Answer:
(9x10^4)+(7x10) = 90,000 + 70 = 90,070
solve for x, using a tangent and secant line
Check the picture below.
[tex]x^2=(8+2)(2)\implies x^2=20\implies x=\sqrt{20}\implies x\approx 4.5[/tex]
The value of x is 4.5 rounded to the nearest tenth.
What is Tangent and Secant of a Circle?Tangent of a circle is defined as the line which passes through exactly one point on the circle.
Secant of a circle is the line which passes through two points on the circle.
Secant-Tangent Rule states that if a tangent and a secant are drawn to a circle from the same point outside the circle, then the square of the length of the tangent segment is equal to the product of the lengths of secant and the segment of secant outside the circle.
Using the theorem, we can say here that,
(8 + 2) 2 = x²
x² = 10 × 2
x² = 20
x = √20
x = 4.472 ≈ 4.5
Hence the value of x is 4.5.
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candace is designing a card game with a standard deck of cards. each player gets points based on collecting groups of cards. which statements are true about certain groups of cards? select all of the true statements.
The true statements are:
a) P(3) = 4/52 or 1/13
b) P(black number cards) = 18/26 or 9/13
c) P(red ace) = 2/52 or 1/26
d) P(face card) = 12/52 or 3/13
Define the term Probability?Probability deals with the study of random events and their likelihood of occurrence. It is computed by dividing the proportion of positive results by the total number of possibilities that could occur.
As we know that the standard deck card has 52 cards, in which 26 red cards (13 are diamonds, 13 are hearts) 26 black cards (13 are clubs, 13 are spades). Where 12 cards are face cards, 36 cards are number cards.
a) P(3) = 4/52 or 1/13: This is true. There are four 3s in a standard deck of 52 cards, so the probability is 4/52 or 1/13.
b) P(black number cards) = 18/26 or 9/13: This is a true. There are 26 black cards, out of those there are 9+9=18 black number cards (2 through 10), so the probability of drawing a black number card is 18/26 or 9/13.
c) P(red ace) = 2/52 or 1/26: This is true. There are two red aces in a standard deck of 52 cards, so the probability of drawing a red ace is 2/52 or 1/26.
d) P(face card) = 12/52 or 3/13: This is a true. There are twelve face cards in a standard deck of 52 cards, so the probability of drawing a face card is 12/52 or 3/13.
e) P(even number card) < P(odd number card): This is a false. There are 5×4=20 even number cards (2, 4, 6, 8, and 10 of each suit) and 4×4=16 odd number cards (3, 5, 7, 9 of each suit) in a standard deck of 52 cards. Therefore, the probability of drawing an even number card, (20/52 or 5/13) is greater than the probability of drawing an odd number card, (16/52 or 4/13).
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Complete question-
What is the slope of the line on the graph?
Options:
A) 1/2
B) 2
C) -1/2
D) -2
Answer:
Slope is -2. So, choice D is the best option.
Step-by-step explanation:
Start with one point then use the formula to get to the next point:
Rise
------
Run
Let's start at (0,5) then count down 2 points, which is the "Rise"(seems like an interesting name to pick but it works).
Next, you go to the right once. Which counts as the "Run".
Remember: The slope is like a ratio, and the "y" will always go as the numerator and the "x" as the denominator. Which is why "Rise" is on top and the "Run" is on the bottom.
So your answer would be 2/1. And that simplifies to 2. But since you went down and not up, it would be negative 2.
Hope this helps and if you have any other questions or need clarification please ask!
The radius of the circular base of a cone measures 2.6 inches, and its slant height measures 1.5 inches.
What is the approximate lateral area of the cone?
Use π≈3.14.
Enter your answer rounded to the nearest tenth in the box.
Answer:
11.6 sq. inches
Step-by-step explanation:
The lateral area of a cone can be found using the formula:
L = πrℓ
where r is the radius of the circular base and ℓ is the slant height.
