 - 21
=1981
No. of ways of selecting the 5 member committee of the department with least one woman by combination= 1981
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A baker has four containers. Three of the containers contain 3/4 pounds of sugar. The fourth container has 1/3 pound of sugar. How many total pounds of sugar does the baker have?
The baker has 13/3 pounds of sugar.
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
We have been given two fractions.
The three containers have 3/4 pounds of sugar and fourth one have 1/2 pounds of sugar.
To find the total sugar, we have to add both the fractions
Total pounds of sugar = Sugar in three containers + sugar in fourth container
= 3/4 + 1/3
= (9 + 4)/3
= 13/3 pounds
So, the total sugar the baker has is 13/3 pounds.
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Students in a fitness class each completed a one-mile
Which statements are true about a histogram with one-
walk or run. The list shows the time it took each person
minute increments representing the data? Select three
to complete the mile. Each time is rounded to the
options.
nearest half-minute.
5.5, 6, 7, 10, 7.5, 8, 9.5, 9, 8.5, 8, 7, 7.5, 6, 6.5, 5.5
O A histogram will show that the mean time iS
approximately equal to the median time of 7.5
minutes.
O The histogram will have a shape that is left-skewed.
O The histogram will show that the mean time is greater iS
than the median time of 7.4 minutes.
O The shape of the histogram can be approximated with
a normal curve.
0 The histogram will show that most of the data is
centered between 6 minutes and 9 minutes.
In linear equation, The histogram will show that most of the data is centered between 6 minutes and 9 minutes.
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.5.5+6+7+10+7.5+8+9.5+9+8.5+8+7+7.5+6+6.5+5.5=111.5
Since there are 15 values,
their mean is 111.5/15=7.43 which is very close to the mean.
A)A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes
D)The shape of the histogram can be approximated with a normal curve.
E)The histogram will show that most of the data is centered between 6 minutes and 9 minutes.
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