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A cup of water at an initial temperature of 81°C is placed in a room at a constant temperature of 24°C. The temperature of the water is measured every 5 minutes during a half-hour period. The results are recorded as ordered pairs of the form (t, T), where t is the time (in minutes ) and T is the temperature (in degrees Celsius).
t T
0 81
5 69
10 60.5
15 54.2
20 49.3
25 45.4
30 42.6
a. Subtract the room temp. from each of the temp. in the ordered pairs. Use a graphing utility to plot the data points (t, T) and (t, T-24). An exponential model for the data (t, T-24) is T-24 = 54.4(0.964)^t. Solve for T.
T=
Graph the model. Compare the result with the plot of the original data.
b. Use a graphing utility to plot the points (t, ln(T-24)) and observe that the points appear to be linear. Use the regression feature of the graphing utility to fit a line to these data. This resulting line has the form ln(T-24) = at + b, which is equivalent to e^(ln(T-24)) = e^(at+b). Solve for T, and verify that the result is equivalent to the model in part (b). Round all numerical values to 3 decimal places).
T=
c. Fit a rational model to the data. Take the reciprocals of the y-coordinates of the revised data points to generate the points. (t, 1/(T-24))
Use a graphing utility to graph these points and observe that they appear to be linear. Use the regression feature of a graphing utility to fit a line to these data. The resulting line has the form 1/(T - 24) = at + b.
Solve for T. (Round all numerical values to 4 decimal places). Use a graphing utility the rational function and the original data points.
T=
Answers
Part (a)
Given data table.
[tex]\begin{array}{|c|c|} \cline{1-2}t & T\\\cline{1-2}0 & 81\\\cline{1-2}5 & 69\\\cline{1-2}10 & 60.5\\\cline{1-2}15 & 54.2\\\cline{1-2}20 & 49.3\\\cline{1-2}25 & 45.4\\\cline{1-2}30 & 42.6\\\cline{1-2}\end{array}[/tex]
where,
t = time in minutesT = temperature in CelsiusIt's unfortunate that T is used twice for these variables. It might cause some confusion.
This is what happens when we subtract 24 from each temperature.
[tex]\begin{array}{|c|c|} \cline{1-2}t & T-24\\\cline{1-2}0 & 57\\\cline{1-2}5 & 45\\\cline{1-2}10 & 36.5\\\cline{1-2}15 & 30.2\\\cline{1-2}20 & 25.3\\\cline{1-2}25 & 21.4\\\cline{1-2}30 & 18.6\\\cline{1-2}\end{array}[/tex]
The graph of each set of points is shown in figure A. I used GeoGebra to make the graph.
The first set of data points are in red. The second set in blue. Notice the set of blue points is the result of shifting the red points 24 units down.
The green exponential model is also shown as the curve through the set of red points.
The green regression exponential model doesn't go through each point perfectly. Rather it tries to get as close as possible.
To go from
T-24 = 54.4(0.964)^t
to
T = 54.4(0.964)^t + 24
we simply add 24 to both sides. This means there isn't much to show in terms of steps when solving for T.
=======================================================
Part (b)
Use spreadsheet technology or something like GeoGebra to generate this data table.
[tex]\begin{array}{|c|c|} \cline{1-2}t & ln(T-24)\\\cline{1-2}0 & 4.043051\\\cline{1-2}5 & 3.806662\\\cline{1-2}10 & 3.597312\\\cline{1-2}15 & 3.407842\\\cline{1-2}20 & 3.230804\\\cline{1-2}25 & 3.063391\\\cline{1-2}30 & 2.923162\\\cline{1-2}\end{array}[/tex]
The values in the 2nd column are approximate.
Then plot each of those points on the same xy grid. Use technology of your choice to determine the regression line is roughly
y = -0.03723x + 3.99739
So we can say
ln(T-24) = -0.03723t + 3.99739
the right hand side fits the format at + b where
a = -0.03723b = 3.99739both of which are approximate.
