Answers
Answer:
a-yes
b-no
c-no
d-yes
e-yes
Related Questions
A round table has a radius of 15 in. A round tablecloth hangs 2 in. over the edge of the entire table. What is the approximate area of the tablecloth
Answers
907 in² is the approximate area of the tablecloth .
What in math is area?
Area is the entire amount of space occupied by a flat (2-D) surface or shape of an object. The area of a plane figure is the space that its perimeter encloses. The quantity of unit squares that completely encircle the surface of a closed figure is its area. Square measurements of area, such as cm2 and m2, are used. The region enclosed by an object's shape is known as the area. The area of a figure or any other two-dimensional geometric shape is how much space it takes up in a plane.
radius of the tablecloth is 15 cm + 2 cm = 17 cm.
A = πr²
= 3.14 * 17 * 17
= 907.46
≈ 907 in²
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Salmon and Federico are choosing a number between 1 & 100, picking a color from ROY G BIV, and picking a letter out of "INDIANA". Either one will go first. State the probability of each situation as a percentage, fraction and decimal.
1. Salmon chooses a composite number, A cool color( G BIV) and an A.
2.Federico chooses a prime number, A color starting with a vowel, and a constanant.
3.Either chooses a number divisible by 7 or 8, any color, and a vowel.
4. Either chooses a number divisible by 5 or 4, blue or green, and L or N
Answers
To determine the probabilities, we need to consider the number of favorable outcomes for each situation divided by the total number of possible outcomes.
1.Probability: 228/700 = 0.3257 ≈ 32.57% ≈ 32.6% (rounded to one decimal place)
2. Probability: 200/3500 = 0.0571 ≈ 5.71% ≈ 5.7%
3. Probability: 504/2100 = 0.24 ≈ 24% (exact fraction)
4.Probability: 180/1400 = 0.1286 ≈ 12.86% ≈ 12.9% (rounded to one decimal place)
1. Salmon chooses a composite number, a cool color (G, B, I, or V), and an A:
a) Composite numbers between 1 and 100: There are 57 composite numbers in this range.
b) Cool colors (G, B, I, or V): There are 4 cool colors.
c) The letter A: There is 1 A in "INDIANA."
Total favorable outcomes: 57 (composite numbers) * 4 (cool colors) * 1 (A) = 228
Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 1 (possible letter) = 700
Probability: 228/700 = 0.3257 ≈ 32.57% ≈ 32.6% (rounded to one decimal place)
2. Federico chooses a prime number, a color starting with a vowel (E or I), and a consonant:
a) Prime numbers between 1 and 100: There are 25 prime numbers in this range.
b) Colors starting with a vowel (E or I): There are 2 colors starting with a vowel.
c) Consonants in "INDIANA": There are 4 consonants.
Total favorable outcomes: 25 (prime numbers) * 2 (vowel colors) * 4 (consonants) = 200
Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 5 (possible letters) = 3500
Probability: 200/3500 = 0.0571 ≈ 5.71% ≈ 5.7% (rounded to one decimal place)
3. Either chooses a number divisible by 7 or 8, any color, and a vowel:
a) Numbers divisible by 7 or 8: There are 24 numbers divisible by 7 or 8 in the range of 1 to 100.
b) Any color: There are 7 possible colors.
c) Vowels in "INDIANA": There are 3 vowels.
Total favorable outcomes: 24 (divisible numbers) * 7 (possible colors) * 3 (vowels) = 504
Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 3 (possible letters) = 2100
Probability: 504/2100 = 0.24 ≈ 24% (exact fraction)
4. Either chooses a number divisible by 5 or 4, blue or green, and L or N:
a) Numbers divisible by 5 or 4: There are 45 numbers divisible by 5 or 4 in the range of 1 to 100.
b) Blue or green colors: There are 2 possible colors (blue or green).
c) L or N in "INDIANA": There are 2 letters (L or N).
