The scale factor can only be found by comparing the lengths of the two segments.
If segment AB' is a dilation of segment AB, then the scale factor of the dilation is the ratio of the length of the dilated segment AB' to the length of the original segment AB.
Mathematically, the scale factor (k) is given by:k = length of AB' / length of AB
Since segment AB' is a dilation of segment AB, we can assume that AB' is longer or shorter than AB. If AB' is longer than AB, then the scale factor k is greater than 1, which means that the segment has been enlarged. If AB' is shorter than AB, then the scale factor k is between 0 and 1, which means that the segment has been reduced. Without knowing the actual lengths of segments AB and AB', we cannot determine the scale factor of the dilation. The scale factor can only be found by comparing the lengths of the two segments.
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Which of the following are true? false? Explain or give examples. (a) The median and the average of any list are always close together. (b) Half of a list is always below average. (c) With a large, representative sample, the histogram is bound to follow the normal curve quite closely. (d) If two lists of numbers have exactly the same average of 50 and the same SD of 10, then the percentage of entries between 40 and 60 must be exactly the same for both lists .
The given statement "histogram is bound to follow the normal curve quite closely and the percentage of entries between 40 and 60 must be exactly the same for both lists." are True. As large representative sample follows normal curve and mean and standard deviation is approx 68%. So, the correct answer true is C), D) are true and A), B) are false.
The median and the average of any list are not always close together.
The median is the middle value in a list when the list is sorted in ascending or descending order, while the average (also called the mean) is the sum of all the values divided by the number of values.
For example, consider the following list
1, 2, 3, 4, 100
The median is 3, while the average is (1+2+3+4+100)/5 = 22.
In this case, the median and the average are not close together at all, since the median is much smaller than the average. So, this statement is false.
Half of a list is not always below average.
This statement is only true if the list is sorted in ascending or descending order. In that case, if the list has an odd number of values, then the median (which is the middle value) is equal to the average. If the list has an even number of values, then the median is the average of the two middle values.
However, if the list is not sorted, then it is possible for more than half of the values to be above the average.
For example, consider the following list
1, 1, 1, 1, 100
The average is 20, but only 2 out of the 5 values are below the average. The given satement is False.
With a large, representative sample, the histogram is likely to follow the normal curve quite closely.
This statement is true, according to the Central Limit Theorem. The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the mean will be approximately normal, regardless of the shape of the population distribution.
For example, if we take a large number of random samples of the same size from a non-normal population (such as a uniform distribution), then the histogram of the sample means will eventually approximate a normal distribution.
If two lists of numbers have exactly the same average of 50 and the same SD of 10, then the percentage of entries between 40 and 60 must be exactly the same for both lists.
This statement is true, since the percentage of entries between 40 and 60 can be calculated using the standard normal distribution.
The z-score for 40 is (40-50)/10 = -1, and the z-score for 60 is (60-50)/10 = 1.
Using a standard normal distribution table or a calculator, we can find that the percentage of values between -1 and 1 is approximately 68%. Therefore, if both lists have the same mean and the same standard deviation, then the percentage of values between 40 and 60 must be 68% for both lists.
So, the correct option for true are C), D) and A), B) are false.
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Find the missing side in each triangle using any method.Check your answers using a different method.
AC=
YC=
tis noteworthy that the picture above has a typo, is not YC, it should be YX.
the triangles are similar by AA, therefore
[tex]\cfrac{16}{8}=\cfrac{YX}{17}\implies 2=\cfrac{YX}{17}\implies 34=YX \\\\\\ \cfrac{16}{8}=\cfrac{30}{AC}\implies 2=\cfrac{30}{AC}\implies AC=\cfrac{30}{2}\implies AC=15[/tex]
When Craig started contributing to superannuation, he paid $500 into the fund at the beginning of each financial year. His fund pays 8.7% p.a annually compounding.
Craig decided to increase his yearly investment to $900 because inflation was increasing the cost of living. He made 4 investments of $500, all the following investments were $900 pa.
Using the formula for sum of a geometric progression to calculate how much Craig's superannuation will be worth at the end of 15 years.
The correct answer is $9732.09, with each amount at the end the two periods of different contribution being $6194.64, and $16,905.13, but please show working out and all steps to produce final answer.
[tex]\Large \textsf{Sum of a geometric progression: $\rm S_n = \frac{a(1-r^n)}{1-r}$ ,}\\\normalsize \textsf{where a = first term, r = common ratio, S$_{\sf n}$ = sum of $n$ terms}[/tex]
Thanks!
