Answer:
The answer is B. 9a2-30a+25
Step-by-step explanation:
First of all, the second sign is going to be +, so you can toss out C and D without checking.
Then you take the square root of the two ends, multiply them, multiply by two and see if it matches.
sqrt(49) * sqrt(16) = 7 * 4 = 28
28 * 2 = 56
56 <> 28
So toss A.
sqrt(9) * sqrt(25) = 3 * 5 = 15
15 * 2 = 30
So the answer is B
(3a - 5)^2 = 9a^2 - 30a + 25
By the way, use ^ to indicate an exponent.
Please show work.
In 2018, the circulation of a local newspaper was 2,125. In 2019, its circulation was 2,250. In 2020, the circulation was 2,350
a. Find the percent of increase in the newspaper’s circulation from 2018 to 2019 and from 2019 to 2020.
b. Which period had a higher percent of increase, 2018 to 2019, or 2019 to 2020?
From 2018 to 2019:
(2250 - 2125)/2150 × 100% = 5.8% roundedFrom 2019 to 2020:
(2350 - 2250)/2250 × 100% = 4.44% roundedPart BCompare the percent increase we obtained:
5.8% > 4.44%Period 2018 to 2019 had a higher percent increase.
100 POINTS AND THE BRAINLIEST!!
1. A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined. Given that the number of men is now 60% of the total members, how many of the 50 new members were women?
2. A rectangle is 50cm long and 40cm wide. Its length is extended by 12% and its width is reduced by 15%. Does the perimeter of the rectangle change? Does the area of the rectangle change? Justify your answer.
Answer:
1) 25 women joined;2) Perimeter stayed same but area became smaller.-----------------------
Question 1Initial number of sports team:
65 + 35 = 100Number after new members joined:
100 + 50 = 15060% of 150 members are men, number of men is:
150*60/100 = 90Number of women:
150 - 90 = 60Number of newly joined women:
60 - 35 = 25Question 2Perimeter of the rectangle:
2(50 + 40) = 2(90) = 180 cmArea of rectangle:
50*40 = 2000 cm²New dimensions:
50 + 12% = 50*1.12 = 56 cm,40 - 15% = 40*0.85 = 34 cm.New perimeter:
2(56 + 34) = 2(90) = 180 cmNew area:
56*34 = 1904 cm²New perimeter is same as previous one but new area is smaller.
What is the relationship between corresponding angles if parallel lines are cut by a transversal 
_ Linear pair
_Congruent
_Supplementary
_Complemantary
Answer:
(b) _Congruent
Step-by-step explanation:
You want to know the relationship between corresponding angles where a transversal crosses parallel lines.
Corresponding anglesThe Corresponding Angles theorem tells you that corresponding angles at a transversal are congruent if and only if the lines are parallel.
Corresponding angles are congruent.
__
Additional comment
This fact is the basis for the simplest method of constructing a line parallel to a given line through an external point. (A transversal is drawn, and the angle is copied, making congruent corresponding angles.)
All of the other angle relationships at a transversal can be derived from this one using the usual relationships of linear pairs and vertical angles.
The SC Electric Company has bid on two electrical wiring jobs. The owner of the company believes that: the probability of being awarded the first job (event A) is 0.17; the probability of being awarded the second job (event B) is 0.5; the probability of being awarded both jobs (A and B) is 0.375. If the owner's beliefs are correct, which of the following statements must be true concerning event A and event B?
Statements must be true concerning event A and event B are that event A and B are independent and not mutually exclusive.
Define mutually exclusive event.Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot obtain both outcomes. Since they do not occur at the same time, such occurrences are also known as disjunct events. Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin flip, which can result in either heads or tails but not both, serve as an obvious illustration.
Given
The owner of the company believes that: the probability of being awarded the first job (event A) is 0.17.
The probability of being awarded the second job (event B) is 0.5; the probability of being awarded both jobs (A and B) is 0.375.
Statements must be true concerning event A and event B:
Event A and B are independent and not mutually exclusive.
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Chris completed a 100-meter breaststroke swimming race in 92.542 seconds.
Michael completed the 100-meter breaststroke swimming race in 95.6 seconds.
