The pair of ratios that will make a proportion include:
A. 1/3 and 12/36
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them.
In this case, it should be noted that 12 over 36 can be reduced to the lowest term. This will be:
12 / 36
= 1/3
Therefore, the correct option is A.
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a square sheet of cardboard, 18 inches on a side, is used to make an open box by cutting squares of equal size from the corners and folding up the sides. what size squares should be cut to obtain a box with largest possible volume?
The dimensions of the box are (S-2x)by(S-2x)byS = 2S/3 by 2S/3 S by S/6 to obtain a box with largest possible volume
What are dimensions ?In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.
CalculationLet S = length of the sides of the square cardboard sheet. Let x = the side of each square cut from the corners. The volume, V, of the box when the sheet is folded up is:
V = (S-2x)(S-2x)x = 4x3 - 4Sx2 + S2x
To find the maximum value, take the derivative of V wrt x, set it to zero, and solve for x:
V ' = dV/dx = 12x2 - 8Sx + S2
0 = 12x2 - 8Sx + S2
0 = (6x-S)(2x-S)
x = S/6 and S/2
To determine which is the max and which is the min, take the second derivative of V wrt x.
V'' = d2V/dx2 = 24x - 8S
At x = S/2, V'' = 24(S/2) - 8s = 4S. Since S>0, the point x=S/2 is a minimum. This makes sense because you have cut away the entire cardboard square.
At x = S/6, V'' = 24(S/6) - 8S = -4S < 0, so x = S/6 is the maximum
The dimensions of the box are (S-2x)by(S-2x)byS = 2S/3 by 2S/3 S by S/6
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if the null hypothesis that two means are equal is true, where will 97% of the computed z values lie between?
If the null hypothesis that two means are equal is true, 97% of the computed z values lie between 2.17.
What is null hypothesis?Any variation between the selected characteristics that you observe in a set of data is thought to be the result of chance, according to the null hypothesis. For instance, any difference between the average earnings in the data and zero is caused by chance if the expected earnings for the gambling game are actually equal to zero. An assertion that there is no correlation between two population parameters is referred to as a null hypothesis. To prepare the ground for additional experimentation or research that explains the position of interest, researchers reject or refute the null hypothesis.
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It's a small sentence word problem, I don't understand it though...
The sentence, using the rational root theorem, is completed as follows:
If a polynomial function f has integer coefficients, then every rational solution of f(x) = 0 has the format p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
What is stated by the rational root theorem?The rational root theorem states that a polynomial with integer coefficients will have every rational solution following the format p/q.
The variables p and q are defined as follows:
Variable p: factor of the constant term, which is the last coefficient of the polynomial function.Variable q: factor of the leading coefficient, which is the first coefficient of the polynomial function.Hence the blanks in this problem are completed, respectively, by:
Constant term and leading coefficent.
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Part A
Steve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80. Let x represent the price per pound for grapefruit, and let y represent the price per pound for oranges. Choose the system of equations that models the situation.
A. 2x + 3y = 7.20
2x + 4y = 8.80
B. 3x + 2y = 7.20
4x + 2y = 8.80
C. 2x + 3y = 7.20
4x + 2y = 8.80
D. 2x + 3y = 8.80
4x + 2y = 7.20
Part B
Steve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80. Let x represent the price per pound for grapefruit, and let y represent the price per pound for oranges. Use the system of equations from Part A to find the price per pound for oranges.
price: $ ____ per pound
System of equations that models the situation is Option C . 2x+3y = 7.20 , 4x+3y = 8.80 and the price per pound for oranges is $1.40.
Given:
Part A
Steve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80.
Let x represent the price per pound for grapefruit, and let y represent the price per pound for oranges.
