Answer:
An experiment
Step-by-step explanation:
An observational study is a study in which the researchers collect data related to what is visible or heard. In this type of study the researchers do not have any control on the variables used for the research work .The researcher do not bring any changes in the behavior of the variables that is they are accepted the way they are.
An experiment is a method used in which the researchers pick up a sample from a group and test them to get a proof or knowledge about something.
Both Observational study as well as an experiment are used in statistics social sciences and psychology etc.
Thus the case given here is an experiment because there is no alterations done with the variables.
The scenario given is an experiment because it deliberately manipulates conditions (music or no music) to test its effect on students' ability to memorize words. By comparing outcomes, this study seeks to establish a causal relationship.
Explanation:The study described in the student's question is an experiment because it involves a deliberate manipulation of conditions to test a hypothesis. The manipulation in this case is the presence or absence of music while memorizing words. Since there are two groups and each group is subjected to different conditions (one with music and one without), this defines a controlled experiment. Experiments involve comparing the outcomes of different treatments, in this case, music or silence, which enables researchers to make causal inferences about the effect of the independent variable (music) on the dependent variable (ability to remember words).
Now, looking at the studies referenced, the effects of music on different cognitive tasks, like memorization and reading comprehension, have been explored in various ways. While some experiments, like the one comparing the memorization of words with and without music, show that silence may be more conducive for memorization, other studies have found positive effects of music on tasks such as reading comprehension or overall task behavior.
a + b = 10
a - b = 2
Solve the system of equations.
Answer:
a=6 b=4
Step-by-step explanation:
they can't both equal 5 so you need to find 2 numbers that add up to equal 10 but when you subtract one from the other it equals 2
please help
As x increases by 1 unit, what is the exponential growth factor?
Answer: The answer is 3, I just finished doing the assignment.
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
walnuts cost $3.60 per pound and peanuts cost $2.70 per pound. For a fundraiser, the softball team will be selling bags of mixed nuts. How many punds of walnuts and how many pounds of peanuts should the team buy in order to make a 60 pound . ixture that will sell for $3.00 per pound?
Answer: 20 pounds of walnuts should be mixed with 40 pounds of peanuts.
Step-by-step explanation:
Let x represent the number of pounds of walnuts that should be in the mixture.
Let y represent the number of pounds of peanuts that should be in the mixture.
The number of pounds of the mixture to be made is 60. This means that
x + y = 60
Walnuts cost $3.60 per pound and peanuts cost $2.70 per pound. The mixture will sell for $3.00 per pound. It means that the total cost of the mixture is 3 × 60 = $180. The expression would be
3.6x + 2.7y = 180- - - - - - - - - - - - -1
Substituting x = 60 - y into equation 1, it becomes
3.6(60 - y) + 2.7y = 180
216 - 3.6y + 2.7y = 180
- 3.6y + 2.7y = 180 - 216
- 0.9y = - 36
y = - 36/ - 0.9
y = 40
x = 60 - y = 60 - 40
x = 20
We would like to construct a 66% confidence interval for the proportion of voters that support building a new prison. What is the appropriate multiplier (z) that would be used in this situation?
Answer:
The appropriate z multiplier for 66% confidence interval is 0.95
Step-by-step explanation:
We are given the following in the question:
Confidence interval:
[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
We have to make a 66% confidence interval for the proportion of voters.
Confidence level = 66%
Significance level =
[tex]\alpha = 1 - 0.66 = 0.34[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.34} = \pm 0.95[/tex]
Thus, the appropriate z multiplier for 66% confidence interval is 0.95
DONT SKIP PLZ
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-3, -1) and point (-2, -4) rounded to the nearest tenth?