Then,
e^(ln(T-24)) = e^(at+b)
T-24 = e^(at+b)
T-24 = e^(-0.03723t + 3.99739)
T-24 = e^(-0.03723t)*e^(3.99739)
T-24 = e^(-0.03723t)*54.45583
T-24 = 54.45583*e^(-0.03723t)
T = 54.45583*e^(-0.03723t) + 24
T = 54.456*e^(-0.037t) + 24
Let's verify that this is equivalent to the model found in part (a).
T = 54.456*e^(-0.037t) + 24
T = 54.456*(e^(-0.037))^t + 24
T = 54.456*(0.963676)^t + 24
T = 54.5*(0.964)^t + 24
which is very close to the model mentioned in part (a). There's some slight rounding error. That's to be expected in problems like this.
-----------------------------
Answer: T = 54.456*e^(-0.037t) + 24
See figure B for the graph. Like with the other regression curve, this straight line doesn't go through all of the points. It tries to get as close as possible.
=======================================================
Part (c)
Refer to the 2nd table mentioned in part (a).
We'll apply the reciprocal to each item in the column labeled T-24.
For instance, the item 57 becomes 1/57 = 0.017544 approximately.
This is what the data table looks like:
[tex]\begin{array}{|c|c|} \cline{1-2}t & 1/(T-24)\\\cline{1-2}0 & 0.017544\\\cline{1-2}5 & 0.022222\\\cline{1-2}10 & 0.027397\\\cline{1-2}15 & 0.033113\\\cline{1-2}20 & 0.039526\\\cline{1-2}25 & 0.046729\\\cline{1-2}30 & 0.053763\\\cline{1-2}\end{array}[/tex]
The values in the 2nd column are approximate.
The set of points and regression line are shown in figure C1. This line does not go through all of the points. Like with the others, it tries to get as close as possible to each point.
Use technology to determine the equation of the regression line is approximately:
y = 0.00121x + 0.01613
Which tells us that
1/(T-24) = 0.00121t + 0.01613
Let's solve for uppercase T.
1/(T-24) = 0.00121t + 0.01613
T-24 = 1/(0.00121t + 0.01613)
T = 1/(0.00121t + 0.01613) + 24
T = 1/(0.0012t + 0.0161) + 24
which is the approximate final answer.
Figure C2 shown below represents the original data points (t, T) in red. The blue curve is y = 1/(0.0012x+0.0161)+24, which is the rational regression curve we just found. This curve tries its best to get as close as possible to each red point.
Compare the regression curves of figure A and figure C2. We have a very close tie in terms of which curve does a better job of fitting the original data.
Related Questions
A fast food chain decides to decrease the size of its soft drink cups by 10%. If the new soft drink
cup holds 27 oz, how much did the original cup hold?
Answers
Answer:
30 oz
Step-by-step explanation:
x = size of original cup
x - (0.10)x = 27 oz
(0.90)x = 27 oz
x = 27 / 0.90 = 30 oz
Alfonso is making chili for a get-together.
His recipe calls for 1 1/2 cups of diced tomatoes for every 3 cups of chili.
He wants to make 13 cups of chili.
How many cups of diced tomatoes should he put in the chili?
Answer is a mixed number
Answers
The cups of diced tomatoes the Alfonso should put in the chili is 6 1/2 cups.
How to calculate the number of cups?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
Let the number of cups be x.
Based on the information, this will be illustrated as:
1.5 / x = 3/13
Cross multiply
3x = 13 × 1.5
3x = 19.5
Divide
x = 19.5 / 3
x = 6 1/2
The cups needed is 6 1/2 cups.
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A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are at least 32 batteries of each type.
A)How many ways can a total inventory of 32 batteries be distributed among the eight different types?
B)How many ways can a total inventory of 32 batteries be distributed among the eight different types if the inventory must include at least four A76 batteries?
C)How many ways can a total inventory of 32 batteries be distributed among the eight different types if the inventory includes at most three A76 batteries?
Answers
Number of ways total inventory of 32 batteries be distributed among the 8 different types - 15257889504
What is a permutation ?The number of possible arrangements for a given set is determined mathematically, and this process is known as permutation. The term "permutation" simply refers to the variety of possible arrangements or orders. The positioning of the permutations matters a lot.
