The correct notation for the 8th term of the expansion (3x – 5)12 would be (3x)^(-5)8.
What is expansion?The term "expansion" describes the process of expanding or expanding. It can be used to describe actual expansion, such as when an organism gets bigger or a gas expands to fill a container. It can also relate to abstract notions such as the development of thoughts or knowledge. Extension in economics refers to growth in the size of the economy or in a specific sector of the economy, such as a rise in goods and services output. The process of conquering or occupying additional areas, such as when a nation extends its borders by conquest or settlement, is another definition of expansion. The act of growing larger or more extensive is generally referred to as expansion.
How to solve?
(3x – 5)12 = (3x)12 – 12(3x)11(5) + 66(3x)10(5^2) – 220(3x)9(5^3) + ... + (-5)12
The 8th term of the expansion (3x – 5)12 is (-5)8(3x)4, which can be written as (3x)^(-5)8.
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Does an X or y-axis scale have to always start at zero?.
No, X or y-axis scale does not have to always start at zero. In a line chart, it's OK to start the axis at a number other than zero
Define axis.A line that is used to take or mark measurements is known as an axis in mathematics. Two crucial axes of the coordinate plane are the x and y axes. A horizontal number line is the x-axis, while a vertical number line is the y-axis. The coordinate plane is created by the perpendicular intersection of these two axes.
Given,
No, X or y-axis scale does not have to always start at zero.
A line chart encodes data using location (x, y coordinates), whereas a bar chart represents data using length. In a line chart, it's OK to start the axis at a number other than zero despite many claims that they are always misleading since this minute difference influences how a reader utilizes the chart.
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A random sample of 49 statistics examinations was taken. The average score, in the sample, was 84 with a variance of 12.25. The 95% confidence interval for the average examination score of the population of the examinations is
76.00 to 84.00
77.40 to 86.60
83.00 to 85.00
68.00 to 100.00
The 95% confidence interval for the average examination score of the population of the examinations is (82.99, 85.01).
We have given that,
Sample mean{[tex]\overline x[/tex]} = 84
Sample standard deviation(S) =3.5
Sample size(n) =49
Level of significance=1-0.95=0.05
Degree of freedom =48
t critical value is (by using t table)(t)= 2.011
Confidence interval formula is
[tex]\overline{x}\pm t\times\frac{S}{\sqrt{n}}[/tex]
Now putting the value
[tex]\overline{x}\pm t\times\frac{S}{\sqrt{n}}=84\pm 2.011\times\frac{3.5}{\sqrt{49}}[/tex]
[tex]\overline{x}\pm t\times\frac{S}{\sqrt{n}}[/tex] = 84 ± 2.011 × 3.5/7
[tex]\overline{x}\pm t\times\frac{S}{\sqrt{n}}[/tex] = 84 ± 2.011 ×0.5
[tex]\overline{x}\pm t\times\frac{S}{\sqrt{n}}[/tex] = 84 ± 1.01
[tex]\overline{x}\pm t\times\frac{S}{\sqrt{n}}[/tex] = (84-1.01, 84+1.01)
[tex]\overline{x}\pm t\times\frac{S}{\sqrt{n}}[/tex] = (82.99, 85.01)
Lower confidence limit= 82.99
Upper confidence limit=85.01
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Work out the values of A and B in these equivalent ratios.
A: 8:5
9:24: B
Answer:
A=3
B=15
Step-by-step explanation:
Since these are equivalent ratios, there is a constant scale factor for each number. As shown in the 8 and 24, we find the scale factor to be 24/8=3. This means that the second ratio's numbers are 3x bigger than the corresponding ones in the first ratio. A = 9/3 = 3, and B = 5*3=15
Sophie wa building a fence around her flower bed. The width mut be twice the length to fit in her backyard. She only ha 72 feet of fencing. What i the maximum width he can build?
The length of the fencing is 12 feet and the width of the fencing is 24 feet.
What is length and width?
The dimensions of length and width are crucial in the study of geometry because they help define the models.
Given in the question,
The width must be twice the length,
So, Let the length as L and and the width will be equal to 2L.
Total fencing = 72 feet.
Assuming the flower bed to be rectangular.