3.2 units
2.9 units
3.4 units
4.1 units
Answer:
The first one: 3.2 units
Answer: 3.2 units
Step-by-step explanation:
The formula for determining the distance between two points on a straight line is expressed as
Distance = √(x2 - x1)² + (y2 - y1)²
Where
x2 represents final value of x on the horizontal axis
x1 represents initial value of x on the horizontal axis.
y2 represents final value of y on the vertical axis.
y1 represents initial value of y on the vertical axis.
From the graph given,
x2 = -2
x1 = - 3
y2 = - 4
y1 = - 1
Therefore,
Distance = √(- 2 - - 3)² + (-4 - - 1)²
Distance = √1² + - 3² = √1 + 9 = √10
Distance = 3.2
Factor completely. If the polynomial is not factorable, write prime.
5.) 3x^3y+x^2y^2+x^2y
6.) 8r^3-64s^6
Step-by-step explanation:
5)
3x³y + x²y² + x²y
x²y (3x + y + 1)
6)
8r³ − 64s⁶
8 (r³ − 8s⁶)
8 (r − 2s²) (r² + 2rs² + 4s⁴)
A prism with a base area of 8 cm² and a height of 6 cm is dilated by a factor of 54 .
What is the volume of the dilated prism?
Enter your answer, as a decimal, in the box.
cm³
Answer:
New base area = 8 x 25/16 = 25/2 = 12•5 cm²
New height = 7•5 cm²
V = 7•5 x 12•5 cm³
V = 93•75 cm³
Step-by-step explanation:
A trampolinist steps off from 15 feet above ground to a trampoline 13 feet below. The function h (t) = -16 t 2 + 15, where t represents the time in seconds, gives the height h, in feet, of the trampolinist above the ground as he falls. When will the trampolinist land on the trampoline?
Answer:
Trampolinist will land on the trampoline after 0.9 seconds.
Step-by-step explanation:
The function h(t) = -16t² + 15 represents the relation between height 'h' above the ground and the time 't' of the trampolinist.
We have to find the time when trampolinist lands on the ground.
That means we have to find the value of 't' when h(t) = 15 - 13 = 2
[Since trampoline is 2 feet above the ground]
When we plug in the value h(t) = 2
2 = -16t² + 15
2 + 16t² = -16t² + 16t² + 15
16t² + 2 = 15
16t² + 2 - 2 = 15 - 2
16t² = 13
[tex]\frac{16t^{2}}{16}=\frac{13}{16}[/tex]
[tex]t^{2}=\frac{13}{16}[/tex]
t = [tex]\sqrt{\frac{13}{16}}[/tex]
t ≈ 0.9 seconds
Therefore, trampolinist will land on the trampoline at 0.9 seconds.
Mitchel climbs 8 feet up the vertical ladder of a slide and zips down the 17-foot slide. How far is the bottom of the ladder from the bottom of the slide
Answer:
the bottom of the ladder from the bottom of the slide is 15 feet far from
the bottom of the slide
Step-by-step explanation:
Given that Mitchel climbs 8 feet up the vertical ladder of a slide and zips down the 17-foot slide.
The slide the vertical ladder and the floor together form a right triangle if we can vizualise.
The hypotenuse would be the slide , and one leg is ladder and other the bottom of the ladder from the bottom of the slide
We have hypotenuse = 17 feet and one leg = 8 feet
So use Pythagorean theorem to find other leg
Other leg = [tex]\sqrt{17^2-8^2} \\=\sqrt{(17+8)(17-8)} \\= 15[/tex]
the bottom of the ladder from the bottom of the slide is 15 feet far from
the bottom of the slide
The cost, in dollars, of producing x belts is given by Upper C (x )equals 751 plus 12 x minus 0.067 x squared. Find the rate at which average cost is changing when 256 belts have been produced.
Answer:
-$0.07846 per belt
Step-by-step explanation:
The average cost per belt is ...
[tex]c(x)=\dfrac{C(x)}{x}=\dfrac{751+12x-0.067x^2}{x}=751x^{-1}+12-0.067x[/tex]
Then the rate of change of average cost is ...