Number of ways total inventory of 32 batteries be distributed among the 8 different types -
39!/30! 7! = 39X38X37X36X35X34X33X32X31 / 7X6X5X4X3X2X1
= 15257889504
Number of ways total inventory of 32 batteries be distributed among the 8 different types, in inventory must include A76 - 35! / 28! 7!
= 35X34X33X32X31X30X29 / 7X6X5X4X3X2X1 = 6714520
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Find the sum of the finite arithmetic sequence.
Sum of the first 150 positive integers
Answers
Answer:
11325
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[a+l]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $l$ is the last term.\\\phantom{ww}$\bullet$ $n$ is the number of terms.\\\end{minipage}}[/tex]
A positive integer is a whole number that is greater than zero.
Therefore:
The first term, a, of the first 150 positive integers is 1.The last term, l, of the first 150 positive integers is 150.The number of terms, n, is 150.Substitute the values into the formula to find the sum of the first 150 positive integers:
[tex]\implies S_{150}=\dfrac{1}{2}(150)\left[1+150\right][/tex]
[tex]\implies S_{150}=75 \cdot 151[/tex]
[tex]\implies S_{150}=11325[/tex]
find the values of the variable, giving brief reasons for your answers.
please help me with the answer. thank you.
Answers
Answer:
a= 108 degrees
b=88 degrees
c= 90 degrees
d= 90 degrees
Step-by-step explanation:
For a degrees since 72 degrees and a degrees make a straight angle:
180-72= a
So, a=108 degrees
Same goes for b degrees:
180-92=b
So, b=88 degrees
For c degrees, you need to know that the sum of the angles in a quadrilateral equal to 360 degrees.
So, 74+a+b+c=360
= 360- (74+108+88)=c
= 90 degrees= c
So since d degrees and c degrees make a straight angle,
180-90=d
90 degrees= d
Think of two numbers that multiply to -24, but add to -14.
Answers
Answer:
x = -7 + √(73)
y = -7 - √(73)
Step-by-step explanation:
Product p = x × y = -24
Somme s = x + y = -14
Then
x and y are solutions to the equation:
z² - sz + p = 0
Then
x and y are solutions to the equation:
z² + 14z - 24 = 0
Using the quadratic formula:
x = ( -14 + √[(14² - 4×(1)×(-24)] ) / ( 2×(1) ) = -7 + √(73)
and
y = ( -14 - √[(14² - 4×(1)×(-24)] ) / ( 2×(1) ) = -7 - √(73)
A one-factor ANOVA is used to evaluate the mean differences among four treatment conditions with a sample of n = 12 participants in each group. For this study, what is dfwithin treatments?
Answers
In this case, with four treatment groups and n = 12 participants in each group, dfwithin treatments would be equal to 3, because there are 4 - 1 = 3 treatment groups.
In a one-factor ANOVA, dfwithin treatments refers to the degrees of freedom within the treatment groups, which is a measure of the amount of variability that is present within each group.
The degrees of freedom within the treatment groups is used to calculate the mean square within treatments (MSwithin), which is a measure of the variability within each group. MSwithin is calculated by dividing the sum of the squared differences between each participant's score and the group mean by dfwithin. This value is then used to determine the statistical significance of the treatment effects, by comparing it to the mean square between treatments (MSbetween), which is a measure of the variability between the treatment groups.
In a one-factor ANOVA, the total degrees of freedom is equal to the number of participants in all of the groups combined (4 groups * 12 participants per group = 48) minus the number of groups (48 - 4 = 44). The degrees of freedom between treatments is equal to the number of groups minus 1 (4 - 1 = 3), and the degrees of freedom within treatments is equal to the total degrees of freedom minus the degrees of freedom between treatments (44 - 3 = 41).
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Suppose that the scores of bowlers in a particular league follow a normal distribution such that the standard deviation of the population is 12 . Find the 95% confidence interval of the mean score for all bowlers in this league using the accompanying data set of 40 random scores. Round your answers to two decimal places and use ascending order.