Total favorable outcomes: 45 (divisible numbers) * 2 (possible colors) * 2 (letters) = 180
Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 2 (possible letters) = 1400
Probability: 180/1400 = 0.1286 ≈ 12.86% ≈ 12.9% (rounded to one decimal place)
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There are black and white counters in a bag in the ratio 20:17
There are 54
more black counters than white counters.
How many black counters are there?
Answers
There are 360 black counters and 306 white counter in 20:17 ratio.
Let's denote the number of black counters by B and the number of white counters by W. We know that the ratio of black to white counters is 20:17, which means that:
B/W = 20/17
We also know that there are 54 more black counters than white counters, which means that:
B = W + 54
We can use substitution to solve for B. Substituting the second equation into the first equation, we get:
(W + 54)/W = 20/17
Cross-multiplying, we get:
17(W + 54) = 20W
Expanding the left side, we get:
17W + 918 = 20W
Subtracting 17W from both sides, we get:
918 = 3W
Dividing both sides by 3, we get:
W = 306
Now we can use the second equation to find B:
B = W + 54 = 306 + 54 = 360
Therefore, there are 360 black counters in the bag.
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The carpet for the office you completed cost $576. If you're using the same carpet in the new client's bedroom, how much will it cost? Round up to the nearest whole dollar. (Hint: You may want to find the area of each room and the cost of the carpet per square foot.)
$360 $280 $64 $225
with explanation please
Answers
The cost of similar carpet in the client's bedroom is $225
Area of Shapes
Given Data
Cost of Carpet = $576Area of Office = 16*19.2 = 307.2 square feetArea of Bedroom = 12*10 = 120 square feetif 307.2 square feet of carpet will cost $576
the 120 square feet of carpet will cost $x
cross multiplying we have
x = 120*576/307.2
x = 69120/307.2
x = $225
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Find the area of a triangle with a =4, b =6, and c =8.
a. 10.2 units 2
b. 8.4 units 2
C.12.4 units
d. 11.6 units 2
Answers
Answer:
d
Step-by-step explanation:
Given 3 sides of the triangle the area (A) can be calculated using Hero's formula.
A = \(\sqrt{s(s-a)(s-b)(s-c)}\)
where s is the semi perimeter of the triangle
s = \(\frac{a+b+c}{2}\) = \(\frac{4+6+8}{2}\) = \(\frac{18}{2}\) = 9 , thus
A = \(\sqrt{9(9-4)(9-6)(9-8)}\)
= \(\sqrt{9(5)(3)(1)}\)
= \(\sqrt{135}\)
≈ 11.6 units² → d
if w2+15=40 what would w be ?
Answers
\(\fbox{w=5 or w=-5}\)
Subtract 15 from both sides:
\(w^2+15-15=40-15\)
\(w^2=25\)
Take square root:
\(w=\) ± \(\sqrt{25}\)
\(w=5\\or\\w=-5\)
Are any of these trees an outlier?
An apple farmer randomly selected 28 trees and weighed the total of all the apples each produced. Here are the results measure in grams:
85, 87, 97, 109, 114, 88, 95, 100, 93, 67, 91, 130, 49, 118, 101, 95, 94, 99, 96, 99, 79, 109, 85, 118, 70, 104, 127, 135.
Answers
Answer:
49
Step-by-step explanation:
49 is the outlier because it's the lowest number in the group of the other trees.
a large company is concerned that many of its employees are in poor physical condition, which can result in decreased productivity. to determine how many steps each employee takes per day, on average, the company provides a pedometer to 50 randomly selected employees to use for one 24-hour period. after collecting the data, the company statistician reports a 95% confidence interval of 4547 steps to 8473 steps. (a) interpret the confidence interval. (b) what is the point estimate that was used to create the interval? what is the margin of error? (c) recent guidelines suggest that people aim for 10,000 steps per day. is there convincing evidence that the employees of this company are not meeting the guideline, on average? explain.
Answers
(a) Confidence interval of 4547 to 8473 steps means the average number of steps taken by employees falls in that range with 95% confidence.