2x + 3y = 7.20
4x + 2y = 8.80
Part B
on solving two equations:
2x + 3y = 7.20 and 4x + 2y = 8.80
2(2x + 3y) - 4x - 2y = 2*7.20 - 8.80
4x + 6y - 4x - 2y = 14.40 - 8.80
4y = 5.60
y = 5.60/4
= $1.40
hence price of oranges per pound is $1.40.
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Am I right or wrong?
Answer:
Step-by-step explanation:
right i think?
Nick's mark on a test was 39.
This mark was 60%.
What was the total possible mark?
Answer:
65
Step-by-step explanation:
Since 39 is 60%, 100/60= 1 2/3
39*1 2/3 is 65
Find two consecutive integers such 4 that times the smaller integer is 50 less than 6
times the larger integer.
The consecutive integers such 4 that times the smaller integer is 50 less than 6 times the larger integer are 22 and 23.
How to calculate the value?Let the consecutive integers be x and x + 1.
In this case, the integers are such 4 that times the smaller integer is 50 less than 6 times the larger integer.
This will be:
4(x) = 6(x + 1) - 50
4x = 6x + 6 - 50
Collect like terms
4x - 6x = -44
-2x = -44
Divide
x = 44/2
x = 22
Also, x + 1 = 22 + 1 = 23
The numbers are 22 and 23.
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find ta , the tension in string a. express the tension in string a in terms of g , m1 , l , d , m2 , and x .
The expression for tension in the string is T = [(L/2)×(m1×g) + (x)×(m2×g)]/d.
We are a diagram that shows two blocks with masses m1 and m2.There are two strings, A and B. Everything is in equilibrium. Equilibrium is a condition of rest or balance caused by opposing forces acting equally. We need to find the tension in string A. Let the tension in the strings A and B be denoted by the variables "Ta" and "Tb", respectively. The net torque at point B must be zero as everything is in equilibrium. The diagram is attached below.
Στ(B) = 0
τ(a) + τ(b) + τ(m1) + τ(m2) = 0
τ = r×F×sin(θ)
d×(Ta)×sin(90°) + 0 - (L/2)×(m1×g)×sin(90°) - (x)×(m2×g)×sin(90°) = 0
d×(Ta) - (L/2)×(m1×g) - (x)×(m2×g) = 0
Ta = [(L/2)×(m1×g) + (x)×(m2×g)]/d
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g a pair of fair dice is rolled. what is the probability of getting a total on the two dice greater than 10
The probability of getting a sum greater than 10 is 1/12.
From the question, we have
total outcomes = 6 ×6 = 36
Number of events of sum greater than 10: {5, 6}, {6, 5}, {6, 6} = 3
Probability = 3/36
=1/12
The probability of getting a sum greater than 10 is 1/12.
Probability:
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
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find 4 numbers if their ratio is 9 11 and their difference is 6
As per the given ratio, the four numbers are 27, 33, 81 and 99.
Ratio:
Ratio means a mathematical expression written in the form of a:b, where a and b are any integers. It expresses a fraction.
Give,
Here we have the ratio 9: 11.
And the difference is 6.
And we need to find the four numbers to it.
Let us consider both the number be 9x, 11x since their ratio is 9:11
And we have assume that our expected answer to be positive (since we are dealing with ratios)
So, their difference can be written as,
=> 11x-9x = 6
When we simplify it, then we get,
=> 2x = 6
Here we need the value of x,
=> x= 3
Now that we know the value of ‘x’ is, we can find required numbers through it,
=> 9x = 9 * 3= 27
=> 11x = 11*3 = 33
=> 27x = 27*3 = 81
=> 33x = 33*3 = 99
Thus, the four numbers are 27, 33, 81, 99.
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What is 3860 rounded to
Step-by-step explanation:
3900 if by hundreds
If by thousands 4000
Find the value of each angle
Answer:
15° and 75°----------------------------
Given is the right triangle.