Substituting in the given values, we have:
L = 3.14 x 2.6 x 1.5
L ≈ 11.6
Rounding to the nearest tenth, the approximate lateral area of the cone is 11.6 square inches.
PLEASE HELP ASAP! How would you classify
Side AD is opposite which angle of triangle ADC?
O.
O.
O.
O.
Optiοn A : Side AD is οppοsite tο the angle ACD in the given triangle ADC.
What is the οppοsite side οf an angle in a triangle?Every triangle has 3 sides and thus 3 angles. Each side οf a triangle has 2 angles οf it fοrmed at the 2 endings οf the side and οne angle is the οne present οppοsite tο the side.
Thus, fοr each side, 2 angles are tοuched and 1 angle at the οppοsite is called the οppοsite angle tο that side.
Here, the triangle is ADC.
The 3 angles οf the triangle are : ADC, ACD, and CAD
Fοr side AD,
The twο angles A ( CAD ) and D( ADC ) are cοnnected with the side AD and are adjacent tο it.
The third angle C ( CAD ) is nοn-adjacent tο side AD and is οppοsite tο it. Hence, Optiοn D is cοrrect.
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find the missing value to the nearest hundredth cos__=7/18
67.11
37.67
22.89
21.25
The missing value is approximately 64.12 degrees, which is closest to option D: 21.25 using inverse cos.
The inverse cosine (or arccosine) of both sides of the equation must be taken in order to locate the missing value in the equation cos = 7/18 to the closest tenth. We will then be able to convert the value of to degrees and round it to the closest hundredth using the value of the radian that is produced.
cos θ = 7/18
= arccos(7, 18, 7)
A 1.1181 radian angle
We can use the conversion factor /180 to convert radians to degrees.
θ = 1.1181 × 180/π
64.12 degrees.
As a result, the figure that is lacking is roughly 64.12 degrees, which is closest to choice D: 21.25.
Due to the periodic nature of the cosine function, there are often two solutions when determining the inverse cosine of a value. But, since the problem states that we should round to the closest hundredth, which suggests a single answer, we can disregard the second option in this instance. By reinserting the value we discovered into the original equation and making sure it equals 7/18, we can further confirm that the result is accurate.
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A video goes viral on social media, the number of views per day can be modeled with the equation y = -0.75x² +9.75x where is the number of days after the video is posted and y is the number of views per day in thousands. According to the model, after how many days do people stop watching the video?
Answer:
Step-by-step explanation:
To find when people stop watching the video, we need to find the maximum point of the quadratic function y = -0.75x² + 9.75x.
The x-coordinate of the maximum point of a quadratic function can be found using the formula x = -b/2a, where a and b are the coefficients of the quadratic function.
Using the formula with a = -0.75 and b = 9.75, we get:
x = -9.75 / 2(-0.75)
x = -9.75 / -1.5
x = 6.5
Therefore, the maximum number of views per day will occur on the 6.5th day after the video was posted.
To determine when people stop watching the video, we need to check the values of y after this point.
When x > 6.5, the quadratic function becomes negative, which means that the number of views per day will start to decrease. Therefore, people stop watching the video after 6.5 days (or sometime around the 7th day).
Cullumber Beauty Corporation manufactures cosmetic products that are sold through a network of sales agents. The agents are paid a commission of 21% of sales. The income statement for the year ending December 31,2022 , is as follows. Under the current policy of using a network of sales agents, calculate the Cullumber Beauty Corporation's break-even point in sales dollars for the year 2022. Break-even point
Cullumber Beauty Corporation's break-even point in sales dollars for the year 2022 is $1,200,000.
What is the break-even point?
The break-even point is defined as the point at which a company's overall costs are equal to its total revenue. The company neither makes a profit nor incurs a loss at this point. The break-even point in dollar amount is calculated by dividing the fixed costs by the contribution margin ratio.The given information is:Net sales revenue = $3,500,000Commission expense = 21% of sales = 0.21 * $3,500,000 = $735,000Net sales revenue − Variable costs = Contribution marginContribution margin − Fixed costs = Operating incomeBreak-even point is the level of sales revenue required to cover all of a company's costs. At this point, the operating income is zero. The fixed expenses are divided by the contribution margin ratio to find the break-even point in dollars.
