Answer;
Option B is correct.
The function increases at a constant multiplicative rate.
Step-by-step Explanation:
Complete Question
A table representing the function f(x) = 2(3/2)ˣ is shown below. What is true of the given function?
x | f(x)
0 | 2
1 | 3
2 | 4.5
3 | 6.75
a) The function increases at a constant additive rate.
b) The function increases at a constant multiplicative rate.
c) The function has an initial value of 0.
d) As each x value increases by 1, the y values increase by 1.
Solution
The function provided is
f(x) = 2(3/2)ˣ
We will take as h of the options one at a time to investigate which one is true.
a) The function increases at a constant additive rate.
A function that increases at an additive rate is one whose value as x increases, also changes with a constant difference between consecutive terms. That is, the consecutive terms of the functions for consecutive whole number values of x, will be like an Arithmetic progression with a constant common difference. If this function increased at an additive rate,
f(1) - f(0) = f(2) - f(1) = f(3) - f(2)
Inserting the values
3 - 2 = 4 5 - 3 = 6.75 - 4.5
1 ≠ 1.5 ≠ 2.25
Hence, this statement isn't true.
b) The function increases at a constant multiplicative rate.
For the function to increase at a multiplicative rate, the consecutive terms of the functions for consecutive whole number values of x will behave like a geometric progression with a common ratio. That is, the division of the (n+1)th term and the nth term of the function will always be a constant. That is,
f(1) ÷ f(0) = f(2) ÷ f(1) = f(3) ÷ f(2)
Inserting the values
(3/2) = (4.5/3) = (6 75/4.5)
1.5 = 1.5 = 1.5
The ratio is truly constant, hence, we can conclude that this statement is true and the function increases at a constant multiplicative rate.
c) The function has an initial value of 0.
For this to be true, f(0) = 0.
But from the table, it is evident that f(0) = 2, hence, the initial value of the function isn't 0 and this statement is false.
d) As each x value increases by 1, the y values increase by 1.
We've already checked the difference between consecutive terms of the functions for consecutive whole number values of x, the difference includes, 1, 1.5 and 2.25. Hence, as each x value increases by 1, the y values do NOT always increase by 1 and this statement is false.
Hope this Helps!!!
Answer:
B
Step-by-step explanation:
Which shows the fractions in order from greatest to least?
A. 3/6, 4/9, 3/7, 3/10
B. 3/10, 3/7,4/9,3/6
C. 3/6, 4/7,4/9,3/10
D. 3/10, 4/9,3/7,3/6
Answer: A
Step-by-step explanation:
3/6= 0.5
4/9= 0.444
3/7= 0.428
3/10= 0.3
0.5 > 0.444....> 0.428 > 0.3
Which of the follow best represents the slip of the line?
A - 3
B -1/3
C 1/3
D 3
Answer:
B
Step-by-step explanation:
The slope is negative since the line decreases from left to right. This means that the slope is -1/3.
-3x-10=32 i couldn't find the answer!!
Answer:
Lets do this step by step
Step-by-step explanation:
I hope this helps
Answer:
-14
Step-by-step explanation:
To solve for x, you would first need to add 10 to both sides. Then you would get -3x-10+10=32+10. Then we simplify that to get, -3x=42. Then, you would divide both sides by -3, to get x=-14
A chemist bought 2390 test tubes and beakers.1034 of them were test tubes and the rest were beakers.How many more beakers did the chemist buy than test tubes?
Answer:
322
Step-by-step explanation:
The question explains that the total of both test tubes and beakers were
= 2390.
If 1034 of them were test tubes, then the number of beakers bought,
= 2390 - 1034
= 1356.
The question requires the answer to how many more beakers than test tubes were bought, and this would mean subtracting the number of beakers from the number of test tubes.
= 1356 - 1034
= 322
Therefore, 322 more beakers than test tubes were bought.
If you borrow $500 for 6 years at an
annual interest rate of 7%, how
much will you pay altogether?
If we borrowed $500 for 6 years at a rate of 7% interest then we will have to pay approximately $750 after 6 years.
Given that principal amount is $500 , years are 6 and rate of interest be 7%.
We are required to find the amount that we have to pay after 6 years if we borrow $500.
Compound interest is the interest that is calculated on the principal plus the accumulated interest at that point of time.
Sum after compounding is given as under:
S=P[tex](1+R)^{N}[/tex]
So we have to just put the values to find the money that we have to pay after 6 years.
S=500[tex](1+0.07)^{6}[/tex]
=500[tex](1.07)^{6}[/tex]
=500*1.5
=$750
Hence if we borrowed $500 for 6 years at a rate of 7% interest then we will have to pay approximately $750 after 6 years.
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what is the sum of (2x−6)+4(x−3)
Answer:
6x - 18
Step-by-step explanation:
2x-6 + 4x-12
6x - 18
Answer:
6x - 18
Step-by-step explanation:
(2x−6)+4(x−3)
Distribute
2x -6 + 4x - 12
Combine like terms
6x - 18
The top of the circular table has a radius of 16 inches.What is the circumfrence of the tabletop? Use 3.14 for pie
Answer:
100.48
Step-by-step explanation:
Using the formula : 2pi times the radius, I can plug the radius in and find the circumference. 2 times pi is 6.28, and the radius is 16. 6.28 times 16 = 100.48.
Can someone please help?? I need help on the Job one
Answer:
The first one
Step-by-step explanation:
The first simbol means that job is part of the Books of the Old Testament which is true, because the Book of Job it is in the Old Testament
Can someone please help me??
Answer:
Step-by-step explanation:
[tex]a^{-m}=(\frac{1}{a})^{m}\\\\\\1)7^{-2}=(\frac{1}{7})^{2}\\\\\\2)(\frac{2}{3})^{-3}=(\frac{1}{\frac{2}{3}})^{3}\\\\=(\frac{3}{2})^{3}[/tex]
Answer:
1) D.
2) A
Step-by-step Explanation:
1) [tex]7^{-2}[/tex]
= [tex](\frac{1}{7})^2[/tex]
2) [tex](\frac{2}{3})^{-3}[/tex]
= [tex](\frac{3}{2})^{3}[/tex]
(2x -2)^-3
can anyone help me with this?
Answer: See below
Step-by-step explanation:
When you see that something is to the power of a negative number, it is another way of saying 1 over.
[tex](2x-2)^-^3=\frac{1}{(2x-2)^3} =\frac{1}{(2x-2)(4x^2-8x+4)} =\frac{1}{8x^3-8x^2+8x-8}[/tex]
Share £90 in the ratio 1:5
HELP ME PLEASE
Answer:
the answer is 15:75
Step-by-step explanation:
(1+5)=6
£90/6=15
So, (1×15):(5×15)
=15:75
factorise: 2x + 6y 2x-4 t + 2t squared
What is the measure of the hypotenuse?
[tex]solution \\ hypotenuse = x \\ base = 12 \\ perpendicular = 5 \\ using \: pythagoras \: theorem \\ {h}^{2} = {p}^{2} + {b}^{2} \\ or \: {x}^{2} = {5}^{2} + {12}^{2} \\ or \: {x}^{2} = 25 + 144 \\ or \: {x}^{2} = 169 \\ or \: x = \sqrt{169} \\ x = 13 \\ [/tex]
hope it helps....
Good luck on your assignment
Answer:
Step-by-step explanation:
using pythagoras theorem which says the square root of the sum of the square of the opposite side and the square of the adjacent side would give the value of the hypotenuse
hyp^2 = opp^2 + adj^2
i dont have the square root symbol but u can solve it either way :
you can input the values given and then collect like terms or u can take the square root of the right side. The right angle would always face the hypotenuse which is the longest side.
hyp = x
x^2=(5)^2 +(12)^2
x^2= 25 +144
x^2=169
take the square of both sides to get your value for x
x= 13
Solve for s 2-2s=3/4s+13
Answer:
s=-4
Step-by-step explanation:
Bring the S to one side and the numbers to the other
-11/4s=11
Then just divide, but when dividing fractions you have to switch the fraction so..
s=11*(-4/11)
s=-4
Select the correct answer.
What is the sum of
-6 4/5 and 6 4/5?
A. 12 4/5
B. 29/5
C. 0
D. -12 4/5
Answer:
0
Step-by-step explanation:
got it right on plato
Answer:
0
Step-by-step explanation:
hopes this helps may yall like and give me 5 stars
is the ordered pair (-4,3) a solution of the equation y=5x + 21
Answer:
Step-by-step explanation:
If you substitute x = -4 in the equation, you should get the y value as 3
y = 5x + 21
= 5* -4 + 21
= -20 + 21
y = -1 ≠ 3
So, (-4, 3) is not a solution
We are given with height= 9 ft. Length=10 ft. Wall Brackets: 48-inch cost $12.95 68-inch cost $16.95 Distance from brackets from ends= 1 foot maximum . What is the total cost of the brackets, before tax?
Answer:
$89.7
Step-by-step explanation:
We are given with
height = 9 feet
length = 10 feet
wall brackets:
48-in costing $12.95
60-in costing $16.95
distance of brackets from ends = 1 foot
maximum distance between brackets= 24 inches
The brackets are
48/12 = 4 feet
and
60/12 = 5 feet
One of each must be used to cover the height of the shelf
The length of the shelf is
60 inch
subtracting 1 in from each side for the allowance
60 - 2 = 58 in
Dividing by 24 inches
58/24 = 2.41 ~ 3
The total cost is
($12.95 + $16.95) * 3 = $89.7
The total cost of the brackets is $89.7
Do you know the answer? if you do I will follow you mark you the best.
Answer:
16:24 is the answer
Hope it helps:)
Step-by-step explanation:
The initial number of cards were
1x:1x
(Equal red cards and black cards)
So, total of 48 and..
24 red cards
24 black cards
Now, since 8 red cards are removed we have,
24-8= 16 red cards
and 24 black cards
So the ratio of red to black is--
16:24
= 2:3 ( i divided both with 8 to simplify )
Pack 48 48/2 =24
Red= 24 24/24 : 24 / 24
Black = 24 1:1
----------------------------------------------------------------
Pack 48 48/2 = 24
Red= 16 24 / 16 : 24 / 24
Black= 24 1,5 : 1
There's 1,5 black cards for each red card
Can someone help me please
Answer:
The answer to number one is 11√17
The answer to number two is 4
Step-by-step explanation:
In number one: once you get both radicands to be equal, then you can add them. Like of it like 3x+2x. The x’s are like terms, so you can add them together.
In number two: the √5 on the top and bottom cancel out. This leaves 12/3 which is equal to 4.
Identify the relationship complementary, or vertical and find the value of x.
Wouldn’t it be complementary?
Also, I know how to find x, I’m just wondering what’s the relationship.
Answer:
It is complementary.
Step-by-step explanation:
It is since the two angles add up to 90 degrees. If they were vertical angles they would be opposite and be made by intersecting lines. Complementary angles - Angles next to each other that add up to 90 degrees. Supplementary angles : Angles that are next to each other adding up to 180 degrees.
Three more than the product of two and a number
Answer:
2x+3
Step-by-step explanation:
+3 " three more than"
2x " the product of two and a number"
2x+3 " three more than the product of two and a number"
ANYONE, PLEASE ANSWER ALL THESE QUESTIONS AND I WILL MARK HIM/HER BRAINLIEST + 57 PTS.
1. A bag contains 15 balls of which 6 are red, the probability of getting a red ball at random from the bag is
A. 9/15:
B. 6/15:
C. 15/9:
D. 15/6:
2. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
A. 8/21:
B. 2/7:
C. 1/3:
D. 2/3:
3. One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
A. 1/13:
B. 1/4:
C. 9/52:
D. 3/13:
Descriptive Type Questions
4. What is the probability from two throws of a dice:
(a) For getting a sum 9 (b) For the total score is a prime number:
5. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?:
Answer:
1.B
2.C
3.D
4.
a)1/9
b)5/12
5.2/5
Step-by-step explanation:
1.
Since there are 15 total outcomes of which 6 are desirable, the probability of randomly getting a red ball is 5/16 or choice B.
2.
Since there are a total of 8+7+6=21 outcomes, out of which 7 are neither red nor green, there is a 7/21=1/3 probability of that outcome, or answer choice C.
3.
Out of the 52 possible outcomes, 12 are face cards. Therefore, the probability of drawing a face card is 12/52=3/13, or answer choice D.
4.
a)
For each die, there are a total of 6 possible outcomes. This means that in total there are 6*6=36 possible combinations. Now, let's do some casework.
If the first die is a 3, then the second die must be a 6. If the first die is a 4, the second die must be a 5. If the first die is a 5, then the second die must be a 4. And if the first die is a 6, then the second die must be a 3. You cannot have any numbers less than 3, because then you would not be able to make the number 9. Therefore, there is a 4/36=1/9 chance of getting a sum of 9.
b)
All of the possible prime numbers that can be formed with the dice are 2, 3, 5, 7, and 11. For 2, there is only one possible situation where this can happen. For 3, there are 2 possible. For 5, there is 4-1, 3-2, 2-3, and 1-4, or 4 possibilities. For 7, there is 1-6, 2-5, 3-4, 4-3, 5-2, and 6-1, or 6 total possibilities. Finally, for 11, there is only 5-6 and 6-5, or 2 possible. In total, the probability of getting a prime sum is 15/36=5/12.
5.
The only numbers which are a multiple of 3 or 5 from 1 to 20 are: 3, 5, 9, 10, 12, 15, 18, and 20. This means that out of the 20 total possible options, 8 of them are a multiple of 3 or 5, which is a total chance of 2/5.
Hope this helps!
Factor 9x6 – 16 y completely.
First factor each term.
9x6 = (__)?
16y6 = ()2
Then use a? - b2 = (a - b)(a + b). Show your work.
9x6 – 16y6 =
Answer:
(3x^3 - 4y^3) ( 3x^3 + 4y^3)
Step-by-step explanation:
9x^6 – 16 y^6
Rewriting as
(3x^3) ^2 - ( 4y^3) ^2
This is the difference of squares a^2 - b^2 = (a-b)(a+b)
(3x^3 - 4y^3) ( 3x^3 + 4y^3)
Answer:
(3x^3 - 4y^3) ( 3x^3 + 4y^3)
In the diagram, AB is parallel to DE. Also, DE is drawn such that the length of DE is half of the length of AB. If sin A = 0.5, then what is sin E?
A) 2
B) 1
C) 0.5
D) 0.25
E) 0.1
Answer:
C
Step-by-step explanation:
PLATO
So, sin E=0.5. Therefore, option C is the correct answer.
Given that, AB║DE and sinA= 0.5.
We need to find the value of sin E.
How to find the value of sin?The value of sinθ must always be between −1 and 1. So the domain of f(x) = sinθ contains all the real numbers, but the range is −1 ≤ sin x ≤ 1. We can also see that the function repeats itself every 360°.
Now, sinA = 0.5
⇒∠A=30°
∠A=∠E=30° (∵∠A and ∠E are alternate angles)
Therefore, option C is the correct answer.
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URGENT!!!!! LAST TWO QUESTIONS!!!!!!! WILL GIVE BRANLIEST!!!AT LEAST TAKE A LOOK!!!!!! PLS HELP!!!
14. Find the missing angle x. ( 155 degrees is on the top left side, FIRST pic below)
19. Triangles ABC and DEF are similar. Find x. SECOND PIC
A) 9.45
B) 6.12
C) 7.23
D) 8.57
Answer:
#14) x is 95 (155-180= 25, 180-25-60= 95)
#19) my best guess is 4 (DE=7 -> AB=11, a 4 unit increase)
i’m really struggling someone help me
Answer:
Identity property of addition ( 3 + 5) + 0 = (3 + 5)
Associative Property of Multiplication [ 3(5) ](4) = (3)[ (5)4
Identity Property of Multiplication 5(1) = 5
Associative Property of Addition 3 + (5 + 7) = (3 + 5) + 7
Commutative Property of Addition 3 + 5 = 5 + 3
Step-by-step explanation:
In QRS m Q = 80 degrees m R = 65 degrees m S = 35 degrees which side of the QRS is the longest
Answer: RS
Step-by-step explanation:
A greater angle of a triangle is opposite a greater side. If angle Q is greater than angle R, then side RS is greater than side QS.
Because Q is the larger angle in the triangle, Then RS is the longest side.
If p q is true, then q p is ____ false
Answer:
True
Step-by-step explanation:
Logic: if 3+4 =7 then 4+3 also = 7 or 3*4 =12 then 4*3 is also 12 etc.
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!!!
Answer:
B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
H(a)= 3a - 4; Find h(8)
Answer:
20
Step-by-step explanation:
You plug 8 into the equation where a is. 8 x 3 = 24 - 4 = 20.