The probability that the student drinks soda, given that they drink coffee, is 0.25.
Let's designate the proportion of students who regularly consume soda as "S," those who frequently consume coffee as "C," and those who regularly consume both as "B."
Since 40% of students frequently consume soda, there are 0.4S kids who do the same.
Additionally, there are 0.3S students who consume coffee because 30% of students do it frequently.
Additionally, since 10% of students consume both beverages, there are 0.1S students who also consume soda and coffee.
Students in the class S = 0.4S + 0.1S = 0.5S either drink soda or both.
The pupils in C = 0.3S + 0.1S = 0.4S either consume coffee or both.
So, given that the student drinks coffee, the probability of drinking soda is:
P(soda | coffee) = P(soda and coffee) / P(coffee)
= 0.1S / 0.4S
= 0.25.
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List all values c guaranteed by the Mean Value Theorem forf(x)=x3+x2−4x+2on the interval[−1,3]
The Mean Value Theorem guarantees that the values of c for f(x)=x^3+x^2-4x+2 on the interval [1,3] are [7,9].
What is function?A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.
Here,
f(c)=f'(b)-f'(a)/(b-a)
f(x)=x^3+x^2−4x+2
f'(x)=3x²+2x-4
x=-1, 3
f'(-1)=3-2-4
=-3
f'(3)=27+6-4
=29
f(c)=29+3/3+1
=32/4
f(c)=8
=[7,9]
The values of c guaranteed by the Mean Value Theorem for f(x)=x^3+x^2−4x+2 on the interval [−1,3] is [7,9].
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What is simplest radical form in math?
The radical form of a number involves a square root. The number under the square root is a natural number or real number.
What is a radical?
The square root or nth root is represented by the symbol. Expression with a square root is referred to as a radical expression. Radicand: A value or phrase contained within the radical symbol. An equation with radical expressions and variables as radicands is referred to as a radical equation.
The term "simplest radical form" refers to an algebraic expression's or number's most basic radical form. If the number or algebraic expression under the radical has no factors that are perfect nth powers, then the radical is said to be in its simplest radical form.
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Maria had $160. She spent 3/8 of her money at the supermarket and 1/4 of it at the hair salon. How much did Maria spend?
Maria spent $100 in total. She spent $60 at the supermarket and $40 at the hair salon.
Explanation:This problem involves calculations with fractions. Maria had $160. She spent 3/8 of it at the supermarket and 1/4 of it at the hair salon. To find out much money she spent, add the fractions and then multiply the result by the total amount of money she had.
To find how much Maria spent at the supermarket, multiply $160 by 3/8: 160 * 3/8 = $60.
To find how much Maria spent at the hair salon, multiply $160 by 1/4: 160 * 1/4 = $40.
Now, add the amounts spent at the supermarket and the hair salon: $60 + $40 = $100. So Maria spent $100 in total.
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if an aircraft is certificated with 275 seats, but only 249 passengers are aboard for that flight segment, how many flight attendants are required? group of answer choices 6 4 7 5
5 flight attendants are required.
The number of flight attendants required on an aircraft is determined by regulatory agencies such as the Federal Aviation Administration (FAA) in the United States and the European Aviation Safety Agency (EASA) in Europe.
The number of flight attendants depends on several factors, including the type of aircraft, the number of passenger seats, the length of the flight, and the number of passenger exits.
The number of flight attendants required can be determined by the following formula:
The minimum number of flight attendants = (N / 50) + 1 where N is the number of passenger seats.
So, for an aircraft with 275 seats and 249 passengers:
(249 / 50) + 1
= 5 flight attendants are required.
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What is the linear velocity in miles per hour of the tip of a lawnmower blade spinning at 3000 revolutions per minute in a lawnmower that cuts a path that is 24 inches wide?
Answer:v = ωr
v = speed in miles per hour (mph)
is the angle's speed in radians per hour.
r is the radius in miles.
(2400-rpm/60 minutes) =
(two radians per rev) Equals __ radians per hour
r=16 inches/2 = (8 inches)
(1/5280 miles/ft) (1/12 feet/in) = ______ miles
v = r = _ miles per hour
Step-by-step explanation:
v = ωr
v = speed in miles per hour (mph)
is the angle's speed in radians per hour.
r is the radius in miles.
