The correct description will be;
⇒ y = - 2x + 3
4x + 2y = 6
These are independent.
⇒ y = -2x + 3
4x + y = 9
These are consistent.
⇒ y = -2x+3
4x + 2y = 9
These are inconsistent.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expressions are,
1. y = -2x+3
4x + 2y = 6
2. y = -2x+3
4x+y=9
3. y = -2x+3
4x + 2y = 9
Now,
From (1);
1. y = -2x+3
4x + 2y = 6
⇒ 2x + y = 3
4x + 2y = 6
⇒ 2x + y = 3
So We get;
⇒ 2/2 = 1/1 = 3/3
⇒ 1/1 = 1/1 = 1/1
These are independent.
From (2);
1. y = -2x+3
4x + y = 9
⇒ 2x + y = 3
4x + y = 9
So We get;
⇒ 2/4 ≠ 1/1
⇒ 1/2 ≠ 1/1
These are consistent.
From (3);
1. y = -2x+3
4x + 2y = 9
⇒ 2x + y = 3
4x + 2y = 9
So We get;
⇒ 2/4 = 1/2 = 3/9
⇒ 1/2 = 1/2 ≠ 1/3
These are inconsistent.
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Mike has a box with 5 white marble, 3 green marble and 2 blue marble. he picks 2 marbles from the box. what is the probability that he will get two green marbles?
Answer:
1/15
Step-by-step explanation:
3/10 x 2/9
Select the graph for the solution of the open sentence. Click until the correct graph appears.
2|x| < 4
Answer:
1st one
Step-by-step explanation:
So 2|x|<4 = |x|<2, and since absolute values are always positive, I believe it is the 1st one.(Sorry if its not right I'm not very good in this area.)
Which of the following terms represents the situation in the graphic below?
a glide a reflection a glide reflection
None of these choices are correct.
Answer:
A glide.
Step-by-step explanation:
The image is a shift or a glide.
Reflection is either changes the arrow direction the other direction.
A glide reflection is both.
designs for their
In popular online role playing game, players can create detailed
character's "costumes," or appearance. Abigail sets up a website where players can
buy and sell
these costumes online. Information about the number of people who
visited the website and the number of costumes purchased in a single day is listed
below.
146 visitors purchased no costume.
230 visitors purchased exactly one costume.
A
31 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase
exactly one costume as a decimal to the nearest hundredth.
The probability that the next person will purchase exactly one costume is 0.57.
what is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given:
146 visitors purchased no costume.
230 visitors purchased exactly one costume.
31 visitors purchased more than one costume.
So, the total number of customers are,
146 + 230 + 31 = 407
The total visitors purchased exactly one costume are 230.
So,
P(Purchase exactly one costume) = 230 / 407 = 0.5651 ≈ 0.57
Hence, the probability that the next person will purchase exactly one costume is 0.57.
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You are looking at buying a gym membership. Total Gym has a starting fee of $100 and costs $20 every month. Fitness Plus Elite costs $25 each month with an initial membership cost of $35. At what month will both memberships cost the same? Write and solve an equation to answer the problem. Explain what the answer means for the problem.
Answer:
The answer is 13 because that is the month that both memberships will cost the same amount of money.
Step-by-step explanation:
First translate the question into equations.
Total Gym:
100+20m
Where "m" equals the amount of months
Fitness Plus Elite
35+25m
Where "m" equals the amount of months
Set the equations equal to each other and solve for m, or the amount of months it takes to get the same price for each membership.
100+20m=35+25m Subtract 35 from both sides.
65+20m=25m Subtract 20m from both sides
65=5m Divide both sides by 5
13=m Both memberships will cost the same amount of money at 13 months. You can substitute this value into the original equations to check your work.
100+20(13)=$360
35+25(13)=$360
The answer is 13 because that is the month that both memberships will cost the same amount of money.
Please helpppppp!!! Find the equation of direction given that y varies directly with x and y is 2 when x is 4
Answer:
y= 1/2x
Step-by-step explanation:
If y is 2 and x is 4
2= 1/2 (4)
2 = 2
if $0.\overline{1331}$ is written as a fraction $\frac{a}{b}$ with $a$ and $b$ being positive integers with a greatest common divisor of 1, what is $a b$?
The value of a is 133 and b is 999.