How much faster was Chris's time than Michael's?
Answer: C its C
Step-by-step explanation:
GOT DANG JUST READ THE ANSWER ITS CCCCCCCCCCCCCCCCCCCCCCCCCCCCC
a) It is known that in a sports club, there are 1000 registered members.
60% of members play Tennis, 50% of members play Cricket,
70% of members play Football, 20% of members play Tennis and Cricket,
40% of members play Cricket and Football and 30% of members play Football and Tennis.
If someone claimed that 20% of members play all the three sports,
what is your opinion and why?
[Use inclusion and exclusion principle to provide your opinion]
Answer:
Using the inclusion and exclusion principle, we can calculate the percentage of members who play all three sports as follows:
60% of members play Tennis, 50% of members play Cricket, and 70% of members play Football.
Therefore, 60% + 50% + 70% = 180% of members play at least one of the sports.
However, this count includes members who play more than one sport, so we need to subtract out the members who play two sports and add back in the members who play all three sports.
20% of members play Tennis and Cricket, 40% of members play Cricket and Football, and 30% of members play Football and Tennis.
Therefore, 20% + 40% + 30% = 90% of members play at least two sports.
Subtracting this number from the total number of members who play at least one sport gives us 180% - 90% = 90% of members who play at least one sport but not all three sports.
To find the number of members who play all three sports, we need to subtract this number from the total number of members who play at least one sport:
180% - 90% = 90% of members who play at least one sport but not all three sports
180% - 90% = 90% of members who play all three sports
Therefore, according to the inclusion and exclusion principle, 90% of members play all three sports.
If someone claimed that 20% of members play all three sports, this would be incorrect based on the calculations using the inclusion and exclusion principle. The correct number of members who play all three sports is 90%, not 20%. This can be verified by using the given information about the percentage of members who play each individual sport and the percentage of members who play two sports in combination.
To clarify, the inclusion and exclusion principle states that to find the number of elements in a union of sets (in this case, the number of members who play at least one sport), we can add the number of elements in each set (the percentage of members who play each individual sport) and then subtract the number of elements that are counted multiple times (the percentage of members who play two sports in combination). We then add back in the elements that were subtracted out in the previous step (the percentage of members who play all three sports).
Using this principle, we were able to calculate that 90% of members play all three sports, rather than the 20% claimed by someone.
Step-by-step explanation:
Answer:
We can conclude that there are 300 members who play tennis only. (total of 600 but 200 for members who play all 3 and 100 for players who play tennis and football)Only X = X - ( (X∩Y - X∩Y∩Z) + X∩Y∩Z + (Z∩X - X∩Y∩Z) )
Only X = 600 - ( (200-200) + 200 + ( 300-200) )
Only X = 600 - (0 + 200 + 100)
Only X = 600 - (300)
Only X = 300
There are 100 members who play cricket only. (total of 500 but 200 for members who play all 3 games and 200 for players who play cricket and football)Only Y = Y - ( (Y∩Z - X∩Y∩Z) + X∩Y∩Z + (X∩Y - X∩Y∩Z) )
Only Y = 500 - ( (400-200) + 200 + ( 200-200) )
Only Y = 500 - (200 + 200 + 0)
Only Y = 500 - (400)
Only Y = 100
There are 200 members who play football only. (total of 700 but 100 for tennis and football players, 200 for 3 games players, and 200 for cricket and football players.Only Z = Y - ( (Y∩Z - X∩Y∩Z) + X∩Y∩Z + (Z∩X - X∩Y∩Z) )
Only Z = 500 - ( (400-200) + 200 + ( 300-200) )
Only Z = 500 - (200 + 200 + 100)
Only Z = 500 - (500)
Only Z = 200
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-It takes a turtle 3 1/4 hours to walk 1/2 miles how many hours does it take to walk one mile?
Using the principle of proportional relationship, the time taken by the turtle to walk one mile is 2.1667 hours
What is proportional relationship?
Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".
Creating a system of proportional expression :
Cross multiply :
1.5t = (3.25 × 1)
1.5t = 3.25
Divide both sides by 1.5
t = (3.25 ÷ 1.5)
t = 2.1667 hours
Therefore, the time taken per mile is 2.1667 hours
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The turtle needs 2.16 hours to move a mile using the proportional relationship principle.