(2400-rpm/60 minutes) =
(two radians per rev) Equals __ radians per hour
r=16 inches/2 = (8 inches)
(1/5280 miles/ft) (1/12 feet/in) = ______ miles
v = r = _ miles per hour
Answe pleaseeeee I really need help will give points
The circle has a radius of 15 and is centered at (-2,4).
What are the equations for circles?The general equation of a circle is [tex](x - h)^{2} + (y - k)^{2} = r^2[/tex], where (h, k) denotes the position of the circle's center and r is the radius.
What do H and K represent when they are encircled?The equation for a circle is [tex](x - h)^{2} + (y - k)^{2} = r^2[/tex], where (h, k) stands for the coordinates of the circle's center and r for the radius. A circle touches the x-axis if it is tangent to it at the coordinates (3, 0).
Equation for a circle is[tex](x+2)^2 + (y-4)=225[/tex]
(-2,4) = represents the location of the circle's center.
[tex]r^2=(15)^2[/tex]
r = 15 = its radius
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Anika is on the crew to set up rides for the state fair. The crew does most of the setup on the day that the fair arrives at the fairground and then continues to work on finishing the setup for about a week to have the rides ready to go in time for the opening of the fair. The scatter plot shows Anika's setup time on different days and the linear model for the data.
(a) What is the equation of the line, written in slope-intercept form? Show how you determined the equation.
(b) Anika arrived on Day 0. Based on the linear model you created in Part A, predict how long Anika worked on Day 0.
(c) Approximately how much did her setup time decrease per day?
a) The linear function for this problem is defined as follows: y = -0.75x + 20.
b) The time that he worked on Day 0 is given as follows: 20 hours.
c) The daily decrease in the setup time is given as follows: 0.75 hours a day.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the output variable relative to the input variable.The intercept b represents the value of y when the graph of the function touches of crosses the y-axis.Two points from the graph are given as follows:
(8, 14) and (16,8).
When x increases by 8, y decays by 6, hence the slope m is given as follows:
m = -6/8
m = -0.75.
Hence:
y = -0.75x + b.
When x = 8, y = 14, hence the intercept b is given as follows:
14 = -0.75(8) + b
b = 14 + 0.75(8)
b = 20.
Hence the function is defined as follows:
y = -0.75x + 20.
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____ 15. if gasoline costs $1.95 per gallon is its cost per liter? [1 quart = 0.946 liter]
If gasoline costs $1.95 per gallon $0.52 is its cost per liter?
One gallon of gasoline costs $1.95. To find the cost per liter, we need to convert gallons to liters. The conversion factor between gallons and liters is 1 gallon = 3.78541 liters.
So, to convert gallons to liters, we multiply the number of gallons by 3.78541.
In this case, the cost of one gallon of gasoline is $1.95. To find the cost per liter, we need to convert $1.95 from dollars per gallon to dollars per liter.
To do this, we divide $1.95 by the conversion factor between gallons and liters:
$1.95 / 3.78541
= $0.52/liter.
Therefore, the cost of one liter of gasoline is $0.52.
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in a convex quadrilateral, the measure of the largest angle is twice the measure of the smallest angle, and the other two angles are both right angles. how many degrees are in the largest angle?
Answer: 90 degrees.
Step-by-step explanation:
Step 1: The smallest angle must be 90/2 = 45 degrees.
Step 2: The largest angle is twice the size of the smallest angle, so it is 90 degrees.
how many elements are in the set {7, 7, 7, 7}?
The set {7, 7, 7, 7} have only one element because we can write that set as {7}.
The empty set and the original set itself are included in the power set, which is a set that contains all other subsets as well. P is typically used to indicate it. The number of subsets that can be generated from a given set determines the cardinality of a power set.
In set theory, the set of all subsets of a Set A, including the Set itself and the null or empty set, is referred to as the power set (or power set). The Power Set of the given set will consist of 2n elements if the given set has n elements. It also symbolizes the power set's cardinality.
The set is {7, 7, 7, 7}.
We can write this set as {7}. So the element of set {7, 7, 7, 7} has one element only.
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now consider the situation when no two people get off at the same floor. before the elevator begins to travel, each of them pushes a button for his or her floor. in how many ways can the elevator buttons be lighted?
The number of ways the elevator buttons can be lighted is (m)(m-1)(m-2)...(m-n+1).
What is Permutations?
The mathematical notion of permutation describes the placement of things in a particular order. It is a method of determining how many unique configurations there are for a given set of objects.
