To evaluate the expression for x = -3, we simply put in -3 whereever we see x in the expression.
Doing this gives us
[tex]2(x-1)\rightarrow2(-3-1)[/tex]We now simplify the expression on the right
[tex]=2(-4)[/tex][tex]=-8[/tex]which is our answer!
I mostly need to know if this are correct and if the answers would gave been affected.
Yes, your answers are correct.
And the answer would be different if the non-Normal because all the calculations are based on a normal ditributed production of the chocolate bars; if the production of the chocalte bars had a non normal distribution, for example a skewed distribution (to the left or to the right) all the values used in the calculation would be different.
Write an equation for the line that passes through the given point and is perpendicular to the graph of the given equation y=-2x-1; (2, -1)
The product of the slopes of the perpendicular lines = -1
If the slope of one is m, then the slope of the other is -1/m
The given equation is y = -2x - 1
The form of the equation is y = m x + b, where
m is the slope of the line
So the slope of the given line is m = -2
To find the slope of the perpendicular line reciprocal it and change its sign
The slope of the perpendicular line = 1/2
Substitute it in the form of the equation
y = 1/2 x + b
To find b substitute x and y of the equation by the coordinates of any point on the line
The line passes through point (2, -1), then
x = 2 and y = -1
-1 = 1/2 (2) + b
-1 = 1 + b
Subtract 1 from both sides to find b
-1 - 1 = 1 - 1 + b
-2 = b
The equation of the perpendicular line is
y = 1/2 x - 2
[tex]y=\frac{1}{2}x-2[/tex]Each gallon of gas cost $2.50. Nathan spent $30 on gas. Which value of x represents the number of gallons of gas Nathan purchased?
we have the following:
[tex]\begin{gathered} x=\frac{30}{2.5} \\ x=12 \end{gathered}[/tex]therefore the number of galllons is 12
Perform the following mathematical operation and report the answer to the appropriate number of significant figures.
We know the least precise place value is in the 10's place.
67.4 +43 +30 + 42.10 = [?]
The least precise place value is in the 10's place is 182.5.
Given that, 67.4 +43 +30 + 42.10.
What are decimal numbers?Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point.
Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value.
Now,
67.4 + 42.10 + 73
= 109.5 + 73
= 182.5
Hence, the least precise place value is in the 10's place is 182.5.
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Select the correct answer.A local magazine, available by subscription and at newsstands, mailed a comment card to each of its subscribers. It asked the readers how satisfied they were with the magazine's coverage of local events and interests. Based on the information received from the comment cards, the magazine created a television ad saying that 97% of its readers were extremely satisfied with the content of the magazine.Why might this sample be biased?A. The magazine changed its content for the issue including the comment card.B. Very few comment cards were returned.C. The survey only considered subscribers, and not those who purchase the magazine at newsstands.D. Not enough comment cards were distributed.
Hello there. To solve this question, we'll analyze each of the options and determine why it is the case for this sample to be biased.
We know that this local maganize is available by subscription and at newsstands and they asked the readers by mailing them comment cards for the subscribers.
A. The magazine changed its content for the issue including the comment card.
Since the question didn't mention this fact, we cannot assume this to be a correct option, we only know they sent comment card to the readers.
B. Very few comment cards were returned
The question says that 97% of the readers were extremely satisfied with the content of the magazine. But we know that these readers that received a comment card were subscribers.
This means that, considering each subscriber sent its comment card back, 3% of them were not satisfied, but we don't know how many subscribers this magazine has.
Hence this answer is not correct as well.
C. The survey only considered subscribers, and not those who purchase the magazine at newsstands.
This might be the answer, considering that the comment card were only mailed to the subscribers and, since we don't know the proportion between subscribers and those who buy at the newsstands, this sample is biased.
D. Not enough comment cards were distributed.
The question said that the magazine mailed a comment card for each of its subscribers, so we cannot take this option into consideration.
[tex]4 \sqrt{5} (3 \sqrt{5} + 8 \sqrt{2} )[/tex]how do u do this
we have
[tex]4\sqrt{5}(3\sqrt{5}+8\sqrt{2})[/tex]Apply distributive property
[tex]4\sqrt{5}(3\sqrt{5})+4\sqrt[]{5}(8\sqrt{2})[/tex][tex]12\sqrt[]{25}+32\sqrt[]{10}[/tex]simplify
[tex]\begin{gathered} 12(5)+32\sqrt[]{10} \\ 60+32\sqrt[]{10} \end{gathered}[/tex]This is solving rational equationsI really need some help. Please explain how you get each step if u can.
