Answer
x = 55/4 or x = 13.75
Step-by-step explanation
By the way, the <b> isn't actually apart of the problem, seems to just be a webpage encoding issue maybe.
A college student is deciding how many hours to work at a part time job(x) and how many hours to work at an internship (y). The job pays $24 and hour, and the internship pays $12 an hour. The student needs to work less than 15 hours a week but needs to earn at least $240 a week to pay expenses. Write 2 systems of inequalities to represent all the combinations of number of hours the student can work at the job and internship
Answer:
x + y < 152x + y ≥ 20-------------------------------
Total hours worked is x + y.
Earning from the part time job is 24x, from the internship is 12y.
Inequality for the number of hours:
x + y < 15Inequality for the earning:
24x + 12y ≥ 240This can be simplified by dividing all terms by 12:
2x + y ≥ 20Answer:
[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]
[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]
Step-by-step explanation:
Part-time job
Let x be the number of hours worked.$24 = pay per hour.Internship
Let y be the number of hours worked.$12 = pay per hour.The student needs to work less than 15 hours a week:
[tex]\implies x+y < 15[/tex]
The student needs to earn at least $240 a week:
[tex]\implies 24x+12y \geq 240[/tex]
Therefore, the system of inequalities is:
[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]
The second inequality can be simplified by dividing each term by 12:
[tex]\implies \dfrac{24x}{12}+\dfrac{12y}{12} \geq \dfrac{240}{12}[/tex]
[tex]\implies 2x+y \geq 20[/tex]
Therefore, a second system of inequalities is:
[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]
To solve the system of equalities, graph both inequalities and shade the overlapping region.
Any (x, y) point in the overlapping region is a solution to the system of inequalities.
Triangle A'B'C' is a reflection of triangle ABC across line BC. Prove that ray BC is the angle bisector of angle ABA'.
Proof of ray BC is the angle bisector of angle ABA' is given.
What are angle bisectors?Angle bisectors are lines that cut across the angle under consideration. The term "bisect" means to divide into two equal portions. The considered angle is therefore divided in half by the bisected halves.
A graph will move exactly to the other side of an axis, such as the x-axis, as if it were a mirror when it is reflected along that axis.
Because it is symmetrical, each point is as far from the axis of reflection as its mirror counterpart.
Triangle A'B'C' is a mirror of triangle ABC over line BC, as shown by the provided issue.
Therefore, <A'B'C' = <ABC
by virtue of congruent triangles' characteristics. Means that if the sides' lengths are equal, the angles' measures are equal, and they may be overlaid.
Therefore, the ray BC is the angle, bisector of angle ABA'.
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Square E has sides of length e cm Square F has sides of length f cm the area of square E is 69% greater than the area of square F
work out the ratio of e:f
Pa brainliest po thanks
Which one. Multiple choice.
In the given relation, 1 is not a domain.
What is domain?The domain of a function is the set of all possible inputs for the function. or we can that in an ordered pair, all the values of x are called domain.
All the values that go into a function. The output values are called the range.
The domain of a function is the set of all possible inputs for the function.
If a function f provides a way to successfully produce a single value y using for that purpose a value for x than that chosen x-value is said to belong to the domain of f.
Given that, a function,
{(5, 1), (4, -3), (3, -1)}
We know, a domain is the set of all "x" values.
Therefore, domain of the function are, 5, 4 and 3
But, if we see, 1 is one of the values of y.
Hence, 1 is not a domain.
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5. Which function g(x) represents the function f(x)
horizontal shift right 1 unit?
a. g(x)= 2/x + 11 + 3
b. g(x) 21x11 + 3
C. g(x) = 2/x - 21+5
d. g(x)= 2/x + 5
6. Which function g(x) represents the function f(x) = 2√x - 1 + 5 after a vertical shift up 8 units and a
horizontal shift left 2 units?
a. g(x)
3 + 13
2√x
b. g(x)= 2√x 2 +8
2√x + 1 + 13
c. g(x)
d. g(x) = 2√x + 2 +8
-
a.
7. Which transformations will map f(x) onto g(x)?
Shifting g(x) 8 units right and 5 units up.
Shifting g(x) 4 units left and 3 units down.
Shifting g(x) 2 units up and 4 units right
d. Shifting g(x) 8 units left and 5 units down.
C.
b.