If there are n persons in the elevator, and each one presses a button for a floor between 1 and m, what would happen? (inclusive). The number of permutations of m things taken n at a time, indicated as P, determines the number of ways the elevator buttons can be lit if no two individuals hit the same floor button and each person pushes a different floor button (m, n).
[tex]The formula for permutations is: P(m, n) = m! / (m - n)!.Therefore, the number of ways the elevator buttons can be lighted is:P(m, n) = m! / (m - n)! = m! / (m - n)! = m! / (m - n)! = m! / (m - n)! = (m)(m-1)(m-2)...(m-n+1).[/tex]
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The number of ways the elevator buttons can be lighted is [tex]m(m-1)(m-2)...(m-n+1)[/tex].
What are Permutations?
The placing of things in a specific order is described by the mathematical concept of permutation. It is a technique for figuring out how many different arrangements of a group of things there are.
It would be inclusive if there were n people in the elevator and each one pressed a button for a floor between 1 and m. If no two people press the same floor button and everyone presses a separate floor button, the number of P permutations of m items taken n at a time defines how many ways the elevator buttons can be lit (m, n).
The formula for permutations is:
[tex]P(m,n)=m(m-1)(m-2)...(m-n+1)[/tex]
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Angle b and angle c are complementary. If angle b is five times the size of angle c which equation can be used to find the measure of angle c?.
If angle b is five times the size of angle c, the equation can be used to find the measure of angle is 5x+x=90°.
because complementary angles complete each other to 90 degrees.
How to find equation aboveThese angles b and c add up to 90° because they are complementary.
Let's say angle C is named x.
angle b is five times the size of angle c, this can be written: 5x
Complementary angles add up 90°, so angle B add angle C equal 90°
the equation to find the measure of angle C is 5x+x = 90°.
Definition of AngleTypes of angles are one of the materials in mathematics that you always encounter at every level of education. Learning about angles is very important, because angles are always present in everyday life and need to be identified.
An angle is a shape formed by two rays having an endpoint at one point. In angles, terms such as the leg of the angle, vertex, and area of the angle are also found.
The legs of the angle are the lines forming the angle. The vertex is the point where the two legs of the angle intersect, and the area of the angle is the area bounded by the two legs of the angle.
Your question is incomplete but most probably your full question was:
Only Interaction Angle B and angle C are complementary: If angle B is five times the size of angle C which equation can be used to find the measure of angle C?
5x+x=180
5x = 180
5x+x=9
5x = 90
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people attending a basketball game either supported the home team or visiting team. Of 2940 of the people attending supported the home team and 560 supported the visiting team, what percentage supported the home team?
The required 84% of the people attending the basketball game supported the home team.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
To find the percentage of people who supported the home team, we need to calculate the proportion of people supporting the home team and convert it to a percentage.
The total number of people attending the game is,
2940 + 560 = 3500.
The proportion of people supporting the home team is,
= 2940 / 3500
= 0.84.
To convert this proportion to a percentage, we multiply it by 100:
= 0.84 × 100 = 84%
Thus, 84% of the people attending the basketball game supported the home team.
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1. (D) Which of the following statements is true?
Explain your answer!
A.
B.
C.
13
19
13
19
13
19
2
2|22|3
Taking LCM and comparing the values we see that: 39/57 > 38/57. Hence, option C is the correct statement.
What is LCM?In mathematics, the value that is equally divided by the two supplied numbers is known as the LCM of any two. Least Common Multiple is its full name. Another name for it is the Least Common Divisor (LCD).
When the fractions' denominators differ, LCM can also be used to add or subtract any 2 fractions. LCM is used to make the denominators common when doing any arithmetic operations using fractions, such as addition and subtraction.
The two values are:
13/ 19 and 2/3
Taking LCM we have:
13(3)/ 19(3) and 2(19) / 3(19)
39/ 57 and 38/57
Hence, comparing the values we see that:
39/57 > 38/57
Option C is the correct answer.
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Find The Length S Of The Circular Arc. (Assume R = 6 And 0 = 126º.) S = O
The required length of the arc of the circle is approximately 13.08 cm.
What is arc?In mathematics, an arc is defined as a portion of the boundary of a circle or a curve. It can also be referred to as an open curve. The boundary of a circle is the perimeter or the distance around a circle, also known as the circumference.