The total perimeter = 2(Length + width)
72 = 2(L + 2L)
72 = 6L
L = 12,
So length will be 12 feet,
And, width will be 2L = 24 feet.
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How do you write three consecutive even numbers?.
Three consecutive even integers can be written with difference of two.
The even integers are defined as the numbers that are completely divisible by two. The complete division means that the result of division will be zero. The even integers are always present after a gap of one number in between.
This means that there is a difference of two numbers between integers. Firstly of all, the first even number is two. Following it four. There is a gap of number that is three. Hence, to find the consecutive even integers, add number two to the number.
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What are prime multiples of 10?.
2, 5 are prime multiples of 10 .
What is a number's prime multiple?
Prime numbers can only be divided by one and by themselves and are therefore never less than one. They can't be produced by adding the number to itself or by multiplying it by two additional whole numbers that aren't 1.What are multiples and prime factors?
A number is said to be prime if it only has the factors 1 and itself. Multiple: A number from the provided times table of numbers. Factor: A number that exactly divides another number. The smallest number that appears in the times tables of the given numbers is known as the LCM.Learn more about prime multiple
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You are shopping for a new computer monitor. It is regularly priced at $200 but it is now on sale for 25% off. After the sale discount is applied, you can also use your 20% off coupon. What is the final price?.
After calculating the individual discount and coupon percentages of the actual price, we find out that the final price of the new computer monitor is $40.
It is given to us that -
The new computer monitor is regularly priced at $200
It is now on sale for 25% off
After the sale discount, we can also use 20% off coupon
We have to find out the final price of the computer monitor.
The initial price of the new computer monitor = $200
After the sale discount of 25% off is applied to the product, the new price of the monitor can be calculated by finding out
25% of $200 = 0.25 * 200 = $50
Now, after calculating the price of the monitor after the sales discount, we have to find out the final price after the 20% off coupon is applied.
So, 20% of $50 = 0.20 * 50 = $10
So, we can conclude that after the sales discount and after a coupon of $10 off is applied, the final price of the computer monitor is -
$50 - $10
= $40
Thus, calculating the individual discount and coupon percentages of the actual price, we find out that the final price of the new computer monitor is $40.
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A highly risk-averse investor is considering adding one additional stock to a 3-stock portfolio, to form a 4-stock portfolio. The three stocks currently held all have b = 1.0, and they are perfectly positively correlated with the market. Potential new Stocks A and B both have expected returns of 15%, are in equilibrium, and are equally correlated with the market, with r = 0.75. However, Stock A's standard deviation of returns is 12% versus 8% for Stock B. Which stock should this investor add to his or her portfolio, or does the choice not matter?
Either A or B, i.e., the investor should be indifferent between the two.
Stock A.
Stock B.
Neither A nor B, as neither has a return sufficient to compensate for risk.
Add A, since its beta must be lower.
As per the standard deviation, The B stock portfolio is more risk-efficient in simple words.
Standard deviation:
Basically, standard deviation means the measure of how dispersed the data is in relation to the mean.
And the low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given,
A highly risk-averse investor is considering adding one additional stock to a 3-stock portfolio, to form a 4-stock portfolio. The three stocks currently held all have b = 1.0, and they are perfectly positively correlated with the market. Potential new Stocks A and B both have expected returns of 15%, are in equilibrium, and are equally correlated with the market, with r = 0.75. However, Stock A's standard deviation of returns is 12% versus 8% for Stock B.
Here we need to find in which stock should this investor add to his or her portfolio, or does the choice not matter.
Here we know that either of these shares would yield the same expected return for the entire portfolio if added to the same share of the portfolio.
So, if stock B is included in the portfolio, the expected standard deviation for the portfolio will be lower, since the standalone deviation is lower.
And therefore, lower risk or volatility, or standard deviation of the portfolio for the same level of the expected return on the new portfolio.
Therefore, the ratio of Sharpe to stock B will be higher. The B stock portfolio is more risk-efficient in simple words.
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a food label states that a serving of a particular product contains 13 grams of total fat and 20 percent of the daily value. this means that
Using food labling :
The product contains 13 grams of total fat and 20 percent of the daily value. this means that
13 grams of fat provides 20% or one-fifth of the recommended total daily fat intake.