A vinculum is a horizontal line that serves a variety of functions in mathematical notation. In decimal numbers, a bar across one or more consecutive digits indicates that the pattern of digits beneath the bar repeats indefinitely.
Given [tex]0.\overline{1331}[/tex]. This means that 1331 repeats many times in this expression. This expression is the same as 1330/9990.
1, 7, 19, and 133 are factors of 133, and 1, 3, 9, 27, 37, 111, 333, and 999 are the factors of 999. From this, the GCD is found to be 1.
Therefore, by simplifying, we get 1330/9990 = 133/999. The answer to a is 133 and b is 999.
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Cheter hope to earn $1200 in interet in 3. 5 year time from $60,000 that he ha available to invet. To decide if it' feaible to do thi by inveting in an account that compound quarterly, he need to determine the annual interet rate uch an account would have to offer for him to meet hi goal. What would the annual rate of interet have to be? Round to two decimal place
The annual interest rate would have to be about 0.57% in order to earn $1200 in interest in 3.5 years. Rounded to two decimal places, the annual interest rate would have to be about 0.57%.
What is an annual interest rate?
The annual interest rate is the percentage of the principal (the initial amount of money invested or borrowed) that is charged as interest on a loan or earned on an investment over a period of one year. It is used to calculate the amount of interest that will be earned or charged over a given period of time.
To determine the annual interest rate that an account would have to offer in order to earn $1200 in interest in 3.5 years, we need to use the following formula:
rate = (interest / principal) * (1 / time)
Where the rate is the annual interest rate, interest is the amount of interest earned, the principal is the amount of money invested, and time is the length of time in years.
Plugging in the given values, we get:
rate = ($1200 / $60000) * (1 / 3.5)
= 0.02 * (1 / 3.5)
= 0.00571428571
Hence, the annual interest rate would have to be about 0.57% in order to earn $1200 in interest in 3.5 years. Rounded to two decimal places, the annual interest rate would have to be about 0.57%.
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Funky Fro-Yo
The school jazz band is playing at Sweet Yo's, a frozen yogurt shop. It costs $5 to get in
the door for the event and if you'd like to eat fro-yo to eat while listening to their tunes
you can fill your cup with yogurt and toppings for $0.40 per ounce.
1. Write an equation that gives the total cost in dollars, d, of attending the event if you
order z ounces of fro-yo.
2. If your cup weighs 14 ounces, how much would you pay in total for the evening?
1) An equation that gives the total cost in dollars, d, of attending the event if you order z ounces of fro-yo is d = $5 + $0.40z
2) 2. If your cup weighs 14 ounces, you would pay $10.6 in total for the evening.
Define equation.A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts.
Given,
The school jazz band is playing at Sweet Yo's, a frozen yogurt shop. It costs $5 to get in the door for the event and if you'd like to eat fro-yo to eat while listening to their tunes you can fill your cup with yogurt and toppings for $0.40 per ounce.
1) Total cost = d
Total ounces = z
Equation
d = $5 + $0.40z
2) If cup weighs 14 ounces
d = $5 + 0.40(14)
d = $5 + $5.6
Total cost:
d = $10.6
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AIR CONDITIONING A commercial air conditioner can cool a large room with a volume of up to 40,000 cubic feet. A rectangular room in a
warehouse is designed to have a length of 75 feet, a width of 50 feet, and a height of 8 feet. The builder wants to make the room larger by
increasing the length and the width by the same amount.
By how many feet can the length and width be increased and still not exceed the capacity of the air conditioner? Round to the nearest tenth of
a foot if necessary.
The maximum length or width we can increase so that it will not exceed the capacity of AC is 100 feet.
What is rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.
Given:
The volume AC can cool, v = 40000 feet³,
The dimensions of the room are 75 feet × 50 feet × 8 feet.,
Calculate the volume of the room as shown below,
Volume = 75 feet × 50 feet × 8 feet
Volume = 30000 feet³
The remaining margin of volume = 40000 - 30000
The remaining margin of volume = 10000 feet³
Thus, the maximum dimension we can increase in length and width is 100 feet.
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In which cases should we use mean, medium, mode, and range etc. respectively?
