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Lesson 14
Reflecting points page 134
How do I upload a picture to get help with this?
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Answer:
Im pretty sure when your writing a question theres a place where you can upload form computer and add a picture.
Step-by-step explanation:
Hope this helps with future questions!
In ΔWXY, w = 880 cm, ∠X=33° and ∠Y=38°. Find the length of y, to the nearest centimeter.
Answers
Answer:
[tex]y\approx573cm[/tex]
Step-by-step explanation:
First, take a look to the picture that I attached, however please note the triangle is not drawn to scale, the figure is just to provide visual aid. As you can see the value of [tex]\angle W =109^{\circ}[/tex] this is because of the sum of the interior angles in a triangle is always equal to 180°. So:
[tex]\angle W + \angle X + \angle Y =180\\\\\angle W = 180- \angle X -\angle Y\\\\\angle W =180-38-33\\\\\angle W=109[/tex]
Now, we can use the law of sines, which states:
[tex]\frac{w}{sin(W)} =\frac{x}{sin(X)} =\frac{y}{sin(Y)}[/tex]
Hence:
[tex]\frac{w}{sin(W)} =\frac{y}{sin(Y)}\\\\\frac{880}{sin(109)} =\frac{y}{sin(38)}\\\\Solving\hspace{3}for\hspace{3}y\\\\y=\frac{880*sin(38)}{sin(109)} \\\\y=572.9999518\approx 573 cm[/tex]
Answer:
573 cm
Step-by-step explanation:
g In American roulette, the wheel has the 38 numbers, 00, 0, 1, 2, ..., 34, 35, and 36, marked on equally spaced slots. If a player bets $1 on a number and wins, then the player keeps the dollar and receives an additional $35. Otherwise, the dollar is lost. Calculate the expected value for the player to play one time. Round to the nearest cent.
Answers
The expected value for the player to play one time in American roulette is -$0.05. This suggests that, on average, the player can expect to lose $0.05 every time they play the game.
Explanation:The expected value for the player to play one time in American roulette can be calculated by multiplying the probability of winning by the amount the player wins and subtracting the probability of losing. In this case, the probability of winning is 1/38, since there is one winning number out of the 38 possibilities. The amount the player wins is $35. The probability of losing is 37/38, since there are 37 losing numbers out of the 38 possibilities. Using these values, the expected value can be calculated as follows:
Expected value = (1/38 * $35) - (37/38 * $1) = -$0.0526
Rounded to the nearest cent, the expected value is -$0.05. This means that, on average, the player can expect to lose $0.05 every time they play the game.
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The expected value for a player betting on a single number in American roulette is approximately -$0.03, indicating an average loss of 3 cents per play.
The question asks for the calculation of the expected value for a player betting on a single number in American roulette.
To find the expected value, we consider the winnings and the probability of winning.
In American roulette, there are 38 equally spaced slots with the numbers 00, 0, and 1 through 36, which means the probability of winning for a player when betting on a specific number is 1/38, and the probability of losing is 37/38.
The payoff for a win is $35 plus the return of the original $1 bet, for a total of $36. If the bet is lost, the player loses their $1 bet.
Using these payouts and their associated probabilities, we can calculate the expected value (EV) as follows:
→ EV = (Probability of Winning) × (Winning Amount) + (Probability of Losing) × (Loss Amount)
→ EV = (1/38) × $36 - (37/38) × $1
To calculate the exact value:
→ EV = (1/38) × 36 - (37/38) × 1
→ EV ≈ 0.9474 - 0.9737
→ EV ≈ -$0.0263
When rounding to the nearest cent, the expected value is approximately -$0.03. This means, on average, the player will lose about 3 cents per play.
(3 + 5) * 2Y = (5 * 8) - (2 * 4). What does Y equal?
Answers
Answer:
pretty sure y should equal 15
The solution of the linear equation (3 + 5) × 2Y = (5 × 8) - (2 × 4) will be 2.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given below.
(3 + 5) × 2Y = (5 × 8) - (2 × 4)
Simplify the equation, then the value of the variable y will be
8 × 2Y = 40 - 8
16Y = 32
Y = 32 / 16
Y = 2
The solution of the linear equation (3 + 5) × 2Y = (5 × 8) - (2 × 4) will be 2.
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A container contains balls numbered from 1 to 55. A ball is drawn randomly. What is the probability that the first ball is number 9 and the second ball is number 41?
