12.5ml of a 60% solution is required to create 50ml of a 15% amount solution. You can compute this using a proportion.
50% x 15% = 7.5 ml, and 7.5 ml x 60% = 12.5 ml
12.5ml of a 60% solution is required to create 50ml of a 15% solution. You can compute this using a proportion. To begin with, we must ascertain how much of the 15% solution is required to make 50ml. To accomplish this, multiply 50 ml by 15%, which yields the answer of 7.5 ml. This means that to make 50ml, 7.5ml of the 15% solution is required. The next step is to calculate how much of the 60% solution is needed to create 7.5ml. To do this, divide 7.5 ml by 60%, which yields the result 12.5 ml. This indicates that in order to create 50ml of the 60% solution, 12.5ml of the 60% solution
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Let F be a function defined for all the nonnegative integers by thefollowing recursive definition.F(0) = 0, F(1) =1F(n+2) = 2F(n) + F(n+1),n Image for Let F be a function defined for all the nonnegative integers by thefollowing recursive definition. F(0) = 0, 0Compute the first six values of F;that is, write the values of F(n) for n = 0, 1, 2, 3, 4, 5.I started off just plugging in 0 andgotF(0+2) = 2F(0) + F(0+1)= 2 = 2(0) + 1= 2 = 3
The first six values of the recursive function F(n+2) = 2F(n) + F(n+1) are 0, 1, 1, 3, 5, and 11.
We are given a recursive function:
F(0) = 0, F(1) = 1
F(n+2) = 2F(n) + F(n+1) , n ≥ 0
For n = 0:
F(0+2) = 2F(0) + F(0+1)
F(2) = 2(0) + 1
F(2) = 1
For n = 1:
F(1+2) = 2F(1) + F(1+1)
F(3) = 2(1) + 1
F(3) = 3
For n = 2:
F(2+2) = 2F(2) + F(2+1)
F(4) = 2(1) + 3
F(4) = 5
For n = 3:
F(3+2) = 2F(3) + F(3+1)
F(5) = 2(3) + 5
F(5) = 11
Hence, F(0) = 0, F(1) = 1, F(2) = 1, F(3) = 3, F(4) = 5, F(5) = 11.
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Alan ran 3.1 miles in 35 minutes. Courtney ran 3.1 miles 5 minutes faster than Alan. Which number line can be used to find how long it took Courtney to run 3.1 miles?
A number line starting from 0 and directed to +30 represents how long it took Courtney to run 3.1 miles
What are algebraic expressions?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 that Alan ran 3.1 miles in 35 minutes and Courtney ran 3.1 miles 5 minutes faster than Alan.
It is given that Courtney ran 3.1 miles 5 minutes faster than Alan. This means that he runs 3.1 miles in (35 - 5) or 30 minutes.
Therefore, a number line starting from 0 and directed to +30 represents how long it took Courtney to run 3.1 miles.
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A fitness center uses a linear model to advise its customers on what their ideal weight should be based on their height. Height as an input is measured in inches (in), and weight as an output is measured in pounds (lbs).
a) The fitness center told two customers that they are at ideal weights. Customer A is 80 inches tall and weighs 200 pounds. Customer B is 5 feet tall and weighs 100 pounds. Determine the slope of the line that represents the relationship between height and weight that the fitness center uses.
b) Use the slope found in part a and the given information to write the point-slope form of the line. c) convert the point slope form of the line found in part b to its slope intercept form, and use it to graph the linear model the fitness center uses. be sure to plot the points given in part a.
d) What is the y-intercept of this linear relationship? What is the meaning of the y-intercept in this context? Does it make sense?
e) If a customer is 85 inches tall and weighs 250 pounds, would the fitness center tell them that their weight is ideal?
f) What would the fitness center recommend to the customer in part e?
Answer:
a) The slope of the line that represents the relationship between height and weight is 0.2 (lbs/in).
b) The point-slope form of the line is: y - 200 = 0.2 (x - 80).
c) The slope intercept form of the line is: y = 0.2x + 40. The graph of this line with the two points can be seen below:
d) The y-intercept of this linear relationship is 40. This means that if a person's height is 0 inches, their ideal weight should be 40 pounds. This makes sense as it is not possible to have a negative height.
e) No, the fitness center would not tell the customer in part e that their weight is ideal, as the linear model suggests that their ideal weight should be 200 pounds, which is lower than the 250 pounds they weigh.
f) The fitness center would recommend that the customer in part e should aim to weigh 200 pounds.