What does the word "proportional" mean?
Proportional relationships form when the ratios of two variables are equal. The fact that one variable is consistently equal to the constant value of the other in a proportionate connection is another way to think of them. The "constant of proportionality" is the name of this constant.
For instance, the time it takes a train to travel 50 kilometers per hour is equal to the time it needs to travel 250 kilometers in 5 hours. e.g., 250km/5 hours at 50 km/h.
Establishing a proportional expression system
Cross multiply :
1.5t = (3.25 × 1)
1.5t = 3.25
t = (3.25 ÷ 1.5)
t equals 2.16 hours
Consequently, the time required for each mile is 2.16 hours.
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What is the probability of NOT selecting a 5 out of a deck of cards
The probability of not drawing a 5 from the deck is 48/52.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
There are 4 number 5's in the deck of 52 cards.
They are as follows:
The 5 of clubs, the 5 of spades, the 5 of hearts, and the 5 of diamonds.
Using the formula,
Probability = (Number of possible outcomes)/(Total number of outcomes)
The probability of drawing a 5 from the deck is 4/52.
The probability of not drawing a 5 from the deck is 48/52.
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Please find what the rent per unit needs to be to have a Net Operating Income (NOI) of $100,000.
Assumptions
Please use the following assumptions below:
Rent per unit (per month)
Vacancy Rate (% of Potential Gross Income) 5%
Operating Expenses (% of Effective Gross Income) 30%
Number of Units 18
*Please fill out the blue area Rent per unit (per month)
Vacancy Rate (% of Potential Gross Income)
Operating Expenses (% of Effective Gross Income)
Number of Units
Applying the net operating income ratio, the rent per unit needs to be $8,354.22 to generate an NOI of $100,000.
What is the NOI?The net operating income (NOI) is the result of the subtraction of the operating expenses from the gross operating income.
The net operating income ratio can be computed by subtracting the given operating expenses ratio from the operating gross income, which represents 100%.
Total
Rent per unit (per month) = $696.19 ($8,354.22/12) $150,376
Vacancy Rate (5% of Potential Gross Income) 7,519
Effective Gross Income $142,857
Operating Expenses (30% of Effective Gross Income) 42,857
Net Operating Income (NOI) $100,000
Number of Units 18
Working Backwards:Gross operating income = net operating income + operating expenses
Operating expenses = 30% of effective gross income
Net operating income = 70% of effective gross income (100 - 30%)
= $100,000
Effective Gross Income (100%) = $142,857 ($100,000 ÷ 70%)
Vacancy rate = 5% of potential gross income
Effective Gross Income = 95% (100 - 5)
Potential gross income = $150,376 ($142,857 ÷ 95%)
Number of units = 18
Rent per unit = $8,354.22 ($150,376/18)
Rent per month = $696.19 ($8,354.22 ÷ 12)
Thus, a rent of $8,354.22 per unit can generate a Net operating income of $100,000.
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How long will it take for a $1000 investment to grow to $1500 at an annual rate of 13%, compounded semiannually? Assume that no withdrawals are made. Do
not round any intermediate computations, and round your answer to the nearest hundredth.
This is a case of Compound Interest.
It takes around 3.22 years for investment to grow to 1500$ from 1000$.
How to calculate Compound Interest?The interest charged on a loan or deposit is known as compound interest. It is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The major distinction between compound and simple interest is this.
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
Annual amount, A=P(1+[tex]\frac{r}{n}[/tex])∧nt
Calculation:Given,
P=1000$
A=1500$
r=13%=0.13
A=P(1+[tex]\frac{r}{n}[/tex])∧nt
n=2(Compounded semi-annually)
⇒1500=1000(1+[tex]\frac{0.13}{2}[/tex])^2t
⇒[tex]\frac{1500}{1000}[/tex]=(1.065)^2t
⇒1.5=(1.065)^2t
Taking log on both sides
㏒(1.5)=2t㏒(0.625)
⇒t=[tex]\frac{log(1.5)}{2log(0.625)}[/tex]
⇒t=3.219years≈3.22years
This is a case of Compound Interest.