Answers
Answer:
1/55 * 1/55 = 1/3025
Step-by-step explanation:
The probability of 2 consecutive events is:
P(A and B) = P(A) * P(B) - where P(something) is the probability of it
so:
P(picking 9) = 1 possibility out of 55 total, so 1/55
P(picking 41) = 1 possibility out of 55 total, so 1/55
Finally:
P(9 and 41) = 1/55 * 1/55 = 1/3025
The probability of drawing a specific number (e.g. 9) from 55 balls is 1/55. After one ball is drawn, the probability of drawing another specific number (e.g. 41) is 1/54. The total probability of these events happening in sequence is (1/55) * (1/54).
Explanation:This problem falls under the category of probability. Probability is a mathematical way of expressing the likelihood of an event happening, using numbers from 0 (impossible) to 1 (certain).
In this case, the total number of balls is 55. Since the ball is drawn randomly, the probability of drawing any specific number (such as 9) on the first draw is 1/55. Similarly, after the first ball is drawn, there are now 54 balls left in the container, but we're again interested in drawing a specific number (41), so the probability for the second draw is also 1/54.
Our task is to find the joint probability of both these events happening - drawing the 9 first and then the 41. To do that, we multiply the probabilities of the individual events, which means the final answer will be (1/55) * (1/54).
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Jennifer starts with a population of 100 amoebas that doubles in size every minute for a number of minutes, m. She writes the expression 100(2m) to find the number of amoeba after m minutes. Nathan starts with a population of 10 amoebas that increases 40% in size every minute for a number of minutes, m. He writes the expression (1+0.4)m to find the number of amoeba after m minutes. Use the drop-down menus to explain what each part of Jennifer's and Nathan's expressions mean.
Answers
Answer:
100(2m)
(1+0.4)
Nathan=0.4 is the percent added =the 40 percent added to the 10 amoebas
Jennifer=the first equation is how many total amoebas Jennifer has in total
Hope this helps!Answer:
Hope this helps!
Step-by-step explanation:
The yearly tuition at lewis college is set at $13,494 for the year maria will graduate, which is a 568% increase from 1995 when her mother graduated from there. How much was tuition when her mother graduated? Round your answer to the nearest dollar
Answers
Answer:
$2375.70
Step-by-step explanation:
5.68x=13,494
x=2375.70
First to answers gets marked brainliest
Drag the tiles to the correct boxes to complete the pairs. Match each event to the probability of its occurrence. the probability of getting a six when a six-sided die is rolled the probability of randomly picking a vanilla-scented candle from a set of 3 vanilla-scented candles, 8 rose-scented candles, and 10 lavender-scented candles the probability of selecting a girl named Maria to be line leader from a class of 32 girls in which 4 students are named Maria the probability of getting an even number when a six-sided die is rolled
Answers
1/2 : the probability of getting an even number when a six-sided die is rolled.
1/6 : the probability of getting a six when a six-sided die is rolled.
1/7 : the probability of randomly picking a vanilla-scented candle from a set of 3 vanilla-scented candles, 8 rose-scented candles, and 10 lavender-scented candles.
1/8 : the probability of selecting a girl named Maria to be line leader from a class of 32 girls in which 4 students are named Maria.
which type of graph would you use to show the number of water bottles sold at four different stores and water bottles come in packs of 20
Answers
Answer:
pictograph
Step-by-step explanation:
i got it right :) so yeah trust me
Math
If A+B+C=pi then prove that cos3A.cos3B+cos3B.cos3C+cos3C.cos3A=1
Answers
Step-by-step explanation:
Given:
A+B+C= π
<=> 3A+3B+3C = 3π
<=> cos(3A+3B) = - cos3C
<=> cos3A.cos3B-sin3A.sin3B = - cos3C
<=> cos3A.cos3B = sin3A.sin3B - cos3C (1)
similarly apply for the other two angles, we have:
cos3B.cos3C = sin3B.sin3C - cos3A (2) cos3C.cos3A = sin3C.sin3A - cos3B (3)Grouping three equations, (1) + (2) + (3), we have:
<=> cos3A.cos3B+cos3B.cos3C+cos3C.cos3A = sin3A.sin3B + sin3B.sin3C + sin3C.sin3A - ( cos3A + cos3B + cos3C )
= 1
Hope it can find you well.
