A variable is a letter or term that represents an unknown number, value, or quantity. Variables are especially useful in algebraic expressions or algebra.
What is meant by variables?In the context of a mathematical problem or experiment, a variable is a quantity that can change. A variable is typically represented by a single letter. Variables are commonly represented by the letters x, y, and z. Any property, number, or quantity that can be measured or counted is defined as a variable.A variable is also referred to as a data item. Age, gender, business income and expenses, country of birth, capital expenditure, class grades, eye color, and vehicle type are all variables.In research, a variable is simply a person, place, thing, or phenomenon that you want to quantify in some way.let a number be x
then "twice the sum of a number be 2x
given
"twice the sum of a number and 7 is negative fifteen"
⇒ 2x + 7 = -15
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Paul sold 162 cups of lemonade in 5 hours. About how many cups of lemonade did she sell each hour?
The number of cups of lemonade sold in each hour is 32.4.
The number of cups of lemonade in each hour is the rate of selling. The rate of selling will be calculated by the formula : number of cups ÷ time.
Keep the values in formula to find the number of cups of lemonade sold each hour
Number of cups of lemonade sold each hour = 162 ÷ 5
Performing division to find the number of cups sold each hour
Number of cups of lemonade sold each hour = 32.4
Thus, each hour, 32.4 cups of lemonade are sold.
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Which statement correctly compares the function shown on this graph with the function y = 3x - 6?
The plotted function and the function y = 3x - 6 represent a straight line and have have same slope and hence, both the lines are parallel to each other.
What is the general equation of a straight line?The general equation of a straight line is of the form -
y = mx + c
where -
[m] is slope of line
[c] is y - intercept
Given is a equation of a straight line and a graph of a straight line.
We have the following equation -
y = 3x - 6
For this equation, the slope of the straight line will be [m] = 3 and the y - intercept would be [c] = - 6. Refer to the graph attached with green color for all the possible set of solution.
Now, the equation of the line plotted on graph -
m = (4 - 0)/(0 + 1.3)
m = 3.07
m = 3 (approx.)
Its y - intercept [c] = 4
Therefore, the equation of the plotted line -
y = 3x + 4
Now, both the lines are plotted on the graph. It can be seen from the graph and from the equation that they have same slope and hence, both the lines are parallel to each other.
Therefore, the plotted function and the function y = 3x - 6 represent a straight line and have have same slope and hence, both the lines are parallel to each other.
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[The complete question needs the plotted graph. It is attached at the end of the answer]
Sammy has 125 saved from his lifegaurding job
Using a linear function, it is found that:
a) The table is completed in the first image at the end of the answer.
b) The function is: s(w) = 125 - 10.50w.
c) The graph of the function is given by the second image at the end of the answer.
Linear functionThe slope-intercept representation of a linear function is shown by the rule presented below:
y = mx + b
The coefficients of the function are presented as follows:
m is the slope of the function, representing the rate of change of the output y in relation of the input x of the function, i.e, by how much y changes when x changes by 1.b is the y-intercept of the function, representing the numeric value of the function when the input x is of 0.In the context of this problem, the slope and the intercept are given as follows:
Slope of -10.50, which is the cost of the bus fare.Intercept of 125, which is how much he has saved from the bus fare.Hence the function is given as follows:
s(w) = 125 - 10.50w.
The numeric values to complete the table are given as follows:
s(6) = 125 - 10.5(6) = 62.s(10) = 125 - 10.5(10) = 20.A similar problem, also focused on linear functions, is presented at https://brainly.com/question/24808124
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A coin is flipped and a spinner is spun.What is the sample space of the experiment?
The sample space is the set of all different outcomes that can show up from the experiment.
Flipping a coin has two possible outcomes: heads or tails.
Spinning the spinner has three possible outcomes: A, B or C.
Draw a tree diagram to represent the sample space:
If we represent results using ordered pairs, the sample space is:
[tex]\mleft\lbrace(H,A\mright),(H,B),(H,C),(T,A),(T,B),(T,C)\}[/tex]Where H stands for heads and T stands for tails.
use the figures below what shows that rectangles are not similar PS.THIS IS JUST HOMEWORK THAT I NEED HELP WITH
Answer is option A
Because the other side (AB) is 15 and the other rectangle (JM) is 10, so the realation between them is 15/10 = 3/2
But, since DC and ML relation is NOT 3/2, then the rectanlges are not similar
Could you teach me how to solve this problem without using a graphing calculator? (My algebra teacher doesn’t allow graphing calculators on the test.)