(b) The point estimate was 6510 and the margin error is 1963
(c) Yes, there is convincing evidence that the employees of this company are not meeting the guideline, on average
If we take many samples of size 50 and calculate many intervals, about 95% of the interval will capture the true average of steps for an employee in a day.
We are 95% confident that the interval from 4547 to 8473 steps contains the true average steps for employees/day.
Point estimate: halfway between 4547 and 8473 = (4547 + 8473) / 2 = 6570The margin of error: (8473 - 4547) / 2 = 1963Since all plausible values in our interval are under 10,000, there is convincing evidence that the employees are not meeting this guideline, on average.
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You are getting ready for Thanksgiving dinner and
trying to find the perfect outfit. You want to wear
your new sweater from Infinity21. The manufacturer
advertises that this sweater is most comfortable to
wear when the temperature satisfies t-56|≤6 de-
grees Fahrenheit. The weather report says it will be
53°F on Thanksgiving Day at mealtime.
Answers
Answer:
It can still be worn if the weather forecast is below the manufacturer's advertisement
Determine if the function defines an inner product on R2, where u -(u1, U2) and v - (v1, v2). (Select all that apply.) (u, v〉 = u1v1. O satisfies (u, v) = (v, u). O does not satisfy 〈u, v) = (v, u) . O satisfies (u, v + w〉 = 〈u, v〉 + 〈u, w). O does not satisfy 〈u, v + w = u, v〉 + 〈u, w〉. O satisfies c〈u, v〉 = 〈cu, v). O does not satisfy c(u, v) = (cu, v〉 a satisfies(v, v〉 0, and 〈v, v)-0 if and only if v = 0. O does not satisfy 〈v, v〉> 0 , and 〈v, v〉 = 0 if and only if v = 0
Answers
The function ⟨u, v⟩ = u1v1 defines an inner product on R2 as it satisfies all the required properties.
Given the function ⟨u, v⟩ = u1v1, let's examine each property:
Symmetry:
⟨u, v⟩ = u1v1
⟨v, u⟩ = v1u1
Since u1v1 = v1u1, the function satisfies the symmetry property
Linearity:
For the first part, let w = (w1, w2) and consider ⟨u, v + w⟩:
⟨u, v + w⟩ = u1(v1 + w1) = u1v1 + u1w1
⟨u, v⟩ + ⟨u, w⟩ = u1v1 + u1w1
The function satisfies the first part of the linearity property.
For the second part, let c be a scalar and consider c⟨u, v⟩:
c⟨u, v⟩ = cu1v1
⟨cu, v⟩ = (cu1)v1 = cu1v1
The function satisfies the second part of the linearity property.
Positive-definiteness:
⟨v, v⟩ =\(v1^2\)
The function satisfies the positive-definiteness property as \(v1^2\) ≥ 0, and \(v1^2\) = 0 if and only if v1 =
0,which means v = (0, 0).
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Solve this equation.
75 – 3.5y – 4y = 4y + 6
Answers
Answer:
y=6
Step-by-step explanation:
75-3.5y-4y=4y+6
combine like terms)
75+(-3.5y-4y)=4y+6
75-7.5y=4y+6
add 4y to each side to combine the terms) 75+(-7.5y-4y)=6
75-11.5y=6
subtract 75 from each side to isolate the variable) -11.5y=-69
divide by -11.5 to isolate the variable) -11.5y/-11.5=-69/-11.5
y=6
Scott is making a dip that has 3 5 of a teaspoon of garlic for every 1 2 of a teaspoon of hot sauce. What is the unit rate of garlic to hot sauce in the dip? 1 3 5 teaspoons of garlic per teaspoon of hot sauce 5 6 teaspoon of garlic per teaspoon of hot sauce 1 1 5 teaspoons of garlic per teaspoon of hot sauce 2 3 teaspoon of garlic per teaspoon of hot sauce
Answers
Answer:
1/ 1 5 teaspoons of garlic per teaspoon of hot sauce
Step-by-step explanation:
Scott is making a dip that has 3 /5 of a teaspoon of garlic for every 1 /2 of a teaspoon of hot sauce.