[tex]c'(x)=-751x^{-2}-0.134\\\\c'(256)=\dfrac{-751}{256^2}-0.067\approx -0.07846[/tex]
The rate at which average cost is changing is about -0.078 dollars per belt.
_____
Note that the cost of producing 256 belts is -$567.91, so their average cost is about -$2.22 per belt.
The student is asked to calculate the rate of change of average cost for producing belts when 256 belts are produced, by finding and evaluating the derivative of the average cost function.
Explanation:The question asks about the rate at which the average cost is changing for the production of belts given a certain cost function C(x) = 751 + 12x - 0.067x2. To find this rate when 256 belts are produced, we need to first calculate the average cost, which is C(x) divided by x, and then take the derivative of the average cost to find its rate of change. The derivative of the average cost function gives us the rate at which the average cost is changing with respect to the number of belts produced. We evaluate this derivative at x = 256 to find the specific rate of change at the production of 256 belts.
Find f (1) pleaseeee
Answer:
f(1) = 4
Step-by-step explanation:
f(1) = 3(1)^2 -(1) + 2 = 4
Just replace all the x's with 1.
Flip a coin 25 times and keep track of the results. What is the experimental probability of landing on tails? What is the theoretical probability of landing on heads or tails?
Answer:
you must flip a coin 25 times and record it on a table for experimental. Theoretical would be 50% chance ( showing working)
The theoretical probability of landing on heads or tails is always 0.5 or 50%. The experimental probability of landing on tails is determined by dividing the number of times you land tails by the total number of flips. Over the long term, thanks to the Law of Large Numbers, these values tend to converge.
Explanation:The subject of the question is the probability of landing on heads or tails when flipping a coin 25 times. The experimental probability of landing on tails can only be determined empirically by actually performing the experiment. After flipping the coin 25 times, you would calculate the experimental probability of landing on tails by dividing the number of times you landed on tails by the total number of flips (25).
On the other hand, the theoretical probability of landing on heads or tails on a single flip of a fair coin is always 0.5, or 50%, due to the nature of the coin having two equally likely outcomes. This is known as the Law of Large Numbers, which states that as the number of trials of a random experiment increases, the experimental probability approaches the theoretical probability.
For example, if we talk about Karl Pearson's experiment, after flipping a coin 24,000 times, he obtained heads 12,012 times. The relative frequency of heads is 12,012/24,000 = 0.5005, which is very close to the theoretical probability (0.5).
Learn more about Probability here:https://brainly.com/question/32117953
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The vertex of a parabolic function is located at (5,−4). One of its zeros (x-intercepts) occurs at x = 7. Where will its other zero (x-intercept) be located?
Answer:
The answer to the question is
Its other zero (x-intercept) will be located at x = -5
Step-by-step explanation:
To solve the question, we note that a parabolic function is of the form
ax² + bx +c = 0
Therefore we have the vertex occurring at the extremum where the slope = 0
or dy/dx =2a+b = 0 also the x intercept occurs at x = 7, therefore when
ax² + bx +c = 0, x = 7 which is one of the solution
when x = 5, y = -4
That is a*25 +5*b + c = -4 also
49*a + 7*b + c = 0
2*a + b = 0
Solving the system of equations we get
a = 0.2, b = -0.4 and c = -7
That is 0.2x² -0.4x -7 = 0 which gives
(x+5)(x-7)×0.2 = 0
Therefore the x intercepts are 7 and -5
the second intercept will be located at x = -5
Final answer:
The other zero of the parabolic function with a vertex at (5, -4), and one zero at x = 7, will be located at x = 3, since it will be symmetrically placed with respect to the vertex.
Explanation:
The vertex of a parabolic function represents the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards. The fact that the vertex of the function is given as (5, -4) and one zero is at x = 7 leads to the conclusion that the other zero must be equidistant from the vertex on the x-axis because a parabola is symmetric about its vertex. Since the distance from the vertex (5) to the given zero (7) is 2 units to the right, the other zero must be 2 units to the left of the vertex. Therefore, the other zero will be at x = 5 - 2, which is x = 3.