The type of function we are going to work with here is an exponential function. These functions are given by equations like:
[tex]f(x)=a\cdot b^x+c[/tex]Where x is the variable and a, b and c fixed parameters. In this case c=0, a=1 and b=13/4. This number b, i.e. the one affected by the exponent is called the base so I'm going to refer to it with that word.
All exponential functions have similar graphs, they pass from being very close, almost pararel to the x-axis and then they begin to rapidly increase toward infinite y values. In the following picture you can see the graph of two exponential functions:
The red graph tends to zero for positive x values, this means that its equation has a negative sign in the exponent:
[tex]\text{red(x)}=b^{-x}[/tex]The blue graph on the other hand tends to zero for negative x values which means that there's no negative sign in the exponent. This is the case of our function r(x) so we can discard the upper left option.
Another thing to take into account is the offset of the function, that number that I labeled as "c" in the first equation. This offset translates the graph upwards or downwards depending on its sign.
For example, in this image the graphs decrease for negative x values which means their exponents don't have a negative sign but they all tend to different values which means their offsets are different. Blue's offset is 0 since it tends to 0 while gray's offset is 1 because it tends to 1. The same way you can deduce that the orange graph has an offset of -2. In the case of our problem, function r(x) doesn't have an offset which means that in one direction it has to tend to 0. This means we can discard the lower rigth option.
We have already discarded two options, if we discard one more we have the answer.
Now let's take r(x) and evaluate it in x=0:
[tex]r(0)=(\frac{13}{4})^0=1[/tex]You don't need a calculator for this because any number raised to 0 lays 1. This means that at x=0 ,i.e. the y-intercept of the graph, the function has y=1.
Lower left graph intercepts the y-axis in 1 while the upper right does it closer to 0 so we can discard this last option.
In summary, we have only one possible option left, the one in the lower left. This is the correct option.
Evaluate the expression 8÷2+54÷9×2×2
We are asked to evaluate the mathematical expression below;
[tex]8\div2+54\div9\times2\times2[/tex]To do this we would use "PEMDAS". PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction.
Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third, and so on, until the calculation is complete.
We will then proceed to solve the expression according to PEMDAS.
[tex]\begin{gathered} 8\div2+54\div9\times2\times2 \\ =\frac{8}{2}+\frac{54}{9}\times2\times2 \\ =4+6\times4 \\ =4+24 \\ =28 \\ \end{gathered}[/tex]Answer: 28
Put the rational numbers in order from least to greatest. -4.2, -4 1/2, -4, 0, 4
Let's express the mixed fraction in decimal.
[tex]-4\frac{1}{2}=-4.5[/tex]Then, from least to greatest, the numbers are
[tex]-4.5,-4.2,-4,0,4[/tex]write an equation, in factored form, of degree 6 polynomial that has four x-intercepts and a y-intercept of 64
ANSWER :
f(x) = (3x-2)(x-3)(x-4)(x-2)^3
EXPLANATION :
A polynomial with a degree of 6 has 6 factors.
f(x) = (x - a)(x - b)(x - c)(x - d)(x - e)(x - f) with 6 roots or x-intercepts.
But the problems states that it has 4 x-intercepts, so we will reduced the number of roots but maintaining the number of factors.
f(x) = (x - a)(x - b)(x - c)(x - d)(x - a)(x - a).
From here, we still have 6 factors but only 4 x-intercepts, the last two factors (x - a) is the same as the first factor.
So we can rewrite this as :
[tex]f(x)=(x-a)^3(x-b)(x-c)(x-d)[/tex]Next is to have a y-intercept of 64, y-intercept is the value of f(x) when x = 0
Substitute 0 to the function.
[tex]\begin{gathered} f(0)=(0-a)^3(0-b)(0-c)(0-d) \\ f(0)=a^3(b)(c)(d) \end{gathered}[/tex]Now we have f(0) = a^3bcd and f(0) = 64 as the definition from above.
We need to find the factors of 64,
64 = 8 x 4 x 3 x 2/3
And we can rewrite the equation as :
[tex]\begin{gathered} f(0)=a^3bcd \\ 64=a^3bcd \\ 8\times4\times3\times\frac{2}{3}=a^3bcd \end{gathered}[/tex]From here, we can observe that,
a^3 = 8 ⇒ a = 2
b = 4
c = 3
d = 2/3
So the function will be :
[tex]\begin{gathered} f(x)=(x-2)^3(x-4)(x-3)(x-\frac{2}{3}) \\ f(x)=(x-2)^3(x-4)(x-3)(3x-2) \end{gathered}[/tex]Explanation in 2/3
Since we only need 4 distinct factors of 64.