3/5 teaspoon of garlic = 1/2 teaspoon of hot sauce
1/2 teaspoon of hot sauce = 3/5 teaspoon of garlic
1 teaspoon of hot sauce =
= 1 × 3/5 ÷ 1/2
= 3/5 ÷ 1/2
= 3/5 × 2/1
= 6/5
= 1 1/5 teaspoon of garlic.
Therefore, the unit rate of garlic to hot sauce in the dip is:
1/ 1 5 teaspoons of garlic per teaspoon of hot sauce
Determine the amount of taxable income of Aaron Rentz in 2020,who is single and has $900 of wages and $1,400 of interest income for the year.Aaron is also a qualifying child of his parents 1$2,000 2$2,300 3$1,200 4$1050 5None of these
Answers
Aaron's taxable income is negative (-$10,100), it means that he does not have any taxable income.
To determine the amount of taxable income for Aaron Rentz in 2020, we need to consider his wages, interest income, and any deductions or credits he may be eligible for.
From the given information, Aaron has $900 of wages and $1,400 of interest income.
In 2020, the standard deduction for a single individual was $12,400. Since Aaron is a qualifying child of his parents, he may not be able to claim his own personal exemption.
To calculate Aaron's taxable income, we subtract the standard deduction from his total income:
Taxable Income = Total Income - Standard Deduction
Taxable Income = $900 + $1,400 - $12,400
Taxable Income = $2,300 - $12,400
Taxable Income = -$10,100
Since Aaron's taxable income is negative (-$10,100), it means that he does not have any taxable income.
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Solve . round the answers to the nearest hundredth. a. , , fd = 2,809 b , , fd = 2,809 c. , , fd = 53 d. , , fd = 53 please select the best answer from the choices provided a b c d
Answers
The correct option is a b c d.
fd = 2,809
We need to round the given answers to the nearest hundredth.
a. 150, 150, fd = 2,809
Now, we need to find 150 such that it is the same percentage as 2,809 of 150.
150 * (2,809/100) = 4.2135 ≈ 4.21
So, 150, 150, fd = 2,809 ≈ 4.21, 4.21, fd ≈ 100
b. 150, 150, fd = 2,809
Now, we need to find 150 such that it is the same percentage as 2,809 of 150.
150 * (2,809/100) = 4.2135 ≈ 4.21
So, 150, 150, fd = 2,809 ≈ 4.21, 4.21, fd ≈ 100
c. 150, 150, fd = 53
Now, we need to find 150 such that it is the same percentage as 53 of 150.
150 * (53/100) = 79.5 ≈ 79.5
So, 150, 150, fd = 53 ≈ 79.5, 79.5, fd ≈ 100
d. 150, 150, fd = 53
Now, we need to find 150 such that it is the same percentage as 53 of 150.
150 * (53/100) = 79.5 ≈ 79.5
So, 150, 150, fd = 53 ≈ 79.5, 79.5, fd ≈ 100
Therefore, the correct option is a b c d.
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Which of the following statement is false? a. all isosceles triangles are similar b. all quadrilateral triangle are similar c. all circle are similar
d. none of the above
Answers
The statement that is false is A.. all isosceles triangles are similar
What is an isosceles triangles?An isosceles triangle in geometry is a triangle with two equal-length sides. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition including the equilateral triangle as an exception.
An isosceles triangle has two of its three sides with equal lengths, and its two base angles are also equal. Although two isosceles triangles can have two sides that are equal on their own, they may not be similar because their sides may be of a different measurement.
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Kate is a buyer for a men’s fashion retail store. She will order a new cloth overcoat from Paris for the fall fashion season. Based on her experience, she expects to sell at least 100 coats, and at most 400, but she feels that any number of sales in between is equally likely. Therefore, she estimates that her sales are uniformly distributed between 100 and 400. The total cost to the store is $100 per coat, and the retail price is set at $180. Any coats left over at the end of season would be sold at $60 each.
part 1: a) How many coats should Kate buy if she wants to maximize profits?
part 2: b) Assume Kate buys the number of coats suggested in part a), what is the probability that the coats sell out? What is the probability that they do not sell out?
