Using the Unique factorization theorem for the following integers the standard factored form of 504 is 2³ x 3²x 7 , for 819 is 3² ×7×13 and for 5,445 is 3²×5×7².
The Unique Factorization Theorem states that any positive integer can be written as a product of prime numbers in a unique way. To write each of the integers in standard factored form.
Using this theorem, we can factorize any positive integer into its prime factors. Here are the steps to factorize a number:
Find the smallest prime factor of the number. Divide the number by this prime factor, and repeat step 1 with the result. Continue this process until the result is 1.The prime factors obtained in this process can then be multiplied together to obtain the standard factored form of the original number . Therefore,
)504 = 2³ x 3² x 7)819 = 3² ×7×13)5,445 =3²×5×7²To learn more about 'Unique Factorization Theorem':
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Which graph is the result of reflecting f(x) = 1/4(8) across the y-axis and then across the x-axis?
O
B
7
6
5
->
32
Shy
-8-7-6-5-4-3-2-1₁ 12 x
The graph οf g(x) is the same as its reflectiοn acrοss bοth the y-axis and the x-axis.
What is a graph?
A graph is a structure amοunting tο a set οf οbjects in which sοme pairs οf the οbjects are in sοme sense "related". The οbjects cοrrespοnd tο mathematical abstractiοns called vertices and each οf the related pairs οf vertices is called an edge.
Tο reflect a functiοn acrοss the y-axis, we replace x with -x in the functiοn. This gives us:
f(-x) = 1/4(8) = 2
This functiοn represents the reflectiοn οf f(x) acrοss the y-axis. Tο reflect this functiοn acrοss the x-axis, we replace f(-x) with -f(-x). This gives us:
-f(-x) = -2
Therefοre, the functiοn that results frοm reflecting f(x) = 1/4(8) acrοss the y-axis and then acrοss the x-axis is:
g(x) = -2
This is a hοrizοntal line that intersects the y-axis at -2. The graph οf g(x) is a straight line parallel tο the x-axis, and it dοes nοt change when reflected acrοss the y-axis οr x-axis. Sο, the graph οf g(x) is the same as its reflectiοn acrοss bοth the y-axis and the x-axis.
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3. Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion.
Test the claim that the mean lifetime of car engines of a particular type is greater than 220,000 miles. Sample data are summarized as n = 23.x=226,450 miles, and s- 11,500 miles. Use a significance
a=0.01. Select the correct test statistic and critical value.
Test statistic: t 2.6898. Critical value: t= -2.508.
Test statistic: t=2.6898. Critical value: t = 2.508.
Test statistic: t = -2.6898. Critical value: t = 12.508.
All change
Test statistic: z = 2.6898. Critical value: z = +2.508.
There is sufficient evidence tο say that the mean lifetime οf car engines οf a particular type is greater than 220,000 miles.
What is Hypothesis Test?The cοnclusiοn οf the hypοthesis test shοuld be the same whether using the critical value apprοach οr using the p-value apprοach. Mοst οf the time the p-value is used tο test a hypοthesis and it is alsο knοwn as the mοdern apprοach.
Hο: μ ≤ 220000
Ha: μ > 220000
Upper Tail
The significance level,
α = 0.01
The sample mean,
¯x = 226450
The sample standard deviation,
s = 11500
The sample size,
n=23
Test statistics:
[tex]$t={\frac{{\bar{x}}-\mu}{{\frac{s}{\sqrt{n}}}}}$[/tex]
[tex]$={\frac{226450-2220000}{\dfrac{11500}{\sqrt{23} y} }$[/tex]
≈ 2.69
Decision rule:
Reject the null if,
p-value ≤α
Decision rule:
Reject the null if,
|Calculated t |≥|Critical t|
Degrees of freedom:
Df = n−1
=22
We can use a t-distribution table, an online tool, or the following excel command to calculate the p-value using excel =TDIST(2.69, 22, 1):
p-value = P(t>2.69)
≈0.0067
Critical value of t using excel: =TINV(0.02, 22)
t(critical) = tα,
df = t(0.01,22)
≈2.51
Decision:
p-value ≈0.0067<α =0.0100
Reject the null.