Fixed expenses = [tex]$900,000[/tex]Net sales revenue − Variable costs = Contribution marginContribution margin − Fixed expenses = Operating income0 = Net sales revenue − Variable costs − Fixed expenses0 = [tex]$3,500,000 − (0.75 × $3,500,000) − $900,0000.25 × $3,500,000 = $900,000$875,000 = $900,000[/tex] − Commission expense[tex]$3,500,000 − $875,000 = $2,625,000[/tex]
Break-even point = $900,000 ÷ (0.75 × $3,500,000)Break-even point = $900,000 ÷ $2,625,000Break-even point = 0.34 ≈ 34%Break-even point in sales dollars = 34% × $3,500,000Break-even point in sales dollars = $1,190,000 ≈ $1,200,000Therefore, Cullumber Beauty Corporation's break-even point in sales dollars for the year 2022 is $1,200,000.
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Which of the following is NOT a reason that Georgia is considered the transportation hub of the South? Responses A It manufactures more automobiles than any other state B It has the busiest airport in the world C It is home to two of the busiest seaports in the U.S. D It is the meeting place of several interstate highways
Answer:
A
Just Because They Produce more Automobiles, does not mean they sell them all, which it also does not tell us the quantity.
PLEASE HELP, GIVING BRAINLIST!
This prism has a right triangle for a base. What is the volume of the prism?
Answer:
volume v = base area * height
= 1/2*9*4 * 8
in 1995, 58% of the cranberries processed by the cooperative were water-harvested. what percentage to they expect to be water-harvested in 1996? group of answer choices about 70% about 87% about 20% about 12% about 99%
In 1996, the cooperative expects approximately 40% of cranberries processed to be water-harvested.
This is a decrease of 18% from 1995. This decrease is likely due to the fact that water-harvested cranberries cost more to process than traditional dry-harvested cranberries.
Additionally, the cooperative may not be able to find enough cranberry farmers willing to switch to the water-harvesting method, which is a labor-intensive process.
Thus, the cooperative is likely to experience a decrease in the percentage of water-harvested cranberries processed in 1996.
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Can you help me with this?
The equation of the line that contains the point (-6, 5) and is parallel to x + 2y = 14 in slope-intercept form is y = (-1/2)x + 2.
What are parallel lines?Due to their similar slopes, parallel lines move in the x direction with the same rate of change. If we know the slope of a line, we can use that slope to determine the slope of any line that is parallel to it. The point-slope form of a line can be used to get the equation of a line that is parallel to a given line and passes through a specified point.
The given equation of the line is:
x + 2y = 14
Rewriting the equation in standard form we have:
y = (-1/2)x + 7
where, -1/2 is the slope of the line.
The slope of two parallel lines are equal. Thus the slope of new line is m = -1/2.
Now, using the point slope form:
y - y1 = m(x - x1)
Substitute the values:
y - 5 = (-1/2)(x - (-6))
y - 5 = (-1/2)x - 3
y = (-1/2)x + 2
Hence, the equation of the line that contains the point (-6, 5) and is parallel to x + 2y = 14 in slope-intercept form is y = (-1/2)x + 2.
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A builder is creating a scale drawing of a plot of land as shown. The original plot of land is 335 meters wide. The drawing uses a 1 scale factor of 500. 7. Find the area of the original plot of land in square meters and the area of the scale drawing in square centimeters. (Example 5)
Answer:
Step-by-step explanation:
36 +55
Decide if the function is an exponential function. If it is, state the initial value and the base.y=5^x
Yes, the function y = 5^x is an exponential function.The initial value of an exponential function is the value of y when x = 0. In this case, when x = 0, y = 5^0 = 1. Therefore, the initial value of the function is 1.The base of an exponential function is the constant factor by which y changes when x increases by 1. In this case, when x increases by 1, y is multiplied by 5. Therefore, the base of the function is 5.
