We have to use the formula [tex]n = log_{r} (1+\frac{S_{n}(1-r) }{a})[/tex] to find the number of terms of a finite geometric sequence.
If a be the first term of a finite sequence, r be the common ratio between consecutive terms and n be the number of terms.
So, we have to use the formula of sum of sequence and then calculate it to reduce the equation to find the value of number of terms, that is n.
Then, Sum of the sequence (Sn) = [tex]\frac{a(1-r^{n}) }{1-r}[/tex]
Here, in the given problem,
Sum(Sn) = 280, First term of the sequence(a) = 40, Common ratio(r) = 0.75
So, Sn = [tex]\frac{a(1-r^{n}) }{1-r}[/tex]
⇒ [tex]1-r^{n} =\frac{S_{n}(1-r) }{a}[/tex]
⇒ [tex]r^{n} =1+\frac{S_{n}(1-r) }{a}[/tex]
⇒ [tex]n = log_{r} (1+\frac{S_{n}(1-r) }{a})[/tex]
Now you have to put the values and get the number of terms.
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7. Sapna travelled 48 km to meet her parents. She travelled the first 18 km by car and the remaining distance by train. Find the fraction of the journey sapna travelled by car and train
The fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.
We know that fraction is an expression in mathematics used to denote the division of two whole numbers.
Given that the total distance = 48 km.
The distance Sapna traveled by car = 18 km.
So, the fraction is = distance traveled by car/total distance = 18/48 = 3/8
The distance Sapna traveled by train = 48 - 18 km = 30 km.
So, the fraction is = distance traveled by train/total distance = 30/48 = 5/8
Therefore the fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.
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John is buying a new car. The value of one car he is considering is $20,000. The value of the car as it ages can be modeled by the function V = 20 , 000 ( 0 . 84 ) t , where t is the number of years from the time of purchase. One of the factors John is using to make his decision is the value of the car over time until it reaches half its original value. What values of domain are reasonable for the given function in this context?
A. all real numbers greater than or equal to 0 and less than 2.8
B. all real numbers greater than or equal to 10,000 and less than or equal to 20,000
C. all real numbers greater than or equal to 0
D. all real numbers greater than or equal to 0 and less than 4
Option D is the correct answer.
All real numbers greater than or equal to 0 and less than 4.
What is Domain?The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined.
Here, The function of the car value is given as:
V(x) = 20000 X (0.84)ˣ
When the car reaches half its value, we have:
V(x) = 10000
Substitute V(x) = 10000 in V(x) = 20000 * (0.84)ˣ
10000 = 20000 X (0.84)ˣ
Divide both sides by 20000
0.84ˣ = 0.5
Take the logarithm of both sides
x log(0.84) = log(0.5)
Divide both sides by log(0.84)
x = 4
This means that the maximum value of x is 4.
Thus, all real numbers greater than or equal to 0 and less than 4.
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3 more than half a number
Answer:
3 + a/2
Step-by-step explanation:
3 + a/2
You have loaned a friend $100 and will charge him 5% annua simple interest when he pays it back.
The annual interest would be $5 if you have loaned a friend $100 and will charge him 5% annually and the total amount would be $105.
What is simple interest?It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount of borrowed amount.
We have:
You have loaned a friend $100 and will charge him 5% annually.
As we know:
A = P(1 + rt)
P = $100
r = 5% = 0.05
t = 1 years
A = 100(1 + 0.05×1)
A = $105
I = A - P = 105 - 100 = $5
Thus, the annual interest would be $5 if you have loaned a friend $100 and will charge him 5% annually and the total amount would be $105.
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A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 80% salt. She wants to obtain 120 ounces of a mixture that is 70% salt. How many ounces of each solution should she use?
Please Expand the following:
3q(r – 2q)
Answer:
3qr - 6q²
Step-by-step explanation:
3q(r - 2q) ← multiply each term inside the parenthesis by 3q
= 3qr - 6q²
Answer:
3qr – 6q²
Step-by-step explanation:
3q(r – 2q)
E X P A N D I N G :-
3qr – 6q²
Solve the following subtraction problem. Remember to borrow as necessary.
9cu yd113cu in
− 4cu ft129cu in
−−−−−−−−−−−−−−−−−−−−−−
The subtraction of the expression will be 238 cubic feet, 551 cubic inches.
What is subtraction?It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.
The expressions are given below.
