Answer:
9. yes
10. no
11. yes
Step-by-step explanation:
A Pythagorean triple are 3 numbers that work out to be sides of a right triangle, for which we use the Pythagorean theorem, a^2 + b^2 = c^2.
"a" and "b" are the legs of the triangle, and "c" is the hypotenuse, which is the longest side.
For problem 9, we can plug in 5^2 + 12^2 = 13^2 and see if it's true. If it is true, those numbers are a Pythagorean triple. If it is false, than they are not.
9. 5^2 + 12^2 13^2 = 169
25 + 144 = 169
Squaring the legs and adding them come up with 169, which is "c" squared, the hypotenuse, or longest leg, 13. So, take the square root of 169, the answer of the left side of the equation, and we see that it works out.
10. 10^2 + 17^2 = 24^2 24^2 = 576
100 + 289 = 289
After doing the left side of the equation by squaring the shorter numbers, those add up to 289. The hypotenuse squared (24^2) = 576, which is not 289, so this set of numbers are not a Pythagorean triple
11. Here, you need to figure out what number 7[tex]\sqrt{5}[/tex] is to see if it's a leg or hypotenuse. I like to make it all into a square root of a number (desymplifying it) first. the 7 comes from a perfect square root, [tex]\sqrt{49}[/tex], so we can multiply these numbers under the radical sign to equal [tex]\sqrt{245}[/tex] which equals about 15.65, so it is the hypotenuse ("c") because it is the largest number.
7^2 + 14^2 (7[tex]\sqrt{5}[/tex])^2 = [tex]\sqrt{245}[/tex]^2 = 245
49 + 196 = 245
245 = 245
a^2 + b^2 = c^2 works out for this equation so it is a Pythagorean triple.
what is the equation of a line that is perpendicular to the line y= -3x+2 and passes through the point (6,8)
The solution is, : y = 1/3x+6, is the equation of a line that is perpendicular to the line y= -3x+2 and passes through the point (6,8).
We know that,
y = -3x+2 is in slope intercept form y = mx+b where m is the slope and b is the y intercept
The slope is -3
Perpendicular lines have slopes that are negative reciprocals
The slope of the perpendicular line is -1/-3 = 1/3
The equation of the new line is
y = 1/3x +b
Using the point that passes through the line ( 6,8) and substituting in for x and y
8 = 1/3(6) +b
8 = 2+b
8-2 =b
6 =b
The equation becomes
y = 1/3x+6.
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a family on a trip budgets $800 for meals and hotel accommodations. suppose the price of a meal is $40. in addition, suppose the family could afford a total of eight nights in a hotel if they don't buy any meals. how many meals could the family afford if they gave up two nights in the hotel? a. 2 b. 1 c. 8 d. 5\
if the family gives up two nights in the hotel, they could afford d) 5 meals
The family has a budget of $800 for meals and hotel accommodations. If they could afford eight nights in a hotel without buying any meals, we can determine the cost of one night at the hotel. To do this, we can divide the total budget by the number of nights:
$800 / 8 nights = $100 per night
Now, let's consider the scenario where the family gives up two nights in the hotel. This would free up $200 from their budget ($100 per night x 2 nights). We can then use this amount to determine how many meals the family can afford by dividing the available funds by the cost of one meal:
$200 / $40 per meal = 5 meals
Therefore, if the family gives up two nights in the hotel, they could afford 5 meals. The correct answer is d. 5.
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Which equation is equivalent to 4x+³ = 64?
O2x+6 = 24
O22x+6=26
O42x+6=42
O4x+3_46
Answer:
x=63/4
Step-by-step explanation:
rearrange the following steps in the correct order to find the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails.
Rank the options below. The probability is 1/16
1/16
Of these, only one will result in four heads appearing, namely THHHH. There are 16 equally likely outcomes of flipping a fair coin five times in which the first flip comes up tails.
The correct order of steps is 1, 2, 3, 4. And the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails, is 1/16.
To find the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails, we need to follow these steps in order:
1. Identify the total number of possible outcomes when a fair coin is flipped five times, which is 2^5 = 32.
2. Determine the number of outcomes in which the first flip is tails, which is also 16.
3. Out of the 16 outcomes where the first flip is tails, identify the number of outcomes in which exactly four heads appear. There is only one such outcome: THHHH.