Score
96
103
94
105
91
101
99
89
94
91
82
94
97
99
89
107
97
100
96
92
96
95
99
90
84
97
99
87
102
92
91
90
88
103
94
90
98
91
87
91
Answers
Mean = 95.125
Variance = 198.90625
Standard deviation = 14.06,
Confidence interval = 95.125 +/- 3.45
To find the 95% confidence interval of the mean score for all bowlers in this league, we need to first calculate the sample mean and sample standard deviation of the given data set.
The sample mean is calculated as follows:
mean = (96 + 103 + 94 + 105 + 91 + 101 + 99 + 89 + 94 + 91 + 82 + 94 + 97 + 99 + 89 + 107 + 97 + 100 + 96 + 92 + 96 + 95 + 99 + 90 + 84 + 97 + 99 + 87 + 102 + 92 + 91 + 90 + 88 + 103 + 94 + 90 + 98 + 91 + 87) / 40mean = 95.125
The sample standard deviation is calculated as follows:
First, we need to calculate the variance of the data set, which is done by taking the sum of the squared differences between each score and the mean, and dividing by the sample size minus 1:
variance = ((96 - 95.125)^2 + (103 - 95.125)^2 + (94 - 95.125)^2 + (105 - 95.125)^2 + (91 - 95.125)^2 + (101 - 95.125)^2 + (99 - 95.125)^2 + (89 - 95.125)^2 + (94 - 95.125)^2 + (91 - 95.125)^2 + (82 - 95.125)^2 + (94 - 95.125)^2 + (97 - 95.125)^2 + (99 - 95.125)^2 + (89 - 95.125)^2 + (107 - 95.125)^2 + (97 - 95.125)^2 + (100 - 95.125)^2 + (96 - 95.125)^2 + (92 - 95.125)^2 + (96 - 95.125)^2 + (95 - 95.125)^2 + (99 - 95.125)^2 + (90 - 95.125)^2 + (84 - 95.125)^2 + (97 - 95.125)^2 + (99 - 95.125)^2 + (87 - 95.125)^2 + (102 - 95.125)^2 + (92 - 95.125)^2 + (91 - 95.125)^2 + (90 - 95.125)^2 + (88 - 95.125)^2 + (103 - 95.125)^2 + (94 - 95.125)^2 + (90 - 95.125)^2 + (98 - 95.125)^2 + (91 - 95.125)^2 + (87 - 95.125)^2) / (40 - 1)variance = 198.90625
The sample standard deviation is then the square root of the variance:
standard deviation = sqrt(198.90625)
standard deviation = 14.06
Now that we have the sample mean and sample standard deviation, we can use these values to calculate the 95% confidence interval of the mean score for all bowlers in this league.
We can use the following formula to calculate the confidence interval:
confidence interval = mean +/- (1.96 * (standard deviation / sqrt(sample size)))
Substituting in the values we calculated above, we get:
confidence interval = 95.125 +/- (1.96 * (14.06 / sqrt(40)))
Hence , confidence interval = 95.125 +/- 3.45
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Answer:
(90.78, 98.22)
Step-by-step explanation:
A 95% confidence interval for μ is (x¯−zα/2σn‾√,x¯+zα/2σn‾√). Here, α=0.05, σ=12, and n=40. Use Excel to calculate the 95% confidence interval.1. Open Excel, enter the given data in column A, and find the sample mean, x¯, using the AVERAGE function. Thus, the sample mean is x¯=94.5.2. Click on any empty cell, enter =CONFIDENCE.NORM(0.05,12,40), and press ENTER.3. The answer rounded to two decimal places is zα/2σn‾√≈3.72. The confidence interval for the population mean has a lower limit of 94.5−3.72=90.78 and an upper limit of 94.5+3.72=98.22.Thus, the 95% confidence interval for μ is (90.78, 98.22).
Please help!!!!!!!!!!!!
Answers
The value of variable x in the equation is x = -3y + 5/ 2
How to solve an equation for a variable?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Therefore, the equation 2x + 3y = 5 can be solved for x as follows:
We have to make x the subject of the formula in the equation.
Subject of the formula is the variable which is expressed in terms of other variables involved in the formula.