Students were divided into two groups. Students in one group were ignored when they talked without raising their hands. Students in the other group were attended to in the teacher's usual manner. The independent variable in this experiment was _____.
Answer:
The independent variable in this experiment was the attention students gets from the teacher
Step-by-step explanation:
An independent variables are variables in maths, statistics and experimental sciences that stands alone and isn't affected by the other variables you are trying to measure.
Final answer:
The independent variable was the teacher's response to the student behavior of either ignoring or attending to students when they talked without raising their hands.
Explanation:
The independent variable in this experiment was the strategy used by the teacher regarding whether or not to ignore the students when they talked without raising their hands.
In experimental design, the independent variable is the condition that is manipulated by the researcher to observe its effects on the dependent variable.
In this case, students in one group were ignored when they spoke without raising their hands, making them the experimental group.
The other group, which the teacher attended to in their usual manner, acted as the control group.
Since the independent variable is the only factor that is intentionally changed to test its impact on outcomes, observing changes in the students' behavior helped determine the effects of this teaching strategy.
Henry is trapped at the roof top of a burning building, which is 24 feet high. In order to rescue him, his father, Diego, must find a ladder which will be used to cross the river, which is 7 feet wide, and go up directly to the top of the building. Help Diego to find the appropriate length of ladder from the other side of the river to the top of the building
Answer: the ladder should be 25 feet
Step-by-step explanation:
The ladder forms a right angle triangle with the building and the river. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the building represents the opposite side of the right angle triangle.
The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.
To determine the length of the required ladder h, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
h² = 24² + 7² = 576 + 49
h² = 625
h = √625 = 25 feet
Dustin bought 9 pencils. Some of the pencils were green and cost $0.90 each. The remainder of the pencils were purple and cost $0.65 each. If Dustin paid $7.10 for all of the pencils, how many green pencils did he buy?
Answer: he bought 5 green pencils
Step-by-step explanation:
Let x represent the number of green pencils that Dustin bought.
Dustin bought 9 pencils. The remainder of the pencils were purple. This means that the number of purple pencils that he bought is 9 - x
Some of the pencils were green and cost $0.90 each. The remainder of the pencils were purple and cost $0.65 each. If Dustin paid $7.10 for all of the pencils, it means that
0.9x + 0.65(9 - x) = 7.1
0.9x + 5.85 - 0.65x = 7.1
0.9x - 0.65x = 7.1 - 5.85
0.25x = 1.25
x = 1.25/0.25
x = 5
A forest ranger sights a fire directly to the south. A second ranger, 99 miles east of the first ranger, also sights the fire. The bearing from the second ranger to the fire is Upper S 29 degrees Upper WS 29° W. How far is the first ranger from the fire?
Answer:
The first ranger is approximately 54.88 miles away from the fire.
Step-by-step explanation:
We have drawn the diagram for your reference.
Given:
Distance between first ranger and second ranger (AB)= 99 miles
Angle between fire and second ranger [tex]\angle B[/tex] = [tex]29\°[/tex]
We need to find the distance between the first ranger from the fire.
Solution:
Let the distance between the first ranger from the fire (AC) be 'x'.
So we can say that;
We know that;
tan of angle B is equal to opposite side divided by adjacent side.
[tex]tan 29\°= \frac{AC}{AB}\\\\tan 29\° = \frac{x}{99}\\\\x= 99\times tan29\°\\\\x \approx 54.88\ mi[/tex]
Hence the first ranger is approximately 54.88 miles away from the fire.