4. Calculate the conditional probability by dividing the number of favourable outcomes (i.e. THHHH) by the number of total outcomes given the condition (i.e. the first flip is tails), which is 1/16.
Therefore, the correct order of steps is 1, 2, 3, 4. And the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails, is 1/16.
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If Alfie designs the wheels to have a diameter of 67. 5mm and a width of 29. 3mm, what volume of plastic will be required to make the cylinder, to the nearest mm3?
To make wheels of a diameter of 67.5 mm and a width of 29.3 mm, Alfie requires 104891.38 cubic mm volume of plastic.
A cylinder is a 3-Dimensional shape with 3 faces that are one curved face and 2 flat ends. The volume of a cylinder is given by the expression:
V = π[tex]r^2h[/tex]
r is the radius
h is the height
Given, diameter = 67.5 mm
radius = d ÷ 2 = 67.5 ÷ 2
= 33.75 mm
height = width = 29.3 mm
Volume = [tex]\frac{22}{7}*33.75*33.75*29.3[/tex]
= 104891.38 cubic mm
Therefore, the volume of the cylindrical wheel that Alfie designed is 104891.38 cubic mm.
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Find the surface area of the pyramid.
19 yd
12 yd
12 yd
Write your question here (Keep it simple and clear to get the best answer)
let's firstly convert the mixed fractions to improper fractions, then subtract.
[tex]\stackrel{mixed}{9\frac{6}{7}}\implies \cfrac{9\cdot 7+6}{7}\implies \stackrel{improper}{\cfrac{69}{7}}~\hfill \stackrel{mixed}{2\frac{3}{7}} \implies \cfrac{2\cdot 7+3}{7} \implies \stackrel{improper}{\cfrac{17}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{69}{7}~~ - ~~\cfrac{17}{7}\implies \cfrac{69-17}{7}\implies \cfrac{52}{7}\implies 7\frac{3}{7}[/tex]
a survey of 500 high school students was taken to determine their favorite chocolate candy. of the 500 students surveyed, 129 like snickers, 118 like twix, 145 like reese's peanut butter cups, 22 like snickers and twix, 54 like twix and reese's peanut butter cups, 55 like snickers and reese's peanut butter cups, and 8 like all three kinds of chocolate candy. how many students like twix and reese's peanut butter cups only? a) 209 b) 46 c) 140 d) 54 e) 148
Therefore, the correct option is (b) 46 that is the number of students who like Twix and Reese's peanut butter cups only (region D) by principle of inclusion-exclusion, we need to subtract the number of students who like Snickers, as well as the number of students who like all three kinds of candy, from the number of students who like Twix and Reese's peanut butter cups along with one or both of the other kinds of candy.
We can start by using the principle of inclusion-exclusion, which tells us that:
|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|
where |X| denotes the number of elements in set X.
Using the numbers given in the problem, we have:
|A| = 129
|B| = 118
|C| = 145
|A ∩ B| = 22
|B ∩ C| = 54
|A ∩ C| = 55
|A ∩ B ∩ C| = 8
Substituting these values into the formula, we get:
|A ∪ B ∪ C| = 129 + 118 + 145 - 22 - 55 - 54 + 8 = 269
This tells us that 269 students like at least one of the three kinds of chocolate candy.
To find the number of students who like Twix and Reese's peanut butter cups only (region D), we need to subtract the number of students who like Snickers, as well as the number of students who like all three kinds of candy, from the number of students who like Twix and Reese's peanut butter cups along with one or both of the other kinds of candy:
|D| = |B ∩ C| - |A ∩ B ∩ C|
= 54 - 8
= 46
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An employee started a new job and must enroll in a new family health insurance plan. One of the plans involves prescription drug coverage. The
employee estimates that the entire family will fill 10 prescriptions per month, totaling $1,250. The employee has two options to choose from:
Option A: $75 monthly premium; 80% coverage for all prescription costs
Option B: $45 monthly premium; 75% coverage for first $600 in prescription costs, then 85% coverage for all prescription costs over $600
Which option would result in the highest overall cost for the employee, and by how much?
O Option A has the highest overall cost by $77.50.
Option B has the highest overall cost by $77.50.
O Option A has the highest overall cost by $32.50.
O Option B has the highest overall cost by $32.50.
