Answer:
Step-by-step explanation:
Hello!
The researcher's objective is to test if the variance of the annual repair costs increases with the age of the automobile, i.e. the older the car, the more the repairs costs. The parameters of the study are the population variances of the annual repair costs of 4 years old cars and 2 years old cars.
X₁: Costs of annual repair of a 4 years old car.
Assuming X₁~N(μ₁;δ₁²)
A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $170
n₁= 26 and S₁= $170
X₂: Costs of annual repair of a 2 years old car.
Assuming X₂~N(μ₂;σ₂²)
A sample of 25 automobiles 2 years old showed a sample standard deviation for the annual repair cost of $100.
n₂= 25 and S₂= $100
a. State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for older automobiles.
H₀: δ₁² ≤ σ₂²
H₁: δ₁² > σ₂²
b. At a .01 level of significance, what is your conclusion? What is the p-value? Discuss the reasonableness of your findings.
This is a variance ratio test and you have to use a Snedecor's F-statistic:
[tex]F= \frac{S^2_1}{S_2^2} * \frac{Sigma_1^2}{Sigma_2^2}~~F_{n_1-1;n_2-1}[/tex]
[tex]F_{H_0}= \frac{28900}{10000}*1= 2.89[/tex]
This test is one-tailed to the right and so is the p-value, you have to calculate it under a F₂₅;₂₄
P(F₂₅;₂₄≥2.89)= 1 - P(F₂₅;₂₄<2.89)= 1 - 0.994= 0.006
Using the p-value approach the decision rule is:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
α: 0.01
The p-value is less than the level of significance, the decision is to reject the null hypothesis.
Then using a 1% level, you can conclude that the population variance of the cost of annual repairs for 4 years old cars is greater than the population variance of the cost of annual repairs for 2 years old cars.
I hope this helps!
what is x= 0.393 as a fraction
Answer:
393/1000
Step-by-step explanation:
Answer:
Step-by-step explanation:
393/1000
Percent of discount 15%
Sale price $146.54
Find a polynomial equation that has zeros at x = −2, x = 0, x = 3 and x = 5
If a polynomial "contains", in a multiplicative sense, a factor [tex](x-x_0)[/tex], then the polynomial has a zero at [tex]x=x_0[/tex].
So, you polynomial must contain at least the following:
[tex](x-(-2)),\quad (x-0),\quad (x-3),\quad (x-5)[/tex]
If you multiply them all, you get
[tex]x(x+2)(x-3)(x-5)=x^4 - 6 x^3 - x^2 + 30 x[/tex]
Now, if you want the polynomial to be zero only and exactly at the four points you've given, you can choose every polynomial that is a multiple (numerically speaking) of this one. For example, you can multiply it by 2, 3, or -14.
If you want the polynomial to be zero at least at the four points you've given, you can multiply the given polynomial by every other function.
To find a polynomial with given zeros, each zero can be plugged into the format (x - a). Doing so with the provided zeros in this question, i.e., -2, 0, 3, and 5, represents the zeroes of the polynomial equation x(x + 2)(x - 3)(x - 5) which simplifies to x4 - 6x3 + 3x2 + 60x.
Explanation:The subject of this question is polynomial equations in mathematics. In order to find a polynomial equation that has zeroes at x = -2, x = 0, x = 3, and x = 5, you can use the fact that the equation (x - a)(x - b)(x - c)(x - d) will have zeros at a, b, c, and d.
By substituting the values for a, b, c, and d into the equation with the zeroes provided (-2, 0, 3, and 5), the polynomial equation that satisfies these zeroes can be expressed as: (x - (-2))(x - 0)(x - 3)(x - 5). Simplifying, this gives: x(x + 2)(x - 3)(x - 5).
To further simplify, we need to multiply these expressions: x*(x+2)*(-x+15)-(2*x-10),which simplifies to: x4 - 6x3 + 3x2 + 60x. This is the polynomial equation that has zeros at x = -2, x = 0, x = 3, and x = 5.
