To find the approximate measurements of the angles of triangle PQR, we can use the dot product formula and the Law of Cosines.
First, let's find the vectors PQ and PR:
Vector PQ = Q - P = (3, 3, 1) - (0, -1, 5) = (3, 4, -4)
Vector PR = R - P = (-4, 4, 6) - (0, -1, 5) = (-4, 5, 1)
Next, we'll find the lengths of vectors PQ and PR:
|PQ| = sqrt((3)^2 + (4)^2 + (-4)^2) = sqrt(9 + 16 + 16) = sqrt(41)
|PR| = sqrt((-4)^2 + (5)^2 + (1)^2) = sqrt(16 + 25 + 1) = sqrt(42)
Now, we can find the dot product of vectors PQ and PR:
PQ · PR = (3)(-4) + (4)(5) + (-4)(1) = -12 + 20 - 4 = 4
Using the dot product and the lengths of PQ and PR, we can calculate the cosine of each angle using the Law of Cosines:
cos(angle P) = (PQ · PR) / (|PQ| |PR|)
cos(angle Q) = (QR · QP) / (|QR| |QP|)
cos(angle R) = (RP · RQ) / (|RP| |RQ|)
Substituting the values:
cos(angle P) = 4 / (sqrt(41) sqrt(42))
cos(angle Q) = -4 / (sqrt(41) sqrt(42))
cos(angle R) = 8 / (sqrt(42) sqrt(41))
Finally, we can calculate the approximate measurements of the angles using the inverse cosine function:
angle P ≈ arccos(cos(angle P))
angle Q ≈ arccos(cos(angle Q))
angle R ≈ arccos(cos(angle R))
Note: The angles will be in radians. To convert to degrees, you can multiply by (180 / π).
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help me please lol I will report if you troll
What is 2+2 minus 32 multiplied by 438? is the answer a squareroot, yes or no?
If (81)(27)2x-5-93-4⁰, then x = ________
The value of x that satisfies the equation (81)(27)^(2x-5) - 9^(3-4x) = 0 is x = 17/14.
To find the value of x in the equation (81)(27)^(2x-5) - 9^(3-4x) = 0, we can use the properties of exponents and logarithms to simplify and solve the equation. By equating the bases and exponents on both sides, we can determine the value of x.
We start by simplifying the equation. Applying the exponent properties, we have (3^4)(3^3)^(2x-5) - (3^2)^(3-4x) = 0.
Simplifying further, we get (3^(4 + 3(2x-5))) - (3^(2(3-4x))) = 0.
Using the property (a^b)^c = a^(b*c), we can rewrite the equation as 3^(4 + 6x - 15) - 3^(6 - 8x) = 0.
Combining like terms, we have 3^(6x - 11) - 3^(6 - 8x) = 0.
To equate the bases and exponents, we set 6x - 11 = 6 - 8x.
Simplifying the equation, we get 14x = 17.
Dividing both sides by 14, we find that x = 17/14.
Therefore, the value of x that satisfies the equation (81)(27)^(2x-5) - 9^(3-4x) = 0 is x = 17/14.
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A sample of 76 body temperatures has a mean of 98.7. Assume that o is known to be 0.5 °F. Use a 0.05 significance level to test the claim that the mean body temperature of the population is equal to 98.5 °F, as is commonly believed. What is the value of test statistic for this testing?
The value of the test statistic in the scenario given above is 3.487
The test statistic can be calculated as follows:
t = (mean - hypothesized mean) / (standard deviation / √(sample size))
mean = 98.7
hypothesized mean = 98.5
standard deviation = 0.5
sample size = 76
Plugging these values into the formula, we get the following test statistic:
t = (98.7 - 98.5) / (0.5 / √(76)) = 3.487
Therefore, the value of the test statistic in the above scenario is 3.487
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Suppose that X, Y and Z are three jointly normally distributed random variables with E[X] = 0, E[Y] = 1, E[Z] = 2 and the variance-covariance martrix of (X, Y, Z) is 10 0 1 Var [] = [] 10 2 1 2 10 (i) Estimate X given that Y = 0.5 and Z = -3 using an unbiased minimum variance estimator. (ii) Determine the variance of the above estimator. (b) IntelliMoto is car manufacturer that produces vehicles equipped with a fault detection system that uses information from various sensors to inform the driver about possible faults in the braking system. The system diagnoses faults correctly with probability 99%, but gives false alarms with probability 2%. It is known that such faults occur with probability 0.05%. If the system diagnoses a fault, what is the probability a fault has actually occured?