According to question:The length of an arc of a circle is given by the formula:
L = θ * r / 180 * π
Where θ is the central angle in radians, r is the radius, and π is pi.
In your case, the radius of the circle is 6, and the central angle is 126°, so we need to first convert 126° to radians:
θ = 126° * π / 180 = 2.18 radians
Substituting the values in the formula, we get:
L = θ * r / 180 * π = 2.18 * 6 / 180 * π = 2.18 * 6 / π = 13.08 cm
So the length of the arc of the circle with radius 6 and central angle 126° is approximately 13.08 cm.
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A man has $215,000 invested in three properties. One earns 12%, one 10% and one 8%. His annual income from the properties is $20,600 and the amount invested at 8% is twice that invested at 12%.
Annual income = 45000 the amount invested at 8% is twice that invested at 12%. 12% property $45000 × 0.12 = 5400
10% property $8000
8% property $7200
What is annual income?The entire amount of money you make during the course of a year is your yearly income, in contrast. Along with your wage, this sum also includes earnings from other sources, such as interest on savings or rent from a home you own. Bonuses and overtime pay are other possible components of your yearly revenue.
let, x in 12%
so, 2x in 8%
and 21,5000 - 3x in 10%
so, annual income = 2x × 0.08 + ( 215000 -3x) × 0.10 + x × 0.12= 20,600
=> x = 45000
so, 2x = 90000
so, 215000 - 3x = 80000
so,
12% property $ 45000
10% property $80000
8% property $90000
b)
12% property $45000 × 0.12 = 5400
10% property $8000
8% property $7200
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use the multiplier method to increase £88 by 14 %
you must show ur workings
find all values of for which this approximation is within of the right answer. assume for simplicity that we limit ourselves to .
The range of the values of x is
|x| [tex]\leq[/tex] 0.5304 [tex]\leq[/tex] 1
Now, According to the question:
Let us consider the polynomial function as f(x) . Hence we need to find
[tex]T_5(x)[/tex] he formula for the Taylor series is:
[tex]T_n(x) =[/tex] Σ[tex]\left \{ {{n} \atop {j=0}} \right.}[/tex] [tex]\frac{f^(^f^)(a)}{f!}[/tex]
Suppose n =5, a=0 then
[tex]T_5 (x)= \frac{f(0)}{0!}(x -0)^0 + \frac{f'(0)}{1!}(x -0)^1+ \frac{f"(0)}{2!}(x -0)^2+...+ \frac{f^(^5^)(0)}{5!}(x -0)^5[/tex]
[tex]T_5(x)=\frac{f(0)}{0!}+ \frac{f'(0)}{1!}x+\frac{f"(0)}{2!}x^{2} + \frac{f"'(0)}{3!}x^3+\frac{f""(0)}{4!}x^4+\frac{f^(^5^)(0)}{5!}x^5[/tex]
From the data:
f(x) = cos x => f(0) = cos(0) = 1
f'(x) = -sin x => f'(0) = -sin(0) = 0
f"(x) = -cos x => f"(0) = -cos(0) = -1
f"'(x) = sin x => f'"(0) = sin(0) = 0
f""(x) = cos x => f""(0) = cos0 = 1
f""'(x) = -sin x => f""'(0) = -sin(0) = 0
Substitute this data in the Taylor series:
[tex]T_5(x)=\frac{f(0)}{0!}+ \frac{f'(0)}{1!}x+\frac{f"(0)}{2!}x^{2} + \frac{f"'(0)}{3!}x^3+\frac{f""(0)}{4!}x^4+\frac{f^(^5^)(0)}{5!}x^5[/tex]
[tex]T_5(x) =\frac{1}{0!}+\frac{0}{1!}x+\frac{(-1)}{2!}x^{2} + \frac{0}{3!}x^3+\frac{1}{4!}x^4+\frac{(0)}{5!}x^5[/tex]
[tex]T_5(x) = 1 - \frac{1}{2!}x^{2} +\frac{1}{4!}x^4[/tex]
Now, the remainder of the Taylor series is Taylor series satisfies the following inequality.