The option that would result in the highest overall cost for the employee is C. Option A has the highest overall cost by $32.50.
How to calculate the valueOption A:
Monthly premium = $75
Out-of-pocket cost for prescriptions = 0.2 × $1250
Total monthly cost = $75 + $250 = $325
Option B:
Monthly premium = $45
Out-of-pocket cost for first $600 in prescriptions = 25% × $600 = $150
Out-of-pocket cost for prescriptions over $600 = $97.50
Total monthly cost = $29250
he correct option is C.
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g suppose we want to test the null hypothesis that, in two independent normal random samples, the variance of the first group is twice as big as that of the second group. that is:
To test the null hypothesis that the variance of the first group is twice as big as that of the second group in two independent normal random samples, you can use the F-test. The null hypothesis (H0) would be stated as follows:
[tex]H0: σ1^2 = 2 * σ2^2[/tex]
To conduct the F-test, calculate the F-statistic using the sample variances (s1^2 and s2^2) from both groups:
F = s1^2 / (2 * s2^2)
Next, compare the calculated F-statistic to the critical F-value found in the F-distribution table at a chosen significance level (typically α = 0.05) and degrees of freedom for both groups (n1-1 and n2-1).
If the F-statistic is greater than the critical F-value, you would reject the null hypothesis, concluding that there is significant evidence that the variance of the first group is not twice as big as that of the second group. If the F-statistic is less than or equal to the critical F-value, you would fail to reject the null hypothesis, indicating that there isn't enough evidence to conclude that the variances are different as stated.
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please help me with the question :))
Answer:
4th option
Step-by-step explanation:
to find the surface you need to find the area of the base square first.
7 in × 7 in = 49 in^2
then find the triangular sides
9 in × 7 in × 1/2 =31.5 in^2
31.5 in^2 × 4 = 126 in^2
so 126in^2 +49in^2 = 175in^2
biochem determine the number of reducing equivalents, where 1 mol of electrons are donated by 1 reducing equivalents, produced by the complete oxidation of linoleic acid (c18h32o2) from part a.express your answer as an integer.
The complete oxidation of linoleic acid (C18H32O2) produces 16 reducing equivalents.
To determine the number of reducing equivalents produced by the complete oxidation of linoleic acid (C18H32O2), we need to follow these steps:
1. Determine the number of hydrogen atoms in linoleic acid: Linoleic acid has the molecular formula C18H32O2, which contains 32 hydrogen atoms.
2. Divide the number of hydrogen atoms by 2: Since 1 mole of electrons is donated by 1 reducing equivalent, and each pair of hydrogen atoms (H2) contributes 2 moles of electrons, we need to divide the number of hydrogen atoms by 2 to find the number of reducing equivalents.
32 hydrogen atoms ÷ 2 = 16 reducing equivalents
So, the complete oxidation of linoleic acid (C18H32O2) produces 16 reducing equivalents.
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the empirical (68-95-99.7%) rule allows statisticians to determine the probability of raw scores occurring within a set of data
The empirical rule (68-95-99.7%) is a widely used guide in statistics that helps determine the probability of occurrence of a raw score in a set of statistical data. This rule, also known as the rule of three sigma.
What is Three-Sigma Rule?
It states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean,on average, 99.7% of the data fall within three standard deviations.
This rule is useful for understanding the distribution of data and can be used to make predictions and draw conclusions about a population based on a sample. Statisticians often rely on this rule when analyzing data and making decisions based on probability calculations.
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suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.52 and a standard deviation of 0.38. using the empirical rule, what percentage of the students have grade point averages that are at least 1.76? please do not round your answer.
The percentage of students with a GPA of at least 1.76 is 100% - 2.5% = 97.5%.
In a bell-shaped distribution, the empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
To find the percentage of students with a GPA of at least 1.76, we need to calculate the number of standard deviations between the mean (2.52) and 1.76.
(2.52 - 1.76) / 0.38 ≈ 2 standard deviations below the mean
Since 95% of the data falls within two standard deviations of the mean, and we're considering two standard deviations below the mean, the remaining 5% is split between the tails. Therefore, 2.5% of the students have a GPA below 1.76.
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The populations and land areas of four cities in Texas are shown. which statements are true? Select three options.