Hence,
2x + 3y = 5
subtract 3y from both sides of the equation
2x + 3y = 5
2x + 3y - 3y = 5 - 3y
2x = 5 - 3y
divide both sides by 2
Therefore,
x = 5 - 3y / 2
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The graphs below have the same shape. f(x)=x². What is the equation of the graph of g(x) ?
A. g(x)=(x-2)²
B. g(x)=(x+2)²
C. g(x)=x²+2
D. g(x)=x²-2
Answers
The equation of the graph of the function g(x) is A. g(x) = (x - 2)²
How to determine the equation of the graph of the function g(x)?From the question, we have the following parameters that can be used in our computation:
f(x) = x²
Also, we have the given graph
From the graph, we can see that the graph f(x) is shifted right y 2 units
This means that
g(x) = f(x - 2)
So, we have
g(x) = (x - 2)²
Hence, the equation is (a) g(x) = (x - 2)²
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A certain game keeps track of the maximum and minimum scores obtained so far. If num represents the most recent score obtained, which of the following algorithms correctly updates the values of the maximum and the minimum?
Answers
following algorithms correctly updates the values, If num is less than the minimum, set the minimum equal to num. Otherwise, if num is greater than the maximum, set the maximum equal to num.
What is algorithm ?An algorithm is a process used to carry out a computation or solve a problem. In either hardware-based or software-based routines, algorithms function as a detailed sequence of instructions that carry out predetermined operations sequentially.The game records the highest and lowest scores that were earned. This indicates that the game already has the highest and lowest score stored in its memory.
Now, if a new score, num, is achieved, the game must compare num with the minimum and maximum scores in order to update the minimum and maximum scores. The minimum score is updated to the score, num if the most recent score, num, is lower than the minimum score.
Additionally, the maximum score is updated to the score, num if the most recent score, num, is higher than the maximum score.
Complete Question :
A certain game keeps track of the maximum and minimum scores obtained so far. If num represents the most recent score obtained, which of the following algorithms correctly updates the values of the maximum and the minimum?
If num is greater than the minimum, set the minimum equal to num. Otherwise, if num is greater than the maximum, set the maximum equal to num.If num is less than the minimum, set the minimum equal to num. Otherwise, if num is greater than the maximum, set the maximum equal to num. If num is less than the minimum, set the minimum equal to num. Otherwise, if num is less than the maximum, set the maximum equal to num. If num is greater than the minimum, set the minimum equal to num. Otherwise, if num is less than the maximum, set the maximum equal to num.To learn more about algorithm refer,
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calculate the length of diagonals of a rectangle with dimensions 5 cm × 12 cm
Answers
Answer:
13
Step-by-step explanation:
5²+12²=25+144=169
square root of 169 = 13
Two friends, Andrew and Liz, are playing a game using this spinner. If the spinner lands on region 1, Andrew wins. If it lands on region 2, Liz wins. If it lands on region 3, nobody wins. Is this a fair game?
Answers
Answer:
Based on the information provided, it does not seem like this game is fair. Since region 1 and region 2 are the same size, each player has an equal chance of winning, but since region 3 is significantly larger than the other regions, neither player has a high chance of winning. This means that one player could potentially win multiple times in a row just by luck, without the other player having a chance to catch up. In order for the game to be considered fair, the relative sizes of the regions should be such that each player has a roughly equal chance of winning.
Answer:
yes. they both have ⅓ chance of winning
Step-by-step explanation:
pls help i will mark brainliest
Determine the value of y for the inequality 4 times the quantity y plus one fifth end quantity is less than or equal to four fifths.
y ≥ 0
y ≤ 0
y is greater than or equal to negative 1 over 40
y is less than or equal to negative 1 over 40
Answers
The value of y of the inequality 4y + 1/5 ≤ 4/5 is: y ≤ 3/20.
How to Solve an Inequality?Inequalities can be solved the way a normal algebraic equation is being solved. It is solved by isolating the value of the variable.
