The width of the bedroom is approximately 7.32 feet.
A rectangle is a four-sided figure with opposite sides being equal and parallel. The area of a rectangle is given by multiplying the length and width of the rectangle.
Let's assume that the width of the bedroom is 'x' feet. We know that the length of the room is 5 feet longer than its width. Therefore, the length of the room will be (x+5) feet.
Now, we can use the given area of the bedroom to set up an equation:
Area of rectangle = Length x Width
84 = (x+5) x x
Simplifying this equation, we get:
84 = x² + 5x
Rearranging, we get:
x² + 5x - 84 = 0
This is a quadratic equation that can be solved using the quadratic formula:
x = (-b ± √(b² - 4ac))/2a
In this case, a = 1, b = 5 and c = -84. Substituting these values in the formula, we get:
x = (-5 ± √(5² - 4(1)(-84)))/2(1)
Simplifying this, we get:
x = (-5 ± √721)/2
We can ignore the negative root since the width of the bedroom cannot be negative. Therefore, the width of the bedroom is:
x = (-5 + √721)/2
x ≈ 7.32 feet
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a certain shop repairs both audio and video components. let a denote the event that the next component brought in for repair is an audio component, and let b be the event that the next component is a compact disc player (so the event b is contained in a). suppose that p(a) 5 .6 and p(b) 5 .05. what is p(bua)?
The probability that the next component brought in for repair is a compact disc player given that it is already known to be an audio component is 0.83 or 83%.
Probability is a fundamental concept in mathematics, statistics, and various fields of science. It is used to measure the likelihood of an event occurring
In the given scenario, we are told that a certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player. We are also given that P(A) = 0.6 and P(B) = 0.5.
The probability of B given A, denoted by P(B|A), represents the probability that event B will occur given that event A has already occurred. In other words, it tells us how likely it is that the next component brought in for repair is a compact disc player given that it is already known to be an audio component.
To calculate P(B|A), we use the formula for conditional probability:
P(B|A) = P(A and B) / P(A)
Here, P(A and B) denotes the probability that both events A and B occur. We know that event B is contained in event A, so it follows that P(A and B) = P(B). Therefore:
P(B|A) = P(B) / P(A)
Substituting the given values, we have:
P(B|A) = 0.5 / 0.6
P(B|A) = 5/6 or 0.83 (rounded to two decimal places)
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Complete Question:
A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A). Suppose that P(A) = .6and P(B) = .5. What is P(B|A) ?
(SAT Prep) Find the value of x
FIND THE VALUE OF x IT IS NOT 5x
Over the summer, a Bee Keeper and their bees was able to produce 636 jars of honey over the course of 12 week.
Answer: I assume you are trying to find how many jars the beekeeper has produced per week.
The answer is: 53
Step-by-step explanation:
We know that he produced 636 jars of honey over 12 weeks.
Therefore, to find out the number of jars he made each week, we divide the amount by the time.
So 636/12
Answer 53.
the area of a square is 64 square yards. find the length of 1 side of the square
Answer:
Step-by-step explanation:
The formula for the Area of a square is:
A=[tex]s^{2}[/tex] Where s is the length of the side of the square.
Substituting and solving for s gives:
64 units2 = [tex]s^{2}[/tex]
√64 units2 =√s2
8 units = s
The formula for the perimeter of a square is:
p=4s
Where s is the length of the side of the square.
there are two urns containing colored balls. the first urn contains 50 red balls and 50 blue balls. the second urn contains 30 red balls and 70 blue balls. one of the two urns is randomly chosen (both urns have equal probability of being chosen) and then a ball is drawn at random from one of the two urns. if a red ball is drawn, what is the probability that it came from the first urn?
If a red ball is drawn from two urns containing colored balls , then the probability that it came from the first urn is 0.625 or 62.5% .
Let A = the event that the first urn is chosen, and
B is = the event that a red ball is drawn.
We have to find P(A|B), which means , the probability that the first urn was chosen given that a red ball was drawn.