Which two values of x are roots of the polynomial below?
x2-11x+17
A. X = 2.5
B. X =
C. X =
D. X =
11--109
4
F. X=
11+√-109
4
11+ √53
2
E. x = 3
11-53
2
need awnser asap if possible
so, x = (11 + [tex]\sqrt{-109}[/tex]) / 4 is not a real root because the square root of a negative number is not a real number. x = 9.140 and x = 1.855 are not roots of the polynomial.
What do you mean by square root?The square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical notation, the square root of a number "x" is represented by the symbol "√x". For example, the square root of 25 is 5, because 5 multiplied by 5 equals 25.
Given by the question.
To find the roots of the polynomial [tex]x^{2}[/tex] - 11x + 17, we can use the quadratic formula:
x = ([tex]\sqrt{b^{2}-4ac }[/tex]) / 2a
Here, a = 1, b = -11, and c = 17.
Substituting these values into the quadratic formula, we get:
x = (11 ± [tex]\sqrt{11^{2}-4(1)(17) }[/tex]) / 2(1)
Simplifying this expression, we get:
x = (11 ± [tex]\sqrt{53}[/tex]) / 2
Therefore, the two roots of the polynomial are:
x = (11 + [tex]\sqrt{53}[/tex]) / 2 and x = (11 - [tex]\sqrt{53}[/tex]) / 2
x= (11+7.280)/2 and x = (11-7.280)/2
x= 18.280/2 and x = 3.71/2
x = 9.140 and x = 1.855
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A high school track team is traveling from Albany to Buffalo for a track meet. The coaches will rent vans that can seat 12 passengers for the trip. If n is the number of track team members and coaches traveling to the track meet, which function represents the number of vans needed for the trip?
Answer: The function that represents the number of vans needed for the trip is:
v(n) = ceil((n+c) / 12)
where ceil(x) is the smallest integer greater than or equal to x, n is the number of track team members, c is the number of coaches, and 12 is the number of passengers that can be seated in each van.
We need to add the number of coaches to the number of team members since they will all be traveling together. The result of the division should be rounded up to ensure that there are enough vans for everyone, even if there are only a few extra passengers.
Note: This assumes that all passengers will be traveling together in the same vans. If the coaches or some of the team members will be driving separately, the function may need to be adjusted accordingly.
Step-by-step explanation:
Select the correct answer. Solve the following equation for x. x2 - 9x + 18 = 0 A. x = -3; x = 6 B. x = 3; x = 6 C. x = -3; x = -6 D. x = 3; x = -6
Answer:B
Step-by-step explanation: x=3;x=6
(a) Use slope-intercept form to write an equation of the line that passes through the given point and has the given slope.
(b) Write the equation using function notation where .
The equation of the line is y = 3x/2 - 8 and can be rewritten using function notation as f(x) = 3x/2 - 8
Slope intercept form:
The slope-intercept form of a line is given by
y = mx + c
Where 'm' is slope and c in y-intercept
Here we have
The coordinate of points (0, -8) and slope (m) = 3/2
As we know the formula for slope intercept form is y = mx + c
Where 'm' is the slope
=> y = (3/2)x + c
=> -8 = 3/2(0) + c
=> c = - 8
Hence, Equation of the line is y = 3/2(x) + (-8)
=> y = 3x/2 - 8
The equation can be rewritten using function notation as follows
=> f(x) = 3x/2 - 8
Therefore,
The equation of the line is y = 3x/2 - 8 and can be rewritten using function notation as f(x) = 3x/2 - 8
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Aileen has 40 colored marbles inside a bag. There are blue, red, and white marbles. All the marbles are the same size. Aileen randomly selects 10 marbles, one at a time, out of the bag and records the color of each marble. Each marble is replaced before the next marble is selected. The table shows her results. Aileen's Bag of Marbles Color of Frequency Marble Blue Red White 3 1 6 Click on the bar graph to show how many blue marbles, red marbles, and white marbles are MOST LIKELY inside Aileen's bag of marbles. Number of Marbles + 28 26 24 22 20 18 16 14 12 10 ∞ CO 8 6 4 2 0
The most likely number of marbles in Aileen's bag is given as follows:
Blue marbles: 12.Red marbles: 4.White marbles: 24.How to obtain the most likely number of marbles?The most likely number of marbles is obtained applying the proportions in the context of the problem.
