From the information provided, the lawn mower is sold at a price which is $75 over the cost of manufacture.
If the cost of manufacture is x, then we would have;
[tex]f(x)=x+75[/tex]Also, the store now sells the lawn mower for 140% of the price paid to the manufacturer. Therefore, we would have;
[tex]g(x)=f(x)1.4[/tex]Hence, if the manufacturer's cost is $230, the customer would be paying g(x). When the cost x is now given as 230, we wou;d have;
[tex]\begin{gathered} f(230)=230+75 \\ f(230)=305 \\ \text{Hence;} \\ g(x)=f(x)1.4 \\ g(x)=305\times1.4 \\ g(x)=427 \end{gathered}[/tex]ANSWER:
The function of the price is;
[tex]f(x)=x+75[/tex]The price a customer pays when the cost of manufacturing is $230 would now be $427
Find the domain. Then use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters. \frac{ \sqrt[]{x-4} }{\sqrt[]{x-6}} AnswerAnswer,AnswerAnswer
The domain of a function is all values of x the function can have.
Since this function has radicals, and the value inside a radical needs to be positive or zero, and also the denominator of a fraction can't be zero, we have the following conditions:
[tex]\begin{gathered} x-4\ge0 \\ x\ge4 \\ \\ x-6>0 \\ x>6 \end{gathered}[/tex]Since the first condition contains the second, so the domain set is represented by the second condition:
[tex](6,\text{inf)}[/tex]11. Let the supply and demand functions for sugar is given by the following equations. Supply: p = 0.4x Demand: p = 100 - 0.4x (a) Find the equilibrium demand.
SOLUTION:
Step 1:
In this question, we are given the following:
Let the supply and demand functions for sugar be given by the following equations. Bye
Supply: p = 0.4x
Demand: p = 100 - 0.4x
a) Find the equilibrium demand.
Step 2:
At Equilibrium,
[tex]\begin{gathered} \text{Supply}=\text{ Demand} \\ 0.\text{ 4 x = 100 - 0. 4 x} \end{gathered}[/tex]collecting like terms, we have that:
[tex]\begin{gathered} 0.4\text{ x + 0. 4 x = 100} \\ 0.8\text{ x = 100} \end{gathered}[/tex]Divide both sides by 0.8, we have that:
[tex]\begin{gathered} x\text{ = }\frac{100}{0.\text{ 8}} \\ x\text{ = 125} \end{gathered}[/tex]
Step 3:
Recall that:
[tex]\begin{gathered} \text{Equilibrium Demand : p = 100 - 0. 4 x } \\ we\text{ put x = 125, we have that:} \\ p\text{ = 100 - 0. 4 (125)} \\ p\text{ =100 -50} \\ p\text{ = 50} \end{gathered}[/tex]CONCLUSION:
Equilibrium Demand:
[tex]p\text{ = 50 units}[/tex]The graph above shows the graph of the cost in blue and revenue in red function for a company that manufactures and sells small radios.ABCD
a) 500 radios
b) Going out = $5000
Coming in = $5000
c) P(x) = 6x - 3000
d) Profit of $900
Explanation:a) To get the number of radios that must be produced to break even, we will equate the cost function and the revenue function:
[tex]\begin{gathered} \cos t\text{ function:} \\ C(x)\text{ = 3000 + 4x} \\ \text{revenue function:} \\ R(x)\text{ = 10x} \\ \\ \text{Break even:} \\ C(x)\text{ = R(x) } \\ \text{3000 + 4x = 10x} \end{gathered}[/tex]collect like terms:
[tex]\begin{gathered} 3000\text{ = 10x - 4x} \\ 3000\text{ = 6x} \\ \text{divide both sides by 6:} \\ x\text{ = 3000/6} \\ x\text{ = 500} \\ \text{If x represents number of radios produced,} \\ \text{Then to break even, 500 radios will have to be produced } \end{gathered}[/tex]b) The dollar amount going in and coming out is gotten by replacing the value of x in both function with 500:
[tex]\begin{gathered} \text{when x = }500 \\ C(x)\text{ = 3000 + 4x = 3000 + 4}(500) \\ C(x)\text{ = }5000 \\ \text{Amount going out = \$5000} \\ \text{when x = 500} \\ R(x)\text{ = 10x = 10(500)} \\ R(x)\text{ = 5000} \\ \text{Amount coming in = \$5000} \end{gathered}[/tex]c) Profit = Revenue - Cost
[tex]\begin{gathered} \text{Profit function, }P(x)\text{= R(x) - C(x)} \\ P(x)\text{ = 10x - (3000 + 4x)} \\ P(x)\text{ = 10x - 3000 - 4x} \\ P(x)\text{ = 6x - 3000} \end{gathered}[/tex]d) To find the profit when the number of radios is 650
[tex]\begin{gathered} \text{Profit function: P(x) = 6x - 3000} \\ \text{for 650 radios, x = 650} \\ P(650)\text{ = 6(650) - 3000} \\ P(650)\text{ = 900} \\ \text{The company will make a profit of \$900} \end{gathered}[/tex]Suppose you are choosing at random from the numbers 1 through 12 (inclusive). If the event E is "the number is even," find the set representing E. Express your answer as a bracketed set in the form {a,b,c,d}.