21x11+ 2 after a vertical shift up 3 units and a
ROD
10
100
X
2 4 6
2
4
+6
e
10
The functions after the translations are given as follows:
5. g(x) = 2|x - 2| + 5. (option C).
6. [tex]g(x) = 2\sqrt{x + 1} + 13[/tex] (option C).
7. The transformation that will map f(x) to g(x) is given as follows:
d. Shifting g(x) 8 units left and 5 units down.
What are the translations?There are four translations, and they are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.For item 5, the translations are given as follows:
Vertical shift up 3 units -> g(x) = f(x) + 3.Horizontal shift right 1 unit -> g(x) = f(x - 1).Hence the function is given as follows:
g(x) = 2|x - 1 - 1| + 2 + 3
g(x) = 2|x - 2| + 5
Meaning that option c is correct.
For item 6, the translations are given as follows:
Vertical shift up 8 units -> g(x) = f(x) + 8.Horizontal shift left 2 units -> g(x) = f(x + 2).Hence the function is then given as follows:
[tex]g(x) = 2\sqrt{x - 1 + 2} + 5 + 8[/tex]
[tex]g(x) = 2\sqrt{x + 1} + 13[/tex]
Meaning that option c is correct.
For the transformations in item 7, we look at the vertex, which is the turning point, hence:
Down 5 units.Left 8 units.Meaning that option d is correct.
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(04.05 MC) Determine if the ordered pair (6, 4) is a solution to the inequality y>-x+7. Yes, because (6, 4) is above the line O No, because (6, 4) is below the line OYes, because (6, 4) is on the line O No, because (6, 4) is on the line 14
No, because (6,4) is on the line.
What is an inequality?A connection between two expressions or values that is not equal to each other is referred to as "inequality" in mathematics.
Given:
Inequality y > -x+7.
To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
To prove that the ordered pair (6, 4) is a solution to the inequality:
We have to find that the ordered pair (6,4) is a solution of given inequality or not.
Inequality y > -x+7.
Substitute x=6
y > -6 + 7
y > 1
The value of y is greater than 1 not equal to 4.
Therefore, (6,4) is not a solution of given inequality.
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Answer:
No, because (6, 4) is on the line
Step-by-step explanation:
got it right
A school requires 2 iPads for every 5 students. How many iPads are needed for 145 students?
Answer:
58 iPads
Step-by-step explanation:
To calculate how many iPads are needed for 145 students, we can use the given ratio of 2 iPads for every 5 students.
First, find out how many groups of 5 students are in 145 students by dividing 145 by 5:
[tex]\sf \dfrac{145\; students}{5\; students/group} = 29\;groups\; of \;5 \;students[/tex]
Now, for each group of 5 students, we need 2 iPads. So, multiply the number of groups of 5 students by 2 to find the total number of iPads needed:
[tex]\sf 29 \;groups \times2\; iPads/group = 58\; iPads[/tex]
Therefore, 58 iPads are needed for 145 students.
For spring break this year your family decided to visit Michigan, but it snows the first weekend you are there. You decide to make a snowman. If the bottom ball is 3 feet across, the middle ball is 2 feet across, and the top is 1 foot across, how much snow is needed to build the whole snowman? Round your answer to the nearest cubic foot.
The snow is needed to build the whole snowman is 19 cubic foot. Hence option A is the correct option.
What is a sphere?
The collection of points in three dimensions that are all the same distance from the center (the radius) or the outcome of rotating a circle around one of its diameters. A sphere's parts and characteristics are comparable to those of a circle.
Given that the diameter of the bottom ball is 3 feet, the diameter of middle ball is 2 feet, and the diameter of the top ball 1.
The radius of a sphere is the half of its diameter.
The radius of the bottom ball is 3/2 feet =1.5 feet
The radius of the middle ball is 2/2 feet = 1 feet.
The radius of the top ball is 1/2 feet = 0.5 feet.
The volume of a sphere is 4/3 × ∏r³.
The volume of bottom ball is 4/3 × ∏ × (1.5)³ cubic foot.
The volume of middle ball is 4/3 × ∏ × (1)³ cubic foot.
The volume of middle ball is 4/3 × ∏ × (0.5)³ cubic foot.
The total amount of snow is
4/3 × ∏ × (1.5)³ + 4/3 × ∏ × (1)³ + 4/3 × ∏ × (0.5)³
= 4/3 × ∏ [1.5³ +1³ + 0.5³ ]
= 4/3 × ∏× 4.5
= 18.84
≈ 19 cubic foot
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100 POINTS IF YOU CAN ANSWER THIS
Which of the following number of selected people having received a ticket would constitute an unusual event?