We are given the following equation:
[tex]\frac{-4}{x+4}=-\frac{3}{x+6}[/tex]we are asked to determine any extraneous solutions. To do that we will determine the values of "x" that solve the equation. First, we will cross multiply the equation:
[tex]-4(x+6)=-3(x+4)[/tex]Now, we can multiply by -1, we get:
[tex]4(x+6)=3(x+4)[/tex]Now we use the distributive property on both sides, we get:
[tex]4x+24=3x+12[/tex]Now, we subtract "3x" from both sides:
[tex]\begin{gathered} 4x-3x+24=3x-3x+12 \\ x+24=12 \end{gathered}[/tex]Now we subtract 24 from both sides:
[tex]\begin{gathered} x+24-24=12-24 \\ x=-12 \end{gathered}[/tex]Therefore, the solution is x = -12. The extraneous solutions are the solutions that are not in the domain of the original function.
In the domain of the original function, we have that the values of:
[tex]\begin{gathered} x=-4 \\ x=-6 \end{gathered}[/tex]Would make the denominators equal to zero, and therefore, they are not in the domain. Since the solution is none of these values there are no extraneous solutions.
Knowledge check that with the kids on the other hand ✋ the
. The function h measures the height.
. The units on h meters.
. h'(t) measures the velocity
. The units on h'(t) are meters per second
. The units on t are seconds
a bank loaned out 2000, part of it at the rate of 8% per year and the rest at 16% per year. If the interest received in one year totaled $2000, how much was loaned at 8%?
The amount loaned at 8% interest is $15000
How to find how much was loaned at 8%?Using the simple interest formula, we find the interest obtained at each rate.
Simple interest, I = PRT where
P = initial amount, R = rate and T = timeNow, the interest obtained at 8%,I₁ = P₁R₁T where
P₁ = amount loaned at 8%, R₁ = rate = 8% per year = 0.08 and T = time = 1 year
Also, the interest obtained at 16%,I₂ = P₂R₂T where
P₂ = amount loaned at 16%, R₂ = rate = 16% per year = 0.16 and T = time = 1 yearSo, the total interest received is I = I₁ + I₂
= P₁R₁T + P₂R₂T
= P₁ × 0.08 × 1 + P₂ × 0.16 × 1
= 0.08P₁ + 0.16P₂
Since the total interest received is $2000,we have that
I = $2000.
So, I = 0.08P₁ + 0.16P₂
0.08P₁ + 0.16P₂ = 2000 (1)
Since the amount loaned by the bank is P = P₁ + P₂ and P = $20000, we have that
P₁ + P₂ = 20000
P₂ = 20000 - P₁ (2)
Substituting equation (2) into (1), we have that
0.08P₁ + 0.16P₂ = 2000 (1)
0.08P₁ + 0.16(20000 - P₁) = 2000
Expanding the brackets, we have
0.08P₁ + 0.16 × 20000 - 0.16P₁ = 2000
0.08P₁ + 3200 - 0.16P₁ = 2000
0.08P₁ - 0.16P₁ = 2000 - 3200
- 0.08P₁ = -1200
P₁ = -1200/-0.08
P₁ = 15000
So, the amount loaned at 8% is $15000
The question seems incomplete, here is the complete question
A bank loaned out $20,000, part of it at the rate of 8 % per year and the rest at 16 % per year. If the interest received in one year totaled $2000, how much was loaned at 8 %
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Which sentence of transformation could be used to show the congruence between the triangles? I’m not sure if the answer is A,B,C or D? Some help would be nice
Answer:
a translation of 1 unit to the right and 3 units up and then a reflection across the y-axis
Explanation:
First, let's identify the coordinates of the vertex R, S, T and its images R', S', and T'.