Using the sum of angles in a triangle and cosine identities, we proved that cos(3A)cos(3B) + cos(3B)cos(3C) + cos(3C)cos(3A) equals 1.
Given that A + B + C = π, we will use trigonometric identities and properties to prove the required equation.
Recall that A + B + C = π implies that A, B, and C are angles of a triangle.We can use the trigonometric identity for the cosine of a sum of angles. Specifically, for any angle θ, cos(π - θ) = -cos(θ).Consider the expression for the sum of angles, we have cos(3(A+B+C)) = cos(3π). Since cos(3π) = -1, this simplifies to cos(3A + 3B + 3C) = -1.Using the triple angle formula for cosine, we know that cos(3x) = 4cos³(x) - 3cos(x). Applying this to each term, we have:cos(3A) = 4cos³(A) - 3cos(A)cos(3B) = 4cos³(B) - 3cos(B)cos(3C) = 4cos³(C) - 3cos(C)By symmetry and considering the angles sum up to π, we simplify the expression cos(3A)cos(3B) + cos(3B)cos(3C) + cos(3C)cos(3A) using cos(π - θ) = -cos(θ).Finally, given the periodic and symmetrical nature of the cosine function in this specific triangular setup, it can be shown algebraically or verified computationally (or by specific known identities for triangle angles) that the overall summation leads to the result of 1.Hence, we have proven that cos(3A)cos(3B) + cos(3B)cos(3C) + cos(3C)cos(3A) = 1 for angles A, B, and C summing up to \pi.
A sample of 81 tobacco smokers who recently completed a new smoking-cessation program were asked to rate the effectiveness of the program on a scale of 1 to 10, with 10 corresponding to "completely effective" and 1 corresponding to "completely ineffective". The average rating was 5.6 and the standard deviation was 4.6. Construct a 95% confidence interval for the mean score. 5.2 < μ < 6.0 0 < μ < 5.6 4.6 < μ < 6.6 5.1 < μ < 6.1
Answers
Answer:
95% confidence interval for the true mean score is [4.6 , 6.6].
Step-by-step explanation:
We are given that a sample of 81 tobacco smokers who recently completed a new smoking-cessation program were asked to rate the effectiveness of the program on a scale of 1 to 10.
The average rating was 5.6 and the standard deviation was 4.6.
Firstly, the pivotal quantity for 95% confidence interval for the true mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average rating = 5.6
s = sample standard deviation = 4.6
n = sample of tobacco smokers = 81
[tex]\mu[/tex] = population mean score
Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.
So, 95% confidence interval for the population mean score, [tex]\mu[/tex] is ;
P(-1.993 < [tex]t_8_0[/tex] < 1.993) = 0.95 {As the critical value of t at 80 degree of
freedom are -1.993 & 1.993 with P = 2.5%}
P(-1.993 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.993) = 0.95
P( [tex]-1.993 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.993 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-1.993 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.993 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.993 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.993 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]5.6-1.993 \times {\frac{4.6}{\sqrt{81} } }[/tex] , [tex]5.6+1.993 \times {\frac{4.6}{\sqrt{81} } }[/tex] ]
= [4.6 , 6.6]
Therefore, 95% confidence interval for the true mean score is [4.6 , 6.6].
Suppose that $77,000 is invested at 5 1/2% interest, compounded quarterly.
a) Find the function for the amount to which the investment grows after t years.
b) Find the amount of money in the account at t=0,3, 6, and 10 years.
Answers
Answer:
a) [tex]A(t) = 77000(1.01375)^{4t}[/tex]
b)
The amount of money in the account at t = 0 years is $77,000.
The amount of money in the account at t = 3 years is $90,711.
The amount of money in the account at t = 6 years is $106,864.
The amount of money in the account at t = 10 years is $132,961.
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.
Suppose that $77,000 is invested at 5 1/2% interest, compounded quarterly.
This means that, respectively, [tex]P = 77000, r = 0.055, n = 4[/tex]
a) Find the function for the amount to which the investment grows after t years.
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 77000(1 + \frac{0.055}{4})^{4t}[/tex]
[tex]A(t) = 77000(1.01375)^{4t}[/tex]
b) Find the amount of money in the account at t=0,3, 6, and 10 years.
