It would take about 2.6 years for the value of the account to reach $5,920, assuming no deposits or withdrawals are made.
We can use the formula for compound interest to solve the problem;
A = [tex]P(1+r/n)^{(nt)}[/tex]
where;
A is the amount after t years
P is principal (the initial amount invested)
r is annual interest rate (as a decimal)
n is number of times the interest is compounded per year
t is the time in years
In this case, we know that;
P = $4,900
r = 0.03 (3% expressed as a decimal)
n = 12 (interest is compounded monthly)
A = $5,920
We can solve for t by plugging in these values and solving for t;
$5,920 = $4,900[tex](1+0.03/12)^{12t}[/tex]
Divide both sides by $4,900;
1.20918367347 = [tex](1+0.03/12)^{12t}[/tex]
Take the natural logarithm of both sides;
ln(1.20918367347) = ln([tex](1+0.03/12)^{12t}[/tex])
Use the property of logarithms that allows us to bring the exponent down;
ln(1.20918367347) = 12t ln(1 + 0.03/12)
Divide both sides by 12 ln(1 + 0.03/12)
t = ln(1.20918367347) / (12 ln(1 + 0.03/12))
t ≈ 2.6 years
Therefore, it would take about 2.6 years.
--The given question is incomplete, the complete question is
"Ella invested $4,900 in an account paying an interest rate of 3% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $5,920?"--
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The solution to a system of two linear equations is x = 3; y = 9.
How could the intersection of the graphs of the two equations be located on a coordinate grid?
What does the solution to a system of two linear equations mean on the graph?
Can you have more than one solution to a Linear system of equations?
Can you have exactly two solutions to a Linear system of equations?
Can you have no solutions to a Linear system of equations?
:: From the origin, move 3 units up and 9 units right
:: The point where the lines cross the y-axis
:: The point that the two lines DO NOT have in common
=
:: No, because lines are straight
POSSIBLE POINTS: 13.0-
From the origin, move 3 units right and 9 units up
::The point of intersection of the two lines
Yes, if both lines are the same exact line :: Yes, if the lines are parallel
:: Yes, because the lines could cross each other twice
The lines intercept at the point (3, 9), and:
A system of linear equations can have one solution, no solutions, and infinite solutions, these are the only options.
How could the intersection of the graphs of the two equations be located on a coordinate grid?If we have a system of equations, the solutions of the system are the points where the graphs of the equations intercept.
Here we know that the solution of the system of linaer equations is (3, 9), this means that the interception of the linear equations is at that point.
Can you have more than one solution to a Linear system of equations?
Yes, you can have:
no solution.
one solution
infinite solutions.
These are the 3 options.
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WILL GIVE TRUE 100 POINTS FOR CORRECT ANSWER AND WILL GIVE BRAINLIEST I will report you if you try to just get the points instead of helping me and getting points
The probability that an intern had a Computer Science Major and did not get hired is 36.2%. The probability that an intern had a major other than Computer Science is 51.2%. The probability that a Computer Science Major was hired is 48.6%. The probability that an intern with a major other than Computer Science was not hired is 68.3%. So, the column A 1,2,3 and 4 matches to c, b, a and d of column B.
Conditional - 48.6% This probability represents the chance that an intern with a Computer Science Major was hired, and is calculated as the number of CS majors hired (58) divided by the total number of CS majors (160). so, 3 matches a.
Joint - 51.2% This probability represents the chance that an intern with a major other than Computer Science was not hired, and is calculated as the number of non-CS majors not hired (36) divided by the total number of non-CS majors (74). so, 2 matches b.
Conditional - 36.2% This probability represents the chance that an intern had a Computer Science Major and did not get hired, and is calculated as the number of CS majors not hired (102) divided by the total number of applicants not hired (138). so, 1 matches c.
Marginal - 68.3% This probability represents the total proportion of interns who were not hired, and is calculated as the total number of interns not hired (138) divided by the total number of applicants (234). so, 4 matches d.
Joint - 43.6% This probability represents the chance that an intern had a Computer Science Major and did not get hired, and is calculated as the number of CS majors not hired (102) divided by the total number of applicants (234).
Marginal - 31.6% This probability represents the total proportion of interns who were hired, and is calculated as the total number of interns hired (96) divided by the total number of applicants (234).
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Find the equation of a line parallel to x-axis at a distance of 2 units below x-axis.
Step-by-step explanation:
its y = 2
......
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.
...
.
.
..
What is the polar form of -2√3-6i?
