The equations that represent the proportional relationships between the variables are as follows:
Problem Variables to use Equation
1. Tyler swimming Time / Distance D = 1.25t
2. Factory production Total quantity, Q, Q = 3s + 8p
and Sparkling / Plain
3. Paint mixture Blue / White Paints 6q = 1.5b + 5w
What is an equation?An equation models a mathematical statement in which two or more expressions (involving numbers, variables, and operands combined) are equated using the equation symbol (=).
Tyler:Speed = 5 m/4s
= 1.25 m/s (5/4)
Swimming equation: D = 1.25t
Where D = distance and t = time spent.
Given the speed and time, we can find the swimming distance covered by Tyler.
Factory:
Bottles of sparkling water = 3
Bottles of plain water = 8
Ratio = 3:8
Production equation, Q = 3s + 8p
Where Q = total quantity, s = sparkling water, and p = plain water
Paint:Blue paint = 1 ½ quarts
White paint = 5 quarts
Ratio = 1.5:5
Production equation, 6q = 1.5b + 5w
Where 6q = 6 quarts, b = blue paint, and w = white paint
Thus, using the equations, we can use the known variables to find the unknown variables.
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What value of k will translate the graph of f(x) = 5x + 6 down by 1 when replaced by f(x) + k?
Step-by-step explanation:
"down by one" means that the y values (the function result values) are all decreased by 1.
so, k = -1
lynn bought a new crash cymbal for her drum set. it costs 120$ but she received a 15% student discount. Roger bought the same crash cymbal from another store for$130 but he used a coupon for $25 off. who got the better deal
lynn got the better deal than Roger.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
lynn bought a new crash cymbal for her drum set. it costs 120$ but she received a 15% student discount.
Convert 15% to decimal form
15%=15/100=0.15
0.15×120=18
So 15% of 120 is 18.
Iynn bought crash cymbal for her drum set is 120-18=102
Roger bought the same crash cymbal from another store for$130
Roger applied coupon of $25.
So 130-25=$105
When we compare both Iynn and Roger, Iynn got the crash cymbal for a better deal.
Hence lynn got the better deal than Roger.
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Explain the steps for (-1/5) divided by 3/10 x (-2.4).
Answer: The correct answer is 14/7
Step-by-step explanation: This is the correct answer because it's explaining how to do it
What integer is closest to 4 √5?
Answer:
it's decimal value then it is 11.1803399.
The integer close to it is 11
Step-by-step explanation:
let's square this :
4² × 5 = 16 × 5 = 80
the closest squared integer is 81 (9²).
so, the closest integer to 4×sqrt(5) is 9.
PLEASE HELP ASAP!! Represent the following expressions as a power of the number a where a≠0.
(a^3)^-2
(a^-1 • a^-2)^-3
((a^2)^-2)^2
After using the property of power, the expressions as a power of the number a is [tex](a^3)^{-2} = a^{-6}[/tex] , [tex](a^{-1}\cdot a^{-2})^{-3} = a^{9}[/tex] and [tex]((a^2)^{-2})^2=a^{-8}[/tex] .
In the given question we have to solve the given expressions as a power of the number a where a≠0.
The first given expression is [tex](a^3)^{-2}[/tex].
Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].
Simplifying the expression.
[tex](a^3)^{-2} = a^{3*(-2)}[/tex]
[tex](a^3)^{-2} = a^{-6}[/tex]
The second expression is [tex](a^{-1}\cdot a^{-2})^{-3}[/tex]
Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].
[tex](a^{-1}\cdot a^{-2})^{-3} = a^{(-1)\times(-3)}\cdot a^{(-2)\times(-3)}[/tex]
[tex](a^{-1}\cdot a^{-2})^{-3} = a^{3}\cdot a^{6}[/tex]
Using the property of sum of power [tex]a^m\cdot a^n=a^{m+n}[/tex]
[tex](a^{-1}\cdot a^{-2})^{-3} = a^{(3+6)}[/tex]
[tex](a^{-1}\cdot a^{-2})^{-3} = a^{9}[/tex]
The third expression is [tex]((a^2)^{-2})^2[/tex].
Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].
[tex]((a^2)^{-2})^2=((a^2)^{(-2)\times2})[/tex]
[tex]((a^2)^{-2})^2=(a^2)^{-4}[/tex]
Again using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].
[tex]((a^2)^{-2})^2=a^{2\times(-4)}[/tex]
[tex]((a^2)^{-2})^2=a^{-8}[/tex]
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rewrite each expression (2+g)8
Answer:
8×2+8×g
Step-by-step explanation:
8x + 16x - 12 = 24x- 12
Does the equation have one,
none, or infinite solutions?
Explain why.
Answer:
Infinite solutions
Step-by-step explanation:
The equation is,
→ 8x + 16x - 12 = 24x - 12
Let's solve for the value of x,
→ 8x + 16x - 12 = 24x - 12
→ 24x - 24x = -12 + 12
→ [ 0 = 0 ]
Hence, it has infinite solution. Because, all the real numbers are suitable.
Answer:
infinite number.
Step-by-step explanation:
Comment
There is only the same letter (x) on both sides of the equation. None of the xs are raised to any power. The power is 1 for all of them. That being so, there is only ONE solution.
x^2 + 5x + 6 would give 2 solutions because the x is raised to the second power.
x^3 + x^2 + 4x + 9 would give 3 solutions.
Solution
8x + 16x - 12 = 24x - 12 This equation is a little different. Both sides are exactly the same -- 24x - 12. That means that there is an infinite number of solutions.
For example let x = 10
The right side = 240 - 12 = 228
The left side = 8*10 + 16*10 - 12 = 228
You can't come up with a number that will make the left side unequal to the right side.
The total number of restaurant-purchased meals that the average person will eat
in a restaurant, in a car, or at home in a year is 169. The total number of these
meals eaten in a car or at home exceeds the number eaten in a restaurant by
13. Twenty more restaurant-purchased meals will be eaten in a restaurant than
78 meals are eaten in a restaurant, 58 meals are eaten in a car, 33 meals are eaten at home and the question is solved by using linear equations.
What is the linear equation?
A linear equation is an algebraic equation of the form y =mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Given that the total number of meals is 169.
Assume that,
a = number of meals eaten in a restaurant
b = number of meals eaten in a car
c = number of meals eaten at home
a + b + c = 169 .....(i)
Since the total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13.
Thus b + c = a + 13 .....(ii)
Again twenty more restaurant-purchased meals will be eaten in a restaurant than at home.
a = 20 + c .....(iii)
Subtract equation (ii) from (i)
a + b + c - b - c = 169 - a - 13
2a = 156
Divide both sides by 2
a = 78
Substitute a = 78 in equation (iii)
78 = 20 +c
c = 58
Putting c =58 and a =78 in equation (ii)
b + 58 = 78 + 13
b = 33
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Question:
The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 169. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13. Twenty more restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of restaurant-purchased meals eaten in a restaurant, the number eaten in a car, and the number eaten at home.
What is the value of csc 47° to the nearest thousandth?
Answer: 1.367
Step-by-step explanation:
csc47° = 1.3673 ≈ 1.367
The value of cosec 47° is 1.367.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
cosec 47°
The value of cosec 47°.
= 1.367334
Rounding to the nearest thousandth.
= 1.367
Thus,
The value of cosec 47° is 1.367.
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A line of best fit was drawn for 5 data points. What is the maximum number
of these data points that may not actually be on the line?
A. 5
B. 3
C. 2
D. 4
Answer:
Step-by-step explanation:
Correct answer is A 5
Given that (x - 5) is a factor of
x³ - 7x² + 2x + a, find the value of a
check your textbook for the remainder theorem, where it states that for a factor (x-5) of f(x) then the remainder will be 0, thus f(5) = 0, what the heck all that means?
well, it means that if we evaluate f(5) our result should be 0, so
[tex]\stackrel{factor}{(x-5)}\hspace{5em}f(5)=(5)^3-7(5)^2+(5)+a=0 \\\\\\ 0=(5)^3-7(5)^2+(5)+a\implies 0=125-175+10+a \\\\\\ 0=-40+a\implies \boxed{40=a}[/tex]
Use the properties of logarithms to rewrite the following expression as a single logarithm. Please see attached pic.
