Answer: To test for unequal variances, we use Welch's t-test, which is a modification of the Student's t-test that adjusts for unequal variances. The null hypothesis for Welch's t-test is that the population means are equal, and the alternative hypothesis is that they are not.
The critical values for a two-tailed test at alpha level 0.10 with degrees of freedom df = 23.99 can be found using a t-distribution table or a calculator and are ±1.717.
For the first sample, we have:
Sample 1: s1 = 10.2, n1 = 22
Sample 2: s2 = 6.4, n2 = 16
Test: Two-tailed
The degrees of freedom can be calculated as follows:
df = ((s1^2 / n1) + (s2^2 / n2))^2 / ((s1^2 / n1)^2 / (n1 - 1) + (s2^2 / n2)^2 / (n2 - 1))
= ((10.2^2 / 22) + (6.4^2 / 16))^2 / ((10.2^2 / 22)^2 / 21 + (6.4^2 / 16)^2 / 15)
= 23.81
The calculated t-value is:
t = (x1 - x2) / sqrt(s1^2 / n1 + s2^2 / n2)
= (0 - 0) / sqrt(10.2^2 / 22 + 6.4^2 / 16) = 0
Since the calculated t-value is within the critical region (-1.717, 1.717), we fail to reject the null hypothesis. We can conclude that there is insufficient evidence to suggest that the population means are different.
For the second sample, we have:
Sample 1: s1 = 0.89, n1 = 25
Sample 2: s2 = 0.67, n2 = 18
Test: Right-tailed
The degrees of freedom can be calculated as follows:
df = ((s1^2 / n1) + (s2^2 / n2))^2 / ((s1^2 / n1)^2 / (n1 - 1) + (s2^2 / n2)^2 / (n2 - 1))
= ((0.89^2 / 25) + (0.67^2 / 18))^2 / ((0.89^2 / 25)^2 / 24 + (0.67^2 / 18)^2 / 17)
= 34.13
The critical value for a right-tailed test at alpha level 0.10 with degrees of freedom df = 34.13 can be found using a t-distribution table or a calculator and is 1.311.
The calculated t-value is:
t = (x1 - x2) / sqrt(s1^2 / n1 + s2^2 / n2)
= (0.89 - 0.67) / sqrt(0.89^2 / 25 + 0.67^2 / 18)
= 2.42
Since the calculated t-value (2.42) is greater than the critical value (1.311), we reject the null hypothesis. We can conclude that there is sufficient evidence to suggest that the population mean of Sample 1 is greater than the population mean of Sample 2.
For the third sample, we have:
Sample 1: s1 = 124, n1 = 12
Sample 2: s2 = 260, n2 = 10
Test: Left-tailed
The degrees of freedom can be calculated as follows:
df = ((s1^2 / n1) + (s2^2 / n2))^2 / ((s1^2 / n1)^2 / (n1 - 1) + (s2^2 / n2)^2 / (n2 - 1))
= ((124^2 / 12) + (260^2 / 10))^2 / ((124^2 / 12)^2 / 11 + (260^2 / 10)^2 / 9)
= 14.23
The critical value for a left-tailed test at alpha level 0.10 with degrees of freedom df = 14.23 can be found using a t-distribution table or a calculator and is -1.345.
The calculated t-value is:
t = (x1 - x2) / sqrt(s1^2 / n1 + s2^2 / n2)
= (0 - 0) / sqrt(124^2 / 12 + 260^2 / 10) = 0
Since the calculated t-value is not less than the critical value (-1.345), we fail to reject the null hypothesis. We can conclude that there is insufficient evidence to suggest that the population mean of Sample 1 is less than the population mean of Sample 2.
The decision rule for all three tests is:
If the calculated t-value is within the critical region, fail to reject the null hypothesis.
If the calculated t-value is greater than the critical value for a right-tailed test, reject the null hypothesis in favor of the alternative hypothesis that the population mean of Sample 1 is greater than the population mean of Sample 2.
If the calculated t-value is less than the critical value for a left-tailed test, reject the null hypothesis in favor of the alternative hypothesis that the population mean of Sample 1 is less than the population mean of Sample 2.