R(-6, -2) ---> R'(5, 1)
S(-5, -5) ---> S'(4, -2)
T(-3, -3) ---> T'(2, 0)
Then, we can observe that the transformation was a translation of 1 unit to the right and 3 units up and the a reflection over the y-axis because:
A translation of 1 unit right and 3 units up is made by the following rule
(x, y) ---> (x + 1, y + 3)
So, each vertex is translated to
R(-6, -2) ---> (-6 + 1, -2 + 3) = (-5, 1)
S(-5, -5) ---> (-5 + 1, -5 + 3) = (-4, -2)
T(-3, -3) ---> (-3+ 1, -3 + 3) = (-2, 0)
Then, the reflection over the y-axis is
(x, y) ---> (-x, y)
So,
(-5, 1) ---> R'(5, 1)
(-4, -2) ---> S'(4, -2)
(-2, 0) ---> T'(2, 0)
Therefore, the answer is:
a translation of 1 unit to the right and 3 units up and then a reflection across the y-axis
Which of the following is true with respect to the following functions:f(x) = 3] x + 14 | g(x)= x4 + 3x2 - 14h(x) = 3% +1i(x) = log2 (x + 1)
To answer the question, let us plot the graphs of all the functions.
f(x):
[tex]f(x)=3|x+14|[/tex]g(x):
[tex]g(x)=x^4+3x^2-14[/tex]h(x):
[tex]h(x)=3^x+1[/tex]i(x):
[tex]i(x)=\log _3(x+1)[/tex]From the graphs shown above, it can be seen that the range of the function i(x) goes from -∞ to +∞. This is the function with the greatest negative range.
Therefore, the correct option is OPTION D
identify the placevalue for each digit in the number 95.26
The place value of;
9 is 9 tens
5 is 5 unit
2 is 2 tenth
6 is 6 hundredth
Solve the system of equations by transforming a matrix representing the system of equation into reduced row echelon form. 2x+y-3z=-19 x+2y+z=-4 x-y+5z=21 what is the solution to the system of equations? Drag a choice into each box to correctly complete the table.
We want to write the following system
[tex]\begin{gathered} 2x+y-3z=-19 \\ x+2y+z=-4 \\ x-y+5z=21 \end{gathered}[/tex]As a matrix. To do that, we just take the coefficients and plug them in the same order in a matrix. Our system can be rewritten as:
[tex]\begin{bmatrix}{2} & 1 & {}-3 \\ {1} & {2} & 1{} \\ {1} & {-1} & {5}\end{bmatrix}=\begin{bmatrix}{-19} \\ {-4} \\ {21}\end{bmatrix}[/tex]Now, to solve this, we can use the gaussian elimination. It consists of adding, multiplying, and changing the order of the rows, until we have an identity matrix on the left side.
Let's start by subtracting the second row from the third row, and subtracting 2 times the second row from the first row.
[tex]\begin{gathered} \begin{bmatrix}{2-2\times1} & 1-2\times2 & {}-3-2\times1 \\ {1} & {2} & 1{} \\ {1-1} & {-1-2} & {5-1}\end{bmatrix}=\begin{bmatrix}{-19-2\times(-4)} \\ {-4} \\ {21-(-4)}\end{bmatrix} \\ \begin{bmatrix}{0} & -3 & {}-5 \\ {1} & {2} & 1{} \\ {0} & {-3} & {4}\end{bmatrix}=\begin{bmatrix}{-11} \\ {-4} \\ {25}\end{bmatrix} \end{gathered}[/tex]Multiplying the first row by (- 1), we have:
[tex]\begin{bmatrix}{0} & 3 & {}5 \\ {1} & {2} & 1{} \\ {0} & {-3} & {4}\end{bmatrix}=\begin{bmatrix}{11} \\ {-4} \\ {25}\end{bmatrix}[/tex]Adding the first row to the third row, we have:
[tex]\begin{gathered} \begin{bmatrix}{0} & 3 & {}5 \\ {1} & {2} & 1{} \\ {0} & {-3+3} & {4+5}\end{bmatrix}=\begin{bmatrix}{11} \\ {-4} \\ {25+11}\end{bmatrix} \\ \begin{bmatrix}{0} & 3 & {}5 \\ {1} & {2} & 1{} \\ {0} & {0} & {9}\end{bmatrix}=\begin{bmatrix}{11} \\ {-4} \\ {36}\end{bmatrix} \end{gathered}[/tex]Multiplying the last row by 1/9:
[tex]\begin{bmatrix}{0} & 3 & {}5 \\ {1} & {2} & 1{} \\ {0} & {0} & {1}\end{bmatrix}=\begin{bmatrix}{11} \\ {-4} \\ {4}\end{bmatrix}[/tex]Now, subtracting the third row from the second row, and subtracting 5 times the third row from the first row, we have:
[tex]\begin{gathered} \begin{bmatrix}{0} & 3 & {}5-5\times1 \\ {1} & {2} & 1-1{} \\ {0} & {0} & {1}\end{bmatrix}=\begin{bmatrix}{11-5\times4} \\ {-4-4} \\ {4}\end{bmatrix} \\ \begin{bmatrix}{0} & 3 & {0} \\ {1} & {2} & 0{} \\ {0} & {0} & {1}\end{bmatrix}=\begin{bmatrix}{-9} \\ {-8} \\ {4}\end{bmatrix} \end{gathered}[/tex]Dividing the first row by 3:
[tex]\begin{bmatrix}{0} & 1 & {0} \\ {1} & {2} & 0{} \\ {0} & {0} & {1}\end{bmatrix}=\begin{bmatrix}{-3} \\ {-8} \\ {4}\end{bmatrix}[/tex]Subtracting the twice the first row from the second row:
[tex]\begin{gathered} \begin{bmatrix}{0} & 1 & {0} \\ {1} & {2-2\times1} & 0{} \\ {0} & {0} & {1}\end{bmatrix}=\begin{bmatrix}{-3} \\ {-8-2\times(-3)} \\ {4}\end{bmatrix} \\ \begin{bmatrix}{0} & 1 & {0} \\ {1} & {0} & 0{} \\ {0} & {0} & {1}\end{bmatrix}=\begin{bmatrix}{-3} \\ {-2} \\ {4}\end{bmatrix} \end{gathered}[/tex]And finally, permuting the first and the second row
[tex]\begin{bmatrix}{1} & 0 & {0} \\ {0} & {1} & 0{} \\ {0} & {0} & {1}\end{bmatrix}=\begin{bmatrix}{-2} \\ {-3} \\ {4}\end{bmatrix}[/tex]And this is our answer.
[tex]\begin{bmatrix}{1} & 0 & {0} \\ {0} & {1} & 0{} \\ {0} & {0} & {1}\end{bmatrix}\begin{bmatrix}{x} \\ {y} \\ {z}\end{bmatrix}=\begin{bmatrix}{-2} \\ {-3} \\ {4}\end{bmatrix}[/tex]Having a hard time explaining to my daughter how to explain her estimate of this problem.
In total Irene makes 4 2/3
She splits the batter into two bowls
Blueberries bowl 2 1/4
walnuts bowl ?
In order to do an estimation
[tex]4\text{ }\frac{2}{3}[/tex][tex]\frac{2}{3}\text{ is close to }\frac{3}{4}[/tex][tex]4+\frac{3}{4}=4\text{ }\frac{3}{4}[/tex]Then for the other fraction
[tex]2\text{ }\frac{1}{4}[/tex][tex]\frac{1}{4}\text{ is close to }\frac{1}{4}[/tex]Therefore we do the next estimation
[tex]4\frac{3}{4}-2\frac{1}{4}=2\text{ }\frac{2}{4}[/tex]The estimation is 2 2/4 cups of batter with walnuts
For an exact value, we do the next operations
In order to know how much batter has walnuts
[tex]4\frac{2}{3}-2\frac{1}{4}=\frac{14}{3}-\frac{9}{4}=\frac{14(4)-9(3)}{12}=\frac{56-27}{12}=\frac{29}{12}[/tex]Then we convert to a mixed number
[tex]2\text{ }\frac{5}{12}[/tex]As we can see our estimation and the actual differ very a little therefore we do a good estimation
Given the following piecewise function, evaluate f(-1).f(x) =3x +4. X < -1-8x +8 x> -1
We have the expression:
[tex]3x+4\text{ if x}\leq-1[/tex]So, when x=-1 we need to use this expression, so lets plot -1 on it:
[tex]3(-1)+4=-3+4=1[/tex]so f(-1)=1.
Suppose you go to a conference attended by 20 Canadians and 20 Americans. How many people must you meet to be certain that you have met two Americans?
There are 20 Canadians and 20 Americans at the conference.
we met the first person may be Canadian or American
Case 1:
If the first person is Canadian
We meet the second person
The second person also maybe Canadian or American
If all the first 20 peoples are Canadian
The next two people should be American
Hence we should meet a minimum of 22 people.
Case 2:
If the first person is American
We meet the second person
The second person also maybe Canadian or American
If all the next 20 peoples are Canadian
Then the 22nd people should be American
Hence we should meet a minimum of 22 people.