Answer:
log4 (70)
Step-by-step explanation:
log4(7) + log4(10) = log4(7 * 10 ) = log4(70)
Solve for x. Enter the solutions from least to greatest. (x + 6)^2 - 16=0 lesser x = greater x =
Answer:
x= -2, -10
Step-by-step explanation:
(x+6)^2-16=0
(x+6)(x+6)-16=0
x^2+6x+6x+36-16=0
x^2+12x+20=0
10+2=12
10(2)=20
(x+2)=0
(x+10)=0
x= -2, -10
2. (01.03 LC)
Landyn is comparing cell phone plans. He does not want to spend more than 10% of his net pay each month. If his current monthly net pay is $560.00, which
plan below fits into his budget? (2 points)
Plan A: 55+55(0.05) -
Plan B: 50+ 50(0.05) -
Plan C: 60+60(0.05) =
Plan A
O Plan B
Plan C
O No plans
The plan that fits to Landyn's budget is plan B
What is percentage and how to calculate it?
A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%." Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. Two methods exist for calculating a percentage. By adjusting the fraction's denominator to 100 and applying the unitary approach.
We are given that Landyn's current monthly net pay is $560
And he does not wish to spend more than 10% of his current net pay
That means not more that $56
Now we are given 3 choices
Out of which the third one is more than 60 hence this rules out the third option. Now the first option the value is 55+55(0.005) which again is more than $56
Consider the option B)
50 + 50(0.05)
= 52.5
Which is less than $56
Hence, The plan that fits to Landyn's budget is plan B
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use the distributive property to solve the equation 2x - 4(x - 2) = - 8 + 4x + 4
A square floor is fitted with rectangular tiles of perimeter 220 cm. Each row carries 20 less tiles than each column. If the length of the floor is 9.6 m; calculate
(a) the dimensions of the tiles.
(b) the number of tiles needed.
(c) the cost of fitting the tiles if the tiles are sold in dozens at Kshs. 1500 per dozen and the labour cost is Kshs. 3000.
The 220 cm (2.2 m) perimeter of the tiles and the 9.6 meter side length of the square floor gives equations with the following solutions;
(a) The dimensions of the tiles are;
Width = 0.3 meters
Length = 0.8 meters
(b) 384 tiles are needed
(c) The fitting cost of the tiles is Kshs 51,000
What is an equation?An equation is a mathematical statement that consists of two expressions connected with an equals sign
Shape of the floor = Square
Shape of the tiles = Rectangular
Perimeter of the tiles = 220 cm = 2.2 m
The number of tiles in each row = 20 + The number of tiles in each column
Length of the floor = 9.6 m
(a) Let w represent the width of the tiles, the length l is found using the equation;
[tex]l = \dfrac{2.2 - 2\cdot x}{2} = 1.1 - x[/tex]
Let n represent the number of tiles in each row, which gives;
The number of tiles in each column = 20 + n
(20+n)·x = n·(1.1 - x)
Which gives;
[tex]x = \dfrac{1.1\cdot n}{2\cdot n+20}[/tex]
The side length of the square floor, s = 9.6
(20+n)·x = n·(1.1 - x) = 9.6
Which gives;
[tex]n\cdot \left(1.1 - \dfrac{1.1\cdot n}{2\cdot n+20}\right) = 9.6[/tex]
Which gives;
0.55·n² - 1.4·n -96 = 0
n = 12 or n ≈ -14.5
The number tiles in each roe, n = 20
Which gives; n·(1.1 - x) = 9.6
20 × (1.1 - x) = 9.6
x = 0.3
The width of each tile, x = 0.3 m
The length of each tiles = 1.1 m - 0.3 m = 0.8 m
(b) The number of tiles in each row, n = 20
The number of tiles in each column = n + 20, which gives;
Number of tiles in each column = 12 + 20 = 32
The number of tiles needed = 12 × 32 = 384