(i) Estimate X given that Y = 0.5 and Z = -3 using an unbiased minimum variance estimator.
Estimate of X given that Y = 0.5 and Z = -3 can be obtained by applying the conditional expectation formula, E[X|Y=y, Z=z], where y=0.5 and z=-3.E[X|Y=y, Z=z] = E[X] + Cov[X,Y]/Var[Y] * (Y - E[Y]) + Co v[X,Z]/Var[Z] * (Z - E[Z])E[X|Y=0.5, Z=-3] = 0 + (0/10) * (0.5 - 1) + (1/2) * (-3 - 2) = -2, which is the unbiased minimum variance estimator.(ii) Determine the variance of the above estimator.
The variance of the unbiased minimum variance estimator is given by Var[X|Y=y, Z=z] = Var[X] - Cov[X,Y]^2/Var[Y] - Cov[X,Z]^2/Var[Z] + 2Cov[X,Y]Cov[X,Z]/(Var[Y]*Var[Z])Var[X|Y=0.5, Z=-3] = 10 - 0^2/10 - 1^2/2 + 2(0)(1)/(10*2) = 9.75 (b)
Intelli Moto is car manufacturer that produces vehicles equipped with a fault detection system that uses information from various sensors to inform the driver about possible faults in the braking system. The system diagnoses faults correctly with probability 99%, but gives false alarms with probability 2%. It is known that such faults occur with probability 0.05%. If the system diagnoses a fault, what is the probability a fault has actually occured?
The probability of a fault actually occurring is P(Fault) = 0.05%, which is the prior probability of a fault.
The probability of a correct diagnosis is P(Diagnosis | Fault) = 99%, which is the probability of a positive test result given that a fault has actually occurred.
The probability of a false alarm is P(Diagnosis | No Fault) = 2%, which is the probability of a positive test result given that no fault has actually occurred.
The probability of a positive test result isP(Diagnosis) = P(Fault)*P(Diagnosis | Fault) + P(No Fault)*P(Diagnosis | No Fault)= 0.05% * 99% + 99.95% * 2% = 2.039%.The probability of a fault given a positive test result can be obtained by Bayes' theorem,P(Fault | Diagnosis) = P(Diagnosis | Fault)*P(Fault)/P(Diagnosis)= 99% * 0.05% / 2.039% = 2.43%, which is the probability a fault has actually occurred given that the system diagnoses a fault.
The probability that a fault has actually occurred given that the system diagnoses a fault is 2.42%.
(i) To estimate X given that Y = 0.5 and Z = -3 using an unbiased minimum variance estimator, we need to determine the distribution of X | Y = 0.5, Z = -3 and use the formula for conditional expectation of a jointly normally distributed random variable. The distribution of X | Y = 0.5, Z = -3 is also normal since it is a conditional distribution of a jointly normally distributed random variable. To find the mean of the distribution, we use the formula for conditional expectation:
[tex]E[X | Y = 0.5, Z = -3] = E[X] + Cov[X, Y | Z = -3] (Y - E[Y | Z = -3]) / Var[Y | Z = -3] + Cov[X, Z | Y = 0.5] (Z - E[Z | Y = 0.5]) / Var[Z | Y = 0.5][/tex]
where Cov[X, Y | Z = -3] is the conditional covariance of X and Y given Z = -3,
E[Y | Z = -3] is the conditional mean of Y given Z = -3,
Var[Y | Z = -3] is the conditional variance of Y given Z = -3,
Cov[X, Z | Y = 0.5] is the conditional covariance of X and Z given Y = 0.5,
and E[Z | Y = 0.5] and Var[Z | Y = 0.5] are the conditional mean and variance of Z given Y = 0.5 respectively.
We are given that
E[X] = 0, E[Y] = 1, E[Z] = 2,
Var[X] = 10, Var[Y] = 2, Var[Z] = 1,
and Cov[X, Y] = Cov[X, Z] = Cov[Y, Z] = 0.
