Step-by-step explanation:
perimeter of a rectangle is 2(length + width)
p= 2[ (2x -3) + (x+2 )]
combines like terms
p = 2 ( 3x -1 )
p = 6x -2
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
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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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 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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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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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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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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She does not want to give up going to the spa by Emily feels that she could cut her costs a bit she’s thinking of getting a 45 minute massage for $80 and a regular manicure and pedicure for $40. If she makes exchange how much will she save?
Answer:
umm i would say 40$
Step-by-step explanation:
sorry if i have misunderstood the question
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
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.
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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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
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.
Can you please help me
Answer:
(c) see below
Step-by-step explanation:
You want the graph of the compound inequality x > -6 or x > -2.
GraphsThe graph of the inequality x > -2 is shown as the top selection.
The graph of the inequality x > -6 is shown as the bottom selection.
You will notice that the bottom graph overlaps and includes the top graph. Hence the "OR" of the inequalities will look like the bottom graph, attached.
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.
DIRECTIONS: Use this information to answer Parts A and B.
Eric lays tile on a floor at a constant rate. He covers a 150-square-foot floor in 3 hours.
Complete the table to show the area Eric can cover in various amounts of time.
Enter the correct answers in the boxes.
The unit rate can be expressed in area covered per hour.
a) The table with the output values is completed on the first image at the end of the answer.
b) The graph of the proportional relationship is given by the second image at the end of the answer.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
He covers a 150-square-foot floor in 3 hours, hence the constant of proportionality is obtained as follows:
k = 150/3 = 50 sq feet per hour.
Then the equation is given as follows:
y = 50x.
Then the numeric values for the table are given as follows:
3 hours: y = 50 x 3 = 150 ft².4 hours: y = 50 x 4 = 200 ft².4.5 hours: y = 50 x 4.5 = 225 ft².5 hours: y = 50 x 5 = 250 ft².6.5 hours: y = 50 x 6.5 = 325 ft².Missing InformationThe problem is given by the image shown at the end of the answer.
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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.
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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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..)
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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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]
There were n signers of the Declaration of Independence. The oldest was Benjamin Franklin, who was y years old.
7 is 10% of y and n is 80% of y. How many signers were there?
Answer:
There were 56 signers.
Step-by-step explanation:
First, set up the two equations for the two situations we are given.
7 is 10% of y . . . . .(1):
[tex]7 = \frac{10}{100}(y)[/tex]
n is 80% of y . . . . .(2):
[tex]n = \frac{80}{100}(y)[/tex]
Now, solve for y in the 1st equation, and substitute y in the second equation to solve for n.
[tex]7 = \frac{10y}{100}[/tex]
[tex]700 = 10y\\[/tex]
[tex]70 = y[/tex]
[tex]n = \frac{80*70}{100}[/tex]
[tex]n = \frac{5600}{100}[/tex]
[tex]n = 56[/tex]
Answer:
56 signers--------------------------------
7 is 10% of y, find y:
7 = 0.1y ⇒ y = 70n is 80% of y, find n:
n = 0.8y = 0.8*70 = 56Questionaire 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.
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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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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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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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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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
Which of the following sets represents a function? {(3, 5), (-1, 7), (3, 9)} {(1, 2), (3, 2), (5, 7)} {(1, 2), (1, 4), (1, 6)} unlimited attempts remain
The set {(1, 2), (1, 4), (1, 6)} represents a function because each value of x corresponds to only one value of y.
In contrast, the sets {(3, 5), (-1, 7), (3, 9)} and {(1, 2), (3, 2), (5, 7)} do not represent functions because they contain multiple values of x that correspond to the same value of y. Specifically, the set {(3, 5), (-1, 7), (3, 9)} contains two values of x (3 and -1) that correspond to the same value of y (7), while the set {(1, 2), (3, 2), (5, 7)} contains two values of x (3 and 1) that correspond to the same value of y (2).
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