So , By Bayes' theorem:
we have , P(A|B) = P(B|A) × P(A) / P(B) ;
Since each urn has an equal probability of being chosen, we have P(A) = P(B) = 1/2 ; and
the probability of drawing a red ball is the same regardless of which urn was chosen.
We need to find P(B|A), the probability of drawing a red ball from the first urn is 50/100 = 0.5 ;
To find P(B), the overall probability of drawing a red ball, we can use the law of total probability:
that is ; P(B) = P(B|A) × P(A) + P(B|A') × P(A') ;
where A' = event that the second urn was chosen.
Now , we find P(B|A'), which is the probability of drawing a red ball from the second urn is = 30/100 = 0.3 ;
We know that P(A') = 1/2 = 0.5 , because there are only 2 urns.
So , we have : P(A|B) = P(B|A)×P(A) / P(B) ;
= (0.5×0.5) / (0.5×0.5 + 0.3×0.5)
= 5/8
= 0.625
Therefore, the probability that the red ball came from the first urn is 0.625 or 62.5% .
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to collect data on the signal strengths in a neighborhood, tracy must drive from house to house and take readings. she has a graduate student, dave, to assist her. tracy figures it would take her eight hours to complete the task working alone, and that it would take dave 12 hours if he completed the task by himself. how long will it take tracy and dave to complete the task together? 3.6 hours 7.2 hours 4.8 hours 6.0 hours
It would take Tracy and Dave approximately 4.8 hours to complete the task together. So, the correct option is C.
To solve this problem, we can use the formula:
time = work / rate
where work is the amount of work to be done (in this case, collecting signal strength data from each house), and rate is the rate at which the work is being done.
Let's start by finding Tracy's and Dave's individual rates:
Tracy's rate: 1 job / 8 hours = 0.125 jobs per hour
Dave's rate: 1 job / 12 hours = 0.0833 jobs per hour
Now, let's find their combined rate when they work together:
Combined rate = Tracy's rate + Dave's rate
Combined rate = 0.125 + 0.0833
Combined rate = 0.2083 jobs per hour
Finally, we can use the formula time = work / rate to find how long it would take them to complete the task together:
time = 1 job / 0.2083 jobs per hour
time ≈ 4.8 hours
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8.70% of is 14?
O 10
O 20
O 30
O 50
The equation 7(2W + 3) = 14W + 20 has no solutions. Change one term in the original equation to create a new equation with one solution.
Answer:
change the 2w value
Step-by-step explanation:
first, check the equation:
14w + 21 = 14w + 20
when subtracting the 14w from both sides you can see that
21 is NOT EQUAL to 20, making the answer NS.
now, reread the question... create a new equation with ONE solution.
to fix this, we need to change the amount of W's, NOT the amount of constant.
let's try out another number in place of 2w
7 ( 3w + 3 ) = 14w + 20
21 w + 21 = 14w + 20
7 w = -1
w = -1/7
so now it is clear. to change the outcome of the equation, try out another value instead of 2w. Maybe try 3w, 3.5w, or maybe even 1w, or 1.5w .
Answer:
change the 2w
Step-by-step explanation:
=> 7 ( 3w + 3 ) = 14w + 20
=> 21 w + 21 = 14w + 20
=> 7 w = -1
=> w = -1/7
So everything is now evident. Change the value of 2w to anything else to alter the equation's result. Try 3w, 3.5w, or even 1w or 1.5w if you can.
Hope it have been helpful.
A circle is graphed on a coordinate grid and then reflected across the y-axis. If the center of the original circle was located at (x , y), which ordered pair represents the center of the new circle after the transformation?
A(-x,y)
B(-x,-y)
C(x,y)
D(x,-y)
The required ordered pair represents the center of the new circle after the transformation is (-x,y). Option A is correct.
What is the transformation of geometry over the coordinate plane?Transform the shapes on a coordinate plane by rotating, reflecting, or translating them.
Here,
If a circle is reflected across the y-axis, its center, which was originally located at (x, y), will move to a new location that is the same distance from the y-axis but on the opposite side. Since the y-coordinate does not change during a reflection across the y-axis, the y-coordinate of the new center will remain the same as the original, which is y.
