Answers
Answer:
I think it is D
Step-by-step explanation:
Its saying that f of x is four times x. So if x was one it could be four. But if x was greater than one it would be higher than one. Therefore, I think that the answer should be all real numbers greater than or equal to four.
Hope this helped!!! Let me know if I was correct. Haven't done this in years.
Answer:
d
Step-by-step explanation:
Related Questions
Question 3
Find the domain and range of the function represented by the graph?
A. Domain: -3
Range: -4<=y<=0
B. Domain: {-3, -2, -1, 0, 1}
Range: {-3, -2, 0, 1}
C. Domain: {-4, -3, 0, 1, 2}
Range: {-4, -3, -2, -1, 0}
D. Domain: -4 <= x<=-3
Range: 0<=y<=1
Answers
Answer:
Domain: \(-3\leq x\leq 1\)
Range: \(-4\leq y\leq 0\)
Step-by-step explanation:
If you find the coordinate of the graph you can get the domain and range
(-3,0), (-2,-4), (-1,-2), (0,0), (1, -4)
Now that we have that find the domain and range
Domain - x coordinate
Range - y coordinate
Domain: (-3, -2, -1, 0, 1)
Range: (-4, -2, 0)
Since the domain ranges from -3 to 1 you can use the inequality \(-3\leq x\leq 1\) to represent the domain and \(-4\leq y\leq 0\) for the range
Professor Kucera creates the Venn diagram below to describe the proportion of students who take chemistry and Spanish at the
University of California, Irvine, Where A = student takes chemistry and B = student takes Spanish. Suppose one student is chosen at random.
Refer to diagram
Find the value of P(AUB) and describe it in words.
A) 0.6. This is the probability that the student takes both chemistry and Spanish.
B) 0.1 This is the probability that the student takes either chemistry or Spanish, but not both.
C) 0.6. This is the probability that the student takes either chemistry or Spanish, or both.
D) 0.1. This is the probability that the student takes both chemistry and Spanish.
E) 0.5 This is the probability that the student takes either chemistry or Spanish, but not both.
Answers
0.6. This is the probability that the student takes either chemistry or Spanish or both. Option C. is the answer
How to find the value of P(AUB) from the Venn diagram and describe it in words?
Probability is a measure of the likelihood of a particular event or outcome occurring.
Given the: Venn diagram where P(A) = 0.2 and P(B) = 0.3 and P(A∩B) = 0.1
Since A = student takes chemistry and B = student takes Spanish
P(A∪B) defines the set of students that take either A or B or both
Thus, P(A∪B) will the addition of P(A), P(B) and P(A∩B). That is:
P(A∪B) = P(A) + P(B) + P(A∩B)
P(A∪B) = 0.2 + 0.3 + 0.1 = 0.6
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In each of (a)-(f), answer the following questions: Is ASB ? Is BSA ? Is either A or B a proper subset of the other? (a) A={3{3},( 3 ) 2 },B={3,{3},{{3}}} Is A⊆B ? Yes No Is B⊆A ? Yes No Is either A or B a proper subset of the other? Yes, A is a proper subset of B. Yes, B is a proper subset of A. No, neither is a proper subset of the other. (b) A {3, 5 2 −4 2 ,24mod7}, B={8mod5} Is A≤B ? Yes No Is B≤A ? Yes No Is either A or B a proper subset of the other? Yes, A is a proper subset of B. Yes, B is a proper subset of A. No, neither is a proper subset of the other. (c) A={{1,2},{2,3}},B={1,2,3} Is ASB ? Yes No Is B⊆A ? Yes No Is either A or B a proper subset of the other? Yes, A is a proper subset of B. Yes, B is a proper subset of A. No, neither is a proper subset of the other. (d) A={a,b,c},B={{a},{b},{c}} Is A⊆B ? Yes No Is B≤A ? Yes No Is either A or B a proper subset of the other? Yes, A is a proper subset of B. Yes, B is a proper subset of A. No, neither is a proper subset of the other. (e) A={ 36 ,{6}},B={6} Is A≤B ? Yes No Is B⊂A ? Yes No Is either A or B a proper subset of the other? Yes, A is a proper subset of B. Yes, B is a proper subset of A. No, neither is a proper subset of the other. (f) A={x∈R∣cos(x)∈Z},B={x∈R∣sin(x)∈Z⟩ Is A⊂B ? Yes No Is B⊂A ? Yes No Is either A or B a proper subset of the other? Yes, A is a proper subset of B. Yes, B is a proper subset of A. No, neither is a proper subset of the other.