Answer:
Mean, median, mode, and range are all statistical measures that are used to summarize and analyze data. Mean is the arithmetic average of a set of numbers, calculated by adding all the numbers together and dividing by the total number of values. Median is the middle value in a set of numbers, which is the value that divides the data into two equal halves. Mode is the value that occurs most frequently in a set of numbers. Range is the difference between the largest and smallest values in a set of numbers.
Mean is commonly used to calculate the average value of a set of numbers. The Median is commonly used to find the middle value in a set of numbers, especially when the data is not evenly distributed. Mode is commonly used to find the most frequent value in a set of numbers. The range is commonly used to find the difference between the largest and smallest values in a set of numbers.
All of these measures are useful for different purposes, and which measure to use will depend on the data and the question being asked. In general, mean is used when the data is evenly distributed, median is used when the data is not evenly distributed, mode is used when the data is categorical rather than numerical, and range is used to measure the spread of the data.
A cabin cruiser traveling with the current went 45 mi in 3 h. Traveling against the current, it took 5 h to go the same distance. Find the rate of the cabin cruiser in calm water and the rate of the current.
The rate of cabin cruiser in calm water id 12 miles/h and the rate of the current is 3 miles/h.
let the speed of cabin cruiser in still water be x miles/h
let the speed of current be y miles/h
during travelling with the current, speed of cabin cruiser = (x+y) miles/h
during travelling against the current, speed of cabin cruiser =(x-y) miles/h
time taken during case 1 = [tex]\frac{45}{x+y}[/tex] =3 h --->given
=> x+y = 45/3
after solving x+y=15 ------ (i)
time taken during case 2(against current) = [tex]\frac{45}{x-y}[/tex] =5 --->given
=> x-y = 45/5
after solving x-y =9 -------- (ii)
adding equation (i) and (ii) we get
x+y+x-y = 15+9
=> 2*x=24
=> x= 12
so x= 12 miles/h
so y=15-x= 15- 12 = 3miles/h
so x = 12 miles/h ,y= 3miles/h
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△ABC ha vertice A(1, 3), B(2, 5), and C(5, 3). What are the coordinate of B′ after the tranformation (x, y) ⟶ (–y, x), then tranlation 1 unit right and 4 unit up? help me out pl
On translating n 1 unit right and 4 unit up , we get the coordinates of B as B'( 3, 9).
The given triangle ABC has the following vertices A(1, 3), B(2, 5), and C(5, 3).
We will apply the translation rule on the following triangle,
T⟨1, 4⟩
A(1, 3)
A( 1+ 1 , 3+ 4 ) = A( 2, 7)
B(2, 5)
B( 2+ 1 , 5+ 4 ) = B( 3, 9)
C(5, 3)
( 5+ 1 , 3+ 4 ) = C ( 6, 7)
Therefore , the coordinates of B' is B'( 3, 9) as calculated after using the rule.
Translation rule is a rule in mathematics which moves a shape left , right , up or down. The newly formed shape is the same as before , just their direction gets changed.
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I need help plssssssss
Answer:
a. 25%
b. 5%
Step-by-step explanation:
a. Take 60000 divided by 240000, then times 100% = 25%
So the solution for a is 25%
b. Take 12000 divided by 240000, then times 100% = 5%
So the answer for b is 5%
whats the coefficient 5.4 ×10^8
The coefficient of the equation A = 5.4 x 10⁸ is c = 5.4
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the coefficient of the equation be c
A = 5.4 x 10⁸ be equation (1)
On simplifying the equation , we get
Group coefficients together and exponents together to multiply the numbers in the scientific notation
So , A = c x bˣ
where c is the coefficient
Substituting the values in the equation , we get
The value of c = 5.4
Therefore , the value of c is 5.4
Hence , the coefficient is 5.4
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Ue the given et to find |X∩Y|. U={a,b,c,d,…,x,y,z} X={t,e,a,,i,n,g} Y={,u,a,v,e}
Ue the given sets U={a,b,c,d,…,x,y,z} X={t,e,a,,i,n,g} Y={,u,a,v,e} therefore the elements in X n Y is a, e
we have to calculate |X∩Y|
U={a,b,c,d,…,x,y,z}
X={t,e,a,,i,n,g}
Y={,u,a,v,e}
X n Y= a, e
because in intersection set the elements coming in XnY is those which are common in X and Y
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A section of roller coaster can be modeled by the function:
F(x) = x5 - 5x4 - 31x3 + 113x2 + 282x - 360.
