The best approximation of the solution to the system to the nearest integer values is ( -5, 1).
We have a system of linear equations, such that
x- y = -6 --(1)
5x + 2y = 23 --(2)
and we have to determine the approximate solution point for this system.
The intersection point of the two graphs ( lines, curves, etc.) is act as the solution to an equation.So, we determine the intersection point between two equations in system . Using the substitution method, substitute the value of x, x = y -6 from (1) to equation(2) ,
=> 5x + 2y = 23
=> 5( y - 6) = 23
=> 5y - 30 = 23
=> 5y = 23 + 30 = 53
=> y = 54/5 = 1.07 ~ 1 ( nearest integer value)
Now, from equation (1), x = y - 6
=> x = 1 - 6 = -5
Thus, the required solution point of system of equations is (-5 , 1).
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Complete question :
What is the best approximation of the solution to the system to the nearest integer values?
x- y = -6
5x + 2y = 23
A) (7, −2)
B) (6, −2)
C) (−2, 7)
D)(−2, 6)
Let A and B be finite sets. Suppose that A has cardinality 6 and B has cardinality 9. What is the cardinality of each of the following sets? (a) AxB (b) The power set P(A)
(a) The cardinality of A x B is 54.
(b) The cardinality of the power set P(A) is 64.
Let A and B be finite sets.
A has cardinality 6 and B has cardinality 9.
|A| = 6 and |B| = 9
A set's size, or the total number of its elements, is indicated by the set's cardinality.
(a) We have to determine the cardinality of A x B.
|A x B| = |A| x |B|
Now putting the value
|A x B| = 6 x 9
|A x B| = 54
(b) We have to determine the cardinality of the power set P(A).
|P(A)| = 2^{|A|}
Now putting the value
|P(A)| = 2^{6}
|P(A)| = 64
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STRUCTURE The graph represents the exponential function f. Find f(7). -2 4 6 Ay 2 (0, -1.5) ƒ(7) = 4 X (2,-6) 4
The numeric value of the exponential function at x = 7 is given as follows:
f(7) = -192.
How to model the exponential function?The definition of an exponential function is given as follows:
y = ab^x
In which the parameters are defined as follows:
a is the initial value.b is the rate of change.When x = 0, y = -1.5, hence the parameter a is given as follows:
y = -1.5.
When x = 2, y = -6, hence the parameter b is obtained as follows:
-1.5b² = -6
b² = 4.
b = 2.
Hence the function is defined as follows:
y = -1.5(2)^x.
Hence the numeric value at x = 7 is given as follows:
y = -1.5(2)^7
y = -192.
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Shown below are three separate pairs of point chargés, pairs A, B, and C. Assume the
pairs interact only with each other. Rank the magnitudes of the force between the
pairs, from largest to smallest.
-49
A of
+3q
B +
C
+2q
O A, B, C
O C, A, B
O C, B, A
O B, A, C
x/2
-2q
+2q
➜
+3q
1 pts
S
Answer:So the the force between the 3rd pair of charges is maximum.Then the force between 2nd pair of charges will come.The least force is between the 1st pair of charges.
Step-by-step explanation:
STEP 1:
In the 1st pair the charges are,
The distance between them is “x”.
The force between them according to coulomb’s law will be,
The minus sign indicates the force is attractive.
The magnitude is .
STEP 2:
For the 2nd pair of charges,
The distance between them is “x”.
The force between them according to coulomb’s law will be,
The magnitude is .
STEP 3:-
For the 2nd pair of charges,
The distance between them is “x/2”.
The force between them according to coulomb’s law will be,
The magnitude is .
CONCLUSION:
So the the force between the 3rd pair of charges is maximum.Then the force between 2nd pair of charges will come.The least force is between the 1st pair of charges.How to graph
7x+10y= – 70
42 is 60% of ______?
Answer:
0.6
Step-by-step explanation:
60% into a decimal is 0.6
you move the decimal two places to the left
Answer:
70
Step-by-step explanation:
Let the number we want is "x".
