The time required to get an accrued amount of $6,450.00 with compoundeded interest on a principal of $3,030.00 at an interest rate of 10.2% per year and compounded 4 times per year is 7.5 years.
What is the time taken to have an accrued amount of $6450?The formula accrued amount in a compounded interest is expressed as;
[tex]A = P( 1 + \frac{r}{n} )^{(nt)}[/tex]
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Principal P = $3,030
Accrued amount A = $6,450
Compounded quarterly n = 4
Interest rate r = 10.2%
Time t = ?
First, convert R as a percent to r as a decimal
r = R/100
r = 10.2/100
r = 0.102
Now, plug these values into the above formula and solve for time t.
[tex]A = P( 1 + \frac{r}{n} )^{(nt)}\\\\t = \frac{In(\frac{A}{p}) }{n[In( 1 + \frac{r}{n}) ]} \\\\t = \frac{In(\frac{6450}{3030}) }{n[In( 1 + \frac{0.102}{4}) ]} \\\\t = 7.501 \ years[/tex]
t = 7.5 years.
Therefore, the time taken to get the accrued amount is approximately 7.5 years.
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What the meaning of "dom(s) = {i : i < n} for some n ∈ N"?
The expression "dom(s) = {i : i < n} for some n ∈ N" represents the domain of a set or function called 's'.
Let's break down the notation:
- "dom(s)" refers to the domain of the set or function 's'. The domain represents the set of all possible input values or elements for which 's' is defined or applicable.
- "{i : i < n}" is a set comprehension notation. It means that the set contains elements 'i' such that 'i' is less than 'n'. In other words, it represents a set of all natural numbers 'i' that are smaller than a specific value 'n'.
- "for some n ∈ N" denotes that there exists a natural number 'n' (n ∈ N) such that the set 'dom(s)' consists of elements 'i' that are less than 'n'.
In summary, the expression states that the domain of set or function 's' consists of all natural numbers 'i' that are smaller than a specific natural number 'n'. The actual value of 'n' is not specified and can vary depending on the specific context or problem.
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Classify each polynomial by degree and number of terms.
10
8x4
5x²-7x+9
2x³ +3
1. Quartic monomial
2. Cubic binomial
3. Quadratic trinomial
4. Quintic quadnomial
Answer:
10: Zero-degree monomial.
8x^4: Quartic monomial.
5x² - 7x + 9: Quadratic trinomial.
2x³ + 3: Cubic binomial.
Step-by-step explanation:
10: This is a constant term, and it can be classified as a zero-degree monomial.
8x^4: This is a monomial with a degree of 4, and it contains one term. It can be classified as a quartic monomial.
5x² - 7x + 9: This is a polynomial with three terms. The highest power of the variable, x, is 2, so it is a quadratic polynomial. Therefore, it can be classified as a quadratic trinomial.
2x³ + 3: This is a polynomial with two terms. The highest power of the variable, x, is 3, so it is a cubic polynomial. Hence, it can be classified as a cubic binomial.
10: Zero-degree monomial.
8x^4: Quartic monomial.
5x² - 7x + 9: Quadratic trinomial.
2x³ + 3: Cubic binomial.
Try to answer the questions below about deductive reasoning and rules.
Using Deduction
What rule does the pattern above
follow?
Please choose the correct answer.
Starting with one, every
consecutive line has one more
marble than the previous line.
Starting with one, every
consecutive line has twice as
many marbles as the previous
line.
O Starting with one, every
consecutive line has one more
than twice as many marbles as
the previous line.
O Starting with one, every
consecutive line has two more marbles than the previous line.
The correct answer is: Starting with one, every consecutive line has two more marbles than the previous line. This is the result inferred using deductive reasoning.
The pattern follows the rule: "Starting with one, every consecutive line has two more marbles than the previous line." This means that the number of marbles in each line increases by two compared to the previous line. For example, if the first line has one marble, the second line will have three marbles, the third line will have five marbles, and so on. This rule establishes a consistent and predictable pattern of adding two marbles to the previous line's count. Deductive reasoning allows us to infer this pattern based on the given information and observations.For more questions on deductive reasoning:
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What set of reflections and rotations would carry rectangle ABCD onto itself?