Conclusion:
There is sufficient evidence to say that the mean lifetime of car engines of a particular type is greater than 220,000 miles.
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Complete question:
Use the quadratic formula to solve. Show work describe solution.
Answer:
Use the quadratic formula to solve. Show work describe solution.
Step-by-step explanation:
The quadratic formula is used to find the solutions (or roots) of a quadratic equation in the form ax^2 + bx + c = 0, where a, b, and c are constants.
The quadratic formula is:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
To use the quadratic formula, we need to plug in the values of a, b, and c from the given equation and solve for x.
For example, let's say we have the equation 2x^2 + 5x - 3 = 0.
Here, a = 2, b = 5, and c = -3.
Plugging these values into the quadratic formula, we get:
x = (-5 ± sqrt(5^2 - 4(2)(-3))) / 2(2)
Simplifying the expression inside the square root:
x = (-5 ± sqrt(49)) / 4
x = (-5 ± 7) / 4
We get two solutions:
x = (-5 + 7) / 4 = 1/2
x = (-5 - 7) / 4 = -3
So the solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3.
These solutions represent the points where the quadratic curve intersects the x-axis. They can also be used to factor the quadratic equation or graph the quadratic function.
Without dividing how can you decide which quotient is greater: 51 +31 or 5 1/4÷2 1/2
Answer:
51 + 31
Step-by-step explanation:
To compare which quotient is greater between 51+31 and 5 1/4 ÷ 2 1/2, we can use estimation.
First, we can estimate 51+31 to be around 80.
Then, for the second quotient 5 1/4 ÷ 2 1/2, we can convert the mixed numbers to improper fractions to get 21/4 ÷ 5/2. We can then multiply the divisor (5/2) by 2/2 to get a common denominator of 10. This gives us 21/4 ÷ 5/2 = 21/4 ÷ 5/10. We can then invert the divisor and multiply to get 21/4 x 10/5 = 21/2 or 10.5.
Since 80 is greater than 10.5, we can conclude that 51+31 is greater than 5 1/4 ÷ 2 1/2.
are the statements equivalent? "the number x is greater than 5 by 3" and x -3=5
Answer:
x=8
Step-by-step explanation:
x-3=5
+3=+3(cancel 3)
_____________
x=8
Solve for x in a triangle
In a right triangle, the trigonometric ratio x must be positive. There isn't an x solution that meets the requirements. The cosine and sine function values given are incompatible with a correct right triangle. x = -0.40
Which triangle is on the right?A right triangle is one with a 90 degree inner angle. The two arms of a right angle are made up of height and base.
The sum of the angles B and C's measurements in a right triangle is 90 degrees (since angle A is 90 degrees).
So we have:
B + C = 90
And since sin C = 3x + 0.31, we know that:
C = sin⁻¹(3x + 0.31)
B + sin⁻¹(3x + 0.31) = 90
Subtracting sin⁻¹(3x + 0.31) from both sides, we get:
B = 90 - sin⁻¹(3x + 0.31)
Now we can use the fact that cos B = x - 0.49:
cos(90 - sin⁻¹(3x + 0.31)) = x - 0.49
Using the identity cos(90 - θ) = sin(θ), we can rewrite this as:
sin(sin⁻¹(3x + 0.31)) = x - 0.49
Simplifying the left side using the inverse sine function, we get:
3x + 0.31 = x - 0.49
Subtracting x and 0.31 from both sides, we get:
2x = -0.80
Dividing both sides by 2, we get:
x = -0.40
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Let be a random variable with the following probability distribution:
Value (P(X=x)
x of X
10) (0.05)
20) (0.65)
30) (0.05)
40) (0.20
50) (0.05)
Find the expectation E (X) and variance Var (X) of X.