The two angles are complementary, so their sum is 90°:
p - 10 + p + 50 = 902p + 40 = 902p = 50p = 25The angles are:
p - 10 = 25 - 10 = 15°p + 50 = 25 + 50 = 75°Answer:
p - 10° = 15° p + 50° = 75°Step-by-step explanation:
Now we have to,
→ find the value of each angle.
Forming the equation,
→ 90° + (p - 10°) + (p + 50°) = 180°
Now the value of p will be,
→ 90° + (p - 10°) + (p + 50°) = 180°
→ (90° - 10° + 50°) + (p + p) = 180°
→ 130° + 2p = 180°
→ 2p = 180° - 130°
→ p = 50°/2
→ [ p = 25° ]
Then the value of other angle is,
→ p - 10° || → p + 50°
→ 25° - 10° || → 25° + 50°
→ 15° || → 75°
Hence, these are the angles.
what is the probability that the lifetime of at least one component exceeds 2? (do not round intermediate values. round your answer to three decimal places.)
The probability that the lifetime of at least one component exceeds 2 is 0.135.
Given that the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image.
We want to find the probability that the lifetime of at least one component exceeds 2.
The probability that the lifetime of at least one component exceeds 2 is P(X>2).
[tex]\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}f(x,y)dydx\end[/tex]
Now, we will substitute the given function, we get
[tex]\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}xe^{-x(1+y)}dydx\end[/tex]
Further, we will simplify this, we get
[tex]\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\left[-e^{-x(1+y)\right]_{0}^{\infty}dx\\ &=\int_{x=2}^{\infty}e^{-x}dx\\ &=\left[-e^{-x}\right]_{2}^{\infty}\\ &=e^{-2}\\ &=0.135\end[/tex]
Hence, the probability that the lifetime of at least one component exceeds 2 for the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image is 0.135.
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write an explanation comparing constant percentage change to constant rate of change. 2. what are some key words in a verbal description that indicate an exponential function can be used to model the situation? what is meant by such words?'
Percentage Change = (ΔV/IV₁I) × 100
Constant rate of Change = (y₂ - y₁)/ (x₂ - x₁)
Constant Percentage Change:
This means that after t period the something has grown to [tex]g^{t} = 1.10^{t}[/tex] it original value .
percentage change formula equals the change in value divided by the absolute value of the original value multiplied by 100.
Constant rate of Change:
In which the rate does not change between different points in the function. in short, constant rate of change refers to the comparison of the way two quantities changes. in equation, the constant rate of change can be seen as a slope.
An exponential function is a function that changes at a constant percentage rate.
An exponential function y of t is characterized by the following property:
when t increases by 1 to find the new value of y the current value by the base.
y- value for t +1 = Base of y - value for t
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Luisa plans to prepare cupcakes for her daughter's birthday. If you spend S/15 on 25 units, how much money do you need to make 80 cupcakes?
The amount that will be spent on the cupcakes is $48.
How to calculate the amount?From the information, Luisa plans to prepare cupcakes for her daughter's birthday and spends $15 on 25 units.
Let the amount spent on 80 cupcakes be x.
This will be illustrated as:
25/80 = 15/x
Cross multiply
25x = 15 × 80
25x = 1200
Divide
x = 1200/25
x = 48
The amount will be $48.
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Multiply. Write your answer as a fraction or as a whole or mixed number.
7 ×
5
6
Answer:210
Step-by-step explanation:
Find the area (in cm) of the rectangle shown.
7
3
Write each equation in slope-intercept form.
9.-10x + 2y = 12
12. 6x-3y=-18
10. 4y + 12x = 16
13.-2x-8y = 24
11. -5x + 15y = -30
14. -4x-10y = -7
Answer:
Step-by-step explanation:
2
Chitchat wireless charges $0. 30 per minute plus a monthly base fee. In september, maggie used 120 minutes and her bill was $51. Write and solve an equation that best represents the scenario.
The equation is 51 = x + 120 × 0.30 that can find the monthly base fee charged by Chitchat wireless.