The inequality given is, 4y + 1/5 ≤ 4/5. Solve as shown below:
Subtract both sides by 1/5:
4y + 1/5 - 1/5 ≤ 4/5 - 1/5 [subtraction property of equality]
4y ≤ 3/5
Divide both sides by 4:
4y/4 ≤ 3/5 / 4
y ≤ 3/5 × 1/4
y ≤ 3/5 × 1/4
y ≤ (3 × 1) / (5 × 4)
y ≤ 3/20
The value of y is: y ≤ 3/20.
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b) What number is 10% text more than 40?
Answers
Answer:
it might be 4
Step-by-step explanation:
that's all I have
I need help these problems
Answers
Step-by-step explanation:
she made shots = 34%of 54
=50*34/100
=17
he made 17 shots
I need help that's all if you cN helpe please do I'm beginning you
Answers
The slope of y = 7x - 10 is 7 while the y-intercept is -10 thus it has a high slope but a lower y-intercept so option (D) is correct.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear function with slope m and y-intercept c is given as y = mx + c.
Compare the given function y = 7x - 10
Slope m = 10
y-intercept = -10
Hence "Y = 7x - 10 has a slope of 7 and a y-intercept of -10, meaning it has a high slope but a low y-intercept".
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An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average claim amount was $1,800. Now there are concerns that if the true mean is actually higher than this they could potentially lose a lot of money. They randomly select 40 claims, and calculate a sample mean of $1,950. Assuming that the standard deviation of claims is $500, and set significance level = :05, test to see if the insurance company should be concerned.
Answers
So, the insurance company should be concerned that they could potentially lose money.
To test whether the insurance company should be concerned about the true mean claim amount being higher than the original estimate of $1,800, we can perform a one-sample t-test.
The null hypothesis for this test is that the true mean claim amount is equal to the original estimate of $1,800, and the alternative hypothesis is that the true mean claim amount is greater than the original estimate.
The t-statistic for this test is calculated as follows:
t = (sample mean - null mean) / (standard deviation / sqrt(sample size))
Plugging in the values from the problem, we have:
t = ($1,950 - $1,800) / ($500 / sqrt(40)) = 2.5.
We can then use a t-table or a computer to find the critical value of t for a one-tailed t-test with 39 degrees of freedom and a significance level of 0.05. The critical value is 1.68.
Since the calculated t-value of 2.5 is greater than the critical value, we can reject the null hypothesis and conclude that the true mean claim amount is significantly greater than the original estimate of $1,800.
Therefore, the insurance company should be concerned that they could potentially lose money.
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To test whether the insurance company should be concerned about the true mean claim amount being higher than the original estimate of $1,800, we can perform a one-sample t-test.
t = (sample mean - null mean) / (standard deviation / sqrt(sample size))
Plugging in the values from the problem, we have:
t = ($1,950 - $1,800) / ($500 / sqrt(40)) = 2.5.
We can then use a t-table or a computer to find the critical value of t for a one-tailed t-test with 39 degrees of freedom and a significance level of 0.05. The critical value is 1.68.
Therefore, the insurance company should be concerned that they could potentially lose money.
Angel wants to invest $4,000.00 in a savings account.
Determine the simple interest rate required for Angel's investment to grow to $13,400.00 in 25 months.
Round your answer to the nearest tenth of a percent and don't forget to include a percent sign, %, in
your answer.
The interest rate required to grow the investment to $13,400.00 is ______
Answers
The interest rate required to grow the investment to $13,400.00 would be = 35%
What is simple interest?Simple interest is the amount of money that is received for a particular period of time due to an investment made to an account.
The principal amount = $4,000.00
The time for investment = 25 months = 2 years
The simple interest = 13,400 - 4000= $9400
The rate (R) = X
The formula for simple interest=
p×t×r/100
9400= 13,400× 2×r/100
Make R the subject of formula;
R = 9400×100/13400×2
R = 940000/ 26800
R= 35%
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The same series of books you've been wanting cost 44$ at
Barnes and no ble and are on sale for 35gat target. If you have a 25.1.
off Coupon for Barnes and noble and a 51. Red card discount at target,
find what the price before tax would be at each of the two
retailers.
Answers
The price before tax of the books at Barnes and Noble would be 44$ - 25.1$ = 18.9$ if you use your coupon.