B
D
O Reflect over the y-axis, reflect over the x-axis, rotate 180°
O Rotate 180°, reflect over the x-axis, reflect over the line y = x
O Reflect over the x-axis, rotate 180°, reflect over the x-axis
O Rotate 180°, reflect over the y-axis, reflect over the line y = x
The set of reflections and rotations that would carry rectangle ABCD onto itself is (a) Reflect over the y-axis, reflect over the x-axis, rotate 180°
How to determine the set of transformationsFrom the question, we have the following parameters that can be used in our computation:
The figure (see attachment)
The figure is located in the second quadrant
So, we have the following series of transformations
Reflection across the y-axis takes the shape to the first quadrantReflection across the x-axis takes the new shape to the fourth quadrantRotation by 180 degrees takes the new shape back to its original positionThis means that the series of transformation is (a)
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PLEASE ANSWER NUMBER 2
Use the Quotient Rule of Logarithms to write an expanded expression equivalent to log6(2y−3y). Make sure to use parenthesis around your logarithm functions log(x+y).
The expanded expression equivalent to log6((2y-3y)/9) using the Quotient Rule of Logarithms is log6(2y) - log6(3y).
The Quotient Rule of Logarithms states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and the denominator. Using this rule, we can expand the given expression log6((2y-3y)/9) as follows:
log6((2y-3y)/9) = log6(2y/9) - log6(3y/9)
Now, let's simplify each logarithmic expression separately:
For the first term, log6(2y/9), we can write it as:
log6(2y/9) = log6(2y) - log6(9)
For the second term, log6(3y/9), we can write it as:
log6(3y/9) = log6(3y) - log6(9)
Combining these expressions, we have:
log6((2y-3y)/9) = (log6(2y) - log6(9)) - (log6(3y) - log6(9))
Now, let's simplify further by distributing the negative sign:
log6((2y-3y)/9) = log6(2y) - log6(9) - log6(3y) + log6(9)
Notice that log6(9) appears both as a subtraction and addition term. This cancels out, resulting in:
log6((2y-3y)/9) = log6(2y) - log6(3y)
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Look at the figure:
An image of a right triangle is shown with an angle labeled x.
If tan x° = a divided by 4 and cos x° = 4 divided by b what is the value of sin x°?
sin x° = 4b
sin x° = b divided by a
sin x° = 4a
sin x° = a divided by b
By using trigonometric functions, the value of [tex]\sin \text{x}^\circ[/tex] is [tex]\frac{\text{a}}{\text{b}}[/tex].
What are trigonometric functions?Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.
Given
[tex]\sin \text{x}^\circ= \ ?[/tex]
[tex]\tan \text{x}^\circ=\dfrac{\text{a}}{4}[/tex]
[tex]\cos \text{x}^\circ=\dfrac{4}{\text{b}}[/tex]
Formula to find [tex]\sin \text{x}^\circ[/tex]
[tex]\sin \text{x}^\circ=\dfrac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\rightarrow\sin \text{x}^\circ=\bold{\dfrac{a}{b}}[/tex]
Therefore, by using trigonometric functions, the value of [tex]\sin \text{x}^\circ[/tex] is [tex]\frac{\text{a}}{\text{b}}[/tex].
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Triangles (C) and (D) can be solved using the Law of Cosines, while triangles (A) and (B) cannot be solved using this theorem due to missing angle measures.
To determine which triangle should be solved by beginning with the Law of Cosines, let's briefly review the Law of Cosines. The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice their product, multiplied by the cosine of the included angle.
Now, let's analyze each given triangle and determine if the Law of Cosines is applicable:
(A) Triangle mZA with mZA = 115, a = 19, b = 13:
To apply the Law of Cosines, we need to have the measures of two sides and the included angle. In this case, we have the measures of two sides (a = 19 and b = 13), but we don't have the included angle mZA. Therefore, we cannot use the Law of Cosines for this triangle.
(B) Triangle m/B with m/B = 48, a = 22, b = 5:
Similar to the previous triangle, we are missing the measure of the included angle. Therefore, we cannot use the Law of Cosines for this triangle either.
(C) Triangle m/A with m/A = 62, mLB = 15, b = 10:
In this triangle, we have the measure of one side (b = 10) and the measures of the other two sides, including the included angle mLB. Therefore, we can apply the Law of Cosines to solve for m/A.
(D) Triangle m/A with m/A = 50, b = 20, c = 18:
Again, we have the measure of one side (b = 20) and the measures of the other two sides. Therefore, we can use the Law of Cosines to solve for m/A in this triangle as well.