[tex]|R_n(x)|\leq \frac{M}{(n +1)^1^!} (x-a)^n^+^1for|x+a|\leq d,here|f^(^n^+^1^)(x)|\leq M\\\\|x|\leq 1,a=0,n=5= > |f^(^6^)(x)|\leq 1[/tex]
Given that the approximation should be within 0.003712
Then,
[tex]\frac{1}{(6)}|x|^6\leq 0.003712\\ \\= > \frac{1}{(6)}|x|^6\leq 0.003712\\ \\= > |x|^6\leq (0.003712)^6\\\\= > |x|^6\leq 0.022272\\\\|x|\leq (0.022272)^\frac{1}{6}\\ \\|x|\leq 0.5304[/tex]
Hence, the range of the values of x is
|x| [tex]\leq[/tex] 0.5304 [tex]\leq[/tex] 1
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The given question is incomplete , complete question is :
Find [tex]T_5(x)[/tex], the degree 5 Taylor polynomial of the function f(x) = cos(x) at
a = 0.
Find all values of x for which this approximation is within 0.003712 of the right answer. Assume for simplicity that we limit ourselves to |x| [tex]\leq[/tex] 1
Question 3 of 10
Find the solution(s) to x2 - 12x + 36 = 0.
A. x = 6 and x = -6
B. x = 6 only
C. x = 4 and x = 9
OD. x = -2 and x = 18
SUBMI
Answer: B. x=6 only
Explanation: A fast way to check these kind of multiple choice questions is to just plug in one of the values into the equation and see if it works. For example you can put (6^2)-(12×6)+36 and it would equal 0 making the equation true. All other options wouldn't have equaled 0 so it would make x=6 the only right option.
Erica is about to sign a lease for an apartment at a rate of $850 per month. She will need to pay the first month’s rent, the final month’s rent, and a $150 security fee. How much will her first payment be?
$1,000
$850
$1,850
$150
The amount of payment for the first month that Erica pays will be $1,000. Then the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Rent = $850 per month
Security fee = $150
Then the amount of payment for the first month that Erica pays will be given as,
⇒ $850 + $150
⇒ $1,000
The amount of payment for the first month that Erica pays will be $1,000. Then the correct option is A.
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ANSWERING ANY QUESTIONS FOR BRAINLIEST ANY QUESTION U MIGHT BE STUCK ON !!!
Step-by-step explanation:
Is power of mind is truee
The concept of the power of the mind is a widely debated topic, with varying opinions and perspectives. Some people believe in the power of positive thinking and visualization to achieve goals and create positive changes in one's life. Others may be more skeptical and question the scientific evidence supporting these ideas. Ultimately, whether or not the power of the mind is "true" is subjective and depends on one's personal beliefs and experiences.
I need help with this, can’t figure out the mistake. Basically just show me the mistake then I can take it from there.
Answer: They needed to find the hypotenuse of the triangle not the sum of the legs.
Step-by-step explanation:
Miguel has 14 action videos and 21
adventure videos. Use a ratio to compare the number of action videos and the number of adventure videos.
The ratio of action videos to adventure videos is 14:21.
What is the ratio of action videos to adventure videos?This question uses the concept of ratios, which is a comparison of two or more values. Ratios are used to compare quantities in a variety of situations.
Count the number of action videos and the number of adventure videos. In this example, there are 14 action videos and 21 adventure videos.
Create a ratio by writing the number of action videos first, followed by a colon, followed by the number of adventure videos. In this example, the ratio is 14:21.
Simplify the ratio if needed. In this example, the ratio is already in its simplest form.
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(1 point) solve the division problem ⎡⎣⎢4−4−40−1−100−1⎤⎦⎥⎡⎣⎢xyz⎤⎦⎥=⎡⎣⎢−434⎤⎦⎥
The solution to the division problem is xyz = −434 with a remainder of 0.
The given equation is [tex]$\frac{4-4-40-1-100-1}{xyz} = -434$[/tex]. To solve this equation, we need to find the value of [tex]$xyz$[/tex]. We can use the distributive property to break up the numerator, yielding [tex]$\frac{(-1)(-100)(-1)}{xyz} = -434$[/tex]. Then, we can multiply both sides by [tex]$xyz$[/tex] to get [tex]$(-1)(-100)(-1)xyz = -434xyz$[/tex] . Since the terms on both sides of the equation are equal, we can simplify to [tex]$(-1)(-1)(-100)xyz = -434xyz$[/tex] . Now, we can factor out the xyz, which yields [tex]$xyz(-1)(-1)(-100) = -434xyz$[/tex]. Since we want to find the value of xyz, we can divide both sides by the common factor of xyz, yielding [tex]$(-1)(-1)(-100) = -434$[/tex] . Finally, we can solve for xyz by multiplying both sides by the common factor of (-1)(-1)(-100), yielding xyz = -434. Therefore, the value of xyz in the given equation is -434.