Mark Me as A Brainelistif f(x) = 3x^2 - 2x +4 and g(x) = 3x - 15
find g(f(x))
Answer: [tex]g(f(x))=9x^2 -6x-3[/tex]
Step-by-step explanation:
[tex]g(f(x))=g(3x^2 -2x+4)=3(3x^2 -2x+4)-15=9x^2 -6x+12-15=9x^2 -6x-3[/tex]
henry bought 5\6 pound of roasted almonds for $5. He wants to know the price per pound.
Answer:
The price per pound is $6.00
Step-by-step explanation:
[tex]\frac{5}{\frac{5}{6} }[/tex] Means the same as
[tex]\frac{5}{1}[/tex] x [tex]\frac{6}{5}[/tex] = 6
The price per pound is $6.00
Which question can he answer using the diagram?
The diagram represent the process of photosynthesis. Using the diagram he can answer the question of (b) What are the inputs and outputs in the process of photosynthesis.
What is called photosynthesis?Plants and other living things employ a process called photosynthesis to transform light energy into chemical energy that can then be released through cellular respiration to power the organism's activities. The process of creating sugars and starches from carbon dioxide and water also known as photosynthesis stores some of this chemical energy in these molecules.
The majority of the energy required for life on Earth is produced and maintained by photosynthesis, which is also substantially responsible for producing and maintaining the oxygen content of the atmosphere.
In this diagram, arrow represent the direction of elements of process.
SO that, Using the diagram he can answer the question of (b) What are the inputs and outputs in the process of photosynthesis.
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This question is related to biology.
What is the value of x at which the minimum value of y = 3x4/3 - 2x occurs on the closed interval (0.11 1 (A) 0 (B) 1/8 )C) 1/2 ( D) 1
The value of x at which the minimum value of y occurs in [0, 1] is B) 1/8
Given y = 3x^(4/3) - 2x
We are asked to determine the value of x at which the minimum value of y occurs in [0, 1].
Now, dy/dx = 0
4x^(1/3) - 2 = 0
x^(1/3) = 1/2
x = 1/8
Here, dy/dx = 0 when x = 1/8
So calculating y at x = 0, 1/8, 1
y(x = 0) = 0
y(x = 1/8) =3 (1/8)^(4/3) - 2/8 = -1/16
y(x = 1) = 1
Hence, y has a minimum value of -1/16 at x = 1/8
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can someone please help me(10 points will give brainliest!!!)
The correct expression is (x+9)/2, The smallest number is 0.104.
The lowest of the following is which?Compare all the digits in ascending order before the decimal, then all the digits in ascending order after the decimal, to find the smallest number.
Sort the following integers in ascending order: 0.1, 0.005, 1000, 1.001, 100, 0.05. The sequence is as follows:
0.005, 0.050, 0.1, 1.001, 100, 1000.
Because the 5 in 0.050 is in the hundredths place whereas the 5 in 0.005 is in the thousandths place, 0.005 is smaller than 0.050.
When we compared two decimal values in Example 1, we saw that 0.2 is greater than 0.15.
The smallest number is 0.104.
The correct expression is (x+9)/2
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in 1998, the university of wisconsin collected data on means of transportation to work. in 2008, betsy (a university of minnesota student) used the data for her own project. betsy is using which data collection method? secondary analysis evaluation research survey experiment field research.
in 1998, the university of Wisconsin collected data on means of transportation to work. in 2008, Betsy (a university of Minnesota student) used the data for her own project. betsy is using Secondary analysis collection method.
Secondary data is information gathered by someone other than the original user. It signifies that the data is already accessible and has been analyzed. Magazines, newspapers, books, and journals are examples of secondary data. It might be published or unpublished data.
Secondary analysis is the use of existing data acquired for the purposes of a previous study to pursue a research interest that is unique from the original work; this might be a new research topic or an alternate viewpoint on the original subject.