Answers
(a) A = {3{3}, (3)2}, B = {3, {3}, {{3}}}
Is A ⊆ B? No
Is B ⊆ A? Yes
Is either A or B a proper subset of the other? Yes, B is a proper subset of A.
(b) A = {3, 5^2, -4^2, 24 mod 7}, B = {8 mod 5}
Is A ≤ B? No
Is B ≤ A? No
Is either A or B a proper subset of the other? No, neither is a proper subset of the other.
(c) A = {{1, 2}, {2, 3}}, B = {1, 2, 3}
Is A ⊆ B? Yes
Is B ⊆ A? No
Is either A or B a proper subset of the other? Yes, A is a proper subset of B.
(d) A = {a, b, c}, B = {{a}, {b}, {c}}
Is A ⊆ B? Yes
Is B ≤ A? No
Is either A or B a proper subset of the other? Yes, A is a proper subset of B.
(e) A = {36, {6}}, B = {6}
Is A ≤ B? No
Is B ⊂ A? Yes
Is either A or B a proper subset of the other? Yes, B is a proper subset of A.
(f) A = {x ∈ R | cos(x) ∈ Z}, B = {x ∈ R | sin(x) ∈ Z}
Is A ⊂ B? Yes
Is B ⊂ A? Yes
Is either A or B a proper subset of the other? No, neither is a proper subset of the other.
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The equations -6x + 3y = 6 and x² + y = 10 intersect at the
coordinates (a, b) and (c,d).
(Hint: (a, b) is in Quadrant III)
What is the value of a?
What is the value of b?
What is the value of c?
What is the value of d?
Answers
The values of the letters in coordinates (a, b) and (c,d) are;
a = -4
b = -6
c = 2
d = 6
We are given two equations;
-6x + 3y = 6 ---(eq 1)
x² + y = 10 ---(eq 2)
We are told that they intersect at coordinates; (a, b) and (c, d).Let us make y the subject in eq 2 to get;
y = 10 - x² --(eq 3)
Let us put 10 - x² into eq 1 to get;-6x + 3(10 - x²) = 6
expanding further gives;
-6x + 30 - 3x² = 6
rearranging gives;
3x² + 6x - 24 = 0
Using online quadratic equation solver, we have;
x = -4 and x = 2
Putting x = -4 into eq 3 gives;
y = 10 - (-4)²
y = 10 - 16
y = -6
Putting x = 2 into eq 3 gives;
y = 10 - (2)²
y = 10 - 4
y = 6
Thus, the coordinates are; (-4, -6) and (2, 6)Comparing with (a, b) and (c,d), we have;
a = -4
b = -6
c = 2
d = 6
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Write True and false
A test statistic based on point estimation is used to construct the decision rule which defines the rejection region.
Answers
The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.
In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.
The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.
Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.
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False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.
The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.
Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.
While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.
The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.
Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.
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Indica el exponente de X
Answers
Answer:
x=56
Step-by-step explanation:
Calculate the interest rate with which the original capital will
grow 7-fold in 11 years, when the accrued interest is added into
capital annually.
it is about compound interest
Answers
The interest rate required for the original capital to grow 7-fold in 11 years with annual compounding is approximately 10.42%.
To calculate the interest rate required for the original capital to grow 7-fold in 11 years with annual compounding, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (7 times the original capital)
P = Principal amount (original capital)
r = Annual interest rate (to be calculated)
n = Number of times interest is compounded per year (assuming it's once annually)
t = Number of years (11 years)
In this case, we have:
A = 7P
n = 1
t = 11
The formula becomes:
7P = \(\( P(1 + \frac{r}{1})^{1 \times 11} \)\)
Simplifying:
7 = \(\( (1 + r)^{11} \)\)
To solve for r, we can take the 11th root of both sides:
\(\( (1 + r) = 7^{\frac{1}{11}} \)\)
Subtracting 1 from both sides:
\(\( r = 7^{\frac{1}{11}} - 1 \)\)
r ≈ 0.1042
Therefore, the interest rate required for the original capital to grow 7-fold in 11 years with annual compounding is approximately 10.42%.
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An adult elephant eats about 300 pounds of food each day. Write an expression to
represent the number of pounds of food a herd of 11 elephants eats in 7 days.