However, the x-coordinate will be negated, since the reflection across the y-axis involves flipping points to the opposite side of the y-axis. Therefore, the center of the new circle will have the coordinates (-x, y).
So the answer is A) (-x, y).
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The value of m so that x+6 is a factor of x³+5x²-4x+m is: a)7 b)-3 c)6 d)12
Need help with this question urgent please
[tex]40(x )+6( 1.5x) = 612.5[/tex]
So C.
B:
49x=612.5
x=12.5$
Using the F’(x) Graph shown, find the Integral from 0 to 1 F’(x)dx if f(5) = -7.8, and f(0) = 3.
Answer:
[tex]-22.8[/tex]
Step-by-step explanation:
[tex]\int^{1}_{0} f'(x) \text{ } dx=f(1)-f(0)=f(1)-3 \\ \\ \\ B=\int^{5}_{1} f'(x) \text{ } dx=12 \implies f(5)-f(1)=12 \\ \\ -7.8-f(1)=12 \implies f(1)=-19.8 \\ \\ \therefore f(1)-3=-19.8-3=-22.8[/tex]
Pls help can u please answer 4 and 5
4A. The number of whole pie shaded are 2
4B . The number of partial pie shaded is 3
4C. The mixed number formed is 2 3/5
5A. The whole number part which is 2 is the quotient
5B. The remainder is 3
What are fractions in math?
In mathematics, a fraction is a number that represents a part of a whole. It consists of two parts: a numerator, which is the part of the fraction that represents the number of parts being considered, and a denominator, which is the number that represents the total number of parts in the whole.
A mixed number is a combination of a whole number and a fraction. It represents a quantity that is greater than the fraction but less than the next whole number.
For example, In the division problem, the dividend is 13 and and the divisor is 5. the division results to mixed number of value 2 3/5.
The mixed number 2 3/5 represents a quantity that is equal to
two whole and three fifths.
converting to improper fractions gives 13/5
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The figure below is a square. Find the length of side x in simplest radical form with a rational denominator.
Answer:
[tex]\frac{5\sqrt{2} }{2}[/tex]
Step-by-step explanation:
The square cut in half makes the right side a right triangle.
The equation for these types of questions is short side * square root of 2 = long side
So that means that x * [tex]\sqrt{2}[/tex] = 10
So then divide by square root of 2 on both sides to cancel it out
x = 10/[tex]\sqrt{2}[/tex]
Then to simplify it multiply the top and bottom by square root of 2, since you can't have an irrational number in the denominator
That makes it [tex]\frac{10\sqrt{2} }{2}[/tex]
Divide 10/2 to make [tex]\frac{5\sqrt{2} }{2}[/tex]
Which digit(s) makes 3,71_ divisible by 3?
A. 3 only
B. 7 only
C. 1 only
D. 1, 4, and 7
Answer: I think B. 7 only
Step-by-step explanation: I hope this helps and I hope everyone is having a good day/Friday&weekend^^
three students are chosen at random from a class of ten girls and twelve boys. what is the probability that at least one is a boy, given that at least one is a girl?
The probability that at least one is a boy, given that at least one is a girl is 0.823
To solve this problem, we can use conditional probability.
Let A be the event that at least one student is a boy, and let B be the event that at least one student is a girl.
We want to find the probability of A given B, denoted as P(A|B).
Let total student is,
Total girls (10) + Total boys (12) = 22
First calculating the probability of event B, which is probability that all three students are boys. This can be calculated as:
P(B) = 1 - (10/22)^3 = 1 - 0.214 = 0.906
The probability of event A intersecting B is then calculated, which is the probability that at least one student is a boy and at least one student is a girl. We can use the complement of this event, which is the likelihood that all three students are male or female:
P(A intersect B) = 1 - P(all girls) - P(all boys)
= 1 - (10/22)^3 - (12/22)^3
= 1 - 0.077 - 0.245
= 0.743
Finally, we use the formula for conditional probability to calculate P(A|B):
P(A|B) = P(A intersect B) / P(B)
= 0.743 / 0.906
= 0.822
Therefore, the probability that at least one student is a boy, given that at least one is a girl, is 0.862.