The true statements about the populations and land areas are:
The population density for City B can be found using the ratio 48,592 : 26.The population density of City B is greater than that of City C.City D has the lowest population density of the four cities.Determining the population densityThe population density of an area is obtained by dividing the population of the city or village by the area or land mass. Population density is defined as the population per unit of land area.
Based on the available information, we can say that the population density of city B is obtained with the ratios of population and density. Also, the calculation of the population densities will show that City B is greater than City C.
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Consider three random variables, U, V, and W. Suppose we know that U = 3V+2 and U = 5W – 23. If E(V) = -5, evaluate E(W). OA-13 13 OB- OC.-3 36 OD 5 O E 2
Consider three random variables, U, V, and W. The answer is E(W) = 2.
To solve for E(W), we need to use the fact that U is equal to both 3V+2 and 5W-23. We can set these two expressions equal to each other:
3V + 2 = 5W - 23
Solving for V in terms of W, we get:
V = (5W - 25) / 3
Now we can use the formula for the expected value of a linear function of a random variable:
E(aX + b) = aE(X) + b
In this case, we have:
V = (5W - 25) / 3
So:
E(V) = E((5W - 25) / 3) = (5/3)E(W) - 25/3
We know that E(V) = -5, so we can substitute that in:
-5 = (5/3)E(W) - 25/3
Solving for E(W), we get:
E(W) = (-5 + 25/3) / (5/3) = 2
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Please help!!!!!
Given the expression: 6x¹0 - 96x²
Part A: Rewrite the expression by factoring out the greatest common factor. (
Part B: Factor the entire expression completely. Show the steps of your work.
The expression using the greatest common factor is 6x²(x⁸ - 16).
The complete factored form of the expression is 6x²(x⁴ + 4)(x² + 2)(x² - 2).
What is the greatest common factor?The greatest common factor of function 6x¹⁰ - 96x², is 6x².
6x¹⁰ - 96x² = 6x²(x⁸ - 16)
The complete factorization of the expression is calculated as follows;
expand the function x⁸ - 16;
x⁸ - 16 = (x⁴ + 4)(x⁴ - 4)
We can also simplify the function x⁴ - 4 further as shown below;
x⁴ - 4 = (x² + 2)(x² - 2)
The complete factored form of the function 6x¹⁰ - 96x² is calculated as;
6x¹⁰ - 96x² = 6x²(x⁴ + 4)(x² + 2)(x² - 2)
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identify the surface with the given vector equation. r(s, t) = s sin(9t), s2, s cos(9t)
The surface with the given vector equation is a portion of a cone with the axis along the y-axis and opening angle of 90 degrees.
The surface with the given vector equation r(s, t) = (s sin(9t), s^2, s cos(9t)) is a helicoid. The helicoid is generated by a line segment moving along a helical path while remaining perpendicular to the helix's axis. In this case, the helicoid has a variable height s^2 and is wrapped around the z-axis with a frequency of 9.
Vector equations are used to represent the lines or planes in a three-dimensional framework. The three-dimensional plane requires three coordinates with respect to the three-axis and here the vectors are helpful to easily represent the vector equation of a line or a plane. In a three-dimensional framework the unit vector along the x-axis is ^i, the unit vector along the y-axis is ^j, and the unit vector along the z-axis is ^k.
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Write the following Numbers in percentage and total percentage
47.5, 64.5, 42, 54.5, 64.5, 54.5, 54.5, 54.5
pls needed urgently
Answer:
To convert each number to a percentage, we can simply multiply it by 100.
47.5 = 47.5%
64.5 = 64.5%
42 = 42%
54.5 = 54.5%
64.5 = 64.5%
54.5 = 54.5%
54.5 = 54.5%
54.5 = 54.5%
To find the total percentage, we can add up all the percentages and divide by the total number of values. In this case, there are 8 values.
Total percentage = (47.5 + 64.5 + 42 + 54.5 + 64.5 + 54.5 + 54.5 + 54.5) / 8
Total percentage = 437.5 / 8 = 54.6875%
Therefore, the total percentage of the given numbers is 54.6875%.
Step-by-step explanation:
To compare the quantitative responses to the two conditions in a paired design, find the difference between the response within each pair. Then compare which of the following to these paired differences? the two-sample z procedures the one-sample z procedures the two-sample t procedures the one-sample t procedures
To compare the quantitative responses to the two conditions in a paired design, the differences between the response within each pair are used. These paired differences can be compared to the appropriate statistical procedures to determine the significance of the results.