8 x 4 x 3 x 2/3
8 x 4 = 32
The product of the 3rd and 4th factor should be 2, in order to get 64.
Since from the first
What is 2/3−3 5/6
Help please.
Answer:
Step-by-step explanation:
First you want to make the denominator the first multiple of both numbers so: 2/3 -3 5/6 = 2/6 - 3 5/6
Next you want to multiply the numerator by the amount of times you had to multiply the denominator so: 4/6 - 3 5/6
Then subtract the answer: 3 1/6
A performer expects to sell 5000 tickets for an upcoming concert.
They plan to make a total of $311000 in sales from these tickets.
Assume that all tickets have the same price.
How much money will they make if they sell 7000 tickets?
Answer:
$435,400
Step-by-step explanation:
Price of one ticket: $311,000/5,000
Price of one ticket: $62.20
Price of 7000 tickets: $62.20 x 7000
Price of 7000 tickets: $435,400
A custormer spends $240 at Kal's on a shopping trip The customer hands the cashier a 25% off coupon. How much should the customor pay for their purchase? Enter your answer in the field below. Thero is a sciontific calculator avalable at tho top of the screen, if you need it.
Let's begin by listing out the information given to us:
Amount spent = $240
discount = 25%
[tex]\begin{gathered} Pay=Amountspent-(AmountSpent\cdot discount)_{} \\ P=240-(240\cdot\frac{25}{100})=240-60 \\ P=180 \end{gathered}[/tex]Therefore, the customer paid $180 for his purchase
1. Hay Story Problems Challenge Question Elliot delivered 630 newspapers in May. He delivered 35 more newspapers in June than May. Which equation can be used to find n, the number of newspapers Elliot delivered during these two months? A 630 + 35 x 2 = n B 630 + 35 = n C 630 + 630 - 35 = n D 630 + 630 + 35 = n Explain to your partner why your answer is correct.
Using elimination method, we get the result 630 + 630 + 35 = n
What is elimination method?
The elimination method involves removing one of the variables from a system of linear equations by adding or subtracting from the system and multiplying or dividing the variable coefficients.
You need an equation that can determine n, 630's total, and 35 more than 630.
More
The value "35 more in June than in May" refers to the value "35 more than 630." That value is represented by the sum (630 +35).
Total two months
In total, there will be two months' worth of delivered papers.
May deliveries + June deliveries = n
630 + (630 +35) = n
Eliminating parentheses, this expression is ...
630 + 630 + 35 = n
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how do you know that the slope of every horizontal line is zero
Let:
[tex]\begin{gathered} P1=(x1,y1) \\ P2=(x2,y2) \end{gathered}[/tex]If the line is horizontal, then:
[tex]y1=y2[/tex]The slope is given by:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ since\colon \\ y1=y2 \\ m=\frac{y1-y1}{x2-x1}=\frac{0}{x2-x1} \end{gathered}[/tex]Zero over any quantity is always zero, so:
[tex]m=\frac{0}{x2-x1}=0[/tex]What is the ones digit in the number 2^2058. Hint: Start with the smaller exponents to find pattern
1) We need to find out a pattern for the powers that have a base 2:
[tex]\begin{gathered} 2^{1}=2 \\ 2^2=4 \\ 2^3=8 \\ 2^4=16 \\ 2^5=32 \\ 2^6=64 \\ 2^7=128 \\ 2^8=256 \\ (\ldots) \end{gathered}[/tex]Note that from 4 to 4 powers the last digit starts to repeat itself.
2) So, let's proceed with this dividing the exponent 2058 by 4:
Now, note that the remainder is 2, therefore we can state that:
[tex]2^{2058}=same\: ones\: digit\: as\colon2^2=4[/tex]The function C(x) = 150 + 3.3x models the cost for a company to produce x units of a product. The function R(x) = 15x models the revenue the company earns if they sell x units of the product. Which function, P(x), models the profit the company earns if they sell x units of the product? (Profit = Revenue - Cost) O P(x) = 18.3x - 150 O P(x) = 11.7x - 150 OPlx) = 150 - 11.7x O P(x) = 18.3x + 150
Answer: We need to find the expression p(x) for profit.
[tex]\begin{gathered} \text{profit = revenue -cost} \\ \therefore\rightarrow \\ P(x)=R(x)-C(x) \\ P(x)=15x-(150+3.3x)=15x-150-3.3x=18.3x-150 \\ \therefore\rightarrow \\ P\mleft(x\mright)=18.3x-150 \\ \end{gathered}[/tex]Therefore the first option represents the profit of the company.