Answers
Part 1: Kate should buy 100 coats to maximize profits.Part 2: The probability that the coats sell out is 0.25 (25%), and the probability that they do not sell out is 0.75 (75%).
To maximize profits, Kate should consider the scenario where she sells all the coats without any left over at the end of the season.
Since the sales are uniformly distributed between 100 and 400, buying 100 coats ensures that she meets the minimum expected sales of 100. Purchasing more than 100 coats would increase costs without a guarantee of higher sales, potentially leading to excess inventory and lower profits.
Given that the sales are uniformly distributed between 100 and 400 coats, Kate's purchase of 100 coats covers the minimum expected sales.
The probability of selling out can be calculated by finding the proportion of the range covered by the desired sales (100 out of 300). Therefore, the probability of selling out is 100/300 = 0.25 or 25%. The probability of not selling out is the complement, which is 1 - 0.25 = 0.75 or 75%.
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The p-value Group of answer choices can be any negative value. must be a number between zero and one. must be a number between -1 and 0. can be any positive value.
Answers
The p-value Group of answer choices can be any negative value must be a number between zero and one by null hypothesis.
The p-value represents the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming the null hypothesis is true. It is a measure of the strength of evidence against the null hypothesis.
The p-value is always between zero and one because it is a probability value. A p-value of zero indicates that the observed result is extremely unlikely to occur under the null hypothesis, while a p-value of one suggests that the observed result is very likely to occur even if the null hypothesis is true. Values between zero and one represent varying degrees of evidence against the null hypothesis.
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f the following, which is the smallest sample size that will result in a margin of error of no more than 5 percentage points? responses 73 73 97 97 271 271 385 385 1,537 1,537 skip to navigation
Answers
The smallest sample size that will result in a margin of error of no more than 5% for a 95% confidence interval is given as follows:
385.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which the variables used to calculated these bounds are listed as follows:
\(\pi\) is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is modeled as follows:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.
We have no estimate, hence we consider that:
\(\pi = 0.5\)
The minimum sample size is obtained as n when M = 0.05, hence:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
\(0.05 = 1.96\sqrt{\frac{0.5(0.5)}{n}}\)
\(0.05\sqrt{n} = 1.96 \times 0.5\)
\(\sqrt{n} = 1.96 \times 10\) (0.5/0.05 = 10).
\((\sqrt{n})^2 = (1.96 \times 10)^2\)
n = 384.16
Hence rounded to 385, as a sample size of 384 would have a margin of error slightly above 0.05.
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Work out the value of 5 to the power of a if it equal 1/125
Answers
Answer:
a = -3
Step-by-step explanation:
Step 1: Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:
5^a = 1/125
Step 2: Take the log of both sides
log(5^a) = log(1/125)
Step 3: According to the power rule of logs, we can bring a down and multiply it by log(5):
a * log(5) = log (1/125)
Step 4: Divide both sides by log(5) to solve for a:
(a * log(5) = log(1/125)) / log(5)
a = -3
Optional 5: We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:
5^-3 = 1/125
1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator
1/125 = 1/125
GIVING BRAINLIEST!!!!
Select the properties that both rectangles and parallelograms always share (u can select more than one answer)
A) four sides of equal length
B) 4 right angles
C) 2 pairs of parallel sides
D) 2 pairs of sides with equal length
E) 2 acute angles and 2 obtuse angles
Answers
Parallelograms don’t need to have right angles
Rectangles don’t always have equal sides
Rectangles have all 90 degree angles
Rika works in the perfume department out Hoover‘s department store she is giving away samples of her new fragrance and a new Santa hand lotion to customers that pass by her station she is required to hand out a total of 114 samples during her shift she has already handed out 36 samples which represents 1/3 Of the number of her fragrance samples and 1/4 of the number of hand lotion samples that she must hand out
Answers
Answer:
21
Step-by-step explanation:
Let P(n) be the statement that a postage of n cents
can be formed using just 3-cent and 5-cent stamps. The parts of this
exercise outline a strong induction proof that P(n) is true for n ≥ 8.