It takes around 3.22 years for investment to grow to 1500$ from 1000$.
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Penny is planning a trip to Egypt. She has mapped out the expected costs of some different components of her trip, and
has compiled them below, including whether the cost is in US
dollars ($) or Egyptian pounds (E).
Item
Cost
Currency
Plane ticket
3,241.77
£
Passport
65.00
$
Tour guide
494.25
£
International phone card
41.38
$
Hotel reservation
398.26
f
Car rental
644.48
£
If the exchange rate of the US dollar to Egyptian pound is 1:5.3841, how much has Penny currently budgeted for her trip,
in US dollars? Round all currencies to two decimal places.
a.
$895.25
b. $993.95
C.
$1,001.63
d
$1.468.01
Penny currently budgeted for her trip, in US dollars is $993.95.
What is Penny currently?
Pennies are constructed of copper-coated zinc. Only nickels—that identical alloy of 75% copper and 25% nickel—are one solid substance.
Given: Exchange rate of the US dollar to Egyptian pound is 1:5.3841
Item Cost Currency Plane ticket =
[tex]3,241.77 £=\frac{3,241.77}{5.3841}=\$ 602.100629632 \approx \$ 602.10[/tex]
Passport = $65.00
Tour guide [tex]$=494.25 £=\$ 91.7980721012 \approx \$ 91.80$[/tex]
International phone card [tex]$=\$ 41.38$[/tex]
Hotel reservation [tex]$=398.26 £=\frac{398.26}{5.3841}=\$ 73.9696513809 \approx \$ 73.97$[/tex]
Car rental [tex]$=644.48 £=\frac{644.48}{5.3841}=\$ 119.700599915=\$ 119.70$[/tex]
Therefore, the total budgeted for her trip, in US dollars= [tex]602.10+91.80+41.38+73.97+119.70+65$ $=\$ 993.95$[/tex]
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Six people start a new town. Every 20 years , the population doubles. After years will the town have more than people? Make the pattern: ____________________Answer the question: ____________________
The complete statement is "After 80 years, the town will have more than 96 people."
What is the population?Generally, A population is the whole set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from whom a statistical sample is taken in statistics.
Here is the pattern:
20 years: 6*2=12 people 40 years: 12*2=24 people 60 years: 24*2=48 people 80 years: 48*2=96 peopleAfter 80 years, the town will have more than 96 people.
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Which composition of two rigid motions maps ️ABC to ️A'B'C'
Answer:
C. Translation [tex](x,y) \longrightarrow (x-7, y+0)[/tex], Reflection in the [tex]y[/tex]-axis
2
Evaluate: 1.5+ (0-1) X2
A) -3
B) 1.5
C) 3
D) 2
Answer:
A) -3
Step-by-step explanation:
To evaluate this mathematical expression, we must follow the following steps:
Perform the operation between parentheses: (0-1) = -1
Multiply the previous result by 2: -1 * 2 = -2
Add 1.5 to the previous result: -2 + 1.5 = -0.5
Therefore, the correct answer to the mathematical expression is A) -3.
Gloria has a study guide for her math, socialstudies, and science classes.she has 3 study guides for language art.Each study guide is 3 pages.How many pagesof study guides does Gloria have in all?
Therefore, number of pages of study guide Gloria have=9
what is Equation?
In mathematics, an equation is a formula that uses the equals symbol (=) to represent how two expressions are equivalent. the act of comparing two things or "the equation of science with objectivity."
given
no. of study guides for language art= 3
no. of pages in each study guides=3
so no. of pages of study guides= no. of study guides for language art*
no. of pages in each study guides
3*3=9
therefore, number of pages of study guide Gloria have=9
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9. Passive solar heating systems use solar collectors.
true or false
Passive solar heating systems use solar collectors. This is false.
What is a solar collector?An apparatus that gathers and/or concentrates solar radiation from the Sun is called a solar collector. These gadgets enable the heating of water for personal use and are primarily used for active solar heating.