[tex]A(0) = 77000(1.01375)^{4*0} = 77000[/tex]
The amount of money in the account at t = 0 years is $77,000.
[tex]A(3) = 77000(1.01375)^{4*3} = 90711[/tex]
The amount of money in the account at t = 3 years is $90,711.
[tex]A(6) = 77000(1.01375)^{4*6} = 106864[/tex]
The amount of money in the account at t = 6 years is $106,864.
[tex]A(10) = 77000(1.01375)^{4*10} = 132961[/tex]
The amount of money in the account at t = 10 years is $132,961.
The function for the investment after t years is [tex]A = 77000(1 + 0.055/4)^{(4t).[/tex] To find the amount in the account at different times, trigger this function with the desired time intervals.
Explanation:The subject of the questions is about compound interest which belongs to the finance section of Mathematics.
To solve problems related to compound interest, a simple formula can be used: [tex]A = P(1 + r/n)^{(nt)[/tex] where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is time the money is invested for in years.
a) First, identify the variables from the question:[tex]P = $77000, r = 5.5/100 = 0.055[/tex](convert the percentage to a decimal), n = 4 (since interest is compounded quarterly).
We can now plug these values into our formula to determine the function: [tex]A = 77000(1 + 0.055/4)^{(4t).[/tex]
b) To find the amount of money in the account at different time intervals, plug the specified values for t into the function. For t = 0, 3, 6, 10 years, simply replace t in A with each of these time intervals and calculate the resulting A.
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Graph the Plane Curve defined by:
x=3cos(t)−t+5, y=sin(t), for t in [0,3π]
Answers
Step-by-step explanation:
Solve the two-step equation and identify the steps.
1.4x + 6.1 = -7.9
1. The first step is to
2. The second step is to
sides.
v on both sides.
von both
The solution is x =
ASAP
Answers
Answer:
1. The first step is to subtract 6.1 on both sides.
2. The second step is to divide by 1.4 on both sides.
3. The solution is x = -10
Step-by-step explanation:
I just finished the Egdenuity Assignment
The steps will be
The first step is to subtract 6.1 on both sides.The second step is to divide by 1.4 on both sides.The solution is x = -10How to solve linear equation of one variable?Step-1: we have to balance each side by simplifing the equation
Step-2: add/substract constant term on both side of the equation to separate variable and constant term on both side
Step-3: divide the coefficient of the variable on both side to make the coefficient of the variable 1.
So according to asked question,
1.4x+6.1=-7.9
Step 1: subtract 6.1 on both sides.
1.4x+6.1-6.1=-7.9-6.1
⇒1.4x=-14
Step 2: divide by 1.4 on both of the sides.
1.4x/1.4=-14/1.4
⇒x=-10
Therefore,
The steps will be
The first step is to subtract 6.1 on both of the sides.The second step is to divide by 1.4 on both of the sides.The solution is x = -10.Learn more about linear equation of one variable
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Exhibit 5-11 The random variable x is the number of occurrences of an event over an interval of 10 minutes. It can be assumed the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in 10 minutes is 5.3. Refer to Exhibit 5-11. The expected value of the random variable x is
Answers
Answer:
The expected value of the random variable x is [tex]E(x) = 5.3[/tex]
Step-by-step explanation:
From the question we are told that
The number of occurance is x
The interval for the x occurance of the event is [tex]t = 10 minutes[/tex]
Generally the expected value is the same as the mean so the expected value the random variable x is
[tex]E(x) = 5.3[/tex]
Find the circumference of a circle with a diameter of 100 feet. Use 3.14 for it (pi).
Answers
Answer: 314
Step-by-step explanation:
3.14 * 100= 314
Answer:
314 feet
Step-by-step explanation:
Circumference of a circle is 2pi*r
Radius = 100/2
Circumference = 2*3.14*50 = 314 feet
what is the value of x?
Answers
Answer:
see below
Step-by-step explanation:
x and 80 are adjacent, supplementary angles
Supplementary angles add to 180
x+80 =180 degrees
Subtract 80 from each side
x+80-80=180-80
x=100
So much dance class is 3 miles away from her home her music class is 12 miles away from her home right now equation that shows the number of times farther so with music class is from her home then the dance class from her home
Answers
The music class is 4 times farther from her home than the dance class.
