The first four terms in the sequence are 30, 90, 270 and 810 respectively.
How to determine the termsWe have that the nth term of the sequence is expressed as;
U = 10 × 3 ^n
Where;
n = number of terms
To determine the first terms, let's substitute the value of n as 1, we get;
U = 10 × 3^1
Multiply the values
U₁ = 30
The second terms, n = 2
U₂ = 10 × 3²
U₂ = 10 × 9
Multiply through
U₂ = 90
The third year, n = 3
U₃ = 10 × 3³
Find the cube of the value and multiply the values
U₃ = 270
The fourth year, n = 4
U₄ = 10 × 3^4
U₄ = 10 × 81
Multiply through
U₄ = 810
Thus, the numbers are 30, 90, 270, 810
Learn more about geometric sequence here:
https://brainly.com/question/1509142
#SPJ1
In the translation T of the graph below, use the figure to describe the following transformation.
The translation T due to the transformation is (5,3)
How to describe the transformation using the figure?Translation can be defined as movement in a straight line
Given the rule: (x,y) → (x + 3, y + 1) as seen in the image. That means (x,y) translated to (x + 3, y + 1). This is what we use to solve this problem.
From the figure, the value of (x, y) can be read i.e. (x, y) = (2,2)
Thus the translation will be:
(x,y) → (x + 3, y + 1)
(2,2) → (2 + 3, 2 + 1) = (5, 3)
Therefore, the translation T of the transformation shown in the graph is (5, 3)
Learn more about translation on:
https://brainly.com/question/29230091
#SPJ1
Here are the first 4 terms of a sequence.
3 9 15 21
a) (i) Write down the next term in the sequence.
(ii) Explain how you got your answer.
b) Work out the 10th term of the sequence.
Solve for x 5 x + 2 = 7 x − 4
Answer: x=3
Step-by-step explanation:
5x+2=7x-4
-5x +4 -5x +4
2x=6
divide both sides by 2
x=3
square tile measures 12 inches on each side. If 1 inch = 2.54 centimeters, determine the area of the tile in square centimeters. Round the answer to the nearest square centimeter. 30 cm2 144 cm2 366 cm2 929 cm2
The area of the tile in square centimeters is 929cm2
The area in square centimeters is calculated as follows
First, let convert the tile measures 12 inches on each side into centimeters
1 inch = 2.54 centimeters
= 12 x 2.54
= 30.48 centimeters
Next is to find the area of the tile in square centimeters
The area of square = (side) x (side) square units
= 30.48 centimeters x 30.48 centimeters
= 929.0304
= 929 square centimeters (rounded)
So, the area of the tile in square centimeters is 929 square centimeters
Read more on the area here : brainly.com/question/2268184
#SPJ1
Answer:
The area of the tile in square centimeters is 929cm2
Step-by-step explanation:
I took the exam and got it right
please help me with this problem, i will give u brainliest. mLNM=…
Check the picture below.
What is the third term of the sequence 20 - n²
A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11.
What is a series?A sequence's series is the total number of terms in the sequence.
A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.
As per the given sequence, 20 - n²
The 20 - n² represents the nth term of the sequence.
Thus a(n) = 20 - n²
For the third term n = 3
a(3) = 20 - (3)²
a(3) = 20 - 9 = 11
Hence "A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11".
For more information about the series,
brainly.com/question/15415793
#SPJ1
an insurance company wants to study whether offering incentives for preventative care reduces overall health care costs. they select a random sample of 200200200 of their customers. they use a random number generator to select 100100100 customer account numbers to offer the incentive. the remaining 100100100 customers are assigned to the control group. what type of experiment design is this?
Using the concepts of probability, we got that that Stratified sampling is the experiment design which an insurance company which wants to study whether offering incentives for preventative care reduces overall health care costs.
In the question, actually the insurance company intends to study and understand the relationship between the health care cost of the customers and the provision of incentives for the preventative care by two groups, each having one of two given attributes under study, which are;
a) One group consist of the customers having high health care cost and offered incentives for preventative care
b) The other group consist of the customers having only high health care cost without incentives
Therefore, the insurance company customers are stratified into the groups based on health care cost and again into the groups that have high health care cost and are offered preventative care and those that have only the high heath care cost, which is the process used to implement the stratified sampling technique.
Hence, an insurance company which wants to study whether offering incentives for preventative care reduces overall health care costs, by selecting a random sample of 200200200 of their customers and using a random number generator to select 100100100 customer account numbers to offer the incentive, the experiment design is named as Stratified sampling.
To know more about probability, visit here:
https://brainly.com/question/11234923
#SPJ4
An arithmetic sequence a starts 24, 20,... Explain how you would calculate the value
of the 20th term.
Answer:
Step-by-step explanation:
first you need to find the nth term
that would be -4n+28
then you just need to substitute 20 into the position of n
-4*20 = -80
-80+28=-52
f(x) = x2. What is g(x)?
g(x)
f(x) = x2
(4,1)
O A. g(x) = 1x2
9(x) = (3)
O B. 9(x) =
O ) (1)
C. g(x) =
( D. (x) = 42
The value of g(x) = 1/16[tex]x^{2}[/tex] = (1/4[tex]x^{2}[/tex]). The correct option is (C).
Given,
In the question:
f(x) = [tex]x^{2}[/tex]
To find the value of g(x)
To see the graph and analysis
Now, According to the question:
We know that:
g(x) = k f(x) = k[tex]x^{2}[/tex]
In the graph, The value are given as:
Plug (4,1) into g(x):
1 = k. [tex]4^2[/tex]
k = 1/16
=> g(x) = 1/16[tex]x^{2}[/tex] = (1/4[tex]x^{2}[/tex])
Hence, The value of g(x) = 1/16[tex]x^{2}[/tex] = (1/4[tex]x^{2}[/tex]). The correct option is (C).
Learn more about Graph at:
https://brainly.com/question/17267403
#SPJ1
Use three unit multipliers to convert 5280ft to meters
The three-unit multipliers are follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters.
What is unit conversion?To convert any unit into another is called a unit conversion.
In order to convert units, we need to care about their dimensions their dimension should not be changed.
For example conversion of a kilometer to a meter is to multiply by 1000 but meter and kilometer both unit is for distance only.
As per the given,5280ft
It is known that 1 ft = 12 inches.
5280ft = 5280 x 12 inches
It is known that 1 inch = 2.54 cm
5280 x 12 inches = 5280 x 12 x 2.54 cm
It is known that 1 cm = 0.01 meter
5280 x 12 x 2.54 cm = 5280 x 12 x 2.54 x 0.01 meter
⇒ 1609.344 meters
Hence "The three-unit multipliers are as follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters".
To learn more about unit conversion,
brainly.com/question/11543684
#SPJ1
I got angle D but I am confused with others I need help ASAP tysm
Considering the figure the unknown angles are
a = 65b = 25c = 25How to determine the unknown anglesUsing the angle in a straight line are supplementary we have
60 + a + 55 = 180
a + 115 = 180
a = 180 - 115
a = 65
applying sum of angles in a triangle equal to 180, b is calculated as follows
a + b + 90 = 180 right angle triangle
substituting for a
65 + b + 90 = 180
b + 155 = 180
b = 180 - 155
b = 25
applying vertical angle theorem
angle c = angle b
angle c = 25
Learn more about angles here:
https://brainly.com/question/29327565
#SPJ1
select function or not a function
Answer:
The graph is a function.
Step-by-step explanation:
Andrea put $52 in the savings account that pays 4% interest how much interest will she earn in one year
Answer: $2.08
Step-by-step explanation: First multiply $52 by 4% as a decimal or 0.04. Then, multiply that by the number of years.
=52(0.04)(1)
=2.08
Graph the line that represents a proportional relationship between d and t with the property that an increase of 5 units in t corresponds to an increase of 8 units in d.
What is the unit rate of change of d with respect to t? (That is, a change of 1 unit in t will correspond to a change of how many units in d?)
The unit rate is
?
Graph the relationship.
The unit rate of change , d with respect to t is = 1.6 .
In the question,
it is given that , the relationship between d and t is proportional
also given that " increase of 5 units in t corresponds to increase of 8 units in d ".
which is represented as 5t = 8d
Divide both sides of the equation 5t = 8d by "5" ,
t = 8/5d
t = 1.6d
next we plot the graph of t = 1.6d
we see that the above equation is a proportional linear equation
and A proportional linear equation is represented as
t = md , Where m represents the unit rate .
So , after comparing , we get
m = 1.6
Therefore , The unit rate of change of d with respect to t is 1.6 .
Learn more about Unit Rate here
https://brainly.com/question/28821706
#SPJ1
the simple interest formula is i = prt where i = the interest p=the principal r is the annual interest rate in the decimal form and t is the time in years. find the simple interest earned for a principal of 2,000 at an 8% interest the ate for 5 years.
The simple interest earned on a 2,000 principal at 8% interest for 5 years is I = $1,937.50.
What is meant by simple interest formula?Simple interest is calculated by multiplying the daily interest rate by the principal and the number of days between payments. Customers who pay their loans on time or early each month save money on interest.Interest-only loans are prevalent for short-term personal loans and car loans. Simply multiply the principal amount by the interest rate and the time to determine simple interest.The written formula is "Simple Interest = Principal x Interest Rate x Time." Simple interest is calculated on the loan principal or the first deposit into a savings account.Due to the fact that simple interest does not compound, a creditor will only pay interest on the principal amount, and a borrower will never be required to pay interest on previously accumulated interest.Therefore,
I = Prt
First, converting R percent to r a decimal
r = R/100 = 3.875%/100 = 0.03875 per year,
then, solving our equation
I = 10000 × 0.03875 × 5 = 1937.5
I = $ 1,937.50
The simple interest accumulated
on a principal of $ 10,000.00
at a rate of 3.875% per year
for 5 years is $ 1,937.50.
To learn more about simple interest formula, refer to:
https://brainly.com/question/20690803
#SPJ13
Select the correct answer.
What is the y-intercept of function f?
What’s 1,598 fewer then 25,876
Answer:
24,278
Step-by-step explanation:
Nathan and Jorge are working on a decimal division problem in
math class. After finishing the problem, it looked like this: 4.76 ÷
2.5 = 0.19. Nathan said that the decimal is incorrectly placed in the
quotient, and Jorge disagrees. Who is right? Explain your answer
Answer:
Nathan
Step-by-step explanation:
4.76 / 2.5
= (476/100) / (25/10)
= (476/100) * (10/25)
= 238/125
= 1.904
Thus, Nathan is right in saying that the decimal is incorrectly placed in the quotient of the given answer 0.19
The price of a pair of Nike Panda's
increases from $52 to $64. What is the
percent increase to the nearest
percent?
Answer: 23%
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!
Desiree and Nicole spent a total of $23.75 on decorations for the school dance. They bought
fifteen rolls of streamers on sale at Party City for $0.75 a roll. The remainder of the money
was spent on ornaments costing $0.50 each. How many ornaments did they buy?
Ornaments:
Streamers:
Total:
Meal Deal £5.00
A sandwich
A dessert
A drink
The following choice is available:
5 different sandwiches
4 different desserts
6 different drinks
a) How many different combinations are possible with the Meal Deal?
b) Two of the desserts are sugar-free.
Three of the drinks are sugar-free.
A Meal Deal combination is selected at random.
Work out the probability that both the dessert and the drink are sugar-free
Give your answer as a fraction.
sara has 20 sweets
12 liquorice sweets , 5 mint sweets and 3 humbugs.
sara takes two random sweets
work out probability that the two sweets will not be the same
If sara takes two random sweets. The probability that the two sweets will not be the same is :111/190.
How to find the probability?Probability of getting two of each sweet:
P( Liquorice) = (12/20)×(11/19)
P (Liquorice) =132/380
P (mints) =(5/20)×(4/19)
P (mints) =20/380
P (Humbugs) =(3/20)×(2/19)
P (Humbugs) =6/380
Probability that two sweets will be the same
P(same) =132/380+20/380+6/380
P(same) =158/380
Hence,
Probability that two sweets will not be the same
P(not same) = 1- (158/380)
P(not same) =380 -158 /380
P(not same) = 222 /380
P(not same) =111 /190
Therefore the probability is 111/190.
Learn more about probability here:https://brainly.com/question/24756209
#SPJ1
How do i solve this one ? (Equilateral Angle ?)
simplify (-5)∧5(-5)∧-6
Answer:
-5 with the exponet of 11
Answer:
-1/5 or -0.2 if you are going by fraction or decimal
a rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). what dimensions should be used so that the enclosed area will be a maximum?
The dimension of each corral should be 25 feet in width and 33⅓ feet in length so that the enclosed area will be a maximum.
Adjacent rectengular corral has length and width with area formula as below.
A = L × W
Given:
The dimension of adjacent rectangular corrals are the same.Adjacent side = 200 feet.Because the dimension of adjacent rectangular corrals are the same, so:
W = 4x
L = 3y
3y + 4x = 200
[tex]y = \frac{200 - 4x}{3} [/tex]
There are two adjacent rectangular corrals, so:
A = 2×L×W
[tex]A = 2 \times \frac{200 - 4x}{3} \times \: x [/tex]
A = ⅓(400x–8x²)
We can differentiate to get the maximum area:
⅓×(400x–8x²) = 0
400–16x = 0
16x = 400
x = 25 feet
Substitute x value (width) to get y value (length):
y = (200–4(25)) ÷ 3
y = (200–100) ÷ 3
y = 100 ÷ 3
y = 33⅓ feet
Learn more about area https://brainly.com/question/14742387
#SPJ4
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The width, labelled x in the figure is 162.5 meters
How to determine the width of the rectangle?From the question, we have the following parameters that can be used in our computation:
Length = 650 - 2x
Width = x
The area of a rectangle is the product of its dimensions
So, we have
Area = Length x Width
Substitute the known values in the above equation, so, we have the following representation
A = (650 - 2x) * x
Evaluate
A = 650x - 2x²
Differentiate and set to 0
650 - 4x = 0
So, we have
4x = 650
Divide by 4
x = 162.5
Hence, the width is 162.5 meters
Read more about rectangles at
https://brainly.com/question/25292087
#SPJ1
Please helppp!
1 :What is the solution to the equation?
−4=x9
2 :Solve for t.
−32=4t
Responses
t=−8
t equals negative 8
A:T = -8
B:T = - 1/8
C:T= 28
D:T=36
3 : What is the solution to the equation?
x−18=−72
4 ;What is the solution to the equation?
−18=x−15
Enter your answer in the box.
5 :What is the solution to the equation?
−24x=−4
Enter your answer as a simplified
The value of the variables in the equation are as follows:
1. x = -4 / 9
2. t = -8
3. x = -54
4. x = -3
5. x = 1 / 6
How to solve an equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Let's find the solution of the equations. The solution of the equation is the value of the variable x. A variable is a number represented by a letter in an equation.
Therefore,
1.
-4 = 9x
divide both sides of the equation by 9
x = - 4 / 9
2.
−32=4t
divide both sides of the equation by 4
t = - 32 / 4
t = - 8
3.
x − 18 = −72
add 18 to both sides of the equation
x - 18 + 18 = -72 + 18
x = -54
4.
−18 = x − 15
add 15 to both sides of the equation
-18 + 15 = x - 15 + 15
-3 = x
x = -3
5.
−24x = −4
divide both sides of the equation by - 24
x = - 4 / -24
x = 1 / 6
learn more on equation here: brainly.com/question/1295184
#SPJ1
Directions: Match the situation provided to the correct equation/inequa
Situation:
Wyatt is saving up
money for a new
game. It costs $60,
including tax. He has
already saved $20.
At least how much
more money, X,
does he need to
save?
Inequality/Equation:
Innquality/Equation:
Solution
Graphed Solution:
Solution
The equation can be given as X+20 = 60
Wyatt needs to save $40 to buy the new game.
What is an equation?
An equation is an expression which has an equality symbol in it.
We are given that, Wyatt is saving up money for a new game. It costs $60,
including tax.
He has already saved $20. At least how much more money, X, does he need to save
Hence the equation can be given as
X + 20 = 60
On solving the equation X = 40
Hence Wyatt needs to save $40 to buy the new game
To learn more about the equation please refer the following link
https://brainly.com/question/22688504
#SPJ1
The geometric mean of a number and nine times the number is 30. What is the number?
18. STREETS If Pine Street is parallel to Locust
Street, find the values of a and b. (Lesson 3-7)
Answer:
b=98 and a=82
Step-by-step explanation:
b and 98 are corrisponding angles which means that they are both 98
a+b=180 because it is a straight line
a+98=180 subtract 98 from both sides a d you get a=82