The polar form of the complex number -2√3 - 6i is r , θ = (2√24 , 60°)
How to find the polar form of the complex number?The polar form of a complex number is given by r = x + iy is r , θ where r = √(x² + y²) and θ = tan⁻¹y/x
So, to find the polar form of the complex number, -2√3 - 6i we proceed as follows. -2√3 - 6i
Since r = x + iy where
x = -2√3 and y = -6So, substituting the values of the variables into the equation, we have that the magnitude r = √(x² + y²)
= √((-2√3)² + ( -6)²)
= √(4 × 3 + 36)
= √(12 + 36)
= √48
= √(24 × 4)
= 2√24
The angle θ = tan⁻¹y/x where
y = - 6 and x = -2√3So, substituting the values of the variables into the equation, we have that
θ = tan⁻¹y/x
= tan⁻¹(-6/-2√3)
= tan⁻¹(3/√3 × √3/√3)
= tan⁻¹(3√3/(√3 × √3)]
= tan⁻¹(3√3/3]
= tan⁻¹√3
= 60°
So, the polar form is r , θ = (2√24 , 60°)
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On a vacation to the mountains, you use 3/7 of a tank of gas to travel 9/14 of the way to the mountains. How much gas is needed to travel 2/3 of the entire distance to the mountains?
Give your answer as a simplified fraction, and do not include the units.
Provide your answer below:
Answer:
Step-by-step explanation:
Answer: 4/9. Based on the given conditions, formulate:: 2/3 * 3/7 / 9/14 Divide a fraction by multiplying its rec.
In a survey, 23 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $33 and standard deviation of $13. Construct a confidence interval at a 95% confidence level.
we can say with 95% confidence that the population mean of how much people spend on their child's last birthday gift is between $27.31 and $38.69.
What is confidence interval?
A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.
Since we want a 95% confidence interval, the level of significance (α) is 0.05/2 = 0.025. We can use a t-distribution table to find the t-score that corresponds to this level of significance and the degrees of freedom (df) = n - 1 = 23 - 1 = 22.
From the t-distribution table, the t-score with 22 degrees of freedom and a 0.025 level of significance is approximately 2.074.
Now we can plug in the values and calculate the confidence interval:
CI = 33 ± 2.074*(13/√23)
= 33 ± 5.693
= (27.307, 38.693)
Therefore, we can say with 95% confidence that the population mean of how much people spend on their child's last birthday gift is between $27.31 and $38.69.
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How many solutions does 12x+5=5+12x have
Answer: infinite
Step-by-step explanation:
infinite
you get 5=5 so ther is not x in the answer and they are equal so for any value you put in x you get a valid answer
Answer:
Only 1
Which X is 0
also can say as infinite
Step-by-step explanation:
Give one pair of supplementary angles and one pair of vertical angles shown in the figure below.
Answer:
supplementary angles: ∠5 and ∠7vertical angles: ∠5 and ∠8Step-by-step explanation:
You want to identify a pair of supplementary angles, and a pair of vertical angles in the given figure.
Supplementary anglesTwo angles are supplementary if they total 180°. This will be the case for any linear pair of angles. A linear pair of angles combines to form a straight line.
Supplementary angle pairs in the figure are ...
(1, 2), (1, 3), (2, 4), (3, 4), (5, 6), (5, 7), (6, 8), (7, 8)
Vertical anglesTwo angles are vertical angles if they are formed by two intersecting lines and if their shared vertex is the point where the lines cross. The angles do not share a side, but have sides formed from opposite rays.
A pair of crossing lines forms two sets of vertical angles.
Vertical angle pairs in the figure are ...
(1, 4), (2, 3), (5, 8), (6, 7)
Your answer will be a pair of angles from the first list, and a pair of angles from the second list. The highlighted pairs are the ones we list at the top of the answer.
__
Additional comment
Angles may be supplementary in a variety of other contexts. Adjacent angles in a parallelogram are supplementary, as are opposite angles in a quadrilateral inscribed in a circle. When parallel lines are crossed by a transversal, consecutive interior angles are supplementary, as are consecutive exterior angles. (There are no parallel lines in the given figure for this problem.)
A fair coin has been tossed a thousand times and the number of heads and tails recorded. Which of the following statements describes a more likely outcome (as compared to the others)? Explain/justify your answer.
A: The number of tails is 601 and the number of heads is 399.
B: 47% of the tosses were heads.