Step-by-step explanation:
A diamond merchant received a shipment of 7/10 of a pound of diamonds. He divided the diamonds into 7 equal lots and sold them to jewelers for making rings and necklaces. What was the weight of the diamonds in each lot?
Write your answer as a fraction or as a whole or mixed number.
The weight of the diamonds in each lot was 1/10 of a pound, or 0.1 pound.
What is arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3, since each term after the first is found by adding 3 to the preceding term.
The nth term of an arithmetic sequence can be found using the formula:
an = a1 + (n-1)d.
The merchant received 7/10 of a pound of diamonds and divided them into 7 equal lots. To find the weight of each lot, we need to divide 7/10 by 7:
(7/10) ÷ 7 = (7/10) × (1/7) = 1/10
Therefore, the weight of the diamonds in each lot was 1/10 of a pound, or 0.1 pound.
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A fair coin is tossed two times. Let X be the number of heads that appear. Obtain the probability distribution of the random variable X. Also compute (a) P(0.5 < X ≤ 4), (b) P(-1.5 < X < 1) and (c) P(X ≤ 2).
The probability distribution of X is
X P(X)
0 1/4
1 1/2
2 1/4
and required values of P(0.5 < X ≤ 4), P(-1.5 < X < 1) and P(X ≤ 2) are 3/4, 3/4 and 1 respectively.
What is Probability distribution?
Probability distribution refers to a function that describes the likelihood of different outcomes in a random event or experiment. It specifies how the total probability of 1 is divided among all the possible outcomes of the event.
There are two main types of probability distributions: discrete and continuous.
A discrete probability distribution assigns probabilities to a finite or countably infinite number of outcomes. Examples of discrete probability distributions include the Bernoulli distribution, the binomial distribution, and the Poisson distribution.
The possible outcomes of tossing a fair coin twice are
{HH, HT, TH, TT}
Let X be the number of heads that appear.
X = 0 if the outcome is TT.
X = 1 if the outcome is HT or TH.
X = 2 if the outcome is HH.
The probability distribution of X is
X P(X)
0 1/4
1 1/2
2 1/4
To compute the probabilities asked for:
(a) P(0.5 < X ≤ 4) = P(X = 1) + P(X = 2) = 1/2 + 1/4 = 3/4.
(b) P(-1.5 < X < 1) = P(X = 0) + P(X = 1) = 1/4 + 1/2 = 3/4.
(c) P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = 1/4 + 1/2 + 1/4 = 1.
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Which answer BEST describes the shape of this distribution
A. bell shaped
B. skewed right
C. skewed left
D. uniform
Answer:
C. Skewed left
Step-by-step explanation:
Hope this helps! =D
The manager of a company wants to find out how many hours the employees worked in the previous month. Which of the following is a statistical question that the manager can ask?
It only seeks a single value and does not involve collecting data to draw general conclusions.
Which of the following is a statistical question that the manager can ask?"Which employee worked the most hours in the previous month?" is not a statistical question because it only seeks a single value and does not involve collecting data to draw general conclusions.
On the other hand, "What is the average number of hours worked by employees in the previous month?" is a statistical question because it involves collecting data on all employees and using it to draw general conclusions about the entire workforce.
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Which two equations would be most appropriately solved by using the zero product property? Select each correct answer. Responses 3x2−6x=0 3 x squared minus 6 x equals 0 4x² = 13 4, x, ² = 13 0.25x2+0.8x−8=0 0.25 x squared plus 0.8 x minus 8 equals zero −(x−1)(x+9)=0
The two equations that can be most appropriately solved by using the zero product property are:
3x² - 6x = 0 and -(x - 1)(x + 9) = 0.
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The zero product property can be used to solve equations that can be factored into the product of two or more expressions, where one or more of those expressions is equal to zero.
Therefore, the two equations that can be solved using the zero product property are:
3x² - 6x = 0
This equation can be factored as:
3x(x - 2) = 0
Using the zero product property, we get:
3x = 0 or x - 2 = 0
Solving for x, we get:
x = 0 or x = 2
-(x - 1)(x + 9) = 0
This equation can be factored using the difference of squares:
-(x - 1)(x + 9) = -(x² - 1² - 9x + 1x) = -(x² - 8x - 9) = 0
Using the zero product property, we get:
x - 1 = 0 or x + 9 = 0
Solving for x, we get:
x = 1 or x = -9
Therefore, the two equations that can be most appropriately solved by using the zero product property are:
3x² - 6x = 0 and -(x - 1)(x + 9) = 0.