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Solve:
3(4 – 2x) = -x+1
Answer:
11/5 =x
Step-by-step explanation:
3(4 – 2x) = -x+1
Distribute
12 -6x = -x+1
Add 6x to each side
12 -6x+6x = 6x-x +1
12 = 5x +1
Subtract 1 from each side
12-1 = 5x+1-1
11= 5x
Divide each side by 5
11/5 =5x/5
11/5 =x
Steps to solve:
3(4 - 2x) = -x + 1
~Distribute
(3 * 4) + (3 * -2x) = -x + 1
~Simplify
12 - 6x = -x + 1
~Subtract 12 to both sides
12 - 12 - 6x = -x + 1 - 12
~Simplify
-6x = -x - 11
~Add x to both sides
-6x + x = -x + x - 11
~Simplify
-5x = -11
~Divide -5 to both sides
-5x/-5 = -11/-5
~Simplify
x = 11/5
Best of Luck!
The coach of an age group swim team needs to assign swimmers to a 200-yard medley relay team to send to the Junior Olympics. Since most of his best swimmers are very fast in more than one stroke, it is not clear which swimmer should be assigned to each of the four strokes. The five fastest swimmers and the best times (in seconds) they have achieved in each of the strokes (for 50 yards) are
Answer:
a) add a dummy stroke to make the problem as an assignment problem of adding 5 strokes to 5 swimmers. see first attachment.
b) applying the Hungarian method.
4.8 0 0.9 4.1 2.5
10.3 0 9.1 1.6 8.7
4.8 0 10.4 1.9 5.1
2.8 0 3.2 2.1 4.7
0 0 0 0 0
Deduct the smallest element in each column from the other elements of the column.
2 0 0 2.5 0
7.5 0 8.2 0 6.2
2 0 9.5 0.3 2.6
0 0 2.3 0.5 2.2
0 0 0 0 0
Which implies:
2 8.2 2.5 6.2
7.5 9.5 0.3 2.6
2 2.3 0.5 2.2
33.8 + 34.7 + 28.5 + 29.2 = 126.2
David = Back Stroke
tony = Breast Stroke
Chris = Butterfly
Carl = Free Style
The question is about assigning swimmers in a team to different strokes to achieve the best total time. It's a combinatorial optimization problem which can be solved by considering all the permutations of swimmers' assignments to each stroke and selecting the one with least total time.
Explanation:The subject of this question is an optimization problem in Mathematics, specifically in the field of Combinatorics. Deciding the arrangement of swimmers to minimize the total time spent can be approached using techniques from this field. Unfortunately, the information provided does not give the exact times of the swimmers, so achieving a detailed solution isn't possible. However, the problem could hypothetically be solved by enumerating all possible assignments of swimmers to strokes and selecting the assignment that has the least total time.
This problem resonates with high school level math, where students begin to tackle optimization problems and permutations.
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The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6. What is the probability that a randomly selected bill will be at least $39.10
Answer:
Probability that a randomly selected bill will be at least $39.10 is 0.03216.
Step-by-step explanation:
We are given that the daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6.
Let X = daily dinner bills in a local restaurant
So, X ~ N([tex]\mu=28,\sigma^{2} =6^{2}[/tex])
The z-score probability distribution for normal distribution is given by;
Z = [tex]\frac{ X -\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean amount = $28
[tex]\sigma[/tex] = standard deviation = $6
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, the probability that a randomly selected bill will be at least $39.10 is given by = P(X [tex]\geq[/tex] $39.10)
P(X [tex]\geq[/tex] $39.10) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{ 39.10-28}{6}[/tex] ) = P(Z [tex]\geq[/tex] 1.85) = 1 - P(Z < 1.85)
= 1 - 0.96784 = 0.03216
Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.85 in the z table which has an area of 0.96784.
Hence, the probability that a randomly selected bill will be at least $39.10 is 0.03216.
The probability that a randomly selected bill will be at least $39.10 is approximately 0.0323.
First, we calculate the z-score for a bill of $39.10 using the formula:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
where X is the value for which we want to find the probability, [tex]\( \mu \)[/tex] is the mean, and [tex]\( \sigma \)[/tex] is the standard deviation.
Given:
[tex]\[ \mu = 28 \] \[ \sigma = 6 \] \[ X = 39.10 \][/tex]
Plugging in the values:
[tex]\[ z = \frac{39.10 - 28}{6} \] \[ z = \frac{11.10}{6} \] \[ z \approx 1.85 \][/tex]
Now, we look up the z-score of 1.85 in the standard normal distribution table or use a calculator to find the probability of a z-score being at least 1.85. This gives us the area to the right of the z-score on the standard normal curve.