The expression 7? (300 ?11) can be used to represent the number of pounds of
food the herd eats in 7 days.
Please help this is due in less than an hour I will give brainliest
Answers
23.0868 libras. porque um elefante come 136 kg de comida por dia em 7 dias ele comeria 952 kg de comida por dia, calculando 952 kg vezes 11 daria 10.472 kg de comida digerida pelos 11 elefantes por semana, e convertendo em libras dariam exatamente 23.0868 libras. Ou seja 11 elefantes comem 23.0868 libras de comida por semana.
Rectangle ABCD is graphed in the coordinate plane. The following are
the vertices of the rectangle: A(-6,-4), B(-4,-4), C(-4,-2), and
D(-6, -2).
What is the perimeter of rectangle ABCD?
units
Stuck? Review related articles/videos or use a hint.
Report a problem
Answers
Answer:
The perimeter of rectangle ABCD can be calculated by adding up the lengths of its sides. Using the distance formula, we can find that AB has a length of 2 units, BC has a length of 2 units, CD has a length of 2 units, and AD has a length of 4 units. Therefore, the perimeter of rectangle ABCD is 10 units.
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I really need help with part a and b, please help. Incorrect answers will be downvoted, correct answers will be upvoted. 1. The army is interested in characterizing the acoustic signature of a helicopter. The following data show measurements of acoustic pressure (made dimensionless) for a two-bladed helicopter rotor through of a rotor revolution. The data points are equally spaced in time, and the period of the data collection is of a second. p=00.00040.0015 0.0028 0.0040 0.0048 0.0057 0.0071 0.0095 0.0134 0.0185 0.02420.0302 0.0364 0.0447 0.0577 0.0776 0.0955 0.0907 -0.0477 -0.0812 -0.0563 -0.0329 -0.0127 0.0032 0.0147 0.0221 0.0256 0.0255 0.0222 0.0170 0.0112 0.0064 0.0035 0.0023 0.0020 0.0019 0.0016 0.0009 0.0002 a) Find the real discrete Fourier transform for this data set. (b) Any term in the Fourier series can be written: ak Cos(kwt)+bk sin(kwt) =ck Cos(kwt+$k) ak Find the ck's and plot their amplitude on a bar graph vs. k to illustrate the relative size of each term in the series. Explain the significance of the plot
Answers
(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.
(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.
To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.
Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.
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A student heats a pot of soup on the stove. At which temperature will the particles in the soup have the greatest kinetic energy
A. 60°F
B. 80°F
C. 100°F
D. 120°F
Answers
Answer:
The answer is B sorry if I'm wrong
Please help!!!!!!
The figure shows the graph of the quadratic function Find the average rate of change between points F and G and between points G and H.
Write down the greater rate of change.
Answers
Answer: 5
Step-by-step explanation:
Between F and G: \(\frac{-5-0}{-3-(-2)}=5\)
Between G and H: \(\frac{3-0}{-1-(-2)}=3\)
So, the greater rate of change is 5.
Geometry: complete this proof (ASAP! It’s urgent)
Answers
Answer:
1. <1 ~= <4 (Given)
2. <2 is supplementary to <1; <3 is supplementary to <4 (Because <1 & <2, <3 and <4 form linear pairs, they are supplementary by the linear pair postulate.)
3. <2 ~= <3 (By the definition of supplementary angles, m<1 + m<2 = 180 and m<3 + m<4 = 180. By definition of congruent angles, m<1 = m<4, therefore m<2 = m<3 by substitution property of equality.)
4. AB ~= BC (Converse of Isosceles Triangles Theorem)
5. Triangle ABC is isosceles (Definition of Isosceles Triangles)
Graph the equation y= 5x - 4
Answers
Answer:
the y intercept will be -4 and the slope would be 5
A passenger elevator in the Sears Tower in Chicago can lift people 960 feet in 1 minute and 30 seconds. How fast must the freight elevator be traveling if it lifts cargo the same height but in 2 minutes and 30 seconds? [
D=rt
D=rt
]
Pilihan jawaban
6.4 feet per second
10.7 feet per second
19.2 feet per second
38.4 feet per second
Answers
If the freight elevator lifts goods the same height in 2 minutes and 30 seconds, it will travel at a pace of 6.4 feet per second.