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A primary credit card holder's card has an APR of 11.99%. The current monthly balance, before interest, is $9,768.26. The cardholder makes a payment of $350 the first 11 months and then pays off the balance at the end of the 12th month. How much interest did the credit card holder pay?
Answer:
Thus, for making installment payments, the credit card holder incurred the additional cost of Option D.
Step-by-step explanation:
The credit card holder paid an additional D. $559.56 over the 12 months versus paying the balance in full before the end of the first month.
How is the additional payment determined?
The additional payment made by the credit card holder results from paying installments instead of clearing the balance in the first month.
Installment plans attract finance charges at an annual percentage rate (APR), which increases the total amount paid.
Therefore, the additional payment is the difference between the total installment payments and the credit card balance at the beginning of the first month.
N (# of periods) = 12 months
I/Y (Interest per year) = 11.99%
PV (Present Value) = $6,299.59
PMT (Periodic Payment) = $-350
Results:
FV = $3,009.15
Sum of all periodic payments = $3,850 ($350 x 11)
Total Interest = $559.57
The total amount paid over the 12 months = $6,859.15 ($3,009.15 + $3,850)
The total amount paid in full in the first month = $6,299.59
Additional payment made via installments = $559.56 ($6,859.15 - $6,299.59)
Thus, for making installment payments, the credit card holder incurred the additional cost of Option D.
Please help quick 55 points giving away!
The correct choice is (4) x² = 34² +29² - 2(34)(29)*cos(56).
What do you Mean by Trigonometry?Trigonometry is one of the branches of mathematics that deals with the relationship between the sides of a triangle (a right-angled triangle) and its angles. There are six types of trigonometry.
We can use the laws of cosines and sines to solve this problem.
According to the law of cosines, we have:
cos(B) = (a² c² - b²) / 2ac
where a, b and c are the lengths of opposite sides of angles A, B and C. In this case, we get that a = 34, b = x, and c = 29, and we know that angle C is 56 degrees . Because:
cos(B) = (34² 29² - x²) / (23429)
According to the Law of Sines, we have:
sin(B) / b = sin(C) / c
Substituting the given values we get:
sin(B) / x = sin(56) / 29
Solving Sin(B) we get:
sin(B) = x * sin(56) / 29
Now we can use the identity sin²(B) cos²(B) = 1 to eliminate sin(B) and solve for x:
(x * sin(56) / 29)² cos²(B) = 1
Expanding and substituting cos(B) from the previous expression, we get:
(x² * sin²(56) / 29²) ((34² 29² - x²) / (2(34)(29))²= 1
Simplifying and solving for x², we get:
x² = 34²+ 29² - 2(34)(29)*cos(56)
Therefore, the correct choice is (4) x² = 34² +29² - 2(34)(29)*cos(56).
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A group of six student's in Mrs. Turner's class is working on a project. The number of hours that each student worked is shown below.
3 hours
5 hours
4 hours
4 hours
2 hours
5 hours
Which statement describes the mean number of hours worked?
The statement that describes the mean number of hours worked through which the relation is satisfied is The mean is the highest number or hours worked by any students in the group
What about mean?
In mathematics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is often called the arithmetic mean, and it is calculated by adding up all the values in the set and then dividing the result by the total number of values.
The formula for the mean is:
mean = (sum of all values) / (total number of values)
For example, suppose we have a set of four numbers: 2, 5, 8, and 11. To find the mean of this set of numbers, we add them up and divide by the total number of values:
mean = (2 + 5 + 8 + 11) / 4
mean = 26 / 4
mean = 6.5
Therefore, the mean of this set of numbers is 6.5. The mean is a commonly used measure of central tendency in statistics and data analysis, and it provides a way to summarize the general trend or average of a data set.
According to the given information:
Mean of the given condition is,
⇒ [tex]\frac{3 + 5 + 4 + 4 + 2 + 5}{6}[/tex]
⇒ [tex]\frac{23}{6}[/tex]
⇒ 3.83 mean of the given condition.