Using a standard normal distribution table or calculator, we find:
[tex]\[ P(Z \geq 1.85) \approx 0.0323 \][/tex]
An online gaming site conducted a survey to determine the types of games people play online. if 1500 people participated in the study how many more would play card games than arcade games (Page 824)
Answer:
315
Step-by-step explanation:
The missing percentages of the given scenario are;
Adventure Games: 22%
Puzzles: 28%
Card Games: 30%
Arcade Games: 9%
Board Games: 11%
So in order to solve the problem, we simply use the pie chart distributions to get the result
Now if look at the percentages, we that card games percentage is 30 while arcade games is 9 so, 21 % of people play more card games.
In terms of number of people = 21/100 x 1500 = 315
Hence out of 1500, 315 people play card games more than arcade
Answer:
The number of more people that played card games than arcade games is 150 people
Step-by-step explanation:
Here we have a pie chart showing games people play in the following proportions
Assumption; Card games = 49%
Arcade games = 32%
Classic = 15%
Kids = 4%
Therefore. if 49% played card games, we have 49% of 1500 which is 735 people, while 32% that played arcade games, we have 39% of 1500 = 0.39×1500 = 585
Therefore, the number of more people that played card games than arcade games = 735 - 585 = 150 people.
Subract 8 from the quotient of 15
Answer: These would be my two thoughts.
Step-by-step explanation:
ANSWER #1. 15-8= 7
ANSWER #2. 3-8= -5
A can of tomato soup is 4 1/4 inches tall and has a diameter of 3 inches. The company that makes the cans uses sheets of metal that are 1000in^2.
1.How many whole cans can the company make out of each sheet of metal?
2. Will there be any metal left over? If so how much?
Answer: a) 21 cans
b) 10.83 square inches.
Step-by-step explanation:
The cans are cylinders of 4 and 1/4 inches tall (or 4.25 in)
and the diameter is 3 inches.
The surface of a cylinder is equal to:
S = pi*r^2 + h*2*pi*r
where r is the radius, half of the diameter, so we have that r = 3in/2 = 1.5 in.
h is the height, h = 4.25 in
pi = 3.14
Then the surface needed for a can is:
S = 3.14*1.5^2 + 4.25*2*3.14*1.5 = 47.1 square inches.
if the sheet is 1000 in^2, we can make an amount of:
N = 1000/47.1 = 21.23
but we can not do a 0.23 of a can, so we need to round down.
A) we can make 21 cans out of a sheet of metal.
B) the 0.23 of a can that we removed earlier is the amount of metal leftover. The total is 0.23*47.1 in^2 = 10.83 in^2
Answer:
Step-by-step explanation:
To determine the amount of metal needed to make each can, we would determine the total surface area of each can. Since the cans are cylindrical, the formula for determining the total surface area of a cylinder is used. It is expressed as
Total surface area = πr² + 2πr
r = radius of the can
h = height of the can
π = 3.14
From information given,
Diameter = 4.25 inches
Radius = diameter/2 = 4.25/2 = 2.125 inches
Total surface area = 3.14 × 2.125² + 2 × 3.14 × 2.125 = 27.5 in²
1) since 1000 in² sheet material is available, the number of cans that can be made is
1000/27.5240625 = 36 cans
2) The amount of metal sheet left is
1000 - (36 × 27.5) = 10 in²
please list
first 5 multiples of:
20
30
first correct answer is the brainliest
Answer:
Step-by-step explanation
First five multiples of 2030 are: 2, 5, 7, 10 an 14
A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 12% chose chocolate pie, and the margin of error was given as plus or minus3 percentage points. What values do ModifyingAbove p with caret, ModifyingAbove q with caret, n, E, and p represent? If the confidence level is 99%, what is the value of alpha?
Answer:
Step-by-step explanation:
.01 (subtract confidence level from 100)
Use the interactive tool to create the three-dimensional
solid from the net.
What is the surface area of the three-dimensional solid
you created?
35 cm2
56 cm2
72 cm2
90 cm2
The surface area of the three dimensional solid is 72 square centimeters and its three dimensional diagram is attached.
Step-by-step explanation:
The given is,
Detailed view or net diagram of the three dimensional diagram.