A. 4
B. 5
C. 1
D. 2
Answer: B
Step-by-step explanation:
Answer: The answer is D. 2 | 0.25
Step-by-step explanation:
I don't really have a good explanation, but I hope it helps!
Kiera's lemon cookie recipe calls for 5 cups of sugar. How much sugar would Kiera use to make 3 5/8 batches of cookies?
Answer:18 1/8
Step-by-step explanation:
5x3=15
5x5/8=25/8=3 1/8
15+3 1/8=18 1/8
I need help with Venn Diagrams . In the screen shot is all the info please help and try your best to explain it thanks.
Answer:
Please see the second image attached to this response post.
Step-by-step explanation:
You have most of the numbers right. So I am going to fill in those in the correct boxes.
We could use set intersection notation but it complicates the explanation so i will just use variables for the missing boxes
For the missing boxes, I am adding variables to denote the missing numbers. The explanation is lengthy. For example, the variable x is the number of readers who read both the Buzz and the Rag less the number of readers who read all three newspapers. The other variables can be interpreted in the same way.
The variable A is the number of readers who read all three newspapers
The number of people who read both Buzz and Rag is x + A, the number who read both Buzz and Gossip is y + A, and the number who read both Rag and Gossip is z + A
So we have
x + A = 76 [a]
y + A = 125 [b]
z + A = 77 [c]
Adding up we get x + y + z + 3A = 76 + 125 + 77 = 278
or
x + y + z + 3A = 278 [1]
If we look at the four unknowns and add them up we get
x + y + z + A
However this is the number of people who are left over from the total readership of 411
Therefore x + y + z + A = 411 -(76 + 63 + 38 + 38)
==> x + y + z + A = 411 - 215
==> x + y + z + A = 196 [2]
Subtract [2] from [1] to get
2A = 278 - 196
2A = 82
A = 41
Now that we have A we can compute x, y and z from equations [a], [b] and [c] to get
x = 35
y = 84
z = 36
Assuming I have not made some silly mistakes, the answer should be as in the second image with all values filled in.
Unfortunately, I have no way of checking the answer so please let me know if all is well.
This is a great question
Good Luck
Look at the triangles shown below.
5
Which statement is TRUE?
Answer: B
Step-by-step explanation:
vertical angles are =
PLEASE HELP Consider triangle ABC and triangle DFE.
Possible answers:
1st blank
A. a reflection of
B. a translation of
C. a translation and dilation of
D. a rotation and reflection of
2nd blank
A. only rigid transformations
B. transformations involving a dilation
3rd blank
A. are congruent
B. are not congruent
C,B and A are the correct options
What is congruent?
Congruent refers to something that is "absolutely equal" in terms of size and form. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, then stack them on top of one another. We will see that they will superimpose, or be positioned entirely on top of, one another. This demonstrates the congruence of the two circles. The circles below may be put perfectly over one another and have the same radius, hence they are considered to be congruent.
triangle DFE is a translation and dilation of triangle ABC
since triangle ABC uses transformations involving a dilation to map onto triangle DFE ,
the triangles are congruent
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PLEASE EXPLAIN AND SHOW YOUR WORK THANK YOU!!
Solve as a MIXED NUMBER:
-2.25 + 0.4x = -2.8
THANK YOU!!!
Answer:
x=-1 3/8
Step-by-step explanation:
-2.25 + 0.4x = -2.8
-2.25 + 2.25 + 0.4x = -2.8 + 2.25 ==> add 2.25 on both sides to isolate x
0.4x = -0.55
(0.4x = -0.55)*20 ==> multiply the equation by 20 to remove decimals
8x = -11
x=-11/8
x=-(3+8)/8 ==> turn x into a mixed number
x=-3/8 - 8/8
x=-3/8 - 1 ==> simplify
x=-1 - 3/8
x=-(1 + 3/8)
x=-1 3/8
Which system of inequalities is shown?
The equations of inequalities are y < 4 and y > x.
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The line of the graph is not solid. The lines of the graph is dotted. Thus the inequality sign will be less than or greater than.
One graph line is parallel to x-axis and it intersect y axis at (0,4).
The equation of the line that is parallel to x-axis and it intersect y axis at (0,a), then the equation of the line is y = a
The equation of the line parallel to x-axis is y = 4.