The set numbers from 1 to 12(inclusive) is:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
The set even numbers are:
2, 4, 6, 8, 10, 12
Given that the event E is "the number is even"
Therefore, the set representing the event E as a bracketed set is:
[tex]E=\mleft\lbrace2,4,6,8,10,12\mright\rbrace[/tex]
The dose of a drug is critical. Too small a dose may be treat a patient effectively, A nurse must give a patient 40mg of a drug for each kilogram of the patient’s mass. If the patient weighs 165lbs how many milligrams of the drug should be given?
EXPLANATION
We need to multiply the number of needed milligrams by the weight of the patient, but first turning the weight in lbs into kilograms,
[tex]?Kilograms=165lbs*\frac{0.453}{1lb}=74.745Kg[/tex]Now, multiplying the obtained weight by the number of miligrams, give us the dose:
[tex]Dose=40\frac{mg}{Kg}*74.745Kg=2989.8mg[/tex]In conclusion, the nurse should give 2989 mg of the drug.
Factoring
64v^4-225w^10
I come up with
(8v^2+15w^2)(8v^2-15w^5) can I simplify it?
Your answer can't be simplified but it's also slightly incorrect. No worries!
You can simplify (64v^4 - 225w^10) by applying the difference of squares --> a^2 - b^2 = (a + b)(a - b)
Here, (64v^4) is a^2, and (225w^10) is b^2.
[tex]\sqrt{64v^4 }[/tex] = a = 8v^2
[tex]\sqrt{225w^{10} }[/tex] = b = 15w^5
Substitute the values:
(8v^2 + 15w^5)(8v^2 - 15w^5)
Therefore, the factorization of [tex]64x^{4} -225w^{10}[/tex] is:
[tex](8v^{2} + 15w^5)(8v^2-15w^5)[/tex]
The factorization is already the simplest. It can't be simplified further.
A cashier has 24 bills, all of which are $10 or $20 bills. The total value of the money is $410. How many of each type of bill does the cashier have?
The cashier has 7 bills of $10 and 17 bills of $20 (found using linear equation).
According to the question,
We have the following information:
A cashier has 24 bills, all of which are $10 or $20 bills. The total value of the money is $410.
Now, let's take the number of $10 bills to be x and the number of $20 bills to be y.
So, we have the following expression:
x+y = 24
x = 24-y .... (1)
10x+20y = 410
Taking 10 as a common factor from the terms on the left hand side:
10(x+2y) = 410
x+2y = 410/10
x+2y = 41
Now, putting the value of x from equation 1:
24-y+2y = 41
24+y = 41
y = 41-24
y = 17
Now, putting this value of y in equation 1:
x = 24-y
x = 24-17
x = 7
Hence, the cashier has 7 bills of $10 and 17 bills of $20 when the total value of the money is $410.
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help pleasesjjsnsbsbbbsbs
Student asking the same question for third time in less than ten minutes. Can't help him or her out with additional information to complete the exercise.
Closing the session!
what is the GCF of 6x+18/x^2-x-12
The GCF of the expression 6x+18/x^2-x-12 is (x+3)
How to find the GCF of the expression?The GCF (Greatest Common Factor) of two or more numbers or expressions is the greatest number or expression among all the common factors of the given numbers or expressions
Given 6x+18/x²-x-12
We can write 6x+18/x²-x-12 as:
6x+18/x²-x-12 = 6x+18/x²-4x+3x-12 By factorization:
= 6(x+3) / (x+3)(x-4)
Since (x+3) is common to both the numerator and the denominator. Therefore, the greatest common factor (GCF) is (x+3)
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In right triangle QRS, m S=73. In right triangle TUV m V=73.
To find:
Which theorem used to prove that both triangles are congruent.