(a) Show that the statements P(8), P(9), and P(10) are true, completing the basis step of the proof.
(b) What is the inductive hypothesis of the proof?
(c) What do you need to prove in the inductive step?
(d) Complete the inductive step for k ≥ 10.
(e – Extra credit 2 pts.) Is P(n) true for n ≥ 8 if you have only
one 5-cent stamp? only two 5-cent stamps?
Answers
The inductive hypothesis is that P(n) is true for all n ≥ 8, and by completing the inductive step, it has been shown that P(n+1) is also true for n ≥ 8 if you have at least three 5-cent stamps.
(a) P(8) is true, since 8 = 3 + 5.
P(9) is true, since 9 = 3 + 3 + 3.
P(10) is true, since 10 = 5 + 5.
(b) The inductive hypothesis is that P(n) is true for all n ≥ 8.
(c) In the inductive step, you need to prove that if P(n) is true for all n ≥ 8, then P(n+1) is also true.
(d) Assume that P(n) is true for all n ≥ 8. We need to prove that P(n+1) is true.
n+1 = (n-2) + 3 + 5
Since P(n) is true for all n ≥ 8, we know that n-2 can be formed using 3-cent and 5-cent stamps. Therefore, n+1 can be formed using 3-cent and 5-cent stamps, so P(n+1) is also true.
(e) No, P(n) is not true for n ≥ 8 if you have only one 5-cent stamp. Similarly, P(n) is not true for n ≥ 8 if you have only two 5-cent stamps.
The inductive hypothesis is that P(n) is true for all n ≥ 8, and by completing the inductive step, it has been shown that P(n+1) is also true for n ≥ 8 if you have at least three 5-cent stamps.
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multiply the polynomials (3x^2-5x+7) and (2x^2-5x+7). Simplify the answer
Answers
The multiplication of polynomials (3x² - 5x + 7) and (2x² - 5x + 7) is:
6x^4 - 25x³ + 60x² - 70x + 49
In this question, we have been given two polynomials 3x² - 5x + 7 and 2x² - 5x + 7
We need to multiply given polynomials.
(3x² - 5x + 7) × (2x² - 5x + 7) ............(Given polynomials)
= 3x²(2x² - 5x + 7) - 5x(2x² - 5x + 7) + 7(2x² - 5x + 7) ..........(Distribute)
= 6x^4 - 15x³ + 21x² - 10x³ + 25x² - 35x + 14x² - 35x + 49 .....(Simplify)
= 6x^4 - 15x³ - 10x³ + 21x² + 25x² + 14x² - 35x -35x + 49
= 6x^4 - 25x³ + 60x² - 70x + 49
Therefore, the multiplication of polynomials (3x² - 5x + 7) and (2x² - 5x + 7) is 6x^4 - 25x³ + 60x² - 70x + 49
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a boat row a boat using a long pole of length 5.30m.when he holds the pole vertically at a particula point in the water such that the pole touches the ground,20% of the pole is underwater.whatis the depth of the water at the point.
Answers
Answer:
1.06m
0.2 × 5.3 = 1.06
Pls help please plot the Ben mark
Answers
Answer:
the answer is 22 at 3 and at 5 then 3 fourth
Mrs. Martz is travelling to 300 miles to Florida
for a vacation. She has already travelled 60% of
the trip. How many miles has she gone?
Answers
Answer:
180 miles
Step-by-step explanation:
YALL REALLY NEED TO
HELP MEEEE
determine if the triangles are similar. Why are they similar or not similar ?
please show work
Answers
Answer:
Not similar
Step-by-step explanation:
In triangle MLN & WXY,
Right angles - > 1
There is nothing common in these 2 triangles other than (1)
Therefore,
Not similar
If y varies jointly as x and z and y=60 when x= 10 and z=-3, find y when x=8 and z=15.