Step:1
Three dimensional diagram of the given net diagram is attached.
From the three dimensional diagram given net diagram is rectangular prism.
Step:2
From the three dimensional diagram
Formula for surface area of the rectangular prism,
[tex]A = 2(wl + lh + hw)[/tex]..............................(1)
Where, w - Width
l - Length
h - Height
From the attachment,
l = 6 cm
w = 2 cm
h = 3 cm
Equation (1) becomes,
[tex]A = 2((6)(2) + (6)(3) + (3)(2))[/tex]
= 2 ( 12 + 18 + 6 )
= 2 ( 36 )
A = 72 squared centimeters
( or )
From the net diagram,
Surface area, A = ((6×3)+(2×3)+(2×6)+(2×3)+(3×6)+(2×6))
= 18 + 6 + 12 + 6 + 18 + 12
= 72
Surface area, A = 72 squared centimeters
Result:
The surface area of the three dimensional solid is 72 square centimeters and its three dimensional diagram is attached.
Answer:72 cm2
Step-by-step explanation:
Which one is correct for this question need help please
Answer:
A is correct, 7 units. Hope this helps! :)
It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 31 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group will be administered a placebo. After one year, 11% of the first group has a second episode and 9% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is more than the true percentage of those in the second group who suffer a second episode? Select the [Alternative Hypothesis, Value of the Test Statistic].
Answer:
We conclude that the true percentage of those in the first group who suffer a second episode is less than or equal to the true percentage of those in the second group who suffer a second episode.
Step-by-step explanation:
We are given that there are 31 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group will be administered a placebo.
After one year, 11% of the first group has a second episode and 9% of the second group has a second episode.
Let [tex]p_1[/tex] = true percentage of those in the first group who suffer a second episode.
[tex]p_2[/tex] = true percentage of those in the second group who suffer a second episode.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1-p_2\leq[/tex] 0 or [tex]p_1\leq p_2[/tex] {means that the true percentage of those in the first group who suffer a second episode is less than or equal to the true percentage of those in the second group who suffer a second episode}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1-p_2[/tex] > 0 or [tex]p_1>p_2[/tex] {means that the true percentage of those in the first group who suffer a second episode is more than the true percentage of those in the second group who suffer a second episode}
The test statistics that will be used here is Two-sample z proportion test statistics;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of people in the first group who suffer a second episode = 11%
[tex]\hat p_2[/tex] = sample proportion of people in the second group who suffer a second episode = 9%
[tex]n_1[/tex] = sample of people in first group = 31
[tex]n_2[/tex] = sample of people in second group = 45
So, the test statistics = [tex]\frac{(0.11-0.09)-(0)}{\sqrt{\frac{0.11(1-0.11)}{31}+ \frac{0.09(1-0.09)}{45}} }[/tex]
= 0.283
Now, at 0.1 significance level, the z table gives critical value of 1.2816 for right-tailed test. Since our test statistics is less than the critical value of z as 0.283 < 1.2816, so we have insufficient evidence to reject our null hypothesis due to which we fail to reject our null hypothesis.
Therefore, we conclude that the true percentage of those in the first group who suffer a second episode is less than or equal to the true percentage of those in the second group who suffer a second episode.
A hypothesis test can determine whether there is enough evidence to support the claim that the new drug is effective in reducing second episodes of heartburn. It involves defining null and alternative hypotheses, calculating a test statistic, and comparing it to a critical value based on the set significance level.
Explanation:We start by defining our null and alternative hypotheses. In this case, we are testing against the claim that the true percentage of those in the first group who suffer a second episode is more than the true percentage of those in the second group who suffer a second episode.
So, our null hypothesis (H0) is: The percentage of heart attempts in group 1 is equal to or less than that of group 2.
And, our alternative hypothesis (Ha) is: The percentage of heart attempts in group 1 is greater than that of group 2.
We conduct the hypothesis test using a standard test of proportions. Calculating our test statistic can be done using the formula: Z = (p1 - p2)/sqrt(p(1 - p)[(1/n1) + (1/n2)])
Where, p1 and p2 are the proportions of the two groups, n1 and n2 are the sizes of the two groups, and p is the combined proportion.