42 = 60% of x
42 = 60/100 x
4200 = 60 x
4200/60 = x
x= 70
in a survey, the of respondents are identified as for and for anything else. the average (mean) is calculated for respondents and the result is
If the of respondents are identified as 1 for "yes" and 2 for "no" and 3 for "maybe" and 4 for "anything else" then , the data are considered at the nominal level of measurement .
The Level Of Measurement of a data set refers to the type of values that a variable can take and the properties that these values have.
In the survey , the respondents are identified as 1 for "yes," 2 for "no," 3 for "maybe," and 4 for "anything else."
These values are categorical, meaning they are names or labels for different categories. The data collected at this level is referred to as nominal level of measurement. This level of measurement is used when the variables are categorical and the order of the categories does not matter.
Therefore , the data collected in this survey is nominal and is used to describe categories or names, rather than numerical values.
The given question is incomplete , the complete question is
In a survey, the of respondents are identified as 1 for "yes" and 2 for "no" and 3 for "maybe" and 4 for "anything else" . the average (mean) is calculated for 665 respondents and the result is 1.5 ,
the data are at what level of measurement ?
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Raj polled 100 students in his class to compare the number of hours that teen boys and girls played video games each week. The results of his survey are shown below. Which statement about his data sets is true?
The statement about Raj's data sets which true is The average boy plays 8.5 hours more per week than the average girl.
About data setTechnically, a dataset is a collection of related items that can be accessed individually or in certain management combinations as a single unit. Datasets can be organized into several types of data structures. Examples of dataset in the business world can be seen from names, salaries, employee contact information, to sales figures, and so on.
In conclusion, a dataset is a collection of data that is ordered and obtained from a collection of information. The collection of information itself is obtained from observation, measurement, study, or analysis to become data. Data can be facts, numbers, names, or even descriptions. Therefore, datasets are closely related to data mining activities which help data scientists analyze data into coherent information.
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Question 1-6
In PQR, PQ=QR. If m/P = (2x - 26) and m/R= (x+17), classify PQR. Select all that apply.
The triangle PQR is an equilateral triangle
How to classify the triangleFrom the question, we have the following parameters that can be used in our computation:
PQ=QR.
m/P = (2x - 26) and m/R= (x+17)
When two sides of a triangle are congruent, then the triangle is an isosceles triangle
Using the above as a guide, we have the following:
2x - 26 = x + 17 --- base angles of an isosceles triangle
So, we have
x = 43
This gives
m/P = 2 * 43 - 26 = 60
m/R= 43 + 17 = 60
If two angles of a triangle measure 60 degrees, then the third angle is 60 degrees
This implies that the triangle is an equilateral triangle
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The measure of the angle Q is 46.4°
How to find the angle?Recall that the sum of the angles of a triangle is equal to 180 degrees
We are told that
PQ = QR
Q = 100°
As PQ and QR are equal so,
By theorem angle opposite to equal sides are equal so,
We can say that angle P = angle R = X
Therefore by angle sum property of the triangle,
angle P + angle Q + angle R = 180°
X +(2x - 26)+ (2x - 26) = 180°
This implies that 5x-52=180
Collecting like terms
5x=180+52
5X = 232°
X =46.4°
Therefore the measure of R = 40°
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y = A system of equations. y equals StartFraction 2 over 3 EndFraction x plus 3. x equals negative 2.x + 3
x = –2
(negative 2, negative StartFraction 15 over 2 EndFraction)
(negative 2, StartFraction 5 over 3 EndFraction)
(negative 2, StartFraction 11 over 6 EndFraction)
(negative 2, StartFraction 13 over 3 EndFraction)
The required point of intersection of the two lines is (-2, 7/3).
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
The equation "y = 2/3x + 3" represents a line in the coordinate plane. It has a slope of 2/3 and a y-intercept 3. The equation "x = -2" represents a vertical line. It has no slope and the x-coordinate of all its points is -2.
Since the two equations represent lines, we can find their point of intersection by setting the two equations equal to each other and solving for y.
So, we have:
2/3x + 3 = y
and
x = -2
Substituting x = -2 into the first equation, we get:
2/3(-2) + 3 = y
Solving for y:
y = -2/3 * -2 + 3 = 4/3 + 3 = 7/3
Thus, the point of intersection of the two lines is (-2, 7/3).