Case 3:
If the first person is American
We meet the second person
The second person also maybe Canadian or American
If the second people is also American
Hence we met 2 Americans in two attempts.
Result:
We need to meet 22 people to meet two americans.
The safe load, L, of a wooden beam of width w, height h and length l, supported at both ends, varies directly as the product of the width and the square of the height and inversely as the length. A wooden beam 5 inches wide, 7 inches high and 144 inches long can hold a load of 8740 pounds. What load would a beam 6 inches wide, 9 inches high, and 216 inches long of the same material, support? Round your answer to the nearest integer if necessary.
Since the load L varies directly with the product of width and square of the height h, and inveresly as the length l, so
[tex]\begin{gathered} L=k(\frac{wh^2}{l}) \\ OR \\ \frac{L_1}{L_2}=\frac{w_1}{w_2}\times\frac{h^2_1}{h^2_2}\times\frac{l_2}{l_1} \end{gathered}[/tex]We will use the second rule
Since L is 8740 pounds when w is 5 in., h is 7 in. and l is 144 in.
[tex]\begin{gathered} L_1=8740 \\ w_1=5 \\ h_1=7 \\ l_1=144 \end{gathered}[/tex]We need to find L when w is 6 in., h is 9 in. and l is 216 in.
[tex]\begin{gathered} L_2=? \\ w_2=6 \\ h_2=9 \\ l_2=216 \end{gathered}[/tex]Let us substitute them in the second rule
[tex]\begin{gathered} \frac{8740}{L_2}=\frac{5}{6}\times\frac{7^2}{9^2}\times\frac{216}{144} \\ \frac{8740}{L_2}=\frac{5}{6}\times\frac{49}{81}\times\frac{216}{144} \\ \frac{8740}{L_2}=\frac{245}{324} \end{gathered}[/tex]By using cross multiplication
[tex]\begin{gathered} 245\times L_2=8740\times324 \\ 245L_2=2831760 \end{gathered}[/tex]Divide both sides by 245
[tex]\begin{gathered} \frac{245L_2}{245}=\frac{2831760}{245} \\ L_2=11558.20408 \end{gathered}[/tex]Round it to the nearest integer
[tex]L_2=11558\text{ pounds}[/tex]The load is 11558 pounds
Is this pretty or no? I’m using it for my wallpaper on my phone… and I just want peoples opinions.
Answer:
eh
Step-by-step explanation:
not really imo
but alas i am not a big fan of boats so i mean
what ever floats your boat (i am so funny)
Anyone willing to help me? i’ll give 17 points
are these equivalent 12:8 and 18:12
To ascertain fi the ratio 12:8 is equivalent to 18:12 we have to reduce the ratios
[tex]12\colon8=\frac{12}{8}=\frac{3}{2}=3\colon2[/tex][tex]undefined[/tex]If the cost of a loaf of bread is now $2.75 and is increasing at 5% per year, what will it cost 10 years from now. Write an exponential equation for this scenario then use it to solve the problem
To estimate the cost (C) after t years with an increasing rate r, use the formula below:
[tex]C(t)=C_0*\left(1+r\right)^t[/tex]
In this question:
C0 = initial cost = $2.75
r = rate = 0.05
t = time = 10 years
Substituting the values in the equation:
[tex]\begin{gathered} C(10)=2.75*\left(1+0.05\right)^{10} \\ C(10)=2.75*1.05^{10} \\ C(10)=2.75*1.629 \\ C(10)=4.48 \end{gathered}[/tex]Answer:
Equation:
[tex]\begin{gathered} C(t)=2.75(1+0.05)^t \\ C(10)=2.75(1+0.05)^{10} \end{gathered}[/tex]Cost: C(10) = $4.48.
what is 10 / 2 / 3 / 4 * 10 * 0 - 5 -10 + 20 * 10 + 10 divided by 10 Champs * 10
Given:
10÷2÷3÷4 x 10 x 0 - 5 - 10 + 20 x 10 + 10 ÷ 10 x 10
To simplify the problem above, use PEDMAS theorem.