Someone has 240$ for a road trip this is 2/5of the coast of the trip how much dose the trip coat
Answer:
$600
Step-by-step explanation:
Divide 240 by 2/5
A deck of 52 cards has only one queen of diamonds. The deck is well-shuffled and you draw the first and last card (without replacement). What is the chance that the first card is a queen of diamonds or the last card is a queen of diamonds
Answer:
3.8% chance
Step-by-step explanation:
Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation.
y = 2.5 when x = 9
1) k = 3.6; xy = 3.6
2) k = 22.5; y = 22.5x
3) k = 22.5; xy = 22.5
4) k= 3.6; y = 3.6
Answer: 3) k = 22.5; xy = 22.5
Step-by-step explanation:
If two variables are inversely proportional, it means that an increase in the value of one variable would cause a corresponding decrease in the other variable. Also, a decrease in the value of one variable would cause a corresponding increase in the other variable.
Given that y varies directly with x, if we introduce a constant of proportionality, k, the expression becomes
y = k/x
If y = 2.5 when x = 9, then
2.5 = k/9
k = 9 × 2.5 = 22.5
Therefore, an equation for the inverse variation is
y = 22.5/x
xy = 22.5
Answer: (3)
k = 22.5; xy = 22.5
Step-by-step explanation:
The variable z is directly proportional to x, and inversely proportional to y. When x is 14 and y is 10, z has the value 26.6.
What is the value of z when x= 24, and y= 15
Answer:
Step-by-step explanation:
If two variables are directly proportional, it means that an increase in one variable will cause a corresponding increase in the other variable.
If two variables are inversely proportional, it means that an increase in one variable will cause a corresponding decrease in the other variable.
The variable z is directly proportional to x, and inversely proportional to y. If we introduce a constant k, the equation would be
z = kx/y
When x is 14 and y is 10, z has the value 26.6. It means that
26.6 = 14k/10
Cross multiplying, it becomes
26.6 × 10 = 14k
266 = 14k
k = 266/14
k = 19
The equation becomes
z = 19x/y
When x = 24, and y = 15, the value of z would be
z = 19 × 24/15
z = 30.4
In the following set, the mode is the most effective measure of central tendency if you want to emphasize how small the values are. 32, 21, 68, 21 True False
Answer:
FALSE
Step-by-step explanation:
The mode is a measure of the number with the highest frequency in a group of data. In the set of values (32, 21, 68, 21), the number that appears most is 21 and this is the mode.
If a set of data has two modes, it is bi-modal. If it has several modes, it is multi-modal
Consider the set of data below
2,2,3,3,5,7,8
The numbers 2 and 3 appears with the same frequency, therefore this set of data is bi-modal.
The ratio of the number of teachers to students in a school is 3:35. The ratio of the number of male students to the number of female students is 2:5 there are 500 female students. How many teachers are there
Answer:
60
Step-by-step explanation:
There are 2+5 = 7 ratio units of students. If we multiply the numbers by 5, we can have a total of 35 ratio units of students: 10 : 25.
Now, we can substitute this into the ratio of teachers to students:
teachers : students = 3 : 35
teachers : (male students : female students) = 3 : (10 : 25)
Then the number of teachers is seen to be 3/25 of the number of female students:
(3/25)(500) = 60 . . . teachers
Chloé had 100 math problems to complete over the 3-day weekend. She recorded the number of problems in her math journal. She completed 39/100 of the problems on Friday,5/10 of the problems on Saturday,and another 15 problems on Sunday. Did chloe fill out her math journal correctly ?
The answer is no, Chloe did not fill out her math journal correctly.
To determine if Chloe completed all 100 math problems correctly, we need to calculate the total number of problems she completed over the weekend.
On Friday, Chloe completed [tex]\( \frac{39}{100} \)[/tex] of the problems. This fraction represents the portion of the total problems she completed on Friday. To find out how many problems this corresponds to, we multiply the total number of problems by this fraction:
[tex]\[ \text{Problems on Friday} = \frac{39}{100} \times 100 = 39 \text{ problems} \][/tex]
On Saturday, Chloe completed [tex]\( \frac{5}{10} \)[/tex] of the problems. Again, we multiply the total number of problems by this fraction to find out the number of problems completed on Saturday:
[tex]\[ \text{Problems on Saturday} = \frac{5}{10} \times 100 = 50 \text{ problems} \][/tex]
On Sunday, Chloe completed another 15 problems.
