The answer of the given question based on probability to compute the variance of X. Round to 2 decimal places the answer is ,Rounding to 2 decimal places, the variance of X is 1.31.
What is Variance?In statistics, variance is measure of how spread out or dispersed set of data is. It is calculated as average of the squared differences from the mean of data. The variance is expressed in units that are square of the units of data, and small variance indicates that data points tend to be close to mean, while a large variance indicates that data points are spread out over wider range of values.
To calculate variance of set of data, first find mean (average) of the data points. Then, for each data point, subtract mean from that data point and square the difference. Next, sum up all squared differences and divide by the total number of data points minus one.
The probability of drawing a red card on any one draw is 1/4, and the probability of drawing a green card is 3/4. Since the draws are made with replacement, the draws are independent, and we can use the binomial distribution to model the number of red cards drawn in 7 draws.
The probability mass function of binomial distribution with parameters n and p are below:
P(X = k) =(n choose k) *p^k*(1-p)^(n-k)
In this case, we have n = 7 and p = 1/4, so the probability mass function of X is:
P(X = k) = (7 choose k) * (1/4)^k * (3/4)^(7-k)
We can use this formula to calculate the probabilities of X taking each possible value from 0 to 7:
P(X = 0) = (7 choose 0) * (1/4)^⁰ * (3/4)^⁷ ≈ 0.1335
P(X = 1) = (7 choose 1) * (1/4)¹ * (3/4)⁶ ≈ 0.3348
P(X = 2) = (7 choose 2) * (1/4)² * (3/4)⁵ ≈ 0.3119
P(X = 3) = (7 choose 3) * (1/4)³ * (3/4)⁴ ≈ 0.1451
P(X = 4) = (7 choose 4) * (1/4)⁴ * (3/4)³ ≈ 0.0415
P(X = 5) = (7 choose 5) * (1/4)⁵ * (3/4)² ≈ 0.0064
P(X = 6) = (7 choose 6) * (1/4)⁶ * (3/4)¹ ≈ 0.0005
P(X = 7) = (7 choose 7) * (1/4)⁷ * (3/4)⁰ ≈ 0.0000
To calculate the variance of X, we need to calculate the expected value of X and the expected value of X squared:
E(X) = Σ k P(X = k) = 0P(X=0) + 1P(X=1) + 2P(X=2) + 3P(X=3) + 4P(X=4) + 5P(X=5) + 6P(X=6) + 7P(X=7) ≈ 1.75
E(X^2) = Σ k²P(X = k) = 0²P(X=0) + 1²P(X=1) + 2²P(X=2) + 3²P(X=3) + 4²P(X=4) + 5²P(X=5) + 6²P(X=6) + 7²P(X=7) ≈ 4.56
Then, we can use the formula for the variance:
Var(X) = E(X²) - [E(X)]² ≈ 4.56 - (1.75)² ≈ 1.03
Rounding to 2 decimal places, the variance of X is 1.31.
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Assuming each draw is a random selection of one card and X = number of red cards drawn. So, the variance of X rounded to two decimal places is 1.31.
What is Variance?In statistics, variance is measure of how spread out or dispersed set of data is. It is calculated as average of the squared differences from the mean of data. The variance is expressed in units that are square of the units of data, and small variance indicates that data points tend to be close to mean, while a large variance indicates that data points are spread out over wider range of values.
The probability of drawing a red card on any one draw is 1/4, and the probability of drawing a green card is 3/4. Since the draws are made with replacement, the draws are independent, and we can use the binomial distribution to model the number of red cards drawn in 7 draws.