Secondary research methods commonly used include data acquisition via the internet, libraries, archives, schools, and organizational reports.
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There are five consecutive odd integers. The sum of the three least integers is more the sum of the 2 greatest. Find the 5 integers
Answer:
The five consecutive odd integers are 11 , 13, 15, 17, and 19. The sum of the three least integers (11+13+15) is 39, and the sum of the two greatest (17+19) is 36.
In a triangle, its height and base have d total length of 45 cm. Find the area of the triangle if its height is twice of its base.
Answer:
Area of Triangle is 225 cm^2
Step-by-step explanation:
Let height of triangle be h
Let the base of triangle be b
It is given that the sum of base and height is 45
b + h = 45 ---------(1)
It is also given that the height is twice of base
2b = h ---------------(2)
by substituting (2) in (1)
b + 2b = 45
3b = 45
b = 15 cm
15 + h = 45
h = 30 cm
Area of triangle is given as
1/2 x b x h
= 1/2 x 15 x 30
= 225 cm^2
The sides of a 45 degree angle and a ______________ degree angle form a straight line.
180
225
270
The angle of the other side of the angle that forms a straight line equals 225°.
What kind of angle does form a straight line?
In this problem we find the case of an angle that generates a straight line. Angles are geometric constructions formed by two semirrays with a common origin.
Straight angles are angles whose measure equals 180° and it may represent a straight line. Then, if one side has a measure of θ degrees, then the measure of the other side is equal to θ + 180°.
If we know that θ = 45°, then the measure of the other side is:
θ' = 45° + 180°
θ' = 225°
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[tex]3\sqrt{6} -2\sqrt54[/tex]
If triangle ABC has the following measurements, find the measure of side c: a = 9 b = 12 C = 64°
A) 18.61
B) 11.42
C) 17.88
D) 5.56
Answer:
B) 11.42
Step-by-step explanation:
Using the Law of Cosines:
[tex]c=\sqrt{a^2+b^2-2ab \cos C}=\sqrt{9^2+12^2-2(9)(12)\cos 64^{\circ}} \approx 11.42[/tex]
what is the function header of the following function?
The Function Header includes the name of the function .
it tells us what type of data it expects to receive and the type of data it will return to the calling function or program.
The body of the function contains the instructions to be executed.
Three parts of function header,
1- return type
2- function name
3- argument list
The function's name is included in the header, which also provides information about the parameters and the type of data the function will return to the caller function or application. The instructions that must be followed are contained in the function's body.
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The complete question is :-
what is the function header and its parts?
Janae and Jerome each have m marbles. Gwen has 4(m + 2) marbles. John has 8m + 4 marbles. If John has more marbles than Janae, Jerome, and Gwen combined, how many marbles might Janae and Jerome each have? Select each possible answer.
The number of the marbles each of them have are 12.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Janae and Jerome each have m marbles. Gwen has 4(m + 2) marbles. John has 8m + 4 marbles.
The number of marbles will be calculated as:-
4(m + 2) = 8m + 4
4m + 8 = 8m + 4
4m = 4
m = 1
Gwen = 4(m + 2) = 4 ( 1 + 2 ) = 12
John = 8m + 4 = 8 + 4 = 12
Hence, the number of the marbles each of them have are 12.
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Yesterday, a movie theater sold 307 bags of popcorn. A large
bag of popcorn costs 3. A small bag
of popcorn costs $1. In all, the movie theater made 509 from popcorn sales. Write and solve a
system of equations to find how many bags of each size of popcorn were sold.
On simplifying the equations and using mathematical operations, 203 $1 bags were sold,
How can math be simplified?Mathematical operations can be made more simpler by using the right order of operations. Exponents, terms in parentheses, multiplying, division, addition, and ultimately subtraction are the right order of operations. You can use the acronym PEMDAS to help you remember this.
Pricing times units sold equals revenue, thus if N is the total amount of $3 bags sold, then 307 - N must represent the amount of $1 bags sold (total sales)
3(N) + 1(307-N) = 515 simplify
3N + 307 - N = 515
2N + 307 = 515 Take 307 off both sides.