What is speed?Speed is the pace at which an item moves along a route in time, whereas velocity is the rate and direction of movement. In other words, velocity is a vector, whereas speed is a scalar number. The sign for speed is v (italic), whereas the symbol for velocity is v. (boldface). A bar is placed over the symbol to represent average values. Speed is defined as the rate at which distance changes over time. It has a distance by time dimension. Thus, the SI unit of speed is defined as a combination of the fundamental units of distance and time. As a result, the SI unit of speed is the metre per second.
Here,
Given that a passenger elevator in the sears tower in Chicago can lift people 960 feet in 1 minute and 30 seconds (1.5 minutes). This means that the lift is travelling with a speed of:
=960/1.5
=640 ft/min
If the elevator lifts cargo through the same height in 2 minutes and 30 seconds (2.5 minutes), then the speed is given by:
=640/2.5
=384 ft/min
=384/60
=6.4 ft/second
The freight elevator be traveling at the speed of 6.4 ft/second if it lifts cargo the same height but in 2 minutes and 30 seconds.
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The sales tax in one town is 8%.So, the total cost of an item can be written as c=0.08cents .what is the total cost of an that sells for $12 ?its due tmrr asap
Answers
The total cost of an item that sells for $12 is $12.96
How to determine the total cost of an item that sells for $12?From the question, we have the following parameters that can be used in our computation:
Selling price = $12
Sales tax = 8%
The total cost of an item that sells for $12 is then calculated as
Total cost = Selling price * (1 + Sales tax)
Substitute the known values in the above equation, so, we have the following representation
Total cost = 12 * (1 + 8%)
Evaluate
Total cost = 12.96
Hence, the total cost is $12.96
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The slope of the line passing through the points (-1, 5) and (1, 6) is no slope 1/2 5/4
Answers
Answer:
1/2
Step-by-step explanation:
Here you utilize the formula of slope which is m = y2-y1/x2 -x1
(-1,5) (1,6)
(x1, y1) ( x2, y2)
m = ( 6-5)/ (1-(-1))
= 1/(1+1)
= 1/2
Answer:
1/2
Step-by-step explanation:
A coin is flipped eight times where each flip comes up either heads or tails. The outcome is the string of 8 heads/tails that is produced. How many possible outcomes
Answers
There are 256 possible outcomes for the string of 8 heads/tails that can be produced when flipping a coin eight times.
When a coin is flipped eight times, there are two possible outcomes for each individual flip: heads or tails.
Since each flip has two possibilities, the total number of possible outcomes for eight flips can be calculated by multiplying the number of possibilities for each flip together.
Therefore, the number of possible outcomes for eight coin flips is:
2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 2^8 = 256
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(x,-4) and (2,8): m = -3 find the missing value. it is in slope formula.
Answers
Answer:
The value of x = 6
Step-by-step explanation:
Given
The point (x,-4)The point (2,8)To determine
m = -3Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
here:
(x₁, y₁) = (x, -4) (x₂, y₂) = (2, 8) m = -3so substitute (x₁, y₁) = (x, -4) , (x₂, y₂) = (2, 8) and m = -3
m = [y₂ - y₁] / [x₂ - x₁]
-3 = [8 - (-4)] / [2 - x]
-3 = [12] / [2-x]
-3 (2-x) = 12
-6+3x = 12
3x = 12+6
3x = 18
divide both sides by 3
3x/3 = 18/3
x = 6
Therefore, the value of x = 6
Manuel wants to buy a bond that will mature to 5000 in eight years. How much should he pay for the bond now if it earns interest at a rate of 3.5% per year, compounded continuously?
Answers
Answer:
$3,778.92
Step-by-step explanation:
You want to know the present value of a $5000 bond that earns 3.5% interest compounded continuously for 8 years.
Compound interestThe compound interest formula is ...
FV = PV(e^(rt))
Filling in the values we know gives us ...
5000 = PV(e^(0.035×8)) ≈ 1.3231298·PV
Then the present value is ...
PV = 5000/1.3231298 ≈ $3778.92
Manuel should pay $3778.92 for the bond.
<95141404393>
The lengths of two sides of a triangle are shown.
Side 1: 8x2 − 5x − 2
Side 2: 7x − x2 + 3
The perimeter of the triangle is 4x3 − 3x2 + 2x − 6.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work. (4 points)
Part B: What is the length of the third side of the triangle? Show your work. (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)
Answers
Answer:
To find the total length of the two sides, we simply add them together:
Total length = Side 1 + Side 2
Total length = (8x^2 - 5x - 2) + (7x - x^2 + 3)
Total length = -x^2 + 8x^2 - 5x + 7x - 2 + 3
Total length = 7x^2 + 2x + 1
Therefore, the total length of the two sides of the triangle is 7x^2 + 2x + 1.
