The amount Lucas would have in his account is $885,000.
The formula that would be used to determine the amount of money Lucas would be in 40 years is:
The formula for calculating future value = A x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
A = amount invested each year = $2000r = interest rate = 10%n = number of years = 40 years$2000 x [(1.1^40 - 1) / 0.1] = $885,000
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Distributive property to simplify 6(8) + 6(-2)
Answer:
36
Step-by-step explanation:
You would multiply 6x8+6x(-2), and that would equal 48+(-12) which is basically 48-12 = 36.
: Một khu đất 20 ha người ta trồng hai loại cây ngô và khoai. Năng suất của ngô tính theo x ha được (5-x/4) tấn trên 1 ha và năng suất của khoai tính theo y ha được (7-y/4) tấn trên 1 ha. Xác định diện tích trồng từng loại cây để sản lượng thu được là lớn nhất.
If Lauren can run
150 feet in 1/3 of
a minute. What
is her unit rate in
feet per minute?
Answer:
450
Step-by-step explanation:
150* 3
hope this helps
Answer:
450
Step-by-step explanation:
150 feet in 1/3 min
? ----- 1 min
150 * 1 = x * 1/3
x = 150 * 3
= 450
What do you measure the amount of water in a vase
HELP ME PLEASE!! I DONT WANT TO FAIL THIS AGAIN.
Answer:
A.
Step-by-step explanation:
You can see that the rate of change of function A is 3. because that's the slope (M) in y=mx+b
5 is slope for B because unit rate is 5 ( 1 to 3 change is +10 so unit rate is 5)
what is 3/4 ÷ 1/6 plz help
Answer:
4.5
Step-by-step explanation:
Please help! Thanks!: If a 95% confidence interval was being calculated using the following expression:
3.2 ± 1.96 ⋅ 1.1
What would be the margin of error for this confidence interval?
If you can please give an explanation on how to solve?
The confidence interval can be calculated from the margin of error, and vice versa,
The margin of error of the confidence interval is 2.156
The confidence interval is given as:
[tex]\mathbf{CI = 3.2 \pm 1.96 \cdot 1.1}[/tex]
The formula of confidence interval is:
[tex]\mathbf{CI = \bar x\pm E}[/tex]
Where E represents the margin of error.
So, by comparison:
[tex]\mathbf{E = 1.96 \cdot 1.1}[/tex]
Multiply
[tex]\mathbf{E = 2.156}[/tex]
Hence, the margin of error of the confidence interval is 2.156
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Find the discriminant of the quadratic equation.
2i2+6i=4
- BRAINLIEST answerer
find an equation for the line below
Answer:
y = 1/3 x + 14/3
Step-by-step explanation:
We can identify the two points shown easily.
They are (-2, 4) and (4, 6).
First, we find the line of the slope of the line that contains those two points.
slope = m = (y2 - y1)/(x2 - x1) = (6 - 4)/[4 - (-2)] = 2/6 = 1/3
Now we use one point and the slope to find the y-intercept.
y = mx + b
Let's use point (4, 6) and the slope, 1/3.
6 = (1/3)(4) + b
18/3 = 4/3 + b
b = 18/3 - 4/3
b = 14/3
The equation is
y = mx + b
y = 1/3 x + 14/3
Use the GCF and the distributive property to find each sum 15 + 57
Answer:
(3*5)+(19*3)
Step-by-step explanation:
both numbers GCF is 3.
(3*5)=15
(19*3)=57
15+57=72
Hope that helps
*WILL GIVE BRAINLIEST FOR BEST ANSWER*
Subtract. Write your answer in scientific notation.
(5.6×106)–(1.1×106)
Answer:
447
Step-by-step explanation:
Last Friday, Erica earned $51 babysitting for 6 hours. At this rate, how many hours would Erica need to babysit in order to earn $272?
Answer: 32 hours
Step-by-step explanation: 51/6 = 8.5
So, Erica makes 8.5 dollars per hour. 272/8.5 = 32. Thus, Erica will need 32 hours.
Brainliest?
f(x) = 9x ^ 2 - 3 then what is f(3) ? Work must be shown for this problem or no credit will be earned.
Answer:
f ( 3 ) = 81
Step-by-step explanation:
→ Substitute in x = 3
9 × 3² - 3
→ Simplify
9 × 9 - 3
→ Simplify again
78
Plzzzzz help
Among the following rational numbers,
which has the greatest value?
A. 0.34
B. 0.34
C. 0.34
D. 0.343
E. 0.3409
Answer:
D. 0.343
Step-by-step explanation:
You can see the first three options as 0.340 so if you substract this number with 0.343 the remainder is positive 3.
This strategy also can be applied to the number 0.3409 but in this occasion the result is different:
[tex]0.343 - 0.3409 = 2.1\times 10^{-3}[/tex]
That is small number but still is positive that's meaning that between 0.343 and 0.3409 the greatest value is 0.343 .
I am having trouble with this problem. I can’t figure it out. I have tried everything but can’t figure it out. After I figure out the problem I have to check it by writing out the problem and replacing the y with the number it equals. At the end it should equal 6
The picture is a different problem but this is what the check looks like
6=-y+42+-2y
Answer:
16 = y
Step-by-step explanation:
So you have the equation 6=-y+42+-2y
Find the y first
6=-y+42+-2y
add all y's together
6=-3y+42
subtract 42 on both sides
-48 = -13y
16 = y
------------------------------------------------
Now do the check:
Plug in 16 where ever it says y in the original equation
6= -(16) + 42 + -2(16)
open the brackets
6= -16+42-32
solve
6=26-32
6 = 6
Hope this helps
Simplify: 7√(1/3) + 2 1/3√(1/3) + 3√(147)
Step-by-step explanation:
7 √(1/3) - 2 1/3 √(1/3) +3√147
→7(1/√3) - (7/3)(1/√3) +3√(3×7×7)
→ (7/√3) - (7/3√3) +3×7√3
→ (7/√3) - (7/3√3) + 21√3
On Rationalising the denominators then
→ [ 7√3/(√3×√3)]-[7√3/(3×√3×√3) +21√3
The Rationalising factor of√3 =√3
→ (7√3/3)-[7√3/(3×3)]+21√3
→ (7√3/3)-(7√3/9)+21√3
LCM of 3 and 9 = 9
→ [(3×7√3)-(7√3)+(9×21√3)]/9
→ (21√3-7√3+189√3)/9
→[(21-7+189)√3]/9
→ [(210-7)√3]/9
→ 203√3/9 Ans.
Hope this helps.
In how many ways can a student answer the questions on the test if the student can leave answers blank
9/x = 27/24 find the proportional relationship
Answer: The answer is 9/8 = 27/24
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 8 people took the trip. She was able to purchase coach tickets for $160 and first class tickets for $950. She used her total budget for airfare for the trip, which was $3650. How many first class tickets did she buy? How many coach tickets did she buy?
Answer:
Money for coach tickets is $1280 and money for first class is $7600
Step-by-step explanation:
8 x 160 = 1280
8x 950 = 7600
Please help me do this question
Step-by-step explanation:
We need to break up the given expression into two separate fractions so that when they are added together, we will get the original expression.
Note that the denominator is made up of two factors, [tex](2x - 1)[/tex] and [tex](x^2 + 1).[/tex] But note that the 2nd factor is a 2nd order polynomial so as a rule, the numerator of the fraction containing this factor must be an (n - 1)-order polynomial, where n is the order. With that in mind, we can write the general form of the partial fractions as follows:
[tex]\dfrac{x + 7}{(2x - 1)(x^2 + 1)} = \dfrac{Ax + B}{x^2 + 1} + \dfrac{C}{2x - 1}[/tex]
[tex]\:\:\:\:=\dfrac{2Ax^2 + Bx - Ax - B + Cx^2 + C}{(2x - 1)(x^2 + 1)}[/tex]
Here, we combined the two fractions to form the equation above. Next, we compare the numerators on either side. Note that we satisfy the equality if we impose the following conditions:
[tex]2A + C = 0\:\:\:\:\:\:\:\:\:\:\:\:\:\:(1)[/tex]
[tex]2B - \:A = 1\:\:\:\:\:\:\:\:\:\:\:\:\:\:(2)[/tex]
[tex]-B + C = 7\:\:\:\:\:\:\:\:\:\:\:\:\:\:(3)[/tex]
To find the values of the constants A, B and C, we need to solve this system of equations. We start by multiplying Eqn(3) by 2 and then adding it to Eqn(2) to get
[tex]-A + 2C = 15\:\:\:\:\:\:\:\:\:\:\:\:\:\:(4)[/tex]
Then, multiply Eqn(1) by -2 to get
[tex]-4A - 2C = 0\:\:\:\:\:\:\:\:\:\:\:\:\:\:(5)[/tex]
Add Eqn(4) to Eqn(5) and we will get
[tex]-5A = 15 \Rightarrow A = -3[/tex]
Now that we know the value of A, we can use this in Eqn(2) to get
[tex]2B - (-3) = 1 \Rightarrow B = -1[/tex]
Next, to solve for C, we use the value of A in Eqn(1) to get
[tex]2(-3) + C = 0 \Rightarrow C = 6[/tex]
Therefore, the given expression can be written as
[tex]\dfrac{x + 7}{(2x - 1)(x^2 + 1)} = \dfrac{6}{2x - 1} + \left(\dfrac{-3x - 1}{x^2 + 1}\right)[/tex]
As a check, let's combine the two fractions together:
[tex]\dfrac{x + 7}{(2x - 1)(x^2 + 1)} = \dfrac{6}{2x - 1} + \left(\dfrac{-3x - 1}{x^2 + 1}\right)[/tex]
[tex]= \dfrac{6x^2 + 6 - 6x^2 - 2x + 3x + 1}{(2x - 1)(x^2 + 1)}[/tex]
[tex]= \dfrac{x + 7}{(2x - 1)(x^2 + 1)}[/tex]
As expected, we got the original expression.
what is the value of x?
(3x-1)º
(3x-1)))))]))))))))])))))))))))))])))))))))))))))))))))))
What is the equation in slope-intercept form of the line that passes through the points (-4, 6) and (-2,5) ?
y=20 - 8
y=-30+4
y=-22 +4
y = -x + 8
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{(-4)}}}\implies \cfrac{-1}{-2+4}\implies \cfrac{-1}{2}\implies -\cfrac{1}{2}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{-\cfrac{1}{2}}[x-\stackrel{x_1}{(-4)}] \\\\\\ y-6=-\cfrac{1}{2}(x+4)\implies y-6=-\cfrac{1}{2}x-2\implies \underset{\textit{slope-intercept form}}{y=-\cfrac{1}{2}x+4}[/tex]
Problem example: For the given sequence: -2,2,6,10,14,18
Write a recursive formula to find the nth term: a = an-1+4
Write a explicit formula to find the nth term: a = -2 + 4(n-1)
What is the 64th term in the sequence?
Answer:
250
Step-by-step explanation:
You can take the explicit formula and simply substitute the n value with 64:
-2 + 4 * (64 - 1)
-2 + 4 * (63)
-2 + 252
250
What is the equation of the line in slop-intercept form?
Enter your answer in the blank spots
y= __x + __
Answer:
y=2x +5
Step-by-step explanation:
so 2 goes in the first blank and 5 goes in the second
Hope this helps!❆
Need this ASAP please
a) x²+6x
b)5x²-x
c)12x²+15x
d)8x²-12xy
The angle of elevation of the top of a pole as seen from a point 13 ft away from the base is double its angle of elevation as seen from a point 47 ft farther from the pole. Find the height of the pole above the level of the observer's eyes. 10) A) 34 ft B) 86 ft C) 60 ft D) 45 ft
The height of the pole above the level of the observer's eyes is 31.42 ft
Let the angle of elevation of the top of the pole from a point 47 ft away be α.
Let the angle of elevation of the top of the pole from the point 13 ft away be β.
Since the angle of elevation of a point 13 feet away is twice that from 47 ft away, we have that β = 2α.
If the height of the pole above the level of the observer's eye is h, we have that
tanβ = tan2α = h/13 and tanα = h/47
From trigonometric identities tan2α = 2tanα/(1 - tan²α)
Substituting the values of the variables into the equation, we have
tan2α = 2tanα/(1 - tan²α)
h/13 = 2h/47 ÷ [1 - (h/47)²]
Dividing through by h, we have
1/13 = 2/47 ÷ [1 - (h/47)²]
Cross-multiplying, we have
1/13 = 2/47 ÷ [1 - (h/47)²]
1 - (h/47)² = 2/47 × 13
1 - (h/47)² = 26/47
(h/47)² = 1 - 26/47
(h/47)² = (47 - 26)/47
(h/47)² = 21/47
Taking square-root of both sides, we have
h/47 = √(21/47)
Cross-multiplyng, we have
h = √(21/47) × 47
h = √(21 × 47)
h = √987
h = 31.42 ft
The height of the pole above the level of the observer's eyes is 31.42 ft
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f(x)=2x^2-3x+5 and g(x)=x-4,
find (f+g)(x)
Answer:
2x^3-2x^2+x
Step-by-step explanation:
Just trust me!
What two numbers multiply to -15 and add to 8
its urgent .have an exam tomorrow .pls help
Sociologists studying social mobility in the U.S. find that the probability that someone who began their career in the bottom 10% of earnings remains in the bottom 10% fifteen years later is 0.59. What is the probability that such a person moves to one of the higher income classes fifteen years later? (Use decimal notation. Give your answer as an exact number.)
probability:
Using probability of complementary events, it is found that there is a 0.41 probability that such a person moves to one of the higher income classes fifteen years later.
When two events are complementary, the sum of their probabilities are 1.
In this problem, either a person moves to a higher income class or they do not, hence, the events are complementary.
0.59 probability that a person does not move to a higher class.Hence, 1 - 0.59 = 0.41 probability that such a person moves to one of the higher income classes fifteen years later.A similar problem is given at https://brainly.com/question/24084986
