Using the profit concept, it is found that:
The inequality is: [tex]1.7x - 179.6 > 0[/tex]The solution is [tex]x > 105.6[/tex]The company must sell at least 106 items to make a profit.Profit is revenue subtracted by operations costs, that is:
[tex]P(x) = R(x) - C(x)[/tex]
In this problem, the functions are:
[tex]R(x) = 7.5x - 100[/tex]
[tex]C(s) = 79.6 + 5.8x[/tex]
Thus, the profit function is:
[tex]P(x) = R(x) - C(x)[/tex]
[tex]P(x) = 7.5x - 100 - 79.6 - 5.8x[/tex]
[tex]P(x) = 1.7x - 179.6[/tex]
It makes a profit if:
[tex]P(x) > 0[/tex]
Thus, the inequality is:
[tex]1.7x - 179.6 > 0[/tex]
The solution is:
[tex]1.7x > 179.6[/tex]
[tex]x > \frac{179.6}{1.7}[/tex]
[tex]x > 105.6[/tex]
Thus, the company must sell at least 106 items to make a profit.
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Which relationship describes angles 1 and 2?
Select each correct answer.
supplementary angles
complementary angles
vertical angles
adjacent angles
Assume that the grasshopper in the food pyramid above must eat half its body weight in grass each day. If an average-size grasshopper weighs 2 grams, and 1 blade of grass weighs 0.1grams (one tenth of a gram), how many blades of grass does the grasshopper need to eat each day?
Answer:
The grasshopper needs to eat 10 blades of grass each day.
Step-by-step explanation:
The grasshopper in the food pyramid above must eat half its body weight in grass each day.
The average weight of the grasshopper is 2 grams.
The weight of one blade of grass is 0.1 grams.
Now,
The weight of grass eating by the grasshopper per day is 1 gram.
Let us assume that the grasshopper eats the "n" number of blades of the grass.
Therefore,
[tex]\begin{aligned}n \times 0.1\;\rm{gm}&=1\;\rm{gm}\\n&=\dfrac{1}{0.1}\\n&=10\end{aligned}[/tex]
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Write three functions.
In the first function, y should vary directly with x.
In the second function, y should vary inversely with x.
In the third function, the relationship between x and y should be neither inverse variation nor direct variation.
Describe the graph of each function and give a real-world example for each.
What is the range of the function f(x) = –2(6x) + 3?
A) (-oo,-2)
B) (-oo,3)
C) [-2,oo)
D) [3,oo
Answer:
The range of the function is (-∞,3)
B is correct.
Step-by-step explanation:
Given: [tex]f(x)=-2(6)^x+3[/tex]
It is an exponential function which coefficient is negative.
Exponential function: [tex]f(x)=ab^x+c[/tex]
If a>0 then range (c,∞)
If a<0 then range (-∞,c)
[tex]-2(6)^x+3\rightarrow ab^x+c[/tex]
[tex]a=-2[/tex]
[tex]c=3[/tex]
Range: (-∞,3)
Hence, The range of the function is (-∞,3)
So i need help (picture included)
suppose that w and t vary inversely and that t=1/5 when w=4. write a function that models the inverse variation and find t when w=9
A. t= 1/5w; 4/45
B. t= 1/5w; 1/5
C. t= 1/20w; 1/80
D. t= 4/5w;4/45
The answer is D. t=4/5w; 4/45
I need help remembering the steps to solve a polynomial equation
Find the function rule.
X: -2, -1, 0, 1, 2
Y: 9,4, -1, -6, -11
The function rule is y = -5x - 1 , obtained by observing the linear relationship where y decreases by 5 as x increases by 1.
To find the function rule that relates the values of x to y , let's first observe the pattern in the given data:
[tex]x & y \\-2 & 9 \\-1 & 4 \\0 & -1 \\1 & -6 \\2 & -11 \\[/tex]
Notice that as x increases by 1, y decreases by 5. This suggests a linear relationship between x and y , where the slope of the line is -5.
The general form of a linear function is ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept.
To find the y-intercept, let's pick any point from the table, for example, when ( x = 0 ), ( y = -1 ).
So, we can plug the values of ( x ) and ( y ) into the linear function formula:
[tex]\[-1 = (-5)(0) + b\][/tex]
[tex]\[-1 = 0 + b\][/tex]
[tex]\[b = -1\][/tex]
Now we have the slope (( m = -5 )) and the y-intercept (( b = -1 )), so the function rule is:
[tex]\[ y = -5x - 1 \][/tex]
Now, let's verify this function rule with another point from the table, for example, when ( x = 2 ):
[tex]\[ y = -5(2) - 1 \][/tex]
[tex]\[ y = -10 - 1 \][/tex]
[tex]\[ y = -11 \][/tex]
This matches the value of ( y ) in the table, confirming that our function rule is correct.
Find the center of the circle whose equation is x² + y² = 4.