Craig's superannuation will be worth of $22,099.77 at the end of 15 years.
Given that Craig made 4 investments of $500 in four years. To find out the superannuation we have to find the remaining 11 investments he made in the remaining 11 years from a total of 15 years.
For the first four investments,
a = $500
r = 1.087 [ given interest rate is 8.7% per annum ]
n = 4
By, substituting all these values in the given equation,
S1 = [tex]\frac{500(1-1.087^{4}) }{1-1.087}[/tex] = $6194.64
Similarly for the remaining 11 years,
a = $900
r = 1.087
n = 11
S2 = [tex]\frac{500(1-1.087^{11}) }{1-1.087}[/tex] = $16,905.13
Total superannuation = S1 + S2 = $6194.64 + $16,905.13 = $22,099.77.
From the above explanation, we can conclude that Craig's total superannuation will be worth $22,099.77
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Each year Upchester United plays against Upchester City in a local derby match. The number of goals scored in a match by United is denoted by u and the number of goals scored in a match by City is denoted by c. The number of goals scored in the past 15 matches are summarised by u ( 1 ) 2 2 5 Σ − = , u ( 1 ) 9 Σ − = , c 39 2 Σ = and c 19 Σ = . a How many goals have been scored altogether in these 15 matches? b Show that u 58 2 Σ = . c Find, correct to 3 decimal places, the variance of the number of goals scored by the two teams together in these 15 matches.
1. The total number of goals for the 15 matches is 43.
2. To show that Σ u² = 58, we use Σ(u - 1)² = 25
Σ(u - 1)² = 25 ⇒ Σ(u² - 2u + 1) = 25
Σu² - 2Σu + Σ = 25 ⇒ Σu² - 2(24) + 15 = 25
Σu² = 25 + 48 - 15 → Σu² = 58
3. The variance of the teams together is 39.311
How did we calculate the total number of goal and variance?1. To find the total number of goals, we must establish that Σ(u + x) is the total number of goals.
TNG = Σu + Σx
Given that Σ(u - 1) = 9, it becomes
Σu - 15 = 9 ⇒ Σu = 9 + 15
Σu = 24
Given that Σu = 24 and Σx = 19
TNG = 24 + 19 = 43
we say
43 ÷ 15 = 2.866
We already know that Σx² = 39, Σu² = 58.
Σ(u - 1)Σx = 9 × 19 = 171
Σux - Σx = 171
Σux - 19 = 171
Σux = 190
Σt² = 58 + 2(190) + 39
= 58 + 380 + 39
= 477
Variance = 477
15 - 2.866
Variance = 477/12.134
Variance = 39.311
The answer provided is based on the full question below;
Each year Upchester United plays against Upchester City in a local derby match. The number of goals scored in a match by United is denoted by u and the number of goals scored in a match by City is denoted by c.
The number of goals scored in the past 15 matches are summarized by
Σ(u - 1)² = 25, Σ(u - 1) = 9 Σx² = 39 and Σx = 19
a How many goals have been scored altogether in these 15 matches?
b Show that Σu² = 58.
c. Find, correct to 3 decimal places, the variance of the number of goals scored by the two teams together in these 15 matches.
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Subtract 3/16-3/9. .. . . .. . . . . . .. . . . .. . . . . . .. . . . . . . . .. . . . ..
Subtracting 3/16-3/9 will gives us: -7/48.
What is subtraction?First step is for us to find a common denominator.
3/16 - 3/9
= (3/16)× (9/9) - (3/9)× (16/16)
= 27/144 - 48/144
Second step is for us to combine the fractions:
3/16 - 3/9
= (27 - 48)/144
= -21/144
= -7/48
Therefore 3/16 - 3/9 is -7/48.
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Each bag of Candy can fill 85 square centimeters. How many bags of candy will Jada need to purchase to fill the pinata?
In the regression model Yi = 30 + B1Xi + B2Di + B3(Xi x Di) + ui, where X is a continuous variable and D is a binary variable, ß3:
A) indicates the slope of the regression when D=1.
B) has a standard error that is not normally distributed even in large samples since D is not a normally distributed variable.
C) indicates the difference in the slopes of the two regressions.
D) has no meaning since (Xi x Di) = 0 when Di = 0.
In the given regression model, Yi = 30 + B1Xi + B2Di + B3(Xi x Di) + ui, B3 represents the interaction term between the continuous variable Xi and the binary variable Di.