(c) The cost of a dozen tiles = Kshs 1,500
The labour cost = Kshs 3,000
Number of dozens of tiles = 384 ÷ 12 = 32
The cost of the tiles C = Kshs 1500 × 32 = Kshs 48000
The total cost = Kshs 48,000 + Kshs 3,000 = Kshs 51,000
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Write an expression that has only one term and is equivalent to the expression below (f × g²) + 5 - (g² × f)
The expression that is equivalent to (f × g²) + 5 - (g² × f) is 5
How to determine the equivalent expression?The expression whose equivalence is to be determined is given as
(f × g²) + 5 - (g² × f)
To start with, we need to remove the brackets in the expression
So, we have the following representation
(f × g²) + 5 - (g² × f) = f × g² + 5 - g² × f
Evaluate the products
This gives
(f × g²) + 5 - (g² × f) = fg² + 5 - fg²
Next, we collect the like terms
So, we have
(f × g²) + 5 - (g² × f) = fg² - fg² + 5
Lastly, we evaluate the like terms
So, we have
(f × g²) + 5 - (g² × f) = 5
The above expression cannot be further simplified
Hence, the equivalent expression is 5
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A tutor has 21 students in their tutor group. Within this group,
15 students have attended at least one tutorial. Calculate the
percentage of students in this tutor group who have attended at least
one tutorial.
Give your answer correct to the nearest whole number.
The percentage of students in the tutor group that have attended at least one tutorial is 71%
How to find the percentage?The percentage of students who have attended at least a single tutorial in the tutor group can be found by the formula:
= Number of students who attended at least one tutorial / Total number of students in tutor group x 100%
Number of students who attended at least one tutorial = 21 students
Total number of students in tutor group = 15 students
The percentage is therefore:
= 15 / 21 x 100%
= 0.7142857 x 100%
= 71.42%
= 71%
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Which of the following has a graph that is wider than the graph of y = 5x² - 3?
-
y = 8x² - 10
y = 5x² + 2
y=-6x² + 1
y = 3x² + 4
The equations y = -6x² + 1 and y = 3x² + 4 both have graphs that are wider than the graph of y = 5x² - 3.To determine which equation has a graph wider than the graph of y = 5x² - 3, we need to compare the coefficients of x² in each equation.
A wider graph indicates a smaller coefficient in front of x², which means the parabola will be less steep and have a broader shape.Let's compare the coefficients:y = 8x² - 10: The coefficient is 8, which is larger than 5. Therefore, this equation does not have a wider graph than y = 5x² - 3.
y = 5x² + 2: The coefficient is 5, which is equal to the coefficient in y = 5x² - 3. Therefore, the graphs of these two equations will have the same width.
y = -6x² + 1: The coefficient is -6, which is smaller than 5. Hence, this equation has a wider graph than y = 5x² - 3.
y = 3x² + 4: The coefficient is 3, which is smaller than 5. Hence, this equation also has a wider graph than y = 5x² - 3.
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SOMEONE PLEASE HELP!
I WILL GIVE BRAINLIEST TO THE FIRST CORRECT ANSWER!! Just Need Help!!!
If you throw exactly two heads in three tosses of a coin you win $41. If not, you pay me $29. If you played this game 713 times how much would you expect to win or lose?
Two heads in three tosses is 3/8, 3/8x713=267.375. 267.375×41=10,962.375.