The probability mass function of binomial distribution with parameters n and p are below:
P(X = k) =(n choose k) [tex]p^{k}*(1-p)^{n-k}[/tex]
In this case,
we have n = 7 and p = 1/4, so the probability mass function of X is:
P(X = k) = (7 choose k) * [tex](1/4)^{k}*(3/4)^{7-k}[/tex]
We can use this formula to calculate the probabilities of X taking each possible value from 0 to 7:
P(X = 0) = (7 choose 0) × (1/4)⁰ × (3/4)⁷
≈ 0.1335
P(X = 1) = (7 choose 1) × (1/4)¹ × (3/4)⁶
≈ 0.3348
P(X = 2) = (7 choose 2) × (1/4)² × (3/4)⁵
≈ 0.3119
P(X = 3) = (7 choose 3) × (1/4)³ × (3/4)⁴
≈ 0.1451
P(X = 4) = (7 choose 4) × (1/4)⁴ × (3/4)³
≈ 0.0415
P(X = 5) = (7 choose 5) × (1/4)⁵ × (3/4)²
≈ 0.0064
P(X = 6) = (7 choose 6) × (1/4)⁶ × (3/4)¹
≈ 0.0005
P(X = 7) = (7 choose 7) × (1/4)⁷ × (3/4)⁰
≈ 0.0000
To calculate the variance of X, we need to calculate the expected value of X and the expected value of X squared:
E(X) = Σ k P(X = k)
= 0P(X=0) + 1P(X=1) + 2P(X=2) + 3P(X=3) + 4P(X=4) + 5P(X=5) + 6P(X=6) + 7P(X=7)
≈ 1.75
E(X²) = Σ k²P(X = k)
= 0²P(X=0) + 1²P(X=1) + 2²P(X=2) + 3²P(X=3) + 4²P(X=4) + 5²P(X=5) + 6²P(X=6) + 7²P(X=7)
≈ 4.56
Then, we can use the formula for the variance:
Var(X) = E(X²) - [E(X)]²
≈ 4.56 - (1.75)²
≈ 1.03
Rounding to 2 decimal places, the variance of X is 1.31.
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The complete question is as follows:
A small deck of four cards consists of one red card and three green cards. Draw 7 times with replacement. Assume each draw is a random selection of one card. Let X = the number of red cards drawn, compute the variance of X. Round to 2 decimal places.
Var(X) =
Question 2
State the probability that a randomly selected, normally
distributed value lies between
a) o below the mean and o above the mean (round to
the nearest hundredths)
b) 20 below the mean and 20 above the mean (round
to the nearest hundredths)
The probability of a randomly selected, normally distributed value lying between 20 below the mean and 20 above the mean is 0.9545 (rounded to the nearest hundredth).
What is the fundamental concept of probability?A number between zero and one represents the probability that an occurrence will take place. An event is a predefined set of random variable outcomes. Only one mutually exclusive event can occur at a time. Exhaustive events encompass or include all possible outcomes.
We can calculate the probabilities of a randomly chosen value falling between different z-scores using the provided standard normal distribution table.
a) The probability of a value being 0 below or above the mean is the same as the probability of a value being -1 to 1 standard deviations from the mean. According to the standard normal distribution table, the probability of a z-score between -1 and 1 is 0.6827. As a result, the probability of a randomly chosen, normally distributed value falling between 0 below and 0 above the mean is 0.6827. (rounded to the nearest hundredth).
b) The probability of a value falling between 20 and 20 standard deviations from the mean is the same as the probability of a value falling between -20/10 and 20/10 standard deviations from the mean (since the standard deviation is 10). According to the standard normal distribution table, the probability of a z-score between -2 and 2 is 0.9545. As a result, the probability of a randomly chosen, normally distributed value falling between 20 below and 20 above the mean is 0.9545. (rounded to the nearest hundredth).
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My little cousin needs help with this can anyone help please.
I’m busy with my tests and I don’t have the time to explain.
Answer:
I don't knowI am sorry I will let someone else answer
Step-by-step explanation:
I will mark you brainiest!
What is the length of BC?
A) 1.7
B) 2.1
C) 3.8
D) 4.6
Answer:
B. 2.1
Step-by-step explanation:
If you draw a line from C to intersect AB perpendicularly at point D so we have 2 right triangles ACD and BCD.
For △ACD, AC is hypotenuse so sinA = CD/AC
=> CD = 5 x sin(20) = 5 x 0.342 = 1.71
then we have AB = AD + BD
Pythagorean theorem: c^2 = a^2 + b^2
for △ACD, 5^2 = 1.71^2 + AD^2
AD^2 = 5^2 - 1.71^2 = 22.0759
AD = 4.70
BD = AB - AD = 6 - 4.70 = 1.30
for △BCD, BC is hypotenuse
BC^2 = BD^2 + CD^2 = 1.30^2 + 1.71^2 = 4.61
BC = √4.61 = 2.1
under the normal distribution, if the mean of the distribution of raw scores is equal to 100, then its equivalent z-score is equal to
The equivalent z-score for a raw score of 115 under a normal distribution with a mean of 100 and a standard deviation of 15 is 1.
Under the normal distribution, if the mean of the distribution of raw scores is equal to 100 and the standard deviation is known, we can use the z-score formula to calculate the equivalent z-score for any given raw score.