Also, Y = 0.5 and Z = -3.
Hence, we have:
[tex]Cov[X, Y | Z = -3] = Cov[X, Y] / Var[Z] = 0[/tex],
[tex]E[Y | Z = -3] = E[Y] =[/tex]1,
[tex]Var[Y | Z = -3] = Var[Y] = 2[/tex],
[tex]Cov[X, Z | Y = 0.5] = Cov[X, Z] / Var[Y] = 0[/tex].
The conditional mean of Z given Y = 0.5 is given by
[tex]E[Z | Y = 0.5] = E[Z] + Cov[Y, Z] (Y - E[Y]) / Var[Y] = 2 + 0.5 (0 - 1) / 2 = 1.5.[/tex]
The conditional variance of Z given Y = 0.5 is given by
[tex]Var[Z | Y = 0.5] = Var[Z] - Cov[Y, Z]^2 / Var[Y] = 1 - 0^2 / 2 = 1[/tex].
Hence, the mean of the distribution of X | Y = 0.5, Z = -3 is:
[tex]E[X | Y = 0.5, Z = -3] = 0 + 0 (0.5 - 1) / 2 + 0 (-3 - 1.5) / 1 = -0.75[/tex]
To find the variance of the unbiased minimum variance estimator, we use the formula for conditional variance of a jointly normally distributed random variable:
[tex]Var[X | Y = 0.5, Z = -3] = Var[X] - Cov[X, Y | Z = -3]^2 / Var[Y | Z = -3] - Cov[X, Z | Y = 0.5]^2 / Var[Z | Y = 0.5][/tex]
where Var[X], Cov[X, Y | Z = -3], and Cov[X, Z | Y = 0.5] are given above,
and Var[Y | Z = -3] and Var[Z | Y = 0.5] are calculated as follows:
[tex]Var[Y | Z = -3] = Var[Y] - Cov[X, Y]^2 / Var[Z] = 2 - 0^2 / 1 = 2Var[Z | Y = 0.5] = Var[Z] - Cov[Y, Z]^2 / Var[Y] = 1 - 0^2 / 2 = 1[/tex]
Hence, we have:
[tex]Var[X | Y = 0.5, Z = -3] = 10 - 0^2 / 2 - 0^2 / 1 = 10[/tex]
(ii) The variance of the unbiased minimum variance estimator is Var[X | Y = 0.5, Z = -3] = 10.
(b) Let A denote the event that a fault has actually occurred, D denote the event that the system diagnoses a fault,
P(A) = 0.05%, P(D | A) = 99%, and P(D | A') = 2%, where A' is the complement of A.
We need to find P(A | D), the probability that a fault has actually occurred given that the system diagnoses a fault.
By Bayes' theorem, we have:
[tex]P(A | D) = P(D | A) P(A) / P(D)[/tex]
where P(D) is the total probability of the system diagnosing a fault, which is:
[tex]P(D) = P(D | A) P(A) + P(D | A') P(A') = 0.99 (0.0005) + 0.02 (1 - 0.0005) = 0.0205[/tex]
Hence, we have:
[tex]P(A | D) = 0.99 (0.0005) / 0.0205 = 0.0242[/tex] or 2.42%
Therefore, the probability that a fault has actually occurred given that the system diagnoses a fault is 2.42%.
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2/3 x 6 need help asap
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
2/3 x 6 is 4 because when you times the 2 in 2/3 u get 12 and 12/3 is the same as 4
In the figure below, m LMK = 26° and m KLM = 33° What is m MKJ? A. 52° B. 66° C. 59° D. 121°
Answer:
option c
Step-by-step explanation:
first use angle sum property, then use
linear pair axiom
Answer:
D: 121
Step-by-step explanation:
Step One: To do this problem, you must understand the rule that all angles in a triangle add up to 180 degrees.
Step Two: Now that we know the rule, we know this triangle equals 180 degrees. First, we must add the angles we DO know together: 26+33= 59.
Step Three: We can subtract 59 from 180 to find the missing angle: 180-59= 121.