Explanation:To find the number of times farther the music class is from her home than the dance class, we first need to determine the distance of each class from her home. The dance class is 3 miles away, and the music class is 12 miles away. To get the ratio of these distances, we divide the distance to the music class by the distance to the dance class. Therefore, the equation that represents the number of times farther the music class is from her home is:
12 miles / 3 miles = 4
So, the music class is 4 times farther from her home than the dance class.
A toy car can go 5 mph. How long would it take to go 7 miles?
Answers
Answer:
by the way what grade are you in? If you are more than 7th grade can you help me? https://brainly.com/question/16233847
35 mph
Step-by-step explanation:
7 times 5
Which is a perfect square? 6 Superscript 1 6 squared 6 cubed 6 Superscript 5
Answers
Answer:
it is b
Step-by-step explanation:6 square
Answer:
b
Step-by-step explanation:
Which number line models the expression 1/8-(-3/4)
Answers
The number line to model the expression 1/8 - (-3/4) would start at 1/8, and move 6/8 steps to the right to reach 7/8 because subtracting a negative is the same as adding a positive.
Explanation:To solve the mathematical expression 1/8 - (-3/4), we need to understand that subtracting a negative number is equivalent to adding a positive number. Hence, we rewrite the expression as 1/8 + 3/4.
Before you can add these two fractions, they must have a common denominator. The least common denominator (LCD) for 8 and 4 is 8, so we rewrite 3/4 as 6/8 to match the denominator of 1/8.
Now, you can add 1/8 + 6/8 to get 7/8.
A number line that models this expression would start at 1/8 and go forward 6/8 (equivalent to 3/4) steps to end at 7/8.
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To model the expression 1/8 - (-3/4) on a number line, you would first convert the expression to 1/8 + 3/4 by changing the minus negative to a plus. Then, find a common denominator and add the fractions to get 7/8. This result is represented on a number line by starting at 1/8 and moving right to reach 7/8.
Explanation:To model the expression 1/8 - (-3/4) on a number line, we need to understand that subtracting a negative is the same as adding its positive counterpart. Therefore, the expression simplifies to 1/8 + 3/4. To add these fractions together, they must have a common denominator. The least common denominator for 8 and 4 is 8. So, we convert 3/4 to 6/8, since 3 multiplied by 2 gives us 6, and 4 multiplied by 2 gives us 8. Adding 1/8 to 6/8 gives us 7/8.
On a number line, we would start at the point representing 1/8 and then move to the right by 6/8 (which represents 3/4) to arrive at 7/8. This portrays the answer to our initial expression, 1/8 - (-3/4) = 7/8.
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What is the combined weight of all the kittens? Weight of kittens: 1/4 pound: 3 kittens. 3/8 pound: 2 kittens. 1/2 pound: 4 kittens. 5/8 pound: 4 kittens
Answers
Answer:
6 pounds
Step-by-step explanation:
1/4 times 3 = 3/4
3/8 times 2: 6/8 = 3/4
1/2 times 4: 4/2 = 2
5/8 times 4: 20/8 = 2 1/2
3/4 + 3/4 = 6/4 = 1 1/2
2 + 2 1/2 + 1 1/2 = 6 pounds
Use this context for the next 4 questions (Questions 1 - 4): Weight of a rock: In a geology course, students are learning to use a balance scale to accurately weigh rocks. One student plans to weigh a rock 20 times and then calculate the average of the 20 measurements to estimate her rock's true weight. A second student plans to weigh a rock 5 times and calculate the average of the 5 measurements to estimate his rock's true weight. Which student is more likely to come the closest to the true weight of the rock he or she is weighing? (i) The student who weighed the rock 20 times. (ii) The student who weighed the rock 5 times. (iii) Both averages would be equally close to the true weight.
Answers
Answer:
The right answer is:
(i) The student who weighed the rock 20 times.
Step-by-step explanation:
Both students are taking a sample from the population. In this case, the population is all the possible weight that can be measured by the scale they are using.
Independently of the sample size, the sampling distribution mean will be centered in the population mean, so they are estimating the true weight of the rock unbiased.
But the spread of the sampling distribution, measaured by the standard deviation, depends on the sample size.
The bigger the sample, the narrower the sampling distribution is expected o be. So it is more likely to be closer to the true mean with a bigger sample.