Divide both sides by 2 if 2N = 208.
The overall amount of $3 bags sold is N = 104.
203 $1 bags were sold, which is 307 - 104.
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I NEED HELP I WILL AWARD 80 POINTS!!!
Hello!
To solve the first problem:
Radii are lines that go from the center of a circle to the edge. There are three of these lines in this circle.
The radii for this circle are lines AD, AC, and AD.
The correct answer choice is answer choice C.
To solve the second problem:
We have two congruent triangles. This means that their sides and angles are identical. We need to find the angles that are equal to that of angles A and C in triangle one.
These would be angles D and F.
The correct answer choice is answer choice A.
Hope this helps!
The length of a living room is 12 feet and its width is 1012feet. The length of the room is being expanded by x feet. Select all the expressions that represent the area of the living room in square feet.
The area of living room is (126 + 10.5x) square feet. The solution has been obtained by using area of rectangle.
What is area of rectangle?
The territory a rectangle occupies inside its four sides or limits is known as its area.
We are given that the length of the room is being expanded by x feet.
This means that the extended length of the room is (12 + x) feet
We are given width of the room to be 10.5 feet
We know that area of a rectangle = length * width
So,
⇒Area = (12 + x) * 10.5
⇒Area = (126 + 10.5x) square feet
Hence, the area of living room is (126 + 10.5x) square feet.
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On a paper sketch the algebra tile shape at right. Write an expression for perimeter and then find the perimeter for each of the given values of x.
According to the problem the algebra tile shape is 13.
What is algebra?Algebra is a branch of mathematics that uses symbols to represent numbers and operations. It helps us to solve problems by using equations and formulas. Algebra is used in many fields, including science and engineering. It is used to solve equations, simplify expressions, and graph functions. Algebraic equations can be used to describe and analyze relationships among different variables. Algebra is also used in applications such as financial planning, engineering, and computer programming. Algebraic equations can be used to solve real-world problems, such as calculating the area of a triangle or finding the maximum profit in a business.
The algebra tile shape at right can be represented as follows:
(x + 1)(x + 2)
The perimeter of the shape can be calculated by adding up the lengths of the four sides. The expression for perimeter is therefore:
Perimeter = 2x + 3
For x = 5, the perimeter is:
Perimeter = 2(5) + 3 = 13
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Onider the expreion (x 6) – 3x What i the value of the expreion evaluated for x = 12?
The value of the expression evaluated for x = 12 which is -26
How to simplify equations?
By multiplying the relevant factors, remove the brackets and parenthesis. As a result, the operations denoted by the brackets can be performed in the following order: multiplication, addition, subtraction, and division.If the words include exponents, grouping can be ruled out using the exponent rule.By adding or subtracting coefficients, combine like terms.Remove parentheses by factoring in multiples. To remove parenthesis in expressions involving exponents, utilize the exponent rules. To combine like terms, add coefficients to them.Add the constants together.(5/6)( (1/2)(12) + 6) - 3(12) =
(5/6)( 6 + 6) - 3(12) =
(5/6)(12) - 3(12) =
(5/6)(12/1) - 3(12) =
60/6 - 3(12) =
10 - 36
-26
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Full question:
consider the expression 5/6(1/2x+6)-3x if x =12
What is the measure of angle P?
Hint: Determine the angles that are supplementary to 130° and 110° and go from there.
Answer: angle p = ____°
The measure of the angles p for the given set of angles of triangle is found as: p = 60°.
Explain the angle sum property of triangles?Three sides, 3 angles, and 3 vertices make up a triangle. A triangle's total internal angles are always equals to 180 degrees. This is referred to as the triangle's angle sum property. Any two triangle sides can add up to a length that is longer than the third side.Supplementary of 110° = 180° - 110°
Supplementary of 110° = 70°
Similarly,
Supplementary of 130° = 180° - 130°
Supplementary of 130° = 50°
Using angle sum property of triangles:
70° + 50° + p = 180
p = 180 - 120
p = 60°
Thus, the measure of the angles p for the given set of angles of the triangle is found as: p = 60°.
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Can anyone pls help me with these questions? I need them by tonight!