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What is the lenght of MN? Important to have calculator in degree mode
Round your answer to the tenths
The length of side MN from triangle MNP is 30.78
Please see the attached picture below as reference of triangle MNP.
From the case, we know that:
∠M = 90°
∠P = 72°
∠N = 18°
PM = 10
To solve this problem we need to find the length of side NP first using cos formula to angle P.
Cos ∠P = PM
NP
Cos 72° = 10 / NP
0.309 = 10 / NP
NP = 32.36
Next, we will use the same approac to angle N:
Cos ∠N = MN
NP
Cos 18° = MN / 32.36
MN = 0.951 x 32.36
MN = 30.78
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Find the volume of the rectangular prism below 1 5/6 ft 1 1/3 ft 2 2/3 ft (V=L X W X H 176/27ft 3 7 14/27 ft 3 10/54ft 3 PLS HELPPP!!!
The volume of the rectangular prism given the length, width and height is 6 14/27 cubic feet.
The correct answer choice is option B
What is the volume of the rectangular prism?Volume of a rectangular prism= length × width × height
Length= 1 5/6 ft
Width = 1 1/3 ft
Height = 2 2/3 ft
Volume of a rectangular prism= length × width × height
= 1 5/6 × 1 1/3 × 2 2/3
= 11/6 × 4/3 × 8/3
= (11 × 4 × 8) / (6 × 3 × 3)
= 352 / 54
= 6 28/54
= 6 14/27 cubic feet
In conclusion, the volume of the rectangular prism is 6 14/27 cubic feet
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Kayla and Leanne share a bag of marbles.
For every 4 marbles Kayla gets, Leanne gets 3.
There are 42 marbles in the bag. How many does each girl get?
Kayla -24
Leanne-18
Step-by-step explanation:
4+3=7
42÷7=6
6x4=24
3x6=18
Answer: Let's call the number of marbles that Kayla gets x. Then, Leanne gets 3x marbles. The total number of marbles that the girls receive is x + 3x = 4x, so 4x must equal 42 marbles:
4x = 42
Dividing both sides by 4:
x = 10.5
Since the number of marbles that each girl receives must be an integer, we round down to the nearest whole number. So, Kayla gets 10 marbles and Leanne gets 3 * 10 = 30 marbles.
Step-by-step explanation:
Exercise 0.2.12. Is there a solution to y' y.such that y(0) (1)? Note: Exercises with numbers 101 and higher have solutions. Exercise 0.2.101. Show that z-e-2t is a solution to z" + 4z' + 4x = 0 Answer Exercise 0.2.102. Is y 2 a solution to y-2y 02 Justify Answer
The function y = e⁻ᵃ is a solution to the differential equation y' + y = 0 that satisfies the initial condition y(0) = 1.
Here we need to find a function that satisfies a differential equation and an initial condition.
The differential equation is given as
=> y' + y = 0.
To solve this differential equation, we need to find the general solution, which is a function that satisfies the equation for all values of t.
The characteristic equation for this equation is
=> m + 1 = 0,
which gives us m = -1 as the only solution.
This means that the general solution can be expressed as y = c1e⁻ᵃ, where c1 is an arbitrary constant.
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f x is a positive real number, then log(xˣ) = if x is a positive real number, then log(xˣ) = x · log(x) x log(x) log(x) · log(x) log(x)
The correct answer is log(x^(x)) = x * log(x).
The logarithmic rule states that log(a^b) = b * log(a).
So, let's apply this rule to log(x^(x)):
log(x^(x)) = x * log(x)
On the right side of the equation, x represents the exponent and log(x) represents the base.
This equation states that the logarithm of x raised to the power of x is equal to x times the logarithm of x.
Now let's simplify the other options:
x * log(x) is already simplified from the equation above, so we don't need to change it.
log(x) * log(x) is simply the logarithm of x raised to the power of 2, which is not equal to the logarithm of x raised to the power of x.
log(x) is the logarithm of x with a base of 10, and log(x) log(x) does not have a valid mathematical interpretation.
Therefore, the correct answer is log(x^(x)) = x * log(x).