#1 Write the quadratic function in vertex
form given a vertex of (-1,-2) and a
second point on the graph at (3,-10)
A. y = -3(x - 1)² + 2
B. y=-34 (x + 1)² + 2
C. y = -2(x - 1)²-2
D. y=-2 (x + 1)²-2
The quadratic function in vertex form is y = -1/2(x + 1)^2 - 2
How to determine the quadratic function in vertex form?The vertex is given as
(h, k) = (-1,-2)
The point is also given as
(x, y) = (3, -10)
Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
Substitute (h, k) = (-1,-2) in y = a(x - h)^2 + k
y = a(x + 1)^2 - 2
Substitute (x, y) = (3, -10)
-10 = a(3 + 1)^2 - 2
So, we have
-10 = a(4)^2 - 2
Add 2 to all sides
-8 = a(16)
Divide by 16
a = -1/2
Substitute a = -1/2 in y = a(x + 1)^2 - 2
y = -1/2(x + 1)^2 - 2
Hence, the equation is y = -1/2(x + 1)^2 - 2
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The expression 81 √ ⋅ 100√ represents the number of feet between home plate and first base. What is the distance, in feet, between home plate and first base? Answers are 19 30 80 and 810.
The distance between home plate and first base is -1 feet
what is distance ?
Distance is a numerical or occasionally qualitative measurment of how far apart objects or point are . in physics or everyday usage , distance may refer to a physical length.
How to determine the number
From the information given, we have that;
The expression for the number of feet between home plate and first base is given as;
√81-√100
Where;
√81 is the number of feet at home plate
√100 is the number of feet at the first base
To determine the distance, we take find the square root of the numbers and substitute, we have;
9 - 10 Find the difference
-1 feet
Thus, the distance between home plate and first base is -1 feet
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What strategy would be the best to solve this problem?To get into shape, Miles ran for 1 minute on Monday, 3 minutes on Tuesday, 6 minutes on Wednesday, and 10 minutes on Thursday. If he continues, how many minutes will Miles run on Sunday?A. guess, check and reviseB. work backwardsC. use a formulaD. look for patterns
As we can see from the given data, that, it gives some informtaion about, an on going process, that is almost in rythm.
[tex]\begin{gathered} 1\text{ minute:Monday} \\ 3\text{minute: Tuesday} \\ 6\text{minute: Wednesday} \\ 10\text{ minutes: Thursday} \end{gathered}[/tex]So, from that we can see that, Mile had increased the running time in a particular pattern, at first he had increased the time by 2, then by 3, then by 4, and so on.
So to find the running time for sunday, we can solve this problem by analysing this pattern.
Therefore the answer is (D): looking for patterns.
If the length is 100 yards and the width is 55 yards, how many yards is the perimeter?
Answer:
perimeter = 310 yards
Step-by-step explanation:
If the length is 100 yards and the width is 55 yards, how many yards is the perimeter?
p = 2l + 2w
perimeter = 2(100) + 2(55)
perimeter = 200 + 110
perimeter = 310 yards
Please help me I’ll mark u brainly
Answer:
a
Step-by-step explanation:
to rotate 180 degrees, simply invert both signs
A cylindrical candle is to be made from 18 in 3 of wax. If the candle’s height is twice its
diameter, what radius and height should it have, to the nearest tenth?
The radius is 1.13 inches and the height of the cylinder is 4.52 inches.
How to calculate the value?From the information, it's important to use the volume of a cylinder to illustrate the information.
Use the volume of a cylinder.
V = πr²h
V = volume.
r = radius
h = height
where:
V = 18
h = 2(2r) = 4r
Plug in the values into the equation and solve for r.
18 = πr²(4r)
18 = 4πr³
Divide both sides of the equation by 4π.
9 / (2π) = r³
r³ = 1.43
r = 1.13 inches.
Finally, multiply the radius by 4 to get the height. This will be:
= 4 × 1.13
= 4.52 inches.
In conclusion, the height is 4.52 inches.
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. La cuarta parte de un número, disminuida en 17,
es igual a 4. Calcula la mitad de dicho número.
Resolviendo una ecuación lineal veremos que el número es 76, y la mitad de ese número es 38.
¿Como calcular la mitad del número?Definamos la variable "x" como el número de la ecuación.
Tenemos la oración matematica:
"La cuarta parte de un número, disminuida en 17, es igual a 4"
Esto se puede escribir como la ecuacion:
(1/4)*x - 17 = 4
Esto es una ecuación lineal que puede ser resuelta para x.