So, it indicate that The mean is the highest number or hours worked by any students in the group.
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8. The percentage of the moon's surface that is visible to someone on the Earth varies due to
the time since the previous full moon. The moon passes through a full cycle in 28 days. The
maximum percentage of the moon's surface that is visible from Earth is 50%. Find a function
for the percentage, P, of the surface that is visible as a function of the number of days, t,
since the previous full moon.
A functiοn fοr the percentage is P = 25cοs(π/14t) + 25.
What is a functiοn?In the case οf a functiοn frοm οne set tο the οther, each element οf X receives exactly οne element οf Y. The functiοn's dοmain and cοdοmain are respectively referred tο as the sets X and Y as a whοle. Functiοns were first used tο describe the idealized relatiοnship between twο varying quantities.
Here, we have
Given:
Tο find the percentage οf the full mοοn, we can write an equatiοn in the fοrm P = Acοs(Bt) + C
After 14 days, the percentage οf the mοοn is zerο
A = (max-min)/2 = 50/2 = 25
The periοd = 28 days
P = Acοs(BT = t) + c
B = 2π/periοd = 2π/28 = π/14
c = min + A = 0 + 25 = 25
We get,
P = 25cοs(π/14t) + 25,
Here, p is the percentage οf the mοοn visible cοmpared tο the previοus full mοοn.
Hence, a functiοn fοr the percentage is P = 25cοs(π/14t) + 25.
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Jasper's aunt gave him a big bin of 500 beads made out of assorted materials to use for the wind chimes he makes. Jasper takes out a handful of beads, looks at the types of beads, then puts them back. Here are the materials of the handful he selected: glass, clay, wood, glass, wood, clay, metal, clay, wood, glass, wood, clay, metal, wood, clay Based on the data, estimate how many glass beads are in the bin. If necessary, round your answer to the nearest whole number.
We can estimate that there are approximately 134 glass beads in the bin.
What is probability?
Probability is a measure of the likelihood of an event occurring.
To estimate the number of glass beads in the bin, we can use the proportion of glass beads in the handful that Jasper selected.
There are 15 beads in the handful, and 4 of them are glass. So, the proportion of glass beads in the handful is:
4/15 ≈ 0.267
We can assume that the proportion of glass beads in the bin is similar to the proportion in the handful. Therefore, we can estimate the number of glass beads in the bin as:
0.267 x 500 ≈ 134
Therefore, we can estimate that there are approximately 134 glass beads in the bin.
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Jasmine asked her classmates to name all the types of trees they found while on a field trip at a local park.
1/7 reported finding a birch tree.
7/9 reported finding a pine tree.
1/4 reported finding a maple tree.
11/23 reported finding an oak tree.
Based on the results, which statements are true? (Pick all that apply)
A. Most students found a pine tree.
B. More students found a maple tree than a pine tree.
C. More students found a birch tree than an oak tree.
D. More students found a pine tree than a birch tree.
E. More students found a maple tree than an oak tree.
The statements that are correct concerning the outcome of events between Jasmine and her classmates include the following:
Most students found a pine tree.
More students found a pine tree than a birch tree. That is option A and D respectively.
How to calculate the number of students per tree?The quantity of students that found birch tree = 1/7 = 0.14
The quantity of students that found pine tree = 7/9 = 0.8
The quantity of students that found maple tree = 1/4 = 0.25
The quantity of students that found oak tree = 11/23 = 0.48
Therefore, the statement that are correct about the outcome of the event between Jasmine and her classmates is as follows:
Most students found a pine tree.
More students found a pine tree than a birch tree.
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An automobile insurance company divides customers into three categories: good risks, medium risks, and poor risks. Assume that of a total of 11,124 customers, 7751 are good risks, 2426 are medium risks, and 947 are poor risks. As part of an audit, one customer is chosen at random. Round your answers to four decimal places if necessary.
a) What is the probability that the customer is a good risk?
b) What is the probability that the customer is not a poor risk?