The z-score formula is given by:
z = (x - μ) / σ
where x is the raw score, μ is the mean of the distribution, σ is the standard deviation of the distribution, and z is the corresponding z-score.
Since the mean of the distribution is 100, we have μ = 100. To calculate the z-score, we need to know the standard deviation of the distribution or have information about the distance of the raw score from the mean in terms of standard deviations.
If we assume that the standard deviation is 15, which is a common value used in educational testing, and the raw score is 115, then the corresponding z-score would be:
z = (115 - 100) / 15 = 1
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Baker School's hockey games are 60 minutes long. Nico played for 30 minutes of the last game. What percent of the game time did Nico play?
Pick the model that represents the problem.
Dude he played for 1/2 of the game half of 60 is 30.
50%.
I'm I missing something?
do you mind helping me with this?
Answer:
125
Step-by-step explanation:
We Take
625 / 5 = 125
So, the answer is 125
Jamie is going to run for
1
2
2
1
start fraction, 1, divided by, 2, end fraction of an hour at a constant rate, and they want to plan what that rate will be.
1. Write an equation that represents the distance Jamie will run in kilometers (
�
dd) at a rate of
�
rr kilometers per hour.
The distance Jamie will run is equal to half of the rate in kilometers per hour, the equation is d = r (1/2)
What is speed and velocity?Speed is a scalar number that represents the rate of movement of an item. It is described as the distance covered in a certain amount of time, regardless of direction. In contrast, velocity is a vector quantity that accounts for both speed and direction. It is characterised as the pace at which an item shifts in a certain direction. In physics, the idea of velocity is crucial since it aids in explaining how an object's location varies over time and is used to compute other crucial variables like acceleration and momentum.
The distance is calculated using the given formula:
Distance = rate (time)
Given that, the time is 1/2 hour thus:
d = r (1/2)
Thus, the distance Jamie will run is equal to half of the rate in kilometers per hour, and the equation is d = r (1/2).
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12. Reason A data set is represented by the box plot shown. Between which two values would the middle 50% of the data be found? Explain.
The middle 50% data of the boxplot will be calculated between the value of 7 to 14.
Explain about the box plot?The variation in information is shown using a boxplot, which is a standardized method based on a five-number summary ("minimum," first quartile ("Q1"), median ("Q3"), and "maximum"). It can reveal information about your outliers' values. Boxplots can also show you exactly securely your data is grouped, whether or not your data is skewed, and whether or not your data is symmetrical.The data set ranges are:
4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
Divide the given data in 4 quartiles Qs;
Q1 = 4 - 6
Q2 = 7 - 10
Q3 = 11 - 14
Q4 = 15 - 17
Thus, 50% data will be lying in Q2 and Q3.
Range - 7 - 14
Thus, the middle 50% data of the box plot will be calculated between the value of 7 to 14.
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Ciara throws four fair six-sided dice. The faces of each dice are labelled with the numbers 1, 2, 3, 4, 5, 6 Work out the probability that at least one of the dice lands on an even number.
The likelihood that one or more of the dice will land on an even number is 1296.
How does probability work?The likelihood of an event is quantified by its probability, which is a number. It is stated as a number between 0 and 1, or in percentage form, as a range between 0% and 100%. The likelihood of an event increasing with probability of occurrence.
According to the given information:Four 6-sided dice are rolled what is the probability that at least two dice show least 2 die the same.
For 2 of the same: 5×5×642) =900
For 3 of the same: 5×643) =120
For 4 of the same: 644) =6
Combined: 900+120+6=1026
Total possibilities: 64=1296
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The probability that at least one of the dice lands on an even number is 15/16 or approximately 0.938.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
We can solve this problem by finding the probability that all four dice land on odd numbers and then subtracting this probability from 1 to get the probability that at least one of the dice lands on an even number.
The probability that one dice lands on an odd number is 3/6 = 1/2, and the probability that all four dice land on odd numbers is:
(1/2) × (1/2) × (1/2) × (1/2) = 1/16
Therefore, the probability that at least one of the dice lands on an even number is:
1 - 1/16 = 15/16
So the probability that at least one of the dice lands on an even number is 15/16 or approximately 0.938.
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which of the following numeric measures would be most likely to produce invalid statistical analysis?
The most likely to produce invalid statistical analysis of numeric measures is Pain rating as: none = 0; slight = 1; much = 2, as it is an ordinal scale of measurement, which does not have equal intervals between the categories. So, the correct answer is B).