Now, we add up the problems completed each day to find the total number of problems completed over the weekend:
[tex]\[ \text{Total problems completed} = \text{Problems on Friday} + \text{Problems on Saturday} + \text{Problems on Sunday} \][/tex]
[tex]\[ \text{Total problems completed} = 39 + 50 + 15 \][/tex]
[tex]\[ \text{Total problems completed} = 104 \][/tex]
Chloe completed a total of 104 problems, which is more than the 100 problems she was supposed to complete. Therefore, she did not fill out her math journal correctly, as she recorded more problems than were assigned.
Chloé's math journal is not filled out correctly.
Let's calculate how many problems Chloé completed each day:
Friday: She completed [tex]\frac{39}{100}[/tex] of 100 problems, which equals 39 problems.Saturday: She completed [tex]\frac{5}{10}[/tex] (or 50%) of 100 problems, which equals 50 problems.Sunday: She completed 15 problems.Adding these up: 39 (Friday) + 50 (Saturday) + 15 (Sunday) = 104 problems.
This must be incorrect since she only had 100 problems to start with. Therefore, Chloé's math journal is not filled out correctly.
what number can you add to √7 to get a rational nember?
Answer:
you will add -√7
Step-by-step explanation:
the only reason you would do that is so that the equation could equal 0
As of a certain date, there had been a total of 14,404 performances of two shows on Broadway, with 2384 more performances of Show A than Show B. How many performances were there of each show?
Answer: show A had 8394 performances.
Show B had 6010 performances.
Step-by-step explanation:
Let x represent the number of performances of show A.
Let y represent the number of performances of show B.
As of a certain date, there had been a total of 14,404 performances of two shows on Broadway. This means that
x + y = 14404 - - - - - - - - - -1
There was 2384 more performances of Show A than Show B. It means that
x = y + 2384
Substituting x = y + 2384 into equation 1, it becomes
y + 2384 + y = 14404
2y = 14404 - 2384
2y = 12020
y = 12020/2
y = 6010
x = y + 2384 = 6010 + 2384
x = 8394
Answer:
show A had 8394 performances.
Show B had 6010 performances.
Step-by-step explanation:
Let x represent the number of performances of show A.
Let y represent the number of performances of show B.
As of a certain date, there had been a total of 14,404 performances of two shows on Broadway. This means that
x + y = 14404 - - - - - - - - - -1
There was 2384 more performances of Show A than Show B. It means that
x = y + 2384
Substituting x = y + 2384 into equation 1, it becomes
y + 2384 + y = 14404
2y = 14404 - 2384
2y = 12020
y = 12020/2
y = 6010
x = y + 2384 = 6010 + 2384
x = 8394
Step-by-step explanation:
A disc of unit radius is tossed at random onto a large rectangular floor, which is tiled with $4 \times 6$ tiles. Find the probability that the disc is contained entirely in a rectangular tile (and does not intersect the border between two tiles).
Answer:
1/3
Step-by-step explanation:
In order for the disc to be entirely contained in a rectangular tile, its center must be at least 1 unit from the nearest edge. Which means there's a 2 by 4 region that the center can lie in.
So the probability is (2×4) / (4×6) = 8/24 = 1/3.
Factor the expression. 16j2 + 24j + 9
(4j – 3)Factor the expression. 16j2 + 24j + 9
(4j – 3)2
(4j + 3)(4j – 3)
(4j + 3)^2
(4j – 9)(4j + 1)^2
(4j + 3)(4j – 3)
(4j + 3)^2
(4j – 9)(4j + 1)
Option C: [tex](4 j+3)^{2}[/tex] is the correct answer.