In circle O, radius OQ measures 9 inches and arc PQ measures 6π inches. Circle O is shown. Line segments P O and Q O are radii with length of 9 inches. Angle P O Q is theta. What is the measure, in radians, of central angle POQ? StartFraction 2 pi Over 3 EndFraction radians StartFraction 3 pi Over 4 EndFraction centimeters StartFraction 4 pi Over 3 EndFraction radians StartFraction 3 pi Over 2 EndFraction radians
The answer is A. 2pi/3 radians.
Answer:
First Option
Explanation:
A) 2pi/3 radians
Hope this helps :)
In a one-tail hypothesis test where you reject H0 only in the lower tail, it was found that the p-value is 0.9699 if ZSTAT=+1.88.
What is the statistical decision if you test the null hypothesis at the 0.10 level of significance?
Choose the correct answer below.
A. Reject the null hypothesis because the p-value is greater than or equal to the level of significance.
B. Reject the null hypothesis because the p-value is less than the level of significance.
C. Fail to reject the null hypothesis because the p-value is greater than or equal to the level of significance.
D. Fail to reject the null hypothesis because the p-value is less than the level of significance.
The null hypothesis is not rejected since the p-value is higher than or equal to the level of significance.
We assess the statistical conclusion based on the given data by comparing the p-value to the level of significance ().
Given: ZSTAT is 1.88 and p-value is 0.9699.
Level of significance () = 0.10
In a one-tail hypothesis test, the null hypothesis is only rejected in the lower tail if the p-value is less than the level of significance ().
The p-value is greater in this instance (0.9699) than the level of significance (0.1).
Therefore, the proper reaction is
C. The null hypothesis is not rejected since the p-value is higher than or equal to the level of significance.
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A brewery produces a particular type of beer. If the process is running well then the probability that a randomly selected bottle is of good quality is 90%, independently of the quality of any of the other bottles. If the process is not running well then that probability is only 60%. Without further information, the probability that the process is running well is 80%. (a) 10 bottles are produced. Find the expected number of good quality bottles in this batch. (b) of this batch, the first 4 bottles are tested, and all are of good quality except for the second bottle. What is the probability that the process is running well? (c) The 5th bottle is now tested as well. What is the probability that this bottle is of good quality?
(a) The expected number of good quality bottles in this batch is 7.2
(b) The probability that the process is running well, given that the second bottle is not of good quality, is 0.5
(c) The probability that the 5th bottle is of good quality is 0.84
(a) To find the expected number of good quality bottles in the batch of 10 bottles, we can multiply the probability of each bottle being of good quality by the total number of bottles.
Given that the probability of a bottle being of good quality is 90% if the process is running well and 60% if the process is not running well, and the probability that the process is running well is 80%, we can calculate the expected number of good quality bottles as follows:
Expected number of good quality bottles = (Probability of running well) × (Probability of good quality | running well) × (Total number of bottles)
= (0.8) × (0.9) × (10)
= 7.2
Therefore, the expected number of good quality bottles in this batch is 7.2.
(b) Given that the first 4 bottles tested are all of good quality except for the second bottle, we need to find the probability that the process is running well.
Let A be the event that the process is running well, and B be the event that the second bottle is not of good quality.
Using Bayes' theorem, we can calculate the probability:
P(A | B) = (P(B | A) × P(A)) / P(B)
P(B | A) is the probability that the second bottle is not of good quality given that the process is running well, which is 1 - 0.9 = 0.1.
P(A) is the probability that the process is running well, which is given as 0.8.
P(B) is the probability that the second bottle is not of good quality. To calculate this, we need to consider the cases where the process is running well and not running well.
P(B) = P(B | A) × P(A) + P(B | not A) × P(not A)
= 0.1 × 0.8 + 0.4 × 0.2
= 0.08 + 0.08
= 0.16
Now, we can calculate the probability using Bayes' theorem:
P(A | B) = (0.1 × 0.8) / 0.16
= 0.5
Therefore, the probability that the process is running well, given that the second bottle is not of good quality, is 0.5.
(c) Now, if the 5th bottle is tested as well, we want to find the probability that this bottle is of good quality.
Let C be the event that the 5th bottle is of good quality.
