20 of the 65 percent pure fruit juice, 10 of the 90 percent pure fruit juice.
What is percentage ?A fraction that is parts out of 100 is referred to as a percentage.100% is the totality. The percentages that make up a whole add up to 100%.When representing a percentage as a number, the % symbol is used. A decimal, fraction, mixed number, integer, or other type of number can be used.In a grid of 100 squares, shading can be used to represent a percentage.
First, we define our variables: let x be the number of pints of the first fruit drink (65% pure fruit juice), and y be the number of pints of the second fruit drink (90%pure fruit juice).
We know that there are 30 total pints of the mixture. Thus:
x+y=30
We also know that 90%of those 30 pints will be pure fruit juice, and all of the pure fruit juice will come from xor y.
For x pints of the first juice, there is .65x pure fruit juice. Similarly, for ypints of the first juice, there is .90y pure fruit juice. Thus, we get:
.65x+.90y=30 ×0.7
Now we solve. First I'll get rid of the decimals in the second equation by multiplying by 100:
65x+90y=2100
Multiply the first equation by 65 on both sides to be able to cancel out one of the terms:
65x+65y=1950
Subtract the second equation from the first equation:
25y=250
y=10
Thus, we need 10 pints of the second fruit juice (90%pure fruit juice). This means that we need 30−10=20 pints of the first fruit juice (65% pure fruit juice).
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four coworkers are discussing their birthdates what is the probability of the months being different?
The probability of four coworkers having different birth months is 0.572 or 55/96
Given there are four coworkers and the condition is they should have different birth months.
As we know probability is the ratio of favorable out comes to the total number of outputs
Favorable outcomes are
For first person 12 months
For second person 11 months
For third person 10 months
For Fourth person 9 months
Total outcomes
For each and every person total outcomes are 12 months which add up to 12 x 12 x 12 x 12 = [tex]12^{4}[/tex]
Now probability will be
Probability = [tex]\frac{(12)(11)(10)(9)}{12^{4} }[/tex]
Probability = 55/96
Hence the probability of four coworkers having different birth months is 55/96
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Directions: write an appropriate equation for the given graph using your knowledge of parent functions and (h,k)
The parent functions are defined with all coefficients with value 1.
They can be linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent...
Then we can pick a function and transform it in order to include the point (-1,5) in the function definition.
We will use the quadratic parent function:
[tex]y=x^2[/tex]We will adjust the coefficient a of the quadratic function in order to include (-1,5)
[tex]\begin{gathered} y=a\cdot x^2 \\ 5=a(-1)^2=a \\ a=5 \end{gathered}[/tex]Then, our transformed function is:
[tex]y=5a^2[/tex]
A 4-pint carton of yogurt costs $5.16.
What’s the price per quart
Using mathematical operations we can conclude that the cost per quart of yogurt is $1.29.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving multiple operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).So, the cost per quart:
The 4-pint carton of yogurt costs $5.16.Meaning that in the carton there are 4 quarts of yogurt.Cost per quart:
= 5.16/4= $1.29Therefore, using mathematical operations we can conclude that the cost per quart of yogurt is $1.29.
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Please list what the tangent parent function.Can you make graph it scale both axes. With a short table of points+ domain and range. If there are asymptotes please identify and label.
First, use a calculator to create a table of values for the function:
[tex]y=\tan (x)[/tex]A table with inputs for x starting at -6.5 reaching the value of 6.5 with steps of 0.5 would be:
Plotting all the points and joining them with a smooth line, we can see that the graph of y=tan(x) is:
As we can see from the graph, the curve has an asymptote at
[tex]\frac{(2k+1)\pi}{2}+\pi k,k\in\Z[/tex]On the other hand, the graph reaches all the real values over the Y-axis. Then, the range of the function is the set of all real numbers.
herefore, the domain is:
[tex]x\in\R-\lbrace\frac{2k+1}{2}\pi|k\in\Z\rbrace[/tex]he range is:
[tex]y\in\R[/tex]nd the asymptotes are:
[tex]x=\frac{2k+1}{2}\pi,k\in\Z[/tex]-1.4 + {-1.2}
Answer in decimals
Please help, you also need to explain your reasoning
The value of x that makes m parallel to n is 90 degrees.
The value of x that makes m and n parallel is 15.
How to find the angles in parallel lines?
When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.
The value of x that makes the line ma and n parallel can be calculated as follows:
180 - x = x (alternate exterior angle)
180 = 2x
x = 180 / 2
x = 90 degrees
2.