For paired designs, the appropriate statistical procedure is the one-sample t procedure. This procedure is used to compare the mean of the paired differences to a hypothesized value, such as zero. The null hypothesis is that the mean difference is equal to zero, indicating no significant difference between the two conditions. If the calculated t-value is greater than the critical value, the null hypothesis can be rejected, indicating a significant difference between the two conditions.
In cases where the sample size is large and the population standard deviation is known, the two-sample z procedure can also be used. This procedure compares the difference between the means of the two samples to a hypothesized value. However, this procedure is less commonly used for paired designs.
The two-sample t procedure is used for independent designs, where two samples are selected from different populations. This procedure compares the means of the two samples to each other, rather than comparing the paired differences within each sample.
In summary, for paired designs, the appropriate statistical procedure is the one-sample t procedure, while the two-sample z procedures and the two-sample t procedures are used for independent designs.
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Which is a function? {(7, 2), (100, 10), (13, –7), (7, 9), (10, 100), (4, –2), (5, 5)} {(1000, 10), (1000, 12), (1000, 16), (100, 5), (100, 7), (78, 3), (90, 5)} {(6, 3), (5, 2), (4, 1), (3, 0), (4, –1), (5 ,–2), (6 ,–3)} {(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}
Answer:
{(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}
Step-by-step explanation:
In a function, all x-coordinates must be different.
{(7, 2), (100, 10), (13, –7), (7, 9), (10, 100), (4, –2), (5, 5)}
7 appears twice as an x-coordinate. Not a function.
{(1000, 10), (1000, 12), (1000, 16), (100, 5), (100, 7), (78, 3), (90, 5)}
1000 appears 3 times as an x-coordinate. Not a function.
{(6, 3), (5, 2), (4, 1), (3, 0), (4, –1), (5 ,–2), (6 ,–3)}
4 appears twice as an x-coordinate. Not a function.
{(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}
All x-coordinates are different. Function.
Two marbles are randomly pick with replacement from a bag containing 2 red marbles, 3 white marbles, 4 green marbles, and 5 yellow marbles. What is the total number of possible outcomes of the experiment?
there are 4 kind of marble
6 possibilities of different chosing
6+4 = 10
Please help quick
In ΔPQR, sin P = 0.4, sin R = 0.5 and r = 14. Find the length of p.
The length of the side p is given as 11.2.
How to solve for length of sides of a triangleBy applying the Law of Sines, we can find the length of any side of the triangle. The law of sines states that for any triangle with sides of lengths a, b, and c opposite angles A, B, and C, respectively.
Mathematically,
sin A / a = sin B / b = sin C / c
In this case, we know the values of sin P and sin R, and the length of side r. We want to find the length of side p. We can set up the equation as follows:
sin P / p = sin R / r
Substituting the given values, we get:
sin P / p = 0.5 / 14
Solving for p, we get:
p = sin P / (0.5 / 14)
p = sin P * 28
p = 0.4 * 28
p = 11.2
Therefore, the length of side p is 11.2.
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Find the number of years for 2700 to grow to 15000 at 6% compound semiannually
It will take approximately 14.4 years for $2,700 to grow to $15,000 at a 6% compound interest rate, compounded semiannually.
A equals the projected value, in this case $15,000.
P is equal to the current value, in this case $2,700.
r = 6%, or 0.06 in decimal form, is the yearly interest rate.
The number n represents the number of times the interest is compounded yearly (because it is compounded twice annually).
t = the duration in years
Using the values we hold in place of:
15000 = 2700(1 + 0.06/2)^(2t)
by 2700, divide both sides.
15000/2700 = (1 + 0.06/2)^(2t)
Simplify:
5.56 = (1.03)^(2t)
Consider both sides' natural logarithms:
ln(5.56) = ln(1.03)^(2t)
Using the logarithm property, ln(ab) = b ln(a),
ln(5.56) = 2t ln(1.03)
Subtract the two sides by 2 ln(1.03):
t = ln(5.56) / (2 ln(1.03))
t ≈ 14.4
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Please help answer this.
