Answer:
x=a-d/c+b
Step-by-step explanation:
a-bx =cx+d
collect like terms
a-d=cx+bx
a-d=x(c+b)
x=a-d/c+b
QUESTION 29
Two variables x and y, assume the values x₁= 2, X2 = -8, X3= 4 X4=1 and y₁
=-3 y2 =-8 y3 = 10 y4=6 Calculate x
OA. -1
OB. -4
OC.-7
OD. -9
The sum of the set of x - values given to us is calculated as; ∑X = -1
How to find the the sum of a set of data?We are given;
X1 = 2, X2 = -8, X3 = 4, X4 = -8 and Y1 = -3, Y2 = -8, Y3 = 10, Y4 = 6
1) ∑X = X1 + X2 + X3 + X4
∑X = 2 + (-8) + 4 + 1 = -1
2) ∑Y = Y1 + Y2 + Y3 + Y4
∑Y = 3 + (-8) + 10 + 6
∑Y = -11
3) ∑ X² = X₁² + X₂² + X₃² + X₄²
∑X² = (2)² + (-8)² + (4)² + (1)²
∑X² = 85
4) ∑Y² = Y₁² + Y₂² + Y₃² + Y₄²
∑X² = (-3)² + (-8)² + (10)² + (6)²
∑X² = 209
Complete question is;
Two variables, X and Y assume the values X1 = 2, X2 = -5, X3 = 4, X4 = 1 and Y1 = -3, Y2 = -8, Y3 = 10, Y4 = 6, respectively. Calculate (a) ∑X, (b) ∑ Y, (c) ∑ X² (d) ∑ Y²
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Find the area for the shaded polygon
Taking the distance between dots as 1 unit, we have;
Area of the blue shaded region = square 10 unitsArea of the yellow polygon = 6 square units Which method can be used to find the area of the shaded figures?Taking the figures as comprising of triangles and trapezoids, we have;
In the blue polygon, we have;
Trapezoid area = ((4 + 3)/2) × 2 = 7
Area of the unshaded triangles = 0.5 × 2 × 1 + 0.5 × 2 × 2 + 0.5 × 2 × 1 = 4
Square area = 3 × 2 = 6
Shaded triangle area = 0.5 × 2 × 1 = 1
Sum of the areas is therefore;
A = 7 - 4 + 6 + 1 = 10
Which gives;
Area of the blue shaded region = 10Area of the lower yellow trapezoid is found as follows;
Trapezoid area = ((2 + 3)/2) × 4 = 10
Unshaded triangle area = 0.5 × 2 × 1 + 0.5 × 3 × 3 = 5.5
Area of the top triangle = 0.5 × 3 × 1 = 1.5
Area of the shaded yellow polygon is therefore;
A = 10 - 5.5 + 1.5 = 6
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A van traveled 216 km in 4 hours. Find its average speed in km/h.
Answer:
86.9 km/h
Step-by-step explanation:
54 mph = 86.9046
Full number: 86.9046 km/h
Find the distance of PQ
P(0,4) and Q(10,-6)
Answer:
PQ ≈ 14.14 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = P (0, 4 ) and (x₂, y₂ ) = Q (10, - 6 )
PQ = [tex]\sqrt{(10-0)^2+(-6-4)^2}[/tex]
= [tex]\sqrt{10^2+(-10)^2}[/tex]
= [tex]\sqrt{100+100}[/tex]
= [tex]\sqrt{200}[/tex]
≈ 14.14 units ( to 2 dec. places )
Answer:
[tex]PQ=10\sqrt{2}\:\: \sf units[/tex]
Step-by-step explanation:
Distance between two points formula
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]
Define the variables:
Let (x₁, y₁) = (0, 4)Let (x₂, y₂) = (10, -6)d = PQSubstitute the defined variables into the distance formula and solve for PQ:
[tex]\implies PQ=\sqrt{(10-0)^2+(-6-4)^2}[/tex]
[tex]\implies PQ=\sqrt{10^2+(-10)^2}[/tex]
[tex]\implies PQ=\sqrt{100+100}[/tex]
[tex]\implies PQ=\sqrt{200}[/tex]
[tex]\implies PQ=\sqrt{100 \cdot 2}[/tex]
[tex]\implies PQ=\sqrt{100}\sqrt{2}[/tex]
[tex]\implies PQ=10\sqrt{2}\: \sf units[/tex]
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Select all the correct graphs.
