Answer:
[tex]T_n = 2n - 1 + T_{n-1}[/tex]
Step-by-step explanation:
Given
[tex]Sequence: -5,-2,3,10,19[/tex]
Required
Find the nth term
We have:
[tex]T_1 = -5[/tex]
[tex]T_2 = -2 = 3 - 5 = 3 + T_1[/tex]
[tex]T_3 = 3 = 5 - 2 = 5 + T_2[/tex]
[tex]T_4 = 10 = 7 + 3 = 7 +T_3[/tex]
[tex]T_5 = 19 = 9 + 10 = 9 + T_4[/tex]
This gives:
[tex]T_2 = 3 + T_1 = 4 - 1 + T_1[/tex]
[tex]T_3 = 5 + T_2 = 6 - 1 + T_2[/tex]
[tex]T_4 = 7 +T_3 = 8 - 1 + T_3[/tex]
[tex]T_5 = 9 + T_4 = 10 - 1 + T_4[/tex]
---
Solving further, we have:
[tex]T_2 = 4 - 1 + T_1 = 2 * 2 - 1 + T_1[/tex]
[tex]T_3 = 6 - 1 + T_2 = 2 * 3 + T_2[/tex]
[tex]T_4 = 8 - 1 + T_3 = 2 * 4 - 1 + T_3[/tex]
[tex]T_5 = 10 - 1 + T_4 = 2 * 5 - 1 + T_4[/tex]
Following the above sequence: the nth term is:
[tex]T_n = 2n - 1 + T_{n-1}[/tex]
Pls help with this math problem
Answer:
y=1/4x+6
Step-by-step explanation:
The formula for writing a slope equation is y=mx+b. The slope is 1/4, or m, and the y-intercept is 6, or b. Don't worry about the x or y, leave them as variables.
5)
Solve: 5x - 7x + 6 = -2(x - 3).
A)
0
B)
mit
2
infinitely many solutions
Answer:
Option C) Infinitely many solutions is correct option.
Step-by-step explanation:
We need to solve the equation [tex]5x - 7x + 6 = -2(x - 3)[/tex] and find value of x
The equation can be solved using DMAS rule.
Solving:
[tex]5x - 7x + 6 = -2(x - 3)[/tex]
Multiply -2 with terms inside the bracket
[tex]5x - 7x + 6 = -2x +6[/tex]
Now, we will combine like terms. Like terms are those terms that have same variable. In our case 5x, -7x and -2x are like terms and 6,6 are like terms.
[tex]5x - 7x +2x=-6 +6\\7x-7x=-6+6\\0=0[/tex]
Solving the equation we get 0=0 it means that the solution will have infinitely many solutions, because it will be true for every value of x.
So, Option C) Infinitely many solutions is correct option.
What is the process of 8q+6=4q-14
Answer:
Step-by-step explanation:
8q+6=4q-14
minus 4q from both sides to get
4q+6=-14
-6 from both sides
4q=-20
divide by 4
q=-5
we can check if this is right by implementing -5 as a substitute for q
-40+6=-20-14
-34=-34
Which fraction is equivalent to (1/2)(1/2)(1/2)
Answer:
3/6 4/8
Step-by-step explanation:
Determine whether or not x = 2 would make the following functions equal. Show your work.
y = 2x + 1 and
y = 4x – 3
Answer:
Yes.
Step-by-step explanation:
Substituting x = 2 into y = 2x + 1,
y = 5
Substituting x = 2 into y = 4x - 3
y = 5
Help me guys, Due now please
Answer:
about 8.3 miles an hour.
Step-by-step explanation:
34/4 is 8.5
90/11 is 8.2
average: 8.3
Ayo help a girly out
(1)Simplify each expression. (Make sure to find those "like" terms)
3x + 9 + 2x − 5
Options: 6x + 4
14x - 5
9x
5x + 4
______________________________________________________________
(2)Simplify each expression. (Make sure to find those "like" terms)
7m + 2(m − 5y)
Options: 14m - 5y
9m - 10y
9m - 5y
7m + 10y
_________________________________________________________________
If you're helping tysm my guy ily
Answer 1: 5x + 4
Answer 2: 9m + -10y
Step-by-step explanation:
To simplify 3x + 9 + 2x − 5, you have to find the like terms which are 3x and 2x, and 9 and -5. So you get 3x + 2x + 9 - 5 which gives you the result of 5x + 4. Now to simplify 7m + 2 (m − 5y), you have to distribute first, so 7m + (2) (m) + (2) (−5y) which gives you 7m + 2m + −10y. So now you just have to add. 7m + 2m = 9m and then you have -10y so basically the answer is 9m + -10y.