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Figure ABCD has vertices A(1, 1), B(1, 4), C(4, 4), and D(4, 1). What are the coordinates of the vertices of Figure
A’B’C’D’ after a reflection across the line x = –2 and a translation 3 units up? Drag numbers to complete the coordinates.
Numbers may be used once, more than once, or not at all.
Answer:A(-5,4),B(-5,6),C(-7,6),D(-7,4)
Step-by-step explanation:If you draw a big enough graph it is easy to do.
Jayden went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 200 mg of sodium and each frozen dinner has 650 mg of sodium. Jayden purchased a total of 13 cans of soup and frozen dinners which collectively contain 4400 mg of sodium. Write a system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased. Define the variables that you use to write the system.
The number of cans are 9 and number of frozen food is 4.
What is a system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given that, Jayden bought cans of soup and frozen dinners. Each can of soup has 200 mg of sodium and each frozen dinner has 650 mg of sodium. Jayden purchased a total of 13 cans of soup and frozen dinners which collectively contain 4400 mg of sodium.
Let she bought x cans and y frozen food.
Therefore, establishing the equations,
x + y = 13
y = 13-x...(i)
200x + 650y = 4400...(ii)
Put eq(i) in eq(ii)
200x + 650(13-x) = 4400
200x + 8450 - 650x = 4400
450x = 4050
x = 9
Put x = 9 in eq(I)
y = 13-9
y = 4
Hence, the number of cans are 9 and number of frozen food is 4.
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Write a compound inequality that represents the annual profits P ( in millions or dollars) from 2006 to 2013
Using inequality views, the compound inequality is given by:
50 ≤ P ≤ 90
An inequality is said to be compounded if it includes two terms, for example:a ≤ x ≤ b
Which has the following interpretation: x is more than a and x is less than b.From the graph, the minimum profit, in millions of dollars, was 50, in 2009.The maximum profit was 90, in 2012.From this, a compound inequality can be written, that the profit is more than 50 and less than 90, thus:50 ≤ P ≤ 90
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Suppose you wanted to reach Alpha Centauri (4.4 ly from the Solar system) in 110 years. Pa How fast would you have to go in km/hr? Express your answer in kilometers per hour to two significant figures. v = 4.3x107 km/hr
the speed from kilometers per year to kilometers per hour 4.3x107 km/hr, the distance of 4.4 light years to kilometers.
1. First, convert the distance of 4.4 light years to kilometers.
1 light year = 9.46x1012 km
4.4 light years = 4.1x1013 km
2. Next, divide the distance by the time to calculate the speed:
Speed = Distance/Time
Speed = 4.1x1013 km/110 years
Speed = 3.7x1011 km/year
3. Finally, convert the speed from kilometers per year to kilometers per hour:
1 year = 8760 hours
Speed = 3.7x1011 km/8760 hours
Speed = 4.3x107 km/hr
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When graphing "AND" inequalites, shading looks like____
When graphing "AND" inequalites, shading looks like Shading that always connects the 2 dots.
What is inequality?An algebraic statement that connects two values that are not equal is referred to as an inequality in mathematics. Inequality signals state that one of the two variables on either side of the inequality could be greater than, greater than or equal to, less than, or less than or equal to another value.
If a linear inequality has a sign that is either (less than) or, you will shade below the boundary line (less than or equal to). In a linear inequality, if the sign is > (greater than) or, you will shade above the boundary line (more than or equal to).
Follow these steps:
Rearrange the equation so "y" is on the left and everything else on the right.
Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)
Shade above the line for a "greater than" (y> or y≥)
or below the line for a "less than" (y< or y≤).
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The figure below is dilated by a factor of 3 3 centered at the origin. Plot the resulting image.
The image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)
How to determine the image of the transformation?The complete question is added as an attachment
The coordinates of the triangle are given as
R = (-4, 1)
S = (-4, 4)
T = (-2, 1)
The transformation is given as
Dilation by a scale factor of 3
Centered at the origin
The rule of the transformations is
(x, y) = 3(x, y)
So, we have
R' = 3 * (-4, 1) = (-12, 3)
S' = 3 * (-4, 4) = (-12, 12)
T' = 3 * (-2, 1)= (-6, 3)
Hence, the image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)
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