HELP ME OUT PLEASE!!!!!!
What is the range of h?
All real numbers greater than or equal to -5
All real numbers greater than or equal to 0
All real numbers
All real numbers greater than or equal to -2
Answers
The range of the function h(x) is -
"all real numbers greater than or equal to -2"
What are functions?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.Any subset of the Cartesian product of two sets X and Y defines a binary relation R ⊆ X × Y between these two sets.A binary relation is univalent (also called right-unique) if -[tex]${\displaystyle \forall x\in X,\forall y\in Y,\forall z\in Y,\quad ((x,y)\in R\land (x,z)\in R)\implies y=z.}[/tex]
A binary relation is total if -[tex]${\displaystyle \forall x\in X,\exists y\in Y,\quad (x,y)\in R.}[/tex]
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a table representing a function.
Range is defined as the set of all possible values of f(x). Therefore, all real numbers greater than or equal to -2, will belong to the range of the function h(x).
Therefore, the range of the function h(x) is -
"all real numbers greater than or equal to -2"
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Related Questions
2. Higher Order Thinking
Tyler's ruler has
markings every inch. How can he use
the ruler to draw a line that is close to 5
of an inch long?
16
Answers
If you measure a flower stem, its termination will be on the eleventh line from the 5 inch mark. The length of the blossom stem is 5 and 11/16 inches.
What is Measurement?
An object or event's attributes are quantified through measurement so that they can be compared to those of other things or occurrences. Measurement, then, is the process of establishing how big or little a physical quantity is in relation to a fundamental reference quantity of the same kind.
We have to measure 5 inches on scale we have to follow these steps:
Step 1: Get a ruler for inches. There will be 12 lines on the ruler that represent inches, indicating that it is an inch ruler. A foot is equivalent to 12 inches (0.305 m). Inches are divided into each foot. On the ruler, each inch is divided into 15 smaller marks for a total of 16 marks per inch.
Step 2: Find out what an inch is. 12 inch markings make up a ruler. The longest lines on the ruler serve to identify them, which are usually the numbered marks. Put one end of the nail, for instance, directly on the left side of the ruler when you need to measure it. The nail is 5 inches long if it terminates just over the long line next to the big number 5.
Step 3: Discover the 1/2 inch markings. The 1/2 inch marks, which are half as long as the inch marks, will be the second-longest lines on the ruler. Due to the fact that it is just half an inch, each 1/2 inch mark will be placed halfway between each inch number. This indicates that the 1/2 inch lines are located immediately between the 0 and 1 inch, 1 and 2 inch, 2 and 3 inch, and so on across the ruler. On a 12 inch ruler, there are a total of 24 of these marks.
Step 4 : Recognize the 1/4-inch markers. There will be a smaller line that represents a 1/4 of an inch halfway between each 1/2 inch line. These markers will indicate 1/4, 1/2, 3/4, and 1 inch inside the first inch. Despite having separate lines, the 1/2 inch and 1 inch markers are still included in the 1/4 inch measures since 2/4 of an inch equals half an inch and 4/4 of an inch equals one inch. On a 12 inch ruler, there are a total of 48 of these marks.
Step 5: Recognize the 1/8-inch scale. The tiny marks on the ruler that are situated between the 1/4-inch markers are the 1/8-inch marks. There are markers that stand for 1/8, 1/4, 3/8, 1/2, 5/8, 6/8, 3/4, 7/8, and 1 (or 8/8) of an inch between 0 and 1 inch. On a 12 inch ruler, there are 96 of these marks in total.
Step 6 : Recognize the 1/16-inch scale. The little lines at the midpoint of each 1/8 inch represent the 1/16 inch. These are the ruler's tiniest lines as well. The 1/16-inch mark is located on the very first line on the ruler's left side. There are symbols that stand for 1/16, 2/16, 1/8, 3/16, 4/16, 5/16, 6/16, 3/8, 1/2, 9/16, 10/16, 5/8, 11/16, 12/16, 3/4, 13/16, 14/16, 7/8, 15/16, and 16/16 of an inch, respectively, between 0 and 1 inch. There are 192 of these lines on the ruler in total.
Hence, If you measure a flower stem, its termination will be on the eleventh line from the 5 inch mark. The length of the blossom stem is 5 and 11/16 inches.
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Can someone help with this?
Answers
The value of f(x) . g(x) is 3x² + 5x - 2 two linear functions multiplied together to form a quadratic function.
What is a composite function?When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
Given, Are two function f(x) 3x - 1 and g(x) = x + 2.
Now, f(x) . g(x) is nothing but multiplication of f(x) and g(x).
Therefore,
f(x) . g(x) = (3x - 1)(x + 2).
f(x) . g(x) = 3x² + 6x - x - 2.
f(x) . g(x) = 3x² + 5x - 2.
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Write one and four hundredths in standard form.
Answers
Answer:
The answer is 1.04
Step-by-step explanation
For 1.04, 4 is in the hundredths place, and 0 is in the tenths place.
An invertible function is represented by the values in the table.
X
f(x)
-3
-4.4
-2
-0.6
Which graph shows the inverse of this function?
-1
0.8
1
1.2
2
2.6
3
6.4
Answers
A function is invertible if and only if for every y in the range of the function, there is one and only one x in the domain such that f(x) = y. The inverse of a function is a new function that "swaps" the x and y values of the original function.
So, the inverse of a function represented by the table you provided would be a new function where the x values are -4.4, -0.6, 0.8, 1.2, 2.6 and 6.4 and the y values are -3, -2, -1, 1, 2 and 3 respectively.
The graph of the inverse function would be a reflection of the original function over the line y=x, meaning that it would be the same shape but flipped across the line y = x.
Let D(p) be the number of iced cappuccinos sold each week by a coffeehouse when the price is p cents.
a) What does the expression D(225) represent?
b) Do you think that D(p) is an increasing function or a decreasing function? Why?
c) What does the following equation tell you about p? D(p)=180
d) The coffeehouse sells n iced cappuccinos when they charge the average price in their area,
t cents. Thus, D(t)=n . What is the meaning of the following expressions: D(1.5t), 1.5D(t), D(t+50), D(t)+50?
Answers
a) The expression D(225) represents the number of iced cappuccinos sold each week by a coffeehouse when the price is 225 cents.
b) Whether D(p) is an increasing or decreasing function depends on the relationship between the price of iced cappuccinos and the number sold. If the price of iced cappuccinos increases, the number sold may decrease (decreasing function) or if the price of iced cappuccinos decreases, the number sold may increase (increasing function) . It's possible that the coffeehouse has made a market research and they know what is the best price for their iced cappuccinos.
c) The equation D(p) = 180 tells you that the coffeehouse sells 180 iced cappuccinos each week when the price is p cents.
d) D(1.5t) represents the number of iced cappuccinos sold each week when the price is 1.5t (1.5 times the average price in the area). 1.5D(t) represents the number of iced cappuccinos sold each week when the price is the average price in the area multiplied by 1.5. D(t+50) represents the number of iced cappuccinos sold each week when the price is t+50 (50 cents more than the average price in the area). D(t)+50 represents the number of iced cappuccinos sold each week when the price is the average price in the area plus 50.
It's important to note that all these expressions doesn't give us any information about the relation between price and quantity sold, they just give us the value of the function for specific values of p.
Please HELP
Tyshawn is ordering a taxi from an online taxi service. The taxi charges four dollars for just a pick up then an additional $1.50 per mile driven. write a linear function in the form of (y= mx+b) to represent the situation.
Answers
The linear function in the form is y = 4x + 1.5 to the situation.
What is meant by function?
Functional refers to an object's operation or usefulness. It also denotes that it relates to how it performs or operates.A mathematical machine known as a function accepts one or more numbers as inputs and outputs another number.One or more functions may be inputs to a functional, which outputs a number. A Functional is a function of Functions, then.All biological activities, including digestion, elimination, respiration, and others, can be performed by a cell.The functional unit of life is referred to be such for this reason. Each and every living thing is made up of cells, which are the smallest unit of life.Initial fee: $4
Per mile: $1.50
Set up an equation where = the taxi charges
Using y = mx + b form:
y = 4x + 1.5
The linear function in the form is
y = 4x + 1.5
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I NEED HELPPPPP PLS HELP
Answers
A cube is a three-dimensional shape with all sides of equal length, width, and height. If the length of the packaging box is 4xy, then all the sides of the cube have the same length 4xy.
What is the straightforward meaning of volume?
The volume of an object is the area occupied inside its three-dimensional boundaries. It is referred to as the object's capability on occasion.
To find the volume of a cube, we use the formula: volume = side x side x side = (side)^3
Therefore, the volume of the packaging box in terms of x and y is (4xy)^3 = (4xy)(4xy)(4xy) = (4xy)^3 = (4x)^3 * y^3 = 64x^3 * y^3
So the volume of the packaging box is 64x^3 * y^3 cubic units.
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Suppose that a firm produces 275,000 units a year and sells them all for $8 each. The explicit costs of production are $1,800,000 and the implicit costs of production are $400,000. The firm earns an accounting profit of
Answers
The firm's accounting profit earnings as required to be determined in the task content is; $0.
What is the firm's accounting profit earnings?As evident in the task content, the firm produces 275,000 units a year and sells them all for $8 each.
Therefore, the total revenue generated from sales is; 275,000 × $8 = $2,200,000.
Hence, since the total cost is the sum of $1,800,000 and $400,000 which is; $400,000 + $1,800,000 = $2,200,000.
Ultimately, the total accounting profit earned is; Revenue generated - Expenses = $2,200,000 - $2,200,000 = $0.
Therefore, the total accounting profit earned is; $0.
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I need help solving this
Answers
The cylinder has a volume of 150.796 in³. The cylinder has a surface area of 175.929 in².
What's volume of cylinder ?The quantity of three-dimensional space that an object or closed surface occupies is referred to as volume in mathematics. The cubic units of volume are m³, cm³, in³, and so on.
How does surface area work?The sum of all of an object's faces is its surface area in three dimensions. Wrapping, painting, and finally building things to achieve the best possible design are examples of real-world applications of the concept of surface areas.
Evaluating :Given that a volume of cylinder = h × r² × π
h = 12 in
r = 2 in
volume = ?
Volume of cylinder = h × r² ×π
= =12 × 3.14×(2)²
=37.68 × 4
=150.796 in³
B). Surface area of cylinder= 2πr² + 2πrh
=2× 3.14 × (2)²+2× 3.14× 2×12
=175.929in²
The formula V=r²(h) can be used to determine a cylinder's volume. Simply multiplying the area of the circular base shape by the height is all that is required to determine a cylinder's volume.
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Kent completed his homework in 52.752 minutes. What is this number rounded to the nearest tenth? Explain how you decided.
Answers
Answer:52.8
Step-by-step explanation:
52.752
in 752 is more than 5 so it gets rounded to 8so it = 52.8
Let f be a continuous function that is defined for all real numbers x and that has the following properties. (0) (x) dx = 1 (ii) S S(x)dx = 10 (a) Find the average (mean) value of f over the closed interval (1,3). (b) Find the value of (25(x)+6)dx. (c) Given that f(x) = ax +b, find the values of a and b.
Answers
The value of a and b is -5/4. The value describes the value of each digit in relation to its position in the number.
What is meant by real numbers?A quantity in mathematics that can be represented by an infinite decimal expansion. In contrast to the counting-derived natural numbers 1, 2, 3,..., real numbers are used to quantify constantly altering quantities such as size and time. The kind of number we typically use, such 1, 15.82, 0.1, 3/4, etc. Real Numbers can be positive or negative, big or tiny, whole values, fractions, or decimal numbers. They are not imaginary numbers, which is why they are termed "Real Numbers." A extremely large actual number is one billion (1,000,000,000). Three types of numbers fall under the heading of "real numbers," which we will discuss in a moment. Real numbers include all types of numbers, including whole, rational, and irrational numbers.(a) Mean Value = [tex]\frac{1}{3-1} \int_1^3 f(x)=\frac{1}{2}-\frac{5}{2}=\frac{5}{4}[/tex]
b) [tex]} \int_3^5 f(x) d x=\int_1^5 f(x) d x-\int_1^3 f(x) d x=10-\frac{5}{2}=\frac{15}{2} \\[/tex]
[tex]& \left.\int_3^5(2 f(x)+6) d x=2 \int_3^5 f(x) d x+6 \int_3^5 d x=2\left(\frac{15}{2}\right)+6 x\right]_3^5=15+6(2)=27 \\[/tex]
c) [tex]} f(x)=a x+b \\[/tex]
[tex]& \left.\int_1^3(a x+b) d x=\frac{a x^2}{2}+b x\right]_{x=1}^3=\frac{9}{2} a+3 b-\frac{a}{2}-b=4 a+2 b=\frac{5}{2} \\[/tex]
Simplifying,
[tex]\left.\int_1^5(a x+b) d x \cdot \frac{a x^2}{2}+b x\right]_{x=1}^5=\frac{25 a}{2}+5 b-\frac{a}{2}-b=12 a+4 b=10 \\[/tex]
[tex]4 a+2 b=5 / 2 \stackrel{n-3}{\rightarrow}-12 a-6 b=-15 / 2[/tex]
Then we get,
[tex]12 a+4 b=10[/tex]
[tex]$ \frac{12 a+4 b=20/2}{ -2 b=5 / 2} b=\frac{-5}{4}[/tex]
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Find a positive value c, for x, that satisfies the conclusion of the Mean Value Theorem for f(x) = 3x^2 - 5x + 1 on the interval [2, 5]. A) c=1 B) c = 0 C)c= 16 D) c=13/6 E) c=7/2
Answers
The Mean Value Theorem states that there exists a point c in the interval of the given function such that the derivative of the function at this point is equal to the average rate of change of the function on the interval. In this case, c = 7/2 satisfies the theorem for f(x) = 3x^2 - 5x + 1 on the interval [2, 5].
Using the Mean Value Theorem, we can find c by solving the equation 3c^2 - 5c + 1 = (3(5)^2 - 5(5) + 1 - (3(2)^2 - 5(2) + 1)) / (5 - 2). Simplifying, we get c = 7/2.
The Mean Value Theorem states that there exists a point c in the interval of the given function such that the derivative of the function at this point is equal to the average rate of change of the function on the interval. To find this point c, we must solve the equation
3c^2 - 5c + 1 = (3(5)^2 - 5(5) + 1 - (3(2)^2 - 5(2) + 1)) / (5 - 2).
This simplifies to c = 7/2, which means that this value of c satisfies the conclusion of the Mean Value Theorem for
f(x) = 3x^2 - 5x + 1
on the interval [2, 5]. This means that for any value of x within the interval, the rate of change of the function is always equal to 7/2.
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jan is laying her tile in the kitchen. the rectangular floor dimensions are 12 ft by 16 ft. it's costs $3.25 per square foot for installation. How much will jan's remodel cost?
Answers
The amount of money which Jan's remodel would cost is equal to $624.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width of a rectangle.L represents the length of a rectangle.Substituting the given points into the area of rectangle formula, we have the following;
Area of rectangle = 12 × 16
Area of rectangle = 192 square feet.
For the total cost, we have the following;
Total cost = Area of remodel × cost per square foot.
Total cost = 192 × 3.25.
Total cost = $624.
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if the probability of a hen truly having french citizenshi pis 0.81, find the proability of exactly two french hens our of the three
Answers
The binomial probability formula calculates the probability of getting exactly "x" successes in "n" independent trials, where each trial has a probability "p" of success.
In this case, the success is a French hen, with probability 0.81, and the number of trials is 3 (the number of hens).
The binomial coefficient "n choose x" represents the number of ways to choose "x" successes from "n" trials. It can be calculated as:
(n choose x) = n! / (x! * (n-x)!)
where n! is the factorial of n, which is the product of all positive integers up to n.
Plugging in the values from the problem, we have:
P(X=2) = (3 choose 2) * (0.81)^2 * (0.19)^1
= (3! / (2! * (3-2)!) ) * (0.81)^2 * (0.19)^1
= 3 * 0.81^2 * 0.19
= 0.324
So, the probability of getting exactly 2 French hens out of 3 is approximately 0.324.
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SOMEONE HELP ME PLEASE I WILL GIVE BRAINLIEST QUICK
Answers
Answer:
Shape A: 647 (area) and 120 (perimeter)
Shape B: 192 (area) and 70 (perimeter)
Step-by-step explanation:
For shape A, we can find the area by:
- splitting the rectangle into 2 (horizontally), one that will have 16 and 12 as the sides, and another with 35 and 13 as the sides. Then, we can multiply the two rectangles and add them to find the area: (16*12) + (35*13) = 647
We can find the perimeter by:
- adding all the numbers: 25+16+12+19+13+35 = 120
For shape B, we can apply the same method as shape A:
- Area: (12*8) + (8*12) = 192
- Perimeter: 12+8+8+7+7+8+8+12 = 70
Answer:
Shape a) Area: (25*16)+(19*13)=400+247=647
Perimeter: 16+12+19+13+35+25=120
Shape b)Area: (12*8)+(12*8)=96+96=192
Perimeter: 12+8+7+8+12+8+7+8 = 70
To find volume: calculate volume of each rectangle, then add them.
[tex]V=Length*width[/tex]
I've highlighted which rectangle to calculate.
To find perimeter: add up all sides.
whats the puzzle answer? i need help on this
Answers
Answer:
next person to answer give them the brainly crow
Step-by-step explanation:
PLEASE HELP WITH 6 THANKS SO MUCH ILY I WILL DO ANYTHING U WANT
Answers
Answer:
A=22 dots
B=51 squares
C=number of squares = the number of squares times 2, plus 2
Step-by-step explanation:
A-
10*2=20
20+2=22
B-
104-2=102
102/2=51
C-
there is only one row so that adds 2 dots and then you multiply the number of squares by 2 then add 2 to the product
Answer:
a) 22 dots
b) 51 squares
c) Number of dots = 4 + 2 x (number of squares - 1)
Step-by-step explanation:
Actually, in this question you are better off solving c) first for the formula and then using it to solve a) and b)
Let's look at the relationship between squares and dots:
Number of squares Number of dots
1 4
2 6
3 8
You can see that as the number of squares increases by 1, the number of dots increases by 2 with 4 dots as the starting point
We can easily come up with a formula by treating this as an arithmetic sequence.
The number of dots represents the term # and the number of dots the actual term value
The difference between consecutive terms is 2 and is called the common difference (d)
The nth term will be referred to using aₙ
So we have
a₁ = 4
a₂ = 6
a₃ = 8
The nth term of any arithmetic sequence is
aₙ = a₁ + d(n-1) where d is the common difference
This is the answer to c). Translating to dots and squares we get
Number of dots = 4 + 2 x (number of squares - 1)
a) Use the formula
a₁₀ = 4 + 2(10-1) = 4 + 2 x9 = 4 + 18 = 22 dots
b) Here we are given the value of term = 104
Substituting we get
104 = 4 + 2(n-1)
104-4 = 2(n-1)
100 = 2(n-1)
n-1 = 100/2 = 50
n = 51
That means the there are 51 squares in the diagram which has 104 dots
Kazuko says the expressions 5x and 6 - x are equivalent expressions, because you
can substitute 1 for x in both expressions and get the same result. Is Kazuko's
reasoning correct? Explain.
Answers
Answer:
Yes, Kazuko's reasoning is correct
Step-by-step explanation:
If u substitute 1 in place of x in both expressions, they both equal 5 when solved
the first pentagon is dilated to form the second pentagon. drag and drop the answer to correctly complete the statement. put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse. the scale factor is response area. a pentagon with a side length of 5. an arrow points to a smaller pentagon with a side length of 1
Answers
The scale factor of the dilated pentagon is the ratio of the side length of the original pentagon to the side length of the dilated pentagon.
In this case, the side length of the original pentagon is 5 and the side length of the dilated pentagon is 1. Therefore, the scale factor is 5:1 or 5/1. To calculate the scale factor, divide the side length of the original pentagon by the side length of the dilated pentagon. In this case, the calculation would be 5 / 1 = 5. The scale factor of the dilated pentagon is 5.
We can also use the formula for finding the scale factor of two figures: Scale Factor = Length of figure 1 / Length of figure 2. In this case, the length of figure 1 is 5 and the length of figure 2 is 1. So, the scale factor is 5.