The equation of line that passes through origin is y = mx
The line passes through the point (1,1).
Putting x = 1 and y = 1 in y = mx:
1 = m
Therefore the equations of lines are y = x and y = 4
The inequality will be y < x or y > x for the line y = x.
The inequality will be y < 4 or y > 4 for the line y = 4.
(-2,0) is a point on the shaded area.
Putting x = -2 and y = 0 in y > x
0 > -2 true.
The inequality is y > x
Putting x = -2 and y = 0 in y < 4
0 < 4 true.
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These figures are similar. The perimeter and area of one are given. The perimeter of the other is also given. Find its area and round to the nearest tenth.
Perimeter= 20m
Area=19.6m^2
Perimeter=34m
What is the Area=
The area of the larger figure that is similar to the smaller one is: 28.2 m².
How to Find the Area of Similar Figures?Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:
Area of figure A / Area of figure B = a²/b².
Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:
Perimeter of smaller figure = 20 m
Area of smaller figure = 19.6 m²
Perimeter of larger figure = 34m
Area of larger figure = x
Therefore:
20/34 = a/b
Simplify:
10/17 = a/b.
Find the area (x) of the larger figure using the formula given above:
10²/12² = 19.6/x
100/144 = 19.6/x
100x = 2,822.4
x = 2,822.4/100
x ≈ 28.2 m²
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a) A larger triangle with a height of 21 cm is made in this way from smaller triangles with a height of 3 cm and an area of 4.8 cm", What is the area of this larger triangle?
Answer:
235.2
Step-by-step explanation:
This is a multistep problem. We'll need to first find the base value of the smaller triangle using the area formula for a triangle:
[tex]\frac{bh}{2}[/tex]
b <-- base
h<--- height
[tex]\frac{b3}{2}=4.8[/tex]
Solve for the b value
3b = 9.6 ---- multiply both sides by 2
b = 3.2 --- divide both sides by 3
3.2 is the base value of our smaller triangle.
Now, with this new information, we need to set up a proportion to find the base value of the larger triangle. A proportion is appropriate for this scenario because the larger triangle was a dilation from the smaller triangle.
[tex]\frac{21}{b} =\frac{3}{3.2}[/tex]
b --- represents the base value
Now solve the proportion by cross multiplying:
3b = 67.2
b = 22.4
Now we have the base value of our larger triangle. Finally, we can find the area of the larger triangle with the area formula:
[tex]\frac{bh}{2} =\frac{22.4(21)}{2} =\frac{470.4}{2} =235.2[/tex]
Josephine started to watch a movie the movie starts at 18:30 the movie was 1 hour and 53 minutes long but part way through it she paused it for 16 minutes what time did the movie end?
Answer:
The movie ended at 7:39 a.m.
Step-by-step explanation:
She started at 6:30. 53 minutes added to that would be 7:23. Another 16 minutes added to that would be 7:39.
The movie will end at 20:39.
What is time conversion?Conversion Time means a time which falls after the Calculation Time and is the time at which the admission of the Ordinary Shares arising on Conversion to the Official List becomes effective.
Given that, Josephine started to watch a movie the movie starts at 18:30 the movie was 1 hour and 53 minutes long but part way through it, she paused it for 16 minutes
The total time taken = 1 hour + 53 minutes + 16 minutes = 1 hours + 69 minutes
= 1 hour + 60 minutes + 9 minutes
= 1 hours + 1 hours + 9 minutes
= 2 hours + 9 minutes
Therefore, total time she took for movie is 2 hr 9 min
Since, the movie started at 18:30,
Therefore, 18:30 + 2 hour 9 minute
= 20 hours + 39 minutes
Hence, The movie will end at 20:39
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which analysis technique simulates a model's outcome many times to provide a statistical distribution of the calculated results?
The answer is that the Monte Carlo analysis simulates a model’s outcome many times to provide a statistical distribution of the calculated results.
Now, what is Monte Carlo analysis technique?
Monte Carlo Analysis is a risk management technique used to conduct a quantitative analysis of risks.
This mathematical technique is used to analyze the impact of risks on your project — in other words, if this risk occurs, how will it affect the schedule or the cost of the project?
So, Monte Carlo Analysis gives you a range of possible outcomes and probabilities to allow you to consider the likelihood of different scenarios.