Out of 10 marbles, from the sample, the results are given as follows:
3 blue marbles.1 red marbles.6 white marbles.Aileen has 40 colored marbles inside a bag, which is four times the size of the sample, hence the most likely number of marbles in Aileen's bag is obtained as follows:
Blue marbles: 12, as 4 x 3 = 12.Red marbles: 4, as 4 x 1 = 4.White marbles: 24, as 4 x 6 = 24.More can be learned about proportions at https://brainly.com/question/24372153
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Help please…… i need it
The sides of 15mm, 28mm and 11mm are the sides of a triangle.
What is the triangle inequality theorem?To determine if three given lengths can form a triangle, we can apply the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
If we add the two shorter sides together, we get [tex]15 + 11 = 26[/tex] . This sum is greater than the longest side, which is [tex]28[/tex] . Similarly, if we add the two smaller sides to the longest side, we get [tex]11 + 28 = 39[/tex] and [tex]15 + 28 = 43[/tex] , which are both greater than the remaining side.
Therefore, the three given lengths satisfy the Triangle Inequality Theorem and can form a triangle.
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After Simon fully charges his electric car, he can drive for up to 350 miles before it runs out of battery. Simon's car was fully charged this morning, and he has driven 140 miles since then.
Let x represent how many more miles Simon can drive without running out of battery. Which inequality describes the problem?
the inequality that describes the problem is x ≤ 210, meaning that Simon can drive at most 210 more miles before his electric car runs out of battery.
If Simon has driven 140 miles since fully charging his car, then the amount of charge remaining in the battery can power the car for x miles. We can set up the following inequality to represent this situation:
x ≤ 350 - 140
The amount of charge left in the battery is shown on the right-hand side of the inequality and is equal to the maximum amount of charge the battery can store (350 miles) minus the amount of charge that has already been utilised (140 miles). The left-hand side of the inequality displays the number of miles Simon can travel until his battery runs out, which is either less than or equal to the battery's remaining charge.
Simplifying the inequality, we get:
x ≤ 210
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i suppose you are going to be visited by a family that has two children. i what is the probability that the family has two boy children?
The probability of a family having two boy children is 0.25, or 25%. This probability is determined by a simple calculation. If there are two children in the family, the probability of each child being a boy is 0.5 (50%), and the probability of both children being boys is 0.5 x 0.5, or 0.25 (25%).
When it comes to probability, the likelihood of an event is determined by the number of possible outcomes. In the case of this question, there are four possible outcomes: two boys, two girls, one boy and one girl, and one girl and one boy. Since each outcome is equally likely, each has a probability of 0.25 (25%).
It is important to note that the probability of a family having two boy children is the same as the probability of a family having two girls. In each case, the probability is 0.25 (25%). This is because the gender of a child is independent of the gender of their sibling.
In conclusion, the probability of a family having two boy children is 0.25 (25%). This probability is determined by the number of possible outcomes, each of which is equally likely. It is also important to note that this probability is the same for a family having two girls.
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Suppose a medical researcher constructs a mathematical model describing the size of a lesion. The model that describes the diameter of a lesion in cm as function of time(days) is given by D(t)= (t-10)^2 ; 0
The graph of the equation is a parabola with its vertex at (10, 0), and it can also be used to calculate the diameter of the lesion for any given time.