C: There were 20 more heads tossed than tails
since the coin is fair the probability of it being heads or tails is exactly 50%. and the experimental probability should be as close as possible to 50% so we immedietly know answer A is wrong since the difference between 601 and 399 is too big. now we have to see if B or C is closer to 50%. to do that we turn C into a percentage and since there were 1000 tosses 10 tosses are 1%. and since there was a difference of 20 tosses in C the difference was 2% in C. and for B we know the experimental probability of heads was 47% and the probability of tails was 53% so the difference for B is 6%. And since 2% is less than 6% the answer C is the most correct. also pls mark as brainliest answer
The equation y = 10x − 22 models the amount of money y, in dollars, that Raina makes babysitting for x hours, after buying some games to take on her babysitting jobs. How many hours does Raina need to babysit to make $28?
Answer: 5 hours
Step-by-step explanation:
Since y = money, plug in 28 for y
28= 10x-22
Add 22 over to the 28 to get 50= 10x
Divide 50 by 10 to find x to be 5 which the hours
Suppose that you are conducting a study on the effectiveness of a new teaching method and that you wish to use a hypothesis test to support your claim regarding the mean test score under this method. What restrictions are there in the wording of the claim? Will your claim become the null hypothesis or the alternative hypothesis, or does it depend on the situation? Give an example of a claim which is incorrectly worded.
Answer & Step-by-step explanation:
In hypothesis testing, the claim being made is called the alternative hypothesis. The null hypothesis is the opposing statement, and it is presumed to be true until sufficient evidence suggests otherwise. The wording of the claim must be specific and precise, and one must clearly state the population, the parameter of interest, and the direction of the hypothesis test (i.e., one-tailed or two-tailed).
For example, a well-worded alternative hypothesis might be "The new teaching method will result in a higher mean test score for students than the traditional teaching method." In this case, the null hypothesis would be "The new teaching method will not result in a higher mean test score for students than the traditional teaching method."
An incorrectly worded claim might be "The new teaching method is better than the traditional teaching method." This claim is too vague because it does not specify in what way the new method is better, nor does it give a direction for the hypothesis test.
In summary, when conducting a hypothesis test to support a claim regarding the mean test score under a new teaching method, the wording of the claim must be specific and precise, and the claim will become the alternative hypothesis.
A bag with 10 marbles has 3 blue marbles, 2 red marbles, and 5 yellow marbles. A marble is chosen from the bag at random. What is the probability that it is not blue
Answer: 7/10 because there are 7 marbles that arent blue
Step-by-step explanation:
i need help with this question but i dont know how to do it please someone help me with this.
Answer:
9^2 + 12^2 = c^2
81 + 144 = c^2
√15 = √c^2
c = 15
Step-by-step explanation:
Select the correct answer. Sam's height is 15 centimeters less than 2 times Martha's height. If Sam is 185 centimeters tall, and Martha's height is x, the relationship between the heights can be represented by the equation 2x − 15 = 185. What is Martha's height? A. 90 B. 95 C. 100 D. 105
The value of Marina's height is, 100 centimeters
Given that;
The relationship between the heights can be represented by the equation,
⇒ 2x − 15 = 185
Where, Martha's height is x
Now, We can simplify as;
⇒ 2x − 15 = 185
Add 15 both side we get;
⇒ 2x = 185 + 15
⇒ 2x = 200
⇒ x = 100
Thus, The value of Marina's height is, 100 centimeters
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3 similar rings and 2 similar bags cost $600. 1 ring and 1 bag cost $225. Find the cost of 1 bag.
Answer:
3r + 2b = 600 ---(1)
r + b = 225 ---(2)
We can solve this system of equations using substitution or elimination method.
Using substitution method, we can solve equation (2) for "r" in terms of "b":
r = 225 - b
Substituting this expression for "r" into equation (1), we get:
3(225 - b) + 2b = 600
Simplifying and solving for "b", we get:
675 - 3b + 2b = 600
-b = -75
b = $75
Therefore, the cost of one bag is $75.
Step-by-step explanation:
use brain
Sketch y=2x-2 and the curve of y=x^2-2+1 on the same cartesian plane to identify the point of intersection?
The sketch of the linear equation y = 2x - 2 and the curve y = x² - 2x + 1 as required is as attached and the points of intersection are; (1, 0) and (3, 4).
What are the points of intersection of the line and the curve?It follows from the task content that the graph of the line and the curve are required to be determined.
The graph is as attached.
By Observation of the graph; the points of intersection of the two graphs as required are; (1, 0) and (3, 4).
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The exponential function h whose graph is given below, can be written as h(x)=a*b^x Complete the equation for f(x)
Answer:
f(x)will be explained above
Find the volume of each cylinder. Use 3.14 for Pi.
