If $700 is invested in an account that pays 3% compounded annually, the total amount, A(t), in the account after t years is Ant 700(1.03)^t.
Required:
a. Find the average rate of change per year of the total amount in the account for the first four years of the investment (from t= 0 to t= 4).
b. Find the average rate of change per year of the total amount in the account for the second four years of the investment (from t=4 to t=8)
c. Estimate the instantaneous rate of change for t =4.
d. The average rate of change per year of the total amount in the account for the first years of the investment â(from t= 0 to t=4â) is ___________â$
e. The average rate of change per year of the total amount in the account for the second years of the investment â(from t= 0 to t=4â) is_____________ â$
f. The instantaneous rate of change for t=4 is about â$_____________
Answer:
21.96 ; 24.72
Step-by-step explanation:
Given that :
Give the equation:
A(t) = 700(1.03)^t
A.)
Average rate of change over the first 4 years ;
(t=0 to t=4)
At t = 0
A(0) = 700(1.03)^0 = 700
A(1) = 700(1.03)^1 = 721
A(2) = 700(1.03)^2 = 742.63
A(3) = 700(1.03)^3 = 764. 9089
A(4) = 700(1.03)^4 = 787.856167
[(721 - 700) + (742.63 - 721) + (764.9089 - 742.63) + (787.856167 - 764.9089)] / 4
= 87.856167 / 4
= 21.96404175
= 21.96
Over the 2nd 4 years :
A(4) = 700(1.03)^4 = 787.856167
A(5) = 700(1.03)^5 = 811.49185201
A(6) = 700(1.03)^6 = 835.8366075703
A(7) = 700(1.03)^7 = 860.911705797409
A(8) = 700(1.03)^8 = 886.73905697133127
[(811.49185201 - 787.856167) + (835.8366075703 - 811.49185201) + (860.911705797409 - 835.8366075703) + (886.73905697133127 - 860.911705797409)] / 4
= 98.88288997133127 / 4
= 24.72
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A rocking horse has a weight limit of 60 pounds.
What percentage of the weight limit is 33 pounds?
What percentage of the weight limit is 114 pounds?
What weight is 95% of the limit?
please answer asap with explanation qwq
Answer:
1. 55%
2. 190%
Step-by-step explanation:
1a. set up an expression.
33/60 = x/100
33 out of 60 is the 33 pounds out of the 60 weight limit. The x is what you're solving for, and the 100 is the given percent, because the percent is always going to be out of 100%.
1b. do cross multiplication; so do 33*100, which equals 3300
1c. divide; 3300 divided by 60, which equals 55.
For the second problem, do the same thing. your expression should be 114/60 = x/100
Find the rate of change in a table
Answer:
excuss me where the picture
Step-by-step explanation:
Marian is making bread, she has 2 4/7 pounds of flour in her pantry. When making the bread, she will use ⅓ of the flour in the pantry. The amount of salt in the recipe is ⅓ of the amount of flour in the recipe. How much salt will Marian need to make bread?
15. Ellen records the time it takes for her to commute to work on 100 consecutive mornings and finds that the times are approximately Normally distributed with a mean of 25 minutes and a standard deviation of 4.6 minutes. What percentage of the time does Ellen’s commute take less than 14 minutes?
(a) 0.8%
(b) 1.1%
(c) 1.6%
(d) 98.3%
(e) 99.2%
16. Ellen records the time it takes for her to commute to work on 100 consecutive mornings and finds that the times are approximately Normally distributed with a mean of 25 minutes and a standard deviation of 4.6 minutes. What percentage of the time does Ellen’s commute take between 14 and 36 minutes?
(a) 0.8%
(b) 1.1%
(c) 1.6%
(d) 98.3%
(e) 99.2%
17. Ellen records the time it takes for her to commute to work on 100 consecutive mornings and finds that the times are approximately Normally distributed with a mean of 25 minutes and a standard deviation of 4.6 minutes. What is the 80th percentile for Ellen’s driving times?
(a) -0.84
(b) 0.84
(c) 3.9
(d) 25.8
(e) 28.9
18. Ellen records the time it takes for her to commute to work on 100 consecutive mornings and finds that the times are approximately Normally distributed with a mean of 25 minutes and a standard deviation of 4.6 minutes. On Tuesday, it takes 19 minutes to get to work. What is the z-score for her commute that day?
(a) -6.0
(b) -1.30
(c) -0.77
(d) 0.77
(e) 1.30
solve for x.
help pls im stressed
Dont be Stressed Im here
X=6
Dependent events can best be described as
two or more events that have the same probabilities.
two or more events that do not have the same probabilities.
a group of events whose later outcomes are not affected by previous outcomes.
a group of events whose later outcomes are affected by previous outcomes.
Answer:
Sonya watched
1
3
of a movie in the morning, and she watched some more at night. By the end of the day, she still had
1
4
of the movie left to watch. How much of the movie did Sonya watch at night?