Solution:
It is given that both triangles are right triangles. So, each one of the corresponding angles is 90 degrees.
angle M is given 73 degrees and angle V is given 73 degrees. So, we can see that two pairs of angles are equal in triangle.
Thus, AA similarity postulate can be use to prove that both triangles are congruent.
Thus, option C is correct.
(a) How high is the javelin when it was thrown? How do you know?(b) How far from the thrower does the javelin strike the ground?
The height of the javelin is given by
[tex]h(x)=-\frac{1}{20}x^2+8x+6[/tex]Here, x is the horizontal distance from the point at which the javelin is thrown.
a)
When the javelin is thrown, the horizontal distance from the point at which the javelin is thrown is zero. So, put x = 0 to find the height of the javelin when thrown. So, the distance:
[tex]\begin{gathered} h(0)=-\frac{1}{20}(0)^2+8(0)+6 \\ =0+0+6 \\ =6 \end{gathered}[/tex]Thus, the height of the javelin when it was thrown is 6 ft.
b)
When the javelin strikes the ground the value of h(x) is zero.
Find the value of x when h(x) is zero.
[tex]\begin{gathered} h(x)=0 \\ -\frac{1}{20}x^2+8x+6=0 \\ -x^2+160x+120=0 \\ x^2-160x-120=0 \end{gathered}[/tex]Now, the roots of the equation are x = 160.74 and x = -0.74.
The distance cannot be negative. So, the javelin is 160.74 ft far from the thrower when it strikes the ground.
a) Jayla says that the equation y=2*3 matches the graph Substitute the ordered pairs (from part() into the equation to prove that jayla is correct. Make sure to show ALL steps
From the graph let's take the points as the ordered pairs:
(3, 3), (4, 5), and (5, 7)
Given the equation:
y = 2x - 3
Let's verify for all points, if the equation matches the graph:
a) (x, y) ==> (3, 3)
Substitute 3 for x and 3 for y in the equation
y = 2x - 3
3 = 3(3) - 3
3 = 6 - 3
3 = 3
b) (x, y) ==> (4, 5)
Substitute 4 for x and 5 for y:
y = 2x - 3
5 = 2(4) - 3
5 = 8 - 3
5 = 5
c) (x, y) ==> (5, 7)
Substitute 5 for x and 7 for y:
y = 2x - 3
7 = 5(2) - 3
7 = 10 - 3
7 = 7
Since the left side equals the right side of the equation, the equation
y=2x-3 matches the graph.
Therefore, Jayla is correct.
Mick O'Meara budgeted $315 per month for electricity and $238 per month for gas. His expenses for a twelve-month period were $3,950 for electricity and $3,055 for gas.How much less did he budget annually for the two expenses than he needed?$339$344$357$369None of these choices are correct.
In order to know how much he budgeted annually for each expense, we need to multiply each month budget by 12:
annual budget for electricity: 12 * 315 = 3780
annual budget for gas: 12 * 238 = 2856
So, the total annual budget was:
3780 + 2856 = 6636
On the other hand, his real expenses for that year were:
3950 + 3055 = 7005
Then, to find how much less he budget than he needed, we can find the difference between those two values:
7005 - 6636 = 369
Therefore, the last option is correct.
zoe is 1.55 meters tall. at 2 pm she measure the lenght of a tree's shadow to be 17.35 meters . she stands 12.7 meters away from the tree so that the tip of her shadow meets the tip of tye tree's shadow. find the height of yhe tree to the nearest hundredth of a meter.
the figure below to better undesrtand the problem
Applying proportion
h/17.35=1.55/(17.35-12.70)
solve for h
h=17.35*1.55/4.65
h=5.78 mAnalyze the general equation of a linear function, y = mx. No matter what value the constant m has, which pair of numerical values (x, y) always satisfies this mathematical equation? Justify your answer.
The pair of numerical values (x,y) that always satisfies the mathematical equation of linear equation y = mx is (0,0).
A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables whose values rely on one another.
The slop-intercept form of a linear equation is y = mx + b.
For y = mx, b = 0.
If we put x = 0 in y = mx, y = 0.
Therefore, y = mx line always passes through (0,0) for any value of m because (0,0) always satisfies the equation y = mx.
Hence, (x,y) = (0,0).
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6. Oliver is playing a game in which he has to choose one of two numbers (2 or 7) and then one of five vowels (a, e, i, o, or u). How many possible outcomes are there? 2 7 There are possible outcomes.
Answer
Number of possible outcomes for everything = 240 ways
Explanation
The number of possible outcomes can be calculated by taking each of these two groups.