5/8x713=445.62, 445.62×29=12,923.125
So 10,962.375-12,923.125=-1960.75
Therefore if you played this game, you would statistically lose $1960.75
Solve 5x² + 1 = 51 by finding square roots.
x = 50, -50
x = √10,-√10
x = 10, −10
x = √50,-√√/50
Answer:
x = √10,-√10
explanation:
5x2 + 1 = 51
you would carry the +1 to the other side making it
5x2=51-1
which is 5x2=50
this equation above can then be turned into
x2=50÷5
which goes on to form the equation
x2=10
this can then be turned into x=the square root of ten
and since it is know that when an equation is x2 whether it is negative or positive it would result in the same answer
but yeah I'm not smart or whatever but I hope this helps
not too sure it's correct though
Evaluate the expression when = =− 5 5 , and . 8 3 x y 10. x + y 11. y x − 12. − + 2x y 13. 3x + y
The numeric value of the expression -b + 8x when b = 5 and x = -6 is given as follows:
-53.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable/variables in the function or in the expression by the value/values at which we want to find the numeric value.
In this problem, the expression is given as follows:
-b + 8x.
The values at which the numeric value is to be found are:
b = 5, x = -6.
Hence:
The lone instance of b is replaced by 5.The lone instance of x is replaced by -6.Thus the numeric value of the expression is obtained as follows:
-5 + 8(-6) = -5 - 48 = -53.
Missing InformationThe problem is given by the image at the end of the answer.
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If the original function is f(x)
What would be the function notation when the function was
Shifted Right 6
The function notation when the function was shifted right 6 is f(x-6).
Given that, the function was shifted right 6 units.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Rule: In function notation, to shift a function left, add inside the function's argument: f(x + b) shifts f(x) b units to the left. Shifting to the right works the same way, f(x - b) shifts f(x) b units to the right.
So, the transformation from the original function to new function is
f(x-6)
Therefore, the function notation when the function was shifted right 6 is f(x-6).
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Determine whether the ratios are equivalent.
85: 210 and 340: 735
These are equivalent. I hope this helps a ton. I had this question on a test. Tell me if its wrong or not. <:
18. MULTIPLE CHOICE
(Lesson 2-6)
(A) X=-4
B) X= 4
Ox=8
(D) X = 20
Solve
3
x + 4
=
2
X-4
Answer:
Step-by-step explanation:
solving 3x+4=2x-4
now 3x-2x=-4-4
⇒ x=-8
(c) x=8 here you have given it as O thank you
1. research institute reported that the average number of weeks an individual is unemployed is 17.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 17.5 weeks and that the population standard deviation is 4 weeks. Suppose you would like to select a random sample of 50 unemployed individuals for a follow-up study.
a. What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean of less than 1 week?
b. What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean?
The probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean is 0.92
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable that represent the avergae number of weeks an individual is unemployed of a population, and for this case we know the distribution for X is given by:
X = N(17.5)
Where μ = 17.5 and σ = 4
Since the distribution for X is normal then, the distribution for the sample mean is given by:
X = N(17.5, σ/√n)
X =N(17.5.4/√50) = 0.566
We select a sample of n =50 people. And we want to find the following probability
P(16.5 < X < 18.5) = P((16.5 -17.5)/(4/√50) < Z < (16.5 -17.5)/(4/√50) )
And using the normal standard table or excel we find the probability:
P(-1.768 < Z 1.768) = P(Z < 1.768) - P(Z< -1.768) = 0.961 - 0.039 = 0.92
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268 + 88 in the form of a(b+c)
Answer:
4(67 + 22)
Step-by-step explanation:
1. Find the greatest common factor(in this case it is 4)
2. Divide both 268 and 88 by 4 and you get 67 and 22
3. Put it in the requested format and you are left with 4(67 +22)
HELP, ASAP PLEASE. 15 POINTS! ( Only 1 picture is attached)
The concentration of the type of antibiotic after 4 hours is; 11.04 parts per million
How to find the input values of functions?
We are told that the equation that models the concentration in parts per million of a type of antibiotic in a human's bloodstream after h hours is;
A(h) = -0.06h² + 2h + 4
where h is the time in number of hours after which the concentration is recorded.
Now, we want to find the concentration after 4 hours and as such we will input 4 for h in the equation to get;
A(4) = -0.06(4²) + 2(4) + 4
A(4) = -0.96 + 12
A(4) = 11.04 parts per million
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What must be added to 4/9 to make a whole?
Answer:5/9
Step-by-step explanation:
