Let g represent gallons of water and let L represent loads.
Here, the gallons of water varies directly with the number of loads, thus we have:
g ∝ L
Now introduce a constant k:
g = kL
65 gallons is used to wash 5 loads, thus we have:
65 = k * 5
Let's solve for k:
65 = 5k
Divide both sides by 5:
[tex]\begin{gathered} \frac{65}{5}=\frac{5k}{5} \\ \\ 13=k \end{gathered}[/tex]To find the amount of water that will be used to wash 8 loads, we have:
g = kl
We are to find g, substitute 13 for k and 8 for l:
g = 13 x 8
g = 104
Therefore, to wash 8 loads, 104 gallons of water is needed.
ANSWER:
104
Identify the coefficient and the exponent for each term of 8x² - 2x.
The coefficients are 4 and 1. The exponents are 8 and -2.
The coefficients are 8 and -2. The exponents are 4 and 0.
The coefficients are 8 and 2. The exponents are 4 and 0.
The coefficients are 8 and -2. The exponents are 4 and 1.
The coefficient of the term 8x² is 8 and the exponent is 2 and the coefficient of the term -2x is -2 and the exponent is 1.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = abˣ in mathematics, where x is the independent variable
From the expression, a is the coefficient, x is the exponent, and b is the variable
For the term, y = abˣ, compared with the general equations;
abˣ = 8x²
a = 8 and x = 2
This indicates that the term's coefficient is 8 and its exponent is 2.
Similarly for the second term -2x
So the coefficient of the term -2x is -2 and the exponent is 1
Hence, the coefficient of the term 8x² is 8 and the exponent is 2 and the coefficient of the term -2x is -2 and the exponent is 1.
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Hello, would you be able to help me with this?
Given: An expression
[tex]\sqrt{10}[/tex]Required: To write the exponent form of the given expression.
Explanation: The square root of a number is the same as having an exponent of 1/2.
For example
[tex]\sqrt{36}=6[/tex]And in exponent form,
[tex]\begin{gathered} \sqrt{36}=(36)^{\frac{1}{2}} \\ =(6^2)^{\frac{1}{2}} \\ =6 \end{gathered}[/tex]Hence for the given expression, we can write it as
[tex]\sqrt{10}=(10)^{\frac{1}{2}}[/tex]Final Answer: Option D is correct.
y=x^2+20
determine if symmetric on the..
x axysis
y axysis
both
The graph of the equation defined by; y = f(x) = x² + 20 as represented in the task content is symmetrical about the y-axis.
To which axis is the graph of the equation given symmetrical about?It follows from the task content that the axis about which the given graph is symmetrical be determined as follows.
Since it follows that for a function to be symmetric about the y-axis;
f(-x) = f(x).
Therefore, we have;
f(-x) = (-x)² + 20.
f(-x) = x² + 20 = f(x).
Hence, the graph is symmetrical about the y-axis.
Also; Since; f(-x) = x² + 20 ≠ - f(x).
It follows that the graph is not symmetrical about the origin and hence, the graph is only symmetrical about the y-axis.
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PLS HELP!!!
When solving the quadratic-2x² - 9x - 5 = 0, the number of real roots is:
A) 2 real roots.
B) 1 real root.
C) No real roots.
D) None of these choices are correct.
the net below is used to form a cylinder with a radius of 5 units
Given,
The radius of the cylinderis 5unit.
Required
The measure of CD.
The length of the CD is equal to the circumference of the base of circle.
So, the length of the cylinder is,
[tex]\begin{gathered} Length=2\pi r \\ =2\times\pi\times5 \\ =10\times\pi \\ =10\pi \end{gathered}[/tex]Hence,the length of CD is 10 pi.
Please help !! (10 pts for easy question)
Answer:
Step-by-step explanation:
If he eats 2 carrot he left with 4 carrot.
If he eats 3 carrot he left with 3 carrot.
If he eats 4 carrot he left with 2 carrot.
Step-by-step explanation:
Consider the provided information,
Max has 6 carrots. He eats more than 1 carrot. He has more than 1 carrot left.
He eats more than 1 carrot that means he can eat 2, 3, or 4 carrots.
Note. He can't eat 5 carrots because 6-5 = 1 which is not more than 1.
If he eats 2 carrot:
6-2=4
If he eats 2 carrot he left with 4 carrot.
If he eats 3 carrot:
6-3=3
If he eats 3 carrot he left with 3 carrot.
If he eats 4 carrot:
6-4=2
If he eats 4 carrot he left with 2 carrot
I'll give brainliest!
Answer: you got 1.9 1.57 2.45 and 2.125
Step-by-step explanation:
10 State if the two triangles are congruent or not congruent. If they are congruent, state the theorem (one of the five) that proves they are congruent. 1 Show Your Work
By theorem we have that if two sides of a triangle are equal, then the angles opposite to those sides are equal, with this or with knowing that the angle between the known sides are equal we conclude that both triangles are equal [the latter solution is using congruency SAS for the triangles, where S is side and A angle.]
40.3% of consumers Believe that cash will be Obsolete in the next 20 years. Assume that three consumers are randomly selected. Find the probability that fewer than three of the selected consumers believe that cash will be obsolete in the next 20 years.
The probability that fewer than three of the selected consumers believe that cash will be obsolete in the next 20 years is 0.538.
How to calculate the probability?The following can be deduced:
p = 40.3% = 0.403
1 - p = 1 - 0.403 = 0.597
n = 6
Therefore X follows the Binomial (6 , 0.403)
The PMF of the Binomial distribution is
P(X = x) = (n C x) * px * (1 - p)n - x ; x = 0 ,1 , 2 , ....., n
Now ,
P(fewer than 3)
= P(X < 3)
= P(X = 0) + P(X = 1) + P(X = 2)
= 0.0453+0.1834+0.3095
= 0.538
The probability is 0.538
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8000 is Shared between Oku and Ojo
In the ratio of 4:5 what is olu’s share and ojo’s
4444 is ratio of ojo’s share and 355.2 is the ratio of olu’s share .
What does a math ratio mean?
When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.the ratio of olu’s share and ojo’s = 4:5
total Shared = 8000
the ratio of olu’s share = 8000 * 4/9
= 888.8 * 4 = 355.2
the ratio of ojo’s share = 8000 * 5/9
= 888.8 * 5 = 4444
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in triangle ABC the angle bisectors drawn from vertices a and b intersect at the point d find the angle abd if angle a =a, angle b=b
Answer:
According to the below diagram, the angle bisectors of ∠A and ∠B are intersecting at point D.
Step-by-step explanation:
What is the area of the parallelogram shown
You calculate for the triangle and the other part separately,
The composition DWhat are the coordinates of point S"?Pozx. 70D, 1(x, y) is appliedto ARST to create the image of AR"S"T", which is notshown.(를)121082+ol 들이-14-12-10-3-6422 4 6 8 10 12x8-10-12-14
SOLUTION
Step 1 :
In this question, we are meant to find the co-ordinates of S,
Where the compostion
Calculate the missing information. Round dollars to the nearest cent and percents to the nearest tenth of a percent.
Item
Bar of soap
Cost
$1.17
Amount of
Markup
$0.79
Selling Price (in $)
$1.96
Percent
Markup
Based on
Cost
X%
Percent
Markup
Based on
Selling Price
%
MY N
The markup indicates the difference between the selling price and the item's cost to the business.In general, a corporation generates more money the higher the markup.The retail price of a product less its cost is known as markup, although the margin percentage is determined in a different way.
Calculate percentage on markup based on cost ?
The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %.The markup percentage, which is computed as (12 - 8) / 8, is 50% for an item that costs the business $8 to produce but is priced at $12.Selling price = cost + markup
= 1.17+0.78
=1.96
percentage markup based on cost = markup/cost*100
0.78/1.17*100
= 66.66
percentage on selling = percentage on markup cost/100+percentage on cost
= 66.66/100%+66.66
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Find the slope and y-intercept for the line. Then write the equation of the line in slope-intercept form.
Slope =
y-intercept = (0,
Equation y
The equation of the line in slope intercept form is y=0(x)+0 or y=0.
What is slope intercept form?
The slope intercept form in the math is one of the forms used to calculate of the equation of a straight line, given the slope of the line and intercept it forms with the y-axis. The slope is the intercept form is given as, y = mx + b, where 'm' is the slope of the straight line and 'b' is the y-intercept.
The equation of any of the straight line can be written as the y=mx+c, where m is its a slope and c is its y-intercept .
Hence, the equation of the line with slope is =0 and y - intercept =0 is y=0(x)+0 or y=0.
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If f(x)=x²+5 and g(x)=3x, find (f . g)(x) and (g . f)(x).
(f . g)(x)= _____ (Simplify your answer.)
The value of the functions are given as;
(f. g)(x) = 9x² + 5
(g . f)(x) = 3x² + 15
What is a function?A function can simply be described as an expression, law, or rule showing or explaining relationship between two variables in an equation.
The variables are namely;
The dependent variableThe independent variableGiven the functions;
fx)=x²+5g(x)=3xTo determine ( f. g)(x), we have to substitute the value of g(x) as x in the function, we get;
(f. g)(x) = (3x)² + 5
expand the bracket
(f. g)(x) = 9x² + 5
To determine (g . f )(x), we have to substitute the value of x in the function
(g . f(x) = 3(x² + 5)
expand the bracket
(g . f)(x) = 3x² + 15
Hence, the values are 9x² + 5 and 3x² + 15
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Ben says this system of equations has one solution. Is he correct? Explain. Choose the correct answer below.Y= 1/4x-4Y= 1/4x-14 A. Ben is incorrect. Since the equations have the same slope, the system has infinitely many solutions. B. Ben is incorrect. Since the equations have the same slope and different y-intercepts, the system has no solution. C. Ben is correct. Since the equations have the same slope, the system has exactly one solution.D. Ben is correct. Since the equations have the same slope and different y-intercepts, the system has exactly one solution.
Let's begin by listing out the given information:
[tex]\begin{gathered} y=\frac{1}{4}x-4--------1 \\ y=\frac{1}{4}x-14-------2 \\ \end{gathered}[/tex]We will observe that both equations have the same slope but different y-intercept. This implies that both equations are parallel to one another. This means that both equations never intersect at any point & as such, have no solution.
Hence, the correct answer is B. Ben is incorrect. Since the equations have the same slope and different y-intercepts, the system has no solution.
I really don't know where to start on this problem and I would like it if some could help me please.
We can draw the following picture:
Since we have a right triangle with hypotenuse equal to 28ft, we can use the trigonometric function. That is, we can write the following relationships:
[tex]\begin{gathered} \sin 30=\frac{RG}{28} \\ \text{and } \\ \cos 60=\frac{RG}{28} \end{gathered}[/tex]both give the same result.
If we use the first one, we have
[tex]\begin{gathered} RG=28\cdot\sin 30 \\ \end{gathered}[/tex]since sin30=0.5, we have
[tex]\begin{gathered} RG=28\cdot(0.5) \\ RG=14 \end{gathered}[/tex]that is, RG = 14 ft, which corresponds to the first option
BC = 20; CD = 15. What is the value of BD − AC.
Answer:
BD - AC = 0
Step-by-step explanation:
BC = 36 , CD = 15 and BD = x
As these are forming right angled triangle,
Using Pythagorean theorem,
Taking square root on both sides
As the given shape is rectangular, the sides parallel to each other will have same values.
AB = 15 , AD = 36 and AC = x
Now,
BD - AC = 39 - 39 = 0
Hence,
BD - AC = 0
A tank truck holds 35.3 kiloliters of oil. How many gallons does it hold?
The truck holds approximately _____ gallons of oil.
round to the nearest hundredth as needed
SLOPE-INTERCEPT FORM: PA
Xander has biked 2 miles so far this week and plans to bike an
average of 6 miles each day over the next several days. Xander
wrote the equation and created the graph to represent x, the number
of days and y, the total number of miles traveled on his bike.
a. Find the slope of the graph. Where do you see this value in
Xander's equation?
b. What value does the graph touch on the y-axis? Where do you
see this value in Xander's equation?
a) The slope of the equation is 6
b) The graph touch the y- axis at (0, 2) , (1, 8) and so on.
what is 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. LHS = RHS is a common mathematical formula.
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:
Xander has biked 2 miles.
and, average of 6 miles each day.
So, if the number of days be x and total number of miles traveled be y.
Then , the equation to represent the situation
y= 6x+ 2
a) the slope of the equation comparing to y= mx +b
So, slope= 6
b) The graph touch the y- axis at (0, 2) , (1, 8) and so on.
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A = {1, 2, 3, 4}
B = {3, 4, 5}
vertical line A intersection B vertical line =
The intersection of vertical lines A and B is 3 and 4.
How to find the intersection of the vertical linesWe are going to apply the sets theory here. In sets theory, the intersection of two elements means the values those elements have in common.
So given: A = {1, 2, 3, 4} and B = {3, 4, 5}
The intersection of A = {1, 2, 3, 4} and B = {3, 4, 5} is {3,4} since they both have 3 and 4 common.
Therefore, vertical lines A and B have intersection of 3 and 4.
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ANSWER ASAP!! Raise the monomial to a power: -2m^3n^2t to the power of 4
Answer:
2^5m^15n^10
Step-by-step explanation:
Answer:
16m^12n^8t^4
Step-by-step explanation:
when raising exponents to another exponent you multiply the exponents
Without graphing, decide whether the system of equations has one solution, no solution, or infinitely many solutions.How many solutions does the system of equations have?y=11x-6y=-6x+11
Answer:
one solution
Explanation:
Given the system of equations:
[tex]\begin{gathered} y=11x-6 \\ y=-6x+11 \end{gathered}[/tex]Equating the two expressions of y:
[tex]\begin{gathered} 11x-6=-6x+11 \\ 11x+6x=11+6 \\ 17x=17 \\ x=\frac{17}{17} \\ x=1 \end{gathered}[/tex]Next, solve for y:
[tex]\begin{gathered} y=11x-6 \\ =11(1)-6 \\ =11-6 \\ y=5 \end{gathered}[/tex]Thus, we conclude that the system of equations has exactly one solution (1, 5).
HELP PLEASEEEEE!!!!!!
[tex]-1\frac{3}{4}[/tex] is located at a point 1.
1.1125 is located at point 6.
14 / 8 is located at point 8.
-0.875 is located at point 3.
What are the locations of the numbers?The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.
A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a fraction is which the numerator is less than the denominator. An example of a mixed number is 1 3/4. An improper fraction is a fraction in which the numerator is greater in value than the denominator. An example of an improper fraction is 14/8.
A negative number is a number that is less than 0. This numbers would be located to the left of 0 on the number line. An example of a negative number is -1.2. A positive number is a number that is greater than 0. These numbers are located to the right of 0 on the number line. An example of a positive number is 1
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PLEASE HELP, NO LINKS!
1. What are the key features that can be identified from a linear graph?
2. What is a relation? What makes it different from a function?
3. How can you determine the domain and range from a function?
4. What is Slope and how is it determined from a graph?
5. How do you determine the intercepts from an equation and graph.
6. Provide an example of the different forms linear equations and functions can be written.
Answer:
1 These 5 main features are the title, scale, points, labels, and line.
2. Relations are a group of ordered pairs from one set of objects to another set of objects while functions are relations that connect one set of inputs to another set of outputs. So all functions are relations while all relations are not functions.
3. To find the domain and range, we simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain. To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y).
4. The slope equation says that the slope of a line is found by determining the amount of rise of the line between any two points divided by the amount of run of the line between the same two points. In other words, Pick two points on the line and determine their coordinates.
5. To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'. To find the y-intercept, plug 0 in for 'x' and solve for 'y'.
6. An example of a linear equation is: 2x + y - 3 = 0. It can be written in the standard form, the slope-intercept form, and the point-slope form. Here we mainly used the slope-intercept form y=mx+c y = m x + c . To write linear equations find the slope and y-intercept and then substitute these values into the equation.
Out of 250 tickets in a raffle, one ticket will win a $430 prize, one ticket will win a $290 prize, one ticket will win a $190 prize, and one ticket will win a $130 prize. The rest will win nothing. If you have a ticket, what is the expected payoff?
The expected value is given by:
[tex]E(x)=\sum ^{}_{}xP(x)[/tex]In this case we have:
[tex]\begin{gathered} E(x)=430(\frac{1}{250})+290(\frac{1}{250})+190(\frac{1}{250})+130(\frac{1}{250}) \\ =4.16 \end{gathered}[/tex]Therefore the expected payoff is $4.16
I need help with this problem it's a two-part thing
To find PQ, notice that M divides PQ into two parts with the same measure.
So, we have:
[tex]10x+3=14x-13[/tex]Now, we can solve the above equation for x, and then find PQ.
To solve the equation, we can apply the same operations on both sides of the equation, until we isolate the variable x and find its value:
[tex]\begin{gathered} 10x+3-14x=14x-13-14x \\ \\ -4x+3=-13 \\ \\ -4x+3-3=-13-3 \\ \\ -4x=-16 \\ \\ \frac{-4x}{-4}=\frac{-16}{-4} \\ \\ x=4 \end{gathered}[/tex]So, using x = 4, we obtain:
[tex]\begin{gathered} PQ=2\cdot(10x+3) \\ \\ PQ=2\cdot(10\cdot4+3) \\ \\ PQ=2\cdot(40+3) \\ \\ PQ=2\cdot43 \\ \\ PQ=86 \end{gathered}[/tex]Therefore, PQ = 86.
KellyConnect
Program X has an annual cost of $35,000 and, in return, is expected to save the
Company C $40,000 during the first year. Assuming the cost and savings are equally
distributed across each month, after how many months will the company recover its
investment in Program X?
The business will need 10.5 months to make back the money it invested in Program X.
How do you determine monthly costs?Actual or anticipated costs for each monthly expense are needed to calculate the average monthly expenses.
How do you figure out the return on investment?By dividing an investment's net profit (or loss) by its initial cost or outlay, we can determine the return on investment.
Program X costs $35,000 per year, but is anticipated to save $40,000 for Company C in the first year.
Considering that the savings and the cost are equal over the course of each month
So, 40000/35000 = 0.875
No. of months to recover = 0.875 × 12
= 10.5 months
Therefore, the duration it will take the business to recover its
Investment in Program X is 10.5 months.
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If Sarah were to paint her living room alone, it would take 5 hours. Her sister Rachel could do the job in 8 hours. How long would it take them working together?
It takes a specific amount of time (T) to finish a particular task (W). The rate of work is the quantity of units of work completed per unit of time (R). Work (W) = Rate (R) Time, thus (T).
They spent 40/13 hours together painting her living room.
What is the relationship between time and work?Time = 1 divided by the rate of work. If a task is completed across x days, then the amount of work completed in a single day is equal to 1/x. Total Work Done = Days * Productivity. Time and effectiveness are inversely related to one another.Time and work concerns concern the simultaneous performance of a person or a group's productivity and the amount of time it takes for them to finish a task. Work is the energy expended to complete a task or produce a deliverable.It takes a specific amount of time (T) to finish a particular task (W). The rate of work is the quantity of units of work completed per unit of time (R). Work (W) = Rate (R) Time, thus (T)sarah does the 1/5 of the job per hour.
Rachel does the 1/8 of the job per hour.
Together, they do 1/5 + 1/8 of the job per hour.
= 13/40 of the job each hour
The inverse of job/hour = hours per job
---> 40/13 hours to do it together.
For a shortcut:
t = 5*8/(5+8) = 40/13 hours
They spent 40/13 hours together painting her living room.
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