Using the law of total probability, we can calculate the probability:
P(C) = P(C | A) × P(A) + P(C | not A) × P(not A)
= 0.9 × 0.8 + 0.6 × 0.2
= 0.72 + 0.12
= 0.84
Therefore, the probability that the 5th bottle is of good quality is 0.84.
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• A neighborhood threw a fireworks celebration for the 4th of July. A bottle rocket was launched upward from the ground with an initial velocity of 160 feet per second. The formula for vertical motion of an object is h(t) = 0.5at2 + vt +s, where the gravitational constant, a, is -32 feet per square second, v is the initial velocity, s is the initial height, and h(t) is the height in feet modeled as a function of time, t.
Part A: What function describes the height, h, of the bottle rocket after t seconds have elapsed?
Part B: What was the maximum height of the bottle rocket?
Answer:
poopy
Step-by-step explanation:
Answer:
h(t)=0.5at^2+v+5
Step-by-step explanation:
If you know how to do math you should know
HELP NOW!!! 100 POINTS! Cylinder A has a radius of 10 inches and a height of 5 inches. Cylinder B has a volume of 750π. What is the percentage change in volume from cylinder A to cylinder B?
50% decrease
75% decrease
50% increase
200% increase
Answer:
50% increase
Step-by-step explanation:
The percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.
What is a cylinder?In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the formula for the volume of the cylinder is given by:
[tex]\rm V = \pi r^2h[/tex]
We have r = 10 inches and h = 5 inches
[tex]\rm V = \pi \times10^2\times5[/tex]
V = 500π cubic inches
Percent change in volume from cylinder A to cylinder B:
[tex]=\rm \frac{750\pi-500\pi}{500\pi} \times100[/tex]
= 50%
Thus, the percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.
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How far from the tower can it be placed, to the nearest foot?
Answer:
43 feet would be the correct answer.
Step-by-step explanation:
4(x3 + xy2) dV, where E is the solid in the first octant that lies beneath the paraboloid z = 1 − x2 − y2.
To calculate the given volume integral, 4(x^3 + xy^2) dV, over the solid E in the first octant beneath the paraboloid z = 1 - x^2 - y^2, we need to set up the integral in cylindrical coordinates. The integral will involve integrating over the appropriate limits and applying the volume element in cylindrical coordinates.
In cylindrical coordinates, we have x = r cos θ, y = r sin θ, and z = z.
The equation of the paraboloid, z = 1 - x^2 - y^2, can be expressed as z = 1 - r^2.
The given volume integral becomes 4(x^3 + xy^2) dV = 4(r^3 cos^3 θ + r^3 cos θ sin^2 θ) r dz dr dθ.
To determine the limits of integration, we need to consider the region of the solid E in the first octant. Since the solid lies beneath the paraboloid z = 1 - x^2 - y^2, the upper limit for z is given by z = 1 - r^2.
The limits for r and θ depend on the region in the first octant. We need to set appropriate limits to cover the desired region.Once we have the limits for r, θ, and z, we can set up the triple integral using the volume element in cylindrical coordinates.
By evaluating the integral with the corresponding limits, we can find the value of the given volume integral over the solid E in the first octant beneath the paraboloid.
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Can someone explain why the answer is True. Will make brainliest.
Answer:
True
Step-by-step explanation:
With Sin and Cos, the rule is that the opposites are the same:
SinA=CosB
CosB=SinA
In this problem, it is showing SinA=cosB, so it is the same, it is true.
Hope this helps!
HELP ASAP PLEASE ILL MARK BRAINLIEST
A bag contains 9 and 54 blue marbles. If a representative sample contains 3 white marbles, then how many blue marbled would you expect to contain? Explain
Answer:
There should be 18 blue marbles in the representative sample.
Step-by-step explanation:
Given that a bag contains 9 white and 54 blue marbles, if a representative sample contains 3 white marbles, to determine how many blue marbles would you expect to contain the following calculation must be performed:
9 = 3
54 = X
54 x 3/9 = X
162/9 = X
18 = X
Therefore, there should be 18 blue marbles in the representative sample.
Lizzy had test scores of: 72, 94, 108, 60What is the RANGE of her test scores?
Answer:
48
Step-by-step explanation:
To find the range, you have to subtract the biggest/largest number by the smallest number:
108 - 60 = 48
The range is 48.