In summary, triangles (C) and (D) can be solved using the Law of Cosines, while triangles (A) and (B) cannot be solved using this theorem due to missing angle measures.
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What are the domain and range of the function f(x) = -log(5-x)+9?
The domain of the function is all real numbers less than 5, and the range is all real numbers greater than or equal to 9.
The given function is f(x) = -log(5-x) + 9.
To determine its domain and range, we need to consider the restrictions on x and the possible values of f(x).
Domain:
The domain refers to the set of all valid inputs or values of x for which the function is defined.
In this case, the function contains a logarithmic term, -log(5-x), which is only defined for positive values inside the logarithm.
Therefore, we must ensure that the expression 5-x is greater than zero:
5 - x > 0
Solving this inequality, we find:
x < 5
Hence, the domain of the function is (-∞, 5).
Range:
The range refers to the set of all possible output values or values of f(x). Since the logarithm term can take any positive value, and we add 9 to it, the range of the function is shifted upward by 9 units.
The range can be defined as all real numbers greater than or equal to 9:
Range: [9, +∞)
To summarize, the domain of the function f(x) = -log(5-x) + 9 is (-∞, 5), and the range is [9, +∞), indicating that f(x) can take any value greater than or equal to 9.
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The distance around a circle is called the ______.
A. volume
B. area
C. circumference
D. diameter
The answer is:
C. circumference
Work/explanation:
Here's the correct answer:
The distance around a circle is called the circumference.
How to find the circumference :
Use [tex]\sf{C=2\pi r}[/tex] or [tex]\sf{C=\pi d}[/tex]Hence, c is correct.classify the sequence of transformation based on weather or not they show congruency by mapping shape l onto shape ll
and there’s a box slipt in half and the first one says “Maps shape l into shape ll” the one next to it says “Does not Map shape l onto shape ll” we have to put those blue boxes in both of them pls help thank this teacher don’t know how to teach
The following sequences of transformations do not show congruency by mapping shape I onto shape II:
a reflection across the y-axis, followed by a 90° counterclockwise rotation about the origin, and then a translation 6 units downa reflection across the x-axis, followed by a 90° clockwise rotation about the origin, and then a translation 4 units downa reflection across the x-axis, followed by a 90° counterclockwise rotation about the origin, and then a translation 6 units downHow to explain the informationThese sequences of transformations do not map shape I onto shape II because they either change the size or shape of the figure. The second sequence of transformations reflects shape I across the x-axis, rotates it 90° clockwise, and then translates it 4 units down.
This results in a figure that is flipped sideways and shifted down. The third sequence of transformations reflects shape I across the x-axis, rotates it 90° counterclockwise, and then translates it 6 units down. This results in a figure that is flipped upside down and shifted to the left.
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Graph the linear equation. Find three points that solve the equation, then plot on the graph. -5x-3y=-7
Answer:
The given linear equation is -5x-3y=-7. To graph the equation, we need to find three points that satisfy the equation and then plot them on the graph.
Let's find the x and y intercepts first.
At x = 0, we have -3y = -7, which gives us y = 7/3. So the y-intercept is (0, 7/3).
At y = 0, we have -5x = -7, which gives us x = 7/5. So the x-intercept is (7/5, 0).
Now, let's choose another point. We can choose any value for x or y and solve for the other variable. Let's take x = 1.
-5(1) - 3y = -7
-3y = -2
y = 2/3
So the third point is (1, 2/3).
Now we can plot these three points on the graph and draw a line passing through them.
Here's the graph:
|
|
| . (1, 2/3)
|
| .
| (0, 7/3)
|
|_________________________
| |
7/5 -7/15
Step-by-step explanation:
Already explained
The cross-section of the prism below is a compound shape formed of two
rectangles.
Work out the volume of the prism.
Give your answer in cm³.
Answer:
V = 4(5)(7) + 6(5)(15) = 140 + 450 = 590 cm³
For the attached graph two questions:
1. What does the slope of the line represent, in context of the problem?
2. What does the y intercept represent, in context of the problem?
The slope of the line represents the speed in miles per hour
The y intercept represents the initial distance
What does the slope of the line representfrom the question, we have the following parameters that can be used in our computation:
The graph
Where, we have
x = time in hours
y = distance in miles
The slope is
slope = change in y/x
So, we can conclude that the slope is the speed
What does the y intercept representBy definition, the y intercept is the initial value of the graph
In this case;
y intercept = initial distance
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URGENT PLEASE!!!!!!!! Which of the following equations is FALSE?