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question 6
pls help me as soon as possible
i'm being timed i only have a hour
Answer:
7.09
Step-by-step explanation:
s = r∅ = 7.09
s = (7 cm)(1.0123) = 7.086
58 deg x π/180 = 1.0123 radians
Answer:
CB ≈ 7.09 cm
Step-by-step explanation:
the length of arc CB is calculated as
AB = circumference of circle × fraction of circle
= 2πr × [tex]\frac{58}{360}[/tex] ( r is the radius )
= 2π × 7 × [tex]\frac{29}{180}[/tex]
= [tex]\frac{14\pi (29)}{180}[/tex]
≈ 7.09 cm ( to 2 decimal places )
F(x) equals -3(x-1) to the power of 2 + 2 and g(x) equals -3(x-1) to the power of 2 -5 . The vertex of g(x) is
The vertex of the function g(x) is (1,-5).
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given functions are f(x)=-3(x-1)²+2 and g(x)=-3(x-1)²-5.
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
(1,-5)
Focus:
(1,-61/12)
Axis of Symmetry:
x=1
Directrix:
y= -59/12
Therefore, the vertex of g(x) is (1,-5).
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Calculate the amount of US dollars you can buy for R12 500 at an exchange
rate of 1 US$ R8,76.
Answer: To calculate the amount of US dollars you can buy for R12,500 at an exchange rate of 1 US$ = R8.76, you can use the following formula:
US$ = R12,500 / R8.76
Plugging in the values, we get:
US$ = R12,500 / R8.76 = 1,421.51
So, with R12,500, you can buy 1,421.51 US dollars at an exchange rate of 1 US$ = R8.76.
Step-by-step explanation:
what is this answer.
Answer:
Step-by-step explanation:
is A
State how the triangles are congruent using SSS, SAS, ASA, AAS, or
HL. If they are not congruent, type NOT.
Here both triangles are congruent by SAS.
What is congruent by SAS?
Side-Angle-Side congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. See if the two triangles given, ABC and XYZ, are congruent according to the ASA rule by looking at the image provided below. According to the ASA congruence rule, two triangles are said to be congruent if two of their respective sides and angles are equal to those of two other triangles and their respective sides and angles, respectively.
In the given triangles it's given that,
in both triangles the two sides are similar along with an angle.
So Here both triangles are congruent by SAS.
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Can anyone help me out please I really need it…
Answer:
x= 39.549°
Step-by-step explanation:
please review answer.
Find the answer pls. this is imo lvl 2 questuin
Answer:
50) i. C 800cm^2
50)ii. B 120cm
Step-by-step explanation:
Use the picture in its given 2-d to mark the unknown measures. Such as, the gray rectangle on top has a bottom that is also 20 and the left side is 15.
The small horizontal jutting out on the left mid-way down is 5cm same as the 5cm just below.
When you mentally "unfold" the shape to its full rectangular shape and size, all the lengths are marked.
Use:
Area=length×width
and,
Perimeter
=L + w + L + w
There are lots of perimeter formulas, for perimeter, you just add up all the sides all the way around the shape.
see image.
Who is funnymike fav badkid?
Answer: badkid jay
Step-by-step explanation: because he gets him everything he ask for and shows favoritism towards him
Answer:
Step-by-step explanation:
PennyWise
NickleSmart
DimeSharp
QuarterIntelligent
according to the american diabetes association (links to an external site.), 34.2 million americans, or 10.5% of the population, had diabetes in the year 2018. what is the probability that a randomly chosen person has diabetes?
The probability that a randomly chosen person has diabetes is 34.2 million / (0.105 * total population).
The probability that a randomly chosen person has diabetes is equal to the number of people who have diabetes divided by the total population:
probability = number of people with diabetes / total population
Substituting the given values:
probability = 34.2 million / (10.5% of the total population)
To calculate this, we need to convert the percentage to a decimal by dividing by 100:
probability = 34.2 million / (0.105 * total population)
Assuming the total population remains constant between 2018 and now, and that the percentage of people with diabetes has also remained constant, we can use this probability to estimate the current number of people with diabetes in the United States.