First group contains 2 elements
Number of possible ways to pick the elements = 2! = 2 × 1 = 2 ways
Second group contains 5 elements
Number of possible ways to pick the elements = 5! = 5 × 4 × 3 × 2 × 1 = 120 ways
Number of possible outcomes for everything = 2! × 5! = 2 × 120 = 240 ways
Hope this Helps!!!
9km 87 m equals
option A = 9.087km
option B= 90.87km
option c = 0.9087km
option D= 908.7km
option e= none of these
please don't give wrong answer
Find the domain of the function represented by the list of ordered pairs
The domain of a function is always represented by the values of X. In the ordered pair, they are always the first value of the pair.
The domain is the first number of each pair.
Domain: {-1, -10, 8, 6}.
Approximate when the function is positive, negative, increasing, or decreasing.
Describe the end behavior of the function.
The function y = - | x | + 1 is increasing on ( - ∞, 0 ) and decreases on ( 0, ∞ ).
A relationship between a group of inputs with each output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Consider the function,
y = - | x | + 1
The non-negative value of a real number x, represented by the symbol |x|, is the absolute value or modulus of x, regardless of its sign.
From the graph, we can approximate that the function is increasing from negative infinity to zero and the function decreases from zero to infinity.
Increasing on: ( - ∞, 0 )
Decreasing on: ( 0, ∞ )
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A parallelogram has an area of 364.5 cm2. If the base is 27 cm, What is the height?
Answer:
Height = 13.5cm
Explanation:
The area of a parallelogram is obtained using the formula below:
[tex]\text{Area}=\text{Base}\times Height[/tex]Substituting the given values:
[tex]\begin{gathered} 364.5=27\times\text{Height} \\ \text{Height=}\frac{364.5}{27} \\ H\text{eight}=13.5\operatorname{cm} \end{gathered}[/tex]Neegan paddles a kayak 21 miles upstream in 4.2 hours. The return trip downstream takes him 3 hours. What isthe rate that Neegan paddles in still water? What is the rate of the current?
System of Equations
When Neegan paddles the kayak upstream, the real rate (speed) is the difference between the rate that Neegan paddles in still water and the rate of the water against his paddling.
When he goes downstream, the real rate is the sum of the rates because the water and Neegan push in the same direction.
He takes 4.2 hours to paddle for 21 miles against the current, so the real rate is 21/4.2 = 5 mi/h
He takes only 3 hours to return, so the real speed is 21 / 3 = 7 mi/h.
Let:
x = rate at which Neegan paddles in still water
y = rate of the current.
We set the system of equations:
x - y = 5
x + y = 7
Adding both equations:
2x = 12
Divide by 2:
x = 6
Substituting in the second equation:
6 + y = 7
Subtracting 6:
y = 1
Neegan paddles at 6 mi/h in still water. The rate of the current is 1 mi/h
(Third choice)
Find the slope of the tangent line when x=3 using the limit definition f(x) = X^2 - 5
SOLUTION
From the limit definition, we have that
[tex]f^{\prime}(x)=\lim _{h\to0}\frac{f(x+h)-f(x)}{h}[/tex]Now applying we have
[tex]\begin{gathered} f\mleft(x\mright)=x^2-5 \\ f^{\prime}(x)=\lim _{h\to0}\frac{f(x+h)-f(x)}{h} \\ =\lim _{h\to0}\frac{((x+h)^2-5)-(x^2-5)}{h} \\ =\lim _{h\to0}\frac{x^2+2xh+h^2^{}-5-(x^2-5)}{h} \\ =\lim _{h\to0}\frac{x^2+2xh+h^2-5-x^2+5}{h} \\ =\lim _{h\to0}\frac{x^2-x^2+2xh+h^2-5+5}{h} \\ =\lim _{h\to0}\frac{2xh+h^2}{h} \end{gathered}[/tex]factorizing for h, we have
[tex]\begin{gathered} =\lim _{h\to0}\frac{h(2x+h)^{}}{h} \\ \text{cancelling h} \\ =\lim _{h\to0}2x+h \\ =2x \end{gathered}[/tex]So, when x = 3, we have
[tex]\begin{gathered} =2x \\ =2\times3 \\ =6 \end{gathered}[/tex]Hence, the answer is 6
Question 2(Multiple Choice Worth 2 points)
(03.01 LC)
Jordan compared 10 books at the school library. The following table shows the number of chapters and the total number of pages for each book.