Answer:
Step-by-step explanation:
a) The probability that the customer is a good risk is given by the ratio of the number of good risks to the total number of customers. Therefore:
P(customer is a good risk) = 7751/11124 = 0.6968 (rounded to four decimal places)
b) The probability that the customer is not a poor risk is equal to the probability that the customer is a good risk or a medium risk. Therefore:
P(customer is not a poor risk) = P(customer is a good risk or a medium risk)
= P(customer is a good risk) + P(customer is a medium risk)
= (7751 + 2426) / 11124
= 0.9239 (rounded to four decimal places)
One hundred adults were asked to name
their favorite sport, and the results are
shown in the circle graph. What percent of
adults preferred soccer or baseball?
Volleyball, 3
Other. 4
Golf, 7
Soccer, 11.
Baseball, 14
Football,39
Basketball, 22
The percentage of adults who preferred soccer or basketball is 25%.
What is circle graph?The size of each slice in a circle graph, also called a pie chart, indicates the proportion or percentage of each category, and the information is displayed as a circle divided into sections or slices. Circle graphs are frequently used to compare various categories in a dataset or to illustrate how various components contribute to the overall. They are particularly helpful when working with data that can be broken down into distinct categories, such survey results or demographic data.
From the circle graph we see that, percentage of adults who preferred soccer is 11%, and the percentage who preferred baseball is 14%.
Thus,
11% + 14% = 25%
Hence, the percentage of adults who preferred soccer or basketball is 25%.
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. Name a fraction that is equivalent to
1/3
Answer:
1/3-equivalent fractions include 2/6, 3/9, 4/12, 5/15, and so on.....
2/6, 3/9, 4/12, and 7/21
If PQRS is a rectangle, PR = 9x + 1, and QS = 13x - 11, find TR. (TR is half of the PR bisecter)
Answer: the length of TR is 24.5.
Step-by-step explanation: 9x + 1 = 13x - 11
22 = 4x
x = 5.5
Presently that we know x, ready to discover the values of PR and QS:
PR = 9x + 1 = 9(5.5) + 1 = 49
QS = 13x - 11 = 13(5.5) - 11 = 56
Since TR is half of the PR bisector, ready to discover it by separating PR by 2:
TR = PR/2 = 49/2 = 24.5
help with statistics
Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data. It is used in a wide range of fields such as science, engineering, social sciences, business, economics, and more.
What is statistics?In statistics, data is collected through various methods such as surveys, experiments, and observations. This data is then analyzed using statistical methods to extract meaningful insights, identify patterns and relationships, and make informed decisions.
Some common statistical techniques include descriptive statistics, inferential statistics, hypothesis testing, regression analysis, and probability theory. These techniques are used to help researchers and analysts to understand and draw conclusions about data, and to test whether their conclusions are statistically significant.
Statistics has many practical applications, such as market research, medical research, quality control, risk assessment, and many others. It plays a critical role in modern society, helping individuals and organizations make informed decisions based on data-driven insights.
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if L(x) =sinx-cosx, then dxy=?
The derivative of L(x) with respect to x is: d/dx [L(x)] = cosx + sinx
Differentiating the function L(x)Given that
L(x) = sin(x) - cos(x)
To find dy/dx for the function L(x) = sinx - cosx, we need to take the derivative of L(x) with respect to x:
d/dx [L(x)] = d/dx [sinx - cosx]
Using the derivative rules, we can find the derivative of sinx and cosx:
d/dx [sinx] = cosx
d/dx [cosx] = -sinx
Therefore, the derivative of L(x) with respect to x is:
d/dx [L(x)] = cosx + sinx
So, dy/dx for L(x) is cosx + sinx.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equations which represents the circle are x²+ (y - 3)² = 36 and
x²+ (y + 8)² = 36.
What is equation of circle?
A circle is a shape made up of all points in a plane that are at a specific distance from the center point.
The standard form for finding the equation of a circle is expressed as follows:
[tex](x-a)^2 + (y-b)^2 =r^2[/tex]
In the equation,
(a, b) is the center of the circle
r is the radius of the circle
We are given that the diameter is 12 units. So,
Radius = 6 units
Since, the center lies on the y - axis so, the center will be of the form (0,b).
Now, on substituting this, we get
⇒ [tex](x-0)^2 + (y-b)^2 =6^2[/tex]
⇒ [tex]x^2 + (y-b)^2[/tex] = 36
So, we get the two equations as:
1. x²+ (y - 3)² = 36
2. x²+ (y + 8)² = 36
Hence, the first and the last option is the correct answer.