3x - 15 + 150 = 180(supplementary angles)
3x = 180 - 150 + 15
3x = 45
x = 45 / 3
x = 15
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GХLauren has a full box of sugar cubes. The box is a rectangular prism with measurements, in centimeters,as shown. The size of each sugar cube is 1 cubic centimeter.2 cmSugar Cubes3 cm-4 cmFelect the numbers from the drop-down menus to complete each sentence.he volume of the box is measured in Choose...num
To find the volume of the prism we just multiply all the measures
[tex]\begin{gathered} V=2\cdot3\cdot4 \\ \\ V=24\text{ cm}^3 \end{gathered}[/tex]The volume is 24 cm³
If the sugar cubes have 1 cm³ of volume, to find how much sugar cubes fit in the box we must divide the volume of the box by the volume of the sugar cubes
[tex]\frac{V}{V_S}=\frac{24\text{ cm}^3}{1\text{ cm}^3}=24[/tex]Therefore we can fit 24 sugar cubes
The heights of 10 year old children has a normal probability distribution with mean of 54.6 inches and standard deviation of 5.7 inches. What is the approximate probability that a randomly selected 10-year old child will be more than 51.75 inches tall?
The approximate probability that a randomly selected 10-year-old child will be more than 51.75 inches tall is 0.6915.
How to calculate the probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. From the information, the heights of 10-year-old children have a normal probability distribution with a mean of 54.6 inches and standard deviation of 5.7 inches.
Based on this, the probability that a randomly selected 10-year old child will be more than 51.75 inches tall will be:
P(X > 51.75)
= P(Z > [(number - mean) / standard deviation)]
= P(Z > [(51.75 - 54.6) / 5.7)]
= P(Z > -0.5)
= 1 - P(Z = -0.5)
This will be looked at in the z table.
= 1 - 0.3805
= 0.6915
Therefore, the probability is 0.6915.
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What is the slope of the line that passes through the points (10, 4)(10,4) and (7, 3)(7,3)? Write your answer in simplest form.
The slope of the line that passes through points (10,4) and (7, 3) is 1/3
Here we are dealing with a slope of a line where a slope of a line is the change in the y coordinate with regard to the change in the x coordinate. If P(x1,y1) and Q(x2,y2) are the two points on a straight line, at that point the slope formula is given by:
m = Change in y-coordinates/Change in x-coordinates
m = (y₂– y₁)/(x₂ – x₁)
Since we are given two points (10,4) and (7, 3), where x₁ and x₂ are 10, 7 whereas y₁ and y₂ are 4, 3
From the formula we get,
m = (y₂-y₁)/(x₂-x₁)
= ( 3-4)/(7 - 10)
= -1/-3
=1/3
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Evalúe the limit. Show steps
After evaluating the limit we have came to find that the limit of [tex]\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}[/tex] as x approaches ∞- is 1
What is limit?The value that a function, sequence, or index approaches as an input, or an index, approaches a particular value is known as a limit in mathematics. Limits, which are essential to calculus and mathematical analysis, are required by the definitions of continuity, derivatives, and integrals.
In addition to being closely related to the concepts of limit and direct limit in category theory, the idea of a limit of a sequence is further generalised to encompass the idea of a limit of a topological network.
A limit of a function is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]
To find the limit we will use L'Hôpital's Rule
Find the derivative
⇒ [tex]\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}[/tex]
⇒ [tex]\lim_{x\rightarrow -\infty }\frac{2x}{2x +0}[/tex]
⇒ [tex]\lim_{x\rightarrow -\infty }\frac{2x}{2x }[/tex]
Evalue -∞ as x
⇒ [tex]\frac{2(-\infty)}{2(-\infty)} }[/tex]
⇒ 1
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What is the difference in
|-3| and -3
Answer:
6, because anything inside | | are positive so -3 will now be 3.
3 minus -3 = 6
Step-by-step explanation:
Hope it helps! =D
There are 110 calories per 177.4 grams of Cereal X. Find how many calories are in 246.5 grams of this cereal.
The amount of calories in 246.5 gm of Cereal 397.5372 calories
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example,
Ram spends 36 Rs. for a dozen (12) bananas. 12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees. As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas. This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
In 177.4 gm of cereal contain 110 calories.
So, 1 gram cereal contain
= 177.4 / 110
= 1.6127
and, 246.5 gm will contain
=246.5 x 1.6127
= 397.5372 calories.
Hence, 397.5372 calories are in 246.5 grams of this cereal.
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PLEASE HELP … Would really appreciate it
The diameter of the outer circle = 12.907 ft
The thickness of the circular pipe = 2.983 ft
The diameter of the inner circle = q = The diameter of the outer circle - The thickness of the circular pipe
⇒ The diameter of the inner circle = 12.907 - 2.983 ft
⇒ The diameter of the inner circle = q = 9.924 ft
What is a Circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. The radius of a circle is the separation between any point on the circle and its center.A circle, specifically, is a straightforward closed curve that separates the plane into its inner and exterior.In common parlance, the word "circle" can apply to either the figure's boundary or its entirety, including its inside; in rigorous technical parlance, the circle only refers to the boundary, and the entire shape is referred to as a disc.To learn more about Circles, refer to:
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Translate the sentence into an equation.
The sum of 4 times a number and 5 is 2.
Use the variable y for the unknown number
Answer:
4y + 5 = 2
Step-by-step explanation:
4y + 5 = 2 Subtract 5 from both sides
4y = -3 Divide both sides by 4
y = [tex]\frac{-3}{4}[/tex]
Answer:
4y+5=2
Step-by-step explanation:
First, replace "a number" with "y"
The sentence becomes: "The sum of 4 times y and 5 is 2"
Replace "is" with the equals sign, "="
The sentence becomes: "The sum of 4 times y and 5 = 2"
Replace "times" with the multiply symbol, " * "
The sentence becomes: "The sum of 4 * y and 5 = 2"
Replace "the sum of ___ and ___" with " ___ + ___"
The sentence becomes: "4*y + 5 = 2".
the " * " isn't needed since 4y implies multiplication already, so you can optionally remove the *
I am a block.I have I flat surfaceI have I curved surface
the shape of the curved surface is the sphere
So, as a part of the shape is flat
The block may represents a semi sphere
A contractor hired 150 workers to pave 30 miles of highway how many workers will they need to hire to pave 20 miles of highway in the same amount of time?
Answer: 100
Step-by-step explanation:
First, we need to know how many workers must be hired to pave one mile.
Which is 5 workers per 1 mile ( 150 / 30 )
Then you can either do
(5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5)
OR
5 x 20 = 100
( if I'm wrong it's like 3 am so I'm a bit slow but I hope I helped )
Trisha's puppy weighs 5 pounds. How many ounces does her puppy weigh?
80 ounces
60 ounces
50 ounces
40 ounces
I NEED TO KNOW NOW PLS HURRY
one number is six less than a second number. Twice the first is 2 more than 4 times the second. Find the numbers
The two numbers are 11, and 5 if the one number is six less than a second number.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
It is given that:
One number is six less than a second number.
Let the number be x and y:
x - 6 = y
Twice the first is 2 more than 4 times a second.
2x = 2 + 4y
After solving the two linear equations:
2x = 2 + 4(x - 6)
2x = 2 + 4x - 24
2x = 22
x = 11
y = 5
Thus, the two numbers are 11, and 5 if the one number is six less than a second number.
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helppppppppppppppppppppppppp me
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]
on the grid, draw 3 triangles with an area of 12 square units.Label the base and height of each triangle
Answer:
Iiiieie I just got off your phone with weee
Step-by-step explanation: why did I get a hold for him or
oh yeah that’s fine I’ll let lol I was thinking of going out to the house for the next few weeks so I’m not good enough for that lol I think it’s so so to do that all day and you can get a hold on you for sure and I can help with your stuff and help me help help you get it
Solve the problem.
2) The length of the base of an isosceles triangle is 28.35 meters. Each base angle is 29.73°. Find the length of each of the two equal sides of the triangle. Round your answer to the hundredths place.
Answer:
20.99 m
Step-by-step explanation:
5.The closed figure with 5 straight line segments is called
Answer: Pentagon
Step-by-step explanation:
A closed figure with 5 straight line segments is called a pentagon. See attached for a visual example.
A segment is a straight line with two distinct endpoints.
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-2(-3)+(-2)(-4)-(-2)=
3000 for 2 years at 2% compounded quarterly
Based on the given parameters, the amount of the investment after 2 years is $3123
How to determine the amount?The given parameters about the compound interest are
Principal Amount, P = $3000
Interest Rate, R = 2%
Time, t = 2
Number of times, n = 4 i.e quarterly
Compound interests are different from simple interest, and they are calculated using the following compound interest formula
CI = P(1 + R/n)^nt - P
To calculate the amount, we have:
A = P + CI
So, the equation becomes
A = P + P(1 + R/n)^nt - P
Evaluate the like terms
A = P(1 + R/n)^nt
Substitute the known values in the above equation
A = 3000 * (1 + 2%/4)^(2 * 4)
Express 2% as decimal
A = 3000 * (1 + 0.02/4)^(2 * 4)
Evaluate the sum
A = 3000 * (1.005)^8
Evaluate the exponent
A = 3000 * 1.041
Evaluate the product
A = 3123
Hence, the value of the investment is $3123
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If line a is parallel to line b what is m ∠1?