The right answer is:
(i) The student who weighed the rock 20 times.
given U=-7i - 5j and V= -6i - 4j find U + V
Answers
Answer:
u+v= -13i-9j
Step-by-step explanation:
u=-7i - 5j and v= -6i - 4j
u+v=-7i-5j+(-6i-4j)=-7i-5j-6i-4j
u+v=-13i-9j
Answer:
U + V= i-9j
Step-by-step explanation:
hello :
U=-7i - 5j and V= -6i - 4j so : U + V=(7i-6i)+(-5j-4j)
U + V= i-9j
Jim’s father is older than 40 but younger than 50.If you can divide his age by 2,4,5,8,or 10 ,there will be a remainder of 1. How old is Jim’s father?
Answers
Answer:
Step-by-step explanation:
all you have to do is divide each number by 4, 41, 42, 43, 44, 45, 46, 47, 48, 49 ,and 50 until you get a remainder of 1. what I mean is do 2 divided by all the number from 40 50 and do the same with 4,5,8 and 10 until you find one of them that has a remainder of 1. (is a lot of work sorry could't tell you the anwer)
An ice cream machine produced 52 ice creams per minute. After reconditioning, its speed increased to 65 ice creams per minute. By what percent did the speed of the machine increase?
Answers
Answer:25 %
Step-by-step explanation:
Given
Earlier machine was producing 52 ice cream per minute and
Now it is Producing 65 ice creams per minute
So percentage increase of the machine [tex]=\frac{\text{final-Initial}}{\text{Initial}}\times 100[/tex]
[tex]=\frac{65-52}{52}\times 100[/tex]
[tex]=\frac{13}{52}\times 100[/tex]
[tex]=\frac{1}{4}\times 100=25\ \%[/tex]
So there is increase of 25 % in speed
A high-profile consulting company chooses its new entry-level employees from a pool of recent college graduates using a five-step interview process. Unfortunately, there are usually more candidates who complete the interview process than the number of new positions that are available. As a result, cumulative GPA is used as a tie-breaker. GPAs for the successful interviewees are Normally distributed, with a mean of 3.3 and a standard deviation of 0.4. What percent of candidates have a GPA above 3.9?
Answers
Answer:
Only 0.0668 of the candidates, or 6.68%, have a GPA above 3.9.
Step-by-step explanation:
The GPA, according to the question, is a random variable normally distributed. A normal distribution is determined by its parameters. These parameters are the population mean, [tex] \\ \mu[/tex], and the population standard deviation, [tex] \\ \sigma[/tex]. The normal distribution for GPA has a [tex] \\ \mu = 3.3[/tex], and [tex] \\ \sigma = 0.4[/tex].
To find probabilities related to normally distributed data, we can use the standard normal distribution. To use it, we first need to find the corresponding standardized score or z-score for the value we want to obtain the probability. This value, in this case, is x = 3.9. The related z-score or standardized value is given by the formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
A z-score tells us the distance from the mean in standard deviations units. A negative value indicates that the value is below the mean. A positive value is, conversely, above the mean.
And we already have all the necessary data to use [1].
Thus
[tex] \\ z = \frac{3.9 - 3.3}{0.4}[/tex]
[tex] \\ z = \frac{0.6}{0.4}[/tex]
[tex] \\ z = 1.5[/tex]
This value for z tells us that the "equivalent" raw score, x = 3.9, is above the mean, and it is at 1.5 standard deviations units from the population mean.
We can find the probabilities for standardized values in the cumulative standard normal table, available on the Internet or in Statistic books (we can also use statistical packages or even spreadsheets).
To use the cumulative standard normal table, we have the z-score as an entry. With this value, we find the z column on this table, and, since it is z = 1.5, we only need to select the first column (which has two decimal places, that is, .00). Then, the cumulative probability for P(z<1.50) = 0.9332.
However, we are asked for the percent of candidates that have a GPA above 3.9 (z-score = 1.50). This probability is the complement of P(z<1.50) or 1 - P(z<1.50). Mathematically
[tex] \\ P(z<3.9) + P(z>3.9) = 1[/tex]
[tex] \\ P(z<1.50) + P(z>1.50) = 1[/tex] (standardized)
[tex] \\ P(z>1.50) = 1 - P(z<1.50)[/tex]
[tex] \\ P(z>1.50) = 1 - 0.9332[/tex]
[tex] \\ P(z>1.50) = 0.0668[/tex]
That is, only 0.0668 of the candidates, or 6.68%, have a GPA above 3.9.