Round your answer to the nearest tenth.
7 mm
8 mm
A cell phone which regularly sell for Ghana cedi 450.00 is on sale for 40% off how are much would you pay for the phone
Answer:
270
Step-by-step explanation:
40% of 450= 180
450-180=270
Answer:
270 Ghana cedi
Step-by-step explanation:
first we need to find what is 40% of 450
to remove the %, divide the 40% with 100
= 40/100 * 450
= 180
so 40% of 450 is 180.
the question says 40% off
= 180 off
sk we minus 180 from 450
450-180 = 270
Find all solutions of the equation in the interval [0, 27).
3 cot²0-1=0
Write your answer in radians in terms of .
If there is more than one solution, separate them with commas.
0=
The solutions of the equation in the interval [0, 27) are: θ = π/3, 2π/3.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operators.
According to given information:Starting with the given equation:
3cot²θ - 1 = 0
Add 1 to both sides:
3cot²θ = 1
Divide both sides by 3:
cot²θ = 1/3
Taking the square root of both sides:
cotθ = ± √(1/3)
Since cotθ = cosθ/sinθ, we can write:
cosθ/sinθ = ± √(1/3)
Multiplying both sides by sinθ:
cosθ = ± √(1/3)sinθ
Squaring both sides:
cos²θ = (1/3)sin²θ
Using the identity sin²θ + cos²θ = 1, we get:
sin²θ + (1/3)sin²θ = 1
Simplifying:
(4/3)sin²θ = 1
Dividing by 4/3:
sin²θ = 3/4
Taking the square root of both sides:
sinθ = ± √(3)/2
We know that θ is in the interval [0, 27). Therefore, the possible solutions are:
θ = π/3 or θ = 2π/3
However, we need to check if these solutions are in the given interval.
For θ = π/3, we have:
0 ≤ π/3 < 27
Therefore, π/3 is a valid solution.
For θ = 2π/3, we have:
0 ≤ 2π/3 < 27
Therefore, 2π/3 is also a valid solution.
Thus, the solutions of the equation in the interval [0, 27) are:
θ = π/3, 2π/3
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Given:
g(x) = 2x^2 + 3x +10
k(x) = 2x +16
Solve the equation g(x) = 2k(x) algebraically for x, to the nearest tenth.
The equation is solved to give 2x² -x - 22
What is a function?A function can be defined as an expression, law or rule that shows the relationship between two variables.
These variables are;
Dependent variableIndependent variableFrom the information given, we have that the functions are;
g(x) = 2x² + 3x +10
k(x) = 2x +16
To determine the equation g(x) = 2k(x), we need to substitute the value into the equation, we have;
2x² + 3x + 10 = 2(2x + 16)
expand the bracket, we have;
2x² + 3x + 10 = 4x + 32
collect the like terms, we have;
2x² - x = 32 - 10
subtract the values
2x² -x = 22
2x² -x - 22
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Jaeger the goat will be tied by a 15-meter chain to the outside of a 10-meter by 16-meter
rectangular shed that is surrounded by grass. Try three different places to attach the chain to
the shed. For each, determine the area of grass that Jaeger could eat. Which of your
locations gives Jaeger the most to eat? (Note: Jaeger cannot walk through the shed.)
a. Sketch each of the solutions of the three different places you happen to pick to attach
the chain to the shed. Accuracy counts. What conclusions can you draw based on
your three test points? Do you see any patterns?
In general, your solution(s) need to have evidence which both supports and helps explain
your solution(s). Evidence can include but is not limited to words, pictures, diagrams, tables,
The second location result in the largest area of grass that Jaeger can eat, which is approximately 353.57 square meters.
We may infer from the facts provided that Jaeger the goat will be confined to a 10- by-16-meter rectangular shelter by means of a 15-meter chain. All of the grass along the chain may be consumed by Jaeger. At three separate points in the shed, we are instructed to locate the patch of grass that Jaeger can eat.
Let's consider the three different locations as follows:
Attach the chain to a corner of the shed.
Jaeger can only eat as much grass as is contained inside a quarter-circle with a radius of 15 meters (the length of the chain) if the chain is fastened to a shed corner. This quarter-circle's area is:
Area = (1/4) x π x (15 meters)²
Area = 176.71 square meters (approx)
Affix the chain to the middle of one of the shed's longer sides.
This semicircle's area is:
Area = (1/2) x π x (15 meters)²
Area = 353. 57 square meters (approx)
To the center of one of the shed's shorter sides, fasten the chain.