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The complete question has been attached below.
How to solve for m? 2=8m
Answer:
2=8m
divide both sides by 8
the 8 cancels out
and your answer is
m= 2/8
Step-by-step explanation:
hope it helped have a nice day!
Explain how the concept of percentage increase and/or decrease is applied to science. You should give real world examples.
Answer:
Step-by-step explanation:
Percentages are used widely and in many different areas. For example, discounts in shops, bank interest rates, rates of inflation and many statistics in the media are expressed as percentages. Percentages are important for understanding the financial aspects of everyday life.
[tex]24 = \frac{8}{3} x[/tex]
Answer: x is equal to 9.
Step-by-step explanation: this can be solve by multiplying both sides of the equation by 3/8:
24 = 8/3x
(3/8) * 24 = (3/8) * (8/3x)
9 = x
Calculating Income Tax Expense
Given the following.
Taxable Income $500k
Future taxable amounts $45k
Future deductible amounts $55k
Beginning Balances DTA $20k
Beginning Balances DTL $50k
Tax rate 40%.
1. What is the income tax payable?
2. What is the DTA year end balance?
3. What is the DTL year end balance?
4. What is the income tax expense?
5. What is the originating/reversing amount for the future taxable amount and for the deductible amount of the current year?
The income tax payable can be calculated as follows:
Taxable income = $500,000
Tax rate = 40%
Income tax payable = $500,000 x 40% = $200,000
What is the DTA year end balance?The DTA (Deferred Tax Asset) year-end balance can be calculated as follows:
Beginning balance DTA = $20,000
Future deductible amounts = $55,000
DTA year-end balance = $20,000 + $55,000 = $75,000
The DTL (Deferred Tax Liability) year-end balance can be calculated as follows:
Beginning balance DTL = $50,000
Future taxable amounts = $45,000
DTL year-end balance = $50,000 - $45,000 = $5,000
The income tax expense can be calculated as follows:
Income tax payable = $200,000
Add: Increase in DTL = $5,000
Less: Increase in DTA = $55,000 - $20,000 = $35,000
Income tax expense = $200,000 + $5,000 - $35,000 = $170,000
The originating/reversing amount for the future taxable amount and for the deductible amount of the current year can be calculated as follows:
Future taxable amount:
Origination amount = $45,000 x 40% = $18,000
Reversing amount = $18,000
Future deductible amount:
Origination amount = $55,000 x 40% = $22,000
Reversing amount = $22,000 - $20,000 = $2,000 (since the beginning balance of DTA was $20,000)
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Consider the verbal phrase.
Two and nineteen hundredths times a number g, plus fifty-nine hundredths
Part A
Enter an expression to represent the verbal phrase.
g +
Part B
Evaluate the expression when g = 3.
3.96
7.16
8.34
8.93
verbal phrase can be represented by 7.16.
What is the verbal phrase?Part A:
The verbal phrase can be represented by the following expression:
[tex]2.19g + 0.59[/tex]
Here, "Two and nineteen hundredths times a number g" can be written as 2.19g, and "plus fifty-nine hundredths" can be written as [tex]0.59[/tex] .
Part B:
To evaluate the expression when [tex]g = 3[/tex], we substitute 3 for g in the expression and simplify:
[tex]2.19g + 0.59[/tex]
[tex]= 2.19(3) + 0.59 [\ Substitute g = 3][/tex]
[tex]= 6.57 + 0.59[/tex]
[tex]= 7.16[/tex]
Therefore, the correct answer is [tex]7.16.[/tex]
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The given question is incomplete. the complete question is given below:
Consider the verbal phrase.
Two and nineteen hundredths times a number g, plus fifty-nine hundredths
Part A
Enter an expression to represent the verbal phrase.
g +
Part B
Evaluate the expression when g = 3.
3.96
7.16
8.34
8.93
6. Katya and Alyse are sewing a border with
yarn on a rectangular blanket. The length of the
long side is 6 feet and the short side is 4 feet.
How many feet of yarn will they need?