The coefficient B3 indicates the difference in the slopes of the two regressions when Di = 0 and Di = 1.
Thus, it shows how the effect of Xi on Yi changes depending on the value of Di.
C) indicates the difference in the slopes of the two regressions.
In the given regression model, ß3 is the coefficient of the interaction term between X and D, which is (Xi x Di). The interaction term shows how the effect of X on Y changes when D changes from 0 to 1.
Therefore, the coefficient ß3 indicates the difference in the slopes of the two regressions (when D = 0 and D = 1), which represents the effect of the interaction between X and D on Y.
Option A is incorrect because the slope of the regression when D=1 is given by the coefficient ß1 (the coefficient of X), not by ß3.
Option B is incorrect because the standard error of the coefficient ß3 can be normally distributed in large samples, even if D is not normally distributed.
Option D is incorrect because the product (Xi x Di) is zero when Di = 0, but ß3 can still have a non-zero value when Di = 0.
C) indicates the difference in the slopes of the two regressions.
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A bank offers a CD that pays a simple interest rate of 7%. How much must you put in this CD now in order to have $10,920 to replace all the windows in your house in 8 years?
You would need to put approximately $19,500 into the CD now in order to have $10,920 in 8 years.
To determine how much you must put into the CD now, we can use the formula for simple interest:
I = P * r * t
Where:
I is the interest earned
P is the principal amount (initial investment)
r is the interest rate
t is the time in years
In this case, we know the interest rate is 7% (or 0.07) and the time is 8 years. We want to find the principal amount (P) that will result in $10,920 in 8 years. So we rearrange the formula to solve for P:
P = I / (r * t)
Substituting the given values:
P = 10,920 / (0.07 * 8)
P = 10,920 / 0.56
P ≈ $19,500
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The Columbia Power Company experiences power failures with a mean of u=210 per day. Find the probability that there are exactly two power failures in a particular day.Group of answer choices0.0270.0850.0180.036
The Columbia Power Company experiences power failures with a mean of µ=210 per day. To find the probability that there are exactly two power failures in a particular day, we can use the Poisson probability formula:
P(x) = (e^(-µ) * (µ^x)) / x!
In this case, x = 2 (since we want to find the probability of exactly two power failures) and µ = 210. Plugging in the values, we get:
P(2) = (e^(-210) * (210^2)) / 2!
Calculating this expression, we get P(2) ≈ 0.018. So, the probability that there are exactly two power failures in a particular day is approximately 0.018.
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A park in a subdivision is triangular shaped. Two adjacent sides of the park are 503 feet and
516 feet. The angle between the sides is 38°. To the nearest unit, what is the area of the park in
square yards?
17,755 square yards
26,632 square yards
8,877 square yards
11,363 square yards
The area of the park in square yards is: 79901 square yards
What is the area of the triangle?We are given that the two adjacent sides of the triangle formed will have the lengths as:
a = 503 ft
b = 516 ft
C = 38°.
Using law of cosines, we have:
c = √(503² + 516² - (2 * 503 * 516 * cos 38))
c = 332 yards
Area of a triangle with three sides given is:
A = √(s(s - a)(s - b)(s - c)
where:
s = (a + b + c)/2
s = (503 + 516 + 332)/2
s = 675.5 yards
A = √(675.5(675.5 - 503)(675.5 - 516)(675.5 - 332))
A = 79901 square yards
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May Someone Help Me?
Assume that a hat contains four​ bills: a
​$5 bill, a $10 ​bill, a ​$20
​bill, and a $100
bill. Each bill is equally likely to be selected. Two bills are to be selected at random with replacement. Construct a sample space and determine the probability that both bills are $100
bills.
The probability that both bills are $100 bills when selecting two bills at random with replacement from the hat is 1/16.
To find the probability that both bills are $100 bills when selecting two bills at random with replacement from a hat containing a $5, $10, $20, and $100 bill, we'll first construct a sample space and then calculate the probability.
Step 1: Construct the sample space.
Since there are four bills and we're selecting two with replacement, there are a total of 4 x 4 = 16 possible outcomes. The sample space is as follows:
{$5, $5}, {$5, $10}, {$5, $20}, {$5, $100},
{$10, $5}, {$10, $10}, {$10, $20}, {$10, $100},
{$20, $5}, {$20, $10}, {$20, $20}, {$20, $100},
{$100, $5}, {$100, $10}, {$100, $20}, {$100, $100}.
Step 2: Determine the probability that both bills are $100 bills.