We can see this probability in the graph below.
En una granja hay 500 animales. Si hay el triple de vacas que de ovejas, ¿ cuantas animales hay de cada especie
Answers
Answer:
Hay 375 vacas y 125 ovejas
Step-by-step explanation:
Para resolver este problema simplemente tenemos que plantear una igualdad entre vacas y ovejas
b = oveja
v = vaca
v = 3b
b + v = 500
reemplazamos la b por (3v) en la segunda ecuacion
b + v = 500
b + 3b = 500
4b = 500
b = 500/4
b = 125
reemplazamos este valor en la primer ecuacion
v = 3b
v = 3(125)
v = 375
Hay 375 vacas y 125 ovejas
What is the value of x in the equation 2(6х+4)- 6+ 2х = 3(4х+3) + 12
оооо
Answers
Answer:X= 19/2
Step-by-step explanation:
Chase and his brother like to play basketball. About a month ago they decided to keep track of how many games they have each won. As of today, Chase has won 18 out of 30 games against his brother
How many games would Chase have to win in a row in order to have a 75% winning record? Chase would have to win _________ games in a row to have a 75% winning record. How many games would Chase have to win in a row in order to have a 90% winning record? Chase would have to win _________ games in a row to have a 90% winning record. Is Chase able to reach a 100% winning record? Chase (is or isn’t) able to reach a 100% winning record because ________________.
Suppose that after reaching a winning record of 90 in part 2, Chase has a losing streak. How many games in a row would Chase have to lose in order to drop down to a winning record below 55% again?
Chase would have to lose _______ games in order to drop down to a winning
Answers
Answer:
Step-by-step explanation:
As of today, Chase has won 18 out of 30 games against his brother. The percentage of games that he has won as of today is
18/30 × 100 = 60%
In order to get 75% wins, let the number of games would be x. Then
(18 + x)/(30 + x) × 100 = 75
100(18 + x) = 75(30 + x)
1800 + 100x = 2250 + 75x
100x - 75x = 2250 - 1800
25x = 450
x = 450/25 = 18
chase has to win 18 games in a row.
In order to get 90% wins, let the number of games would be y. Then
(18 + x)/(30 + x) × 100 = 90
100(18 + x) = 90(30 + x)
1800 + 100x = 2700 + 75x
100x - 75x = 2700 - 1800
25x = 900
x = 900/25 = 36
chase has to win 36 games in a row in order to have a 90% winning record.
(18 + x)/(30 + x) × 100 = 100
100(1800 + x) = 100(30 + x)
1800 + 100x = 3000 + 100x
100x - 100x = 3000 - 1800
Therefore, it is impossible to for chase to reach a 100% winning record because he has already had some losses.
2) for a wining record of 90, the total number of games played is
30 + 36 = 66 games and the total number of wins was 18 + 36 = 54
In order to get 55% losses, let the number of games would be z. Then
(54 + z)/(66 + z) × 100 = 55
100(54 + z) = 55(66 + z)
5400 + 100z = 3630 + 55z
100z - 55z = 3630 - 5400
45z = - 1770
z = - 1770/45 = - 40
chase has to lose 40 games in a row in order to drop down to a winning record below 55% again.
Chase would need to win 6 more games for a 75% win record, 108 more games for a 90% win record. He could never achieve a 100% win record due to past losses. If he reached a 90% win record and then lost, he would need to lose 20 games to drop below a 55% record.
Explanation:To calculate how many games Chase needs to win to achieve a 75% winning record, a solution is needed for the equation (18 + x) / (30 + x) = 0.75, where x represents the additional games won. The solution is x = 6. Therefore, Chase must win an additional 6 games without losing to reach a 75% win record.
For a 90% winning record, we solve the equation (18 + x) / (30 + x) = 0.9. The solution is x = 108. Therefore, Chase must win an additional 108 games without losing to reach a 90% winning record.
Chase is unable to reach a 100% winning record because he has already lost some games and it isn't possible to change those past results.
In the event that Chase reaches a 90% winning record and then begins to lose, we need to find out the number of games he would need to lose to drop to a win rate below 55%. We can solve this by calculating the equation (126) / (138 + y) = 0.55, where y is the lost games. Solving for y, we get y = 20, so Chase would have to lose 20 games in a row.
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