Therefore, the scale factor of the first pentagon to the second pentagon is 5.
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a gallup poll report revealed that 72% of teens said they seldom or never argue with their friends. Yvonne wonders whether this result holds true in her large high school. so she surveys a random sample of 150 students at her school.
Answers
It is likely that the result of the Gallup poll generally holds true for Yvonne's school.
Yvonne can calculate the sample proportion of teens who report that they seldom or never argue with their friends by using the formula:
P = (number of teens who report that they seldom or never argue with their friends / sample size)
For Yvonne's survey of 150 students, if 108 of them report that they seldom or never argue with their friends, then the sample proportion is:
P = (108/150) = 0.72
This result is very close to the 72% reported in the Gallup poll. Therefore, it is likely that the result of the Gallup poll generally holds true for Yvonne's school.
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Solve the following linear equation.
4x+8=4(x+4)−8
Answers
The equation 4x+8=4(x+4)−8 can be simplified by distributing the 4 on the right side of the equation:
4x+8=4x+16-8
Subtracting 4x from both sides:
8=16-8+8
Which simplifies to:
8=8
This is a true statement, so x could be any real number. The solution to the equation is x is any real number or x∈R.
Divide the following and then check by multiplying.
7)84
Select the correct choice below and, if necessary, fill in the answer box to complete your choice
OA. The quotient does not have a remainder. The quotient is
B. The quotient has a remainder not equal to 0. The quotient is
OC. The quotient is undefined.
help!
Answers
If a company has issued 2 million shares, the share price is $125 per share, and the company has generated $18 million in earnings, calculate the PE ratio. Give your answer to 2 decimal places.
Answers
Answer:
P/E = 125/9= 13.89:1
Step-by-step explanation:
2mm shares at $ 125/share
18mm earnings so earnings per share EPS = 18/2 =9
The P/E ratio is calculated by dividing the stock's current price by its latest earnings per share.
P/E = 125/9= 13.89:1
Answer:
Step-by-step explanation:
The earnings per share can be calculated as
Earnings per Share =Total EarningsTotal Shares=$18,000,0002,000,000=$9.
Therefore the PE ratio is
PE Ratio =$125$9≈13.89.
9. Choose Efficient Methods Explain
how you can make 5-3 a simpler
problem. Then subtract.
7
10
Answers
The lowest corresponding fraction of the integer is its simplest form. so we get the answer is 0.96.
What is an efficient strategy?A method is considered efficient if it can generate an answer quickly and without needing a page of computations. A successful strategy is one that solves every issue of a certain class (i.e., one that is generalizable to many problems using the same operation).
The lowest corresponding fraction of the integer is its simplest form.
Take the denominator's LCM as the first step. Step 2: Multiply the numerator and the denominator by the same number to convert the denominators to the LCM Value. Step 3: Subtract the numerator once the denominator is equal. Step 4: If required, simplify the resultant fraction.
5-3 a simpler problem. Then subtract.7 /10
5 / 3 - 7 / 10 =
50 - 21 / 30 = 29 / 30 = 0.96 .
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if Q(x)=8x^2+10 find Q(1/4)
Answers
The value of Q (1/4) as required to be determined in the task content is; 10 ½.
What is the value of the function instance Q (1/4)?It follows from the task content that the value of the function instance Q (1/4) is to be determined based on the given function definition; Q(x)=8x^2+10.
Hence, since the given function is; Q (x) = 8x² + 10.
The function instance Q (1/4) can be evaluated as follows;
Q (1/4) = 8 ( 1/4 )² + 10
= 8 • 1/16 + 10
= 1/2 + 10
= 10 ½.
Ultimately, the value of the function instance Q (1/4) is; 10 ½.
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PLEASE WHAT IS THIS?!!? WHATS THE ANSWER?
Answers
Answer: bottom right
A market strategy is implemented in order to expedite the placement of collaborators towards economically affected groups. These measures should not be seen in a lucrative way and for this reason they plan that their income from "q" collaborators, will be part of a function I(q)=60q-0.02q^2. The initial cost of the expenses is $300 for rights, in addition it would have unit costs per worker equivalent to $50.
a) Calculate the model that would explain the utility that could be obtained.
b) Determine the number of workers that would originate the maximum benefit for the collaborators. How much is this utility?
c) Represent the income function graphically, obtain the maximum income and interpret it.