This circular sector's area will be as follows:
Area = (90/360) x π x (15 meters)²
Area = 176.71 square meters (approx)
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What are the exact values of a and b?
A
30°
10
b
a = 5, b=5√√/3
O a=5, b= 10√/3
O a=5√√3,b=5
O a = 5,b= 5√2
The value of a and b in the figure are 5 and 5√3.
We have,
From the figure,
Sin 30 = a/10
Cos 30 = b/10
Now,
Sin 30 = 1/2
Cos 30 = √3/2
Now,
1/2 = a/10
a = 5
√3/2 = b/10
b = 5√3
Thus,
The value of a and b are 5 and 5√3.
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what is the distance between (3,-4) and (6,9)
Answer: 5,922 km
Step-by-step explanation: multiply the value in kilometers by the conversion factor '0.62137119223742'.
So, 5922 kilometers = 5922 × 0.62137119223742 = 3679.76020043 miles.
What is the exact value of tan(sin−1(−12))cos(tan−1(1))?
Enter your answer, as a simplified fraction, in the box.
The exact value of trigonometrical identity [tan{sin⁻¹(-1/2)]/[cos{tan⁻¹(1)}] is -(√2/√3).
Given that the trigonometrical identity is [tan{sin⁻¹(-1/2)]/[cos{tan⁻¹(1)}].
In order to solve the expression:
The known values are:
sin⁻¹(-1/2) = -π/6
tan⁻¹(1) = π/4
Now we can substitute these values into the expression:
[tan{sin⁻¹(-1/2)]/[cos{tan⁻¹(1)}] = [tan(-π/6)]/[cos(π/4)]
Using the fact that tan(-x) = -tan(x) and cos(π/4) = sin(π/4) = √2/2, we can simplify:
[tan{sin⁻¹(-1/2)]/[cos{tan⁻¹(1)}] = -tan(π/6)/[√2/2]
Using the fact that tan(π/6) = 1/√3, we can simplify further:
[tan{sin⁻¹(-1/2)]/[cos{tan⁻¹(1)}] = -[1/√3]/[√2/2]
[tan{sin⁻¹(-1/2)]/[cos{tan⁻¹(1)}] = -(√2/√3).
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3.1 Create an activity where procedural and conceptual understanding co- exists. Revisit your content areas and choose a problem to solve and demonstrate how procedural and conceptual knowledge can be linked to the teaching and learning process. (6)
Write an equation to describe the relationship in each table
for the first table to find the equation of its line you need to find the gradient(m). to do that you take 2 points then subtract the first y from the second y. so 12-9=3 then do the same with the x so 5-2=3 then divide the first by the second and 3÷3=1 so the gradient(m) is 1. so the equation is in the form y=mx+c and since we know m is 1 the equation will be y=x+c. to find c we take a point on the line and replace the numbers so 9=2+c must be true and for it to be true c must be 7. so the equation of the line is y=x+7. also pls mark as brainliest answer
Which set of side lengths form a right triangle?
8, 15, 16
10, 13.5, 17.8
4.2, 5.3, 6.5
12, 35, 37
1: Wrong
2: Wrong
3: Wrong
4: CORRECT equal to 1369
Mickey and Minnie Mouse are purchasing a new home. Their annual property taxes are estimated to be $5,467, and their homeowner's insurance policy has an annual cost of $1,440. They must also purchase flood insurance, since they live in below sea level, at an additional cost of $1,262 per year. How much will they be required to put into their escrow account each month to cover these costs?
Result:
Mickey and Minnie Mouse will need to put $680.75 into their escrow account each month to cover the property taxes, homeowner's insurance, and flood insurance costs.
What is an escrow account?An escrow account is like a savings account that is managed by a mortgage servicer. The portion deposited into an escrow account usually covers estimated property taxes and your homeowners and mortgage insurance premiums.
To calculate the monthly amount Mickey and Minnie Mouse need to put into their escrow account for property taxes, homeowner's insurance, and flood insurance, we will first add up the total annual costs for these expenses:
Property taxes: $5,467
Homeowner's insurance: $1,440
Flood insurance: $1,262
Total annual costs = $5,467 + $1,440 + $1,262 = $8,169
Next, we divide the total annual costs by 12 to get the monthly escrow amount:
$8,169 / 12 = $680.75
Therefore, $680.75 is the amount they will need to put into their escrow account each month.
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I need help with this
Answer:
11
Step-by-step explanation:
7x + 33 = 10x
3x = 33
x = 11
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