Answer:
The center of circle is [tex](0,0)[/tex]
Step-by-step explanation:
We need to find the center of the circle of the equation [tex]x^{2}+y^{2}=4[/tex]
Since, the general equation of circle is [tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex]
Where (h,k) is center of circle and r is radius.
Re-write the circle equation is [tex]x^{2}+y^{2}=4[/tex] as,
[tex]x^{2}+y^{2}=2^{2}[/tex]
Compare [tex]x^{2}+y^{2}=2^{2}[/tex] with [tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex]
so, [tex](x-0)^{2}+(y-0)^{2} = 2^{2}[/tex]
Hence, the center of circle is [tex](0,0)[/tex]
A company produces plates with area A=πr^2, where r is the radius of the plate. Find the inverse by solving for r without switching the variables.
The inverse is r=____
Explain your reasoning.
Final answer:
The inverse of the formula A = πr^2 is found by dividing the area A by π and then taking the square root of the resulting quotient, which gives r = √(A/π). The accuracy of this inverse is limited by the number of significant figures in the original measurement of the radius.
Explanation:
To find the inverse of the formula A = πr^2 for the area of a circle, we want to solve for the radius r in terms of A. We follow these steps:
Starting with A = πr^2, divide both sides of the equation by π to isolate r^2: A/π = r^2.
Take the square root of both sides of the equation to solve for r: r = √(A/π).
The inverse is therefore r = √(A/π).
When using a calculator, it is important to remember that the number of significant figures in a given measurement limits the accuracy of the calculations. As shown in the example, if the radius has two significant figures, the calculated area has to be limited to two significant figures as well, thus A=4.5 m².
How many drivers who start driving before they are 20 are convicted of a traffic violation within the first year of driving?
determine if the number is written in scientific notation. if not explain 5.6 x 10^12
A. no its not written as a power of 10
B.no the first factor is not a number between 1 and 10
C. yes the number is written in scientific notation
Explain your answer please
Answer:
C. Yes, the number is written in scientific notation.
Step-by-step explanation:
We have been given a number [tex]5.6\times 10^{12}[/tex]. We are asked to determine whether our given number is written in scientific notation or not.
We know that when a number greater than 1 and less than 10 is multiplied by a power of 10, then the number is written in scientific notation.
Upon looking at our given number we can see the number 5.6 is between 1 and 10. In addition, 5.6 is being multiplied by 10 to the power 12.
Therefore, our given number is written in scientific notation and option C is the correct choice..
A small toy car costs $3 . A large toy car costs 5 times as much as the small one . Aaron wants to buy one of each . Which equation can he use to find the cost (a) of the two cars ?
(A) 5x a = $3 +. $3
(B) 5x ($3 + $3 ) = a
(C) $3 +(5 x $3 ) =a
(D) (5 x $3 ) \ 3 = a
(/) division
Answer: the answer is B
Step-by-step explanation:
The equation used to find the cost (a) of the two cars will be $3 +(5 x $3 ) =a. The correct option is C.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a small toy car costs $3. A large toy car costs 5 times as much as the small one.
The equation can be written as:-
a = $3 + ( 5 x $3 )
Therefore, the equation used to find the cost (a) of the two cars will be $3 +(5 x $3 ) =a. The correct option is C.
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Which of these numbers is an irrational number? of these numbers is an irrational number? 3⁄5, Square root of 4, Square root of 25, Square root of 20, 5/3
Kenya has 2 hours to work a 100 problem math test. At what rate must she work in order to finish in 2 hours?
A) 0.83 problems per minute
B) 1.23 problems per minute
C) 1.35 problems per minute
D) 1.41
problems per minute
What does this quote tell us about the media’s influence during the Nixon investigation?
"We saw the public man in his first administration, and we were impressed. Now in about 300,000 words we have seen the private man, and we are appalled." – Clayton Kirkpatrick, editor of the Chicago Tribune, a newspaper that published the entire transcript of Nixon’s released communications
A. The media shared real evidence and their opinions on it, which probably influenced citizen opinion. B. The media disapproved of the president’s private actions but still supported and re-elected him. C.The media rallied behind the president because of his great record during his first term in office. D. The media could not publish or discuss real evidence related to the president or the investigation. please help me.
the answer for u is
2 hours=120 minutes
You simply just do 120/100=1.2
So the answer is B. 1.23 or 1.2 (rounded) per minute
Evaluate the exponential expression. Write your answer as a fraction in simplest form.
(2^3)^-2
BRAINLIEST!
A store manager wishes to investigate whether there is a relationship between the type of promotion offered and the number of customers who spend more than $30 on a purchase. Data will be gathered and placed into the two-way table below.
Answer:
D. The manager should check both relative frequencies by row and by column to look for an association.
Step-by-step explanation:
the correct answer would be D
I'm confused on what this is asking me to do. Can someone explain to me, please?
Suppose you’re making a triangle where you know the measures of two angles and the length of the side between those two angles. Write two angle measures and the length of the side between them for your triangle. You can use any measurements you want as long as they could really be used to form a triangle.
45% of 40 is 18% of what number?