Suppose a medical researcher constructs a mathematical model describing the size of a lesion. The model that describes the diameter of a lesion in cm as function of time(days) is given by [tex]D(t)= (t-10)^2[/tex]; 0. We will solve this problem by finding the answer step by step. FunctionThe function of the lesion's size over time is provided by the equation D(t)= (t-10)2, where t is the time in days and D(t) is the diameter of the lesion at the time t.
The origin of this equation is given by D(t) = f(t), where the variable t represents the independent variable, and the variable D(t) represents the dependent variable. To calculate the diameter of the lesion over time, substitute values of t into the equation D(t) = (t-10)2. When t = 0, for instance, D(0) = (0-10)2 = 100. This means that the lesion's diameter at time zero is 100cm.
The model's interpretation The mathematical model that describes the diameter of a lesion as a function of time was created by a medical researcher. The equation D(t) = (t-10)2 represents this model. The researcher's model indicates that the diameter of the lesion is equal to the square of the difference between the time and ten. The difference between the time and ten is squared, which means that the model represents a parabolic curve.
The question is, "Suppose a medical researcher constructs a mathematical model describing the size of a lesion. The model that describes the diameter of a lesion in cm as a function of time (days) is given by D(t)= (t-10)^2; answer in 200 words."
The given equation is a quadratic function, which is expressed as[tex]D(t)= (t-10)^2.[/tex]This means that the diameter (D) of the lesion is dependent upon the time (t) that has passed since the lesion's onset. Specifically, the diameter of the lesion will increase as the time since onset increases.
The graph of this equation will be a parabola with its vertex at (10, 0). This is because, when t=10, the diameter of the lesion (D) will be zero. As t increases, the graph will move up and to the right, forming a parabola with a positive slope.
In addition to describing the diameter of the lesion as a function of time, the equation also allows us to calculate the diameter of the lesion for any given time. To do this, we can plug in the desired time value for t, and calculate the resulting diameter.
For example, if the medical researcher wants to determine the diameter of the lesion when t=15 days, they can plug in 15 for t, and calculate that the diameter of the lesion at that time is 25 cm. This can be found by plugging in 15 for t and calculating [tex]D(15)=(15-10)^2[/tex]=25 cm.
In conclusion, the equation[tex]D(t)= (t-10)^2.[/tex]is a quadratic function that describes the diameter of a lesion in cm as a function of time (days). The graph of the equation is a parabola with its vertex at (10, 0), and it can also be used to calculate the diameter of the lesion for any given time.
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Helppppppppppppppppppppppp
Answer:
no
Step-by-step explanation:
You want to know if a triangle with sides 54, 66, and 87 is a right triangle.
Pythagorean theoremThe side lengths of a right triangle will satisfy the relation given by the Pythagorean theorem. Here, that would require ...
54² +66² = 87²
2916 +4356 = 7569
7272 = 7569 . . . . . . . . . false — not a right triangle
Triangle WXY is not a right triangle, so XY is not tangent to circle W.
__
Additional comments
The parity of the integer side lengths of a right triangle is always even. That is, there can be two odd side lengths, but never just one odd side length.
Side lengths 54 and 66 are even, while length 87 is odd. There is only one odd side length, so this triangle cannot be a right triangle.
A tangent always meets a radius at right angles, so XY is a tangent if and only if angle X is a right angle.
Los números que hace verdadera a una ecuación se les denomina
Please help 20 points I’ve been struggling :(
5x + 4y = -16
Complete the steps to convert the equation in standard form to Slope intercept form
Answer: I'm pretty bad at math, but I made it more simple for you :)
Step-by-step explanation:
The answer is y = 4 + 5x/4
I hope it helped a bit sorryy
the probability that a student at certain high school likes art is 35%. the probability that a student who likes art also likes science is 22%. find the probability that a student chosen at random likes science given that he or she likes art. round to the nearest tenth of a percent.
