Question:
Identify the like terms in the algebraic expression
[tex]\frac{2x}{5} -5.2y +2.2 + \frac{x}{3}[/tex]
Answer:
The like terms in the given expression are [tex]\frac{2x}{5}[/tex] and [tex]\frac{x}{3}[/tex]
Step-by-step explanation:
Given:
[tex]\frac{2x}{5} -5.2y +2.2 + \frac{x}{3}[/tex]
Required:
Identify the like terms
To solve this, we need to understand what like term is all about.
Like term simply refer to terms or entities that have the same variable and exponents (power)
From the expression above, there are two variables;
x and y.
To get the like terms of x and/or y;
we simply look for another occurrence of x and/or y in the expression; and this occurrence must have the same exponent as x and/or y.
For x
[tex]\frac{2x}{5}[/tex] and [tex]\frac{x}{3}[/tex] have the same variable and exponent; Hence, they are like terms
There's only one occurrence of variable y;
Conclusively, the like terms in the given expression are [tex]\frac{2x}{5}[/tex] and [tex]\frac{x}{3}[/tex]
2x/5 and -5.2y
hope this helps
A restaurant offers a $12 dinner special that has 5 choice for an appetizer, 13 choices for an entree and 4 choice for a dessert how many different meals are available when you select an appetizer an entree and dessert?
To find total choices, multiply the quantity of each part by each other:
5 x 13 x 4 = 260
Answer: 260 different meals.
A survey was conducted with a population size of 500 resulted in 1/3 of all taxpayers having adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of itemized deduction was $16,642 from a sample size of 75 and a standard deviation of $2,400. What is the probability the itemized deductions were within $200 of the sample mean?
Answer:
52.84% probability the itemized deductions were within $200 of the sample mean
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 16642, \sigma = 2400, n = 75, s = \frac{2400}{\sqrt{75}} = 277.13[/tex]
What is the probability the itemized deductions were within $200 of the sample mean?
This is the pvalue of Z when X = 16642 + 200 = 16842 subtracted by the pvalue of Z when X = 16642 - 200 = 16442. So
X = 16842
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16842 - 16642}{277.13}[/tex]
[tex]Z = 0.72[/tex]
[tex]Z = 0.72[/tex] has a pvalue of 0.7642
X = 16442
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16442 - 16642}{277.13}[/tex]
[tex]Z = -0.72[/tex]
[tex]Z = -0.72[/tex] has a pvalue of 0.2358
0.7642 - 0.2358 = 0.5284
52.84% probability the itemized deductions were within $200 of the sample mean
In two or more complete sentences, identify the parent function, and describe the transformations that were applied to
obtain the graph. f(x) equals 2x+6+3
Answer:
Step-by-step explanation:
Transformed of the function has been given as,
f(x) = [tex]\sqrt{(2x+6)}+3[/tex]
= [tex]\sqrt{2}(\sqrt{x+3})+3[/tex]
Parent function of this transformed function = [tex]\sqrt{x}[/tex]
Vertical stretch = By a factor of [tex]\sqrt{2}[/tex]
Horizontal shift = 3 units to the left
Vertical shift = 3 units up
Now we can summarize these transformations as,
1). Parent function g(x) = [tex]\sqrt{x}[/tex] has been vertically stretched by a factor of [tex]\sqrt{2}[/tex]
2). Followed by the translations of 3 units left and 3 units up.
A new American graduate is contemplating buying a Japanese, German, or an American car. No matter the type of car, he plans to buy a new one at the end of 8 years. Japanese car will cost $30,000 and have a fuel usage of 23 Miles Per gallon (mpg) for the first 2 years, and will decrease by 3% per year thereafter. Repair cost will start at $700 per year, and increase by 3% per year. At the end of year 8, the car can be sold for $5000. Insurance cost will be $700 for the first year, increasing by 2% per year thereafter. A German car will cost $45,000 and have fuel usage of 21mpg for the first 5 years, and decrease by 1% thereafter to year 8. Repair cost will start at $1000 in year 1 and increase by 4% per year. It will have a salvage value of $7000 at the end of year 8. Insurance cost will be $850 the first year, increasing by 2% per year thereafter. The American car will cost $35,000 and have fuel usage of 20mpg for the first 3 years, and will decrease by 3% per year thereafter. Repair cost will be $800 in year 1, increasing by 4% per year thereafter. Being an American, the graduate will price the pride of owning an American car at $0.4 for every 20 miles driven, increasing by 2% per year. Insurance cost will be $800 per year increasing by 2.2% per year. The car can be sold for $5500 at the end of year 8. If the graduate anticipates driving 150000 miles by the end of year 8 and the average interest rate is expected to remain at 5% per year, which car is economically affordable based on present worth analysis? Assume fuel cost will be $3 per gallon in year 1 and increase by an average of 2% per year. Show all your workings.
Answer:
The best option is to buy Japanese Car.
Step-by-step explanation:
Fuel usage per year is 150000/ 8 = 18750 miles per year
Fuel cost (year 1 -8) = $3.0, $3.06, $3.12, $3.18, $3.25, $3.312, $3.38, $3.5
Japanese Car:
Fuel usage 18750 / 23 = 815 * $3 = $2446
Fuel charges (year 1 -8) = $2445, $2494, $2623, $2758. $2900, $3050, $3207, $3372
Repair Cost (year 1 - 8) = $700, $721, $742, $764, $787, $811, $835, $860
Insurance cost (Year 1 - 8) = $700, $714, $728, $742, $757, $772, $788, $804
Present value of cost at 5% = 24674.07
Cost of car is $30,000
Total cost = $54674.07
Amercian Car:
Cost $35,000
Fuel usage 18750/20 = 937.5 * $3 per gallon = $2812.5.
Fuel charges (year 1 -8) = $2812, $2913, $2986, $3011. $3098, $3124, $3176, $3208
Repair Cost (year 1 - 8) = $800, $894, $921, $978, $1109, $1176, $1207, $1301
Insurance cost (Year 1 - 8) = $800, $827, $876, $898, $908, $932, $954, $934
Present value of cost at 5% = 25302.18
Cost of car is $35,000
Total cost = $60302.
German Car:
Cost = $45,000
Fuel usage 18750 / 21 = 892 * $3 = $2678
Fuel charges (year 1 -8) = $2679, $2732, $2786, $2842. $2899, $2987, $3077, $3171
Repair Cost (year 1 - 8) = $1000, $1040, $1081, $1124, $1169, $1216, $1265, $1316
Insurance cost (Year 1 - 8) = $850, $867, $884, $902, $920, $938, $957, $976
Present value of cost at 5% = 27105.73
Cost of car is $45,000
Total cost = $72105.
Use the following information for questions 8-10: A professional basketball player has an 81% success rate when shooting free throws. Let the random variable X represent the number of free throws he makes in a random sample of 10 free throws (assume this experiment meets all binomial requirements). What is the expected number of free throws he will make
Answer:
The expected number of free throws he will make is 8.1.
Step-by-step explanation:
For each free throw, there are only two possible outcomes. Either he makes it, or he misses each. Each free throw is independent of other free throws. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
A professional basketball player has an 81% success rate when shooting free throws.
This means that [tex]p = 0.81[/tex]
Sample of 10 free throws
This means that [tex]n = 10[/tex]
What is the expected number of free throws he will make
[tex]E(X) = np = 10*0.81 = 8.1[/tex]
The expected number of free throws he will make is 8.1.
g(x)=\dfrac{x+6}{2}g(x)=
2
x+6
g, left parenthesis, x, right parenthesis, equals, start fraction, x, plus, 6, divided by, 2, end fraction
What is the domain of g?g
Answer:
all real numbers
Step-by-step explanation:
The fraction simplifies to the polynomial ...
g(x) = (1/2)x +3
Every polynomial has a domain of "all real numbers."
Answer: All Real Values of X
Step-by-step explanation:
Khan said so
a parabola intersects the x axis at x=2 and x=8. What is the x corrdinate
Answer:
The x coordinate of the parabola's vertex is: 5
Step-by-step explanation:
Although you didn't finish the phrases of the question, if they were asking the x-value for the x-coordinate of the parabola's vertex, which is a typical question for this type of problem, recall that the vertex is position equidistant from the parabola's branches because the parabola is a symmetric figure.
Therefore we need to find the point half way between x = 2 and x = 8.
Notice that the distance between these two points is "6" units, and half of such distance is "3" units, so the vertex must be located 3 units to the right of 2 (or equivalently 3 units to the left of 8).
Therefore, the x-coordinate of this parabola's vertex is "5"
What is the amplitude ? How do I find it? do I add 7.7 to (-6.7) then divide? Thank you in advance
Answer:
7.2
Step-by-step explanation:
The amplitude is half the difference between the maximum and the minimum.
A = (7.7 − (-6.7)) / 2
A = 7.2
Each situation described bellow requires inference about a mean or means. Identify each as involving (1) a single sample, (2) matched pairs, or (3) two independent samples.
1- Looking back on love. Choose 40 romantically attached couples in their midtwenties. Interview the man and woman separately about a romantic attachment they had at age 15 or 16. Compare the attitudes of men and women.
2- Chemical analysis. To check a new analytical method, a chemist obtains a reference specimen of known concentration from the National Institute of Standards and Technology. She then makes 20 measurements of the concentration of this specimen with the new method and checks for bias by comparing the mean result with the known concentration.
3- Chemical analysis, continued. Another chemist is checking the same new method. He has no reference specimen, but a familiar analytic method is available. He wants to know if the new and old methods agree. He takes a specimen of unknown concentration and measures the concentration 10 times with the new method and 10 times with the old method.
Answer:
1) matched samples
2) single sample
3) independent samples
Step-by-step explanation:
1) couples were taken and their behaviors matched
2) only one sample was used
3) two different samples were used and their average compared.
The 4th time of me posting this question
Cora has some ice cream that she is serving for her friends. If Cora gives 1/6 of a quart of ice cream to each of her 8 friends, how much ice cream does she serve in total?
Answer:
8/6 of a quart (4/3)
Step-by-step explanation:
thats more than she has, unless she has 2 quarts
The answer is 4/3
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Math Problem, Please Help.....
∆LMN ∼ ∆PON. What is the value of x? Select one: a. 28 1/3 b. 36 c. 20 d. 25
Answer:
b. 36
Step-by-step explanation:
x/12=42/14x=12*3x=36For the results of a certain survey, the estimated probability of being a car owner was 0.77 for males and 0.62 for females. Express each of these as a conditional probability. The probability of being a car owner (CO ) was 0.77 for males (M). Express this as a conditional probability.
Answer:
P(CO|M)=0.77 for male
and P(CO|M^c)=0.62 for female
Step-by-step explanation:
When we talk of conditional probability, we refer to the measure of the probability of an event given that another event has occurred
Here, we are to express the results of the survey as a conditional probability.
For the male part of the question, the conditional probability means that, given that the person is a male, the probability that he is a car owner would be;
P(CO|M)=0.77
For the female part of the question, what we have as a conditional probability is that if a person is a female that she is a car owner is;
P(CO|M^c)=0.62
Please kindly understand that the term M^c refers to M complement in words
Determine whether the underlined value is a parameter or a statistic. In a national survey of high school studentsIn a national survey of high school students (grades 9 to 12 )comma(grades 9 to 12), Modifying 25 % with underline25% of respondentsof respondents reported that someone had offered comma sold comma or given them an illegal drug onreported that someone had offered, sold, or given them an illegal drug on schoolschool property. nbspproperty. Is the value a parameter or a statistic?
Answer:
Parameter
Step-by-step explanation:
Parameter is a value that summarizes the data/information about a population in its entirety while a statistics summarizes the data/information about a small part/sample of the population.
In this context the underlined 25% represents the parameter because the value is a numerical measurement describing a characteristic of a population which are the national high school students.
just do the one that says dessert dont worry about the other box. And the little boxes with the numbers in it, those r the answer.
Answer:
33
Step-by-step explanation:
OK so you just got to add the 15 with 18 and you'll get 33
Answer:
33
Step-by-step explanation:
suppose that y and z are points on a number line if y z equals 16 + y lies at -4 where could z be located
Corrected Question
Suppose that y and z are points on a number line if yz equals 16 and y lies at -4. Where could z be located?
Answer:
z would be located at -4.
Step-by-step explanation:
If the product of y and z, yz=16
Point y lies at -4.
Substituting y=-4 into yz=16, we obtain:
[tex]-4z=16[/tex]
Divide both sides by -4
[tex]z=-4[/tex]
Therefore, z would be located at -4, which is the same point at which y is located.
y and z are the same points on the number line.
We know our result is correct because the product of two negative numbers is positive.
Help is appreciated!! ❤
Simplify the expression (5 + √3)(5 - √3)
A new American graduate is contemplating buying a Japanese, German, or an American car. No matter the type of car, he plans to buy a new one at the end of 8 years. Japanese car will cost $30,000 and have a fuel usage of 23 Miles Per gallon (mpg) for the first 2 years, and will decrease by 3% per year thereafter. Repair cost will start at $700 per year, and increase by 3% per year. At the end of year 8, the car can be sold for $5000. Insurance cost will be $700 for the first year, increasing by 2% per year thereafter. Page 2 of 3 Examiners: Dr. A. Afful-Dadzie, and Dr. A. Karimu A German car will cost $45,000 and have fuel usage of 21mpg for the first 5 years, and decrease by 1% thereafter to year 8. Repair cost will start at $1000 in year 1 and increase by 4% per year. It will have a salvage value of $7000 at the end of year 8. Insurance cost will be $850 the first year, increasing by 2% per year thereafter. The American car will cost $35,000 and have fuel usage of 20mpg for the first 3 years, and will decrease by 3% per year thereafter. Repair cost will be $800 in year 1, increasing by 4% per year thereafter. Being an American, the graduate will price the pride of owning an American car at $0.4 for every 20 miles driven, increasing by 2% per year. Insurance cost will be $800 per year increasing by 2.2% per year. The car can be sold for $5500 at the end of year 8. If the graduate anticipates driving 150000 miles by the end of year 8 and the average interest rate is expected to remain at 5% per year, which car is economically affordable based on present worth analysis? Assume fuel cost will be $3 per gallon in year 1 and increase by an average of 2% per year. Show all your workings. (20 marks)
Answer:
The best option is to buy Japanese Car.
Step-by-step explanation:
Fuel usage per year is 150000/ 8 = 18750 miles per year
Fuel cost (year 1 -8) = $3.0, $3.06, $3.12, $3.18, $3.25, $3.312, $3.38, $3.5
Japanese Car:
Fuel usage 18750 / 23 = 815 * $3 = $2446
Fuel charges (year 1 -8) = $2445, $2494, $2623, $2758. $2900, $3050, $3207, $3372
Repair Cost (year 1 - 8) = $700, $721, $742, $764, $787, $811, $835, $860
Insurance cost (Year 1 - 8) = $700, $714, $728, $742, $757, $772, $788, $804
Present value of cost at 5% = 24674.07
Cost of car is $30,000
Total cost = $54674.07
Amercian Car:
Cost $35,000
Fuel usage 18750/20 = 937.5 * $3 per gallon = $2812.5.
Fuel charges (year 1 -8) = $2812, $2913, $2986, $3011. $3098, $3124, $3176, $3208
Repair Cost (year 1 - 8) = $800, $894, $921, $978, $1109, $1176, $1207, $1301
Insurance cost (Year 1 - 8) = $800, $827, $876, $898, $908, $932, $954, $934
Present value of cost at 5% = 25302.18
Cost of car is $35,000
Total cost = $60302.
German Car:
Cost = $45,000
Fuel usage 18750 / 21 = 892 * $3 = $2678
Fuel charges (year 1 -8) = $2679, $2732, $2786, $2842. $2899, $2987, $3077, $3171
Repair Cost (year 1 - 8) = $1000, $1040, $1081, $1124, $1169, $1216, $1265, $1316
Insurance cost (Year 1 - 8) = $850, $867, $884, $902, $920, $938, $957, $976
Present value of cost at 5% = 27105.73
Cost of car is $45,000
Total cost = $72105.
1.Colin walked a distance of 15 miles in 6 hours.
Work out Colins average speed.
Give your answer in miles per hour.
2.Tim drives at an average speed of 80km per hour for 3 hours 45 minutes.
Work out how many kilometres Tim drives.
i will mark you the brainiest
Answer:
1. 2.5 miles
2. 21.33 km
Step-by-step explanation:
15miles/6hours=2.5 miles
80km/3.75min=21.33km
Hope this helped!!!
What else would need to be congruent to show that ABC PQR by SSS?
Answer:
A
Step-by-step explanation:
The SSS is the side-side-side way to prove the triangles are congruent, so each side needs to have a match between triangle 1 and triangle 2. Since AC and BC are congruent to sides, that leaves AC. Hope this helps :)
To prove that both triangles are congruent, the additional information needed is: A. AB ≅ PQ.
What is the SSS Congruence Theorem?Two triangles with three pairs of corresponding congruent sides can be proven to be congruent to each other based on the SSS congruence theorem.
We are already given that two pairs of corresponding sides of the two triangles are congruent. To prove that triangles ABC and PQR are congruent by SSS, the additional information needed is: A. AB ≅ PQ.
Learn more about SSS congruence theorem on:
https://brainly.com/question/2102943
#SPJ5
The expression represents the cost of Janelle’s cell phone bill, where m represents the number of minutes of use.
0.05m + 12
What is the constant in the expression?
0.05
12
m
0.05m
Answer:
B) 12
Step-by-step explanation:
it is the only term that isnt connected to a variable / is a variable.
i got this right on edg2020.
(geometry) PLZ HELP ASAP
Answer: 323
Step-by-step explanation:
Well, I see a trapeze, but i guess it refers the rectangle of sides 19 and 17. The area is:
[tex]A=a\times b=323 \;in^2[/tex]
What’s the correct answer for this?
Step-by-step explanation:
Second option is the correct answer
Answer:
B
Step-by-step explanation:
Area of sector = m/360(πr²)
A light bulb consumes 15300 watt-hours in 4 days and 6 hours . How many watt-hours does it consume per day?
Answer:
3600 per 24 hour period or 1 day.
Step-by-step explanation:
24 x 15300/(4 x 24+6)=3600
Answer:
3600
Step-by-step explanation:
It consumes 3600 watt hours per day. Steps are included below.
We know that there is 24 hours in a day so we times 24 by the consumes watt hours that is 15300. So 24 times 15300. After that we need to time 4 times 24+6 = the answer that is 3600. That how you get the answer.
Steps:
1: 24*15300/(4*24+6)=3600
Answer: 3600 watt hours per day
Hope this helps.
Please answer this correctly
Answer:
98.5
Step-by-step explanation:
64.4 x 2= 128.8
325.8-128.8=197.0
197 /2 = 98.5
brainliest plzz
Answer:
Hey mate,
here is your answer. Hope it helps you.