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The function f is defined for all numbers x by f(x)=x^2+x. If t is a number such that f(2t)=30, which two of the following could be the number t ?
Indicate two such numbers.
−5
−3
−1/2
2
5/2
The two numbers which could be used for two in function are 5/2 and - 3.
What is function?The definition of a function is a "well-behaved" relation is one in which, given a starting point, we know the exact one ending spot to go to; given an x-value, we get only and precisely one corresponding y-value. Because functions pair information, they are all relations, but not all relations are functions. A subset of all of your relations are well-behaved family members, just as all mathematical relations are well-behaved functions.)
Given f(x)=x²+x
and f(2t)=30
When x = 2t, x²+x = 30
Substitute the value of x in function
(2t)²+2t = 30
4t² + 2t = 30
2(2t² + t) = 30
2t² + t = 15
2t² + 3t - 5t - 15 = 0
2t(t +3) - 5(t + 3)
(2t - 5)(t + 3)
t = 5/2
t = -3
Thus, The two numbers which could be used for two in function are 5/2 and - 3.
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Write the log equation
as an
exponential equation. You do not need to solve for x.
In (4) = 3x +1
Answer:
Step-by-step explanation:
Ln means log to the base e and 3x+1 is an exponent
So the answer is:
4 = e^(3x+1).
How many ounces are 30 grams?
Answer:
for an approximate result, divide the mass value by 28.35
so the answer is 1.058 ounces
30 grams of ounces would be 1.05822.
What is meant by ounces?An ounce weighs 28 grams. A quarter ounce weighs 7 grams. A half ounce weighs 14 grams. One-eighth of an ounce weighs 3.5 grams. A gram is a unit of weight equal to one thousandth of a kilogram, whereas an ounce is a unit of mass equal to 28.35 grams.
In both the US and Imperial measurement systems, a measure of mass. An ounce is roughly the same weight as a slice of bread. 28.349523125 grams is the precise weight.
Everywhere that isn't metric, including the United States and a few other countries, uses ounces as the basic unit of mass. In actuality, 28.35 grams or such make up 1 ounce.
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Solve y' - (x +y - 1)2
Given equation is a first-order nonlinear ordinary differential equation (ODE): y' - (x + y - 1)^2 = 0
What is differential equation ?
A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.
This equation can be solved using various methods, such as numerical methods or analytical methods like the implicit function theorem or the method of characteristics. However, finding an exact solution can be challenging and may not always be possible.
If you would like to find an approximate solution to this ODE, you could use numerical methods such as Euler's method, Runge-Kutta method, or the finite difference method. These methods can provide a numerical approximation to the solution for a given range of x and a specified initial condition.
The given equation is a first-order nonlinear ordinary differential equation (ODE):
y' - (x + y - 1)^2 = 0
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Discussion topic
Solving quadratic equations is one of the main topics of this unit. Some quadratic equations can be solved with only one method, some can be solved with multiple methods, and some can't be solved at all. Think about a lask in your daily life that can be accomplished in a variety of ways. How do you decide the best course of action for accomplishing that task? How is this process like choosing a method for solving a quadratic equation that can be solved in multiple ways?
Factoring, utilizing square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic equations.
What is Quadratic Equation ?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x² (a ≠ 0) for an equation to be a quadratic equation. The x² term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term. The numerical values of a, b, and c are often expressed as integral values rather than fractions or decimals.
Factoring, utilizing square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic problem.
To factor an equation with quadratic terms:
Convert the equation to standard form with a zero on one side.Factor the non-zero sideReset each component to zero (Remember: a product of factors is zero if and only if one or more of the factors is zero).Solve each of the ensuing equations.To learn more about Quadratic Equation refer to :
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A family has $1,000 to invest and is considering two options: investing in government bonds that offer 2% simple interest, or investing in a savings account at a bank, which charges a $20 fee to open an account and pays 2% compound interest. Both options pay interest annually.
The family would more likely choose the stock option, if the period of investment is 20 years,after calculating the simple & compound interest.
$999.60 is 1.02 times $980, and $1,019.59 is 1.02 times $999.60.