Through the absorption of sunlight, a solar thermal collector gathers heat. Commonly, a solar hot water heater is referred to as a "solar collector," but the term can also refer to large power generation facilities like solar parabolic troughs and solar towers or non-water heating equipment like solar air heaters.
In conclusion, it's false.
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Questionaire image below
Answer:
15 years old45 liters of sugar solutionStep-by-step explanation:
You have ages in the ratio 3:5:7, with the average age being 25, and you want to know the age of the youngest. You have 45 L of a solution in the ratio sugar : salt = 1 : 2, and you want to know how much sugar solution to add to make the ratio 2 : 1.
AgesThe age ratios are an arithmetic progression with an odd number of terms, so the middle one is the average. That is, the average age of 25 years corresponds to 5 ratio units. Then the youngest boy is ...
3/5 × 25 = 15 . . . . years old
SolutionThe ratio 1 : 2 of sugar solution to salt solution tells you that the fraction that is sugar is 1/(1+2) = 1/3 of the whole amount, or ...
sugar solution = 1/3 · 45 L = 15 L
Then the salt solution is ...
salt solution = 45 L -15 L = 30 L . . . . . . . or (2/3·45 L)
To make the solution have twice as much sugar solution as salt solution, we need a total of 2·(30 L) = 60 L of sugar solution. We already have 15 L, so we need to add ...
added sugar solution = 60 L -15 L = 45 L
45 L of sugar solution must be added to make the sugar : salt ratio be 2 : 1.
__
Additional comment
The "solution" problem can also be worked by considering "ratio units." The original sugar:salt ratio is 1:2. To make it be 2:1 while keeping the salt constant, we need to increase the ratio from 1:2 to 4:2. That is, we need to add 4-1 = 3 units of sugar solution. The 45 L amount is the amount of 1+2=3 units of solution, so we need to add 45 L of sugar solution.
Which of the following is equivalent to 5/13³?
Answer:
D 13 [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
I’m ur math man
Solve.
Six times a number is equal to the number increased by 10. Find the number.
When 6 times a number is equal to the number increased by 10. The number is 5.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number be represented as x.
Six times a number is equal to the number increased by 10. This will be:
(6 × x) = x + 10
6x + x = 10
Collect the like terms
6x - x = 10
5x = 10
Divide.
x = 10 / 2
x = 5.
The number is 5
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explain how you would compare "-2/3" and "-1/4." use words and numbers to explain your answer
0.4166667 is the difference between 2/ 3 and 1 /4.
Explain about the fractions?A fraction is a symbol used in mathematics to represent a part or element of the whole. It represents the proportional components of the whole. A fraction is made up of the denominator and the numerator. The top number is the numerator, and the lower number is the denominator.
More manageable pieces of a whole are represented by fractions. The components could be combined to make one thing or several things. In any instance, they come together to create the concept of a whole. As parts of wholes or sets, as the result of dividing two numbers, as the ratio of two quantities, as operators, and as measures are only a few examples of how to use fractions, they are all examples of fractions.
= 2/3 - 1/4
= 512
= 0.4166667
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What is the solution to f(x) = -4 when f(x) = 3x + 5 ?
Answer: x=-3
Step-by-step explanation:
-4=3x+5
isolate x by moving all other variables to the right
-4-5=3x+5-5
-9=3x
x=-3
Answer:
-7
Step-by-step explanation:
To find the solution you'd have to plug in the -4 for every x you see but in this solution there is only one x so then you'd plug it in for that x. So then you'd have f(-4= 3(-4) + 5 and then you'd solve it. To solve it you would first multiply the 3 with the -4 because when something is in a parenthesis and there is a number beside with no sign that means you multiply. When you multiply you should get -12. After you get -12 you add 5 and your answer is -7.
When they give you an equation with an f(x) they sometimes give you inputs which you plug in to get your output. -4 was an input and -7 (your answer) is an output.
(hopefully you understood how i solved..)
In July, Lily's family used 12,568 gallons of water. In August, they used 11,562 gallons of water.
What is the percent decrease in their water usage? Round your answer to the nearest
whole-number percent.