A walkway bridge will be placed at one of the zeros. What are the possible
locations for the walkway bridge?
The possible locations for the walkway bridge are 1, 5, and 6.
What is factorization?
Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.
Here, we have
Given
The function can model a section of a roller coaster:
F(x) = x⁵ - 5x⁴ - 31x³ + 113x² + 282x - 360.
We have to find the possible locations for the walkway bridge.
Now, we factorize the given function
F(x) = x⁵ - 5x⁴ - 31x³ + 113x² + 282x - 360
F(x) = (x-1)(x+3)(x+4)(x-5)(x-6)
then, x - 1 = 0, x+3 = 0, x+4 = 0, x-5 = 0, x-6 = 0
x = 1, -3, -4, 5, 6, becausex>0
s0, x = 1, 5, 6
Hence, the possible locations for the walkway bridge are 1, 5, and 6.
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if the probability that a baby born in a certain hospital will speak in the next day is , what is the probability that at least babies out of a cluster of babies will speak tomorrow?
The probability that at least 2 babies out of a cluster of 5 babies will speak tomorrow is 47/128.
The probability that less than 2 babies will speak is
5C0 * (0.25)^0 * (0.75)^5 + 5C1 * (0.25)^1 * (0.75)^4
= (0.75)^5 + 5 * 0.25 * (0.75)^4
(0.75)^5+5*0.25*(0.75)^4 = 81/128
Therefore,
probability that 2 or more will speak is
= 1- 81/128 = 47/128
The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability p) or failure (with probability display style q=1-pq=1-p).
This distribution is used in probability theory and statistics. A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results.
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FILL IN THE BLANK. _________ are the characteristics of the individuals of the population being studied.
Answer:
Variables
Step-by-step explanation:
Variables are the characteristics of the individuals of the population being studied.
Evaluate:
10 Σn=1 8(1/4) n -1= [?]
Mixed Number Form is 102184532768.
Evaluate:10 Σn=1 8(1/4) n -1= [?]10∑n=18(14)n−1
The sum of a finite geometric series can be found using the formula a(1−rn1−r)
where a is the first term and r
is the ratio between successive terms.
Find the ratio of successive terms by plugging into the formula r=an+1an
and simplifying.
r=14
Find the first term in the series by substituting in the lower bound and simplifying.
a=8
Substitute the values of the ratio, first term, and number of terms into the sum formula.
81−(14)101−14
Simplify.
34952532768
The result can be shown in multiple forms.
Exact Form:
34952532768
Decimal Form:
10.66665649…
Mixed Number Form:
102184532768
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True or false. When writing a ratio (fraction) in math, it does not matter which value goes in the numerator and which goes in the denominator of the ratio.
Answer:
False
Step-by-step explanation:
The first value given is the numerator even if its greater than the denominator.
Write a word problem for the following linear function y = 2x + 14
Delilah is baking cupcakes for her brother's birthday party. She has already made 14 cupcakes and is making 2 cupcakes per hour. How many cupcakes will she have in 10 hours? How many hours does it take to make 20 cupcakes?
help pls i don’t understand this cause my teacher can’t teach
Answer:
A
Step-by-step explanation:
cos A = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{18}{30}[/tex] = [tex]\frac{3}{5}[/tex]
A rectangular closet is 4 feet long. It is 3 times as wide as it is long.
Label the diagram with the dimensions of the closet.
12
ft
4
ft
4
ft
4
ft
4
ft
Great job!
Find the perimeter of the closet.
12 ft
4 ft
4 ft
4 ft
4 ft
The perimeter of the closet is
feet.
The dimensions of the closet are 4 feet long and 12 feet wide and the perimeter is 32 feet
What is the perimeter of a rectangle?The perimeter of a two-dimensional shape is the total length of the outline. To find the perimeter of a rectangle, we add the lengths of all four sides.
P=2(l+w) where l=length and w = width
Given here rectangular closet is 4 feet long and It is 3 times as wide as it is long. Thus its width would be 12 feet
Now perimeter of the closet using the formula above we get
P = 2(4+12)
= 32 feet
Hence the perimeter is equal to 32 feet.