Step-by-step explanation:
x+x+64.4+64.4=325.8
2x+ 128.8 =325.8
2x = 325.8 - 128.8
2x = 197
x= 197/2
=98.5 inches
Please answer this question !! Will give brainliest !
Answer & Step-by-step explanation:
In order to find the y-intercept of this equation, we must turn this equation into a slope-intercept equation. The equation for slope-intercept form is y=mx+b. We can do this by using these steps. Our goal is to get y by itself on one side.
6x - 2y - 9 = 0
Step 1: Add 9 on both sides of the equation.
6x - 2y = 9
Step 2: Subtract 6x on both sides of the equation. Once you subtract, make sure you put the -6x in front of 9 so we are following the rules of variables and exponents.
-2y = -6x + 9
Step 3: Divide -2 on both sides of the equation.
y = 3x - [tex]\frac{9}{2}[/tex]
So, the y-intercept is -[tex]\frac{9}{2}[/tex]
Eric’s average income for the first 4 months of the year is $1,450.25, what must be his
average income for the remaining 8 months so that his average income for the year is
$1,780.75?
Answer:[tex]\$1946[/tex]
Step-by-step explanation:
Given
Eric average income for four months is [tex]S_1=\$1450.25[/tex]
average Annual income [tex]S=\$1780.75[/tex]
Average income [tex]=\dfrac{\text{Total salary}}{\text{Time }}[/tex]
Sum of 4 month salary [tex]=4\times S_1[/tex]
Sum of 4 month salary [tex]=\$5801[/tex]
Average salary of remaining 8 months[tex]=S_2[/tex]
Sum of last 8 months salary[tex]=8\times S_2[/tex]
So average Salary [tex]S=\dfrac{4\times S_1+8\times S_2}{12}[/tex]
[tex]\Rightarrow 1780.75=\dfrac{4\times 1450.25+8\times S_2}{12}[/tex]
[tex]\Rightarrow 21,369=5801+8\times S_2[/tex]
[tex]\Rightarrow 15,568=8\times S_2[/tex]
[tex]\Rightarrow S_2=\dfrac{15,568}{8}=\$1946[/tex]
So, average salary of remaining 8 months is [tex]\$1946[/tex]
A population of bacteria is growing at a rate of 20% per hour. If the population starts at 320, what is it an hour later?
Answer:
384.
Step-by-step explanation:
The population is given by the expression;
[tex]Y(t) = Pr^{t}[/tex]
Where;
Y(t) is the number of bacteria at time, t.
P is the starting amount.
r is the growth rate.
Given that, P = 320, r = 20% = 0.2, t = 1
Substituting the parameters into the equation;
[tex]Y(t) = Pr^{t}[/tex]
Y(1) = 320 * 0.2¹
Y(1) = 320 * 0.2
Y(1) = 64.
Therefore, the population of bacteria increases hourly by 64.
An hour later; 320 + 64 = 384.
A modified roulette wheel has 32 slots. One slot is 0, another is 00, and the others are numbered 1 through 30, respectively. You are placing a bet that the outcome is an odd number. (In roulette, 0 and 00 are neither odd nor even.) a. What is your probability of winning? The probability of winning is StartFraction 15 Over 32 EndFraction . (Type an integer or a simplified fraction.) b. What are the actual odds against winning? The actual odds against winning are
Answer:
(a)[tex]\dfrac{15}{32}[/tex]
(b) 17:15
Step-by-step explanation:
(a)
The roulette wheel has 32 slots (inclusive of 0 and 00)
Number of Odd Numbers between 1 to 30 =15
Since you are placing a bet that the outcome is an odd number.
[tex]P(\text{Winning})=\dfrac{\text{Number of Odd Numbers}}{\text{Total Number of Slots}} \\=\dfrac{15}{32}[/tex]
(b) The actual odds against winning
[tex]\text{Actual Odds against Winning})=\dfrac{32-15}{15}\\=\dfrac{17}{15}[/tex]
Therefore, the actual odds against winning are 17:15