Answer:
20 feet
Step-by-step explanation:
The border of the blanket refers to the perimeter of the blanket so to find the perimeter of a rectangle all we have to do is add all the sides together 2 long sides and 2 short sides.
perimeter=6+6+4+4=20
What happens to a consistent slope when the y value decreases and the x value remains the same over time?
A. Y intercept will be less and X will be less
B. Y intercept will be less and X intercept will be greater
C. Y intercept will be greater and X will be greater
D. Y intercept will be greater and X will be less
The correct answer is: E. None of the above. The y-intercept and x-intercept will remain the same, and the consistent slope will not be affected by changes in the y value when x remains constant.
What is slope?
In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.
If the y value decreases and the x value remains the same over time, this means that the slope remains constant. A consistent slope means that the relationship between the two variables is fixed, regardless of the values of the variables. Therefore, the y-intercept will not change as it only depends on the value of y when x=0. The x-intercept will also not change, as it only depends on the value of x when y=0.
Therefore, the correct answer is:
E. None of the above. The y-intercept and x-intercept will remain the same, and the consistent slope will not be affected by changes in the y value when x remains constant.
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A large production facility uses two machines to produce a key part for its main product. Inspectors have expressed concern about the quality of the finished product. Quality-control investigation has revealed that the key part made by the two machines is defective at times. The inspectors randomly sampled 35 units of the key part from each machine. Of those produced by machine A, 5 were defective. Seven of the 35 sampled parts from machine B were defective. The production manager is interested in estimating the difference in proportions of the populations of parts that are defective between machine A and machine B. From the sample information, compute a 98% confidence interval for this difference.
The range of the 98% confidence interval for the percentage of faulty components that differ between machines A and B is about between -0.2448 and 0.1305. (rounded to 4 decimal places).
How can you figure up a confidence interval for the proportional difference?Define the populations of interest and the characteristic you want to compare (e.g., proportion of success or failure).Collect random samples from each population and record the number of occurrences of the characteristic of interest in each sample.Calculate the sample proportions ([tex]p_1 \;and \;p_2[/tex]) by dividing the number of occurrences by the sample size for each population.Calculate the standard error (SE) of the difference in proportions using the sample proportions, sample sizes, and appropriate formula (SE = [tex]\sqrt{ [(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)}[/tex], where[tex]p_1 \;and \;p_2[/tex] are the sample proportions and[tex]n_1 \;and \;n_2[/tex] are the sample sizes for the two populations, respectively).Determine the appropriate critical value from the probability distribution (e.g., standard normal distribution for large sample sizes or t-distribution for small sample sizes) based on the desired confidence level.Calculate the margin of error (ME) by multiplying the standard error by the critical value (ME = critical value * SE).Construct the confidence interval by adding and subtracting the margin of error from the sample statistic (e.g., the difference in sample proportions, or the ratio of sample proportions).Interpret the confidence interval, stating that we can be [confidence level]% confident that the true population parameter falls within the calculated interval.Given:
Sample proportion from machine A ([tex]p_1[/tex]) = 5/35 = 0.14285714285714285
Sample proportion from machine B ([tex]p_2[/tex]) = 7/35 = 0.2
Sample size from machine A ([tex]n_1[/tex]) = 35
Sample size from machine B ([tex]n_2[/tex]) = 35
Standard error (SE) = [tex]\sqrt{ [(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)}[/tex]
= [tex]\sqrt{[0.14285714285714285 * (1 - 0.14285714285714285) / 35] + [0.2 * (1 - 0.2) / 35] }[/tex]
= 0.07058061453775912 (rounded to 11 decimal places)
Margin of error (ME) = Critical value * Standard error
= 2.660 * 0.07058061453775912 (using z-score for a 98% confidence level)
= 0.18765117789861733 (rounded to 11 decimal places)
Confidence interval (CI) = Sample statistic ± Margin of error
= [tex](p_1 - p_2) \pm ME[/tex]
= (0.14285714285714285 - 0.2) ± 0.18765117789861733
= -0.05714285714285715 ± 0.18765117789861733
The 98% confidence interval for the difference in proportions of defective parts between machine A and machine B is approximately -0.2448 to 0.1305 (rounded to 4 decimal places).
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$2000 are invested in a bank account at an interest rate of 5 percent per year.
Find the amount in the bank after 7 years if interest is compounded annually.