For example, let’s say you don’t know how long your project will take. You have a rough estimate of the duration of each project task. Using this, you develop a best-case scenario (optimistic) and worst-case scenario (pessimistic) duration for each task.
You can then use Monte Carlo to analyze all the potential combinations and give you probabilities of when the project will complete.
Other major benefits of this technique is -
1. It Provides early indication of how likely you are to meet project targets.
2. Can be used to create a more real budget and schedule.
3. Predicts the likelihood of schedule .
4. Gives quantitative measure of risks to assess impacts
5. Provides objective data for decision making.
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What is the experimental probability that the coin will land on heads?
Step-by-step explanation: Without more information, it is impossible to determine the experimental probability that a coin will land on heads. The experimental probability of an event is determined by performing experiments and observing the results. For example, if we were to flip a coin 10 times and it landed on heads 6 times, we could say that the experimental probability of the coin landing on heads is 6/10, or 0.6. However, without knowing the results of any experiments, it is impossible to determine the experimental probability of the coin landing on heads.
Answer: We should ASSUME 1/2 or 50%
Step-by-step explanation: Since we don't know the exact number of times the person flipped the coin, we must infer you mean he/she flips the coin once. So, If a coin has 2 sides and the probability is 100% total, we can write an expression to help us solve:
P(Probability)= 100/2
P= 50% or 1/2
How I got 50% or 1/2 is I took the whole probability (100%) and divided it by 2. (2 sides on a coin)
I hope this helped (at least)
A group of 200 adults were asked whether they exercise and what they are vegetarian
Step-by-step explanation:
(a) What percentage of the adults exercise?
₹
(b) What percentage of the adults are vegetarian?
€
(c) What percentage of the adults who are vegetarian exercise? [ (d) Is there evidence that adults who are vegetarian tend to be exercisers more often than average?
Yes, because the percentage found in part (c) is much greater than the percentage found in part (a).
Yes, because the percentage found in part (c) is much greater than the percentage found in part ((b).
No, because the percentage found in part (c) is about the same as the percentage found in part ((a).
No, because the percentage found in part (c) is about the same as the percentage found in part ((b).
Aniyah invests $2300 in one account and $1400 in an account paying 4 % higher interest. At the end of one year she had earned $130 in interest. At what rates did she invest
She invested $2300 at 2% and $1400 at 6% interest.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, P₁ = $2300, P₂ = $1400, t₁ = t₂ = 1 and r₂ = r₁ + 4.
The sum of the simple interests from both these accounts is $130.
Therefore, (2300×r₁×1)/100 + (1400×(r₁ + 4)×1)/100 = 130
2300r₁/100 + 1400r₁/100 + 5600/100 = 130.
2300r₁ + 1400r₁ + 5600 = 13000.
3700r₁ = 7400.
37r₁ = 74.
r₁ = 2% and hence r₂ = 6%.
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x = [?]
4x-2 3x + 14
Write a rule for the glide reflection that maps ABC with vertices A(-4,-2), B(-2, 6).
and C(4, 4) to A'B'C' with vertices A'(4, -2), B(6, -6), and C'(12,-4).
The glide reflection that maps ABC to A'B'C' is given as follows:
Reflection over the line y = x - 9.Translation right 8 units.What is a glide reflection?The glide reflection is a combination of a reflection with a translation.
The line of reflection passes through the midpoint of a pair of vertices, being perpendicular to the vertex.
The midpoint of segment A'B' is given as follows:
x = (4 + 6)/2 = 5.y = (-2 - 6)/2 = -4.The slope of this segment is given as follows:
m = (-6 - (-2))/(6 - 4) = -1.
Then the slope of the reflection line is of:
m = 1.
(as the reflection line is perpendicular to the segment, meaning that the multiplication of their slopes is of -1).
Then:
y = x + b.
When x = 5, y = -4, then the intercept b is calculated as follows:
-4 = 5 + b
b = -9.
Thus the reflection line is of:
y = x - 9.
Then the translation is given subtracting the coordinates of one of the vertices, as follows:
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What is the slope of y = − 5 + 4x
Write a cosine function that has a midline of 3, an amplitude of 5 and a period of 2.
Y = 2*cos(3pi*x) + 5 is the cosine function with a midline of 5, an amplitude of 2, and a frequency of 3/2.
What is a Cosine Function?A crucial periodic function in trigonometry is the cosine function.
Utilizing the unit circle will make understanding the cosine function the simplest.