It means that the differences between the categories are not necessarily equivalent, and therefore, any statistical analysis based on this scale may not accurately reflect the true relationship between variables.
The other options (blood pressure in mmHg, oxygen saturation in percentage, neonatal birth weight in kilograms) are measured on interval or ratio scales, which have equal intervals between values and can be used for meaningful statistical analysis. so, the correct option is B).
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____The given question is incomplete, the complete question is given below:
Which of the following numeric measures would be most likely to produce invalid statistical analysis?A)Analysis of patients' blood pressures in mmHgB)Pain rating as: none = 0; slight = 1; much = 2C)Assessment of oxygen saturation in percentageD)Analysis of neonatal birthweight in kilogr
a rectangular prism with a volume of 20 in^3 is dialited with a scale facotr of 2. what is the volume of the new figure?
The volume of the new rectangular prism is 160 in³ after it has been dilated with a scale factor of 2.
In this case, the scale factor is 2, which means that the dimensions of the original figure will be multiplied by 2 to get the dimensions of the new figure.
Volume of rectangular prism = length x width x height
20 = l x w x h
Next, we need to find the new dimensions of the rectangular prism after it has been dilated by a scale factor of 2. We can do this by multiplying each dimension of the original rectangular prism by 2.
New length = 2 x l
New width = 2 x w
New height = 2 x h
Now we can find the volume of the new rectangular prism by using the same formula as before, but with the new dimensions:
Volume of new rectangular prism = (2 x l) x (2 x w) x (2 x h)
Simplifying this expression, we get:
Volume of new rectangular prism = 8 x (l x w x h)
We know that l x w x h is equal to the volume of the original rectangular prism, which is 20 in³. So we can substitute this value into the expression to get:
Volume of new rectangular prism = 8 x 20 in³
Volume of new rectangular prism = 160 in³
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A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute. (a) Find the rates of change of the radius when r-70 centimeters and r 95 centimeters. r 70 X cm/min r = 95 X cm/min
When the radius of spherical balloon r = 70 cm, the rate of change of the radius is approximately 0.002 cm/min and when the radius is 95 cm then the rate of change of the radius is approximately 0.001 cm/min.
The volume of a sphere is given by V = (4/3)πr^3, where r is the radius. Differentiating both sides with respect to time t, we get:
dV/dt = 4πr^2(dr/dt)
where dV/dt is the rate of change of the volume and dr/dt is the rate of change of the radius.
We are given that dV/dt = 900 cm^3/min.
When r = 70 cm, we can solve for dr/dt as follows:
900 = 4π(70)^2(dr/dt)
dr/dt = 900 / (4π(70)^2) ≈ 0.002 cm/min
Therefore, when r = 70 cm, the rate of change of the radius is approximately 0.002 cm/min.
Similarly, when r = 95 cm, we can solve for dr/dt as follows:
900 = 4π(95)^2(dr/dt)
dr/dt = 900 / (4π(95)^2) ≈ 0.001 cm/min
Therefore, when r = 95 cm, the rate of change of the radius is approximately 0.001 cm/min.
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If the area of one side of this cube is 25 cm^2
2
, what is the area of the whole surface of the cube?
cm^2
2
Answer:
150 cm2
Step-by-step explanation:
Given side of cube's area = 25. Since Side's a square,
Edge^2 = 5^2 = 5 cm
Total surface area: 6*a² = 6*5*5 = 150 cm2
For the functions f(x)=−7x+3 and g(x)=3x2−4x−1, find (f⋅g)(x) and (f⋅g)(1).
Answer: (f⋅g)(1) = 10.
Step-by-step explanation:
To find (f⋅g)(x), we need to multiply the two functions f(x) and g(x) together. This can be done by multiplying each term of f(x) by each term of g(x), and then combining like terms. We get:
(f⋅g)(x) = f(x) * g(x)
= (-7x+3) * (3x^2 - 4x - 1)
= -21x^3 + 28x^2 + x - 3x^2 + 4x + 1
= -21x^3 + 25x^2 + 5x + 1
To find (f⋅g)(1), we can substitute x=1 into the expression for (f⋅g)(x):
(f⋅g)(1) = -21(1)^3 + 25(1)^2 + 5(1) + 1
= -21 + 25 + 5 + 1
= 10
Therefore, (f⋅g)(1) = 10.
