Consider the data below:
x = 12, 5, 8, 1
y = 2, 3, -1, 7
Determine the following:
a)
1 − (Σxy)2 =
b)
Σ(x − 2) =
c)
Σ(y − y2) =
Answers
a) 1 − (Σxy)2 = -137
b) Σ(x − 2) = 20
c) Σ(y − y2) = -21
These calculations are based on the given data and the formulas provided for each expression.
To determine the given expressions, we need to calculate the necessary sums and perform the indicated calculations using the given data.
a) To calculate 1 − (Σxy)2, we first need to calculate Σxy. Let's multiply the corresponding elements of x and y and sum them up:
Σxy = (12 * 2) + (5 * 3) + (8 * -1) + (1 * 7) = 24 + 15 - 8 + 7 = 38
Now, we can calculate 1 − (Σxy)2:
1 − (Σxy)2 = 1 − 38^2 = 1 − 1444 = -137
b) To calculate Σ(x − 2), we need to subtract 2 from each element of x and sum them up:
Σ(x − 2) = (12 − 2) + (5 − 2) + (8 − 2) + (1 − 2) = 10 + 3 + 6 - 1 = 20
c) To calculate Σ(y − y2), we need to subtract y2 from each element of y and sum them up:
Σ(y − y2) = (2 − 2^2) + (3 − 3^2) + (-1 − (-1)^2) + (7 − 7^2) = (2 − 4) + (3 − 9) + (-1 - 1) + (7 - 49) = -2 - 6 - 2 - 42 = -52
a) 1 − (Σxy)2 equals -137.
b) Σ(x − 2) equals 20.
c) Σ(y − y2) equals -21.
These calculations are based on the given data and the formulas provided for each expression.
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Related Questions
Pls help it due soon
Answers
Answer:
I need help with math too. Can u help me and I’ll help u
Step-by-step explanation:
whats the answer to 5^-2
Answers
Hey!!
Solution,
(5)^-2
=1/5^2
=1/25
The answer is 1/25
hope it helps
Good luck on your assignment
Please help me :( and thank you ❤️
Answers
Answer:
1. is ounces
2. you would use ounces
3. 3.5 x 16 = 56
4. .5, 1, 1.5, 2, 2.5
Write an expression that is equivalent to 7 3/4+3 5/6-1 3/4 that uses addition instead of subtraction.
\(7 \frac{3}{4} + 3 \frac{5}{6} - 1 \frac{3}{4} \)
Answers
Answer:
I'm not sure
Step-by-step explanation:
Sorry
Round 2.486 to the nearest hundredth.
Answers
Answer:
2.490
Step-by-step explanation:
It is over the half point so, if it's over round up. if not, round down.
Determine if the statement is true or false, and justify your answer. If (u1, u2, u3) spans R3, then so does (u1, u2, uz, u). O False. Consider u4 =0 True, the span of a set of vectors can only increase (with respect to set containment) when adding a vector to the set. O True, since the span of {ul, u2, u3, u4} is a subset of the span of {u1, u2, us), O False. Consider u4
Answers
The statement is false because adding a vector to a set of vectors can increase its span, but the new span is not necessarily the same as the original span.
The statement is false. To prove this, consider three vectors u1, u2 and u3 that span R3, and a vector u4 that is not a linear combination of
u1, u2 and u3.
The span of
{u1, u2, u3, u4}
will be a subset of the span of
{u1, u2, u3}.
This means that the span of
{u1, u2, u3, u4}
will contain all the vectors that the span of {u1, u2, u3} contains, plus the vector u4. However, it does not necessarily mean that the span of
{u1, u2, u3, u4} will be the same as the span of {u1, u2, u3},
as there may be other vectors that are in the span of
{u1, u2, u3, u4}
but not in the span of {u1, u2, u3}. Hence, the statement is false.
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The complete question is
Determine if the statement is true or false, and justify your answer. If (u1, u2, u3) spans R3, then so does (u1, u2, uz, u). O False. Consider u4 =0 True, the span of a set of vectors can only increase (with respect to set containment) when adding a vector to the set. O True, since the span of {ul, u2, u3, u4} is a subset of the span of {u1, u2, us), O False. Consider u4 = 0. The span of {u1, u2, u3, u4} is a subset of the span of {u1, u2, us}, but the span of {u1, u2, u3, u4} is not the same as the span of {u1, u2, us}.
What is the probability that a student‘s favorite hobby is roller skating ?Theoretical =Experimental =
Answers
The theoretical probability is given by 1 over the number of hobbies.
If there is a total of 8 hobbies, the probability of a student having a specific hobby is:
\(P=\frac{1}{8}\)The experimental probability is given by the number of students with that hobby over the total number of students. If 3 students have the hobby roller skating among the 24 students surveyed, the probability is:
\(P=\frac{3}{24}=\frac{1}{8}\)When converting measurements in the metric system, you can move the decimal point to the left or to the right why? Select all that apply.
A When converting from smaller to larger units zero dividing by the power of 10
B Moving a decimal point is The same thing as adding or subtracting
C The metric system is based on powers of 10
DWhen converting some larger to smaller unit, you are applying by the power of 10
Answers
Answer:
C The metric system is based on powers of 10
Step-by-step explanation:
Over the last three evenings, Jane received a total of 80 phone calls at the call center. The second evening, she received 2 times as many calls as the thirdevening. The first evening, she received 8 fewer calls than the third evening. calls did she receive each evening?
Answers
Solution:
This is a question on word problem.
We develop each statement into mathematical expressions.
Let the following letters represent the calls received for three evenings
\(\begin{gathered} a=\text{first evening} \\ b=\text{second evening} \\ c=\text{third evening} \end{gathered}\)The statements are written as equations below;
\(\begin{gathered} \text{Jane received a total of 80 phone calls. This means;} \\ a+b+c=80\ldots\ldots.\ldots..\ldots\ldots\ldots\ldots.\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ \\ The\text{ second evening, she received 2 times as many calls as the third evening. This means;} \\ b=2c\ldots\ldots\ldots\ldots\ldots\ldots\ldots.\ldots.\text{.}(2) \\ \\ \text{The first evening, she received 8 fewer calls than the third evening. This means;} \\ a=c-8\ldots\ldots\ldots\ldots\ldots.\ldots\ldots(3) \end{gathered}\)Substituting equations (3) and (2) in equation (1);
\(\begin{gathered} a+b+c=80 \\ (c-8)+2c+c=80 \\ \text{Collecting the like terms;} \\ c+2c+c=80+8 \\ 4c=88 \\ \text{Dividing both sides by 4 to get c;} \\ c=\frac{88}{4} \\ c=22 \end{gathered}\)Substituting the value of c in equations (2) and (3) to get b and a respectively,
\(\begin{gathered} b=2c \\ b=2(22) \\ b=2\times22 \\ b=44 \\ \\ \\ a=c-8 \\ a=22-8 \\ a=14 \end{gathered}\)Therefore,
First evening = 14 phone calls
Second evening = 44 phone calls
Third evening = 22 phone calls
what is the measure of angle B in degrees?
Answers
Answer:
119
Step-by-step explanation:
First find c. It is a straight line so 180. 180-112=68. 68+51=119. 180-119=61. 180-61=119.
Explanation: Take measurement angle C and add 51 degrees. You will now have 163 degrees. Take the area of a triangle (180) and minus 163 from 180 to get 17. May I please have brainliest?
Karen spent all but $8 of her savings in three stores. In each store she spent $2 less than half of what she had when she went in. How much money did Karen have at the start?
Please HELP!
Answers
Answer:
36 dollars
Step-by-step explanation:
We need to think backwards to solve this question.
(8 - 2) x 2 = 12
(12 - 2) x 2 = 20
(20 - 2) x 2 = 36
Can anyone help I keep getting it wrong
Answers
Answer:
C
Step-by-step explanation:
F=9/5C + 32 solve for C
Answers
To solve for C let us do these steps
1. Put the term of C on one side and the other terms on the other side
Subtract 32 from both sides to move the term 32 to the other side
\(\begin{gathered} F-32=\frac{9}{5}C+32-32 \\ F-32=\frac{9}{5}C \end{gathered}\)2. Make the coefficient of C = 1
Divide both sides by 9/5
\(\begin{gathered} \frac{F-32}{\frac{9}{5}}=\frac{\frac{9}{5}C}{\frac{9}{5}} \\ \frac{5}{9}(F-32)=C \\ C=\frac{5}{9}(F-32) \end{gathered}\)You can Multiply the bracket (F- 32) by 5/9
\(C=\frac{5}{9}F-\frac{160}{9}\)Marcus wants to end the semester with at least an 85 test average in his math class. On his first 3 tests, he earned 83, 97, and 80. What will he have to earn on his fourth test to have at least an 85 average? Let g represent the grade needed on his fourth test.
Write an inequality that models the situation.
Solve the inequality, and then explain what the solution means.
Answers
Answer:
Step-by-step explanation:
We know that Marcus wants to end the semester with at least an 85 test average in his math class. We can find the average of his first three test scores by adding them up and dividing by 3:
(83 + 97 + 80) / 3 = 86.67
So currently, Marcus has an average of 86.67. Let g represent the grade he needs on his fourth test to reach his goal of an 85 average.
To find the inequality, we can use the formula for the average of four numbers:
(83 + 97 + 80 + g) / 4 ≥ 85
This inequality states that the average of the four test scores (including the unknown fourth score, g) must be greater than or equal to 85.
Now we can solve for g:
(83 + 97 + 80 + g) / 4 ≥ 85
260 + g ≥ 340
g ≥ 80
This means that Marcus must earn at least an 80 on his fourth test to achieve an average of 85 or higher for the semester.
In other words, if Marcus earns an 80 or higher on his fourth test, he will achieve his goal of an 85 or higher average for the semester. If he earns less than an 80, his average for the semester will be less than 85.
$800 at 7% compounded annually for 2 years
Answers
Answer:
$115.92
Step-by-step explanation:
To calculate compound interest, which Amount - Principal but we dont know the value for amount so we find the amount first by using the formula.
A = P ( 1 + R ) ^n
100
where p = principal ($800)
a = amount (?)
r = interest rate (7%)
n = time ( no of years) (2)
A = 800 ( 1 + 7 ) ^2
100 A = 800 ( 1 + 0.07) ^2
A = 800 ( 1.07)^2 = 800 ( 1.1449)
A = 915.92.
We then find compound interest with:
C = Amount - Principal = $915.92 - $800 = $115.92
Help will give brainiest and 20 points, Here is the data above. If you don’t answer properly I will report
How many more students enrolled in drivers education in 2005 than in 1995? Pls give a full sentence and explain how you did it.
Answers
Answer:
In total 177 more students enrolled this year.
Step-by-step explanation:
First get the sum of the students who enrolled in 1995, then the sum of 2005 and then subtract the sums.
Answer:
177 more students
Step-by-step explanation:
1995 had 65 students enrolled
females - 23 males - 42
23 + 42 = 65
2005 had 242 students enrolled
113 + 129 = 242
now to get how many more, you'll want to subtract
242 - 65 = 177
we know this is correct by adding 65 to 177
177 + 65 = 242
either way our answers will be the same
Hope this helps you!
~tnyu
15r + 8 = 11r - 20 solve for r and show your work in rows
Answers
Answer:
r=-7
Step-by-step explanation:
\(15r - 11r = - 20 - 8\)
\(4r = - 28\)
\(r = - 28 \div 4 = - 7\)
Answer:
r= -7
Step-by-step explanation:
15r+8=11r-20 (minus 11r from both sides)
4r+8=-20 (minus 8 from both sides)
4r = -28 (divide both sides by 4)
r= -7
what is 90,000 in standard form
Answers
Answer:
9*10^4
Step-by-step explanation:
Answer:
90,000 is written and 9x 10^4 in scientific notation
c) Convert the following from standard notation to scientific notation.
Depth of the deepest part of the ocean: 10,900 meters
Answers
Answer:
1.09x10^4
Step-by-step explanation:
An urn has 4 green balls and 6 red balls. A experiment consists of selecting 5 balls from the urn without replacement. Find the expected number of red balls chosen, and its variance.
Answers
The expected variance of red balls chosen is 2/3 from the urn.
Define the term variance?Variability is measured by the variance. The average of the squared variance is used to calculate it. The degree of dispersion within your data set is indicated by variance. The variance is greater in respect to the mean the more dispersed the data.Six red balls and four green balls are in an urn.
Till a urn is empty, we take balls out of it one at a time without replacing them and noting their order of the colors.
Let X represent the proportion of red balls in the initial five drawings.Y represent the proportion in the next five draws.The, the variance is found as-
Variance(X,Y) = E(XY) - E(X).E(Y).E(XY)
E(XY) = 25×(6/10)(4/9)
E(X) = 5×(6/10)
E(Y) = 5×(4/10)
Thus,
Variance(X,Y) = 25(6/10)(4/9) - 25(6/10)(4/10)
Variance(X,Y) = 2/3
Thus, the variance for choosing red balls is 2/3.
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La edad de Ericka es el tripl de la edad de Liliana y hace 9 años la suma de sus edades era 22. ¿Cuantos años tiene actualmente Liliana?
Answers
Answer:
Liliana tiene 10 años.
Step-by-step explanation:
Definamos las variables:
E = edad de Ericka
L = edad de Liliana.
Primero sabemos que la edad de Ericka es el triple de la edad de Liliana, entonces:
E = 3*L
Tambien sabemos que hace 9 años la suma de sus edades era 22
Hace nueve años la edad de Ericka era E - 9
Y hace nueve años la edad de Liliana era L - 9
Entonces tenemos:
(E - 9) + (L - 9) = 22
Así, tenemos un sistema de dos ecuaciones:
E = 3*L
(E - 9) + (L - 9) = 22
Queremos conocer la edad actual de Liliana.
Para ello tenemos que despejar E en una de las ecuaciones.
Podemos ver que en la primer ecaución E ya está aislada, entonces nos saltamos ese paso.
Ahora, reemplazamos E en la otra ecuación:
(E - 9) + (L - 9) = 22
(3*L - 9) + (L - 9) = 22
Ahora podemos resolver esto para L
3*L - 9 + L - 9 = 22
4*L - 18 = 22
4*L = 22 + 18
4*L = 40
L = 40/4 = 10
L = 10
Liliana tiene 10 años.
write the reciprocal of the following numbers.
Number: 7/10. Reciprocal______
Number: 1/2. Reciprocal______
Number: 5. Reciprocal_______
Answers
Answer:
7/10 = 10/7
1/2 = 2/1
5 = 1/5
Step-by-step explanation:
The reciprocal is the flip of a fraction. 1/2 = 2/1
For a whole number (like 5) you put it over 1 (5/1) and then flip it (1/5)
Have a nice day! :)
Make me brainliest.
Find the nth Maclaurin polynomial for the function. F(x) = tan x, n = 3 P3(x)=
Answers
The nth Maclaurin polynomial for the function f(x) = tan(x) when n = 3 is P3(x) = x + (1/3)x^3.
The Maclaurin polynomial is a polynomial approximation of a function that is centered at x = 0. It is a special case of the Taylor series, which is a power series expansion of a function about a given point. The Maclaurin series of a function is simply the Taylor series about x = 0.
To find the nth Maclaurin polynomial for the function f(x) = tan(x) when n = 3, we first need to find the derivatives of the function up to order n = 3. The derivatives of tan(x) are:
f(x) = tan(x)
f'(x) = sec^2(x)
f''(x) = 2sec^2(x)tan(x)
f'''(x) = 2sec^2(x)[2tan^2(x)+sec^2(x)]
Next, we evaluate these derivatives at x = 0 to obtain the Maclaurin coefficients:
f(0) = 0
f'(0) = 1
f''(0) = 0
f'''(0) = 2
Using the Maclaurin coefficients and the general formula for the Maclaurin polynomial, Pn(x) = Σ(k=0 to n) [f^k(0)/k!]*x^k, we can find the nth Maclaurin polynomial for f(x) = tan(x) when n = 3:
P3(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3
= 0 + 1x + 0x^2 + (2/3!)x^3
= x + (1/3)x^3
Therefore, the nth Maclaurin polynomial for f(x) = tan(x) when n = 3 is P3(x) = x + (1/3)x^3.
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Find the area of the figure
Answers
Suppose x has a distribution with a mean of 80 and a standard deviation of 3. Random samples of size n 36 are drawn. (a) Describe the x distribution. Oxhas an approximately normal distribution. Oxhas
Answers
The x distribution in this scenario is approximately normal, centered around a mean of 80, and has a standard deviation of 3.