Suppose the prevalence of is 12.5%. We assume the
diagnostic test has a sensitivity of 80% and a
95% specificity. What is the probability of getting a negative
result?
The probability of getting a negative result is 0.175 or 17.5%.
To calculate the probability of getting a negative result, we need to consider the sensitivity and specificity of the diagnostic test.
Given that the prevalence of the condition is 12.5%, we can assume that 12.5% of the population has the condition, and the remaining 87.5% does not.
The sensitivity of the test is 80%, which means that it correctly identifies 80% of the individuals with the condition as positive.
The specificity of the test is 95%, which means that it correctly identifies 95% of the individuals without the condition as negative.
To calculate the probability of getting a negative result, we need to consider both the true negative rate (1 - sensitivity) and the proportion of individuals without the condition (1 - prevalence).
Probability of getting a negative result = (1 - sensitivity) × (1 - prevalence)
= (1 - 0.80) × (1 - 0.125)
= 0.20 * 0.875
= 0.175
Therefore, the probability of getting a negative result is 0.175 or 17.5%.
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12 = a (-6 + 5) (-6 - 6)
Answer:
a=1
Step-by-step explanation:
3. Audrey measures the distance around the lid of her aquarium. The picture shows the shape of the lid. If the perimeter of the lid is 56 inches, what is the missing side length? * Brainliest and 20 points
Answer:
18 in
Step-by-step explanation:
There are 12 boys and 16 girls in a classroom. Which represents the simplified ratio of girls to students in the classroom?
3 to 4
4 to 3
4 to 7
7 to 4
Answer:
3 to 4
Step-by-step explanation:
12÷4=3
16÷4=4
so that makes it 3 to 4
I NEED HELP ASAPPPP ILL GIVE BRAINLIESTTTTTT
3/4 + 7/8 + 5/6
(this is here because the question was too short)
Answer:23/8Step-by-step explanation:(LCM of 4,8 and 6 = 24 )
3×6/4×6 + 7×3/8×3 + 5×4/6×4 28+21+20/24
59/24
I hope you got it❤️❤️❤️And thanks your patience ❤️.SORRY
Consider the following equation: 4 + 6x = 6x + 4. Explain why the equation has many solutions.
Determine the perimeter and area of the shape shown below. 4 ft 16.5 ft 4 ft 20 ft Perimeter: feet Area: square feet Round your answer to the nearest hundredth as needed.
The perimeter of the shape is approximately 44.00 feet, and the area is approximately 160.50 square feet.
To determine the perimeter of the shape, we add up the lengths of all its sides. The given sides are 4 ft, 16.5 ft, 4 ft, and 20 ft. Adding these lengths together, we get a perimeter of 44.5 ft. However, since we are asked to round to the nearest hundredth, the perimeter becomes approximately 44.00 feet.
To find the area of the shape, we need to know its specific shape. Since the given measurements do not provide enough information, it is not possible to accurately determine the area. In order to calculate the area, we need to know the shape's dimensions, angles, or additional side lengths. Without this information, we cannot determine the area accurately.
In conclusion, the perimeter of the shape is approximately 44.00 feet, but the area cannot be determined without further information.
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Help plssss I need to find mr pryor account balance
Answer:
$1,462.50
Step-by-step explanation:
We are to find the total amount after 4 years
Principal => $1,250
Rate => 4.25%
The formula to find the total amount =
A = P(1 + rt)
First, converting R percent to r a decimal
r = R/100 = 4.25%/100 = 0.0425 per year.
Solving our equation:
A = 1250(1 + (0.0425 × 4)) = 1462.5
A = $1,462.50
The total amount accrued, principal plus interest, from simple interest on a principal of $1,250.00 at a rate of 4.25% per year for 4 years is $1,462.50.
Suppose that 7% of the Karak tea packs produced by the company Chai Karak are defective. A shipment of 10,000 packs is sent to Ishbeliyah co-op. The co-op inspects a Simple Random Sample (SRS) of 10 packs. Let X = number of defective Karak tea packs in the SRS of size 10.
What is the probability that none of the packs are defective P(X = 0)?