Answer:
Step-by-step explanation:
Look at the original value of the gallons of water =12568 this is in July
Look at the value of the gallons of water in August =11,562
Find the difference between the two values=12568-11562=1006
Place the larger value of gallons of water first, as you are going from a large number to a small number you are decreasing by 1006
We put this value of the difference over the original gallons of water and then multiply by 100%
1006/12568 x100%=
This can be done on your calculator
1006÷12568 x100=8.004455761
Rounding to the nearest whole percent gives 8% decrease
For the piecewise function below, which of the following statements are true?
Please help will give brainlist if correct!
The correct option is (b) i.e. f(0) > f(2).
What is Domain?
The entire range of independent variable values is the domain of a function. In straightforward terms, this definition means The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain.
We have,
f(x) = (x+2)^2 - 1 , -4 ≤ x ≤ 0
-x + 1 , 0 ≤ x ≤ 2
5/2 log ( -x +5) - 1 , 2 < x < 5
Now, f(0) = (x+2)^2 - 1
= (0+2)^2 - 1
= 4 - 1 = 3
Similarly, f(2) = - x +1
= - 2 + 1
= - 1.
Hence, f(0) > f(2) because 3 > -1.
∴ The correct option is (b).
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The distance a freely falling body covers in the nth second is given by S(n)=d(n)-d(n-1). Show s(n) in terms of g, in simplified form.
Answer:
Step-by-step explanation:
[tex]s=ut+\frac{1}{2}gt^2\\if ~the~body~falls~freely,~then~at~t=0,d=0\\s_{n}=d_n=\frac{1}{2}gn^2\\S_{n-1}=\frac{1}{2}g(n-1)^2\\distance~covered ~in~nth~second\\S(n)=d(n)-d(n-1)=\frac{1}{2}gn^2-\frac{1}{2}g(n-1)^2=\fracg[n^2-(n-1)^2]\\=\frac{1}{2}g{(n+n-1)(n-n+1)]\\=\frac{1}{2}g(2n-1)[/tex]
A certain volcano has an elevation of 13,410 feet. A nearby oceanic trench has an elevation of 21,795 feet below sea
level. Find the difference in elevation between those two points.
Of 400 college students, 120 are enrolled in math, 220 are enrolled in English, and 55 are enrolled in both. If a student is selected at random, find the probability that the student is
(a) enrolled in mathematics.
(b) enrolled in English.
(c) enrolled in both.
(d) enrolled in mathematics or English.
(e) enrolled in English but not in mathematics.
(f) not enrolled in English or is enrolled in mathematics.
The probability that the student is
(a) enrolled in mathematics is equal to [tex]\frac{3}{10}[/tex]
(b) enrolled in English is equal to [tex]\frac{11}{20}[/tex].
(c) enrolled in both is equal to [tex]\frac{11}{80}[/tex].
(d) enrolled in mathematics or English is equal to [tex]\frac{57}{80}[/tex].
(e) enrolled in English but not in mathematics is equal to [tex]\frac{33}{10}[/tex].
(f) not enrolled in English or is enrolled in mathematics is equal to [tex]\frac{23}{80}[/tex].
What is probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The total number of students in college is 400.
Students enrolled in Mathematics = 120.
Students enrolled in English = 220.
Students enrolled in both Mathematics and English = 55.
(a) The probability that the student is enrolled in mathematics is the Number of students enrolled in mathematics divided by the total number of students which is equal to [tex]\frac{120}{400} =\frac{3}{10}[/tex].
(b) The probability that the student is enrolled in English is the Number of students enrolled in English divided by the total number of students which is equal to [tex]\frac{220}{400} =\frac{11}{20}[/tex].
(c) The probability that the student is enrolled in Both is equal to the number of students enrolled in Both divided by the total number of students which is equal to [tex]\frac{55}{400} =\frac{11}{80}[/tex].
(d) The probability that the student is enrolled in mathematics or English is the Number of students enrolled in mathematics or English that is the Number of students in (Maths+English - Both) divided by the total number of students which is equal to [tex]\frac{120+220-55}{400} =\frac{285}{400}=\frac{57}{80}[/tex].