Food level :
food labels contain a lot of information about most packaged foods. Food labels are called "Nutrition Facts".itle or Job:
The US government requires food labels on most packaged foods. Labels provide complete, useful and accurate nutritional information. The government encourages food manufacturers to improve the quality of their products so that people can make healthier food choices.
Serving Sizes
Label serving sizes are based on the average amount of food people typically eat.
Label serving sizes are not necessarily healthy serving sizes.
Amount Per Serving
Total calories per serving are displayed in large print. This allows the consumer to count the number of calories per serving like total fat. Sodium; Total Carbs
PERCENT DAILY VALUE (% DAILY VALUE)
Many nutrients have a Percent Daily Value (%DV). This indicates how much each serving contributes to the total recommended daily intake of each nutrient. increase. This means that 13 grams of fat provides 20% or one-fifth of the recommended total daily fat intake.
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jalen has columbian coffee worth $3 per pound that he wishes to mix with 30 pounds of brazilian coffee worth $8 per pound to get a mixture/blend that he would sell for $4 per pound. how many pounds of the cheaper coffee should he use?
120 pounds of the cheaper coffee should be use to get a mixture/blend that he would sell for $4 per pound.
How to solve an equation?An equation is an expression that can be used to show the relationship between variables and numbers.
Let x represent the amount of cheaper coffee.
Jalen has columbian coffee worth $3 per pound that he wishes to mix with 30 pounds of brazilian coffee worth $8 per pound to get a mixture/blend that he would sell for $4 per pound.
Hence:
3x + 8(30) = 4(x + 30)
3x + 240 = 4x + 120
x = 120
120 pounds of the cheaper coffee should be use
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Question
The function C(x)=17.5x−10 represents the cost (in dollars) of buying x tickets to the orchestra with a $10 coupon.
a. How much does it cost to buy 5 tickets?
It costs $
to buy 5 tickets.
b. How many tickets can you buy with $130?
You can buy
tickets.
Answer:
a. $77.5
b. 8 tickets
Step-by-step explanation:
a. Replacing x with 5 in the equation to get the cost of 5 tickets would look like this:
C(x = 5) = 17.5x - 10 = 17.5(5) - 10 = 87.5 - 10 = 77.5
b. There's no smart way to do this aside from picking a number of tickets that costs less that $130 and checking the total cost to buy another ticket until we go over $130
From a, we know that 5 tickets is $77.5
and every additional tickets costs $17.5
so 6 tickets is $77.5 + $17.5 = $95
so 7 tickets is $95 + $17.5 = $112.5
so 8 tickets is $112 + $17.5 = $130
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 given that he or she is a root beer drinker.
The probability that the person is over 40 given that he or she is a root beer drinker is 62.75%
The fact that
The ratio of the event space's size to the sample space's size represents an event's probability.
The total number of outcomes equals the size of the sample space.
The number of outcomes in the event you are interested in is the event space.
so
P = event space size divided by sample space size
step 1
determine the likelihood that the person is over 40 years old.
The sample size is 255.
event space size = 85
P=85/255------> P=1/3
step 2
determine the likelihood that they consume root beer.
The sample size is 255.
event space size = 75
P=75/255------> P=5/17
step 3
determine the likelihood that the individual is over 40 years old or that
They consume root beer.
so
P=(1/3)+(5/17)——-> P=(17*1+3*5)/51------> P=32/51-----> 0.6275——> 62.75%
therefore, the response is
32/51 or 62.75%
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A plant nursery is having a sale. potted begonias are marked down 27%, and tomato seedlings are marked down 35%. if you pay $6.57 each for two potted begonias and $2.60 each for three tomato seedlings, how much did you save? please select the best answer from the choices provided a b c d
The amount of money saved from the marked down prices at the plant nursery is $7.46 .
Let the cost of the potted begonias be x.
They are marked down 27%
Price at which they are sold = 0.73 x
Therefore : 0.73x = 6.57 or, x = 9
Money saved = (9 - 6.57) × 2 = $4.86
Let the cost of the tomato be x.