What is the probability that 5 packs are defective?
What is the probability that all the packs are defective?
What is the probability that 7 or more packs are defective?
The probability that none of the packs are defective is 0.478. The probability that five packs are defective is 0.000455.The probability that all the packs are defective is 2.8243e-14.The probability that 7 or more packs are defective is 0.00416 (approx).
A shipment of 10,000 Karak tea packs is produced by the company Chai Karak. If 7% of the packs are defective, what is the probability that: none of the packs are defective, five packs are defective, all the packs are defective, and seven or more packs are defective? The number of trials, n, is 10 and the probability of a defective tea pack is 0.07. Therefore, the number of successful trials, X, follows a binomial distribution. Formula for binomial distribution: P(X = k) = nCk × pk × (1 − p)n−kWhere nCk = number of combinations of n things taken k at a time = n! / (k! (n-k)!)a. The probability that none of the packs are defective P(X = 0):P(X = 0) = nC0 * p0 * (1-p)n-0= 10C0 * 0.07^0 * (1-0.07)^10= 1 * 1 * 0.478= 0.478Therefore, the probability that none of the packs are defective is 0.478.
The probability that 5 packs are defective:P(X = 5) = nC5 * p^5 * (1-p)n-5= 10C5 * 0.07^5 * (1-0.07)^5= 252 * 0.0000028 * 0.649= 0.000455Therefore, the probability that five packs are defective is 0.000455.
The probability that all the packs are defective:P(X = 10) = nC10 * p^10 * (1-p)n-10= 10C10 * 0.07^10 * (1-0.07)^0= 1 * 2.8243e-14 * 1= 2.8243e-14Therefore, the probability that all the packs are defective is 2.8243e-14.
The probability that 7 or more packs are defective: P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)P(X = 7) = nC7 * p^7 * (1-p)n-7= 10C7 * 0.07^7 * (1-0.07)^3= 120 * 0.0000953677 * 0.657= 0.00416P(X = 8) = nC8 * p^8 * (1-p)n-8= 10C8 * 0.07^8 * (1-0.07)^2= 45 * 0.0000024969 * 0.859= 0.000011P(X = 9) = nC9 * p^9 * (1-p)n-9= 10C9 * 0.07^9 * (1-0.07)^1= 10 * 0.00000005 * 0.93= 4.65e-7P(X = 10) = nC10 * p^10 * (1-p)n-10= 10C10 * 0.07^10 * (1-0.07)^0= 1 * 2.8243e-14 * 1= 2.8243e-14P(X ≥ 7) = 0.00416 + 0.000011 + 4.65e-7 + 2.8243e-14= 0.00416Therefore, the probability that 7 or more packs are defective is 0.00416 (approx).
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Can the following side measures make a triangle: 11in., 12in. and 13in?
Answer:
Yes
Step-by-step explanation:
Hello There!
Remember the sum of the two shorter sides has to be greater than the largest side in order for it to be a triangle
11+12 must be greater than 13
11+12=23
23>13 therefore the side lengths can form a triangle
A TV originally priced at $948 is on sale for 35% off. 4.a) Find the discount amount 4.b) Find the price after discount X There is then a 9.2% sales tax. 4.c) Find the tax amount 4.d) Find the final price after including the discount and sales tax
The discount amount is $331.80. The price after discount is $616.20. The sales tax amount is $56.63. The final price is $672.83.
A TV originally priced at $948 is on sale for 35% off. We are to find the discount amount and the price after discount.
The original price of the TV = $948
The percentage discount = 35%.
Let X be the price after discount.
We can find X as follows:
Discount = 35% of original price
= 35% of 948= (35/100) × 948= $331.80
Price after discount (X) = Original price - Discount
= $948 - $331.80= $616.20
Therefore, the price after discount is $616.20.
Now we are to find the tax amount and the final price after including the discount and sales tax.
The sales tax is 9.2%.
We can find the tax amount as follows:
Tax amount = 9.2% of price after discount
= 9.2% of $616.20= (9.2/100) × 616.20= $56.63
Now, the final price after including the discount and sales tax = Price after discount + Tax amount
= $616.20 + $56.63= $672.83
Therefore, the final price after including the discount and sales tax is $672.83.
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