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if a mixture has an ee of 90%, what is the percentage of each enantiomer? a) 65% : 35% b) 55% : 45% c) 80% : 20% d) 95% : 5% like 0
Percentage for each enantiomer is 95%, 5%. Option (d) is Correct.
We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100. A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The symbol "%" is frequently written after the number to indicate percentages. %, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
% ee = % enantiomer A - % ensarstomer B
wheee ee is enantiomeric excess.
ee = 90%.
In the provided options, 90%. the difference is given by subtracting 95%, 5%
95% - 5% = 90%
4th option is 5%, 90% correct.
Percentage of each enantiomer is 95%, 5%.
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Given the equation
2x² = 12x - 5
enter the values of a, b, and c, where a is a positive integer.
The values of a= 2, b= -12 and c= 5.
What is Quadratic Equation?Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term.
Quadratic equations are another name for it.
The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.
Given:
Equation: 2x² = 12x - 5
Rewriting the equation
2x² - 12x + 5 =0
We know that the standard form of Quadratic Equation is
ax² + bx + c = 0
where a, b, and c are integers and a ≠ 0.
Now, Comparing the standard equation with Given equation we get
a= 2, b= -12, c= 5
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number of bacteria double every 20 minutes. if the initial population is 20 how many are there after 3 hours
There are 10240 bacteria after 3 hours.
Initial population = 20
Time period = 3 hours
Time period in minutes = 3 hours x 60 minutes = 180 minutes
Number of doublings = 180 minutes / 20 minutes = 9 doublings
Final population = 20 x 2^9
Final population = 20 x 512
Final population = 10240
Bacteria doubling is the process in which one bacterial cell divides into two identical daughter cells. This process is known as binary fission and is the primary way bacteria reproduce. During this process, a single bacterium first replicates its single chromosome, which is then partitioned into two identical parts. The single cell then divides into two daughter cells, each containing one of the replicated chromosomes. This process is incredibly fast and can occur in as little as twenty minutes.
Bacterial doubling is an important process, as it allows bacteria to rapidly increase in number and spread. In optimal conditions, a single bacterial cell can divide into two daughter cells every twenty minutes, and this can continue for many generations. For this reason, bacteria can quickly become abundant in a given environment and pose a potential threat to human health. Fortunately, antibiotics are often able to help control bacterial doubling and limit the spread of certain bacteria.
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Varsity Press, a published of college textbooks, received a $70,000 promissory note at 12% ordinary interest for 60 days from one of its customers, Reader's Choice Bookstores. After 20 days, Varsity Press discounted the note at the Grove Isle Bank at a discount rate of 14.5%. The note was made on March 21.
a.) What was the maturity date of the note?
b.) What was the maturity value of the note?
c.) What was the discount date of the note?
d.) What proceeds did Varsity Press receive after discounting the note?
Answer:c
Step-by-step explanation: i did the test
In the figure below, mzPQR= 75° and m2 1=28°.
Find m2 2.
P
1
R
2
Q
ma
The measurement of m∠2 = 47°.
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Given that m∠PQR = 75° and m∠1 = 28°.
From the figure ∠PQS = m∠1 and ∠SQR = m∠2
The angle ∠PQR can be written as the sum of two angles.
∠PQR = ∠PQS + ∠SQR
∠PQR = m∠1 + m∠2
Putting m∠PQR = 75° and m∠1 = 28°:
75° = 28° + m∠2
Subtract 28° from both sides:
m∠2 = 75° - 28°
m∠2 = 47°
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he provider ordered lactated ringers (lr) to infuse at 75 ml/hr for the next 24 hours. how many liters of lr will infuse? (record answer to the tenth [one decimal place]. do not use a trailing zero.)
he provider ordered lactated ringers (lr) to infuse at 75 ml/hr for the next 24 hours. 18.0 liters of lr will infuse with rate of infusion.
First, we need to determine how many milliliters of LR will be infused over 24 hours. So, we need to multiply the rate of infusion (75 mL/hr) by the number of hours (24). This will give us the total number of milliliters that will be infused. In this case, it is 75 x 24 = 1800 mL. To determine the number of liters, we need to divide this by 1000 since there are 1000 mL in 1 L. Therefore, 1800 mL/1000 = 1.8 L. We can round this number up to the tenth (one decimal place), and the answer is 18.0 L.
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