Explanation:
The given expression is [tex]16 j^{2}+24 j+9[/tex]
We need to factor the expression.
Let us rewrite the expression as
[tex](4j)^{2}+24 j+(3)^2[/tex]
Also, we can rewrite the term [tex]24j[/tex] as [tex]2(4)(3)j[/tex]
Thus, we have,
[tex](4j)^{2}+2(4j)(3)+(3)^2[/tex]
Hence, the equation is of the form,
[tex](a+b)^{2}=a^{2}+2 a b+b^{2}[/tex]
where [tex]a=4 j[/tex] and [tex]b=3[/tex]
Hence, the factor of the expression can be written as [tex](4 j+3)^{2}[/tex]
Thus, the factored expression is [tex](4 j+3)^{2}[/tex]
Therefore, Option C is the correct answer.
Final answer:
The factored form of the expression 16j^2 + 24j + 9 is (4j + 3)².
Explanation:
To factor the expression 16j2 + 24j + 9, we look for two binomials ((aj + b)(cj + d)) that when multiplied together, give us the original quadratic expression. The factors of 16j2 are 4j imes 4j, and the factors of 9 are 3 imes 3. Our binomial factors will have the format (4j + 3).
Expanding the binomial (4j + 3)², we have:
(4j + 3) imes (4j + 3)
= 16j2 + 12j + 12j + 9
= 16j2 + 24j + 9
This matches the original expression exactly, so the factored form of the expression is (4j + 3)².
Please help!!! ASAP someone please
Answer:
0.31 yr
Step-by-step explanation:
The formula for interest compounded continuously is
[tex]FV = PVe^{rt}[/tex]
FV = future value, and
PV = present value
If FV is twice the PV, we can calculate the doubling time, t
[tex]\begin{array}{rcl}2 & = & e^{rt}\\\ln 2 & = & rt\\t & = & \dfrac{\ln 2}{r} \\\end{array}[/tex]
1. Brianna's doubling time
[tex]\begin{array}{rcl}t & = & \dfrac{\ln 2}{0.065}\\\\& = & \textbf{10.663 yr}\\\end{array}[/tex]
2. Adam's doubling time
The formula for interest compounded periodically is
[tex]FV = PV\left (1 + \dfrac{r}{n} \right )^{nt}[/tex]
where
n = the number of payments per year
If FV is twice the PV, we can calculate the doubling time.
[tex]\begin{array}{rcl}2 & = & \left (1 + \dfrac{0.0675}{4} \right )^{4t}\\\\&= & (1 + 0.016875 )^{4t}\\& = & 1.016875^{4t}\\\ln 2& = & 4 (\ln 1.01688)\times t \\& = & 0.066937t\\t& = & \dfrac{\ln 2}{0.066937}\\\\& = & \textbf{10.355 yr}\\\end{array}[/tex]
3. Brianna's doubling time vs Adam's
10.663 - 10.355 = 0.31 yr
It would take 0.31 yr longer for Brianna's money to double than Adam's.
A daycare charges a base fee of 333 dollars plus 0.500.500, point, 50 dollars per minute for late (after closing time) pick-ups. Albin had to pay 10.5010.5010, point, 50 dollars for a late pick-up. Albin uses the equation, 10.50=0.50a+310.50=0.50a+310, point, 50, equals, 0, point, 50, a, plus, 3 to represent the situation.
Answer:
a represents the Number of Minutes Late, (a=15 in this case)
Step-by-step explanation:
If the daycare charges a base fee of $3 plus $0.50 per minute late for late pickups(after closing time).
Albin on arrival for pickup had to pay $10.50;
She uses the equation
10.50=0.50a+3
0.50a=10.50-3
0.50a=7.50
a=7.50/0.5
a= 15
It means Albin was 15 minutes late to a pickup.