Based on the information in the problem, the calculated test statistic value and the critical z-value for a one-tailed test at the significance level 0.1, we can make a decision to reject or fail to reject the null hypothesis. If the calculated absolute z-value is greater than the critical z-value, we reject the null hypothesis and conclude that there is enough evidence at the 0.1 level. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim.
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The solid S has a base region B defined by the curves y = 5x − x 2 and y = x. (A) Find the volume of S if the cross-sections through S perpendicular to the x-axis are squares with an edge along the base. (B) Find the volume of S if the cross-sections through S perpendicular to the x-axis are equilateral triangles with an edge along the base. 3 (C) Find the volume of S if the cross-sections through S parallel to the x-axis are semicircles with their diameter along the base. (D) Find the volume of S if the cross-sections through S parallel to the x-axis are isosceles right triangles with a leg along the base.
Answer:
a) The volume of S is 34.13
b) The volume of S is 14.8
c) The volume of S is 5.17
d) The volume of S is 11.33
Step-by-step explanation:
a) The cross section area is equal to:
[tex]A=a^{2} =((5x-x^{2})-x)^{2} =(4x-x^{2} )^{2}[/tex]
The volume of S is equal to:
[tex]Vol_{S} =\int\limits^4_0 {A(x)} \, dx =\int\limits^4_0 {(4x-x^{2})^{2} } \, dx =34.13[/tex]
b) The cross section area is equal to:
[tex]A=\frac{a^{2}\sqrt{3} }{4} =\frac{\sqrt{3} }{4} ((5x-x^{2} )-x)^{2} =\frac{\sqrt{3} }{4} (4x-x^{2} )^{2}[/tex]
The volume of S is equal to:
[tex]Vol_{S} =\int\limits^4_0 {A(x)} \, dx =\frac{\sqrt{3} }{4} \int\limits^4_0 {(4x-x^{2})^{2} } \, dx =14.8[/tex]
c)
[tex]y=5x-x^{2} \\\frac{dy}{dx} =0\\5x-x^{2} =0\\x=5/2\\y(5/2)=25/4\\y=5x-x^{2} \\x^{2} -5x+y=0\\x=\frac{5+-\sqrt{25-4y} }{2}[/tex]
The cross section area is equal to:
[tex]A_{1} =\frac{1}{2} \pi r_{1}^{2} =\frac{1}{2} \pi (\frac{1}{2} (\frac{5+\sqrt{25-4y} }{2} -\frac{5-\sqrt{25-4y} }{2} ))^{2} =\frac{1}{8} \pi (25-4y)\\A_{2} =\frac{1}{2} \pi r_{2}^{2}=\frac{1}{2}\pi (\frac{1}{2} (y-\frac{5-\sqrt{25-4y} }{2} ))^{2} =\frac{1}{32} \pi (2y-5+\sqrt{25-4y} )^{2}[/tex]
The volume of S is equal to:
[tex]Vol_{S} =\int\limits^a_b {A_{1}(y) } \, dy+\int\limits^4_0 {A_{2}(y) } \, dy ,where-a=25/4,b=4\\Vol_{S} =\int\limits^a_b {\frac{1}{8}\pi (25-4y)} \, dy +\int\limits^a_b {\frac{1}{32}\pi (2y-5+\sqrt{25-4y} )^{2} } \, dy =5.17[/tex]
d) The cross section area is:
[tex]A_{1} =\frac{1}{2}ab=\frac{1}{2} a^{2} =\frac{1}{2} (\frac{5+\sqrt{25-4y} }{2}-\frac{5-\sqrt{25-4y}}{2} )^{2} =\frac{1}{2} (25-4y)\\A_{1}=\frac{1}{2}ab=\frac{1}{2} a^{2} =\frac{1}{2}(y-\frac{5-\sqrt{25-4y}}{2}} )^{2} =\frac{1}{8} (2y-5+\sqrt{25-4y}})^{2}[/tex]
The volume of S is equal to:
[tex]Vol_{S} =\int\limits^a_b {A_{1}(y) } \, dy +\int\limits^4_0 {A_{2}(y) } \, dy ,where-a=25/4,b=4\\Vol_{S}=\int\limits^a_b {\frac{1}{2}(25-4y) } \, dy +\int\limits^4_0 {\frac{1}{8}(2y-5+\sqrt{25-4y})^{2} } \, dy =11.33[/tex]
Write the equation for the line graphed below.