Answer:Let be a random variable with the following probability distribution
Value x of X / P (X=x)
20 / 0.05
30 / 0.05
40 / 0.35
50 / 0.20
60 / 0.35
Find the expectation of E(X) and variance Var (X) of X.
(A) E (x) = ?
(B) Var (X) =?
Step-by-step explanation:
A recent Health of Boston report suggests that 14% of female residents suffer from asthma as opposed to 6% of males (Boston Globe, August 16, 2010). Suppose 250 females and 200 males responded to the study.
Let p1 represent the population proportion of females with asthma and p2 the population proportion of males with asthma. Let females and males represent population 1 and population 2, respectively.
a. Develop the appropriate null and alternative hypotheses to test whether the proportion of females suffering from asthma is greater than the proportion of males.
H0: p1 − p2 ≤ 0; HA: p1 − p2 > 0
H0: p1 − p2 = 0; HA: p1 − p2 ≠ 0
H0: p1 − p2 ≥ 0; HA: p1 − p2 < 0
b. Calculate the value of the test statistic and its associated p-value. (Round intermediate calculations to 4 decimal places, "test statistic" value to 2 decimal places and "p-value" to 4 decimal places.)
Test statistic p-value c. At the 5% significance level, what is the conclusion? Do the data suggest that females suffer more from asthma than males?
No, since we reject H0
No, since we do not reject H0
Yes, since we reject H0
Yes, since we do not reject H0
The data suggest that females suffer more from asthma than males.
The null and alternative hypotheses for this problem are:
H0: p1 - p2 = 0; HA: p1 - p2 ≠ 0
The value of the test statistic is 3.7775 and its associated p-value is 0.0002. At the 5% significance level, the conclusion is that we reject the null hypothesis, and therefore we can say that the data suggest that females suffer more from asthma than males.
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A geometric sequence has first term 5 and common ratio 2. the sum of the first n terms of the sequence is 163 835. What is n ? [Answer format: integer, no units]
First term in a geometric sequence is 5, and common ratio is 2. The sum of the first n terms of the sequence is 163,835.
The following formula can be used to calculate the sum of the first n terms of a geometric sequence:
Sn = a (1 - rn) over (1 - r),
where
a is the first term,
r is the common ratio, and
n is the number of terms.
So, Sn = a (1 - rn) over (1 - r) => 163835 = 5 (1 - 2n) over (1 - 2).
Simplifying it, we have
163835 = 5 (1 - 2n) over (-1)
=> 163835 = -5 + 10n
=> 163840 = 10n
=> n = 16,384.
Therefore, the value of n is 16,384.
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She begins at sea level, which is an elevation of 0 feet.
She descends for 50 seconds at a speed of 5 feet per second.
She then ascends for 54 seconds at a speed of 4.4 feet per second.
Answer:
The diver descends:
50 seconds x 5 feet/second = 250 feet
The diver ascends:
54 seconds x 4.4 feet/second = 237.6 feet
Therefore, the total change in elevation is:
250 feet (descent) - 237.6 feet (ascent) = 12.4 feet
So, the diver's final elevation is:
0 feet (starting elevation) - 12.4 feet (change in elevation) = -12.4 feet
Therefore, the diver ends up 12.4 feet below sea level.
Answer:
it is 1
Step-by-step explanation:
its is 1 2 3 hsvs jafsnsjhd jsusgsmsi jshsbjdg
A company that chipe crystal bowis claims that bowls anive undamaged in 95 percent of the shipments. Let the randomi variable represent the number of shipments with undamaged bowis in 25 randomly elected shipments, Fandom variable Grotows a binomial distribution with a mean of 23.75 shipments and a standard deviation of approximately 1.09 shipments. Which of the following is the best interpretation of the mean?A. Every shipment of 25 bowls will have 23.75 undamaged bowlsB. Every slypment of 25 bowls will have 23.75 damaged bowl.C. On average the company receives 23.25 is before receiving the first her with a damaged bowlD. For possible shipments of 25 average number of damaged shipment equal to 23.75E. for all possible shipment of size 25 the average number of undamaged shipment equal to 23.75
The best interpretation of the mean is A) "Every shipment of 25 bowls will have 23.75 undamaged bowls."