They are marked down 35%
Price at which they are sold = 0.65 x
Therefore : 0.65x = 2.60 or, x = 4
Money saved = (4 - 2.60) × 3 = $4.20
Total money saved = $ (4.20 + 4.86 ) = $9.06
Discounts are price cuts made by store owners on goods or services that would otherwise be sold for the indicated price. Usually, this portion of the rebate is given to increase sales or get rid of extra inventory.
The List Price or Marked Price is the cost of a product as declared by the seller or manufacturer, exclusive of any discounts. The selling price is really the final price at which an item is sold after any discounts or price drops from the list price.
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Evan is single and has AGI of $277,300 in 2019. His potential itemized deductions before any limitations for the year total $52,300 and consist of the following:
Medical expenses (before the AGI limitation)$29,000
Interest on home mortgage 8,700
State income taxes 9,500
Real estate taxes 3,600
Charitable contributions 2,500
After all necessary adjustments are made, what is the amount of itemized deductions Evan may claim? If required, round the medical deduction to the nearest dollar and use the rounded amount in subsequent computations.
Evan's total itemized deduction is $
22,470
Evan's total itemized deduction is found as $24,400.
Define the term itemized deduction?The costs you incurred for state and local income as well as sales taxes, property investment taxes, personal state taxes, mortgage interest, including disaster losses are all included in itemised deductions. You can also count charitable donations and a portion of your out-of-pocket medical and dental costs.Only if medical expenses exceed 7.5% of your AGI may they be written off:
$277,300 x 7.5% = $20,797.50
Medical expenses: = $29,000 - $20,797.50
Medical expenses = $8,202.50.
Evan can write off $8,700 in interest on a mortgage.
$5,000 is the maximum deduction for state plus local taxes for just a single filer.
Contributions to charities are also tax deductible up to $2,500
Deductions totaled = $8,202.50 + $8,700 + $5,000 + $2,500
Deductions totaled = $24,402.50
Thus, Evan's total itemized deduction is found as $24,400.
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1. robin works as a server in a small restaurant, where she can earn a tip (extra money) from each customer she serves. the histogram below shows the distribution of her 60 tip amounts for one day of work.
The histogram below shows the distribution of her 60 tip amounts for one day of work.
a) The tips distribution is severely skewed to the right and unimodal. There is a large spread and high variability with a range of $22.50.b) The median is the average of the 30 th and 31st values, and a change in data value from $8 to $18 will not move the middle number.How to interpret Histogram?a) The distribution of tips is skewed right, whith a gap betwen 15 to 20 and a posible out lier at or above 20. The mean will be larger than the median, and the median will be in the $2,5 to $5 bar. Most tips are $5 or less, but there is some high variability with a range of $22.50.
b) The mean would increase because $18 is farther from the mean than $8. Also, more skew is added to the grapht $18 may be an out lier. This results in a larger mean.
The median: Should not change very much. The median is the average of the 30 th and 31st values, and a change in data value from $8 to $18 will not move the middle number.
Your question is incomplete, but most probably the complete question can be seen in the attachment.
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two-thirds of the global population within an eight-hour flight distance and have captured a significant market share over the last few years
The findings indicate that just 11% of the world's population used air travel in 2018, with less than 4% of those trips being international. In developed nations alone, about half of the population travels by air at least once a year.
Believe it or not, less than 20% of people on the planet have ever taken a single trip. In Asia alone, 100 million individuals will take their first flight this year alone.
Keep in mind that flights more than 6 hours are considered long-range, while trips longer than 10 hours are also not unusual. In the event of unforeseen turbulence, it's crucial to always have your seat belt secured.
Flight durations during the duty periods are limited to a maximum of 8 hours for one-pilot flight crews and 10 hours for two-pilot flight crews. Any additional commercial flying that the flight crew does during the allotted 8 or 10 hours of flight time is included.
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a sample of 400 observations will be taken from an infinite population. the population proportion equals 0.8. find the probability that the sample proportion will be greater than 0.74.
The probability is 99.87 that the sample proportion will be greater than 0.74.
Define the term Normal probability distribution?The z-score of such a measure X in a collection with mean μ and standard deviation σ is given by:z = (x - μ)/σ
The Z-score calculates the deviation of the measure from the mean in standard deviations. We examine now at z-score table after determining the Z-score to determine the p-value connected to it. The likelihood that the measure's value is less than X, or the percentile of X, is represented by this p-value. The likelihood that the value of both the measure exceeds X is calculated by deducting 1 from the pvalue.μ = E(X)
σ = √V(X)
n = 400 ; p = 0.8
Thus,
μ = E(X) = np = 400 x 0.8 = 320
σ = √V(X) = √np(1 - p) = √(400 x 0.8 x 0.2) = 8
The probability that given sample proportion would be greater than 0.74.
= 74% of the 400
= 0.74 x 400 = 296
Thus, p -value when x = 296
z = (x - μ)/σ
x = (296 - 320)/8
z = -3
p value = 0.0013
probability = 0.13
Thus, greater than 0.74.
1 - 0.0013 = 0.9987
Thus, the probability is 99.87 that the sample proportion will be greater than 0.74.
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suppose i have an orgnization that has 60 members, i'm going to pick one person at random to be the president, another person to be the vice president, and a third person to be the treasurer. how many ways can this be done
There are [tex]\frac{60!}{57!}[/tex] ways we can do it.
Since organization has 60 members from which we haveto pick one person at random to be the president, another person to be the vice president and a third person to be the transformer,
the president can be select in 60c1 = [tex]\frac{60!}{1! 59!}[/tex]
= [tex]\frac{60 *59!}{1*59!}[/tex]
= 60 ways
After this for vice president we have 59 members from which vice president can be select in 59c1 = 59 ways.
and for treasure we have 58 members from which treasure can be select in 58c1 = 58 ways.
∴ No. of ways in which we can select president, vice president and treasure = 60 × 59 × 58
= [tex]\frac{60 * 59 * 58 * 57!}{57!}[/tex]
= [tex]\frac{60!}{57!}[/tex]
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How do you tell if a function is a power function?.
A power function is the function that is defined with equation consisting of one variable of a fixed power, where all the number and coefficients of the variables belong to real numbers.
Then, let f(x) be a function that defines the variable x;
say, f(x) = 4x³ + 5x² + 7x + 10.
For f(x) to be a power function; f(x) = xⁿ
Then f(x) is a power function with the highest power being 3 of the variable 'x'.
Linear and Quadratic equations are both power functions of power 1 and 2 respectively in the variable x.
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g in 2022, the maximum credit for child and dependent care expenses is $2,100 if only one spouse is employed and the other spouse is a full-time student.
The Child and Dependent Care Credit is a tax credit that helps parents and families pay for the care of their children and other dependents while they work, are looking for work, or are going to school.
Childcare and nursing care costs money! Luckily, there are tax deductions to cover the costs. If you had to pay someone to care for your children, family members, or spouse, find a job, go to school, or because of a disability, Child and Dependent Care credits are available.
You are generally eligible for the Child and Caregiver Tax Credit if you meet all of the following conditions:
Wages from work. If you are married and are filing a joint tax return, your spouse must also have income.Your application status is Single, Married and Co-Applicant, Head of Household, or Eligible Widow with her one dependent child.You (and your spouse in the case of a joint application) have income from employment or self-employment. You are exempt from this obligation if you were a full-time student or severely disabled.You paid someone to provide care for a beneficiary, but the provider is a dependent, beneficiary's parent, spouse, or child under the age of 19 (whether or not you are a dependent). It was not a person who could claim as a person.If you (and your spouse, if you are married) work, seek employment, attend school, or are disabled, you must pay for child care and maintenance.For year 2022, the Child and Caregiver Tax Credit is non-refundable. For eligible employment-related expenses, taxpayers can claim up to $3,000 for each eligible individual or one child, and up to $6,000 for two or more eligible individuals or children.
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What does M mean in parallel lines?.
m mean slope in parallel lines and it is always same in two parallel lines.
Given:
Linear equations are generally described by the slope-intercept
represented by the equation y = mx+b
where m = slope
b = y-intercept.
In parallel lines:
Slope is always same means that two parallel lines have same slopes because those are not intersect at any point.
Example:
y = 3x + 4
here slope m = 3
The parallel line to this equation is also have the same slope.
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which of the following techniques is used in predictive analytics? a. optimization models b. data visualization c. data dashboards d. linear regression
Option d is correct that is linear regression. So, linear regression is used in predictive analytics.