Right triangles
RS = 32
QT = 16
RT = 16
QS = 32
Answer:
The equation QS = 32 is false.
Step-by-step explanation:
In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Given:
QT = 16
RT = 16
QS = 32
We can apply the Pythagorean theorem to the right triangle:
RT^2 + QT^2 = QS^2
Substituting the given values:
16^2 + 16^2 = 32^2
Calculating:
256 + 256 = 1024
However, we find that 512 (the sum of the squares of the other two sides) does not equal 1024 (the square of the hypotenuse). This contradicts the Pythagorean theorem, which means the equation QS = 32 is false.
Suppose that IQ scores have a bell-shaped distribution with a mean of 97
and a standard deviation of 17
. Using the empirical rule, what percentage of IQ scores are at least 46
? Please do not round your answer.
Therefore, approximately 0.3% of IQ scores are at least 46.
The empirical rule, also known as the 68-95-99.7 rule, states that in a bell-shaped distribution:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.
Given a mean IQ score of 97 and a standard deviation of 17, we can calculate the number of standard deviations below the mean that a score of 46 corresponds to:
Number of standard deviations = (46 - 97) / 17 = -3
Since the empirical rule tells us that approximately 99.7% of the data falls within three standard deviations of the mean, we can conclude that the percentage of IQ scores that are at least 46 is 0.3% (100% - 99.7%).
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There are 50 total battles. Ryan wins 10 of them. Using this equation, when I double wins by 2 and substrate by total battles how am I able to find the difference between wins and losses by doubling wins?
This equation works every time and I don’t understand why you double by two and how that works.
W= wins
L= Losses
D= Difference between W&L
TB= total battles
2W - TB = D
2(10) — 50 = -30
Wins is down by 30 ^^
W — D = L
10 - (-30)= 40
Or even if you did losses instead of wins.
2L — TB = D
2(40) — 50 = 30
L — D = W
40 - 30 = 10
Please just explain how doubling losses or wins will get me the difference between them.
The equation you provided, 2W - TB = D, is a way to find the difference between wins and losses by doubling the number of wins and subtracting the total number of battles. Let's break it down to understand why it works.
First, let's define the variables:
W = number of wins
L = number of losses
D = difference between wins and losses
TB = total battles
The equation 2W - TB = D can be understood as follows:
Doubling the number of wins (2W) represents a hypothetical scenario where every win is counted twice.
Subtracting the total number of battles (TB) from the doubled wins accounts for the fact that the total number of battles includes both wins and losses.
The resulting value (D) represents the difference between wins and losses.
Let's consider an example using your values:
Total battles (TB) = 50
Wins (W) = 10
Using the equation 2W - TB = D:
2(10) - 50 = D
20 - 50 = D
D = -30
In this example, the difference (D) between wins and losses is -30, indicating that there are 30 more losses than wins.
The same principle applies when using losses instead of wins. For example, the equation 2L - TB = D can be used to find the difference between wins and losses by doubling the number of losses and subtracting the total number of battles.
In summary, by doubling either the wins or losses and subtracting the total battles, you can find the difference between wins and losses. This approach takes into account the total number of battles and provides a measure of the difference between the two.
Perform the operation.
(2x+7)2
The simplified expression for (2x+7)2 = 4x^2 + 28x + 49.
A simplified expression is an algebraic expression that has been rewritten in a more concise and easier to understand form. This can be done by combining like terms, removing unnecessary parentheses, and using the correct order of operations.
To perform the operation [tex](2x + 7)^{2}[/tex] we need to square the entire expression (2x+7).
(2x+7)2 = (2x+7)(2x+7)
The expression inside the parentheses is multiplied by itself. This is called squaring the expression.
To expand the expression, we can use the distributive property:
(2x+7)(2x+7) = 2x(2x) + 2x(7) + 7(2x) + 7(7)
Simplifying the expression, we get:
(2x+7)2 = 4x^2 + 28x + 49
In words, we can say that the square of 2x + 7 is equal to 4x squared plus 28x plus 49.
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For which equations is x = 9 a possible solution? Check all that apply.
Answer:
The x is an invisible number that is always represented by 1 so you have to solve the equation.
discuss three dramatic techniques that makes the play look back in anger interesting
The three dramatic techniques that make "Look Back in Anger" interesting are social realism, strong language and rhetoric, and character conflict and dynamic relationships.