The question states that the company claims that 95% of their shipments arrive undamaged. This implies that the probability of a bowl being damaged in a shipment is 0.05.
Since the random variable G follows a binomial distribution with n=25 (number of shipments) and p=0.05 (probability of a shipment having a damaged bowl), the mean of G is given by np = 25 x 0.05 = 1.25.
However, the question asks about the number of undamaged bowls in a shipment, which is simply the number of bowls in a shipment minus the number of damaged bowls.
Therefore, the mean number of undamaged bowls in a shipment is 25 - 1.25 = 23.75. This means that on average, a shipment of 25 bowls will have 23.75 undamaged bowls.
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The number 2 is the first even counting number,4 is the second even number, 6 is the third even number, and so forth. What is the sum of the first 25th even counting numbers
The number 2 is the first even counting number,4 is the second even number, 6 is the third even number, and so forth. the sum of the first 25th even counting numbers is 650.
Since we are given that the first even counting number is 2 and each subsequent even counting number can be obtained by adding 2 to the previous one. so by using the formula for finding the 25th term of an arithmetic series which :
an=a+(n-1)d, where the nth term d is a common difference and a is the first term so, the 25th term is 2 + (25-1)*2 = 2 + 48 = 50. Now for finding the sum of the first 25 even counting numbers, we use the formula which is Sn = n /2 * (a1 + an), where Sn is the sum of the first n terms of the series, a1 is the first term, and an is the nth term. since in this n=25, a1=2 and an=50, so after substituting the values we get S25 = 25/2 * (2 + 50) = 25/2 * 52 = 650
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How is pi and apple pie related to each other?
Answer: Pie is the unofficial food of Pi Day; its symbol, π, is often carved into pie crusts.
Step-by-step explanation:
Answer:
You can divide and divide, but with pi, you never reach the end of the digits after a decimal point.
Step-by-step explanation:
This is why most people know pie as 3.14. It also means that the circumference is a bit more than 3 times the size of the diameter. It doesn't matter what circle you measure—the relationship will always be the same.
The research department at the home office of automobile accidents,the characterstics of the driver, and so an. A random sample 400 police written on single persons revealed 120 had at least one accident in previous three year period
The study collected data from a random sample of 400 police reports on single persons. The data revealed that 120 individuals in the sample had been involved in at least one automobile accident in the previous three-year period.
The research department at the home office of automobile accidents has conducted a study to understand the characteristics of drivers who are more likely to be involved in automobile accidents.
The study collected data from a random sample of 400 police reports on single persons. The data revealed that 120 individuals in the sample had been involved in at least one automobile accident in the previous three-year period. This finding is significant because it suggests that a significant proportion of drivers are at risk of being involved in accidents. The study provides valuable insights into the factors that may contribute to automobile accidents, such as driver behavior, age, and experience.
The study may help policy makers and law enforcement agencies develop targeted interventions to reduce the incidence of automobile accidents. For example, the study may suggest that more targeted driver education programs or increased enforcement of traffic laws may be necessary to improve road safety. Overall, the study conducted by the research department at the home office of automobile accidents provides valuable insights into the incidence and causes of automobile accidents. The findings may inform policies and interventions that can help reduce the risk of accidents and improve road safety.
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Can someone help me to work this out???????????????????????
Answer:
80 degrees
Step-by-step explanation:
Remember that corresponding angles are equal!
angle CBD and angle BFH are obviously corresponding angles.
(SEE ATTACHMENT IF YOU DON'T UNDERSTAND)
So, angle CBD = angle BFH = 100 degrees.
The angles of a line add to 180 degrees
angle BFH is 100 degrees and one part of this line. So the other part (aka angle x) is 180 - 100 = 80 degrees.