The price before tax of the books at Target would be 35$ - 51.1$ = -16.1$ if you use your Red card discount. However, the final price of the books cannot be negative, so the price before tax of the books at Target would be 35$ if you use your Red card discount.
Construct a cumulative frequency distribution
765-799| 22
Answers
The steps to construct a cumulative frequency distribution table are mentioned above.
What is cumulative frequency distribution? What is a mathematical function, equation and expression? cumulative frequency : A cumulative frequency is defined as the total of frequencies, that are distributed over different class intervals. function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is to construct a cumulative frequency distribution table.
Since the data is not given, we can write the steps to construct a frequency distribution table. The steps to create a cumulative frequency distribution table are mentioned below -
find the individual frequencies for each distinct value or category.arrange the obtained data in ascending order.the cumulative frequency of a distinct category is calculated by finding the sum of a category’s frequency and the total frequencies of all categories below it. the cumulative frequency of the first category equals the category’s individual frequency.Therefore, the steps to construct a cumulative frequency distribution table are mentioned above.
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Last week Scott ran 43 miles less than James. Scott ran 5 miles. How many miles did James run?
A. 35
B. 44
C. 38
D. 48
Answers
Answer:
D) 48
Step-by-step explanation:
Let s = Scott
Let j - James
s = 5
s + 43 = j Substitute 5 for s
5 + 43 = j
48 = j
(Graphing Proportional Relationships MC)
The table shows a proportional relationship between x and y
x 4.5 // 8.2 // 2.4
----------------------------------------
y 13.5 // 24.6 // 7.2
Which of the following correctly describes the graph of the relationship?
A line that goes through (0, 0) and (13.5, 4.5)
A line that goes through (4.5, 13.5) and (24.6, 8.2)
A line that goes through (13.5, 4.5) and (8.2, 24.6)
A line that goes through (0, 0) and (4.5, 13.5)
Answers
The option that correctly describes the graph of the relationship is; D: A line that goes through (0, 0) and (4.5, 13.5)
How to find the slope between two coordinates?
The formula for the slope between two coordinates is;
Slope = (y₂ - y₁)/(x₂ - x₁)
Let us take two coordinates from the table which are;
(2.4, 7.2) and (4.5, 13.5)
Thus;
Slope = (13.5 - 7.2)/(4.5 - 2.4)
Slope = 3
Now, looking at the options, the first 3 cannot be correct because they have mixed up x-coordinate values with y-coordinate values.
Let us check the last option which is a line that goes through (0, 0) and (4.5, 13.5). Thus;
Slope = (13.5 - 0)/(4.5 - 0)
Slope = 13.5/4.5
Slope = 3
Thus, we conclude that it is correct.
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Data collected on the discharge of the Colorado River and the speed are given in the table:
Discharge (ft3) Speed
1.3 2.3
2.2 0.99
5.8 3.5
11 5
12 16
14 22
16 27
21 14
49 33
51 35
What is the value of the correlation coefficient and its interpretation?
0.76; There is a strong, positive association between discharge and speed.
0.87; There is a strong, positive association between discharge and speed.
−0.76; There is a strong, negative association between discharge and speed.
−0.87; There is a strong, negative association between discharge and speed.
Answers
Answer:
The value of the correlation coefficient is 0.87, which means there is a strong, positive association between discharge and speed. A positive correlation means that as one variable increases, the other variable also increases. In this case, as the discharge of the Colorado River increases, the speed of the river also increases. The strength of the association is indicated by the magnitude of the correlation coefficient, which ranges from -1 to 1. A value of 0.87 is considered a strong positive correlation, indicating that there is a strong relationship between the two variables.
find a direct relationship between x and y.
x=t-5 and y=t^2-6t
Answers
The direct relationship of the variables is y = (t^2 - 6t)/(t - 5) * x
How to determine the direct relationship?From the question, we have the following parameters that can be used in our computation:
x = t - 5 and y = t^2 - 6t
The direct relationship between x and y is calculated using
Y = (y/x) * X
Substitute the known values in the above equation, so, we have the following representation
y = (t^2 - 6t)/(t - 5) * x
Hence, the direct relationship is y = (t^2 - 6t)/(t - 5) * x
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Suppose we roll a fair die four time. What is the probability that a 6 occurs on exactly one of the rolls?