"Look Back in Anger" by John Osborne is a play known for its compelling portrayal of post-war disillusionment and social critique. Here are three dramatic techniques used in the play that contribute to its enduring interest:
1. Social Realism: Osborne employed social realism, depicting the gritty realities of working-class life, alienation, and societal discontent. This authenticity and portrayal of relatable characters and situations engage the audience emotionally and intellectually.
2. Strong Language and Rhetoric: The play is characterized by sharp, biting dialogue and impassioned monologues. The use of strong language and rhetoric adds intensity, captures the characters' frustrations, and conveys their anger and disillusionment effectively.
3. Character Conflict and Dynamic Relationships: The play revolves around intense conflicts between characters, particularly the central couple, Jimmy and Alison. Their volatile relationship and the clash between Jimmy's anger-fueled rebellion and Alison's desire for a different life create tension and keep the audience engaged.
Overall, these dramatic techniques of social realism, powerful language, and dynamic relationships make "Look Back in Anger" interesting by effectively portraying societal issues, engaging the audience emotionally, and highlighting the complexities of human interactions.
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A bag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue).
A. 9
B. 4/3
C. 1/4
D. 3/4
Please select the best answer from the choices provided.
Please awnser asap I am
Stuck
Answer:
it is too blury to read
Step-by-step explanation:
Elsevier logo el Home
Find the area of the combined rectangles.
9 ml
1 2 3 4
The area is
11 ml
19 ml
square miles.
2 ml
8 ml
5
7 ml
To find the area of the combined rectangles, we need the dimensions (length and width) of each rectangle. However, the provided text and numbers do not seem to correspond to a clear description of the rectangles or their dimensions. Could you please provide more specific information or clarify the question?
Which pair of angles are interior angles?
Solve for f: 6f + 9g = 3g + f
f = f equals StartFraction negative 8 g Over 3 EndFraction.
f = f equals StartFraction negative 6 g Over 5 EndFraction.
f = f equals StartFraction negative 5 g Over 6 EndFraction.
f = f equals StartFraction 12 g Over 7 EndFraction.
The solution for f in terms of g is: f = -6g / 5. Out of the answer options provided, none of them exactly match this solution.
To solve for f in the equation 6f + 9g = 3g + f, we can simplify the equation and isolate the variable f.
Starting with the given equation as follows:
6f + 9g = 3g + f
We can combine like terms by subtracting f from both sides and subtracting 3g from both sides:
6f - f = 3g - 9g
Simplifying further we get:
5f = -6g
To solve for f, we divide both sides of the equation by 5:
f = -6g / 5
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Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is your decision if α = 0.01?
Select one:
a.
Reject the null hypothesis and conclude the newscast does not reach 41% of the audience.
b.
Fail to reject the alternate and conclude the newscast does not reach 41% of the audience.
c.
Reject the alternate and conclude the newscast reaches about 41% of the audience.
d.
Fail to reject the null hypothesis.
Based on the information given, the null hypothesis states that the newscast reaches 41% of the viewing audience, while the alternate hypothesis states that it does not reach 41% of the audience. So, the correct answer is d. Fail to reject the null hypothesis.
To determine the decision, we need to perform a hypothesis test using the given significance level α = 0.01. This significance level represents the maximum acceptable probability of making a Type I error, which is rejecting the null hypothesis when it is actually true.
In the survey of 100 viewers, 36% indicated that they watch the late evening news on the local CBS station. To test the hypothesis, we can use a one-sample proportion test. We compare this sample proportion to the claimed 41% to see if there is a significant difference.
Using a statistical calculator or software, we calculate the p-value associated with the observed sample proportion. If this p-value is less than α (0.01), we reject the null hypothesis. If the p-value is greater than or equal to α, we fail to reject the null hypothesis.
Based on the decision criteria, if the p-value is less than 0.01, we would reject the null hypothesis and conclude that the newscast does not reach 41% of the audience. However, if the p-value is greater than or equal to 0.01, we would fail to reject the null hypothesis. To summarize, the correct decision, given α = 0.01, would be d. Fail to reject the null hypothesis.
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A university is interested in determining the average statistics anxiety score for all undergraduate students in the U.S. For a random sample of 33 undergraduate students, it is found that the average average statistics anxiety score is 39.4 with a standard deviation of 0.9. Assume that the statistics anxiety scores for all undergraduate students in the U.S is normally distributed. A 98% confidence interval for the true mean statistics anxiety score μ is closest to.