Thus, x is 80 degrees.
a careless university student leaves her iclicker device behind with probability 1/4 each time she attends a class. she sets out with her iclicker device to attend 5 different classes (each class is in a different lecture theatre). part 1) if she arrives home without her iclicker device and she is sure she has the iclicker device after leaving the first class, what is the probability (to 3 significant figures) that she left it in the 5th class? probability
The probability of leaving it in any given class is 1/4, the probability of leaving it in the 5th class is 1/4, or[tex]0.250 (25.0%).[/tex]
The probability that the student left her iClicker device in the 5th class is 0.250 (25.0%). This is because the probability of leaving it in any given class is 1/4, and as she attends 5 different classes,
there is 5/4 or 1.25 chances of her leaving it in the 5th class.
To explain further, the probability of an event can be calculated by dividing the number of ways the event can occur by the total number of possible outcomes. In this case, the event is leaving the iClicker device in the 5th class, and the total number of possible outcomes is 5 (for the 5 classes).
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Ben knows that a line passes through the point (-3, 8) and has a slope of -3/4, but he needs to find the equation of the line. Therefore, he should substitute 8 for_______
and he should substitute -3 for _________, and he should substitute -3/4 for __________ into the Point-Slope Formula. He will need to __________ and simplify before solving for y = mx + b form.
Answer:
Ben knows that a line passes through the point (-3, 8) and has a slope of -3/4, but he needs to find the equation of the line. Therefore, he should substitute 8 for_______
and he should substitute -3 for _________, and he should substitute -3/4 for __________ into the Point-Slope Formula. He will need to __________ and simplify before solving for y = mx + b form.
Step-by-step explanation:
To use the Point-Slope formula to find the equation of the line, Ben should substitute the following values:
Substitute 8 for y, since the point (-3, 8) has a y-coordinate of 8.
Substitute -3 for x, since the point (-3, 8) has an x-coordinate of -3.
Substitute -3/4 for m, since the line has a slope of -3/4.
The Point-Slope formula is:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 8 = (-3/4)(x - (-3))
Simplifying the right-hand side, we get:
y - 8 = (-3/4)(x + 3)
To get the equation in y = mx + b form, we can start by distributing the (-3/4) to the x and the 3:
y - 8 = (-3/4)x - 9/4
Adding 8 to both sides, we get:
y = (-3/4)x + 23/4
So the equation of the line is y = (-3/4)x + 23/4.
Between which consecutive integer does the square root of 138 lie
The square root of 138 is between 11 and 12. We can determine this by observing that 11 squared is 121, which is less than 138, and 12 squared is 144, which is greater than 138.
Therefore, the square root of 138 must lie between 11 and 12. Another way to approach this problem is to use estimation. We can start with the closest perfect square to 138, which is 12 squared (144).
Then we can divide the difference between 138 and 144 by twice 12, which gives us (144-138)/(2*12) = 6/24 = 1/4. This means that the square root of 138 is approximately 12 - 1/4 = 11.75, which is between 11 and 12.
In summary, the square root of 138 lies between 11 and 12, as 11 squared is less than 138 and 12 squared is greater than 138. Alternatively, we can estimate the square root of 138 as 11.75, which is also between 11 and 12.
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Find an expression which represents the difference when (9x-4)(9x−4) is subtracted from (7x-2)(7x−2) in simplest terms.
Find the product of (7-8x)(3x^3-2x^2+x)
Answer:
Step-by-step explanation:
To find the product of (7-8x)(3x^3-2x^2+x), we need to use the distributive property of multiplication over addition/subtraction.
First, let's distribute the 7 across the second factor:
(7)(3x^3) - (7)(2x^2) + (7)(x)
This simplifies to:
21x^3 - 14x^2 + 7x
Next, we need to distribute the -8x across the second factor:
(-8x)(3x^3) + (-8x)(-2x^2) + (-8x)(x)
This simplifies to:
-24x^4 + 16x^3 - 8x^2
Now, we can combine the two simplifications:
(7-8x)(3x^3-2x^2+x) = 21x^3 - 14x^2 + 7x - 24x^4 + 16x^3 - 8x^2
Finally, we can combine like terms to simplify the expression:
-24x^4 + 37x^3 - 22x^2 + 7x
Therefore, the product of (7-8x)(3x^3-2x^2+x) is -24x^4 + 37x^3 - 22x^2 + 7x.