Thus, we have:
Find the slope between the given points and write an equation in slope-intercept form. (2, -9) and (8, -6)
The slope of a line is given by the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1, y1) and (x2, y2) are the coordinates of two points where the line passes through. By replacing (2, -9) and (8, -6) into the above equation, we get:
[tex]m=\frac{-6-(-9)}{8-2}=\frac{-6+9}{6}=\frac{3}{6}=\frac{1}{2}[/tex]Then, the slope of the given line is 1/2. The equation of a line can be written in slope-intercept form like this:
y = mx + b = (1/2)x + b
We can find the value of b by replacing the coordinates of one of the point where the lie goes through, let's take (2, -9), then we get:
-9 = (1/2)(2) + b
-9 = 1 + b
-9 - 1 = 1 - 1 + b
-10 = b
b = -10
Then, we can rewrite the above equation to get: y = (1/2)x - 10
ess BosseCoursesRead bar graprisBella counted the number of students who play various instruments in her school's marching band and graphedthe results.file48> 1 34032ASCNumber of students24As16MY8Со0TATUSFluteSaxophone DrumsTrombone TrumpetMYInstrumentProWhich instruments did the same number of students play?ProChoose 2 answers:TeaFluteTrombone
SOLUTION:
Step 1 :
In this question, we are told that Bella counted the number of students who play various instruments in her school's marching band and graphed
the results.
We are asked to find the instruments did the same number of students play.
Step 2:
From the graph, we can see clearly that the same number of students play
Saxophone and Drums.
CONCLUSION:
SAXOPHONE -- OPTION D
DRUMS -------------OPTIO
You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say theywill make you play a game. Your sister says she wants you to spin a spinner with six outcomes, numbered 1 through 6, on it. She will give you $3 times the number thatthe spinner lands on. Your mother says she wants you to spin a spinner with two outcomes, blue and red, on it. She will give you $9 if the spinner lands on blue and $21 ifthe spinner lands on red. Determine the expected value of each game and decide which offer you should take.AnswerKeypadKeyboard ShortcutsExpected value for your sister's game:Expected value for your mother's game: SWhich offer should you take?your sister's offeryour mother's offer
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
expected value of each game = ?
Step 02:
Expected value:
Sister:
total outcomes = 6
1 - 6
probability = 1/6
1 | 2 | 3 | 4 | 5 | 6
$3 | $3 | $3 | $3 | $3 | $3
1/6 | 1/6 | 1/6 | 1/6 | 1/6 | 1/6
[tex]\text{expected value = \$3}\cdot\frac{1}{6}+\text{ \$3}\cdot\frac{1}{6}+\text{ \$3 }\cdot\text{ }\frac{1}{6}\text{ + \$3}\cdot\frac{1}{6}+\text{ \$3}\cdot\frac{1}{6}\text{ + \$3 }\cdot\text{ }\frac{1}{6}[/tex]expected value (sister) = $3
Mother:
total outcomes = 2
blue - red
probability = 1/2
blue | red
$9 | $21
1/2 | 1/2
[tex]\text{expected value = \$9 }\cdot\text{ }\frac{1}{2}\text{ + \$21}\cdot\frac{1}{2}[/tex]expected value (mother) = $15
The answer is:
Expected value (sister) = $3
Expected value (mother) = $15
Mother's offer.
Consider the first few terms as well as the last few terms of the sum. Find a way to simplify and use your observation to evaluate the sum. Write the exact answer. Do not round.
The first three terms of the sum are:
[tex]\begin{gathered} \frac{1}{3}-\frac{1}{3+1}=\frac{1}{3}-\frac{1}{4}\to\text{first} \\ \frac{1}{4}-\frac{1}{4+1}=\frac{1}{4}-\frac{1}{5}\to\text{second} \\ \frac{1}{5}-\frac{1}{6}\to\text{ third} \end{gathered}[/tex]On the other hand, the three last terms of the sum are
[tex]\begin{gathered} \frac{1}{10}-\frac{1}{10+1}=\frac{1}{10}-\frac{1}{11}\to\text{tenth} \\ \frac{1}{11}-\frac{1}{12}\to\text{ eleventh} \\ \frac{1}{12}-\frac{1}{13}\to\text{twelfth} \end{gathered}[/tex]Notice that there is a -1/4 in the first term, a 1/4 in the second term, a 1/5 in the second term, and 1/5 in the third term, and so on. Once we add those factors, the result will be zero. Thus, the result of the sum is equal to the first number in the first term minus the second number in the twelfth term.
[tex]\begin{gathered} \sum ^{12}_{i=3}(\frac{1}{i}-\frac{1}{i+1})=\frac{1}{3}-\frac{1}{13}=\frac{13-3}{39}=\frac{10}{39} \\ \Rightarrow\sum ^{12}_{i=3}(\frac{1}{i}-\frac{1}{i+1})=\frac{10}{39} \end{gathered}[/tex]The answer is 10/39
Need help with this thanks! The first equation is 4x-3
EXPLANATION
We can affirm by the triangle midsegment theorem that the segment DF is half of the segment BC, therefore:
[tex]DF=\frac{1}{2}BC[/tex]Plugging in the terms into the expression:
[tex](4x-3)=\frac{1}{2}(6(x+1))[/tex]Applying the distributive property and removing the parentheses:
[tex]4x-3=3x+3[/tex]Subtracting -3x to both sides:
[tex]4x-3x-3=3[/tex]Subtracting terms:
[tex]x-3=3[/tex]Adding +3 to both sides:
[tex]x=3+3[/tex]Adding numbers:
[tex]x=6[/tex]In conclusion, the value of x is 6
textFor this fraction 12/13 the numerator is
It is given that the fraction is:
[tex]\frac{12}{13}[/tex]If a fraction is given by:
[tex]\frac{p}{q}[/tex]Then p is called numerator and q is called denominator.
Hence the numerator is 12 and denominator is 13.
The population of a certain species of owl at a wildlife preserve can beapproximated by the functionN(t) =20401+39e-0.51where N(t) represents the number of owls and t is the time (in years).a.) What was the initial population of the owls?b.) How many owls will there be in the wildlife preserve in the long run? Inother words, what is the limit as t approaches infinity?c.) how many years will it take until there are 950 owls in the wildlife preserve?
Question A.
The initial population ocurrs at t=0. Then, by substituting this value into the given model ,we get
[tex]N(0)=\frac{2040}{1+39e^0}[/tex]which gives
[tex]\begin{gathered} N(0)=\frac{2040}{1+30} \\ N(0)=\frac{2040}{40} \\ N(0)=51 \end{gathered}[/tex]then, the answer is 51 owls.
Question B.
The limits when t approaches to + infinity is
[tex]\begin{gathered} N(0)=\frac{2040}{1+39e^{-\infty}} \\ N(0)=\frac{2040}{1+0} \\ N(0)=\frac{2040}{1}=2040 \end{gathered}[/tex]then, the answer is 2040 owls.
Question 15.
In this case, we need to find t when N(t) is 950, that is,
[tex]950=\frac{2040}{1+39e^{-0.5t}}[/tex]By moving the denominator to the left hand side, we have
[tex](1+39e^{-0.5t})950=2040[/tex]then, by moving 950 to the right hand side, we obtain
[tex]\begin{gathered} (1+39e^{-0.5t})=\frac{2040}{950} \\ 39e^{-0.5t}=\frac{2040}{950}-1 \end{gathered}[/tex]which is
[tex]39e^{-0.5t}=1.147368[/tex]so, we get
[tex]\begin{gathered} e^{-0.5t}=\frac{1.147368}{39} \\ e^{-0.5t}=0.029419 \end{gathered}[/tex]By applying natural logarithms to both sides, we have
[tex]\begin{gathered} -0.5t=\ln (0.029419) \\ t=\frac{-\ln(0.029419)}{0.5} \end{gathered}[/tex]then, the answer is
[tex]t=7.05[/tex]By rounding o the neares interger, the answer is 7 years
15/9 equals 40 over n
Given the following equation:
[tex]\begin{gathered} \frac{15}{9}=\frac{40}{n} \\ \\ \end{gathered}[/tex]You need to solve for the variable "n" in order to find its value.
The steps are shown below:
1. You can multiply both sides of the equation by "n":
[tex]\begin{gathered} (n)(\frac{15}{9})=(\frac{40}{n})(n) \\ \\ \frac{15n}{9}=40 \end{gathered}[/tex]2. Now you need to multiply both sides of the equation by 9:
[tex]\begin{gathered} (9)(\frac{15n}{9})=(40)(9) \\ \\ 15n=360 \end{gathered}[/tex]3. Finally, you can divide both sides of the equation by 15:
[tex]\begin{gathered} \frac{15n}{15}=\frac{360}{15} \\ \\ n=24 \end{gathered}[/tex]The answer is:
[tex]n=24[/tex]