Answer:
Lacy is 13 and Jack is 52
Step-by-step explanation:
In 3 years their ages will add up to 71 so you have to subtract 6 as there are two of them to get 65. Lacy's age is represented by x and since Jack is 4 times older his age is represented by 4x. So added together their age is 5x. So 5x=65. Then 65/5=13. So 13=x. So Lacy is 13 and Jack is 52 as 13x4 is 52.
What is the x-coordinate of the point shown in the graph?
______
Answer:
Hey there!
The x coordinate would be -5.
Let me know if this helps :)
As we can see in the Graph,
x-coordinate = - 5y-coordinate = - 7
The state of Georgia is divided up into 159 counties. Consider a population of Georgia residents with mutually independent and equally likely home locations. If you have a group of n such residents, what is the probability that two or more people in the group have a home in the same county
Answer:
[tex]\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }[/tex]
Step-by-step explanation:
number of counties = 159
n number of people are mutually independent and equally likely home locations
considering the details given in the question
n ≤ 159
The number of ways for people ( n ) will live in the different counties (159) can be determined as [tex](\left \{ {{159} \atop {n}} \right} )[/tex]
since the residents are mutually independent and equally likely home locations hence there are : [tex]159^{n}[/tex] ways for the residents to live in
therefore the probability = [tex]\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }[/tex]
Please help this is due at 11:59 and im really stuck.
9514 1404 393
Answer:
B B C C A A
Step-by-step explanation:
If we number the equations 1 to 6 left to right, then we have ...
B - can be put (y = 2x)B - can be put (y = (1/9)x)C - other, not a proportional relationshipC - other, y = 5/x, an inversely proportional relationshipA - has the form, k = 0.04A - has the form, k = -11What is the sum of the geometric sequence?
Answer:
B. 259
Step-by-step explanation:
6^(i - 1) for i = 1 to 4
sum = 6^(1 - 1) + 6^(2 - 1) + 6^(3 - 1) + 6^(4 - 1) =
= 6^0 + 6^1 + 6^2 + 6^3
= 1 + 6 + 36 + 216
= 259
Answer: B. 259
Express b+1/3b-2 with “b” as the subject
Answer:
b = [tex]\frac{1+2a}{3a-1}[/tex]
Step-by-step explanation:
Given
a = [tex]\frac{b+1}{3b-2}[/tex] ( multiply both sides by 3b - 2 )
a(3b - 2) = b + 1 ← distribute left side
3ab - 2a = b + 1 ( subtract b from both sides )
3ab - b - 2a = 1 ( add 2a to both sides )
3ab - b = 1 + 2a ← factor out b from each term on the left side
b(3a - 1) = 1 + 2a ( divide both sides by 3a - 1 )
b = [tex]\frac{1+2a}{3a-1}[/tex]
Answer:
[tex]→a = \frac{(b + 1)}{(3b - 2)} \\ a(3b - 2) = (b + 1) \\ 3ab - 2a = b + 1 \\ 3ab - b = 2a + 1 \\ b(3a - 1) =( 2a + 1) \\ \boxed{b = \frac{(2a + 1)}{(3a - 1)} }✓[/tex]
b = (2a+1)/(3a-1) is the right answer.five hundred seven billion,six hundred forty million,seven hundred forty-two thousand,seventy two
Answer:
507,640,142,072
Step-by-step explanation:
not sure what you are asking but I hope this helps! :D
I WILL RATE YOUR BRAINLIEST Marius opened a savings account. The sequence {200, 208, 216.30, 225, …} describes the amount of interest he earns each year his account is active. If this pattern continues, how much total interest will Marius have earned by the 30th year the account is active?
Answer:
11,215Step-by-step explanation:
Given the sequence of interest earned by Marius on his savings account as
200, 208, 216.30, 225, …, the sequence of interest forms a geometric sequence since they have a common ratio.
[tex]r =\frac{T_2}{T_1}= \frac{T_3}{T_2}= \frac{T_4}{T_3}\\ r =\frac{208}{200}= \frac{216.30}{208}= \frac{225}{216.30} \approx 1.04[/tex]
To get how much total interest will Marius have earned by the 30th year the account is active, we will find the sum of the first 30 terms of the geometric sequence as shown.
[tex]S_n =\frac{ a(r^n-1)}{r-1} \ for \ r> 1\\ \\\\ n = 30, a = 200, r = 1.04\\S_{30} = \dfrac{ 200(1.04^{30}-1)}{1.04-1}\\\\S_{30} = \dfrac{ 200(3.243-1)}{0.04}\\\\S_{30} = \dfrac{ 200(2.243)}{0.04}\\\\S_{30} = \dfrac{ 448.6}{0.04}]\\\\S_{30} = 11,215[/tex]
Hence total interest that Marius will earn by the 30th year the account is active is 11,215.
the correct answer is
S30= 200(1-1.04^n)/1-1.04
i took the test
Find the sum of 1 + 3/2 + 9/4 + …, if it exists. This is infinite series notation. The answer is NOT 4.75.
Answer:
D
Step-by-step explanation:
First, this looks like a geometric series. To determine whether or not it is, find the common ratio. To do this, we can divide the second term and the first term, and then divide the third term and the second term. If they equal to same, then this is indeed a geometric series.
[tex](3/2)/(1)=3/2\\(9/4)/(3/2)=(9/4)(2/3)=18/12=3/2[/tex]
Therefore, this is indeed a geometric series with a common ratio of 3/2.
With just this, we can stop. This is because since the common ratio is greater than one, each subsequent value is going to be bigger than the previous one. Because of this, the series will not converge. Therefore, the series has no sum.
To see this more clearly, imagine a few more terms:
1, 1.5, 2.25, 3.375, 5.0625...
Each subsequent term will just increase. The sum will not converge.
Answer:
No Sum --- it doesn't exist.
Step-by-step explanation:
The partial sums get arbitrarily large--the go to infinity.
The geometric series you are trying to sum has common ratio = 3/2.
The sum of the infinite series exists only when |common ratio| < 1.
The formula for the partial sum of n terms is (r^(n+1) - 1) / (r - 1) = (1.5^(n+1) - 1) / 0.5, or in decimals instead of fraction.. i.e. 1 + 1.5 + 2.25 + 5.0525 + 25.628 + 656.840..... therefore It would take a long time but you'd be adding up forever and goes to infinity.
:( I Need help! Show work please! Aviva has a total of 52 coins, all of which are either dimes or nickels. The total value of the coins is $4.70. Find the number of each type of coin.
Answer:
42 Dimes, 10 Nickels.
Step-by-step explanation:
Dimes are worth $0.10, nickels are worth $0.05.
If D = number of dimes, and N = number of nickels, then the following equations are true:
0.10D + 0.05N = 4.70
D + N = 52
Next, let's multiply the first equation by 10 so that we can subtract the second one from it.
D + 0.50N = 47
(-) D + N = 52
Subtracting the second equation from the first one gives:
-0.5N = -5
-0.5N/-0.5 = -5/-0.5
N = 10
Finally, substitute N in the original second equation to find D.
D + 10 = 52
D + 10 - 10 = 52 - 10
D = 42
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! Given this frequency chart of 1490 passengers from the Titanic who died, choose the class(es) whose relative frequency would comprise just under, 1/2 of a pie chart
Answer:
b and eStep-by-step explanation:
Second and Third which gives in total:
0.112 + 0.354 = 0.466This is under 1/2 and greater than Crew.
5/3 x 6/7 real quick plz
Answer:
10/7 or 1 3/7. I hope this helps,
Step-by-step explanation:
60 is x% of 12. Find the value of x.
Answer:
20
Step-by-step explanation:
We can set up a percentage proportion to find the value of x.
[tex]\frac{12}{x} = \frac{60}{100}[/tex]
Now we cross multiply:
[tex]100\cdot12=1200\\\\1200\div60=20[/tex]
Hope this helped!
Find the slope of the line containing the points (7,5) and (2, 4).
Answer:
1/5
Step-by-step explanation:
the two points are(7,5) and (2,4)
let,(x1,y1)=(7,5) and (x2,y2)=(2,4)
slope (m)=y2-y1/x2-x1
=4-5/2-7
=-1/-5
=1/5(minus ,minus are cut)
What is the area of the region bounded by the three lines with equations $2x+y = 8$, $2x-5y = 20$ and $x+y = 10$?
Answer:
42
Step-by-step explanation:
A graphing tool is useful for finding the points of intersection of these lines. If the equations are numbered 1, 2, 3 in the order given, we can find the points of intersection to be ...
equations 1, 2: A(5, -2)
equations 2, 3: B(10, 0)
equations (3, 1): C(-2, 12)
Then the area can be found from the coordinates using the formula ...
A = (1/2)|x1(y2-y3) +x2(y3-y1) +x3(y1-y2)|
= (1/2)|5(0-12) +10(12-(-2)) -2(-2-0))| = (1/2)|-60 +140 +4|
A = 42
The area of the triangular region is 42 square units.
Please help answer the following questions!!! :D I will do anything in return!
Evaluate f(g(3)) if f(x)=6x−4 and g(x)=x2.
(Please Explain! Thank you)
Answer: 50
Step-by-step explanation:
f(x) = 6x-4 and g(x) = x^2
f(g(3)) means what is the value of the function f when it is evaluated at the value of g(3).
So g(x) is x^2 so g(3) is 3^2 = 9
Therefore we put 9 in for f(g(3))= f(9) = 6(9) - 4 = 54 - 4 = 50
if 2/-5 x=-10/x what is the value of x
Answer:
± 5
Step-by-step explanation:
2x/-5 = -10/x
2x^2 = 50
x^2 = 25
x = ± 5
Answer:
x=5
Step-by-step explanation:
Start with writing it like 2x/-5= -10/x
Then cross multiply: 2[tex]x^{2}[/tex]= 50
Divide by 2: [tex]x^{2}[/tex]=25
Square root of 25: 5
x=5
Find the sum of the first 100 terms of the sequence below:
-19, -15, -11, -7, -3, ...
S100
Answer:
17900
Step-by-step explanation:
First term a = -19
common difference d = -15-(-19) = 4
number of terms, n = 100
sum of first 100 terms,
n/2(2a+(n-1)d)
= 100/2(2×(-19)+(100-1)4)
= 50×(-38+99×4)
= 50×358
= 17900
Use the model to show to help find the sum 0.34 plus 0.49
Answer/Step-by-step explanation:
The idea to use in solving this problem using the model, is to express the number of shaded boxes in fraction form.
Thus, the blue red shaded boxes has 34 boxes shaded out of 100 boxes. This represents [tex] \frac{34}{100} [/tex]. This will give us 0.34.
The other shaded boxes represents [tex] \frac{49}{100} = 0.49 [/tex].
Using the model, we can solve 0.34 + 0.49.
Add both fractions together.
[tex] \frac{34}{100} + \frac{49}{100} = \frac{34+49}{100} [/tex]
[tex] \frac{83}{100} = 0.83 [/tex]
Determina el valor absoluto de 13 – 11|
Responder:
2
Explicación paso a paso:
El valor absoluto de una expresión es el también conocido como valor positivo devuelto por la expresión. Una expresión en un signo de módulo se conoce como valor absoluto de la expresión y dicha expresión siempre toma dos valores (tanto el valor positivo como el negativo).
Por ejemplo, el valor absoluto de x se escribe como | x | y esto puede devolver tanto + x como -x debido al signo del módulo.
Pasando a la pregunta, debemos determinar el valor absoluto de | 13-11 |. Esto significa que debemos determinar el valor positivo de la expresión como se muestra;
= | 13-11 |
= | 2 |
Este módulo de 2 puede devolver tanto +2 como -2, pero el valor absoluto solo devolverá el valor positivo, es decir, 2.
Por tanto, el valor absoluto de la expresión es 2
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now, in about how many years will it take to reach $20 per month? Use the equation 20 = 8(1.2)x to solve the problem. Round to the nearest year. 1 year 5 years 2 years 16 years
Answer:
6 years
Step-by-step explanation:
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:
[tex]y=ab^x[/tex]
Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8
[tex]y=ab^x\\8=ab^0\\a=8[/tex]
Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2
Therefore:
[tex]y=ab^x\\y=8(1.2^x) \\[/tex]
To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x
[tex]20=8(1.2)^x\\20/8=1.2^x\\1.2^x=2.5\\Taking \ natural\ log\ of \ both\ sides:\\ln(1.2^x)=ln2.5\\xln(1.2)=0.9163\\x=0.9163/ln(1.2)\\x=5.026[/tex]
x = 6 years to the nearest year
Answer:
5 years
Step-by-step explanation:444
Janet invests a sum of EUR in an account that offers 3.5% simple interest. After ten years her investment is worth 7425 EUR. How much did she invest?
We need to find the amount of money Janet invested in 10 years to yield 7425 EUR
She invested EUR 21,214.29
Simple interest = P × R × T
Where,
P = principal = ?
R = interest rate = 3.5% = 0.035
T = Time = 10 years
Simple interest = 7425 EUR
Simple interest = P × R × T
7425 = p × 0.035 × 10
7425 = p × 0.35
7425 = 0.35p
Divide both sides by 0.35
P = 7425 / 0.35
= 21,214.285714285
Approximately,
P = EUR 21,214.29
https://brainly.com/question/10936433
Manuel says that he can solve the equation 3n = 21 by multiplying both sides by ⅓. Explain why this is correct.
Step-by-step explanation:
はい、両側を削除して、3を掛けて7にします
Step-by-step explanation:
Given:
3n = 21
if we multiply both sides by 1/3, we will get:
3n = 21
3n x (1/3)= 21 x (1/3)
3n/3 = 21/3
n = 21/3
n = 7
Hence we can indeed solve for n by multiplying both sides by (1/3)
Which equation is represented by the table?
Emily made a pot cream of pumpkin soup for thanksgiving dinner she put 5 cups of cream in the soup she poured the soup into 24 small bowl show much cream measured in oz is used for each small bowl of soup?
Answer:
each bowl can contain 5/3 oz. of soup.
Step-by-step explanation:
1 cup = 8 oz.
8 oz.
5 cups x -------------- = 40 oz.
1 cup
to get the measurement of each bowl,
40 oz. divided into 24 bowls.
therefore, each bowl can contain 5/3 oz. of soup.
A contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the table below. Susan wishes to determine how much to haul from each pit to each site to minimize the total cost for purchasing and hauling gravel. Pit Hauling cost per Ton at Site Price per ton Site 1 Site 2 Site 3 North $30 $60 $50 $100 South $60 $30 $40 $120 Now suppose that trucks (and their drivers) need to be hired to do the hauling, where each truck can only be used to haul gravel from a single pit to a single site. Each truck can haul 5 tons, and the cost per truck is five times the hauling cost per ton given above. Only full trucks would be used to supply each site.
Required:
Formulate this problem as a transportation problem with two sources and three destinations.
https://www.chegg.com/homework-help/questions-and-answers/contractor-susan-meyer-haul-gravel-three-building-sites-purchase-much-18-tons-gravel-pit-n-q8579741
Write 4–6 sentences explaining why it is important to have precise definitions in mathematics.
write 32 1/2 in radical form
Answer:
Nothing further, the simplest answer is 32 1/2
Step-by-step explanation:
Simplify the following expression:
Step-by-step explanation:
[tex]{ \bf{( \frac{ - 10 {a}^{3} {b}^{5} \times 6 {a}^{6} {b}^{2} }{ {12a}^{9} {b}^{5} } ) {}^{3} }} \\ \\ = { \sf{( \frac{ - 60 {a}^{9} {b}^{7} }{12 {a}^{9} {b}^{5} } ) {}^{3} }} \\ \\ = { \sf{(5 {b}^{2}) {}^{3} }} \\ = { \sf{125 {b}^{5} }}[/tex]
For the function y=f(x), find f’(a)
Answer:
-1/4
Step-by-step explanation:
f(x) = 1/(x+1)
f(a) = 1/(a+1)
f'(a) = {(a+1)×d/da (1) - d/da (a+1) × 1}/(a+1)²
f'(a) = {(a+1)×0 - 1×1}/(a+1)²
f'(a) = (0-1)/(a²+2a+1)
f'(a) = -1/(1+2a+a²)
putting a = 1
f'(a) = -1/(1+2+1)
f'(a) = -1/4