Answers
The model that would explain the utility is U(q) = - 0.02q^2 - 300 + 10q.
The maximum number of workers is 250 and utility is 950
The model that would explain the utilityFrom the question, we have the following parameters that can be used in our computation:
The total income as I(q) = 60q - 0.02q^2.
The total cost as C(q) = 300 + 50q.
The utility model can then be calculated as
U(q) = I(q) - C(q)
So, we have
U(q) = 60q - 0.02q^2 - 300 - 50q.
U(q) = - 0.02q^2 - 300 + 10q.
The maximum number of workers and utilityWe have
U(q) = - 0.02q^2 - 300 + 10q.
Differentiate and set to 0
-0.04q + 10 = 0
So, we have
-0.04q = -10
This gives
q = 250 --- max workers
Recall that
U(q) = - 0.02q^2 - 300 + 10q.
So, we have
U(250) = - 0.02* 250^2 - 300 + 10 * 250
U(250) = 950 --- amount of utility
The income functionSee attachment for the graph of I(q)=60q-0.02q^2
On the graph, we have the interpretation to be a maximum income of $45000 at 1500 workers
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the steps on how to solve multiplying rational expressions involving quadratics with leading coefficients of 1
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Fully factor the numerator and denominator of each rational expression. Write as one fraction by multiplying the numerators together and multiplying the denominators together.
Multiplication:
Step 1: Factor both the numerator and the denominator.
Step 2: Write as one fraction. Write it as a product of the factors of the numerators over the product of the factors of the denominators. DO NOT multiply anything out at this point.
Step 3: Simplify the rational expression.
Step 4: Multiply any remaining factors in the numerator and/or denominator.
Multiplying Rational Expressions Involving Quadratics with Leading Coefficients of 1
Step 1: Fully factor the numerator and denominator of each rational expression.
Step 2: Write as one fraction by multiplying the numerators together and multiplying the denominators together.
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Find the value of 80 ÷ 10^4. Explain the change in value between 80 and 80 ÷ 10^4.
Answers
Answer:
8÷10^3 (8×10^-3)
Step-by-step explanation:
8÷1000 can be considered final answer
And can be written 8÷10^3 or 8×10^-3
[tex]80÷10^4
\\ =80÷10000
\\ = \frac{80}{1000} (multiply \: and \: divide \: left \: and \: right) \\ = \frac{8}{1000} = \frac{1}{125} (cancel \: common \: factor \: 8)
[/tex]
A sphere of radius r is cut by a plane h units above the equator, where h < r. Find the volume of solid (spherical segment) above the plane.____A manufacturer drills a hole through the center of a metal sphere of radius R. The hole has a radius r. Find the volume of the resulting ring.____
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The volume of the spherical segment above the plane is[tex](1/3) *\pi * (r^2 - (r-h)^2) * h[/tex] and the volume of the ring resulting from drilling a hole through the center of a sphere is [tex]\pi * (R^2 - r^2) * R.[/tex].
A sphere of radius "r" is cut by a plane "h" units above the equator. To find the volume of the solid (spherical segment) above the plane, we first need to find the height of the segment, which is (r - h). Then, we can use the formula for the volume of a spherical segment: [tex](1/3) * \pi * (r^2 - (r-h)^2) * h.[/tex]
A manufacturer drills a hole through the center of a metal sphere of radius R. The hole has a radius r. To find the volume of the resulting ring, we can use the formula for the volume of a cylindrical ring: [tex]\pi * (R^2 - r^2) * h[/tex], where h is the height of the ring. Since the hole goes all the way through the sphere, the height of the ring is equal to the radius of the sphere, R. So the volume of the ring is [tex]\pi * (R^2 - r^2) * R[/tex].
In the first problem, the volume of the solid (spherical segment) above the plane is [tex](1/3) * \pi * (r^2 - (r-h)^2) * h[/tex]. In the second problem, the volume of the resulting ring is [tex]\pi * (R^2 - r^2) * R.[/tex]
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