The value of sin A to the nearest hundredth is,
⇒ sin A = 0.86
We have to given that;
Triangle ABC shown in figure, with sides of lengths,
AB = 11
BC = 9.5
CA = 6
Hence, We get;
sin A = BC / AB
sin A = 9.5 / 11
sin A = 0.86
Thus, The value of sin A to the nearest hundredth is,
⇒ sin A = 0.86
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in a survey of 282 college students, it is found that 64 like brussels sprouts, 94 like broccoli, 58 like cauliflower, 26 like both brussels sprouts and broccoli, 28 like both brussels sprouts and cauliflower, 22 like both broccoli and cauliflower, and 14 like all three vegetables. how many of the 282 students do not like any of these vegetables?
There are 128 students who do not like any of these vegetables.
How to solve this problem?
To solve this problem, we can use the principle of inclusion-exclusion. We start by adding up the number of students who like each vegetable:
Number who like brussels sprouts = 64
Number who like broccoli = 94
Number who like cauliflower = 58
Next, we subtract the number of students who like more than one vegetable once:
Number who like both brussels sprouts and broccoli = 26
Number who like both brussels sprouts and cauliflower = 28
Number who like both broccoli and cauliflower = 22
We can't just subtract the number who like all three vegetables once, since we have now subtracted them twice (once for each pair of vegetables). So we need to add them back in once:
Number who like all three vegetables = 14
Now we can calculate the number of students who like at least one vegetable:
Number who like at least one vegetable = 64 + 94 + 58 - 26 - 28 - 22 + 14
Number who like at least one vegetable = 154
Finally, to find the number of students who do not like any of these vegetables, we subtract this from the total number of students:
Number who do not like any of these vegetables = 282 - 154
Number who do not like any of these vegetables = 128
Therefore, there are 128 students who do not like any of these vegetables.
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At Western University, the historical mean of scholarship examination scores for freshman applications is 900. A historical population standard deviation σ = 180 is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.
State the hypotheses.
The null hypothesis would be that there is no significant difference between the mean examination score for the new freshman applications and the historical mean of 900. The alternative hypothesis would be that there is a significant difference between the two means.
To determine if the mean examination score for new freshman applications has changed. To do this, you'll need to state your null and alternative hypotheses using the historical mean and given terms.
Step 1: State the null hypothesis (H₀)
The null hypothesis assumes that there is no significant change in the mean examination score for new freshman applications. In this case, the null hypothesis is that the mean remains equal to the historical mean of 900.
H₀: μ = 900
Step 2: State the alternative hypothesis (H₁)
The alternative hypothesis represents a significant change in the mean examination score for new freshman applications. In this case, the alternative hypothesis is that the mean is not equal to the historical mean of 900.
H₁: μ ≠ 900
So, your hypotheses are as follows:
- Null hypothesis (H₀): μ = 900
- Alternative hypothesis (H₁): μ ≠ 900
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PLEASE HELP ME I BEG OF YOU!!!!!
SHOW ALL WORK!
Answer:
243π
Step-by-step explanation:
Area of the entire circle = πr² = π18² = 324π
Area of sector = (90/360)π(18)² = 81π
Shaded area = 324π - 81π = 243π
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) {1/5, 1/2, 1/6, 1/3, 1/7, 1/4, 1/8, 1/5,...}
This sequence does not converge because it does not approach a single value as n goes to infinity. The sequence appears to oscillate between certain values, specifically {1/5, 1/2, 1/6, 1/3, 1/7, 1/4, 1/8, 1/5,...}.
Therefore, the limit does not exist (DNE).
The given sequence is {1/5, 1/2, 1/6, 1/3, 1/7, 1/4, 1/8, 1/5,...}. To determine whether this sequence converges or diverges, let's find a pattern:
The numerators are always 1. To find the pattern in the denominators, we can examine their differences: (5-2), (6-2), (7-3), (8-4), and so on. We observe that the differences are increasing by 1 each time: 3, 4, 4, 4,...
Now let's write down the denominators based on this pattern: 5, 2, 6, 3, 7, 4, 8, 5,... . The denominators repeat after every four terms, which means the sequence is periodic with a period of 4.
A periodic sequence does not have a unique limit because the terms keep oscillating between different values. Therefore, this sequence diverges, and the answer is DNE (does not exist).
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What is the surface area of the cylinder with height 2 km and radius 7 km? Round your answer to the nearest thousandth.
Answer:
395.84km²
Step-by-step explanation: