Answer:
The sum is -1/2
Step-by-step explanation:
Your question is not too clear to me but if I reframe it, it will turn to this;
Find the sum of In{1 - (1/n^2)} for n >= 2
£n>=2 = In{1 - (1/2^2)} + In{1 - (1/3^2)} + In{1 - (1/4^2)} + ......
£n>=2 = In{1 - (1/4)} + In{1 - (1/9)} + In{1 - (1/16)}
£n>=2 = In(3/4) + In(8/9) + In(15/16)
£n>=2 = -0.287 + -0.117 + -.064 = −0.468
£n>=2 = -0.5 by approximation
£n>=2 = -1/2 is the sum and by evaluation it converge.
Robert surveyed 300 of the students in his school about their favorite color. 70% said their favorite color was blue. How many students' favorite color was blue?
Answer:
210
Step-by-step explanation:
We can get 10% of 300 by doing 300 / 10 which is 30. 70 / 10 is 7, so we need 7 lots of 10% to work out 70%. Therefore, 30 * 7 students said that their favourite colour was blue, which is 210.
Answer:
210
Step-by-step explanation:
So 70% OF 300 students said their favorite color was blue
OF means multiply and 70% is equal to .70 so,
.70 x 300 = the number of students that said their favorite color was blue
=210
So, the number of students that said their favorite color was blue is 210 students. :)
Is f(x) = 3x2 - 6x + 2 an example of a quadratic?
Yes
No
Find the unique solution to the following linear system X = (0 -1 2 3)X + (e' -e')
X(0)=(5 4)
It looks like the system is supposed to be
[tex]\mathbf x'=\begin{bmatrix}0&-1\\2&3\end{bmatrix}\mathbf x+\begin{bmatrix}e^t\\e^{-t}\end{bmatrix}[/tex]
with the initial condition, [tex]\mathbf x(0)=\begin{bmatrix}5&4\end{bmatrix}^\top[/tex].
Compute the eigensystem for the coefficient matrix:
[tex]\begin{vmatrix}-\lambda&-1\\2&3-\lambda\end{vmatrix}=\lambda^2-3\lambda+2=(\lambda-1)(\lambda-2)=0[/tex]
[tex]\lambda_1=1\implies\begin{bmatrix}-1&-1\\2&2\end{vmatrix}\mathbf v_1=\mathbf 0\implies\mathbf v_1=\begin{bmatrix}1\\-1\end{bmatrix}[/tex]
[tex]\lambda=2\implies\begin{bmatrix}-2&-2\\2&1\end{bmatrix}\mathbf v_2=\mathbf 0\implies\mathbf v_2=\begin{bmatrix}1\\-2\end{bmatrix}[/tex]
So we have the characteristic solution,
[tex]\mathbf x_c=C_1e^{\lambda_1t}\mathbf v_1+C_2e^{\lambda_2t}\mathbf v_2[/tex]
[tex]\mathbf x_c=C_1e^t\begin{bmatrix}1\\-1\end{bmatrix}+C_2e^{2t}\begin{bmatrix}1\\-2\end{bmatrix}[/tex]
For the non-homogeneous part, we can guess a particular solution of the form
[tex]\mathbf x_p=te^t\begin{bmatrix}a\\b\end{bmatrix}[/tex]
(We might have started with [tex]e^t[/tex] instead, but that is already accounted for in the first characteristic solution.)
Its derivative is
[tex]{\mathbf x_p}'=e^t\begin{bmatrix}a\\b\end{bmatrix}+te^t\begin{bmatrix}a\\b\end{bmatrix}=e^t\begin{bmatrix}at+a\\bt+b\end{bmatrix}[/tex]
Substitute [tex]\mathbf x_p[/tex] into the system and solve for [tex]a,b[/tex]:
[tex]e^t\begin{bmatrix}at+a\\bt+b\end{bmatrix}=te^t\begin{bmatrix}0&-1\\2&3\end{bmatrix}\begin{bmatrix}a\\b\end{bmatrix}+e^t\begin{bmatrix}1\\-1\end{bmatrix}[/tex]
[tex]\begin{bmatrix}at+a\\bt+b\end{bmatrix}=\begin{bmatrix}-bt+1\\(2a+3b)t-1\end{bmatrix}[/tex]
[tex]\implies a=1,b=-1[/tex]
and so the particular solution is
[tex]\mathbf x_p=te^t\begin{bmatrix}1\\-1\end{bmatrix}[/tex]
The general solution to the system is then
[tex]\mathbf x=\mathbf x_c+\mathbf x_p[/tex]
[tex]\mathbf x=C_1e^t\begin{bmatrix}1\\-1\end{bmatrix}+C_2e^{2t}\begin{bmatrix}1\\-2\end{bmatrix}+te^t\begin{bmatrix}1\\-1\end{bmatrix}[/tex]
Use the given initial conditions to solve for the remaining coefficients.
[tex]\mathbf x(0)=\begin{bmatrix}5\\4\end{bmatrix}[/tex]
[tex]\implies\begin{bmatrix}5\\4\end{bmatrix}=C_1\begin{bmatrix}1\\-1\end{bmatrix}+C_2\begin{bmatrix}1\\-2\end{bmatrix}[/tex]
[tex]\implies C_1=14,C_2=-9[/tex]
Then the solution to the initial value problem is
[tex]\mathbf x=14e^t\begin{bmatrix}1\\-1\end{bmatrix}-9e^{2t}\begin{bmatrix}1\\-2\end{bmatrix}+te^t\begin{bmatrix}1\\-1\end{bmatrix}[/tex]
[tex]\mathbf x=\begin{bmatrix}14e^t-9e^{2t}+te^t\\-14e^t-18e^{2t}-te^t\end{bmatrix}[/tex]
On a map scale, 2 inches represents 60 miles. Which graph best shows the relationship
between x, the number of inches on the map, and y, the actual distance in miles?
Answer:
c best shows the best relationship
The length of a rectangle is 6 more than its width. The perimeter is 48 inches. What is the length?
Answer:
[tex]15[/tex] inches
Step-by-step explanation:
Let the width be x.
Length = [tex]6+x[/tex]
Perimeter = Length + Length + Breadth + Breadth
Perimeter = [tex](6+x)+(6+x)+x+x=48[/tex]
[tex]6+x+6+x+x+x=48[/tex]
[tex]4x+12=48[/tex]
Subtract 12 from both sides:
[tex]4x+12-12=48-12[/tex]
[tex]4x=36[/tex]
Divide both sides by 4:
[tex]\frac{4x}{4}=\frac{36}{4}[/tex]
[tex]x=9[/tex] (Width)
Length = [tex]9+6=15[/tex] inches.
Answer:
l = 15 inches
Step-by-step explanation:
l = w + 6
p = 2l + 2w
substitute l into equation p
48 = 2(w + 6) + 2w
distribute the 2 into the parentheses
48 = 2w + 12 + 2w
combine like terms
48 = 4w + 12
subtract 12 from both sides
36 = 4w
divide by 4
9 = w
plug w into equation l
(9) + 6 = 15
l = 15 inches
The scale from an actual triangle to the drawing at the right is 30:1. The scale from the same triangle to Jorge's drawing of the triangle is 101. Is this drawing or Jorge's drawing larger? Explain your answers.
Answer:
The actual triangle is larger
Step-by-step explanation:
Given
[tex]Scale = Actual Triangle : Drawing[/tex]
[tex]Scale = 30 : 1[/tex]
[tex]Jorge = 101[/tex]
Required
Determine which is bigger
The answer to this question can be extracted from the given scale.
The question says: the scale from the actual triangle to the drawing is 30 : 1.
This implies that;
If Jorge's drawing is 101, then the actual length is 30 * 101 =3030
Since, 3030 > 30, then
We cam conclude that the actual triangle is bigger
Please help ive been stuck on this question all weekend long !!
Answer:
The answer is 57.
Step-by-step explanation:
You have to substitute w = 2 into the expression :
[tex]8 {w}^{2} + 8w + 9[/tex]
[tex]let \: w = 2[/tex]
[tex]8 {(2)}^{2} + 8(2) + 9[/tex]
[tex] = 32 + 16 + 9[/tex]
[tex] = 57[/tex]
Answer:
57
Step-by-step explanation:
[tex]8*2^{2}+8*2+9\\8*4+16+9\\32+16+9\\48+9\\57[/tex]
A right rectangular prism has a base area of 2 1/2 square inches and a height of 11 1/2 inches.
What is the volume of the prism?
Answer:14in 3
Step-by-step explanation:
4/5 × 2 3/8 - 2 × 3/5
Pentagon ABCDE was enlarged:
What is the ratio of enlargement to the original? Convert the ratio to a percent.
Answer/Step-by-step explanation:
The ratio of the enlargement to the original = A'E' to AE = A'E':AE = A'E'/AE
AE = 2.5
A'E' = 4
Ratio of the enlargement to the original = 4:2.5 = 1.6:1
To convert to percentage, divide 4 by 2.5 and multiply by 100.
[tex] = \frac{4}{2.5}*100 [/tex]
[tex] = 1.6*100 [/tex]
[tex] = 160 percent [/tex]
Is the square root of 21 a rational number
Answer:
No
Step-by-step explanation:
But as we've stated, these prime factorizations are unique, so this can't be right. Therefore 21≠a2 , so a≠√21 , meaning that our earlier assumption of √21 being rational turns out to be wrong, therefore √21 is irrational.
Suppose a couple has two children, and you know that at least one is a boy. If the probabilities of having a boy or a girl are both 0.5 for any birth, what is the probability that the couple has two boys in this situation? When calculating this conditional probability, you may want to think of the ordered sample space for two kids as S = {bb, bg, gb, gg} . We can assume that births are independent events.
Answer:
The probability of having two boys = 25%
Step-by-step explanation:
The ordered sample space for two kids is given as S = {bb, bg, gb, gg},
where bb = two boys, bg = a boy and a girl, gb = a girl and a boy, and gg = two girls, in that particular order.
bb occurs 1/4 times
and 1/4 = 0.25 or 25%
Calculating the probability of having two boys is given as the probability of having a boy multiplied by the probability of having a boy
= 0.5 x 0.5
= 0.25
= 25%
This agrees with the ordered sample space given above.
Which expression is NOT equivalent to 60+1260+12?
Answer:60+1260+13 isnt equivalent
Step-by-step explanation:
Find an equation of the line through (3,8) and parallel to y = 4x - 3.
Answer: y=4x-4
Step-by-step explanation:
To find the equation fo the line parallel to the given line, we can use the given point to find the y-intercept. We know that the slope must stay the same because parallel lines NEVER touch or cross. This means that the slope MUST be the same.
y=4x+b
We can use the given point to find the y-intercept.
8=4(3)+b [multiply]
8=12+b [subtract both sides by 12]
b=-4
Now that we have found the y-intercept, we can complete the equation.
y=4x-4
In Nebraska, the mean rain-fed corn yield of harvested fields are normally
distributed, produce 147.2 bushels per acre with a standard deviation of 33 bushels per acre.
How many bushels per acre are produced if a field is in the top 25%?
O 180.2
O 125.2
O 155.45
O 169.2
Answer: 169.2 per acre are produced if a field is in the top 25%.
Step-by-step explanation:
Given: The mean rain-fed corn yield of harvested fields are normally distributed, produce 147.2 bushels per acre with a standard deviation of 33 bushels per acre.
Let X denote the mean rain-fed corn yield of harvested fields.
Let x denotes the number of bushels per acre are produced if a field is in the top 25%.
Top 25% on a density curve means , (100-25%)i.e. 75% area lies below x.
I.e.
[tex]P(X<x)=P(\dfrac{X-\mu}{\sigma}<\dfrac{x-147.2}{33})=0.75\\\\\Rightarrow\ P(Z<\dfrac{x-147.2}{33})=0.75\ \ [Z=\dfrac{X-\mu}{\sigma}][/tex].
Z-score for p-value of 0.75 (one tailed)=0.67 [By z-table]
Then, [tex]\dfrac{x-147.2}{33}=0.6744[/tex]
[tex]\Rightarrow\ {x-147.2}=33\times0.67\\\\\Rightarrow\ {x-147.2}=22.11\\\\\Rightarrow\ {x}=22.11+147.2=169.31[/tex]
Here approx value is 169.2 (from options).
So, 169.2 per acre are produced if a field is in the top 25%.
A concerned parent wants to determine the amount of time spent on the phone by her child's friends. Which sample is likely to bias the results of the study by reporting less than the actual time? Group of answer choices
Answer: The answers to the questions by 10 of the friends
Step-by-step explanation:
The options to the question are:
a. The answers to the questions by the parents of 10 of the friends.
b. The results of a national poll of 1800 students in the same age group as the child.
c. The answers to the questions by 10 of the friends.
d. The answers to the questions by 10 people from the parents office.
From the question, we are informed that a concerned parent wants to determine the amount of time spent on the phone by her child's friends. The sample that is likely to bias the results of the study by reporting less than the actual time is the answers to the questions by 10 of the friends.
This is because since the questions are being asked from her friends, there'll be bias as the friends won't want to give the exact time used on phone, hence, they'll hold back some information.
POS
In a game, two cards are drawn, and then multiplied. The winner is the person with the largest product. Explain who won the game.
-8
4
-6
-6
SOFIA
Luke
O Luke 36 < 32
O Sofia, 32 36
O Luke. -32 < 36
O Sofia, 32 - 36
Answer:
Luke, -32 < 36
Step-by-step explanation:
The two cards drawn by Sofia has values of -8 and 4 respectively. The product of her cards = -8 × 4 = -32. (Negative × positive = (negative)
The two cards drawn by Luke has values of -6 and -6 respectively. The product of his cards = -6 × -6 = 36 (negative × negative = positive).
36 greater than -32.
Luke had the largest product because -32 < 36.
Jonathon has 3/4 pound of grapes. How many 1/8 pound servings can Jonathon make from his grapes? Do not include units. *
Answer:
This would be 6 of 1/8 pound of serving
Answer:
6 out of 1/8
Step-by-step explanation:
what is the answer for 7.42 ÷ 1.75 = ______
Answer:
4.24
Step-by-step explanation:
3 – (–3) + 7 – 4 =
A)
14
B)
12
C)
2
D)
9
Answer:
D) 9Step-by-step explanation:
[tex]3 - (-3) + 7 - 4 =\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:\:\\\\\mathrm{Apply\:rule\:}-\left(-a\right)\:=\:+a\\\\-\left(-3\right)=+3\\\\=3+3+7-4\\\\3+3=6\\\\=6+7-4\\\\6+7=13\\\\=13-4\\\\13-4\\=9[/tex]
A rectangular piece of paper has an area of 119 square Inches and a perimeter of 48 inches What are the dimensions of the paper?
Answer:
17in by 7in
Step-by-step explanation:
17x7=119
17+17+7+7=48
Question 6 (0.5 points)
Find the midpoint of the line segment with endpoints (9, -8) and (-6, -3)
0 (0.5, -4.5)
(1.5.-5.5)
0 (7.5, -2,5)
O(-21, 2)
Question 710 5 noints)
Answer:
Step-by-step explanation:
(9-6)/2 = 3/2 = 1.5
(-8-3)/2 = -11/2 = -5.5
(1.5, -5,5)
solve for X: 5X +2 = 4X -9
Answer:5X+2=4X-9\quad :\quad X=-11
Step-by-step explanation:
5X+2=4X-9
5X+2-2=4X-9-2
5X=4X-11
5X-4X=4X-11-4X
X=-11
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ \: \: X \: = - 11}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{5 \: X + 2 = 4 \: X - 9}[/tex]
Move 4 X to left hand side and change it's sign
Similarly, move 2 to right hand side and change it's sign
[tex] \longrightarrow{ \sf{5 \: X - 4 \: X = - 9 - 2}}[/tex]
Collect like terms
[tex] \longrightarrow{ \sf{X = - 9 - 2}}[/tex]
The negative and positive integers are always subtracted but posses the sign of the bigger integer
[tex] \longrightarrow{ \sf{X = - 11}}[/tex]
Hope I helped!
Best regards! :D
What is the product of Three-fourths and Negative StartFraction 6 over 7 EndFraction?
Answer:
-9/14
Step-by-step explanation:
product of Three-fourths and Negative StartFraction 6 over 7 EndFraction
[tex] = \frac{3}{4} \times \bigg( - \frac{6}{7} \bigg) \\ \\ = \frac{3 \times ( - 6)}{4 \times 7} \\ \\ = - \frac{18}{28} \\ \\ = - \frac{9}{14} \\ [/tex]
Answer:
-9/14 so the answer is B
Step-by-step explanation:
Hope this helps
There are only a few roller coasters in the world whose path takes them underground. Suppose a portion of the roller coaster can be modeled by the function f(t) = (t2 − 13t + 40)(t2 − 2t + 3), where t represents the time elapsed in seconds since passing point A on the roller coaster and f(t) represents the height in feet above the ground. What am I supposed to write on the ticket?
Answer:
the blanks are in this order the top two are 5 and 8
then (-,+,+)
then (-,-,+)
then (+,+,+)
last (+,-,+)
Step-by-step explanation:
Triangle ABC has coordinates A(-2,0), B(0,2) and C(-4, 3). It is reflected across the line y = 2/5x - 2. About where is B’ located? What is the equation of the line that joins CC’? (2 points)
Answer:
B' is at (2.76,-4.9)
Equation of CC' is 11.38x+4.55y= -31.86
or at its slope-intercept form:
y= (-11.38x - 31.86)/4.55
Step-by-step explanation:
Sickle-cell disease is a painful disorder of the red blood cells that in the United States affects mostly African-Americans. To investigate whether the drug hydroxyurea can reduce the pain associated with sickle-cell disease, a study by the National Institutes of Health gave the drug to 150 sickle-cell sufferers and a placebo to another 150. The researchers then counted the number of episodes of pain reported by each subject. What is the response variable in this study
Answer:
The response variable is the episodes of pain reported
Step-by-step explanation:
A response variable, also known as the dependent variable or explanatory variable, is the variable that is not under the direct control of the researcher, but whose value varies with the changing of the independent variable. The response variable is the focus of the experimental question.
In this example, the effect of the drug hydroxyurea is to be tested on sickle-cell patients, hence the drug used is the independent variable, because the experimenter can choose to give the subjects either hydroxyurea or a placebo, hence it is under the direct control of the experimenter. However, the result ( differences in episodes of pain) is a response to the administered drug or placebo.
How many three-digit numbers are multiples of neither 5 nor 7?
Answer:
590Step-by-step explanation:
Total 3-digit numbers 100 to 999
999 - 99 = 9003 digit multiples of 5; 100 to 995
smallest one 100 = 5*20greatest one 995 = 199*5number 199 - 4 = 1953 digit multiples of 7:
smallest one 105/7 = 15greatest one 994/7 = 142number 142 - 14 = 128Total multiples of either 5 or 7 :
195 + 128 = 323This number includes multiples of both 5 and 7
We need to exclude half of the multiples of 5*7= 35 as they are counted twice:
smallest one 105 = 35*3greatest one 980 = 28*35number 28 - 2 = 26Half of this is 26/13 = 13
323 - 13 = 310The difference of 900 and 310 is the answer:
900 - 310 = 5905√3+3√12 can anyone help me figure this out
Answer:
18.29
Step-by-step explanation:
hope this helped
really need this, it will help alottt
Answer:
[tex]\huge\boxed{m = \frac{y-b}{x}}[/tex]
Step-by-step explanation:
In order to solve for [tex]y=mx+b[/tex] and we want to solve for [tex]m[/tex], we want to get m on one side of the equation.
[tex]y = mx+b[/tex]
Let’s subtract b from both sides.
[tex]y - b = mx[/tex]
Now we can divide both sides by x so we have m on one side of the equation.
[tex]\frac{y-b}{x} = m[/tex]
Hope this helped!