[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25} } } )[/tex]
find the value of y ~
The simplification of the given expression
[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25)} } } [/tex]
is y = 7
How to simplify expressions?[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25)} } } [/tex]
find the square root of 25
[tex]y =( \sqrt{47 + \sqrt{9 - 5} } [/tex]
simplify root 9 - 5
[tex]y = ( \sqrt{47 + \sqrt{4} } [/tex]
find the square root of 4
[tex]y = ( \sqrt{47 + 2)} [/tex]
Add root 47 and 2
[tex]y = ( \sqrt{49} )[/tex]
Find the square root of 49
y = 7
Therefore, the solution to the given expression is y = 7
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A triangular prism has height 20 cm.
Its triangular face has base 7 cm and height 10 cm.
A. what is the volume of the prism?
B. suppose you triple the height of the prism.what happen to the volume?
C. suppose you triple the base of the triangular face.what happen to the volume?
D. suppose you triple the height of the triangular face.what happen to the volume?
E. suppose you triple all 3 dimensions.what happen to the volume?
Answer:
A. The volume of the triangular prism can be calculated using the formula V = (1/2)bh × h, where b is the base of the triangular face and h is the height of the prism. Thus, V = (1/2)(7 cm)(10 cm) × 20 cm = 700 cubic centimeters.
B. If the height of the prism is tripled to 60 cm, then the new volume would be V' = (1/2)(7 cm)(10 cm) × 60 cm = 2100 cubic centimeters. Thus, the volume is tripled.
C. If the base of the triangular face is tripled to 21 cm, then the new volume would be V' = (1/2)(21 cm)(10 cm) × 20 cm = 2100 cubic centimeters. Thus, the volume is tripled.
D. If the height of the triangular face is tripled to 30 cm, then the new volume would be V' = (1/2)(7 cm)(30 cm) × 20 cm = 2100 cubic centimeters. Thus, the volume is tripled.
E. If all three dimensions (base, height of triangular face, and height of prism) are tripled, then the new volume would be V' = (1/2)(21 cm)(30 cm) × 60 cm = 18900 cubic centimeters. Thus, the volume is multiplied by a factor of 27.
0.0125 inches thick
Question 4
1 pts
The combined weight of a spool and the wire it carries is 13.6 lb. If the weight of the spool is 1.75 lb.,
what is the weight of the wire?
Question 5
1 pts
In linear equation, 11.85 pounds is the weight of the wire.
What is linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Total weight of pool having 16 wires =13.6 pounds
Weight of the pool =1.75
Therefore the weight of the wire alone = 13.6 - 1.75
= 11.85 pounds
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ab and bc are perpendicular lines find the value of x of 25
Answer:
If the time is 3:45 how many minutes is it slow or fast
Math
rade> Y.9 Solve two-step equations: complete the solution GK7
2(p+ 4) = 12
P + 4 =
Social studies
Complete the process of solving the equation.
Fill in the missing term on each line. Simplify any fractions.
Р
Submit
Recommendations
Divide both sides by 2
Subtract 4 from both sides
P = 2 is the answer to the equation 2(p + 4) = 12.
Is it an equation or an expression?An expression is made up of a number, a variable, or a combination of a number, a variable, and operation symbols. Two expressions are combined into one equation by using the equal symbol. For illustration: When you add 8 and 3, you get 11.
Divide the two among the terms between the parenthesis:
2p + 8 = 12
Add 8 to both sides of the equation, then subtract 8:
2p + 8 - 8 = 12 - 8
2p = 4
multiply both sides by two:
2p/2 = 4/2 \sp = 2
p = 2 is the answer to the equation 2(p + 4) = 12 as a result.
Simply put p = 2 back into the equation and simplify to obtain p + 4:
[tex]p + 4 = 2 + 4 = 6[/tex]
Hence, p + 4 = 6.
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2 PART QUESTION PLS HELP Harris has a spinner that is divided into three equal sections numbered 1 to 3, and a second spinner that is divided into five equal sections numbered 4 to 8. He spins each spinner and records the sum of the spins. Harris repeats this experiment 500 times.
Question 1
Part A
Which equation can be solved to predict the number of times Harris will spin a sum less than 10?
A) 3/500 = x/15
B) 12/500 = x/15
C) 12/15 = x/500
D) 3/15 = x/500
QUESTION 2
Part B
How many times should Harris expect to spin a sum that is 10
or greater?
_______
Accοrding tο the data, the answers tο Questiοns 1 and 2 are: Harris shοuld anticipate spinning a sum οr less 10 apprοximately 367 times and a tοtal that is 10 οr larger apprοximately 133 times.