9 cubic yd 113 cubic in and 4 cubic ft 129 cubic in
1 cubic yard = 27 cubic feet
1 cubic feet = 1728 cubic inches
Then the subtraction will be
242 cu ft 1841 cu in
− 4 cu ft 1290 cu in
238 cu ft 551 cu in
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If f(n)= n²-n, then f(-4) is
O-20
12
-12
20
Answer:
20
Step-by-step explanation:
Plug in -4 for n:
(-4)^2 - (-4) = 16 + 4 = 20
Let f(x)=(3)^x−3. What is f(0) in fraction form?
Answer:
1/27
Step-by-step explanation:
We can substitute x=0 into the function to get:
f(0) = 3^(0-3)f(0) = 3^(-3)f(0) = 1/270000
O
1. Simplify 3 + 2 - 1
+6
2-5
03 A
О 25
Answer:
10
Step-by-step explanation:
3+2-1+6=5-1+6=4+6=10
What is 4 third written in expanded form
the answer to this asap please!
The required work done is 62400 J.
work done to lift a 1500 N object from the ground to the top of a 40 m building if the cable weighs 3 N per m
work done, is define as the product of force and displacement.
since,
work done to lift 1500N to height of 40 m is:
W= FS
= 1500 x 40 = 60000J
now work done for rope
is given by
w = mgΔx(40-x)
w= [tex]\int _0^{40}\left mg(40-x\right)dx[/tex]
w=[tex]3\int _0^{40}\left(40-x\right)dx[/tex]
w= 3[tex][40x-x^2/2]\left \{ {{40} \atop {0}} \right.[/tex]
w= 3[1600-800]
w = 2400
Total work done for lifting 1500N to 40m height
= 6000+2400=62400J
Thus the required work done to lift 1500N weight to 40m is 62400J.
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The function below has at least one rational zero.
Use this fact to find all zeros of the function.
f(x)=7x³ +9x²-12x-4
Answer:
Using the rational root theorem, we know to divide the function by (x - 1).
(7x³ + 9x² - 12x - 4) / (x - 1) = 7x^2 + 16x + 4
Now we can further factorize 7x^2 + 16x + 4 into (7x + 2) and (x + 2).
Therefore, the original function can be rewritten as (x - 1) (7x + 2) (x + 2).
Using the factorized form above, the zeros of the function are 1, -2/7, and -2.
Question:-
[tex] \dfrac{1}{2} + \dfrac{1}{4} [/tex]
Help!!
:"(
[tex]{\huge \underline{{ \fbox \color{red}{A}}{\fbox \color{green}{n}}{\fbox \color{purple}{s}}{\fbox \color{brown}{w}}{\fbox \color{yellow}{e}}{\fbox \color{gray}{r } }}}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \red{ \dfrac{1}{2} + \dfrac{1}{4} = \dfrac{3}{4} }[/tex]
Step by step explanation :-
The only thing you have to do is add the numerator to the denominator, in this case you have to add the first ones from the front, which can be these 2+1/4, which would result in 3/4, and this is called the Commutative Property.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \gray{ \dfrac{1}{2} + \dfrac{1}{4} = \dfrac{1}{4} + \dfrac{1}{2} }}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \green{\dfrac{2 + 1}{4} = \dfrac{1 + 2}{4} }}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed {\bf \blue{\dfrac{3}{4} = \dfrac{3}{4}} }[/tex]
Answer :- The answer is 3/4
¿What is commutative property?
It is to change different ways in order of the addends the result would be the same.
Example :-
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed {\bf \blue{\dfrac{a}{b} + \dfrac{c}{d}} = {\dfrac{c}{d} + \dfrac{a}{b}} }[/tex]
I hope I've helped : )
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: Final \:\: value = \cfrac{3}{4}[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{1}{2} + \cfrac{1}{4} [/tex]
[ take LCM ]
[tex]\qquad \tt \rightarrow \: \cfrac{2}{4} + \cfrac{1}{4} [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{2 + 1}{4} [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{3}{4} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
find the distance between the pair of points (7,6) and (4,10)
Answer:
5 units
Step-by-step explanation:
to find out the answer for this you must first find the distance between 7 and 4 and then 6 and 10
then you would square them and then add them
lastly you would take the square root of that and youd have your answer
so
7 - 4 = 3
6 - 10 = -4 (just use 4)
3^2 + 4^2 = 9 + 16 = 25
then you take the square root of this
sqrt(25) = 5
that is your answer
To solve this problem, you will use the Distance Formula to find the distance between two coordinate points.
Set Up the Distance FormulaThe Distance Formula is defined as follows:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
We must title our points by the standard coordinate naming system:
[tex](x_1, y_1) \ \text{and} \ (x_2, y_2)[/tex]
Therefore, our points can be labeled:
[tex]x_1 = 7[/tex][tex]y_1 = 6[/tex][tex]x_2 = 4[/tex][tex]y_2 = 10[/tex]Substitute Known Values for VariablesNow, substitute the known values as the variables in the Distance Formula:
[tex]d=\sqrt{(4 - 7)^2 + (10 - 6)^2}[/tex]
You must know the BPEMDAS acronym, which stands for:
Brackets
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Simplify the expression using BPEMDAS:
[tex]d=\sqrt{(-3)^2 + (4)^2}[/tex]
Remember that when a number is raised to the 2nd power, it is the same thing as multiplying the number by itself:
[tex]-3\times-3 = 9[/tex]
[tex]4\times4=16[/tex]
Simplify further by removing the parentheses:
[tex]d=\sqrt{9+16}[/tex]
Compute the additive operation:
[tex]d=\sqrt{25}[/tex]
Simplify the RadicandThe number that is placed inside of a square root symbol (or a radical symbol) is referred to as the radicand.
In this situation, the radicand is 25.
To simplify the radicand, you may either use a calculator to compute the result, or you can determine which number raised to the 2nd power will result in a final answer of 25.
In this case, we can determine that 5² will result in a final answer of 25.
[tex]5^{2} = 25[/tex]
The final answer is 5 units.
meijun had some money. she used 1/3 of it on a watch and 1/9 of it on a gift. the watch and the gift cost $144 altogether. how much money did she have at first?
Answer:
$324
Step-by-step explanation:
let x be the amount of money she had at first , then
[tex]\frac{1}{3}[/tex] x + [tex]\frac{1}{9}[/tex] x = 144 ( multiply through by 9 to clear the fractions )
3x + x = 1296
4x = 1296 ( divide both sides by 4 )
x = 324
she had $324 at first
4x+7-(x+6)=68
Solve.
[tex]4x + 7 - (x + 6) = 68 \\ \\ 4x + 7 - x - 6 = 68 \\ \\ 3x + 1 = 68 \\ \\ 3x = 68 - 1 \\ \\ 3x = 67 \\ \\ x = \frac{67}{3} \\ \\ x = 22.3[/tex]
The value of x is 67/3 or 22.3 .
Hi!
__________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]
x=
[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]
First let's distribute the minus sign.
[tex]\twoheadrightarrow\sf 4x+7-x-6=68[/tex]
[tex]\bullet[/tex] Add 6 to both sides
[tex]\twoheadrightarrow\sf 4x+7-x=74[/tex]
[tex]\bullet[/tex] Subtract the x's
[tex]\twoheadrightarrow\sf 3x+7=74[/tex]
[tex]\bullet[/tex] Subtract 7 from both sides
[tex]\twoheadrightarrow\sf3x=67[/tex]
[tex]\bullet[/tex] Divide both sides by 3
[tex]\twoheadrightarrow\sf x=\cfrac{67}{3}[/tex]
[tex]\bullet[/tex] Great job! We solved for the variable
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
--
Giving the brainliest to those who answer!
Find two positive numbers such that their sum is 60 and their product is a maximum. Select one: O a. 30 and 30 O b. 25 and 35 O c. 1 and 59 O d. 20 and 40
Answer:
B: 25 and 35
Step-by-step explanation:
25 product 35 875
The power 3 Superscript negative 3 equals StartFraction 1 Over 27 EndFraction . Which expression is equivalent to 3 Superscript negative 3?
Applying the negative exponent, it is found that the equivalent expression to [tex]3^{-3}[/tex] is [tex]\frac{1}{27}[/tex].
How to deal with a negative exponent?When we have a negative exponent, we use a fraction, with the term with the exponent going to the denominator, as follows:
[tex]a^{-b} = \frac{1}{a^b}[/tex]
Hence, in this problem, the equivalent expression is:
[tex]3^{-3} = \frac{1}{3^3} = \frac{1}{27}[/tex]
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please help! due very soon!
Answer:
{x | x = -6, -1, 0, 3}
(first option listed)
Step-by-step explanation:
The domain of a function is all possible x-values for that function
So, we can see (from the x-value portion of our table) that the possible x-values are:
-6 , -1, 0, and 3
We write domain and range in lowest - highest number value order, so we write our domain as such:
{x | x = -6, -1, 0, 3}
{range is all possible y-values, and this would include -7 , 1, 9, and -2}
hope this helps!!
can someone turn the equation 3−2=13 into a word problem. (i already know answer)
The word problem for given equation is : When 3 is multiplied with x and subtracted by 2 multiplied by y , the number obtained is 13. Solve the equation for x =1 .
The complete equation will be 3x - 2y =13
What is an Equation ?When an algebraic expression is equated by an equal sign to a constant or any other algebraic expression , then an equation is formed .
The equation given in the question is
3x-2y =13
When 3 is multiplied with x and subtracted by 2 multiplied by y , the number obtained is 13. Solve the equation for x =1 .
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What is the rule for the reflection?
rx-axis (x, y) - (-x, y)
ry-axis (x, y) (-x, y)
rx-axis (x, y) - (x, y)
ry-axis (x, y) (x, −y)
When reflected over ry-axis (x, y) (-x, y) , rx-axis (x, y) (x,-y) , Option A and D is the correct answer.
What is rule for the reflection ?The rule for reflection is when an object or a coordinate point is reflected over x axis then the coordinate of the x axis remains the same while the y coordinate changes to be additive inverse.
Vice Versa happens when reflected over y axis.
So,
rx-axis (x, y) - (-x, y) --> (x,-y)
ry-axis (x, y) (-x, y)
Therefore Option A and D is the correct answer.
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Answer: its A not A & D
Step-by-step explanation:
A paramedic maintains a time card for hours she works on the rescue squad. How many hours did she work per week ?
39 hours; she works per week if the paramedic maintains a time card for hours she works on the rescue squad.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
A paramedic maintains a time card for the hours she works on the rescue squad shown in the table:
We can write a mixed fraction in a fraction:
6 1/2 = 13/2
8 1/2 = 33/2
7 3/4 = 31/4
8 1/12 = 97/12
8 5/12 = 101/12
Adding all the fractions:
[tex]=\rm \dfrac{13}{2}+\dfrac{33}{4}+\dfrac{31}{4}+\dfrac{97}{12}+\dfrac{101}{12}[/tex]
[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{97}{12}+\dfrac{101}{12}[/tex]
[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{198}{12}[/tex]
[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{33}{2}[/tex]
[tex]=23+\dfrac{64}{4}[/tex]
= 39 hours
Thus, 39 hours; she works per week if the paramedic maintains a time card for hours she works on the rescue squad.
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Which of the following equations would correspond to a conic section formed when a plane intersects a cone parallel to the base?
x2 + y2 = 32
x squared over 2 squared plus y squared over 3 squared equals 1
x2 = 8y
x squared over 2 squared minus y squared over 3 squared equals 1
The equation of the circle, ellipse, and hyperbola will be x² + y² = 3², x² + y² / 3² = 1, and x² / 2² - y² / 3² = 1, respectively.
What is the conic section?The curve that is derived from the section of the cone is known as conic section.
The following equations are given below.
x² + y² = 3², this is the equation of the circle.
x² + y² / 3² = 1, this is the equation of the ellipse.
x² / 2² - y² / 3² = 1, this is the equation of the hyperbola.
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Students returning to a secondary school have to pass through a check point at the rate of 50 per though. The average time for checking is 35 seconds. The arrival rate and service rate follow a Poisson distribution. There is a delay and the principal is willing to include another check point to reduce the average time of checking to 28 seconds if the idle time is less than 10% and the average queue length is more than 10 students, check whether the introduction of an extra check point is justifiable.
The average queue length is greater than 10 students, the introduction of an extra checkpoint is justifiable.
How to explain the information?Since the arrival rate and service rate follow a Poisson distribution, we can use the Poisson arrival rate formula to calculate the average queue length.
Average queue length = (arrival rate * service time) / (1 - arrival rate * service time)
For the given problem, the average queue length is:
Average queue length = (50 * 35) / (1 - 50 * 35)
= 175
Since the average queue length is greater than 10 students, the introduction of an extra checkpoint is justifiable.
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PLEASE HELP!!!!
Which operation should you perform last in the expression 3^2 + 2?
Answer: the +2
Step-by-step explanation: PEMDAS. Exponents are before addition in the sequence. I hope this helps!
(The E standing for exponents and the A standing for addition)
A man wants to cut down a tree in his yard. To ensure that the tree doesn’t hit anything, he needs to know the height of the tree. He measures the distance from the tree at 14 m and the angle of elevation to the tree at 88°. What is the height of the tree to the nearest tenth of a meter
Answer:
400.9 m
Step-by-step explanation:
Account earns 8.5% interest. If you invest $6,609 now how much interest will you earn in 5years
Answer:
simple interest is $281(nearest whole number)
Step-by-step explanation:
S. I=PXTXR
100
P=$6609
T=5
R=8.5 or 85/10
S. I=6609X5X85
100X10
=280.8825
=281
what is the value of the rational expression below when is equal to 5?
15-(5)/5-10=10/-5=-2 hope it helps!