The 98% confidence interval for the true mean statistics anxiety score μ is approximately (39.023, 39.777).
To calculate the 98% confidence interval for the true mean statistics anxiety score μ, we can use the formula:
[tex]\[\text{CI} = \bar{X} \pm Z \cdot \left(\frac{\sigma}{\sqrt{n}}\right)\][/tex]
where [tex]\bar{X}[/tex] is the sample mean (39.4), Z is the Z-score corresponding to the desired confidence level (in this case, 98% corresponds to a Z-score of 2.33), σ is the population standard deviation (0.9), and n is the sample size (33).
Plugging in the values, we get:
CI = 39.4 ± 2.33 * (0.9/√33).
Calculating this expression, we find:
CI = 39.4 ± 2.33 * (0.162),
CI ≈ 39.4 ± 0.377.
Therefore, the 98% confidence interval for the true mean statistics anxiety score μ is approximately (39.023, 39.777).
This means that we are 98% confident that the true average statistics anxiety score for all undergraduate students in the U.S. falls within this interval.
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Bob and Jack enter a 1000 km go-kart race. Bob drives 4 km/h faster than Jack does, but his go-kart gets a flat tire, which takes 30 minutes to repair. If both of them finish the race in a tie, how fast was each boy going during the race?
The Jack's speed was approximately 85.44 km/h, and Bob's speed was approximately 89.44 km/h.
Let's assume that Jack's speed during the race was "x" km/h. Since Bob was driving 4 km/h faster than Jack, his speed was "x + 4" km/h.
When Bob got a flat tire, he had to stop and repair it, which took 30 minutes. During this time, Jack continued to race. Since both of them finished the race in a tie, it means that Bob caught up to Jack after his tire was repaired.
In 30 minutes, Jack traveled a distance of (x/2) km because the time is half of an hour. During the same time, Bob was stationary due to the tire repair.
Once Bob's tire was fixed, he started racing again and caught up to Jack. At this point, both Bob and Jack had covered the same distance.
So, Bob's time to complete the race was the same as Jack's time plus the 30-minute tire repair time.
We can set up the equation:(1000 km) / (x + 4 km/h) = (1000 km - x/2 km) x km/h
Simplifying the equation, we get:1000x = (1000 - x/2)(x + 4)
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Choose the best graph that represents the linear equation:
-x = 2y + 1
The line slants downward from left to right, indicating that as x increases, y decreases.
The given linear equation is -x = 2y + 1. To represent this equation graphically, we need to rearrange it into the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.Rearranging the given equation, we get:2y = -x - 1
Dividing both sides by 2:y = (-1/2)x - 1/2
The slope of the line is -1/2, which means that for every unit increase in x, y decreases by 1/2 unit. The y-intercept is -1/2, indicating that the line intersects the y-axis at (0, -1/2).
Based on this information, the best graph that represents the linear equation y = (-1/2)x - 1/2 is a straight line with a negative slope of -1/2, starting at the point (0, -1/2) and extending infinitely in both directions.
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Mr Mangena invested an amount of R13 890,00 divided in two different schemes, A and B, at the simple
interest rate of 14% per annum and 11% per annum respectively. If the total amount of simple interest earned
in three years is R5 508,00, what was the amount invested in Scheme B?
The amount invested in Scheme B is R6,000.
Let's assume that Mr Mangena invested "x" amount in Scheme A and "y" amount in Scheme B.So, as per the problem, the total amount invested by Mr Mangena in Scheme A and Scheme B is equal to R13,890. Hence,x + y = 13,890This is our first equation.
The second equation is that after 3 years, the total interest that Mr Mangena earned was R5,508. Now, we know that the interest earned is simply the product of principal, rate of interest and time. The rate of interest is given as 12% for Scheme A and 10% for Scheme B. Hence, we can write the following equation:0.12x * 3 + 0.10y * 3 = 5,508This is our second equation.
We have two equations and two variables. We can solve these equations simultaneously to get the values of x and y, and hence, we can find the amount invested in Scheme B.x + y = 13,890 ................... Equation 1 0.12x * 3 + 0.10y * 3 = 5,508 .............. Equation 2 Simplifying Equation 1, we get:x = 13,890 - ySubstituting this value of x in Equation 2, we get:0.12(13,890 - y) * 3 + 0.10y * 3 = 5,508Simplifying this equation, we get:y = R6,000.
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