The probability that a student chosen at random likes science given that he or she likes art is 41.4%
In our case, we want to find P(Science|Art), which is the probability of a student liking science given that he or she likes art. Using Bayes' theorem, we have:
P(Science|Art) = P(Art|Science) x P(Science) / P(Art)
We know that P(Art) = 0.35 and P(Science|Art) = 0.22. To find P(Art|Science), we can use the formula:
P(Art|Science) = P(Science|Art) x P(Art) / P(Science)
We don't know P(Science) yet, but we can calculate it using the fact that:
P(Science) = P(Science|Art) x P(Art) + P(Science|Not Art) x P(Not Art)
where P(Not Art) is the probability that a student does not like art, which is 1 - P(Art) = 0.65. We are given that P(Science|Not Art) = 0.15, which is the probability that a student who does not like art likes science. Substituting these values, we get:
P(Science) = 0.22 x 0.35 + 0.15 x 0.65 = 0.1855
Now we can substitute all the values into Bayes' theorem:
P(Science|Art) = 0.22 x 0.35 / 0.1855 = 0.414 or 41.4%
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EASY MATH HELP
PIC DOWN BELOW
the medians intersect at the coordinate (__,__)
Write any fractions simplified
The medians intersect at the coordinate (4, 5/3).
How to find the intersection point of medians?
The medians of a triangle intersect at a point known as the centroid. The coordinate of centroid is given by:
Centroid of the triangle = ((x₁+x₂+x₃)/3 , (y₁+y₂+y₃)/3)
where (x,y) are the coordinates of the vertices
The coordinate of the vertices of the triangle are (0,0), (5,0), and (7,5). Using the formula:
Centroid of the triangle = ((x₁+x₂+x₃)/3 , (y₁+y₂+y₃)/3)
Centroid of the triangle = ((0+5+7)/3 , (0+0+5)/3)
Centroid of the triangle = (12/3, 5/3)
Centroid of the triangle = (4, 5/3)
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Connor is working two summer jobs, making $8 per hour walking dogs and making $12 per hour landscaping. In a given week, he can work a maximum of 15 total hours and must earn no less than $160. If Connor worked 12 hours walking dogs, determine the maximum number of whole hours landscaping that he can work and still meet his requirements. If there are no possible solutions, submit an empty answer.
The maximum number of hours Connor can work in landscaping is 5 hours.
What is the inequalities?In mathematics, inequalities are statements that compare two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), and "!=" (not equal to).
Let's denote the number of hours Connor works in landscaping as x. Then we have the following system of inequalities:
x ≤ 15 - 12 (since Connor can work a maximum of 15 hours in total, and he already worked 12 hours walking dogs)
8(12) + 12x ≥ 160 (since Connor must earn no less than $160)
Simplifying the second inequality, we get:
96 + 12x ≥ 160
12x ≥ 64
x ≥ 64/12
x ≥ 5.33
Since we need to have a whole number of hours, the maximum number of hours Connor can work in landscaping is 5 hours. We can check that this satisfies both inequalities:
5 ≤ 15 - 12
5.33 (rounded up to the nearest whole number) × 12 + 8(12) = 68. 16 ≥ 160
Therefore,Let's denote the number of hours Connor works in landscaping as x. Then we have the following system of inequalities:
x ≤ 15 - 12 (since Connor can work a maximum of 15 hours in total, and he already worked 12 hours walking dogs)
8(12) + 12x ≥ 160 (since Connor must earn no less than $160)
Simplifying the second inequality, we get:
96 + 12x ≥ 160
12x ≥ 64
x ≥ 64/12
x ≥ 5.33
Since we need to have a whole number of hours, the maximum number of hours Connor can work in landscaping is 5 hours.
We can check that this satisfies both inequalities:
5 ≤ 15 - 12
5.33 (rounded up to the nearest whole number) × 12 + 8(12) = 68. 16 ≥ 160
Therefore, the answer is 5.
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