They may choose bonds or savings account depending on the assumptions they make about the time frame of the investment.
The value of the bonds b=1,000+20x and value of the stocks is s=980⋅(1.02)x , where x is the number of years since the investment were made.
For 10 years, the value of the bond will be
b=1,000+200=1,200 dollars.
The value of the stock will be s=980⋅(1.02)10≈1,195 dollars.
They should choose the bond option if the period of investment is 10 years.
For 20 years, the value of the bond will be
b=1000+400=1,400 dollars.
The value of the stock will be 980⋅(1.02)20=1,456980⋅(1.02)20=1,456 dollars.
So they choose the stock option, if the period of investment is 20 years.
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The complete question is attached below.
Identify the independent and dependent variable.
The equation A = 25w gives the area A (in square feet) of a rectangle dance floor with a width of w feet.
Thank you
The independent variable is the width of the dance floor (w), while the dependent variable is the area of the dance floor (A). Changes in w will affect the value of A.
Independent variable: w Dependent variable: AThe equation A = 25w describes the relationship between the area (A) of a rectangle dance floor and its width (w).
The independent variable is w, which is the width of the dance floor. This means that any change in the width of the dance floor will affect the area of the dance floor. The dependent variable is A, which is the area of the dance floor. This means that any change in the area of the dance floor will depend on the width of the dance floor.Thus, if the width of the dance floor is increased, the area of the dance floor will also increase.
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Find the value of for which the area encloed by the curve =−^2 and =^2− i equal to 56
The value of i is -56/a, Since the value of a is unknown, we cannot determine the exact value of i.
The area enclosed by the curve y = -x² and y = x² - i is the difference of the areas between these two curves.
To find the area enclosed by the curve y = x², we need to find its definite integral with respect to x from -∞ to ∞.
The definite integral of y = x² with respect to x from -∞ to ∞ is:
∫[-∞,∞] x² dx = (x³/3) from -∞ to ∞
Since the definite integral of an infinite function from -∞ to ∞ is undefined, we cannot find the exact value of the area enclosed by the curve y = x².
However, we can use the definite integral of y = x² - i with respect to x from -∞ to ∞ to find the area enclosed by the curve y = x² - i:
∫[-∞,∞] (x² - i) dx = (x³/3 - i * x) from -∞ to ∞
Again, the definite integral of an infinite function from -∞ to ∞ is undefined, so we cannot find the exact value of the area enclosed by the curve y = x² - i.
Since the area enclosed by the curve y = -x² is the same as the area enclosed by the curve y = x² but with the opposite sign, the difference of the areas enclosed by the two curves is equal to 56:
Area enclosed by y = x² - i - Area enclosed by y = -x² = 56
The first equation, y = -x^2, is a parabola that opens downwards.
The second equation, y = x^2 - i, is also a parabola but is translated downward by i units.
The area enclosed by the two curves will be the difference between the area under y = -x^2 and the area under y = x^2 - i.
The area under y = -x^2 can be calculated as follows:
A = ∫[-a,a] -x^2 dx = -(1/3) x^3 |^a_-a = (1/3) a^3
Where a is the x-value at which the two curves intersect.
The area under y = x^2 - i can be calculated as follows:
B = ∫[-a,a] (x^2 - i) dx = (1/3) x^3 - i x |^a_-a = (1/3) a^3 - i a
The area enclosed by the two curves is then given by:
C = B - A = (1/3) a^3 - i a - (1/3) a^3 = -i a
Since we know that the area enclosed by the curves is 56, we can set up the equation:
-i a = 56
So,
i = -56/a
Since a value is unknown, we cannot determine the exact value of i. However, we can use this equation to find the value of i for different values of a.
Therefore, The value of i is -56/a, Since the value of a is unknown, we cannot determine the exact value of i.
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QUESTION CORRECTION: Find the value of i for which the area enclosed by the curve =−x² and =x²− i equal to 56.
The value of i is -56/a, Since the value of a is unknown, we cannot determine the exact value of i.
The area enclosed by the curve y = -x² and y = x² - i is the difference of the areas between these two curves.