Step-by-step explanation:
SORRY WRONG
Dependent event is,
D) a group of events whose later outcomes are affected by previous outcomes.
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We know that;
The two events Event A and event B are said to be dependent if the occurrence of one outcome affects the occurrence of the other outcome.
Since, If we have a bag containing 5 blue marbles, 2 red marbles and 3 green marbles then if we draw first marble and then draw second without replacement.
Then, the event of drawing a blue marble first and then a green marble are dependent events.
Hence, Dependent event is,
a group of events whose later outcomes are affected by previous outcomes.
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At a store, a hat has a regular price of x dollars. During sale, the price of the hat
is discounted by 20%. The expression 0.8x describes the discounted price, in dollars,
of the hat. Which expression also describes the discounted price, in dollars, of the hat?
Answer:
x - 0.2x
Since the price of the hat is labelled = x,
The percentage discount on the hat price = 20%,
Thus, the discount = 20% of the price marked
= Twenty percent of x
=0.2 x =0.2 x
Therefore, the hat's new price = Marked price - Discount
= x- 0.2 = x
Answer:
D) x - 0.2x
Step-by-step explanation:
The hat has a regular price of x dollars.
This price is reduced by 20% so the relevant expression for the discount is; 20% * x or; 0.2x
The discounted price will be the price of the hat less the discount which means the formula will be;
= Price - discount
= x - 0.2x
A group of eight individuals with high cholesterol levels were given a new drug that was designed to lower cholesterol levels. Cholesterol levels, in mg/dL, were measured before and after treatment for each individual, with the following results: Subject Before After 1 283 215 2 299 206 3 274 185 4 284 212 5 255 178 6 275 212 7 293 192 8 277 196 Can you conclude that the mean cholesterol level after treatment is less than the mean before treatment
It can be concluded that the mean cholesterol level after treatment is less than the mean before treatment.
Let the hypothesis be:
H₀: The difference in the mean is less than or equal to 0.
H₁: The difference in the mean is greater than 0.
Here, the sample size, n = 8.
Assume, α = 0.05.
First, find the mean of the differences.
[tex]\bar{d}=\frac{(283-215)+(299-206)+...+(277-196)}{8}[/tex]
[tex]=79.375[/tex]
Now, the standard deviation of the difference is:
[tex]s_d=\sqrt{\frac{(68-79.375)^2+...+(81-79.375)^2}{8-1}}[/tex]
[tex]=13.3838[/tex]
The t value is:
[tex]t=\frac{\bar{d}}{\frac{s_d}{\sqrt{n}}}[/tex]
[tex]=16.7745[/tex]
Now, the degree of freedom is 8 - 1 = 7.
The p-value corresponding to this is 0.0005, which is less than the value of 0.05.
So, reject H₀.
Hence, it can be concluded that the mean cholesterol level after treatment is less than the mean before treatment.
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SOMEONE HELP I NEED TO PASS
what is 550 x 34 ?????
Answer:
18,700
Step-by-step explanation:
Answer:
18,700
Step-by-step explanation:
i hope this helps
I need help with this please
Starting at a fixed time, each car entering an intersection is observed to see whether it turns left (L), right (R), or goes straight ahead (A). The experiment terminates as soon as a car is observed to turn left. Let X = the number of cars observed. What are possible X values? List five different outcomes and their associated y values.
Answer:
Outcomes are { L, RL, AL, RAL, ARL }
Associated X values are { 1, 2, 2, 3, 3 }
Step-by-step explanation:
As given,
left = (L),
right = (R)
goes straight ahead = (A)
Now,
The Sample space become = { L, RL, AL, RAL, ARL }
In L -
Number of cars = 1
In RL-
Number of cars = 2
In AL-
Number of cars = 2
In RAL-
Number of cars = 3
In ARL-
Number of cars = 3
Pls I need help I will mark Brainly
Answer:
(10⁰x 10¹ x 1¹⁰)< (10⁰ + 10¹x 1¹⁰)<(10⁰ + 10¹ + 1¹⁰)< (10 x 10¹)
Step-by-step explanation:
increasing order-
(10⁰x 10¹ x 1¹⁰)
(10⁰ + 10¹x 1¹⁰)
(10⁰ + 10¹ + 1¹⁰)
(10 x 10¹)
PLEASE HELP I WILL GIVE BRAINLEST!!
Answer:
8 1/8
Step-by-step explanation:
I used a calculator....
(hope this helps :P)
Solve the inequality
-2(5x + 1) > 48
Answer:
x<-5
Step-by-step explanation:
-10x-2>48
-10x-2+2>48+2
-10x>50
-10x/-10 > 59/-10
= x<-5
Order of operations. Need to find the unknown number. Help?