(e) The probability that the student is enrolled in English but not in mathematics is the Number of students enrolled in (English- enrolled in both) divided by the total number of students which is equal to [tex]\frac{220-55}{400} =\frac{165}{400}=\frac{33}{80}[/tex].
(f) The probability that the student is neither enrolled in mathematics nor English is the Total Students - (Maths+English-both) divided by the total number of students which is equal to [tex]\frac{400-(120+220-55)}{400} =\frac{115}{400}=\frac{23}{80}[/tex].
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each system of equations to its graph. y = 2x + 1 y = x + 2 y = 3x y = x + 3 y = 2x − 2 y = x − 2 y = 2x + 3 y = x + 5 y = 4x + 2 y = 3x + 2 Graph shows a system of equations plotted on a coordinate plane. A line goes through (minus 3, 0) and (0, 3). Another line goes through (minus 1, minus 3) and (1, 3). Both the lines intersect at (1.5, 4.5).
In the given equation, Y = 3x is at (0, 3) and a line passes through (-3, 0).
What do you mean by Equation?A mathematical statement known as equation is given by joining two expressions with the equal sign. For instance, 3x - 5 = 16 is an equation. This equation can be solved, and the result shows that the value of the variable x is 7.
A mathematical equation links the two phrases on either side of the sign. It typically only contains an equal sign and one variable. similar to 2x - 4 = 2.
Either identities or conditional equations can be used to classify equations. Each value of the variables corresponds to a specific identity. A conditional equation can only be true for a certain range of variable values. An equation is represented by two expressions being separated by the equals sign ("=").
A line goes through (- 3, 0) and (0, 3)
The equation is
y - y1 = y2 - y1/ x2- x1
y - 0 = 3 - 0 / 0 - (-3) (x - (-3)
y = x + 3
y = 3x
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Write an expression to model the interest earned on each account, then find the balance of each option after 3 years. Complete the table. Round your responses to the nearest whole cent, if necessary.
The missing parts of the table for the compound interest problem are;
2) $487.91
3) 435(1.039)^(t) and $487.91
4) 435(e)^(0.039t) and $499
How to find the compound interest?1) In this account, we are given the formula for the compound interest as;
P(1 + rt)
The balance after t years is expressed as;
435(1 + 0.039t)
Balance after 3 years is;
435(1 + 0.039(3)) = $485.90
2) In this account, we are given the formula for the compound interest as;
P(1 + (r/n))^(nt)
The balance after t years is expressed as;
435(1.039)^(t)
Balance after 3 years is;
435(1.039)^(3) = $487.91
3) Same as 2 above
4) In this account, we are given the formula for the compound interest as;
P₀e^(rt)
The balance after t years is expressed as;
435(e)^(0.039t)
Balance after 3 years is;
435(e)^(0.039 * 3) = $499
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Find x and the length of side UR
The value of x in the parallelogram is zero.
How to find the sides of a parallelogram?A parallelogram is a two-dimensional geometrical shape(quadrilateral) whose sides are parallel to each other.
Therefore, the properties of a parallelogram are as follows:
opposite sides are equalopposite sides are parallel to each otherThe opposite angles are equalEach diagonal bisects the parallelogram into two congruent trianglesThe consecutive or adjacent angles are supplementaryTherefore, let's find the value of x using the properties of a parallelogram.
Hence,
ST = RU
2x + 15 = x + 15
2x - x = 15 - 15
Therefore,
x = 0
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the ucl for a process where the process mean is 35, sample size is 25 and the average sample standard deviation is 5, will be 38.
The upper control limit(UCL) is 160
sample mean X =35
sample size n =25
sample size n=25, average sample standard deviation is 5
Upper control limit is shown by the top dashed line (UCL). The data that is plotted on the control chart is used to calculate the upper control limit. It is positioned 3 sigma off the average line (of the data being plotted).
A control chart is made up of various components. It has an average line and two control limits. The lower control limit is represented by the dashed bottom line (LCL). The statistic's average is represented by the solid center line. The higher control limit appears as the top dashed line (UCL).
a)
Upper control limit(UCL) =X+A2R =160
Control line (CL) = X=35
Lower control limit (LCL)=X-A2R =90
Hence, The upper control limit (UCL) is 160
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