To find the area enclosed by the curve y = x², we need to find its definite integral with respect to x from -∞ to ∞.
The definite integral of y = x² with respect to x from -∞ to ∞ is:
∫[-∞,∞] x² dx = (x³/3) from -∞ to ∞
Since the definite integral of an infinite function from -∞ to ∞ is undefined, we cannot find the exact value of the area enclosed by the curve y = x².
However, we can use the definite integral of y = x² - i with respect to x from -∞ to ∞ to find the area enclosed by the curve y = x² - i:
∫[-∞,∞] (x² - i) dx = (x³/3 - i * x) from -∞ to ∞
Again, the definite integral of an infinite function from -∞ to ∞ is undefined, so we cannot find the exact value of the area enclosed by the curve y = x² - i.
Since the area enclosed by the curve y = -x² is the same as the area enclosed by the curve y = x² but with the opposite sign, the difference of the areas enclosed by the two curves is equal to 56:
Area enclosed by y = x² - i - Area enclosed by y = -x² = 56
The first equation, y = -x^2, is a parabola that opens downwards.
The second equation, y = x² - i, is also a parabola but is translated downward by i units.
The area enclosed by the two curves will be the difference between the area under y = -x^2 and the area under y = x² - i.
The area under y = -x^2 can be calculated as follows:
A = ∫[-a,a] -x²dx = -(1/3) x³ |^a_-a = (1/3) a³
Where a is the x-value at which the two curves intersect.
The area under y = x^2 - i can be calculated as follows:
B = ∫[-a,a] (x² - i) dx = (1/3) x³ - i x |^a_-a = (1/3) a³ - i a
The area enclosed by the two curves is then given by:
C = B - A = (1/3) a³ - i a - (1/3) a³ = -i a
Since we know that the area enclosed by the curves is 56, we can set up the equation:
-i × a = 56
So,
i = -56/a
Since a value is unknown, we cannot determine the exact value of i. However, we can use this equation to find the value of i for different values of a.
Therefore, The value of i is -56/a, Since the value of a is unknown, we cannot determine the exact value of i.
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QUESTION CORRECTION: Find the value of i for which the area enclosed by the curve =−x² and =x²− i equal to 56.
Thrice a number when increased by 6 gives 24
Answer:6
Step-by-step explanation:
Let the number be x.
Now, 3x+6=24
3x=24-6
3x=18
x=18/3
x=6
Answer:
6
Step-by-step explanation:
We can work the problem backwards
Since something gives 24 that means it equals 24
= 24
Something increased by 6, so something added by 6
Something + 6 = 24
Making something = x
x + 6 = 24
If we subtract 6 from both sides
x = 18
Trice a number, so divide this number by 3
x = 6
Trice of 6 is 18... 18 increased by 6 gives 24
Sara's credit card balance information for last month is shown in the table below. Her finance charge is based on her average daily balance. What was her average daily balance for this month? Round to the nearest penny.
The average daily balance for this month will be $1,026.45.
What is the average daily balance?Your charge card's average daily balance is calculated by dividing the total balance on your card at the conclusion of each day by the length of time in a billing cycle, which can range from 28 to 31 days depending on the month. You can total the following to find your daily balance: The card's balance when the day began.
Average daily balance = (Sum of daily balance) / (Number of days)
Number of days Balance Daily balance
4 $758 $3,032
12 $879 $10,548
10 $1,015 $10,150
5 $1,618 $8,090
Then the average daily balance is given as,
Average daily balance = ($3,032 + $10,548 + $10,150 + $8,090)
(4 + 12 + 10 + 5)
Average daily balance = $31,820 / 31
Average daily balance = $1,026.45
The average daily balance for this month will be $1,026.45.
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jorge wants to warm up some tomato soup wich option is a better deal per ounce: one 30 ounce container soup for 5.28 or two 14 ounce container of soup for 2.38 each
To solve this we would divide the pirce of the soups by their container ounces
$2.38÷14=$.17 per ounce
$5.28÷30=$.176 per ounce
We do not use a thrid decmal place when talking about money so we would round $.176 (since the third decmial place is greater than or equal to 5) up to $.18
Therefore Two 14 ounce containers of soup is a better deal per ounce.