Find the amount in the bank after 7 years if interest is compounded quaterly.
Find the amount in the bank after 7 years if interest is compounded monthly.
Finally, find the amount in the bank after 7 years if interest is compounded continuously.
The amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.
Simple interest calculation.
Using the formula A = P(1 + r/n)^(nt), where:
A = the amount in the account after t years
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
a) If interest is compounded annually:
A = 2000(1 + 0.05/1)^(1*7) = $2,835.08
b) If interest is compounded quarterly:
A = 2000(1 + 0.05/4)^(4*7) = $2,888.95
c) If interest is compounded monthly:
A = 2000(1 + 0.05/12)^(12*7) = $2,905.03
d) If interest is compounded continuously:
A = Pe^(rt) = 2000e^(0.05*7) = $2,938.36
Therefore, the amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.
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Marcus buys a car for $45,000. If he finances it for 5
years at an annual interest rate of 8.5%, what will his
monthly payment be?
Answer:
M ≈ $933.24
Step-by-step explanation:
To calculate Marcus's monthly payment for financing his car for 5 years at an annual interest rate of 8.5%, we can use the formula for the monthly payment on a loan:
M = P * (r/12) * (1 + r/12)^n / ((1 + r/12)^n - 1)
where:
M is the monthly payment
P is the principal (in this case, $45,000)
r is the annual interest rate (in this case, 8.5%)
n is the number of monthly payments (in this case, 5 years * 12 months/year = 60 monthly payments)
Substituting the given values, we get:
M = $45,000 * (0.085/12) * (1 + 0.085/12)^60 / ((1 + 0.085/12)^60 - 1)
Using a calculator, we get:
M ≈ $933.24
Therefore, Marcus's monthly payment for financing his car for 5 years at an annual interest rate of 8.5% is approximately $933.24.
Plot the following points on graph paper and connect them in the order given.
Then connect points A and D.
A(-3, 4), B(1,6), C(5,-2), and D(1,-4)
If ABCD is rotated 90° clockwise (U) about the origin to form A'B'C'D', what
are the coordinates of the vertices of A'B'C'D'?
A graph of the points is shown in the image below.
If ABCD is rotated 90° clockwise (U) about the origin to form A'B'C'D', the coordinates of the vertices of A'B'C'D'
What is a rotation?In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
Additionally, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).
Next, we would apply a rotation of 90° clockwise to the coordinate of quadrilateral ABCD as follows;
(x, y) → (y, -x)
Coordinate A = (-3, 4) → Coordinate A' = (4, -(-3)) = (4, 3)
Coordinate B = (1, 6) → Coordinate B' = (6, -(1)) = (6, -1)
Coordinate C = (5, -2) → Coordinate C' = (-2, -(5)) = (-2, -5)
Coordinate D = (1, -4) → Coordinate D' = (-4, -(1)) = (-4, -1)
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In a survey, 150 shoppers were asked whether they have access to a computer at home and if they have a personal e-mail account. Their responses are summarized in the following table. E-Mail account No e-mail account Computer access at home 44 22 No computer access at home 7 77 (a) What percentage of the shoppers have an e-mail account? (b) What percentage of the shoppers do not have computer access at home?
a.) Approximately 80.67% of the shoppers have an e-mail account.
b.) Approximately 19.33% of the shoppers do not have computer access at home.
How are percentages calculated?(a) To find the percentage of shoppers who have an e-mail account, we need to add the number of people who have an e-mail account (44) to the number of people who do not have a computer at home but may still have an e-mail account (77).
44 + 77 = 121
So, 121 out of 150 shoppers have an e-mail account. To find the percentage, we can divide 121 by 150 and multiply by 100:
121/150 * 100 = 80.67%
Therefore, approximately 80.67% of the shoppers have an e-mail account.
(b) To find the percentage of shoppers who do not have computer access at home, we need to add the number of people who do not have a computer at home (7) to the number of people who have an e-mail account but may or may not have computer access at home (22).
7 + 22 = 29
So, 29 out of 150 shoppers do not have computer access at home. To find the percentage, we can divide 29 by 150 and multiply by 100:
29/150 * 100 = 19.33%
Therefore, approximately 19.33% of the shoppers do not have computer access at home.
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