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2. Use the Rational Root Theorem to list all possible rational roots for the equation.
3x³ +9x-6=0
2
O±1, 12, 13, 16, ±, ± -
6,±3⁄3,±0
T
تانی
O±1, ±3, ±6
2
O±1, ± 2, ±3, ±6, ± -, ± -, ±=
3 3
NI
3
1/3
WIN
112
±1, +2, +3, +9,-,-
, -, ±一,土
13
MIN
3
2
The possible rational roots of the equation 3x³ + 9x - 6 = 0 are given as follows:
± 1/3, ± 2/3, ± 1, ± 2, ± 3, ± 6.
How to obtain the potential zeros of the function?To obtain the possible rational zeros of the function, we use the Rational Zero Theroem.
The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.
The parameters for this function are given as follows:
Leading coefficient of 3.Constant term of 6.The factors are given as follows:
Factors of 3: {1, 3}.Factors of 6: {1, 2, 3, 6}.Hence the possible roots are given as follows:
± 1/3, ± 2/3, ± 1, ± 2, ± 3, ± 6.
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An 18- ounce jar of peanut butter retails for $1.30. What is the unit price in dollars? Round to the nearest cent
Answer:
7 cents
Step-by-step explanation:
0.072222 rounded to the nearest cent is 0.07
at a football match , there are 29800 people correct to the nearest 100.
at the end of the football match, the people leave at a rate of 400 people per minute , correct to the nearest 50 people
calculate the lower bound for the number of minutes it takes for all the people to leave
The lower bound for the number of minutes it takes for all the people to leave is 67 minutes.
What is lower bound?
Lower bound refers to the smallest possible value in a range or interval of values. In the context of measurements or estimates, it represents the minimum value that a quantity or measurement is expected to be, based on the precision or accuracy of the measuring instrument or method.
To calculate the lower bound for the number of minutes it takes for all the people to leave, we need to use the following formula:
Lower bound = (total number of people - 0.5) / departure rate (in people per minute)
Using the given information, we have:
Total number of people = 29800 (correct to the nearest 100)
Departure rate = 400 (correct to the nearest 50)
To ensure we have a conservative estimate, we will round down the total number of people to 29750 and round up the departure rate to 450.
Therefore, the lower bound for the number of minutes it takes for all the people to leave is:
Lower bound = (29750 - 0.5) / 450
= 66.1 (rounded up to the nearest minute)
So the lower bound for the number of minutes it takes for all the people to leave is 67 minutes.
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statistics is a rigorous branch of mathematics that deals with group of answer choices data mining visualization understanding data linear regression all of the above
Statistics is a rigorous field that provides a set of tools and techniques for understanding and making decisions based on data. Correct option is C.
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. Statistics is used in a wide range of fields, from business and finance to social sciences, engineering, and healthcare.
One of the key goals of statistics is to summarize and make sense of complex data, and this is often done through the use of visualization techniques such as histograms, scatterplots, and box plots.
Statistics also involves techniques such as data mining, which involves the use of algorithms and computational methods to analyze large data sets, and linear regression, which is a technique for modeling the relationship between two variables.
In addition to its practical applications, statistics is also important for understanding the world around us. It can be used to test hypotheses, evaluate the reliability of data, and make predictions about future events. Overall, statistics plays a vital role in modern society by helping us make sense of the vast amounts of data that we encounter every day.
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Complete question is:
Statistics is a rigorous branch of mathematics that deals with
group of answer choices
A. data mining
B. visualization
C. understanding data
D. linear regression
E. all of the above
what number solves the equation 1/3x = -20
Answer:
x=-60
Step-by-step explanation:
Answer:
-60
Step-by-step explanation:
1/3 x = -20 Multiply both sides by 3
3(1/3) x = 3(-20)
x = -60
Check
1/3(-60) = -20
-20 = -20