What are a fοrmula and an equatiοn?Yοur example is an equatiοn since an equatiοn that's any statement with an equal's sign. The usage οf equatiοns in mathematical expressiοns is widespread because mathematicians adοre equal signs. An equatiοn is a cοllectiοn οf guidelines fοr prοducing a specific οutcοme.
Part A: Tο calculate the likelihοοd that Harris will spinning a sum οr less 10, multiply the οverall number οf spins by the chance οf οbtaining a sum οr less 10. The οutcοmes οf the first spinner's spin are 1, 2, and 3, while the results οf the secοnd spinner's spin are 4, 5, 6, 7, and 8. Hence, the amοunts οr less 10 are:
1 + 4 = 5
1 + 5 = 6
1 + 6 = 7
1 + 7 = 8
1 + 8 = 9
2 + 4 = 6
2 + 5 = 7
2 + 6 = 8
2 + 7 = 9
3 + 4 = 7
3 + 5 = 8
3 + 6 = 9
There are 11 amοunts that cοuld be less than ten. The number οf successful results divided by the entire number οf pοssibilities, which is 11/15, represents the likelihοοd οf receiving a payοut οf less than 10 in a single spin. Harris will therefοre spin a tοtal less than 10 times, and the equatiοn tο estimate this is:
11/15 = x/500
After finding x, we οbtain:
x = (11/15) x 500
x = 366.67, which rοunds up tο 367
Sο, Harris shοuld expect tο spin a sum less than 10 abοut 367 times.
Part B: Tο determine hοw frequently Harris shοuld anticipate spinning a sum οf ten οr mοre, we can deduct the times that he shοuld anticipate spinning a sum lοwer than ten frοm the οverall number οf spins:
500 - 367 = 133
Therefοre, Harris shοuld expect tο spin a sum that is 10 οr greater abοut 133 times.
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The linear sf of two similar shapes is 2:5 if the area of the similar shapes is 78cm determine the area of the bigger solid
The area of the bigger solid is 67.24 cm².
How to calculate the area of solid ?Assume the smaller shape has a length of 2x and a width of 2y. The larger shape would then have 5x length and 5y width.
Because the area of a rectangle is the product of its length and width, the area of the smaller shape is:
Area of smaller shape = 2x * 2y = 4xy
We know that the similar shapes have an area of 78 cm2. As a result, we can write:
4xy + larger area = 78
(larger shape area) / (smaller shape area) = (linear scale factor)²
Substituting the values from the problem yields:
(larger shape area) / (4xy) = (5/2)2 = 25/4
When we multiply both sides by 4xy, we get:
larger shape area = (25/4) * 4xy = 25xy
Now we can plug the expression we discovered for the area of the smaller shape into the equation we found earlier:
4xy + 25xy = 78
29xy = 78
xy = 78/29
Substituting this xy value into the expression we discovered for the area of the larger shape yields:
larger shape area = 25xy = 25 * (78/29) = 67.24 cm2 (rounded to two decimal places)
As a result, the larger shape has an area of approximately 67.24 cm2.
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Solve the following problems.
Given: AABC, DE AC,
BD DC, mZ1=m22,
mZBDC= 100°
Find: m< A, m< b , m
The value of the angles in the triangle are:
∠A = 60°, ∠B = 80° and ∠C = 40°
How to find the value of m∠A, m∠B, m∠C in the triangle?
We are given that BD = DC
Thus, ∠DBC = ∠BCD ---- 1 (angle in isosceles triangle)
We also have ∠BDC = 100°
In ΔBDC
∠BDC + ∠DBC + ∠BCD = 180° (sum of angles of triangle is 180°)
Using 1:
∠BDC + 2∠DBC = 180°
100° + 2∠DBC = 180°
2∠DBC = 180 - 100
2∠DBC = 80
∠DBC = 80/2
∠DBC = 40°
∠DBC = ∠BCD = ∠2 = 40°
Thus, ∠C = 40°
We are given that m∠1 = m∠2
Thus, ∠1 = ∠2 = 40°
Now, ∠BDC + ∠BDA = 180° (Linear pair)
100° + ∠BDA = 180°
∠BDA = 180 - 100
∠BDA = 80°
In ΔABD
∠ABD + ∠BDA + ∠BAD = 180° (sum of angles of triangle is 180°)
∠1 + ∠BDA + ∠BAD = 180°
40° + 80° + ∠BAD = 180°
120° + ∠BAD = 180°
∠BAD = 60°
So, ∠A = 60°
∠B = ∠1 + ∠2 = 40° + 40° = 80°
Therefore, ∠A = 60°, ∠B = 80° and ∠C = 40°
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Complete Question
m∠1=m∠2
D∈
AC
, BD = DC
m∠BDC = 100°
Find: m∠A, m∠B, m∠C
Given that x is a positive integer less than 100, how many solutions does the congruence x+13=55 (mod 34) have?