The equation representing the scenario will be formed through following components.
Total bill = monthly base fee + number of minutes × cost per minute
In the above mentioned equation, let us assume the monthly base fee to be x. Now, keep the values in formula to find the value of x.
51 = x + 120 × 0.30
Performing multiplication on Right Hand Side of the equation
51 = x + 36
Rewriting the equation according to x
x = 51 - 36
Performing subtraction on Right Hand Side of the equation
x = 15
Thus, the monthly base fee is $15.
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When the product of 6 and the square of a number is increased by 5 times the number, the result is 4. Select all of the values that the number could be. 2.
The answer to the given question is -4/3 or 1/2
The product of 6 and the square of a number is increased by 5 times the number, the result is 4.
Firstly, let's write the algebraic expression for the above statement and represent the number as x.
The algebraic expression can be written as:
(6 x x²) + 5x = 4
6x² + 5x = 4
The other expression can also be written as:
6x² + 5x - 4 = 0
Secondly, we must factorize the algebraic expression to solve for x.
6x² - 3x + 8x - 4 = 0
3x (2x - 1) + 4 (2x + 1) = 0
(3x + 4)(2x - 1) = 0
Thirdly, we need to solve for x.
3x + 4 = 0
3x = -4
Now, we need to divide both sides by 3.
3x/3 = -4/3
x = -4/3
or
2x - 1 = 0
2x = 1
Now, we need to divide both sides by 2.
2x/2 = 1/2
x = 1/2
Hence, the values that the number could be is -4/3 or 1/2.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The graph of the exponential function f(x) = (3/4)ˣ is attached below and this is also option A in the question given
Graph of Exponential FunctionAn exponential graph is a curve that represents an exponential function. An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid.
In the given function
f(x) = (3/4)ˣ,
we can use a graphing calculator to plot the graph while applying the values from the table of function.
Comparing the graph plotted and the options given, the answer is option A
Kindly find the attached graph below
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Which set of coordinates represents Figure MNOP reflected across the x-axis?
The set of coordinates after the reflection is (c) M' = (-3, -4) N' = (2, -3) O' = (1, -1) P' = (-2, -2)
How to determine the coordinates after the reflection?The graph represents the given parameter
On the graph, we have the following coordinate points
M = (-3, 4)
N = (2, 3)
O = (1, 1)
P = (-2, 2)
The rule of the reflection is given as:
Reflection across the x-axis
Mathematically, this is represented as
(x, y) ⇒ (x, -y)
When this is applied to the points, we have the following representation
M' = (-3, -4)
N' = (2, -3)
O' = (1, -1)
P' = (-2, -2)
Hence, the set of coordinates is (c)
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solve 1/3 x= -4/5
-2 2/5
4/15
2 2/5
-4/15
solve 1/3 x= -4/5
1/3 * -4/5 = -4/15
-2 2/5
4/15
2 2/5
-4/15
Answer:
first option
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] x = - [tex]\frac{4}{5}[/tex]
multiply both sides by 15 ( the LCM of 3 and 5 ) to clear the fractions
5x = - 12 ( divide both sides by 5 )
x = - [tex]\frac{12}{5}[/tex] = - 2 [tex]\frac{2}{5}[/tex]
At 10:00 am Han and Tyler both started running toward each other from opposite ends of a 10 mile path along a river. Han runs at a pace of 12 minutes per mile. Tyler runs at a apce of 15 minuttes per mile
The Answer is Han will cover 2.5 miles distance
What is distance ?
Distance is the total path covered by a object or person. As its name implies, any distance formula outputs the distance (the length of the line segment). In coordinate geometry, there is a number of formulas for finding distances, such as the separation between two points, the separation between two parallel lines, the separation between two parallel planes, etc.
Han and Tyler both started running toward each other from opposite ends of a 10 mile path along a river.
We need to find the distance run by Han after a half hour.