(1/4)*x - 17 = 4
(1/4)*x = 4 + 17 = 19
x = 4*19 = 76
Entonces la mitad del número es:
x/2 = 76/2 = 38
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Hello, I need help with this precalculus homework question, please?HW Q9
Solution
- The question would like us to determine the difference expression that corresponds to the following logarithm
[tex]\log_a(\frac{M}{N})[/tex]- In order to solve this question, we should apply the Law of Logarithm which states that:
[tex]\log A-\log B=\log(\frac{A}{B})[/tex]- Applying this law, we have:
[tex]\begin{gathered} \text{ Let A from the formula be M and Let B from the formula be N from the question} \\ Note\text{ that }a\text{ in the question is represented by 10 from the formula. The base 10 in logarithm is usually not } \\ \text{ indicated} \\ \\ \log_a(\frac{M}{N})=\log_aM-\log_aN \end{gathered}[/tex]Final Answer
The answer to the question is
[tex]\operatorname{\log}_{a}(\frac{M}{N})=\operatorname{\log}_{a}M-\operatorname{\log}_{a}N[/tex]What is the measure of the base of the rectangle if the area of the triangle is 28 ft?
Answer:
14 ft
Step-by-step explanation:
The base of the rectangle and triangle is same.
Triangle area formula:
A = bh/2GivenA = 28 ft²,h = 4 ft.Find bSubstitute the values:
28 = 4b/228 = 2bb = 28/2b = 14 ftAnswer is 14 ft.
Explanation.Triangle Area Use Formula.
A = bh/2A = 28 ft2
H = 4 ft
B Value.
28 = 4b/2
28 = (4/2)b
28 = 2b
b = 28/2
b = 14
_____________________
Class: Middle School
Lesson: Triangle
[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}[/tex]
Crossfire Company segments its business into two regions—East and West. The company prepared a contribution format segmented income statement as shown below:
Total Company East West
Sales $ 1,120,000 $ 770,000 $ 350,000
Variable expenses 840,000 616,000 224,000
Contribution margin 280,000 154,000 126,000
Traceable fixed expenses 155,000 65,000 90,000
Segment margin 125,000 $ 89,000 $ 36,000
Common fixed expenses 70,000
Net operating income $ 55,000
Required:
1. Compute the companywide break-even point in dollar sales.
2. Compute the break-even point in dollar sales for the East region.
3. Compute the break-even point in dollar sales for the West region.
4. Prepare a new segmented income statement based on the break-even dollar sales that you computed in requirements 2 and 3. What is Crossfire’s net operating income (loss) in your new segmented income statement?
5. Do you think that Crossfire should allocate its common fixed expenses to the East and West regions when computing the break-even points for each region?
what’s the correct answer answer asap for brainlist
Answer:
B
I hope that this helps
f(x) = x2What is f(x) + f(x) + f(x)?DONE
If we have the function
[tex]f(x)=x^2[/tex]Then
[tex]\begin{gathered} f(x)+f(x)+f(x)=x^2+x^2+x^2 \\ =3x^2 \end{gathered}[/tex]This also can be written in the form
[tex]f(x)+f(x)+f(x)=3f(x)=3x^2[/tex]We see that both answer are the same, like it should be.
Given a normal distribution with m = 100 and s = 10, what is the probability that a. X >75 b. X < 70 c. X < 80 or X > 110
Given a normal distribution with m = 100 and s = 10, the probabilities are;
a) X > 75 = 0.0062
b) X < 70 = 0.00135
c) X < 80 or X > 110 = 0.053954
What is the Probability from z-score?
We are given;
Population mean; m = 100
standard deviation; s = 10
The z-score is gotten from the formula;
z = (X - m)/s
Thus;
1) Probability that X > 75 is;
z = (75 - 100)/10
z = -2.5
From online p-value from z-score calculator, we have;
probability = 0.0062
2) Probability that X < 70 is;
z = (70 - 100)/10
z = -3
From online p-value from z-score calculator, we have;
probability = 0.00135
3) Probability that X < 80 is;
z = (80 - 100)/10
z = -2
From online p-value from z-score calculator, we have;
probability = 0.02275.
Probability that X > 110 is;
z = (110 - 100)/10
z = -1
From online p-value from z-score calculator, we have;
probability = 0.158655
Thus, P(0.02275 < x < 0.158655) = 0.053954
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Solve for z.
z² = 0.64
Answer:
Step-by-step explanation:
z 3 = 0.64 Take the specified root of both sides of the equation to eliminate the exponent on the left side. z = 3 √ 0.64 The result can be shown in multiple forms. Exact Form: z = 3 √ 0.64 Decimal Form: z = 0.86177387