Choose the graphs that indicate equations with no solution.
The graph first, and the graph fifth have no solution because there are no intersection options (A) and (E) are correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The graph of equations is shown in the graph.
As we know, if two equations of a function intersect on the coordinate plane that means they have a solution.
If there will be no intersection then the equations have no solution.
Thus, the graph first, and the graph fifth have no solution because there are no intersection options (A) and (E) are correct.
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4 Which of the following is the solution to 8√3+7√3?
O 15√9
O 15√6
O 15/3
O 56√3
Answer:
15√3
Step-by-step explanation:
after grouping and adding them to get 15√9
then you apply Surds
three times the difference between t and y"
Answer: 3(t-y)
Step-by-step explanation:
The term difference refers to subtraction, so that means t-y in parenthesis since you would have to solve that first.
Then after you'd solve that, then you would multiply it by 3
Hope I helped :)
What is the answer I need help!
Express tan α using x?
Answer:
This questions seems to be incomplete but generally tan with x is expressed as
tan(x) =
What is the slope of the line that passes through the points (8, 0) and (-4, -8)?
Write your answer in simplest form.
Answer:
Step-by-step explanation:
(-8 - 0)/(-4 - 8)= -8/-12 = 2/3
The slope of the line that passes through the points (8, 0) and (-4, -8) exists at 0.66667.
How to estimate the slope of the line?The slope or gradient between two points in the Cartesian coordinate system. The slope exists the amount of slant a line retains and can maintain a positive, negative, zero, or undefined value.
Using the slope formula [tex](y_2 - y_1)/(x_2 - x_1)[/tex]
[tex]x_1 = 8, y_1 = 0[/tex] and [tex]x_2 = -4 , y_2= -8[/tex]
slope [tex]= (y_2 - y_1)/(x_2 - x_1)[/tex]
= ((-8) - 0) / ((-4) - (8))
= (-8) / (-12) = (-2) / (-3)
= 0.66667
Therefore, the slope of the line that passes through the points (8, 0) and (-4, -8) exists at 0.66667.
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Mr. and Mrs. Chan want to buy new furniture that has a cash price of $6230. On the installment plan, they must pay %25 of the cash price as a down payment and make twelve monthly payments of $415. How much interest did they pay due to financing?
The interest due on financing option is $307.50
What is interest on financing?
Interest on financing is the extra amount paid by the couple when their total payments are compared to the cash price of $6,230.
The total payments would be the 25% down payment plus the sum of the twelve monthly payments of $415 each
Down payment=cash price*25%
Down payment=$6230*25%
Down payment=$1,557.50
Total monthly payments=amount of each monthly payment*number of monthly payments
monthly payment=$415
number of monthly payments=12
Total monthly payments=$415*12
Total monthly payments=$4,980
Total payment under financing=Down payment +Total monthly payments
Total payment under financing=$1,557.50+$4,980
Total payment under financing=$6,537.50
Interest=$6,537.50-$6,230
Interest on financing=$307.50
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SV is angle bisector of
Answer:
Sv is angle bisector of rst.2/3 of Ram money = 1/2 of Hari money. They have altogether 1400. Find the amount of money each.
Solving a system of equations we will see that Hari has 800 and Ram has 600.
How much money does each have?Let's define the variables:
R = money that Ram has.H = money that Hari has.We know that:
(2/3)*R = (1/2)*H
We also know that in total they have 1400, then:
R + H = 1400.
So we have the system of equations:
(2/3)*R = (1/2)*H
R + H = 1400.
In the first equation we can isolate R.
R = (3/2)*(1/2)*H = (3/4)*H
Now we can replace that in the other equation:
(3/4)*H + H =1400
H*(7/4) = 1400
H = (4/7)*1400 = 800
So Hari has 800, and:
R + H = 1400
R = 1400 - H = 1400 - 800 = 600
Hari has 800 and Ram has 600.
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The walls of a square room with side length s are being torn down and rebuilt. The area of the new room can be represented by 1.75s(2s + 3).
Which expression represents the area of the new room?
3.75s + 4.75
3.75s2 + 4.75s
3.5s2 + 5.25s
3.5s + 5.25
The expression that represents the area of the new room is (c) 3.5s^2 + 5.25s
How to determine the area of the new room?The given parameters are:
Wall =Square
Length = s
When the wall of the square room is torn down and rebuilt, the area of the new room is represented by 1.75s(2s + 3).
This means that
Area= 1.75s(2s + 3)
Expand the expression
Area= 1.75s * 2s + 1.75s * 3
Evaluate the products
Area= 3.5s^2 + 5.25s
This means that the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s
Hence, the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s
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The following formula models the number of automobiles, A,in thousands, that Washington residents purchased
x years after 1980.
A=2x2+24x+300
A) Write an equation that you can use to determine the first year in which residents purchased approximately 566 thousand cars.
B) Now solve your equation and specify the first year (for example, enter 2019 and not 39) in which residents purchased approximately 566 thousand cars.
Considering the given quadratic equation for the number of automobiles, we have that:
A) The equation to be solved is: x² + 12x - 133 = 0
B) The first year was of 1987.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
The number of automobiles, in x years after 1980, is modeled by:
A(x) = 2x² + 24x + 300.
The amount is of 566,000 when A(x) = 566, hence the equation is:
2x² + 24x + 300 = 566
2x² + 24x - 266 = 0
x² + 12x - 133 = 0
The coefficients are a = 1, b = 12, c = -133, hence:
[tex]\Delta = 12^2 - 4(1)(-133) = 676[/tex][tex]x_1 = \frac{-12 + \sqrt{676}}{2} = 7[/tex][tex]x_2 = \frac{-12 - \sqrt{676}}{2} = -19[/tex]Time is a positive measure, hence we take the solution of 7, 1980 + 7 = 1987, which is the year.
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WILL GIVE BRAINLIEST
Given that two arcs of a circle are congruent, their measures are equal by the definition of congruence. Central angle
measures are equal to their intercepted arcs, so by the transitive property, the two central angle measures are equal. By
definition, the two angles are also congruent. Since all radii are congruent, the two triangles are congruent by SAS. Finally,
the intercepted chords are congruent by CPCTC.
Drag the statements to the positions that match the summary of Jeremy's proof.
A student bought a truck for 4000 down with payments of 250 for 4yrs what’s the total cost
The total cost of the truck is $16,000
What is the total cost?
We know that first, we have a down payment of $4000.
And then we have a monthly payment of $250 for 4 years. In each year there are 12 months, then in 4 years there are:
4*12 = 48 months.
Then the student needs to pay $250 48 times, this is:
$250*48 = $12,000
Then the total cost is:
$12,000 + $4,000 = $16,000
The total cost of the truck is $16,000
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irections: Simplify each expressio
25-(√16-1)-(3-9)²
Answer:
-14
Step-by-step explanation:
[tex]\sqrt{16} = 4\\\\(\sqrt{16} - 1) = (4 -1) =3\\\\(3-9) = (-6)\\\\(3-9) ^2 = (-6)^2 = 36\\\\25 - 3 - 36 = 25 - 39 = -14\\[/tex]
u0ukj787y8fr7hjhy7 which one
If ABC and DEF are complementary, then the value of x will be,
90 - ABC = x
90 - 53 = x
x = 37°
Answer:
x=37
Step-by-step explanation:
complementary means when added up they bring 90
so, 53+x=90
x=90-53
x=37
mark me brainliest if it helped pls :)
A 30g bullet travelling horizontally at 50 m/s penetrates 10 cm into a wooden block. The average force exerted by the block is:
The average force exerted by the block exists at -375 N.
How to find the average force exerted by the block?Given:
Initial Velocity, u = 50m/s
Displacement, s = 10cm = 0.10m
Mass, m = 0.03Kg
Using the relation,
[tex]$v^{2}-u^{2}=2 a s[/tex]
Substitute the values in the above equation, we get:
[tex]$&0^{2}-50^{2}=2 \mathrm{a}(0.10) \\[/tex]
[tex]$ \mathrm{a}= -12500 \mathrm{~ms}^{-2}[/tex]
We know that, f = ma
Putting the values, we get:
f = (0.03)(-12500)
f = -375 N
The average force exerted by the block exists at -375 N.
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(pls help)
5. Write the rule for the linear function. Remember a function rule is written using using f(x).
The linear function whose points are given is f(x)=[tex]x/5 +1[/tex]
Given the points of the function f(-10)=-1,f(0)=1,f(10)=3.
We are required to find the function whose points are given.
Function is relationship between two or more variables that are expressed in equal to form. In function each value of x must have a corresponding y value.
x value is known as domain and y value if known as codomain of the function.
Take two points (-10,-1) and (0,1) and we can form one equation as under:
y+1=(1+1/0+10) * (x+10)
y+1=2/10 (x+10)
y+1=x/5 +10/5
y+1=x/5+2
y=x/5+2-1
y=x/5+1
Hence the linear function whose points are given is [tex]f(x) = x/5 +1[/tex]
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Using the quote, "Those of us on the margins wonder if our stories matter" what is the significance of the quoted text?
The significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality.
What is a quote?Quote means to cite something as a form of proof. It has several other senses as a verb and a noun. It should be noted that to quote something or someone is to repeat the exact words they said or to recite the exact words written in a book.
Great speakers often quote other inspiring people when making speeches. When you quote, you include the words and ideas of others in your text exactly as they have expressed them.
You signal this inclusion by placing quotation marks (“ ”) around the source author's words and providing an in-text citation after the quotation.
In this case, the significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality. A quotation is the repetition of a sentence, phrase, or passage from speech or text that someone has said or written.
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You can now sell 50 cups of lemonade per week at 39¢ per cup , but demand is dropping at a rate of 5 cups per week each week. Assuming that raising the price does not affect demand , how fast do you have to raise your price if you want to keep your weekly revenue constant.
Answer:
3.9¢ per cup per week
Step-by-step explanation:
Revenue is the product of price and quantity sold. The rate of change in any of these quantities can be found by solving the derivative equation at using the given values.
Relation of rates of changeRevenue (r) is the product of price (p) and quantity sold (q):
r = pq
Differentiating with respect to time, we have ...
r' = p'q +pq'
Given valuesThe values given for the problem are ...
r' = 0p' = rate to be foundp = 39 (cents per cup)q' = -5 (cups per week)q = 50Using the above derivative relation, we have ...
0 = p'(50) +39(-5) . . . . . . fill in given values
Solutionp' = 195/50 = 3.9 . . . . . . add 195, divide by 50
The price must be raised at the rate of 3.9 cents per week to maintain unchanging revenue.
What is the solution to 3/4 a>-16?
O a>-21/3
O a<-21
O a> 21-1/
O a <21/13
[tex] \frac{3a}{4} > - 16 \\ 3a > - 64 \\ a > \frac{ - 64}{3} \\ a > 21 \frac{1}{3} [/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{\dfrac{3}{4}a > -16}[/tex]
[tex]\huge\textbf{Simplifying it:}[/tex]
[tex]\mathsf{\dfrac{3}{4}a > -16}[/tex]
[tex]\mathsf{\dfrac{3}{4}a > - \dfrac{16}{1}}[/tex]
[tex]\huge\textbf{Divide \boxed{\dfrac{4}{3}} to both sides:}[/tex]
[tex]\mathsf{\dfrac{4}{3}\times\dfrac{3}{4}a > -16\times\dfrac{4}{3}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{a > \dfrac{4}{3}\times -16}[/tex]
[tex]\mathsf{a > - \dfrac{16}{1} \times\dfrac{4}{3}}[/tex]
[tex]\mathsf{a > \dfrac{-16\times4}{1\times3}}[/tex]
[tex]\mathsf{a > \dfrac{-64}{3}}[/tex]
[tex]\mathsf{a > -\dfrac{64}{3}}[/tex]
[tex]\mathsf{a > -21 \dfrac{1}{3}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{- \frak{21\dfrac{1}{3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Landon Wallin is an auto mechanic who wishes to start his own business. He will need $4200 to purchase tools and equipment. Landon decides to finance the purchase with a 36-month fixed installment loan with an APR of 5.5% a) Determine Landon's finance charge. b) Determine Landon's monthly payment.
Landon's finance charge is $613.2
Landon's monthly payment is; $80.22
How to find the finance charge?
It is convenient to compute the monthly payment first, then figure the total amount repaid and the finance charge.
The amortization formula is:
A = Pr/(1 - (1 + r)⁻ⁿ)
where;
A is the monthly payment
P is the loan amount
r is the monthly interest rate
n is the number of months
b) Using the above formula, we can get the monthly payment as;
A = $4200(0.055/12)/(1 - (1 +0.055/12)⁻⁶⁰) = $19.708333/0.23995049
A = $80.22
The monthly payment amount is $80.22
a) 60 monthly payments add up to;
$80.22 × 60 = $4813.2
Since $4200 of that amount is principal, the finance charge is;
$4813.2 - $4200.00 = $613.2
Landon's finance charge is $613.2
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Determine if the series converges or diverges. If the series converges, find its sum.
9
Σ n(n+3)
n=1
OA. The series diverges.
OB. The series converges to
11
2
7
OC. The series converges to
2
D. The series converges
15
-
2
The true statement about the series [tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex] is that (a) the series diverges
How to determine if the series diverges or converges?The series is given as:
[tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex]
Take the limit of the function to infinity
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)}[/tex]
This gives
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty * (\infty +3)}[/tex]
Evaluate the sum
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty * \infty}[/tex]
Evaluate the product
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty}[/tex]
Evaluate the quotient
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = 0[/tex]
Since the limit is 0, then it means that the series diverges
Hence, the true statement about the series [tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex] is that (a) the series diverges
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Answer:
B. The series converges to [tex]\displaystyle{\frac{11}{2}}[/tex].
Step-by-step explanation:
Before evaluating the infinite series, the expression can be decomposed as the sum of two fractions (partial fraction decomposition) as follows.
Let [tex]\textit{A}[/tex] and [tex]\textit{B}[/tex] be constants such that
[tex]{\displaystyle{\frac{9}{n\left(n+3\right)}}}} \ \ = \ \ \displaystyle{\frac{A}{n} \ \ \ + \ \ \frac{B}{n+3}}[/tex]
Multiply both sides of the equation by the denominator of the left fraction,
[tex]n\left(n+3\right)[/tex], yielding
[tex]9 \ \ = \ \ A\left(n+3\right) \ \ + \ \ B \-\hspace{0.045cm} n[/tex]
Now, let [tex]n \ = \ 0[/tex], thus
[tex]\-\hspace{0.2cm} 9 \ \ = \ \ A\left(0 + 3\right) \ + \ B\left(0\right) \\ \\ 3 \-\hspace{0.035cm} A \ = \ \ 9 \\ \\ \-\hspace{0.11cm} A \ \ = \ \ 3[/tex].
Likewise, let [tex]n \ = \ -3[/tex], then
[tex]\-\hspace{0.5cm} 9 \ \ = \ \ A\left(-3 + 3\right) \ + \ B\left(-3\right) \\ \\ -3 \-\hspace{0.035cm} B \ = \ \ 9 \\ \\ \-\hspace{0.44cm} B \ \ = \ \ -3[/tex]
Hence,
[tex]\displaystyle{\sum_{n=1}^{\infty} {\frac{9}{n\left(n+3\right)}}} \ = \ \displaystyle\sum_{n=1}^{\infty} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right)[/tex].
First and foremost, write the nth partial sum (first nth terms) of the series,
[tex]\displaystyle\sum_{n=1}^{n} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \displaytstyle{\frac{3}{1} \ - \frac{3}{4} + \ \frac{3}{2} \ - \frac{3}{5} \ + \frac{3}{3} \ - \frac{3}{6} \ + \frac{3}{4} \ - \frac{3}{7}} \\ \\ \\ \-\hspace{3.58cm} + \ \displaystyle{\frac{3}{5} \ - \ \frac{3}{8} \ + \ \frac{3}{6} \ - \ \frac{3}{9} \ + \ \frac{3}{7} \ - \ \frac{3}{10}} \\ \\ \\ \-\hspace{3.58cm} + \ \ \dots[/tex]
[tex]+ \ \ \displaystyle{\frac{3}{n-3} \ - \ \frac{3}{n} \ + \ \frac{3}{n-2} \ - \ \frac{3}{n+1}} \\ \\ \\ \ + \ \frac{3}{n-1} \ - \ \frac{3}{n+2} \ + \ \frac{3}{n} - \ \frac{3}{n+3}}[/tex].
Notice that the expression forms a telescoping sum where subsequent terms cancel each other, leaving only
[tex]\displaystyle\sum_{n=1}^{n} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \displaytstyle{\frac{3}{1} \ + \ \frac{3}{2} \ + \frac{3}{3} \ - \ \frac{3}{n+1}} - \ \frac{3}{n+2} \ - \ \frac{3}{n+3}}}[/tex].
To determine if this infinite series converges or diverges, evaluate the limit of the nth partial sum as [tex]n \ \rightarrow \ \infty[/tex],
[tex]\displaystyle\sum_{n=1}^{\infty} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \lim_{n \to \infty} \left(\displaytstyle{\frac{11}{2} \ - \ \frac{3}{n+1} \ - \ \frac{3}{n+2} \ + \ - \ \frac{3}{n+3}\right) \\ \\ \\ \-\hspace{3.25cm} = \ \ \ \displaystyle{\frac{11}{2} \ - \ 0 \ - \ 0 \ - \ 0} \\ \\ \\ \-\hspace{3.25cm} = \ \ \ \displaystyle{\frac{11}{2}[/tex]
urgent need of assistance
Answer:i got 329
Step-by-step explanation:
I need help
Please help ASAP
Answer:
The volume of the solid is [tex]1,021m^3[/tex]
Step-by-step explanation:
1. Cylinder
For find the volume of a cylinder we use the next formula:
[tex]V_{cylinder} = \pi h r^2 = \pi \cdot 9m\cdot (5m)^2 \approx 706.86m^3[/tex]
Then the volume of the cylinder is equal to [tex]706.86m^3[/tex]
2. Cones
For find the volume of a cone we use the next formula:
[tex]V_{cone} = \pi \frac{h}{3} r^2 = \pi \cdot \frac{6m}{3} \cdot (5m)^2 \approx 157.08m^3[/tex]
However there are two cones so we have to multiply the volume of one cone for two and we get the total volume for the cones which is [tex]314.16m^3[/tex]
3. Sum of the volumes
Finally we sum the volumes of the cylinder and the cones for get the final result
[tex]V_{cylinder} + V_{cones} = 706.86m^3 + 314.16m^3 \approx 1021m^3[/tex]
So approximating the result is [tex]1021m^3[/tex]
A psychologist wants to estimate the proportion of people in a population with IQ scores between 80 and 140. The IQ scores of this population are normally distributed with a mean of 110 and a standard deviation of 15. Use the standard normal table to estimate the proportion.
Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Considering the mean of 110 and the standard deviation of 15, we have that:
80 = 110 - 2 x 15.140 = 110 + 2 x 15.These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
More can be learned about the Empirical Rule at brainly.com/question/24537145
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what the difference between graphing lines and graphing inequalities?
what the difference between arithmetic and geometric ?
how do you explain using sigma notation ?
how to simplify into logarithmic?
Answer:
Step-by-step explanation:
graphing lines is just what it sounds like, you are taking the equation of the line and putting it on the graph. graphing inequalities shows the area of the coordinate plane that satisfies the inequality, it almost always splits the graph.
arithmetic: -6 , 1 , 8 , 15 , 22
geometric: 2 , 4 , 8 , 16, 32