On solving the provided question, we can say that in the quadrilateral BD = 11, BC = 8, DC = 8 and perimeter of ABCD is = 38
what is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
in the quadrilateral
BD = 11 ( equal angle have equal sides)
BC = 8
DC = 8
perimeter of ABCD is = 38
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what is the fourier transform of x(t)=2sin(2πf0t)cos(2πf0t)
The Fourier transform of x(t) = 2sin(2πf0t)cos(2πf0t) is π/2)δ(f - f0) + (π/2)δ(f + f0).
A Fourier transform (FT) is a mathematical operation that separates functions into frequency components. The output of the transform is shown as a function of frequency. The most frequent transformations include functions of time or space, and the function that results depends on the frequency of the input variable (either time or space). Analysis is the name given to the process.
The Fourier transform of x(t) = 2sin(2πf0t)cos(2πf0t) is,
X(f) = (π/2)δ(f - f0) + (π/2)δ(f + f0),
where δ is the Dirac delta function.
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The function h is given by h (a) = In(t sint + 5)dt for 1 <<7. On what intervals, if any, is I decreasing?A 2.0294.413B 4.3235.461C 14.322 and 5.461 <<7D There are no intervals on which h is decreasing.
For the function h (a) = In(t sint + 5)dt the decreasing interval is 14.322
The function h is a mathematical expression that relates a variable "a" to the result of an integral of another function.
In this specific case, the integral is calculated for the function "t sin t + 5" with respect to "t" from 1 to "a".
We can use differentiation to find the critical points of "t sin t + 5" and determine if it is increasing or decreasing over the interval.
We find that the function has a critical point at t = π/2, where it changes from increasing to decreasing. This means that the function h is decreasing over the interval (π/2, 7).
However, for values of "a" less than π/2, the function being integrated is increasing, meaning the function h is also increasing for those values of "a".
Therefore, option (c) is correct.
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Activity 5:Fantastic Four
Answer:
Step-by-step explanation:Answer: Quadralateral has 4 sides shape all of not 4 sides that is not quadralateral. Example of quadralateral: Parallelogram. Rectangle.
Answer:
nice
Step-by-step explanation:
what are the variables in the situation? how are they related? How is this relationship shown in a table, graph, and equation?
The graph of a proportional relationship is simply a straight line that passes through the origin
What is Proportional relationships?Proportional relationships are used to relate variables that have equivalent ratios.
Using tables
Assume the variables are x and y.
To make use of tables, then the values of x and y must change at a constant rate.
Take for instance, the following table of values
x: 1, 2, 3
y: 2, 4, 6
Notice that, as x increases by 1; y increases by 2.
Such relationship is a proportional relationship
Using equations
A proportional relationship is represented by the following equation
Where k represents the proportionality constant, and k is not equal to 0
An example of such equation is
Using graphs
The graph of a proportional relationship is simply a straight line that passes through the origin, and does not have an undefined slope or a slope of 0
Therefore, The graph of a proportional relationship is simply a straight line that passes through the origin
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Line f has an equation of 6x + y = 7. Perpendicular to line f is line g, which passes through the point (-10, -1). what is the equation of line g
(Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.)
Answer:
y = (1/6)x - 5/3
Step-by-step explanation:
Please find the attachment for detail
You have been saving up to buy an electric guitar. You found one on eBay for a total cost of $378.56. Your parent agrees to pay 3/4 of the cost for you. How much will you have to pay if you only pay 1/4 of the cost?
Answer:
You will have to pay 1/4 * $378.56 = $94.64 of the cost for the electric guitar on eBay
Answer: $94.64
Step-by-step explanation:
378.56 x 0.75 = 283.92
378.56 - 283.92 = $94.64
Can anyone solve this
The value of Trigonometric function is
sin Q = 5/13
cos Q = 12/13
tan Q = 5/12
sin S = 12/13
cos S = 5/13
tan S = 12/5
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
RS = 5
RQ = 12
QS = 13
Using Trigonometry
sin Q = P/H
= 5/13
and, cos Q = B/H
= 12/13
and, tan Q = P/B
= 5/12
and, sin S = P/H
= 12/13
and, cos S = B/H
= 5/13
and, tan S = P/B = 12/5
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