Answers
The probability that a 6 occurs on exactly one of the rolls after rolling a fair die four times is 0.385.
What are the 3 types of probability?The Three Kinds of Probability
Classical: (equally probable outcomes) (equally probable outcomes) Let S be the sample space (the collection of all unique outcomes that might occur).
Subjective Probability. Definition of Relative Frequency.
What is the formula to find out probability?Formula used to find probability
The probability is often defined as the proportion of positive outcomes to all outcomes in the sample space. It is written as, the likelihood of an event
P(E) = (Number of favorable outcomes) ÷ (Sample space).
As die is rolled 4 times ,
X≈ binomial(4, 1/6)
P(X=r) = nCr (p)^r (q)^(n-r)
P(X = 1) = 4C1 × (1/6)^1 × (5/6)^3
= 4 × 1/6 × (5/6)^3
∴P(X = 1) = 0.257
The probability that a 6 occurs on exactly one of the rolls after rolling a fair die four times is 0.385.
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Using substitution to solve the following system of linear equations, what is the y-coordinate for the solution? 6x + y = -32 y = x - 4 Select one:a. y = -8b. y = 8c. y = 2d. y = -4
Answers
Therefore , the answer to this problem is that y-coordinate for the solution is option a) y = -8
What does equation mean?A number, a variable, or a mix of both are used in an expression coupled with specific operation symbols. An equal sign is used to denote the division of two expressions that make up an equation.
Here,
6x + y = -32 and
y = x - 4
=> 6x +( x - 4) = -32
=>7x -4=-32
=>7x =-28
=> x = -4
Thus,
y = -4 - 4 = -8
Therefore , the y-coordinate comes out to be y = -8
Thus, the correct option in the following option is option a)y=-8.
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What values of y and z make AFGHACBD?
2z+14
+2
2y+35
G
I
>
N
H
7y
B
32-1
D
Answers
Step-by-step explanation:
To make the equation AFGHACBD true, the value of y must be 7, and the value of z must be 32-1=31.
Here is how the equation works out:
2z + 14 = 2 * 31 + 14 = 68
2y + 35 = 2 * 7 + 35 = 49
68 + 2 = 70
70 > 49
49 + 7y = 49 + 7 * 7 = 98
98 > 70
70 + 32 - 1 = 70 + 31 = 101
101 > 98
98 + 2y + 35 = 98 + 2 * 7 + 35 = 146
146 > 101
So, the values of y and z that make the equation AFGHACBD true are y=7 and z=31.
Makayla wants to make 200 ml of a 18% saline solution but only has access to 8% and 24% saline mixtures. Which of the following system of equations correctly describes this situation if x represents the amount of the 8% solution used, and y represents the amount of the 24% solution used?
O a.) 0.24x +0.08y= 0.18(200) x+y = 200 O b.) 0.08x +0.24y = 200 x+y=0.18(200) O c.) 0.08x+0.24y = 0.18(200) x+y=200 O d.) 0.24x +0.08y = 200 x+y=0.18(200)
Answers
The formulae that specify how much 8% solution and how much 24% solution were utilized are [tex]x+ y=200 and x+3y=450.[/tex]
What is an equation ?A mathematical equation is a formula that uses the equals symbol (=) to link two expressions and represent their equivalence. A mathematical statement that demonstrates the equality of two mathematical expressions is an equation in algebra, in its most basic form. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
Let x and y be the volume of the 8% and 24% solutions, respectively, that were utilized.
The entire solution volume, as stated in the question, will be 200ml. The resulting equation is: [tex]x +y=200[/tex]
Now that it has been stated that 8%, 18%, and 24% saline mixes would be employed as the solution, the following equation will be:
[tex]0.08x+ 0.24y=0.18*200\\8x/100+24/100=18/100*200\\8x+24y=3600\\\\8(x+3y)=3600\\ x+3y=450\\[/tex]
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(4+√5)/(√5 -2) rationalize the denominator and simplify
Answers
Answer: 13 + 6√5
Step-by-step explanation: None