Answer:
y = 1/2x -1
Step-by-step explanation:
to find the y-intercept you find where the line crosses the y axis
for the slope you need to use the equation
change of y2 - change of y1
change of x2 - change of x1
y=ax+b
(-2; -2); (0;-1); (2; 0)
-1=a*0+b => b=-1
0=a*2+b
0=a*2-1
a*2=1 => a=1/2
y=x/2 -1
There are four steps in solving one's personal financial challenges:
1. considering opportunity costs
2. assessing risks and returns
3. setting short- and long-term goals
4. assessing needs and wants
Which of these is the correct order of these steps?
O 2,3,1,4
O 1,2,3,4
O4, 1,2,3
3,1.4.2
Answer:
a
Step-by-step explanation:
The order of four steps are Assessing needs and wants, Considering opportunity costs, Assessing risks and returns and Setting short- and long-term goals, Option C is correct.
What is Finance?Finance is the study and discipline of money, currency and capital assets.
The correct order of the four steps in solving one's personal financial challenges is indeed:
Assessing needs and wants
Considering opportunity costs
Assessing risks and returns
Setting short- and long-term goals
Hence, the order of four steps are Assessing needs and wants, Considering opportunity costs, Assessing risks and returns and Setting short- and long-term goals, Option C is correct.
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classify each pair of the angles as one of the following
Answer:
where are the angles? I can't see anything
Answer:
Please provide pictures!!
Step-by-step explanation:
20 times the sum of 4 and 2
Answer:
120
Step-by-step explanation:
add 4 and 2 then multipy by 2 and add a zero
Michelle borrows a total of $2500 in student loans from two lenders. One charges 4.2% simple interest and the other charges 6.8% simple interest. She is not required to pay off the principal or interest for 3 yr. However, at the end of 3yr, she will owe a total of $354 for the interest from both loans. How much did she borrow from each lender?
Let x represent amount borrowed at 4.2% and y represent amount invested at 6.8%.
We have been given that Michelle borrows a total of $2500 in student loans from two lenders. We can represent this information in an equation as:
[tex]x+y=2500...(1)[/tex]
[tex]y=2500-x...(1)[/tex]
We are also told that at the end of 3 years, she will owe a total of $354 for the interest from both loans.
Amount of interest earned at a rate of 4.2% in 3 years would be [tex]0.042\cdot 3\cdot x=0.126x[/tex].
Amount of interest earned at a rate of 6.8% in 3 years would be [tex]0.068\cdot 3\cdot y=0.204y[/tex].
We can represent this information in an equation as:
[tex]0.126x+0.204y=354...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]0.126x+0.204(2500-x)=354[/tex]
[tex]0.126x+510-0.204x=354[/tex]
[tex]-0.078x+510=354[/tex]
[tex]-0.078x+510-510=354-510[/tex]
[tex]-0.078x=-156[/tex]
[tex]\frac{-0.078x}{-0.078}=\frac{-156}{-0.078}[/tex]
[tex]x=2000[/tex]
Therefore, Michelle borrowed $2000 at 4.2%.
Upon substituting [tex]x=2000[/tex] in equation (1), we will get:
[tex]y=2500-2000=500[/tex]
Therefore, Michelle borrowed $500 at 6.8%.
She borrowed $ 2000 from the 4.2% lender and $ 500 from the 6.8% lender.
Since Michelle borrows a total of $ 2500 in student loans from two lenders, and one charges 4.2% simple interest and the other charges 6.8% simple interest, and she is not required to pay off the principal or interest for 3 yr, but at the end of 3yr, she will owe a total of $ 354 for the interest from both loans, to determine how much did she borrow from each lender, the following calculation must be performed:
4.2 x 3 = 12.6 6.8 x 3 = 20.4 2500 x 0.126 + 0 x 0.204 = 315 2000 x 0.126 + 500 x 0.204 = 354
Therefore, she borrowed $ 2000 from the 4.2% lender and $ 500 from the 6.8% lender.
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HELP ASAP PLEASE!!!
Which of the following lines are parallel?
a. line c and line d
b. line b and line c
c. line a and line b
d. line d and line e
You may pick more than one.