Step-by-step explanation:
To find the length of the third side of the triangle, we need to use the formula for the perimeter of a triangle:
Perimeter = Side 1 + Side 2 + Side 3
We are given the perimeter of the triangle as 4x^3 - 3x^2 + 2x - 6 and we know the lengths of Side 1 and Side 2. Therefore, we can rewrite the formula as:
4x^3 - 3x^2 + 2x - 6 = (8x^2 - 5x - 2) + (7x - x^2 + 3) + Side 3
Simplifying the right-hand side:
4x^3 - 3x^2 + 2x - 6 = 7x^2 + 2x + 1 + Side 3
Side 3 = 4x^3 - 3x^2 + 2x - 6 - 7x^2 - 2x - 1
Simplifying further:
Side 3 = 4x^3 - 7x^2 - x - 7
Therefore, the length of the third side of the triangle is 4x^3 - 7x^2 - x - 7.
Yes, the answers for Part A and Part B show that the polynomials are closed under addition and subtraction.
Closure under addition means that when two polynomials are added, the result is also a polynomial. In Part A, we added the two polynomials 8x^2 - 5x - 2 and 7x - x^2 + 3 to get the total length of the two sides of the triangle, which is 7x^2 + 2x + 1. Since the total length is also a polynomial, this shows that the polynomials are closed under addition.
Closure under subtraction means that when one polynomial is subtracted from another polynomial, the result is also a polynomial. In Part B, we subtracted the two polynomials 8x^2 - 5x - 2 and 7x - x^2 + 3 from the given perimeter of the triangle, 4x^3 - 3x^2 + 2x - 6, to get the length of the third side of the triangle, which is 4x^3 - 7x^2 - x - 7. Since the length of the third side is also a polynomial, this shows that the polynomials are closed under subtraction.
Therefore, the answers for Part A and Part B demonstrate that the polynomials are closed under addition and subtraction.
Help please I need help. :)
Answers
Answer:
yes
Step-by-step explanation:
How many solutions to this
Answers
Answer:
one
Step-by-step explanation:
one equation
tanks Please brianlist
the mean score on a statistics exam is 82. if your exam score is 2.12 standard deviations below the mean, which of the following scores could be your exam score? (there may be multiple correct answers, click all that apply) group of answer choices
a. 85 b. 90 c. 70 d. 80
Answers
60.8 is less than 70 or 80, we can eliminate answer choices (c) and (d) as possible answers.
To solve this problem, we need to use the formula for standard deviation:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
In this case, we know that the mean score is 82, and your exam score is 2.12 standard deviations below the mean. So we can set up the equation:
z = (x - 82) / σ = -2.12
Now we need to find the possible values of x (your exam score) that satisfy this equation. We can rearrange the equation to solve for x:
x = z * σ + μ
Plugging in the values we know, we get:
x = -2.12 * σ + 82
We don't know the value of σ, so we can't solve for x exactly. But we can use some logic to eliminate some of the answer choices.
Since your exam score is below the mean, we know that x < 82. That means we can eliminate answer choices (a) and (b), since they are both above 82.
To eliminate answer choices (c) or (d), we need to know whether 2.12 standard deviations below the mean is less than or greater than the value of σ.
If σ is relatively small, then a score that is 2.12 standard deviations below the mean will be much lower than 70 or 80. But if σ is relatively large, then a score that is 2.12 standard deviations below the mean could be closer to 70 or 80.
Unfortunately, we don't know the value of σ, so we can't say for sure whether (c) or (d) is a possible answer. However, we can make an educated guess based on the range of possible values for σ.
Since the standard deviation of exam scores is typically in the range of 10-20 points, we can assume that σ is at least 10.
With that assumption, we can calculate the minimum possible value of x:
x = -2.12 * 10 + 82 = 60.8
Since 60.8 is less than 70 or 80, we can eliminate answer choices (c) and (d) as possible answers.
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Destini has $64 to spend on a new game. If she spends 5/8 of her money on the
game, how much money will she have remaining?
Answers
Answer:
She will have $24 remaining.