Given that,
We have to find which of the following techniques is used in predictive analytics.
We know that,
What is predictive analytics?Predictive analytics, a subset of advanced analytics, employs historical data, statistical modeling, data mining, and machine learning to forecast future outcomes. Businesses utilize predictive analytics to find opportunities and threats by analyzing trends in this data.
We get,
The predictive analysis technique that is most frequently used is linear regression. By using linear relationships between a dependent variable and one or more independent variables, it makes predictions about the target's future.
Therefore, Option d is correct that is linear regression. So, linear regression is used in predictive analytics.
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What is the final step in solving the inequality 2/5 4x 6x 4 x 3 x 3x 3x 3?.
The final step in solving the given inequality is defining the range according to the final value of x as (-Inf,3).
In Variable based math, inequality is a numerical explanation that shows the connection between two articulations utilizing the imbalance image. The articulations on the two sides of a disparity sign are not equivalent. It implies that the articulation on the left-hand side ought to be more prominent than or not exactly the articulation on the right-hand side or the other way around.
On the off chance that the connection between two mathematical articulations is characterized utilizing the imbalance images, then it is called exacting disparities.
We have inequality as –2(5 – 4x) < 6x – 4
Step1: -10+8x<6x-4
Step2:8x-6x<-4+10
Step3:2x<6
Step4:x<3
Step5:Range of value of x as (-Inf,3)
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(Complete question) is:
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
As part of a study of corporate employees, the director of human resources for PNC Inc. wants to compare the distance traveled to work by employees at its office in downtown Cincinnati with the distance for those in downtown Pittsburgh. A sample of 35 Cincinnati employees showed they travel a mean of 370 miles per month. A sample of 40 Pittsburgh employees showed they travel a mean of 380 miles per month. The population standard deviations for the Cincinnati and Pittsburgh employees are 30 and 26 miles, respectively. At the 0.05 significance level, is there a difference in the mean number of miles traveled per month between Cincinnati and Pittsburgh employees? a. Is this a one-tailed or a two-tailed test? O One-tailed test O Two-tailed test b. State the decision rule. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) c. Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)
1) Given data information.
2) z = (Xcin -Xpit)/ (σ^2cin/n[tex]c_i_n[/tex] + σ^2pit/n[tex]p_i_t[/tex] ) ...(1)
3) [tex]z = \frac{370-380}{\sqrt{\frac{30^2}{35} -\frac{26^2}{40} } } = -1.532[/tex]
[tex]P_v[/tex] = 2 × P(Z < -1.532) = 0.126
4) Comparing the p value with the significance level α = 0.05 we see that
[tex]P_v[/tex] > α so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and a wouldn't be a significant difference in the average of the two groups
Given,
In the question:
1) Data given and notation
[tex]X_c_i_n[/tex] = 370 represent the mean for the sample of Cincinnati
[tex]X_p_i_t[/tex] = 380represent the mean for the sample Pittsburgh
σ[tex]_c_i_n[/tex] = 30represent the population standard deviation for the sample Cincinnati
σ[tex]p_i_t[/tex] = 26 represent the population standard deviation for the sample Pittsburgh
[tex]n_c_i_n[/tex] = 35 sample size for the group Cincinnati
[tex]n_p_i_t[/tex] = 40 sample size for the group Pittsburgh
z would represent the statistic (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:
Null hypothesis: μ[tex]c_i_n[/tex] = μ[tex]p_i_t[/tex]
Alternative hypothesis: μ[tex]c_i_n\neq[/tex] μ[tex]p_i_t[/tex]
We have the population standard deviation's, so for this case is better apply a z test to compare means, and the statistic is given by:
z = (Xcin -Xpit)/ (σ^2cin/n[tex]c_i_n[/tex] + σ^2pit/n[tex]p_i_t[/tex] ) ...(1)
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
3) Calculate the statistic
With the info given we can replace in formula (1) like this:
[tex]z = \frac{370-380}{\sqrt{\frac{30^2}{35} -\frac{26^2}{40} } } = -1.532[/tex]
4) Statistical decision
Since is a bilateral test the p value would be:
[tex]P_v[/tex] = 2 × P(Z < -1.532) = 0.126
Comparing the p value with the significance level α = 0.05 we see that
[tex]P_v[/tex] > α so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and a wouldn't be a significant difference in the average of the two groups.