Answer:
The answer is d: LINE D AND LINE E
The other answer is c LINE A AND LINE B
Step-by-step explanation:
a) What fraction is equal to 50% of 1/3
b) What fraction is equal to 75% of 1/2
Answer:
a) 1/6
b) 3/8
Step-by-step explanation:
Even i struggle with fractions but im sure you will get it one day (✿◡‿◡)
You come up with what you think is a great idea for a new advertising campaign for your company. Your boss is worried that the ads will cost a lot of money and she wants to be 99% confident that the ads increase sales before rolling the new ads out nationwide. You run the ads in a typical city and take a random sample to see if people who saw the ad are more likely to buy the product. When you reported the results to your boss, you made a Type II error. 18. Explain in words the statistical meaning of this type of error.
Answer:
Type II error will be made if we conclude that the new advertising campaign does not increases the sales when in fact the sales are increased after the advertising campaign.
Step-by-step explanation:
A type II error is a statistical word used within the circumstance of hypothesis testing that defines the error that take place when one is unsuccessful to discard a null hypothesis that is truly false. It is symbolized by β i.e.
β = Probability of accepting H₀ when H₀ is false.
In this case we need to test the hypothesis whether the new advertising campaign increases the sales or not.
The hypothesis can be defined as:
H₀: The new advertising campaign does not increases the sales.
Hₐ: The new advertising campaign increases the sales.
The confidence level wanted here is 99%.
The type II error will be made if we conclude that the new advertising campaign does not increases the sales when in fact the sales are increased after the advertising campaign.
The type II error could have been made because of the following reasons:
The sample size selected is too small. The smaller the sample size, greater is the probability of type II error. Significance level of the test must be small. If the significance level is small then the rejection regions decreases. Thus, reducing the chances of correctly rejecting the null hypothesis.Thus, the type II error might have been committed because of small sample size or small significance level.
Round 43.3333 to the nearest hundredth.
A) 43.3
B) 43.33
C) 43.34
D) 43.4
Answer: B
Step-by-step explanation:
Can't really explain it. A tenth is .1, a hundredth is .01
A family of recurrences has the following form for constants a and c: T(1) = a T(n) = T(n-1) + c for n > 1 Solve this recurrence for T(n) in terms of a and c. Then demonstrate that you have the solution by identifying, from the list below, the correct formula for T(n) in terms of specific values of a and c. a) If a=1 and c=3, then T(n) is 3n - 2. b) If a=1 and c=3, then T(n) is n + 2. c) If a=3 and c=5, then T(n) is 3n + 2. d) If a=3 and c=5, then T(n) is 5n + 3.'
Answer:
T(n) = cn +(a-c)
Step-by-step explanation:
Note that T(1) = a, then T(2) = a+c, T(3) = (a+c)+c = a+2c, T(4) = (a+2c)+c = a+3c. Thus, our hypotheis is that T(n) = a+(n-1)c. We will prove this by strong induction.
Note that T(1) = a = a+(1-1)c. So the base case is proved. Assume that the result is true for all k<n. Then
T(n) = T(n-1)+c = (a+(n-2)c)+c = a+(n-1)c= cn+ (a-c).
So, by induction, the result holds.
Note that if a=1 and c = 3 then T(n) = 1+(n-1)3 = 3n-3+1 = 3n-2, which invalidates option b)
If a=3 and c=5 then we have that T(n) = 5n+(3-5) = 5n-2, which invalidates c) and d).
Then the formula is correct.
Answer:
(a) is correct
[tex]T(n) = a+(n-1)c[/tex]
Step-by-step explanation:
Notice that according to the information that you are given
[tex]T(1)=a \\T(2)=T(1)+c = a+c\\T(3)=T(2)+c = a+c+c = a+2c[/tex]
If you think about it there is a clear pattern, it would be
[tex]T(n) = a+(n-1)c[/tex]
Now notice that (a) is correct if we set a=1 and c=3 we get
[tex]T(n) = 1+3(n-1) = 3n-2[/tex]
find the illegal values of b in the fraction 2b2+3b-10/ b2-2b-8
Answer:
-2 and 4
Step-by-step explanation:
When you look for values that make an expression “illegal” the first step is to look for 3 things.