Answers
Answer:
y = -240
Step-by-step explanation:
If y varies jointly as x and z, then y/(xz) = k where k is the constant of proportion
60/10(-3) = 60/-30 = -2 = k
Now, y/(xz) = -2
y/8(15) = -2
y/120 = -2
y = -240
Find the mean for the data set. 6, 14, 7, 4, 12, 8, 13, 4, 18, 14
Answers
Answer:
Concept:
Mean is just another name for average. To find the mean of a data set, add all the values together and divide by the number of values in the set. The result is your mean!
The values are given below as
\(6,14,7,4,12,8,13,4,18,14\)The image below shows how to calculate the mean
By substituting values, we will have
\(\begin{gathered} \bar{x}=\frac{\sum ^{}_{n\mathop=0}x}{n} \\ n=10 \end{gathered}\)\(\begin{gathered} \bar{x}=\frac{6+14+7+4+12+8+13+4+18+14}{10} \\ \bar{x}=\frac{100}{10} \\ \bar{x}=10 \end{gathered}\)Hence,
The mean = 10
To calculate the variance, we will use the formula below
\(^{}\sigma^2=\frac{\sum ^{\infty}_{n\mathop=0}(x-\bar{x})^2}{n}\)\(\begin{gathered} \sigma^2=\frac{\sum ^{\infty}_{n\mathop{=}0}(x-\bar{x})^2}{n} \\ (x-\bar{x})^2=(6-10)^2+(14-10)^2+(7-10)^2+(4-10)^2+(12-10)^2+(8-10)^2+(13-10)^2+(4-10)^2+(18-10)^2+(14-10)^2 \\ (x-\bar{x})^2=16+16+9+36+4+4+9+36+64+16 \\ (x-\bar{x})^2=210 \end{gathered}\)\(\begin{gathered} \sigma^2=\frac{\sum ^{\infty}_{n\mathop{=}0}(x-\bar{x})^2}{n} \\ \sigma^2=\frac{210}{10} \\ \sigma^2=\frac{210}{10} \\ \sigma^2=21 \end{gathered}\)Hence
The variance = 21
To calculate the standard deviation,
\(\begin{gathered} \sigma=\sqrt[]{variance} \\ \sigma=\sqrt[]{21} \\ \sigma=4.58 \end{gathered}\)Hence,
The standard deviation is = 4.58
What are all values of x for which the function f is defined by f(x)= x^3 +3x^2 -9x +7 is increasing?a) -31d) x <-1 or x > 3e) all real numbers
Answers
The values of x for which the function f(x) = x³ + 3x² - 9x + 7 is increasing are (-∞, -3) and (1, +∞).
To find the values of x for which the function f(x) = x³ + 3x² - 9x + 7 is increasing, we need to take the derivative of the function and determine where the derivative is positive.
f(x) = x³ + 3x² - 9x + 7
f'(x) = 3x² + 6x - 9
To find where f(x) is increasing, we need to find the values of x where f'(x) > 0.
3x² + 6x - 9 > 0
Simplifying this inequality, we get
x² + 2x - 3 > 0
Factoring the left side of the inequality, we get
(x + 3)(x - 1) > 0
The critical points of f(x) occur when f'(x) = 0 or when the denominator of f'(x) is undefined. The denominator of f'(x) is always defined, so we only need to find where f'(x) = 0
3x² + 6x - 9 = 0
Dividing both sides by 3, we get
x² + 2x - 3 = 0
Factoring the left side of the equation, we get
(x + 3)(x - 1) = 0
So the critical points of f(x) are x = -3 and x = 1.
Now we can use a sign chart to determine the intervals where f'(x) > 0.
Learn more about critical points here
brainly.com/question/30325317
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The given question is incomplete, the complete question is:
What are all values of x for which the function f is defined by f(x)= x³ +3x² -9x +7 is increasing?