The congruence x + 13 ≡ 55 (mod 34) simplifies to x ≡ 12 (mod 34). There are three solutions for x less than 100 that satisfy this congruence.
The given congruence is x + 13 ≡ 55 (mod 34). Simplifying this, we get x ≡ 12 (mod 34).
We need to find the number of solutions for x that are less than 100 and satisfy this congruence.
The general solution for the congruence x ≡ 12 (mod 34) is x = 12 + 34k, where k is an integer.
The solutions that are less than 100 are obtained when k = 0, 1, or 2.
Thus, the number of solutions is 3.
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Find the average rate of change of the area of a circle withrespect to its radius r as r changes from2 to each of the following.(i) 2 to 3 (ii) 2 to 2.5 (iii) 2 to 2.1
The average rate of change is 5π; for r changing from 2 to 2.5, it is 2.5π, and for r changing from 2 to 2.1, it is 4.1π.
The area of a circle is given by the formula A = πr². To find the average rate of change of A with respect to r, we can take the derivative of A with respect to r:
dA/dr = 2πr
This tells us how much the area changes for a small change in the radius. To find the average rate of change over a larger interval, we can use the formula:
ΔA/Δr = (A2 - A1)/(r2 - r1)
where A1 and A2 are the areas at the initial and final radii, and r1 and r2 are the initial and final radii.
(i) For r changing from 2 to 3:
ΔA/Δr = (π(3)² - π(2)²)/(3 - 2) = 5π
The average rate of change of the area with respect to the radius is 5π.
(ii) For r changing from 2 to 2.5:
ΔA/Δr = (π(2.5)² - π(2)²/(2.5 - 2) = 2.5π
The average rate of change of the area with respect to the radius is 2.5π.
(iii) For r changing from 2 to 2.1:
ΔA/Δr = (π(2.1)² - π(2)²)/(2.1 - 2) = 4.1π
The average rate of change of the area with respect to the radius is 4.1π.
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A fair coin is tossed five times. What is the theoretical probability that the coin lands on the same side every time??
A) 0.1
B) 0.5
C) 0.03125
D) 0.0625
Answer:
The answer is C
Step-by-step explanation:
Assuming this is a fair coin, the theoretical probability of the coin going on one side, let's say heads, is 50%, or 0.5. So what's the chance the coin lands head 5 times? To do this we do 0.5^5 OR 0.5*0.5*0.5*0.5*0.5. Both of these answers equal 0.03125. So C is the Answer. Hope this helps :D
construct shear and bending diagrams for the following beams. show your equations used to create the plots. p p p p l/2 l/4 l/4 p p p l/3 l/3 l/3
The shear force and bending moment diagrams for the given beam will have multiple segments of different shapes and slopes, reflecting the variation of loads along the length of the beam.
To construct the shear and bending diagrams for the given beam, we need to analyze the beam for the different sections where the load is applied. We can break down the beam into five sections:
Leftmost section (0 ≤ x ≤ L/4)
Second section (L/4 < x ≤ L/2)
Third section (L/2 < x ≤ 5L/12)
Fourth section (5L/12 < x ≤ 7L/12)
Rightmost section (7L/12 < x ≤ L)
We can use the equations for shear and bending moments to create the plots:
For section 1: 0 ≤ x ≤ L/4
The shear force diagram will be constant since there is no load applied in this section. The bending moment diagram will be a sloping line, which will be zero at x = 0 and will increase linearly with x as we move toward the right end of the section.
For section 2: L/4 < x ≤ L/2
The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a maximum value at the midpoint of the section.
For section 3: L/2 < x ≤ 5L/12
The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. At x = 5L/12, a load of P/3 is added, causing the shear force to increase suddenly. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local minimum at x = 5L/12.
For section 4: 5L/12 < x ≤ 7L/12
The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local maximum at x = 7L/12.
For section 5: 7L/12 < x ≤ L
The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. At x = L/3, a load of P/3 is added, causing the shear force to decrease suddenly. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a minimum value at the midpoint of the section.