Which equation could represent the shown graph below
Oy=√x-2
O y = √x+2
O y = -√x+2
O y = -√x-2
Mei Mei has a part-time job at an ice skating rink selling hot cocoa. She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit. Based on the line of best fit, how many hot cocoas would you predict Mei Mei to sell if the day’s high temperature were 42^{\circ} ∘ F?
The following table shows how many hot cocoas Mei Mei would likely sell if the day's high temperature was 42 oF:
58.
How is a linear function defined?
The following is the definition of a linear function's slope and intercept:
y = mx + b.
The slope, or m, indicates the rate of change.
The value of y at x=0 is represented by the intercept, b.
At y = 100, where the function meets the y-axis, the intercept b is defined as follows:
b = 100.
As y decays to 94 when x rises to six, the slope m is calculated as follows:
m = (94 - 100)/(6 - 0) (6 - 0)
m = -1.
As a result, the function that forecasts how much hot chocolate will be sold at a high temperature.
Lack of Information
The graphic provided at the end of the response provides the linear function's graph.
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Solve each inequality (show work)
Answer:
5 less than or equal to x
Step-by-step explanation:
make x subject
If Alyssa has 6 shirts, 4 skirts, and 10 pairs of shoes, how many possible outfits can she make?
Answer: 240
You multiply them. 6x4x10 :)
The number of different outfits made by Alyssa as per the given number of shirt , skirts and shoes is equal to 240 outfits.
To find the number of possible outfits Alyssa can make, you multiply the number of choices for each item of clothing:
Number of shirts = 6
Number of skirts = 4
Number of pairs of shoes = 10
Substitute the values and multiply with each other
Total number of possible outfits
= 6 (shirts) × 4 (skirts) × 10 (shoes)
= 240 outfits.
Therefore, Alyssa can make 240 different outfits using her 6 shirts, 4 skirts, and 10 pairs of shoes.
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Find the probability of
drawing a spade, then
drawing a face card out of a
deck
The likelihood of pulling a spade followed by a face card from a deck is 3/52, or roughly 0.0588. (rounded to four decimal places).
What is the probability?The probability of drawing a spade from a deck of 52 cards is 13/52, or 1/4, since there are 13 spades in the deck.
Once a spade has been drawn and not returned to the deck, there are now 51 cards left in the deck, of which 12 are face cards (the Jack, Queen, and King of each suit). Therefore, the probability of drawing a face card given that a spade has already been drawn is 12/51.
To find the probability of both events happening together (drawing a spade and then a face card), we can multiply the probabilities of each event:
P(drawing a spade, then drawing a face card) = P(drawing a spade) x P(drawing a face card given that a spade has been drawn)
= (1/4) x (12/51)
= 3/52
Therefore, the probability of drawing a spade, then drawing a face card out of a deck is [tex]3/52[/tex] , or approximately [tex]0.0588[/tex] (rounded to four decimal places).
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Please help it’s for tmr, I only have 0 minute left
Leo has a number of toy soldiers between 27 and 54. If he wants to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
Leo has 48 toy soldiers.
What is the key concept is used to solve the question ?
This problem involves finding a number that satisfies certain conditions related to division with remainders. Specifically, the number must be divisible by 4 with no remainder, must leave a remainder of 6 when divided by 7, and must leave a remainder of 3 when divided by 5.
Calculating the number of toy soldiers :
Let's start by using the first condition to narrow down the possibilities for the number of toy soldiers. We know that the number must be divisible by 4 with no remainder, and it must be between 27 and 54. The multiples of 4 in this range are 28, 32, 36, 40, 44, 48, and 52.