Number of Chapters 3 4 8 10 16
Total Pages 25 38 85 76 180
Which data display would you use to represent this data?
O Histogram
Scatter plot
O Line graph
O Line plot
To represent the data, histogram would have been used.
Jordan compared 10 books at the school library. The following table shows the number of chapters and the total number of pages for each book.
Number of Chapters 3 4 8 10 16
Total Pages 25 38 85 76 180
In a histogram, a graphical representation of the distribution of data is done. The histogram is represented by a set of rectangles, adjacent to each other and each bar represent a kind of data.
Here the number of chapters can be kept in x axis and the total number of pages can be kept in the y axis.
Therefore, histogram would be used to display the data.
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The entire company went in together to buy lottery tickets. Inside the safe are two different types of lottery tickets. The Mega Million Tickets cost $5 each and the Scratch Off Tickets cost $2 each. They bought 60 tickets totaling $246. what are my x and y variables?x=y=
we have the following system
[tex]\begin{gathered} \begin{cases}x+y=60 \\ 5x+2y=246\end{cases} \\ \end{gathered}[/tex]where x is the number of mega million ticktets and y the number of scratch off tickets, so we have that y=60-x and we get that
[tex]\begin{gathered} 5x+2(60-x)=246 \\ 5x-2x+120=246 \\ 3x=126 \\ x=\frac{126}{3}=42 \end{gathered}[/tex]so they bought 42 mega million tickets and 18 scratch off
what is the surface are of this cone rounded to the nearest tenth of a square foot?
ANSWER
[tex]282.7ft^2[/tex]EXPLANATION
Recall, the formula for calculating the surface area of a cone is;
[tex]A=\pi r^2+\pi r\sqrt{r^2+h^2}[/tex]Given;
[tex]\begin{gathered} radius(r)=5 \\ height(h)=12 \end{gathered}[/tex]Substitute the values into the formula;
[tex]\begin{gathered} A=\pi 5^2+\pi 5\sqrt{5^2+12^2} \\ =\pi5^2+\pi5\sqrt{25+144} \\ =25\pi+5\pi\times13 \\ =25\pi+65\pi \\ =90\pi \\ =90\times3.14 \\ =282.74 \\ \cong282.7 \end{gathered}[/tex]Need help asap please and thank you
Answer:
y=[tex]\frac{1}{2}[/tex]x+1
Step-by-step explanation:
y=mx+b
m is the slope of the line, which you find by counting the rise over run between two points. In this case its up one, and right two, or [tex]\frac{1}{2}[/tex].
b is the y intercept, or where the line crosses the y axis
I need help with question 12 please in a hurry I understand already
Trigonometric Ratios
The figure is a triangle with hypotenuse of h = 25 feet. The angle of elevation is 35°.
20) Determine if the number is rational (R) or irrational (I)
EXPLANATION:
Given;
Consider the number below;
[tex]97.33997[/tex]Required;
We are required to determine if the number is rational or irrational.
Solution;
A number can be split into the whole and the decimal. The decimal part of it can be a recurring decimal or terminating decimal. A recurring decimal has its decimal digits continuing into infinity, whereas a terminating decimal has a specified number of decimal digits.
The decimal digits for this number can be expressed in fraction as;
[tex]Fraction=\frac{33997}{100000}[/tex]In other words, the number can also be expressed as;
[tex]97\frac{33997}{100000}[/tex]Therefore,
ANSWER: This is a RATIONAL number
The function f(x) is graphed below. what is true about the graph on the interval from x = y to x = ∞?* it is positive and increasing* it is positive and decreasing * it is negative and increasing* it is negative and decreasing
Looking at the graph, we will the following:
The portion ab is increasing
The portion bc is decreasing
The portion cd is decreasing
The portion de is increasing
The portion ef is increasing
The portion fg is decreasing
The portion beyond g is increasing
In the interval x = y to x = ∞, we will observe that the graph is positive & increasing
Hence, the first option is correct (it is positive and increasing)
A total of 350 pounds of cheese is packaged into boxes each containing 1 5 pointsand 3/4 pounds of cheese. Each box is then sold for $1.75. What is the totalselling price of all of the boxes of cheese?150350450550
To solve the exercise, you can first know how many boxes of cheese result with the amount of 350 pounds of cheese.
For this, you can use the rule of three, like this
[tex]\begin{gathered} 1\text{ box}\rightarrow1\frac{3}{4}\text{ pounds of cheese} \\ x\text{ boxes}\rightarrow350\text{ pounds } \end{gathered}[/tex]So, you have
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