8 + 2 x 5 = m
9 - 7 + 2 = k
7 x 8 - 6 = g
16 + 4 divide 2 = s
12 - 6 divide 2 = y
36 divide 6 + 13 = f
Answer:
m = 18
k = 4
g = 50
s = 18
y = 9
f = 19
Step-by-step explanation:
B
C
x
50°
A
D
ABCD is a rectangle.
AC and BD are straight lines.
The angle between AC and BD is 50°.
Work out the size of the angle marked x.
Answer:
The answer is : x = 130 degrees
HELP NOWWWWW PLEASEEEEE
How many 1/3's are in 1 and 2/3?
Answer:
5 thirds
Step-by-step explanation:
Make 1 2/3 into a improper fraction. Now you have 5/3. 5/3-(1/3*5)=0
Therefore, 5x1/3=5/3=1 2/3
Answer:
This guy is wrong. 1 2/3 is equal to 5/3. But that is not the answer(like that dummy above said)
The Question is asking "How many 1/3's are in 1 2/3" (5/3)
The answer is 5, not 5/3's.
I need help with this.
Answer:
Hypotenuse equals 6 and Y (longer leg) equals 3 square root of 3
Step-by-step explanation:
According to the 30-60-90 triangle rule, The hypotenuse is always 2 times greater than the shortest leg, and the longer leg is always the square root of 3 tie greater than the shortest leg.
Add and
subtract fraction. X+5=23
(11 - 3) x [ 15 + (10 - 5)] write 3 steps using pemdas
Answer:
160
Step-by-step explanation:
pls help me on this........
Answer:
9x+9
it the 3rd one
Which of the following is not true about the boundary line in the graph of a linear inequality in two variables?
A. The points on the boundary line are always solutions to the linear inequality.
B. The boundary line separates the ordered pair solutions to the inequality from the ordered pairs that are not solutions to the inequality.
C. A solid line is used when the inequality is non-strict ( ≤ or ≥ ).
D. A dashed line is used when the inequality is strict ( < or > )
D. A dashed line is used when the inequality is strict ( < or > )
A linear inequality in two variables is obtained by taking a linear equation in two variables, and replacing the equality sign with any one of the four inequality signs: <,>,=<,>=.
The graphed region of points satisfying the inequality is always half of the plane bounded by the corresponding line.
When the inequality is [tex]\leq[/tex] or [tex]\geq[/tex], the line is included. Otherwise, the line is excluded.
So, A dashed line is used when the inequality is strict ( < or > ) is not true about the boundary line in the graph of a linear inequality in two variables
Therefore, the correct option is D.
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Multiply. Write the answer in simplest form. 1/5 . 2/9
2/45 in simplest form
Plz, Help me! I will give a point if you help answer! with 5 star rating, Thanks, and Brainliest!
Answer:
-4/10+(-7/10)= -1 1/10(the bottom left one)
Step-by-step explanation:
starts from 0 and subtract 4/10. From there you subtract 7/10 more.
You randomly draw a marble from a bag of marbles that contains 3 blue marbles, 4 green marbles, and 5 red
marbles.
What is P(draw a blue marble)?
Which expression is equivalent to – 12 + (-4/5) + 31 and includes the correct justification for the equivalence?
Answer:
b
Step-by-step explanation:
Kevin has 1,066 trading cards. Each album holds 26 cards. How many albums does Kevin need to hold all his cards?
Answer:
41
Step-by-step explanation:
Ok so you would divide 1,066 by 26 which would equal 41. Have a great day!
5
B
C
Find the composition of
transformations that
map ABCD to EHGF.
Reflect over the [? ]-axis,
then translate
(x+[ ], y+[ ]).
Note: Enter x ory for axis.
4
3
2
D
H
4
813
2
1
0
4
6
7
Answer:
Step-by-step explanation:
Reflect over the Y axis, then translate (x+[-2], y+[-3])
The composition of transformations that map ABCD to EHGF will be [(x + 6), (y + 1)].
What is geometric transformation?Change is referred to as transformation. As a result, a geometric transformation entails making modifications to any geometric shape.
Vertices of the quadrilateral ABCD having coordinate A,B,C,D are (-5, 2),(-3, 4), (-2, 4),(-1, 2) respectively.
The image quadrilateral A'B'C'D' is formed by reflecting the supplied quadrilateral ABCD across the x-axis.
The rule for a point's reflection across the x-axis is:
(x, y) → (x , -y)
The picture point A' coordinates will be,
A(-5, 2) → A'(-5, -2)
Point E is produced by translating point A', as shown in the diagram. The rule for translating a point by h units right and k units up is as follows:
A'(x+h, y+k) → E(x', y')
By comparing coordinates of A' and E,
-5 + h = 1
h = 6
-2 + k = -1
k = 1
That is to say, the translation rule will be:
[(x + 6), (y + 1)]
Hence, the composition of transformations that map ABCD to EHGF will be [(x + 6), (y + 1)].
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