In the sample space, there's only 1 outcome where both bills are $100 bills: {$100, $100}. Since there are 16 possible outcomes in total, the probability of both bills being $100 bills is:
1 (desired outcome) / 16 (total outcomes) = 1/16
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Geometry Pleeeease help !!!!Find the values of x and y. Write your answer in simplest form.
The value of x is 1.5 and value of y is 1.8 from the given triangle.
In the right triangle let us find the hypotenuse
9²+6²=x²
81+36=x²
117=x²
Take square root on both sides
√117=x
x=10.8=11
11/y=6
value y=11/6=1.8
9/x=6
x=9/6
=1.5
Hence, the value of x is 1.5 and value of y is 1.8 from the given triangle.
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If we have an effect, would error variance go away?
No, the presence of an effect does not necessarily imply that error variance will go away.
Why could not error variance go away?The presence of an effect does not necessarily imply that error variance will go away. In fact, error variance is an inherent part of any statistical model and represents the amount of variation in the response variable that is not explained by the predictor variables.
Even if a predictor variable has a significant effect on the response variable, there may still be some unexplained variation in the response that is attributable to error variance.
It is important to take into account and control for error variance in any statistical analysis, as it can affect the precision and accuracy of the estimates of the model parameters and can also influence the interpretation of the results.
One way to control for error variance is to use appropriate statistical methods, such as analysis of variance (ANOVA), regression analysis, or other modeling techniques that take into account the variability in the data.
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Find the height and slant height of the cone.
Round your answers to the nearest whole
number.
Surface area = 75.4 cm²
22
h≈
l
3 cm
cm
cm
The Height ≈ 4 cm and the Slant height ≈ 5 cm.
To solve for the height and slant height of the cone, we first use the formula for the surface area of a cone:
Surface Area = πrℓ + πr²,where r is the radius of the base, ℓ is the slant height, and π is approximately 3.14.
Since we are given the surface area (75.4 cm²) and the radius (3 cm), we can substitute these values into the formula and solve for ℓ:
75.4 = 3.14(3)(ℓ) + 3.14(3)²75.4 = 9.42ℓ + 28.2646.14 = 9.42ℓℓ ≈ 4.89Now that we have the slant height, we can use the Pythagorean theorem to find the height, h:
h² + 3² = 4.89²h² + 9 = 23.92h² ≈ 14.92h ≈ 3.86Rounding to the nearest whole number, we get the height ≈ 4 cm and the slant height ≈ 5 cm.
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Find the length of the missing measurement
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=2\\ h=1.6\\ A=2.2 \end{cases}\implies 2.2=\cfrac{1.6(2+b)}{2} \\\\\\ 4.4=1.6(2+b)\implies \cfrac{4.4}{1.6}=2+b\implies 2.75=2+b\implies \boxed{0.75=b}[/tex]
. use a model to predict the car's value after 5 years, rounded to the nearest dollar.
The predicted value of the car after 5 years is $6,000 (rounded to the nearest dollar).
To predict the car's value after 5 years, we can use a linear regression model. We will use the data points given in the problem statement to find the equation of a straight line that fits the trend in the data. Once we have this equation, we can plug in the value of 5 for x to predict the corresponding value of y, which represents the car's value after 5 years.
Using the data points (1, 18000) and (3, 12000), we can find the slope of the line:
slope = (y2 - y1) / (x2 - x1) = (12000 - 18000) / (3 - 1) = -3000
Next, we can use the slope-intercept form of a line to find the equation of the line:
y = mx + b, where m is the slope and b is the y-intercept
Using the point (1, 18000) and the slope we just found, we can solve for b:
18000 = -3000(1) + b
b = 21000
So, the equation of the line is:
y = -3000x + 21000
To predict the car's value after 5 years, we can plug in x = 5 and solve for y:
y = -3000(5) + 21000 = 6000
Therefore, the predicted value of the car after 5 years is $6,000 (rounded to the nearest dollar).
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___________ is the study of the possible payoffs and probabilities associated with a decision alternative or a decision strategy in the face of uncertainty.
Decision analysis is the study of the possible payoffs and probabilities associated with a decision alternative or a decision strategy in the face of uncertainty.
This approach helps decision-makers evaluate various options and make informed choices under uncertain conditions.
The study of the possible payoffs and probabilities associated with a decision alternative or a decision strategy in the face of uncertainty is known as decision analysis.
Decision analysis is a systematic approach to decision-making that uses mathematical and statistical tools to evaluate different alternatives and their associated risks and rewards.