Step-by-step explanation:
5/8 of 64 is 40
Subtract 40 from the original number, 64
You get 24
Need help on this question asap please
Answers
Answer:
8 m
-----------------Work--------------
2*3 = 6
Ratio
2*4 = 8
Please help!!
Evaluate 2x4y for x = 2 and y = 4.
A.-64
B.1/8
C.1/2
Answers
Step-by-step explanation:
2x4y. x=2. y=4
2(2)4(4) Pemdas
2x2=4 4x4=16
4x16
64
This problem has two parts (a) If there are 4 colors of jellybeans and you are trying to fill up a jar that holds 50 beans, how many different color combinations exist (assuming no restrictions on the distributions of the colors)? (b) How many distinct solutions (using non-negative integers) are there to the following equation: x1 +x2+x3 + x4 +x5 +x6 +x7 =20.
Answers
(a) The number of different color combinations for filling up a jar with 50 jellybeans of 4 different colors, with no restrictions on the distribution of colors, is 4^50.
(b) The number of distinct non-negative integer solutions to the equation x1 +x2+x3 + x4 +x5 +x6 +x7 =20 is 230,230, which is found using the stars and bars method.
(a) Since there are 4 colors of jellybeans and no restrictions on the distribution of colors, we can choose any combination of colors to fill up the jar. Each jellybean can be one of 4 colors, so the number of different color combinations is 4^50.
(b) This is a classic stars and bars problem. We need to find the number of non-negative integer solutions to the equation x1 +x2+x3 + x4 +x5 +x6 +x7 =20. To solve this, we can imagine representing each x variable with a star ( * ), and using bars ( | ) to separate the stars into 7 groups, with each group representing one of the x variables. For example, the solution x1=2, x2=3, x3=0, x4=5, x5=4, x6=1, x7=5 would be represented as:
**|***||*****|||||||||
There are a total of 20 stars in this diagram, and 6 bars separating them into 7 groups. The number of solutions is equal to the number of ways to arrange the 20 stars and 6 bars, which is (20+6) choose 6, or 26 choose 6, which is equal to 230,230. Therefore, there are 230,230 distinct solutions to the equation x1 +x2+x3 + x4 +x5 +x6 +x7 =20.
Learn more about non-negative integer solutions:
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Two angles of a triangle are 40° and 30°. What type of a triangle can it be?
Answers
Hint: The sum of the interior angles of a triangle is 180 degrees.
(The general formula (n-2)*180.) Do the calculations to find the missing angle of triangle.
At 4:00 a.m., the outside temperature was -28°F. How much warmer does 1 pc
it have to get to reach 0°F?
Answers
Step-by-step explanation:There's a hundred and four days of summer vacation
'Til school comes along just to end it
So the annual problem for our generation
Is finding a good way to spend it
Like maybe
Building a rocket or fighting a mummy
Or climbing up the Eiffel Tower
Discovering something that doesn't exist
Or giving a monkey a shower
Surfing tidal waves, creating nanobots
Or locating Frankenstein's brain
Finding a dodo bird, painting a continent
Or driving our sister insane
This could possibly be the best day ever
And the forecast says that tomorrow will likely be
A million and six times better
So make every minute count
Jump up, jump in and seize the day
And let's make sure that in every single possible way
Today is gonna be a great day
Crossing the tundra or building a roller coaster
Or skiing down a mountain of beans
Devising a system for remembering everything
Or synchronizing submarines
Racing chariots, taming tiger sharks
Constructing a portal to Mars
Building a time machine, stretching a rubber tree
Or wailing away on guitars
This could possibly be the best day ever
And the forecast says that tomorrow will likely be
A million and six times better
So make every minute count
Jump up, jump in and seize the day
And let's make sure that in every single possible way
Today is gonna be a great day
Let's put our heads together and design a master plan
We may miss dinner but I know mom will understand
We've got our mission and some pliers
Yogurt, gumballs and desire
And a pocketful of rubber bands
The manual on handstands
A Unicycle, compass
And a camera that won't focus
And a canteen full of soda
Grab a beach towel
Here we go!
This is Ferb-tastic!
This could possibly be the best day ever
And the forecast says that tomorrow will likely be
A million and six times better
So make every minute count
Jump up, jump in and seize the day
And let's make sure that in every single possible way
Seriously, this is gonna be great!
This could possibly be the best day ever
Today is gonna be a great day
This could possibly be the best day ever