Han will cover a distance in 12 minutes=1 mile
Han will cover a distance in 1 minute= 1/12mile
Han runs distance in 30 minutes=30*1/12 miles
Hence, Han runs 2.5 miles after half hour.
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What function is represented in the table? HELP!!!!
Answer:
below
Step-by-step explanation:
y = 3 * 2^x plug in the values of x (first column) to get the values in the second column
Three students share 8 blocks of clay equally How much clay does each student get? 8+3= Each student's share is blocks of clay
Answer:
11?
Step-by-step explanation:
since 8+3 = 11 won't each student get 11 because they equally share it and in total 11 x 8 = 88 so they have to share 11 blocks of clay.
4. At an amusement park, the cost for an adult admission is a, and for a child the cost is c. For a group of six
that included two children, the cost was $325.94. For a group of five that included three children, the cost was
$256.95. All ticket prices include tax. Write a system of equations, in terms of a and c, that models this
situation. Use a system of equations to determine the exact cost of each type of ticket algebraically.
The system of equation for each condition will be; 2a + 3c = 325.94 and
2a + c = 162.97 and exact cost of each type of ticket is a = $57.99 and
c = $46.99
What is linear equation?A linear equation is an algebraic equation of the form y = mx+b. involving only a constant and a first-order term, where m is the slope and b is the y-intercept.
At an amusement park, the cost for an adult admission is a and for a child the cost is c. For a group of six that included two children, the cost was $325.94. For a group of five that included three children, the cost was $256.95 and all ticket prices include tax.
According to question,
2a + 3c = $325.94
4a + 2c = $256.95
2a + c = $162.97
Solving the equation by using elimination method, we get,
a = $57.99 and c = $46.99
Hence, The system of equation for each condition will be; 2a + 3c = 325.94 and 2a + c = 162.97 and exact cost of each type of ticket is a = $57.99 and c = $46.99
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Angel simplified both sides of an equation. Both sides of the equation have a variable expression with the same coefficient but different constants. Explain how to determine the number of solutions of the equation.
The number of solutions of the system of equations is given by:
Zero.
How to obtain the number of solutions of the system of equations?The number of solutions of a system of equations is obtained considering the coefficients and the constants of each side of the expression.
If the sides have different coefficients, then it will guarantee that the solution has only one solution, as there will be a division by a term different of zero.
If the sides have the same coefficients and then different constants, as is the case in this problem, the number of solutions is of zero, as a number different of zero will be divided by zero.
If the sides have the same coefficients and the same constants, then the number of solutions is of infinity, as the equivalent solution will be obtained with a division of zero by zero, that can be any value.
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if the individual outcomes of a phenomenon are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions, we say the phenomenon is
If the individual outcomes of a phenomenon are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions, this phenomenon is called random phenomenon.
A phenomenon is random if individual outcomes are uncertain, but there is in spite of that, a regular distribution of outcomes in a great number of repetitions.
The probability of any outcome of a random phenomenon can be
described as the proportion of times the outcome would happen in a very lengthy chain of repetitions.
The outcome of any individual coin toss is random. But the outcome over many tosses is foreseeable, as long as the trials are individualistic (i.e., the outcome of a new coin flip is not impacted by the outcome of the preceding flip).
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The screen of a tablet is shaped like
a rectangle. Find the area of the screen by
A = bh, when b = 7 in and
A h = 11 in.
The screen of a tablet is shaped like a rectangle. then the area of the screen is 77 square inches.
What is the area of a rectangle?
If the length of the rectangle is 'l' and the breadth of the rectangle is 'b', then the area of the rectangle can be calculated as
Area = Length * Breadth
The length of the screen is 11 in. and the breadth of the screen is 7 in.
Then the area of the screen,
Area = length * breadth
= 11 * 7
= 77 square inches.
Hence, the screen of a tablet is shaped like a rectangle. then the area of the screen is 77 square inches.
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