Draw a unit circle on the coordinate plane, center the angle at the origin, and label one side as the positive x-axis for the supplied angle measure.
The point where the other side of the angle intersects the circle has an x-coordinate of cos(), and a y-coordinate of sin().
According to our answer-
B = 2pi/T, where T is the period and T = 1/f is the frequency; T is the period
Determines horizontal phase shift by using
C =determines vertical shift.
When solving the given issue, D = midline = 5
A = amplitude = 2.
B = 2pi/T = 2pi/(2/3) = 3pi since frequency = 3/2 means that the period is T = 2/3, which is the reciprocal of the frequency.
C = 0.
The result of adding everything up is A = 2, B = 3pi, C = 0, and D = 5.
so,
A*cos(B(x-C)) + D = y
y = 2*cos(3pi(x-0)), plus 5.
y = cos(3pi*x) * 2 * + 5
Hence, Y = 2*cos(3pi*x) + 5 is the cosine function with a midline of 5, an amplitude of 2, and a frequency of 3/2.
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40 PTS
TWO PART QUESTION NEED! :)))
You decide to invest $500 into a 4-year CD that pays 2.85% interest
compounded monthly.
Use the compound interest formula:A = P(1 + r/n) ^nt to give:
Part a. The future value in 4 years.
Part b. The interest gained in 4 years.
The future value of investment is $560.30, and interest gained in 4 years is 136.8%
What is compound interest?The interest regarding loan or investment that increases exponentially with respect to time is called compound interest.
Why is compound interest used?We use compound interest so as to enhance our investment in a large scale.
Given, Amount invested, P= $500
compound interest rate, r= 2.85%
number of time period, t = 4 years
number of times interest applied per time period, n =12 (as interest compound monthly)
Final amount, A
we used compound interest formula, A= P(1+r/n)∧nt
A= 500(1+0.0285/12) ∧12×4
Final amount, A= $560.30
The future value = $560.30
Interested gained in 4 years with compound monthly =2.85x12x4 =136.8%
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is it possible for the results of a study to show a non-zero correlation, even though the correlation for the general population is zero?
True, is it possible for the results of a study to show a non-zero correlation, even though the correlation for the general population is zero.
When a correlation is statistically significant, it is a significant and strong correlation. Even a very slight association can be statistically significant with a very large sample size.
While the correlation for the entire population is zero, it is nevertheless feasible for a sample to have a true, non-zero correlation.
When there is no association in a correlational analysis, what happens?
The variables fluctuate in opposite directions when there is a negative correlation. There is no association between the variables if there is zero correlation.
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One gallon of gasoline in Buffalo, New York costs $2.29. In Toronto, Canada, one liter of gasoline costs $0.91. There are 3.8 liters in one gallon. How much does one gallon of gas cost in Toronto? Round your answer to the nearest cent.
Answer: One gallon of gas in Toronto would cost approximately $3.43. To find this, first convert the price of gasoline in Buffalo to liters. Since there are 3.8 liters in one gallon, one gallon of gas in Buffalo costs $2.29 * 3.8 liters = $8.69. Next, divide the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.91 / 3.8 liters/gallon = $0.24/liter. Finally, multiply the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.24/liter * 3.8 liters/gallon = $0.91/gallon. Round this to the nearest cent to find that one gallon of gas in Toronto costs $0.91/gallon = $<<0.91/gallon=0.91>>0.91.
Work out:
(1.2 × 10′²) × (2 × 10ª)/3 x 10-5
Give your answer in standard
form.
The standard form of the expression is [tex]0.000286 \times 10^a[/tex].
What is a standard form?
A standard form is a document that contains predetermined information in a specific format, such as a contract or agreement. Standard forms are often used to ensure uniformity and efficiency among different parties. Standard forms may include a variety of information, including contact details, payment information, and other important details related to a transaction. By utilizing a standard form, individuals and organizations are able to save time and effort when completing administrative tasks. Standard forms can also be used to ensure that all parties involved in a transaction are aware of the terms and conditions.
The given expression is
[tex]=(1.2 \times 10^2) \times \frac{(2 \times 10^a)}{3} \times 10^{-5}\\\\=129 \times\frac{2}{3}\times\frac{10^a}{3}\times0.00001\\\\=0.000286 \times 10^a[/tex]
Hence, the standard form of the expression is [tex]0.000286 \times 10^a[/tex].
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