It involves identifying the possible alternatives, the possible outcomes, and the likelihood of each outcome, and then using this information to select the best course of action.
Decision analysis is commonly used in a wide range of fields, including business, engineering, healthcare, and environmental management.
In business, decision analysis is often used to evaluate investment opportunities, new product development, and strategic planning.
In engineering, decision analysis is used to evaluate design options and project risks.
In healthcare, decision analysis is used to evaluate treatment options and medical technology.
In environmental management, decision analysis is used to evaluate the risks and benefits of different policies and regulations.
The key steps in decision analysis include defining the problem, identifying alternatives, assessing probabilities, evaluating outcomes, and selecting the best alternative.
This involves a range of techniques, such as decision trees, utility theory, sensitivity analysis, and Monte Carlo simulation.
These techniques help decision-makers to evaluate the trade-offs between risks and rewards and make informed decisions in the face of uncertainty.
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Isla walked 3/4 mile each way to and from school on Wednesday. How many miles did isla walk that day
Answer:
Step-by-step explanation:
20.9 miles
What's Factoring Quadratics (when a does not = 1)
Factoring quadratics is a technique used to simplify and solve quadratic equations. When the leading coefficient (a) of the quadratic equation is not equal to 1, it becomes slightly more complicated to factor. To factor quadratics when a does not equal 1, one must use a method called grouping.
The first step is to multiply the coefficient of the leading term (a) by the constant term (c) of the quadratic equation. This gives you two numbers that add up to the coefficient of the middle term (b). These two numbers will be used to group the terms in the quadratic equation.
Next, the quadratic equation is split into two parts, where each part includes two terms that are grouped based on the two numbers obtained in the first step. From here, factoring can be done using the distributive property.
Once the equation is factored, it can be solved by setting each factor equal to zero and solving for the variables. It's important to remember to check solutions by plugging them back into the original equation.
In conclusion, factoring quadratics when a does not equal 1 involves using a method called grouping to factor the equation. This technique is slightly more complicated than when a equals 1, but it can still be easily mastered with practice.
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Which test should he use to analyze the data?
a. single sample t-test
b. independent t- test
c. paired t-test
d. One way ANOVA
To provide an accurate answer, I would need more context about the data and the research question being asked. However, I can provide a brief explanation of each test option:
a. Single sample t-test: Used when comparing a sample mean to a known population mean.
b. Independent t-test: Used when comparing the means of two independent groups.
c. Paired t-test: Used when comparing the means of two related groups or repeated measures.
d. One-way ANOVA: Used when comparing the means of three or more independent groups.
Please provide more information about the data and research question so I can recommend the appropriate test to analyze the data.
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Consider one side ab of a square abcd on the line y=2x-17 and the other two vertices c,d on the parabola y=x^2
The minimum intercept of line CD on the y-axis is 1.
Since AB is on the line y=2x-17, we can write the equation of the line as y=2x-17. We know that AB is a side of a square, so its length is equal to the distance between A and B. Therefore, we need to find the coordinates of A and B. Since the square is symmetric with respect to the line y=2x-17, the x-coordinate of the midpoint of AB is (17/2). Therefore, the x-coordinates of A and B are (17/2)-s and (17/2)+s, where s is half the length of AB.
Now, we need to find the value of s. Since AB is a side of a square, it is equal in length to the distance between C and D. We can find the equation of the line CD by using the coordinates of C and D, which are (x, x²) and (y, y²), respectively. Substituting these coordinates into the equation of the line, we get:
x² = 2x - 17 (equation 1)y² = 2y - 17 (equation 2)Solving for x and y in equations 1 and 2, we get:
x = 1 ± √18y = 1 ± √18Since AB is a side of a square, its length is equal to the distance between C and D, which is:
√[(y^2-x²)²+(y-x)²]
= √[(2√18)²+2²]
= 2√82
Therefore, s = √82.
Finally, we can find the y-intercept of CD by plugging in x=0 into the equation of the line CD, which is:
y = x + (y-x)/2y = (x+y)/2Substituting the values of x and y, we get:
y = (1 + √18)/2Therefore, the minimum intercept of line CD on the y-axis is 1.
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The complete question is:
Consider one sides AB of a square ABCD in order on line y=2x−17, and other two vertices C, D on y=x². The minimum intercept of line CD on the y-axis is
Jules is working on a title for his most recent work. he wants to call it "x meters under the sea" where x is rounded to the nearest whole number. to determine x he needs to find the number of meters in 20,000 leagues. he knows that there are 1609.3 meters in 1 mile. he also knows that there are 3.452 miles in 1 league. what is the correct value for x?
Answer: To find the number of meters in 20,000 leagues, we first need to convert the number of leagues to miles:
20,000 leagues * 3.452 miles/league = 69,040 miles
Next, we can convert the miles to meters:
69,040 miles * 1609.3 meters/mile = 111,030,472 meters
So the number of meters in 20,000 leagues is approximately 111,030,472 meters. To round this to the nearest whole number and use it as the value of x in the title, we can round it to:
x = 111,030,472 rounded to the nearest whole number = 111,030,000 meters
Therefore, Jules can call his most recent work "111,030,000 meters under the sea".
what is the length of x?
Answer:
x= 50!
Step-by-step explanation:
To find the hypotenuse, add the squares of the other sides, then take the square root.
Your bedroom measures 278
meters by 314
meters. What is the area?
Answer:
The area is 278 m × 314 m = 87,292 m^2.
Show that the numbers are all rational by writing each number as a ratio of integers.
0.3737373737...
0.3737373737... is a rational number and can be written as the ratio of two integers 37 and 99.
Let x = 0.3737373737...
Multiplying both sides of the equation by 100, we get:
100x = 37.37373737...
Subtracting x from 100x, we get:
99x = 37
Hence, x = 37/99, which is a rational number.
Therefore, we have shown that 0.3737373737... is a rational number and can be written as the ratio of two integers 37 and 99.
To check our answer, we can simplify 37/99 by dividing both the numerator and denominator by their greatest common factor, which is 1. This gives us the same expression, 37/99, confirming that it is indeed a rational number.
In general, any decimal that has a repeating pattern can be written as a ratio of two integers and is therefore a rational number. This is because the repeating pattern can be expressed as a finite sequence of digits that can be represented as a fraction with a power of 10 in the denominator, which can be simplified to a ratio of two integers.
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You are asked to solve for y in the equation –3 = 5y – 2x, given that x = –4. What is the first step you would take? A. Substitute –4 for x in the equation. B. Add 3 to both sides of the equation. C. Divide both sides of the equation by 3. D. Add 2x to both sides of the equation. Please select the best answer from the choices provided A B C D
Answer:
to get y easily you have to substitute for x in the first equation. the answer is A
Step-by-step explanation:
proving it:
-3=5y-2(-4)
-3=5y+8
then you can collect the like terms to get the final answer.
In a school election, Jared recieved 76 votes. 60% of the students did not vote for him. What was the total number of votes cast?
The total number of votes cast in the school election was 190.
Let's assume the total number of votes cast is represented by "T".
Since 60% of the students did not vote for Jared, it means that 40% of the students voted for him. We can calculate 40% of the total number of students as:
40% = 0.4
0.4T = Votes for Jared
We know that Jared received 76 votes, so we can set up the equation:
0.4T = 76
To find the total number of votes cast, we can solve for T:
T = 76 / 0.4
T = 190
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In a Poisson distribution, μ = 4.
a) What is the probability that x = 2? (Round the final answer to 4 decimal places.)
b) What is the probability that x ≤ 2? (Round the final answer to 4 decimal places.)
c) What is the probability that x > 2? (Round the final answer to 4 decimal places.)
The probability that x = 2 is approximately 0.1465, the probability that x ≤ 2 is approximately 0.2381, and the probability that x > 2 is approximately 0.7619, in a Poisson distribution with μ = 4.
a) The probability that x = 2 in a Poisson distribution with μ = 4 is given by the probability mass function:
[tex]P(x=2) = (e^-4)(4^2)/2! ≈ 0.1465[/tex]
b) The probability that x ≤ 2 in a Poisson distribution with μ = 4 is given by the cumulative distribution function:
P(x ≤ 2) = P(x=0) + P(x=1) + P(x=2)
[tex]= (e^-4)(4^0)/0! + (e^-4)(4^1)/1! + (e^-4)(4^2)/2![/tex]
≈ 0.2381
c) The probability that x > 2 in a Poisson distribution with μ = 4 is given by subtracting the probability of x ≤ 2 from 1:
P(x > 2) = 1 - P(x ≤ 2)
= 1 - 0.2381
≈ 0.7619
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A scale drawing of a billboard uses the scale 4 cm :11 ft. The
length of the billboard in the drawing is 15 cm. How long is the
actual billboard?
1.81.8 ft
2.41.25 ft
3.2.93 ft
4.165 ft