Explanation
hen a line instersects a pair of paralle lines diverse angles are created
If you copy A of the corresponding angles and you translate it along the transversal, it will coincide with the other corresponding angle (B)
so angles A and B are called
Corresponding angles, those angles are congruents
[tex]m\measuredangle A=m\measuredangle B[/tex]hence, if the lines in the problem are parellel, is must fit
[tex]m\measuredangle1=40\text{ \degree}[/tex]therefore, the answer is
[tex]a)40\text{ \degree}[/tex]I hope this helps you
Use two unit multipliers to convert 75 square inches to square feet.
In order to use two unit multipliers we will convert from square inches to cm using the following unit multiplier:
[tex]\frac{6.4516}{1^{}}\frac{cm^2}{in^2}\text{.}[/tex]and then we will convert from square cm to square feet, using the following unit multiplier:
[tex]\frac{0.00107639}{1}\frac{ft^2}{cm^2}.[/tex]Answer:
[tex]75in^2=75in^2(\frac{6.4516}{1^{}}\frac{cm^2}{in^2})(\frac{0.00107639}{1}\frac{ft^2}{cm^2})=0.520833ft^2.[/tex]In this diagram, angle ABC has been mapped onto angle A'B'C' by a series of rigid motions. Which statement best describes one way to prove that the triangles are congruent?
A) Rigid motions preserve distance and angle measure. This means that AB approximately= A'B', BC approximately=B'C', and angle A approximately= angle A', so the triangles are congruent by SAS.
B) Rigid motions preserve distance and angle measure. This means that AB approximately= A'B', BC approximately=B'C', and angle B approximately= angle B', so the triangles are congruent by SAS.
C) Measure the areas of angle ABC and angle A'B'C' to confirm that their areas are equal. This means that AB approximately= A'B', BC approximately= B'C', and AC approximately= A'C', so the triangles are congruent by SSS.
D) Measure the perimeters of angle ABC and angle A'B'C' to confirm that their perimeters are equal. This means that AB approximately= A'B', BC approximately= B'C', and AC approximately= A'C', so the triangles are congruent by SSS.
The correct answer is Option B.
By air, the distance from city A to city B is 3001 miles less than the distance from city C to city D. If the total of these
← two distances is 7869 miles, find the distance from city C to city D.
miles
D
***
The distance from city C to city D is 5435 miles
What is basic algebra ?The area of mathematics known as algebra aids in the representation of issues or circumstances into mathematical statements. To create a meaningful mathematical expression, it requires variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including coordinate geometry, calculus, and trigonometry. 2x + 4 = 8 is a basic algebraic expression.When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, we obtain algebraic expressions as the mathematical statement.
The distance from city A to city B is 3001 miles Let distance from city A to city B x and distance from city C to city D y
The distance from city A to city B is 3001 miles
x= y - 3001....(i)
x+ y = 7869....(ii)
y- 3001 +y = 7869
2y = 10870
y=5435
The distance from city C to city D is 5435
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Find the value of x,y and z
○ x=70,y=58,z=53
○ x=80,y=38,z=63
○ x=85,y=38,z=63
○ x=80,y=48,z=63
Answer:
(b) x=80, y=38, z=63
Step-by-step explanation:
You want to know the values of x, y, and z, given they are angle measures in a diagram showing two triangles.
Linear pairThe angles that form a linear pair are supplementary:
x° +100° = 180°
x = 80 . . . . . . . . . divide by °, subtract 100
Angle sum theoremThe angle sum theorem tells you that the sum of angles in a triangle is 180°.
y° +62° +80° = 180°
y = 38 . . . . . . . . . . . . divide by °, subtract 142
In the other triangle, the same relation holds:
z° +100° +17° = 180°
z = 63 . . . . . . . . . . . . divide by °, subtract 117
The values of x, y, and z are ...
(x, y, z) = (80, 38, 63)
2 to 4 and 11 to 11/2 are they proportional
Explanation:
In this case we must compare 2 to 4 and 11 to 11/2
1. The first ratio given is 2 to 4
[tex]r_1=\frac{2}{4}=\frac{1}{2}[/tex]So, the first ratio is 1/2
2. The second ratio given is 11 to 11/2
[tex]\begin{gathered} r_2=\frac{11}{\frac{11}{2}}=\frac{2\cdot11}{11} \\ r_2=2 \end{gathered}[/tex]Finally, since r1 ≠ r2 they are not proportional
ANSWER:
they are not proportional