1) a variable in a denominator
- we have b, a variable, in the denominator of this expression
- values in the denominator cannot be 0
2) variables under even roots
- variables under even roots are a restriction because even roots are undefined when there are negative values under them
- there are no roots in this case so we dont have to worry about that
3) the literal letters: “log” in the expression
- there’s no “log” in the expression so we dont have to worry about that
—moving on—
We have a variable in the denominator, b.
The expression is a quadratic:
b^2 - 2b - 8
You have to find values that make this quadratic 0.
So you can make an equation setting the quadratics equal to 0.
b^2 - 2b - 8 = 0
Solve for b
Factor:
(b - 4)(b + 2) = 0
Because of zero product property we can say:
b = -2, b = 4.
If these values are plugged into your expression, it will be “illegal,” or “undefined,”
If the height of the parallelogram shown is increased by 1 cm and the base is increased by 2 cm, what is the area of the new parallelogram?
28 cm2
39 cm2
55 cm2
60 cm2
Answer:
55 cm2
Step-by-step explanation:
The area of the new parallelogram is 55 sq.cm, the correct option is C.
What is a Parallelogram?A polygon with four sides such that the opposite sides are parallel and equal is called a Parallelogram.
The height of the parallelogram is 4 cm
The base of the parallelogram is 9cm
The height of the parallelogram is increased by 1 cm
New height = 5cm
The base of the parallelogram is increased by 2 cm
New base = 11 cm
Area of a parallelogram is = Base * Height
Area of parallelogram is = 5 * 11 = 55 sq.cm
Therefore, the area of the new parallelogram is 55 sq.cm.
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A __________ determines how far a particular value is from the mean relative to the data set's standard deviation. a. percentile b. coefficient of variation c. z-score d. variance
Answer:
z-score
Step-by-step explanation:
Z-score gives the relative value of any data population in relation to its mean. It depicts at what distance any data is from the mean. In technical terms it can be termed as the number of times a data is data away from the mean. Positive value of z score means value is more than mean while a negative value signifies data is less than that of mean.
Z – score is primarily used in qualitative analysis of numerical data by the statistician after data is arranged in normal distribution form. Z score of 0 means the value is same as mean while z-score of value 1 means data is one standard deviation away from the mean.
The z-score is the measure that determines the distance of a value from the mean in terms of standard deviations which is option c.
A z-score determines how far a particular value is from the mean relative to the data set's standard deviation. Given an experimental value, X, the mean, μ (mu), and the standard deviation, σ (sigma), the z-score is calculated using the formula Z = (X - μ) / σ. A z-score represents the number of standard deviations an experimental value is above or below the mean. For example, if a data value has a z-score of 2, it is two standard deviations above the mean. Contrarily, a z-score of -1.5 indicates that the value is one and a half standard deviations below the mean. Z-scores are used across various fields to compare different values within a data set or among different data sets with different means and standard deviations.
The length of the base of an isosceles triangle is x. The length of a leg is 3x-6. The perimeter of the triangle is 51. Find x
Answer:
x = 9
Step-by-step explanation:
The perimeter is the sum of the lengths of the base and the two equal legs:
51 = x + 2(3x -6)
51 = 7x -12 . . . . . eliminate parentheses
63 = 7x . . . . . . . . add 12
9 = x . . . . . . . . . . divide by 7
The triangle shown below has an area of 121212 units^2
2
squared.
Find xxx.
Answer:
4
Step-by-step explanation:
Let's set up an equation using the formula for the area of a triangle.
Hint #22 / 3
\begin{aligned} \text{Area of a triangle} &= \dfrac12 \cdot \text{base} \cdot \text{height}\\\\ 12&= \dfrac12 \cdot 6 \cdot x \\\\ 12&= 3x \\\\ \dfrac{12}{\blueD{3}}&= \dfrac{3x}{\blueD{3}} ~~~~~~~\text{divide both sides by } {\blueD{ 3}}\\\\ \dfrac{12}{\blueD{3}}&= \dfrac{\cancel{3}x}{\blueD{\cancel{3}}}\\\\ x &=\dfrac{12}{\blueD{3}}\\\\ x &=4\end{aligned}
Area of a triangle
12
12
3
12
3
12
x
x
=
2
1
⋅base⋅height
=
2
1
⋅6⋅x
=3x
=
3
3x
divide both sides by 3
=
3
3
x
=
3
12
=4