Answer:
70
Step-by-step explanation:
Let x be the number of kangaroos adopted last year.
Twice the number adopted last year is 2x.
So, the number adopted this year is 2x - 24.
Equating this to the given number of kangaroos adopted this year, we have:
2x - 24 = 116
Adding 24 to both sides, we get:
2x = 140
Dividing both sides by 2, we get:
x = 70
So, the number of kangaroos adopted last year was 70.
You deposit $9000 in a savings account that earns 3.6% annual interest compounded monthly.
Answer:
A(t) = 9000(1 + 0.036/12)^12t
[Function formula for the compound interest]
A = 9000(1 + 0.036/12)^12t
[General formula for the compound interest]
A(1) ≈ 9329.40 $
[Compound interest over 1 year]
Step-by-step explanation:
Compound interest formula:
A = P(1 + r/n)^nt.
P is the principal or starting amount.
r is the interest rate.
n is the number of times compounded per year.
t is the period of time.
Given P is 9000, r is 3.6% or 0.036, n is 12 or monthly, and t is variable.
The following function represents the relationship over time:
A(t) = 9000(1 + 0.036/12)^12t
Determine the solutions of the equation:
the absolute value quantity four thirds times x plus 2 end quantity minus 6 equals 0
The solutions of the given absolute value equation |4/3 x + 2| - 6 = 0 are x = 3 and x = -6.
What is Absolute Value Equations?Absolute value equations are kind of equations which includes the absolute value symbol in the expression.
For example : |x - 5| = 4 is an absolute value equation.
The given absolute value equation is,
four thirds times x plus 2 end quantity minus 6 equals 0.
|4/3 x + 2| - 6 = 0
Isolating the absolute value quantity on one side,
|4/3 x + 2| - 6 + 6 = 0 + 6
|4/3 x + 2| = 6
This can be written as,
4/3 x + 2 = 6 and 4/3 x + 2 = -6
Solving each of these,
4/3 x + 2 = 6
4/3 x = 4
x = 3
4/3 x + 2 = -6
4/3 x = -8
x = -6
Hence the value of x are 3 and -6.
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an advertising company designs a campaign to introduce a new product to a metropolitan area of population 5 million people. let p(t) denote the number of people (in millions) who become aware of the product by time t. suppose that p increases at a rate proportional to the number of people still unaware of the product. the company determines that no one was aware of the product at the beginning of the campaign, and that 10% of the people were aware of the product after 10 days of advertising. the number of people who become aware of the product at time t is:
The number of people who become aware of the product at time t is [tex]p(t) = 5(1 - 0.9^{\frac{t}{10} })[/tex]
The advertising company wants to introduce a new product to a population of 5 million people. They assume that no one was aware of the product at the beginning of the campaign. They also know that after 10 days of advertising, 10% of the people became aware of the product. To find out how many people become aware of the product at time t, they use a function called p(t).
The function p(t) represents the number of people (in millions) who become aware of the product by time t. The company assumes that the rate at which p increases is proportional to the number of people still unaware of the product. This means that the more people who are unaware of the product, the faster the number of people who become aware of it will increase.
To express the proportionality mathematically, we can use the equation:
p'(t) = k [5 - p(t)]
Where p'(t) is the rate of change of p with respect to time t, and k is the proportionality constant that determines the speed of the increase. The quantity (5 - p(t)) represents the number of people who are still unaware of the product at time t. This means that as p(t) gets closer to 5 million, the rate of increase of p(t) will slow down.