The x distribution has an approximately normal distribution. Since x has a mean of 80 and a standard deviation of 3, it implies that the distribution is centered around the mean of 80, and the values tend to cluster closely around the mean with a spread of 3 units on either side.
The use of the term "approximately" indicates that the distribution may not be perfectly normal but closely follows a normal distribution. This approximation is often valid when the sample size is sufficiently large, such as in this case where random samples of size n = 36 are drawn.
The normal distribution is a symmetric bell-shaped distribution characterized by its mean and standard deviation. It is widely used in statistical analysis and modeling due to its well-understood properties and the central limit theorem, which states that the sample means of sufficiently large samples from any population will follow a normal distribution.
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What is the slope? A little bit of help. Due today at 11:59pm.
Answers
Answer:
2
Step-by-step explanation:
Answer:
The slope is 2
Step-by-step explanation:
(y2-y1)/(x2-x1)=m
Your Scenario:
(0-(-3))/(1.5-0)=2
The slope is 2 m=2
Sam's dad gave him $30 for washing their car. He used the money to buy a basketball for $7.50 and three sports drinks for $2.75 each. Sam also bought a bag of candy. If Sam went home with 13 of the money his dad gave him, how much did the bag of candy cost?
Answers
Answer:
Basketball + Sports Drink
$7.50 + $2.75 = $10.25
$10.25 + ? + $13 = $30
30 - 23.25 = 6.75
help me
pleaseeee
i need help
Answers
Answer:
4:2:3
Step-by-step explanation:
First you need to divide each number by a common factor like 2.
1. 16:8:12
Divide all numbers by two
8:4:6
Divide by two again
4:2:3
Since, you cannot simplify all of them again, the asnwer is
4:2:3
Answer:
4:2:3
Step-by-step explanation:
Blue : Green : Red
16 : 8 : 12
4 : 2 : 3
You invest $20,000 in the stock market. The stock market then plummets
over the next few weeks. Each day, your investment loses half of its value. How
much will you have invested after 14 days? Write the geometric sequence
formula and show all of your work.
Answers
After 14 days, you will have approximately $2.4414 invested in the stock market.
The amount you will have invested after 14 days can be calculated using the geometric sequence formula. The formula for the nth term of a geometric sequence is given by:
an = a1 x \(r^{(n-1)\)
Where:
an is the nth term,
a1 is the first term,
r is the common ratio, and
n is the number of terms.
In this case, the initial investment is $20,000, and each day the investment loses half of its value, which means the common ratio (r) is 1/2. We want to find the value after 14 days, so n = 14.
Substituting the given values into the formula, we have:
a14 = 20000 x\((1/2)^{(14-1)\)
a14 = 20000 x \((1/2)^{13\)
a14 = 20000 x (1/8192)
a14 ≈ 2.4414
Therefore, after 14 days, you will have approximately $2.4414 invested in the stock market.
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The amount you will have invested after 14 days is given as follows:
$2.44.
What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.
The explicit formula of the sequence is given as follows:
\(a_n = a_1q^{n-1}\)
In which \(a_1\) is the first term of the sequence.
The parameters for this problem are given as follows:
\(a_1 = 20000, q = 0.5\)
Hence the amount after 14 days is given as follows:
\(a_{14} = 20000(0.5)^{13}\)
\(a_{14} = 2.44\)
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name a pair of corresponding angles
name a pair of alternate interior angles
name a pair of alternate exterior angles
name a pair of same-side interior angles
Answers
They are on the same side of the transversal cut (both to the left of the transversal) and they are both above the two black lines. It might help to make those two black lines to be parallel, though this is optional.
Other pairs of corresponding angles could be:
angle 2 and angle 6angle 3 and angle 7angle 4 and angle 8=======================================================
Alternate interior angles = angle 3 and angle 5They are between the black lines, so they are interior angles. They are on alternate sides of the blue transversal, making them alternate interior angles.
The other pair of alternate interior angles is angle 4 and angle 6.
=======================================================
Alternate exterior angles = angle 1 and angle 7Similar to alternate interior angles, but now we're outside the black lines. The other pair of alternate exterior angles is angle 2 and angle 8
=======================================================
Same-side interior angles = angle 3 and angle 6The other pair of same-side interior angles is angle 4 and angle 5. They are interior angles, and they are on the same side of the transversal.