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PLEASE HELP ME!!! Type the correct answer in each box. Use T for true and F for false.
Complete the truth table for the contrapositive of a conditional statement.
р
T
T
LL
LL
q
T
F
T
LL
P→q
T
F
T
T
~9~p
The answer will of given mathematical logic will be T F T T F respectivelly.
What fundamental ideas underlie mathematical logic?A negation, conjunction, and disjunction are the fundamental mathematical logics. The symbols for negation, conjunction, and disjunction in mathematical logic are "," "," and "v," respectively.
What is the purpose of mathematical logic?Logical proofs frequently employ mathematical logic. Proofs are legitimate arguments that establish the veracity of mathematical assertions. A series of statements make up an argument. The conclusion is the last assertion, and the premises are all the statements that came before it (or hypothesis).
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The complete truth table is shown in the below diagram.
≈ q → ≈ p: True False True True
Define the conditional statement for contrapositive?The contrapositive of a conditional statement is a new conditional statement that is formed by negating both the hypothesis (the "if" part) and the conclusion (the "then" part) of the original statement, and switching their positions. The truth table for the contrapositive of a conditional statement has the same number of rows as the truth table for the original statement.
For example, if the original statement is "If it is raining, then the ground is wet", then the contrapositive would be "If the ground is not wet, then it is not raining."
According to the given table the contrapositive of a conditional statement q and p is defines as;
True
False
True
True
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What is the amount of interest to be paid if u got a reducing balance loan of $2700 and you will repay it over 5 years by quarterly installments of $1899.75 at interest rate 14% p.a. (compounded quarterly)
The total interest to be paid over the 5-year period is $403.22.
What is reducing balance loan?In a loan with a declining balance, interest is added to the outstanding balance at the start of each period, such as each month or each quarter. The outstanding balance, which decreases as the borrower makes repayments, is used to determine the interest rate. As a result, the borrower gradually pays less interest and more of each payment is used to lowering the main balance due. The lowering balance approach is frequently applied to mortgages, personal loans, and auto loans.
Given that, the quarterly installments are $1899.75.
For the entire year for a total of 5 years the total amount is:
Total amount = 4 * 5 * $1899.75 = $37995
For reducing balance loan the interest is calculated as:
For the first quarter, the interest to be paid is:
interest = (total amount - 0) * (0.14 / 4)
interest = (37995 - 0) * (0.14 / 4) = $94.50
Similarly for the remaining quarters we have:
Second quarter = $87.95
Third quarter: $81.05
Fourth quarter: $73.76
Fifth quarter: $65.96
The total interest to be paid over the 5-year period is:
$94.50 + $87.95 + $81.05 + $73.76 + $65.96 = $403.22
Hence, the total interest to be paid over the 5-year period is $403.22.
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Elizabeth works as a server in coffee shop, where she can earn a tip (extra money) from each customer she serves. The histogram below shows the distribution of her 60 tip amounts for one day of work. 25 g 20 15 10 6 0 0 l0 15 20 Tip Amounts (dollars a. Write a few sentences to describe the distribution of tip amounts for the day shown. b. One of the tip amounts was S8. If the S8 tip had been S18, what effect would the increase have had on the following statistics? Justify your answers. i. The mean: ii. The median:
a. Histogram shows tip amounts ranging between $6 and $25, skewed to the right with a longer tail of higher tips.
b. Increasing the $8 tip to $18 would increase the mean since total tip amount increases by $10 spread out over 60 customers. Median won't be affected since changing one value does not alter the middle value.
a. The histogram shows that Elizabeth received a range of tip amounts, with the majority of tips falling between $6 and $25. The distribution is skewed to the right, with a longer tail of higher tip amounts.
b. i. The mean would increase because the total tip amount would increase by $10, and this increase would be spread out over the 60 customers.
ii. The median would not be affected because it is the middle value when the data is ordered, and changing one value does not change the middle value.
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-0.1x^2+10=0
find the x
Answer:
x = ±10
Step-by-step explanation:
1) Subtract 10 from both sides.
[tex]-0.1 \times x^2=-10[/tex]
2) Divide both sides by -0.1.
[tex]x^2=\frac{-10}{-0.1}[/tex]
3) Simplify [tex]\frac{-10}{-0.1}[/tex] to 100.
[tex]x^2=100[/tex]
4) Take the square root of both sides.
[tex]x=\pm \sqrt{100}[/tex]
5) Since 10 * 10 is 100, the square root of 100 is 10.
[tex]x=\pm10[/tex]