Next, we can use the second condition to eliminate some of these possibilities. If we divide each of these numbers by 7, we get the following remainders:
28 ÷ 7 = 4 remainder 0
32 ÷ 7 = 4 remainder 4
36 ÷ 7 = 5 remainder 1
40 ÷ 7 = 5 remainder 5
44 ÷ 7 = 6 remainder 2
48 ÷ 7 = 6 remainder 6
52 ÷ 7 = 7 remainder 3
The only number in our list that leaves a remainder of 6 when divided by 7 is 48, so we can tentatively conclude that this is the number of toy soldiers.
Finally, we can check the third condition to make sure that 48 leaves a remainder of 3 when divided by 5. Indeed, 48 ÷ 5 = 9 remainder 3, so all of the conditions are satisfied.
Therefore, we can confidently say that Leo has 48 toy soldiers.
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Consider the circuit depicted in the diagram. Part (a) Write the equation which results from applying the loop rule to loop akledcba. Part (b) If the current going through the center of the loop is 65 A, what is the current going through the top, in amps?ξ = 24.0ν b 0.10Ω Β, 5.0Ω ε2, 48.0ν RS 20 Ω a τη: R w- 40 Ω e 0.50 Ω ΓΑ *0.20 Ω R 78 Ω 36.0V ξ: 6.0ν 9 10.05 Ω h
The equation which results from applying the loop rule to loop akledcba is Ia + Ik + Il + Ie + Id + Ic + Ib + Ia
The current going through the top is 2.71 A.
Itop = 65 A - (24.0 V/0.10 Ω) - (5.0 Ω * 2) - (48.0 V/20 Ω) - (40 Ω * 0.50 Ω) - (36.0 V/6.0 Ω) - (10.05 Ω * 0.20 Ω) - (78 Ω * 0.20 Ω) = 2.71 A.
For Part (a), the equation resulting from applying the loop rule to loop akledcba is:
Iakledcba = Ia + Ik + Il + Ie + Id + Ic + Ib + Ia
For Part (b), if the current going through the centre of the loop is 65 A, then the current going through the top in amps is:2.71 A.
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P(A) = 1/2 P(B) = 3/4 and P(A U B) = 3/8 Find P(A n B)
Answer:
P(A n B) = 1/4
Step-by-step explanation:
We know that:
P(A U B) = P(A) + P(B) - P(A n B)
Substituting the given values, we get:
3/8 = 1/2 + 3/4 - P(A n B)
Simplifying, we get:
P(A n B) = 1/4
Answer: P ( A n B ) = 7/8
Step-by-step explanation: P ( A U B ) = P(A) + P(B) - P( A n B )
3/8 = 1/2 + 3/4 - P( A n B )
3/8 = 5/4 - P ( A n B )
P ( A n B ) = 5/4 - 3/8
P ( A n B ) = 7/8
Select all of the reasons that the range is an appropriate measure of variability to describe the variation in the hours slept by eighth graders.
A double box plot showing hours sleeping. For seventh graders, the left whisker is at 7.5, the left edge of the box is at eight, the line inside the box is at 8.5, the right edge of the box is at nine, and the right whisker is at 9.5. For eighth graders, the left whisker is at seven, the left end of the box is at 7.5, the line inside the box is at eight, the right end of the box is at 8.5, and the right whisker is at nine. Screen reader support enabled.
All of the reasons that the range is an appropriate measure of variability to describe the variation in the hours slept by eighth graders include the following:
A. The data are evenly distributed between 7 hours and 9 hours.
D. There is no outlier in the data.
What is a range?In Mathematics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.
Mathematically, the range of a data set can be calculated by using the following mathematical equation;
Range = Highest number - Lowest number
By critically observing the double box-and-whisker plots or box plot for the variation in the hours slept by eighth graders, we can logically deduce that there is no outlier in the data because they are evenly distributed and centered about the mean.
In conclusion, the box-and-whisker plot or box plot is symmetrical.
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Answer:
Step-by-step explanation:
Yeah what the other guy said
what is -0.33333333333 as a fraction
Answer:
-1/3
Step-by-step explanation:
Answer:
-1/3
Step-by-step explanation: