C. 2%; exponential decay
You can use the fact that increasing power of values lying between 0 and 1 results in less and less values.
The percent rate of change in given function is -2%
The function represents exponential decay.
Given that:The function: [tex] y = (0.98) ^ x[/tex]To find:Percent rate of change in given function.Is it representing exponential growth or exponential decay?Finding percent rate of change in given function:
For finding this, first find how much the output y changes if we change x from x to x + 1.
Output when x = x: [tex]y = (0.98)^x[/tex]
Output when x = x+1: [tex]y = (0.98)^{x+1}[/tex]
Difference in output if x goes from x to x+1: [tex](0.98)^{x+1} - (0.98)^x = (0.98)^x(0.98 - 1) = -0.02 \times (0.98)^x[/tex] (this change occurs if we increase input x by 1 unit, thus this also represents the rate)
Rate of change of function per unit increment = [tex]-0.02 \times (0.98)^x[/tex]
The percentage of rate of change is found as:
[tex]\text{Percent rate of change\:} = \dfrac{\text{Rate of change} \times 100}{\text{previous value}} = \dfrac{-0.02 \times (0.98)^x \times 100}{(0.98)^x} \\\\ \text{Percent rate of change\:} = -2\%[/tex]
Thus, the percent rate of change is -2%
The negative sign shows that the value is decreasing, thus showing that function shows exponential decay.
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Rewrite in y=mx+b form
- (y + 2) = 2(2x + 1)
Answer:
y=-4x-4
Step-by-step explanation:
Answer:
y=-4x+4
Step-by-step explanation:
Use order of operations, PEMDAS, to put it in y=mx+b form.
John and Robin like to collect stones. John has n stones, and Robin has 68 stones. Together they have a total of 98 stones, Write an equation to describe this situation.
Answer:
n+68=98 find n (n=30)
Step-by-step explanation:
Classify this triangle by its sides?
Answer:
Scalene
Step-by-step explanation:
Could somebody please help me with these?? It's due tomarrow
Example for Table 1:
y = x + 6
So if X=-8
1st Row -8+6=-2
2nd Row -4+6=2
3rd Row -2+ 6=4
4th Row -9+6=-3
5th Row 2+6=8
So for any table, the X in the table rule is the X that you are working on.
Answer:
i got you:
1) -2, 2, 4, -3, 8
2) 37, -3, 29, -67, -75
3) -36, 4, -4, -20, -12
4) -10, 6, -4, 8, 4
5) -2, 18, -16, 6, -10
6) -4, -15, 2, 0, -6
7) -25, 23, 5, 29, 11
8) 24, 38, -60, 3, 10
9) 2, 4, 9, -1, -3
10) -14, -8, -15, -10, -16
11) 9, 18, -21, -3, -24
12) -10, 35, -73, 71, -19
hope that helps
Step-by-step explanation:
3. Ivan has completed 45% of his walk.
He has already walked 9 km. How much farther does he have left to walk?
Answer:
11
Step-by-step explanation:
The required distance left to the walk will be 11 km.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Let the total distance of the walk would be x km
As per the given information, the required solution would be as:
⇒ 45% of x = 9
45% is expressed as 45/100 in fractional form
⇒ (45/100)x = 9
45/100 is expressed as 0.45 in decimal form
⇒ 0.45x = 9
⇒ x = 9/0.45
⇒ x = 20
So the total distance of the walk is 20 km
Since he has already walked 9 km.
So, he has left to the distance of the walk = 20 - 9 = 11 km
Therefore, the required distance left to the walk will be 11 km.
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Here are the ingredients to make 12 cupcakes.
For 12 cupcakes
200 g butter
200 g caster sugar
4 eggs
250 g flour
Mark is making cupcakes to sell at his school play.
Mark wants to make 1 cupcake for each adult and 2 cupcakes for each child.
There will be 152 adults and 80 children at the school play.
Mark can get these ingredients from the school kitchen.
5 kg butter
5 kg caster sugar
90 eggs
5 kg flour
Make a shopping list of any ingredients Mark still needs, showing the amount of each
ingredient.
Answer:
Mark needs 2 kg butter, 2 kg caster sugar, 14 eggs, and 1.5 kg flour.
Step-by-step explanation:
Alright, first you double the number of kids, as Mark wants each kid to have two cupcakes, not one. (Then add 80+80 to get 160)
Now add the adults to children: 160+152=312
now divide by 12 to see how many batches of cupcakes he needs to make.
312÷12=26 So he needs to make 26 batches
Now here are the ingredients needed to make 12 batches of cupcakes (I multiplied the amount of each ingredient by 26)
5200 g (5.2 kg) butter, 5200 g (5.2 kg) caster sugar, 104 eggs, and 6500 g (6.5 kg) flour.
now make the measurements the same as Mark's ingredients (or the other way around)
(to save time I am not showing each one, just the normal ingredients turned into kg and compared)
5 kg butter < 5.2 kg butter
5 kg caster sugar < 5.2 kg butter
90 eggs < 104 eggs
5 kg flour < 6.5 kg flour
Now do a little subtraction.....
5.2 kg-5 kg = 2 kg butter is needed....
5.2 kg - 5 kg = 2 kg caster sugar is needed....
104 - 90 = 14 eggs needed....
6.5 kg - 5 kg = 1.5 kg flour needed....
And there you go!!! Hope this helped!!! :D
The amount of ingredients that Mark still requires after getting it from the kitchen is needed.
The amount of ingredients Mark still needs is
200 g of butter
200 g of caster sugar
14 eggs
1500 g of flour
The number of cupcakes that are needed for 152 adults and 80 children is
[tex]152+2\times 80=312[/tex]
For the 12 cupcakes the ingredients are
200 g butter
200 g caster sugar
4 eggs
250 g flour
For 1 cupcake the ingredients are
[tex]\dfrac{200}{12}=\dfrac{50}{3}\ \text{g}[/tex] of butter
[tex]\dfrac{200}{12}=\dfrac{50}{3}\ \text{g}[/tex] of caster sugar
[tex]\dfrac{4}{12}=\dfrac{1}{3}[/tex] eggs
[tex]\dfrac{250}{12}=\dfrac{125}{6}\ \text{g}[/tex] of flour
For 312 cupcakes
[tex]312\times \dfrac{50}{3}=5200\ \text{g}[/tex] of butter
[tex]312\times \dfrac{50}{3}=5200\ \text{g}[/tex] of caster sugar
[tex]312\times \dfrac{1}{3}=104[/tex] eggs
[tex]312\times \dfrac{125}{6}=6500\ \text{g}[/tex] of flour
The required ingredients are
[tex]5200-5000=200\ \text{g}[/tex] of butter
[tex]5200-5000=200\ \text{g}[/tex] of caster sugar
[tex]104-90=14[/tex] eggs
[tex]6500-5000=1500\ \text{g}[/tex] of flour
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what is 65% of 80 ??????????????
Answer:
Step-by-step explanation:
65% of 80 is
65*80/100=52
Answer:
52
Step-by-step explanation:
Calculate percentage:
'Percentage' is obtained by multiplying 80 by 65%.
65% × 80 =
(65 ÷ 100) × 80 =
(65 × 80) ÷ 100 =
5,200 ÷ 100 =
52
Checking:
How do we check the result?
If 65% × 80 = 52 =>
Divide 52 by 80...
... And see if we get as a result: 65%.
Calculate the percent value:
52 ÷ 80 =
0.65 =
0.65 × 100/100 =
(0.65 × 100)/100 =
65/100 =
65%
Simplify: (3x-4)+(-2x+8).
Answer:
Step-by-step explanation:
x+4
Below are two parallel lines with a third line intersecting them.
Answer:
77
Step-by-step explanation:
180-103=77
Brian can iron 3 shirts in 5 minutes. If Brian irons at a constant rate, how many shirts can he iron in 30 minutes? WILL GIVE BRANLIEST
Answer:
18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
30/5 = 6
6 * 3 = 18
What is m∠DEF?
Enter your answer in the box.
There is a triangle DEF in which side DE is congruent to side EF and G is the midpoint of the side DF. Segment EG intersect the side DF at point G. The measure of angle DEG is (3y+4) degrees and the measure of angle FEG is (5y-10) degrees.
Answer:
m<DEF = 8y - 6
Step-by-step explanation:
Given that: DEG = [tex](3y +4)^{o}[/tex], and FEG = [tex](5y-10)^{o}[/tex].
The given triangle is an isosceles triangle with sides DE ≅ DF.
But,
m<DEF = DEG + FEG
= [tex](3y +4)^{o}[/tex] + [tex](5y-10)^{o}[/tex]
= 3y + 4 + 5y - 10
= 8y - 6
m<DEF = 8y - 6
Therefore, the measure of < DEF is 8y - 6.
A new watch costs $120 at the store. If it goes on sale for 75% off and has a sales tax of 6%, what is the final cost of the watch?
I will give you 15 points
Answer: A, D
Step-by-step explanation:
1 and 2 is all I need and you guys would help me from not getting beat
Answer:
1. -10
2. -11
Step-by-step explanation:
13 Points. Find the perimeter.
Answer:
15.7 cm
Step-by-step explanation:
The perimeter of the entire circumference is
entire perimeter = 2п r
п = 3.14 (aprox)
r = radius = 3cm
entire perimeter = 2*3.14*3 = 18.84 cm
the entire perimeter of the circumference corresponds to 360 degrees
then,
proportions:
18.84 cm ⇔ 360°
F cm ⇔ 300°
F = 18.84*300/360
F = 15.7 cm
convert 2 3/4 into a improper faction
Answer:
11/4
Step-by-step explanation:
2 times 4 equals 8 and plus 3 equals 11 and dem is 4 so 11/4
Answer:
[tex]\frac{11}{4}[/tex]
Step-by-step explanation:
[tex]2\frac{3}{4}[/tex]
To get an improper fraction do the multiply and add shortcut. Do the denominator times the whole number ( 2 x 4). You will get 8, next add 8 with 3. You still keep the denominator, so your final result is [tex]\frac{11}{4}[/tex]
Which expression is equivalent to?
i need to drag one into the box to match them
Answer:
54÷9 = 6 so for the second box is 6 hot dogs per person
54÷27= 2 third box is 2 hot dogs per person
54÷54= 1 fourth box is 1 hot dog per person
You pay $11.20 to buy drink boxes for the football team. Each drink box cost $0.40. How many drink boxes did
you buy?
Please help, I will be giving brainlist.
Answer:
b
Step-by-step explanation:
Answer:
o B 6 inches.
Step-by-step explanation:
Proportions:
13 in ⇔ 9.75 in
8 in ⇔ X in
X = 8*9.75/13
X = 6 in
Over the summer Marty reads 4 times as many pages as the number of pages Nelson and Jennifer read combined Marty reads 1,860 pages and Nelson reads 240 pages
Help me out please and thank you ;)
The slope of the line below is 5. Which of the following is the point-slope form
of the line?
(-1,3)
5
A. y + 3 = -5(x - 1)
B. y + 3 = 5(x - 1)
C. y - 3 = 5(x+1)
D. Y-3 = -5(x + 1)
The point-slope form of the line in the graph is y-3 = 5(x+1). The correct option is C.
What is the point-slope form of the line?The point-slope form of the line is y-y₁ = m( x-x₁)
Here, m is the slope of the line.
The graph given in the question has a slope of 5
It passes through the point ( -1,3)
The point slope form of the line is
y - 3 = 5 ( x - (-1))
y-3 = 5(x+1)
This is represented by option C.
To know more about the Point-slope form of the line
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what are the relative max and min. of this graph?
Relative Max is 6
Relative Min is -8
4.3 m to centimeters
Answer: 430 cm
Step-by-step explanation:
Answer:
430 cm
Step-by-step explanation:
43 multiplied by 10 is 430
- IZ
- -
M = 9
7. Carlene has $300 in her wallet but she doesn't realize that she has a hole in her wallet!
Every step she takes, she loses five dollars. How far will she walk before she only has $150 left
in her wallet? Write a sentence explaining your solution.
Click to add text
Explanation:
ick to add speaker notes
Step-by-step explanation:
Subtract initial amount (300) and final (150). from there you get 150 dollars that was lost. We know that every step you 5 dollars so then divide 150 and 5 to get 30. So the distance was 30 steps.
Can you guys please help me!!
Answer:
a. 32
b. 32
Step-by-step explanation:
a. 12 + 4y
They gave us the value of "y" which is "5", and substitute that into the expression.
12 + 4y
12 + 4(5)
12 + 20
32
b. 4 (y + 3)
They gave us the value of "y" which is "5", and substitute that into the expression.
4 ( y + 3 )
4 ( 5 + 3)
Distributive property (multiply what is in the parenthesis by what is out of it (4))
4 * 5 + 4 * 3
20 + 12
32
Hope this helped!
Have a supercalifragilisticexpialidocious day!
Solve 6 - 5x = 7 + 3x
Answer:
hol up
x=-1/8 negative one over eight
Step-by-step explanation:
What is the solution for -3w-4=w+4
Answer:
uhh
Step-by-step explanation:
carrot?
What are the answers to these questions