Answer:
45% of 40 is 18% of 100
Step-by-step explanation:
45% of 40 is 18% of what number
First we find out what is 45% of number 40
45% times 40
[tex]\frac{45}{100} * 40= 18[/tex]
Now we find
18 = 18% of what number
Let the unknown number be x
18 = 18% * x
[tex]18= \frac{18}{100} * x[/tex]
18 = 0.18 * x
Divide by 0.18 on both sides
100= x
So 45% of 40 is 18% of 100
The complete statement is 45% of 40 is 18% of 100
How to determine the number that completes the statementFrom the question, we have the following parameters that can be used in our computation:
45% of 40 is 18% of what number
Represent the number with x
So, we have
45% of 40 is 18% of x
Express as an equation
45% of 40 = 18% of x
Next, we have
18 = 0.18x
Divide through by 0.18
x = 100
Hence, 45% of 40 is 18% of 100
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abcd is an isosceles trapezoid with legs AB and CD and base BC. If the length of AB is 7y-4, the length of BC s 4y-6 and the length of CD is 8y-18, find the value of y. 30 points for brainliest!
The value of 'y' in the isosceles trapezoid ABCD is 14 and this can be determined by using the properties of isosceles trapezoid.
Given :
ABCD is an isosceles trapezoid with legs AB and CD and base BC.If the length of AB is (7y - 4), the length of BC s (4y - 6) and the length of CD is (8y - 18).The two legs are of equal length In any isosceles trapezoid that means:
7y - 4 = 8y - 18
Add 18 on both sides in the above equation.
7y - 4 + 18 = 8y - 18 + 18
7y + 14 = 8y
Now, subtract 7y on both sides in the above equation.
7y + 14 - 7y = 8y - 7y
Simplify the above expression in order to get the value of 'y'.
y = 14
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The teacher bought new crayons for her class. She bought 7 packs of 9 crayons. She already has 17 crayons in her classroom. She wants to divide the crayons evenly between her 10 students. How many crayons will each student receive? Use c as the variable. Write an equation and solve the problem.
Which property is illustrated by this problem?
(3+4) + 5 = 3 + (4+5)
A. Associate property of addition
B. Additive identity
C. Commutative property of addition
Help please!
The length of a football field is 67 yards greater than the width the perimeter of the field is 346 yard. Find the length and width of the football field.
Find the value of y when x equals -14 -2x-3y=49
Show that all of the powers in the prime-power factorization of an integer n are even if and only if n is a perfect square
HELP ASAP!!!!!!!!!!!!!!!!!!!!
a. 49
b. 12
c. 7
d. 1
Calculate the maximum volume of a box that has no top and that is to be manufactured from a 30 inch by 20 inch piece of cardboard
Evaluate a/b for a= 1/2 and b= - 3/7
A) - 7/6
B) 3/14
C) - 3/14
D) - 32/21
Please explain your answers.
Thanks! : )
Answer: -7/5
Substitute the value of the variable into the expression and simplify.
Exact Form: −7/6
Zaira spent 55 hours in 2 weeks working on a science project. she worked 32 hours the first week. Write and solve an addition equation to find the amount of time she spent working the second week.
0.025 milliliters is the same as: cm3 and L
0.025 milliliters is equal to 0.025 cubic centimeters and 0.000025 liters. The conversion is based on the fact that 1 milliliter is equivalent to 1 cubic centimeter, and there are 1000 milliliters in 1 liter.
To convert 0.025 milliliters to cubic centimeters (cm³) and liters (L), we need to understand the relationships between these units.
Cubic Centimeters (cm³):
Since 1 milliliter is equivalent to 1 cubic centimeter, 0.025 milliliters is equal to 0.025 cubic centimeters.
Liters (L):
There are 1000 milliliters in 1 liter. Therefore, to convert milliliters to liters, we divide the volume in milliliters by 1000.
0.025 milliliters ÷ 1000 = 0.000025 liters.
In summary, 0.025 milliliters is equivalent to 0.025 cubic centimeters and 0.000025 liters.
The question probable may be:
What would be the value of 0.025 milliliters in cm^3 and also in L.
0.025 milliliters is equivalent to 0.025 cubic centimeters because 1 milliliter equals 1 cubic centimeter. Also, 0.025 milliliters is equal to 0.000025 liters as there are 1,000 milliliters in a liter.
Explanation:The student's question is: 0.025 milliliters is the same as how many cubic centimeters (cm3) and liters (L). This is a conversion problem involving units of volume. From the provided information, we understand that 1 milliliter (mL) is exactly equal to 1 cubic centimeter (cm3). Therefore, if the student has 0.025 mL, this is directly equivalent to 0.025 cm3 because the conversion factor between mL and cm3 is 1.
Furthermore, recalling that 1 liter is equal to 1,000 milliliters, and since we are given a volume in milliliters, we can convert this to liters by dividing by 1,000. Consequently, 0.025 mL is equal to 0.025 / 1,000 L, which simplifies to 0.000025 L.