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a shopper purchased 7 t shirts and 5 pairs of pants for $200. the next day, he purchased 5 t-shirts and one pair of pants for $112. what is a system of equations that represents the soulution? How much does each t-shirt and each pair of pants cost?
The system of equations are 7x + 5y = 200 and 5x + y = 112. The cost of each t shirt is $20 while the cost of each pants is $12.
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
Let x represent the cost of each t shirt and y represent the cost of each pants.
The shopper purchased 7 t shirts and 5 pairs of pants for $200, hence:
7x + 5y = 200 (1)
Also, he purchased 5 t-shirts and one pair of pants for $112, hence:
5x + y = 112 (2)
Solving the two equations simultaneously gives:
x = 20, y = 12
The system of equations are 7x + 5y = 200 and 5x + y = 112
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Benita buys 2 shirts for the same price, s. The sales tax rate is 6.5%.
Write an expression to represent the total cost of the shirts in two different ways.
The two different expressions for the total cost will be written as:-
C = 2S x 1.065
C = 0.13S + 2S
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Benita buys 2 shirts for the same price, s. The sales tax rate is 6.5%.
The two expressions for the total cost of the two shirts will be:-
C = 2S x ( 1 + 0.065)
C = 2S x ( 1.065)
The second way of writing the expression is:-
C = 2S x 0.065 + 2S
C = 0.13S + 2S
Hence, the expressions are C = 2S x 1.065 and C = 0.13S + 2S.
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evaluate x(2y+z)² for x=2, y=3, z=4
Answer: Plugging in the values x=2, y=3, and z=4 into the expression x(2y+z)², we get:
2(2(3)+4)² = 2(10)² = 2 * 100 = 200
So the expression evaluates to 200.
Step-by-step explanation:
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Two hundred ninety-five people go to the public swimming pool on a hot summer day. The daily prices are 1.75 for children and 2.00 for adults. The reci[pnts admission total of 560.75 dollars. How many children and adults were there
The number of children and adult that were there are 117 aand 178 respectively.
How to find the number of children and adult?Two hundred ninety-five people go to the public swimming pool on a hot summer day. The daily prices are 1.75 for children and 2.00 for adults. The recipients admission total of 560.75 dollars.
The number of children and adult can be calculated as follows;
Using equations,
let
x = number of children
y = number of adult
Therefore,
x + y = 295
1.75x + 2y = 560.75
multiply equation(i) by 2
2x + 2y = 590
1.75x + 2y = 560.75
subtract the equation
0.25 x = 29.25
x = 29.25 / 0.25
x = 117
Hence,
y = 295 - 117
y = 178
Therefore,
number of children = 117
number of adult = 178
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Today, Thurber tudie math for 15 minute and he tudie cience for 75 minute. From now on, Thurber plan to tudy math for 50 minute per day and to tudy cience for 30 minute per day. Will Thurber ever have tudied the ame total amount of time for both math and cience? Explain. Ue the drop-down menu to complete the entence. 5
day from today, Thurber will have tudied
Chooe. Of math and
Chooe. Minute of cience. I need help jut pleae give me the anwer i feel my i light headed
After three days Thurber will have studied the same total amount of time for both math and science and the time is 165 minutes for both.
How do you find the time in math?Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present, and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.The equation for calculating time is [Time = Distance ÷ Speed].Seconds, minutes, hours, days, weeks, months, and years are the fundamental units of time. To determine the time of day, we use seconds, minutes, and hours; to determine the date, we use days, months, and years. The smallest units of time are seconds, minutes, and hours, while the larger ones are days, months, and years.Given data :
Today, he studies 15 minutes math and 75 minutes science and from now on, 50 minutes math and 30 minutes science. So if he studies for 1 day total time for math and science will be:
Math = 15 + 50 = 65
Science = 75 + 30 = 105
2nd day:
Math = 65 + 50 = 115
Science = 105 + 30 = 135
3rd day:
Math = 115 + 50 = 165
Science = 135 + 30 = 165
So, after three days Thurber will have studied the same total amount of time for both math and science and the time is 165 minutes for both.
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