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Select the correct answer.
Victor solved this inequality as shown:
Step 1: 3x − 5 > x + 5
Step 2: 2x − 5 > 5
Step 3: 2x > 10
Step 4: x > 5
What property justifies the work between step 3 and step 4?
A.
division property of inequality
B.
inverse property of multiplication
C.
subtraction property of inequality
D.
transitive property of inequality
The correct justification for moving from step 3 to step 4 in victor's solution is A. division property of inequality
What is division property of inequality?According to the division property of equality, if we divide an equation's two sides by the same number, the equation doesn't change.
Let's say you have two identically sized pizzas. You divide each one into halves and serve your buddies one half of each pizza. You will have equal pieces of both pizzas left over if you measure
as regards the Victor's problem division of both sides of the equation by 2 is achieved by the division property of inequality
Instance of division property of inequality dividing by 2
Step 3: 2x > 10
Step 4: x > 5
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let x be the distance from the foot of the ladder to the wall and lket y be the distance from the top of the ladder to the ground. write an equation relating to x and y
The equation which relates the x and y will be x² = 169 - y² according to the given triangle formed.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.
As per the given,
Length of ladder = 13 foot
By Pythagoras's theorem,
x² + y² = 13²
x² = 169 - y²
Hence "The equation which relates the x and y will be x² = 169 - y² according to the given triangle formed".
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Complete data of the question follows,
Given that the polynomial f(x) has 5 intercepts, which of the following most accurately describes the degree of f(x)? Select the correct answer below: O The degree of f(x) is at most 5. O The degree of f(x) is at least 4. O The degree of f(x) is at most 4 O The degree of (x) is at most 2 O The degree of (x) is at least 2. O The degree of f(x) is at least 5.
The solution is the degree of f(x) is at least 5.
Given info,
The polynomial f(x) has 5 intercepts.
The solution required,
The polynomial f(x) has 5 intercepts.
→ if the function has n intercept then the polynomial function has at least n degrees.
→ There is 5 intercept, then the polynomial function has at least 5 degrees.
→ The degree of f(x) is at least 5.
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What does 0 on the x-axis mean?.
Answer:
Its the Origin
Step-by-step explanation:
Its ZERO
switch the order of integration for the double integrals below from dy dx to dx dy, or vice versa. (hint: draw the region on the xy-plane to understand the order.) you are not required to evaluate/solve the double integral: just rewrite it. (a) z 2 0 z 3y 0 (x 4 y e 4yx) dx dy
The order of integration for the double integrals below from dy dx to dx dy, or vice versa is I = ₀∫⁴ √x∫y² eˣ/y² dydx
We need to switch the order of integration
I = ₀∫⁴ ₀∫ⁿ √(xy) dxdy
From n = 0 to n = 4
y = 0 to y = n
Taken horizontal strip
on strip values of y will be fixed and values of x will be varied.
Limits of y are
y = 0 to y = 4
limits of x are
x = y to x = 4
I = ₀∫⁴ ₀∫ⁿ √(xy) dxdy
I = ₀∫² ₀∫y² eˣ/y² dxdy
Taking vertical strip
on strip values of x will be fixed and values of x will be varied.
limits of x are
x = 0 to x = 4
Limits of y are
y = √x to y = 2
I = ₀∫⁴ √x∫y² eˣ/y² dydx
Therefore, the order of integration for the double integrals below from dy dx to dx dy, or vice versa is I = ₀∫⁴ √x∫y² eˣ/y² dydx
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Is it possible to have a triangle with 3cm 5cm 8cm?.
No, it is not possible to have a triangle with 3cm 5cm 8cm because the total of the triangle's two sides, 3 cm and 5 cm, is not greater than the third side, 8 cm.
Define triangle.A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Given,
Sides 3cm, 5cm and 8 cm
Three sides are provided, measuring 3 cm, 5 cm, and 8 cm. We are aware that the third side is always greater than the sum of any two triangle sides. The triangle cannot exist because the total of the triangle's two sides, 3 cm and 5 cm, is not greater than the third side, 8 cm.
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