To solve this equation, we need to use calculus. Integrating both sides of the equation, we get:
ln|5 - p(t)| = kt + C
Where C is the constant of integration. To determine the value of C, we use the initial condition that p(0) = 0. This means that at the beginning of the campaign, no one was aware of the product. Substituting this into the equation, we get:
ln|5 - 0| = k(0) + C
Simplifying, we get:
C = ln(5)
Substituting this value into the equation, we get:
ln|5 - p(t)| = kt + ln(5)
To find the value of p(t) at a specific time t, we can solve for p(t) by taking the exponential of both sides of the equation:
[tex]|5 - p(t)| = e^{kt+ln(5)}[/tex]
Simplifying, we get:
[tex]5 - p(t) = 5e^{kt}[/tex]
Or:
[tex]p(t) = 5(1 - e^{kt})[/tex]
To find the value of k, we can use the fact that 10% of the people were aware of the product after 10 days of advertising. This means that:
p(10) = 0.1(5) = 0.5
Substituting this into the equation, we get:
[tex]0.5 = 5(1 - e^{10k})[/tex]
Solving for k, we get:
k = -0.1 ln(0.9)
Substituting this value into the equation for p(t), we get:
[tex]p(t) = 5(1 - e^{-0.1ln(0.9)t})[/tex]
Simplifying, we get:
[tex]p(t) = 5(1 - 0.9^{\frac{t}{10} })[/tex]
This is the formula that tells us how many people will become aware of the product at time t.
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how many ways can aileen choose 2 pizza toppings from a menu of 18 toppings if each topping can only be chosen once?
The number of ways to choose 2 toppings from a menu of 18 toppings is a classic example of a combinatorial problem.
We have a set of 18 items (toppings), and we want to know how many ways there are to choose 2 of these items. The answer is given by the binomial coefficient C(18, 2), which is the number of ways to choose 2 items from a set of 18 items, where order does not matter and repetition is not allowed.
The formula for a binomial coefficient is:
C(n, k) = n! / (k! * (n - k)!)
where n! means n factorial, which is the product of all positive integers from 1 to n. So, for example, 5! = 5 * 4 * 3 * 2 * 1 = 120.
Using this formula, we can calculate the number of ways to choose 2 toppings from a menu of 18 toppings:
C(18, 2) = 18! / (2! * (18 - 2)!) = 18 * 17 / (2 * 1) = 153 ways
So there are 153 different ways to choose 2 toppings from a menu of 18 toppings.
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**EASY POINTS**
2 part question:
1. There is a circular running path in the park. The diameter of the circle is 350 m. What is the length of one lap around the path?
2. Jimmy jogs 3 laps of the circle in question #1 every morning. How long does he jog in 5 days?
Answer:
The length of one lap around the path is 2π x 350 m, which is equal to 2200 m.
Jimmy jogs 2200 m x 3 laps x 5 days, which is equal to 33000 m or 33 km.
Step-by-step explanation:
need answers ASAP!!!!!!!!!!!!!!
The diameter of a fountain is 9 meters. A sidewalk that is 0.7 meters will be built around it. Find the diameter
Round to the nearest tenth
An estimated Rs. 1863.40 will be needed to cement the route.
What is meant by Cost?A mathematical formula known as a cost function can be used to determine the overall cost of production for a given quantity of goods produced. We'll go into more detail about the cost function below. Representation of unit expenses in relation to the production of 1 or more units during a construction project. For instance, the most popular cost function has the formula y = a + bx, where y is the total cost, an is the total fixed cost, b is the variable cost per unit of production or sales, and x is the number of units produced or sold. This formula sums the fixed costs and the variable costs to represent the total cost.Diameter of park [tex]$=7 \mathrm{~m}$[/tex]
so, radius of park [tex]$=\mathrm{r}_1=3.5 \mathrm{~m}$[/tex]
Width of park [tex]$=0.7 \mathrm{~m}$[/tex]
Bigger radius of park [tex]$=\mathrm{r}_2=0.7+3.4=4.2 \mathrm{~m}$[/tex]
Now, Area of path = area of bigger circle -area of smaller circle
[tex]$=\pi r_2^2-\pi r_1^2=$ $\pi\left(r_2^2-\mathrm{r}_1^2\right)=\frac{22}{7}\left(4.2^2-3.5^2\right)=\frac{22}{7}(17.64-12.25)=16.94 \mathrm{~m}^2$[/tex]
Also, Cost of expenditure = rate [tex]$\times$[/tex] area [tex]$=110 \times 16.94=1863.40$[/tex]
Cost of Expenditure of cementing the path is Rs. 1863.40.
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an equation for the line with a slope of 3 and passing through the point (5, 7).