I hope this helps you bro
Suppose you want to start saving for retirement. You decide to continuously invest $20000 of your income each year in a risk-free investment with a 7% yearly interest rate, compounded continuously.
If yy is the value of the investment, and tt is in years:
dydt=dydt=
Your answer should be in terms of yy.
You start investing at t=0t=0 so y(0)=0y(0)=0.
y(t)=y(t)=
What is the size of your investment after 30 years.
Answer:
Following are the solution to the given points:
Step-by-step explanation:
p= amount at any time
then [tex]\frac{dp}{dt}=0.07 p[/tex]
[tex]p=p_0 (1+e^{0.07 t) \\\\[/tex]
[tex]P_0=\ principle \ amount \\\\ interest \ =p-p_0=p_0e^{0.07t}\\\\ p=y\frac{dy}{dt}=0.07y_0[/tex]
at time [tex]= t\ years[/tex]
[tex]\frac{dp}{dt}\\\\c_0=\$ \ 20000\ year\\\\p \to p+dp\\\\ dp=0.07p+c_0[/tex]
y= amount at any times
[tex]\frac{dy}{dt}=0.07y+c_0\\\\dt= \frac{dy}{c_0+0.07y}[/tex]
For point a:
[tex]\frac{dy}{dt}=20000+0.07 y[/tex]
For point b:
[tex]\frac{dy}{20000+0.07 y}=dt\\\\\frac{1}{0.07}|n(\frac{0.07y+20000}{20000})=t\\\\\frac{0.07y}{20000}+1=e^{0.07t}\\\\y=7.1428\times 10^4[e^{0.07t} -1]\\\\y=\frac{20000}{0.07}[e^{0.07t}-1]\\\\[/tex]
For point c:
[tex]y(30)=827391.75[/tex]
John has two different sugar syrups. Syrup A is 2 parts of sugar and 8 parts of water, and Syrup B is 3 parts of sugar and 5 parts of water. How much of each should john mix together to get 280 quarts of syrup that is 3 parts sugar and 7 parts water.
Answer:
Volume of syrup A = 120 quarts
Volume of syrup B = 280 - 120 = 160 quarts .
Step-by-step explanation:
Syrup A : 2 parts sugar , 8 parts of water .
Total = 10 parts
Syrup B : 3 parts sugar , 5 parts of water .
Total = 8 parts .
Mixture required 280 quarts , 3 parts sugar , 7 parts water
In 280 quarts , sugar = 280 x 3 / ( 3 + 7 )
sugar = 84 parts
Let volume of syrup A be x , volume of syrup B = 280 - x
sugar A = 2 x / 10 = 0.2 x
sugar B = 3 ( 280 - x ) / 8 = .375 ( 280 - x )
Total sugar = .2 x + .375 ( 280 - x ) = 84 .
.2 x + 105 - .375 x = 84
105 - 84 = .375 x - .2 x = .175 x
.175 x = 21
x = 21 / .175 = 120
Volume of syrup A = 120 quarts
Volume of syrup B = 280 - 120 = 160 quarts .
John mixes 120 quarts of syrup A and 160 quarts of syrup of B together to get 280 quarts of syrup that is 3 parts sugar and 7 parts water.
Given that,
John has two different sugar syrups.
Syrup A is 2 parts of sugar and 8 parts of water, and Syrup B is 3 parts of sugar and 5 parts of water.
We have to determine,
How much of each should john mix together to get 280 quarts of syrup that is 3 parts sugar and 7 parts water.
According to the question,
Syrup A: 2 parts sugar, 8 parts of water.
Total number of parts = 10 parts
Syrup B : 3 parts sugar, 5 parts of water.
The total number of parts = 8 parts.
The mixture required 280 quarts, 3 parts sugar, 7 parts water,
In 280 quarts, parts of sugar are,
[tex]= \dfrac{280 \times 3 }{ ( 3 + 7 )}\\\\= \dfrac{280 \times 3}{10}\\\\= 84[/tex]
Let the volume of syrup A be x,
And the volume of syrup B be 280 - x
[tex]Sugar\ A = \dfrac{2x}{10} \\\\Sugar \ A = 0.2 x[/tex]
[tex]Sugar \ B = \dfrac{3 ( 280 - x ) }{8 }\\\\Sugar \ B= .375 ( 280 - x )[/tex]
The total amount of sugar is,
[tex]0.2 x + 0.375 ( 280 - x ) = 84 \\\\0.2 x + 105 -0 .375 x = 84\\\\105 - 84 = 0.375 x - 0.2 x = 0.175 x\\\\ 0.175 x = 21\\\\x = \dfrac{21}{0.175}\\\\x = 120[/tex]
Therefore,
The volume of syrup A = 120 quarts
Volume of syrup B = 280 - 120 = 160 quarts
Hence, John mixes 120 quarts of syrup A and 160 quarts of syrup of B together to get 280 quarts of syrup that is 3 parts sugar and 7 parts water.
For more details, refer to the link.
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❌Will mark brainliest answer
Select all the correct answers.
Which equations have one solution?
The zookeeper has 3 cups of frog food. She feeds the frogs
1/4 cup of food each day. How many days of frog food does
she have?
Answer:
12 days.
Step-by-step explanation:
The number of days of frog food the zookeeper has is A = 12 days
What do you mean by an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It displays the similarity of the connections between the phrases on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
Given data ,
Let the number of days of frog food the zookeeper has be A
Now , the value of A is
The number of cups of frog food she has = 3 cups
The number of cups of frog food she feed every day = ( 1/4 ) cups per day
Now , the equation is
A = number of cups of frog food she has / number of cups of frog food she feed every day
On simplifying the equation , we get
The number of days of frog food the zookeeper has A = 3 / ( 1/4 )
The number of days of frog food the zookeeper has A = 3 x 4
The number of days of frog food the zookeeper has A = 12 days
Hence , the number of days is 12 days
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Tony uses the length of his hand to measure the size of his desk. He finds the top of his desk to be about "3 hands by 9 hands" in size. Jacqueline uses her hand and finds the same desk to measure about "4.25 hands by 12.75 hands" in size.
Tony's hand is how many times as long as Jacqueline's hand?___________ times as long
What is the measure of Tony's hand using Jacqueline's hand as the "unit ruler"?
Jacqueline's hand is how many times as long as Tony's hand?__________ times as long
What is the measure of Jacqueline's hand using Tony's hand as the "unit ruler"?
Answer:
the answer isto get a brain idiot
Step-by-step explanation:
yyyh
What is equal to 3.6 x 0.005
Answer:
0.018
Step-by-step explanation:
basta yan ang sagot
Answer: 0.018
Step-by-step explanation: insta: camryn_boeling
log, 7 1/2
Solve in exponential form
Answer:
7 = x^1/2.
Step-by-step explanation:
logx 7 = 1/2
Converting to exponential form ( the value of the log is the exponent and x is the base):
7 = x^1/2
I need help please.
Answer:
12% or c
Step-by-step explanation:
590/670 = 88.059 rounded to 88
100 - 88 = 12
Answer: c
Step-by-step explanation: 80/670 = ____/100 then cross multiply
Which equation is equivalent to the given equation?
X^2-14x=-48
Answer:
(x-6)(x-8)=0
Step-by-step explanation:
x^2-14x+48=0
Factorizing
x^2-8x-6x+48=0
(x^2-8x)+(-6x+48)=0
x(x-8)-6(x-8)=0
(x-6)(x-8)=0
Can you help me? I will give the brainleist
Answer:
18
Step-by-step explanation:
P = (3+6)*2 = 18
please help me!
7. Two hours after leaving his home, Nolan traveled a distance of 120 miles. Distance in this scenario is represented by d and time is represented by t.. [2 points]Part A. Assuming that Nolan travels at the same speed during his trip, which of the following statements can be used to describe the distance Nolan may have traveled?
a.Nolan traveled 180 miles after 3 hours.
b.Nolan traveled 60 miles after 2 hours
.c.Nolan traveled 120 miles after 1 hour.
d. Nolan traveled 60 miles after 0 hours.
Part B. Write an equation that represents the distance traveled by the car for an amount of time. Then name the dependent variable
.a.d=120t, d is the dependent variable
b.d=60t, d is the dependent variable
c.d=120t, t is the dependent variable
d.
d=60t, t is the dependent variable
Answer:
bueh
Step-by-step explanation:
Factor 9x2 + 25 over the set of complex numbers.
Enter your answer in the box.
The set of complex numbers are x= +5/3i and x= -5/3i.
What is the complex number?A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z.
The given expression is 9x²+25
9x²=-25
x²=-25/9
x=√(-25/9)
x=±5/3i
x= +5/3i or -5/3i
Therefore, the set of complex numbers are x= +5/3i and x= -5/3i.
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Based on the following scenarios, match the scenario with the correct type of problem. Group of answer choices
a. A local Toyota dealership wants to estimate the average cost of maintenance repairs car owners spend per year. They send out a survey asking locals to report the cost for their vehicle over the past year.
b. The University of Florida wants to estimate what number of students visit Library West multiple times per week. They ask the following question: "Do you visit Library West more than twice a week?"
c. A local Toyota dealership wants learn about customers use of the vending machines in the waiting area lobby. They ask the question: "Do you purchase food or drink from the vending machines?"
d. The University of Florida wants to estimate how long students visit Library West per week. They send out a survey and ask respondents to write down how many hours per week they visit Library West.
Options for each question:
1. One proportion
2. One mean
Answer:
Matching the scenario with the correct type of problem:
a. one mean
b. one proportion
c. one proportion
d. one mean
Step-by-step explanation:
A one-proportion problem is tested using the one-sample proportion test. This estimates the proportion of a population by comparing the proportion to a target or reference value. On the other hand, a one-mean problem is tested using the one-sample t-test. This tests whether a population mean is significantly different from some hypothesized value.
If 8% of a number is 40, find 2% of that number.
Answer:
10%
Step-by-step explanation:
0.08×anumber=40,then 0.02x=?
x=40/0.08=500
0.02×500=10
What proportion can be used to find 65% of 90?
Answer:
C. 65/100 = x/90
Step-by-step explanation:
65% of 100 is 65/100 as 65% of 90 is x/90.
You can find the correct answer by cross multiplying to see if the part / whole = percent / 100.
In the box, type the number that correctly completes the sentence.
Andrew bought a sandwich for $4.37. If he gives the cashier a $10 bill, he
should receive $
in change.
In the equation y = 2x + 5, what values represent the m (slope) and the b (y-intercept)?
Answer:
m(slope)=2
b(y-intercept)=5
Step-by-step explanation:
Answer:
2x represents the slope and 5 represents the y intercept.
Question 4
0/20 pts
PLEASE HELP!!!: The slope of a line is –3 and the
y-intercept is (0,4). What is the
equation of the line in slope-intercept
form?
9514 1404 393
Answer:
D. y = -3x +4
Step-by-step explanation:
The slope-intercept form is ...
y = mx + b
where m is the slope (-3) and b is the y-intercept (4). Putting these values into the form gives ...
y = -3x +4 . . . . . matches choice D
20points. Find an equation for the linear graph.
Use the two endpoints to find the slope:
(0,2) and ( 5,5.5)
Slope = change in y over change in x:
Slope = (5.5-2)/(5-0) = 3.5/5 = 0.7
The y intercept is the y value when x is 0, which is 2
Equation: c = 0.7x + 2
4x4=(blank)+(blank)=blank
Answer:
i think it would be 4x4=8+8=16
Sam earned $154 washing 7 cars. He earned the same amount for washing each car
Select all the equations that show reasonable estimates for the amount Sam eamed washing each car
A $140 = 7 = $20
B. $190 = 9 = $10
C. $160 = 8=320
D. $150 = 5= $10
E $150 = 3= $50
Answer:
the answer is A cause you divide 7 by 140 and the answer is 22 so 20 is the closest
please help I am confused i'll answer one of your questions!! I got it wrong the first time
Answer:
Step-by-step explanation:
22.2
Answer:
22.2
Step-by-step explanation:
1. What is the 15th partial sum of the geometric sequence (262,144; 32,768; 4,096; 512; ...)? Round to the nearest whole number, if needed.
Answer:
[tex]S_{15} = 299593[/tex]
Step-by-step explanation:
Given
[tex]262144,\ 32768,\ 4096,\ 512; ...[/tex]
Required
Determine the 15th partial sum
The nth partial sum of a geometric series is:
[tex]S_n = a* \frac{1 - r^n}{1 - r}[/tex]
In this case:
[tex]a = 262144[/tex]
[tex]n = 15[/tex]
r is calculated as:
[tex]r = \frac{32768}{262144}[/tex]
[tex]r = 0.125[/tex]
Substitute values for a, r and n in [tex]S_n = a* \frac{1 - r^n}{1 - r}[/tex]
[tex]S_{15} = 262144* \frac{1 - 0.125^{15}}{1 - 0.125}[/tex]
[tex]S_{15} = 262144* \frac{1}{0.875}[/tex]
[tex]S_{15} = \frac{262144* 1}{0.875}[/tex]
[tex]S_{15} = \frac{262144}{0.875}[/tex]
[tex]S_{15} = 299593.142857[/tex]
[tex]S_{15} = 299593[/tex] -- approximated