Answer:
y – 7 = 3(x – 5)
Step-by-step explanation:
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \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}{7}=\stackrel{m}{ 3}(x-\stackrel{x_1}{5}) \\\\\\ y-7=3x-15\implies {\Large \begin{array}{llll} y=3x-8 \end{array}}[/tex]
Jamarie and DJ go bowling. Jamarie knocks a total of 26 pins. DJ knocks down three times as
many. How many did they knock down together?
Show your work
In total they knocked down 104 pins.
I got this by multiplying 26 by 3, which equals 78, then adding 26 to 78 to get the final answer, 104.
Hope this helps!
A pyrotechnician plans for two fireworks
to explode together at the same height In the air. They travel
at
speeds shown below. Firework B is launched 0.25 s before Firework A. How many seconds after
B Firework B launches will both fireworks explode?
Firework A
Firework B
340 ft/s
260 ft/s
The mentioned scenario can be calculated using the distance equation, the number of seconds in which explosion would occur is 1.125 seconds.
What is the relationship between time, speed and distance ?The distance covered by the object is equal to the product of the speed of object and the time required for it.
Distance = Time x speed
Firework A :
D = 360xt - - - (1)
Firework B:
D = 280x(0.25) + 280xt
D= 70 + 280xt - - - (2)
Equate equation (1) and (2) :
360t = 280t + 70
Collect like terms
360t - 280t = 70
80t = 70
t = 70/80
t = 0.875 seconds
0.875 + 0.25 = 1.125 seconds
Hence, the fireworks will explode after 1.125 seconds of launching Firework B.
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After arguing for two weeks, Tony convinced his parents to have his birthday party at FlyZone trampoline park. As soon as he gets there, Tony spends time practicing flips on the trampolines. Then, he spends
3
4
of an hour eating birthday cake with his friends. In all, Tony spends 1
1
4
hours at FlyZone.
Which equation can you use to find the amount of time t Tony practices flips?
The amount of time that Nora practices flips is; t = 1 ¹/₄
How to Solve Algebra problems?
The BODMAS rule would be used to simplify the expression, BODMAS is an abbreviation for bracket, of, division, multiplication, addition and subtraction. It dictates the order in which a mathematical expression should be solved.
We are told that;
Nora spends time practicing flips on the trampolines. Let this be t.
Then, she spends 1/2 of an hour eating birthday cake with her friends.
Thus, total amount of time spent on flips and eating with her friends is;
t + ¹/₂ = 1 ³/₄
t = 1 ³/₄ - ¹/₂
t = 1 ¹/₄
Thus , the amount of time that Nora practices flips is; t = 1 ¹/₄
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Given question is incomplete , Complete Question is;
After arguing for two weeks, Nora convinced her parents to have her birthday party at FlyZone trampoline park. As soon as she gets there, Nora spends time practicing flips on the trampolines. Then, she spends 1/2 of an hour eating birthday cake with her friends. In all, Nora spends 1 3/4 hours at FlyZone. Which equation can you use to find the amount of time Nora practices flips?
Solve this equation for (t) to find the amount of time Nora practices flips
Question 7(Multiple Choice Worth 2 points) (09.06 LC) How many hectometers are in 580 millimeters? O 0.0058 hectometers O0.058 hectometers O58,000 hectometers O 580,000 hectometers
Answer: B. 0.058 hectometers
Step-by-step explanation: To convert millimeters to hectometers, you need to divide the number of millimeters by 10,000.
Given that there are 580 millimeters, the conversion to hectometers can be calculated as follows:
580 millimeters ÷ 10,000 = 0.058 hectometers
In August, 18% of the middle school students voted in a school election. The number of students who voted was 213. How many students are in the middle school?
If 18% of middle school student voted in a school election and number of students who voted is 213 , then the total students in the middle school is approximately 1184 students .
Let "x" be = total number of middle school students.
We know that 18 percent of the students voted = 0.18x, and is equal to 213 ;
that means , ⇒ 0.18x = 213 ;
Now we need to solve for x,
We divide both sides by 0.18 ;
⇒ x = 213/0.18 ;
Simplifying, we get:
⇒ x = 1183.33
Since the number of students cannot be in decimal ,
So , the actual number of students must be greater than or equal to 1183.33.
Therefore, the middle school has approximately 1184 students.
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B) Mr. S Ralph spends $165. 31 on oranges INCLUSIVE of a 15% sales tax. Her total is $165. 31 with tax. (115% = original price is 100% plus tax of 15%). Calculate the ORIGINAL PRICE of the oranges, which means the cost of the oranges
without the tax
The total cost of the item would be [tex]$115[/tex].The original price of oranges purchased by Mr. S Ralph can be calculated by subtracting the sales tax from the total cost.
Sales tax is calculated as a percentage of the original price. In this case, the sales tax is 15%, meaning that the original price can be found by dividing the total cost (which includes the sales tax) by 1.15.To calculate the original price of the oranges, divide the total cost of $165.31 by 1.15. This gives us a total of $143.87. Thus, the original price of the oranges purchased by Mr. S Ralph is $143.87 without the sales tax included.Sales tax is a form of taxation imposed by governments on goods and services. Generally, for the majority of goods and services, the sales tax is calculated as a percentage of the original price. This means that the total cost of the goods or services can be calculated by adding the percentage of sales tax to the original price.For example, if an item costs $100, and the sales tax rate is 15%, the total cost of the item would be calculated by multiplying the original price by 1.15 (100% + 15% = 115%). The total cost of the item would be [tex]$115[/tex].
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David and Alec are comparing the international calling plans on their cell phones. On his plan,
David pays $4 just to place a call and $1 for each minute. When Alec makes an international
call, he pays $1 to place the call and $2 for each minute. A call of a certain duration would
cost exactly the same under both plans. What is the duration?
Write a system of equations, graph them, and type the solution.
3 minutes is the cost of the call that is same for both plans
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's assume the call duration in minutes is represented by x.
For David, the cost of the call can be represented by the equation: C(d) = 4 + x
For Alec, the cost of the call can be represented by the equation: C(a) = 1 + 2x
Since the cost of the call is the same for both plans, we can set the two equations equal to each other and solve for x:
4 + x = 1 + 2x
Solve for x.
3 = x
Hence, the call duration that costs the same on both plans is 3 minutes.
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Daniella and her 10 friends are collecting shells on the beach to make crafts. After
they have collected the shells and put them in a pile, they split them evenly among
the group. Each person gets 4 shells. How many shells did they collect as a group?
Select the correct equation and solve for s.
4+ s = 11; s = 7
s/10 = 4; s = 40
4s = 11; s = 2.75
s/11 = 4; s = 44
Daniella and her friends collected a total of 44 shells.
What is linear equation ?
Linear equation can be defined as equation in which highest degree is one.
Given ,
Daniella and her 10 friends are collecting shells on the beach to make crafts.
After they have collected the shells and put them in a pile, they split them evenly among the group. Each person gets 4 shells.
The correct equation for this problem is:
s = 11 x 4
where s is the total number of shells collected.
Simplifying this equation, we have:
s = 44
Therefore, they collected a total of 44 shells.
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The ratio of the sides of a triangle are 3:5:12. If the perimeter of the triangle is 100 units, determine the length of the shortest side.
The measure of the length of the shortest side will be 15 units.
What is a ratio?If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. How frequently one value contains or is contained within another is shown by the numerical connection between the two values.
Given that the perimeter of the triangle is 100 and the ratio of the sides of the triangle is 3:5:12.
The length of the shortest side will be calculated as:-
3x + 5x + 12x = 100
20x = 100
x = 20
Length = 3x
Length = 3 x 5 = 15 units
Hence, the shortest side will be 15 units.
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pls help asap it’s annoying me
Answer:
b. 53.1°
c. 126.9⁰
Step-by-step explanation:
These are SSA triangles; use Law of Sines to find the unknown angle:
b) sin30/15 = sinA/24
sinA(15) = sin30(24)
sinA = sin30(24)/15 = 0.80
m∠A = sin⁻1(0.80) = 53.1°
c) m∠A = 180 - 53.1 = 126.9⁰
Answer:
∠ BAC = 53.13° , ∠ BAC = 126.87°
Step-by-step explanation:
using the Sine rule in Δ ABC
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex]
where a is the side opposite ∠ A and c is the side opposite ∠ C
here a = BC = 24 and c = AB = 15 , then
[tex]\frac{24}{sinA}[/tex] = [tex]\frac{15}{sin30}[/tex] ( cross- multiply )
15 sinA = 24 sin30° ( divide both sides by 15 )
sin A = [tex]\frac{24sin30}{15}[/tex] , then
A = [tex]sin^{-1}[/tex] ( [tex]\frac{24sin30}{15}[/tex] ) = 53.13°
(b)
acute angle BAC = 53.13°
(c)
the sine of an angle is positive in both the first and second quadrant , so
obtuse angle BAC = 180° - 53.13° = 126.87°
Please help!!
Solve for x
Answer: x=8
Step-by-step explanation: since we know 2 sides of both quadrilaterals and they are similar,
just put 32/40 = 24/3x+6 ,
cross multiply ( 32 x 3x+6 and 40 x 24),
they become 96x +192 = 960.
move 192 to the other side and divide both sides by 96
amy invested $223 in the banck and a year later has $280,98 . by what percent has changed
Find the equation of the line that cuts the x-axis at x = 1 and whose slope is -1.
The equation of the line that cuts the x-axis at x = 1 and has a slope of -1 is y = -x + 1.
What is slope-intercept form?The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
Since the line has a slope of -1 and cuts the x-axis at x = 1, we can find the y-intercept by using the point-slope form of the line equation:
y - y₁ = m(x - x₁)
y - 0 = -1(x - 1)
y = -x + 1
So the equation of the line that cuts the x-axis at x = 1 and has a slope of -1 is y = -x + 1.
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2. Divide R3 520 in the ratio 11:12:17.
Answer:
Rs 3520 is divided in the ratio 11:12:17 as rs 968, rs 1056, and rs 1469
Step-by-step explanation:
According to the question, we have to divide rs 3520 in the ratio 11:12:17
let the common ratio be x
so, total share= (11+12+17)x = 40 x
for the first person, share would be (11x/40x)*(Rs 3520)
=Rs 968
for the second person, share would be (12x/40x)*(Rs 3520)
=Rs 1056
for the third person, share would be (17x/40x)*(Rs 3520)
=Rs 1496
The shares are Rs 968, Rs 1056, and Rs 1469
hope this helps :)
Find the indicated probability. The manager of a used car lot took inventory of the automobiles on his lot and constructed the following table based on the age of his car and its make (foreign or domestic)A car was randomly selected from the lot. Given that the car selected is older than two years old, find the probability that it is not a foreign car.
The probability that, if the car selected is older than two years old, it is not a foreign car is 57/118, so the correct option is A.
How to find the probability?We want to find the probability that if the car selected is older than two years old, it is not a foreign car.
Looking at the table, we can see that there are 200 - 82= 118 cars older than two years.
And of these 118 cars, 25 + 10 + 26 = 61 are foreign cars.
Then the number of non-foreign cars is:
118 - 61 = 57
And the probability will be equal to the quotient between the number of non-foreigner cars and the total number:
P = 57/118
So the correct option is A.
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a bin of 50 manufactured parts contains 3 defective parts and 47 nondefective parts. a sample of 6 parts is selected from the 50 parts. write down an expression for the number of different samples of size 6 that contain exactly 2 defective parts.
The expression for the number of different samples is: C(3, 2) x C(47, 4) = 3 x C(47, 4) = 3 x
(47! / (4! x 43!)).
The number of different samples of size 6 that contain exactly 2 defective parts can be calculated using the binomial coefficient formula:
C(3, 2) x C(47, 4)
where C(n, k) represents the number of ways to choose k objects from a set of n objects.
In this case, we first choose 2 defective parts from the 3 defective parts in the bin, which can be done in C(3, 2) ways. Then we choose 4 nondefective parts from the 47 nondefective parts in
the bin, which can be done in C(47, 4) ways. We multiply these two quantities together to obtain the total number of different samples of size 6 that contain exactly 2 defective parts.
Therefore, the expression for the number of different samples of size 6 that contain exactly 2 defective parts is:
C(3, 2) x C(47, 4) = 3 x C(47, 4) = 3 x (47! / (4! x 43!))
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4,400 is placed in an account with an annual interest rate of 8. 25%. How much will be in the account after 22 years to the nearest cent
If $4400 is placed in account at 8.25% for 22 years , then the final amount received after 22 years will be $26480.08 .
We use the formula for compound interest to find the final amount :
that is ⇒ A = P(1 + r)ˣ ;
where: A = the amount of money in the account after "x years" ;
P(initial amount) = $4400 ; r (interest rate) = 0.0825 ;
⇒ x(time) = 22 years
we get ;
⇒ A = 4400×(1 + 0.0825)²² ;
⇒ A = 4400×(1.0825)²² ;
⇒ A = 4400×6.018028 ;
⇒ A = 26480.08 ;
Therefore , the amount in the account after 22 years is $26480.08 .
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i need help with this one?
The best description of the transformation for the image being projected on the retina is A. A dilation with a scale factor between 0 and - 1 and center at the nodal point.
How does the nodal point dilate the retina ?An mage is inverted and reversed as it passes through the lens of the eye, and is then projected upside down and reversed onto the retina. The process of transforming the image is called "rectification."
In mathematical terms, a dilation would have taken place because the object was shrunken by the eyes at the nodal point. When an object shrinks , then the scale factor is between 0 and 1 but because this image is inverted, the scale factor is between 0 and - 1.
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Mae Ling earns a weekly salary of $320 plus a 6. 0% commission on sales at a gift shop. How much would she make in a work week if she sold $4,500 worth of merchandise?
Mae Ling make $590 in a work week if she sold $4,500 worth of merchandise.
The given is:
We need to find how much she would earns in a work week
Mae Ling earns a weekly salary of $320
She earns a 6.0% commission on sales
She sold by $4,500 in that week
Add $320 to the product of 6.0% and $4,500
She made = 320 + (6.0% × 4,500)
6.0% = 6.0 ÷ 100 = 0.06
She made = 320 + (0.06 × 4,500)
She made = 320 + 270
She made = 590
She would make $590 in a work if she sold $4,500 worth of merchandise.
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b. Isabella has a second tray that has a length of 5/3 inches and a width of 13/4 inches
and a height of 5/2 inches. What is the volume of the second tray?
Answer: approx 13.54 (full decimal : 13.416666667)
Step-by-step explanation:
Area = Base Area x Height OR Length x Width x Height
5/3 x 13/4 x 5/2
5 x 13 x 5 = 325
3 x 4 x 2 = 24
325/24 = approx 13.54
In a geometric sequence, the first term, a_1, is equal to 3, and the third term, a_{3}, is equal to 192 Which number represents the common ratio of the geometric sequence?
Answer:
r = 8
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
given a₁ = 3 and a₃ = 192 , then
a₁ = 3 → (1)
a₁r² = 192 → (2)
divide (2) by (1) on both sides
[tex]\frac{a_{1}r^2 }{a_{1} }[/tex] = [tex]\frac{192}{3}[/tex] ( cancel a₁ on numerator/ denominator of left side ), then
r² = 64 ( take square root of both sides )
r = [tex]\sqrt{64}[/tex] = 8
Rewrite in simplest rational exponent form square root of x times the fourth root of x. Show each step of your process.
We can simplify the expression to get:
[tex]\sqrt[4]{x^3}[/tex]
How to simplify the expression?Here we want to simplify the following expression:
[tex]\sqrt[]{x} *\sqrt[4]{x}[/tex]
Remember that a square root is equivalent to a power of 1/2, and the fourth root is equivalent to a power of 1/4.
Then we can write:
[tex]\sqrt[]{x} *\sqrt[4]{x} = x^{1/2}*x^{1/4}[/tex]
Now in the product we just add the exponents:
[tex]\sqrt[]{x} *\sqrt[4]{x} = x^{1/2}*x^{1/4} = x^{1/2 + 1/4} = x^{3/4} = \sqrt[4]{x^3}[/tex]
That is the expression si,plified.
Learn more about square roots at:
https://brainly.com/question/98314
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