The area of the rectangle is 23.375 sq feet.
What is area of rectangle ?
The area of a rectangle is the product of its length and width. It is a measure of the region enclosed by the rectangle. In the context of geometry, the area is expressed in square units, such as square inches, square feet, or square meters.
Given by the question:
To find the area of the rectangle, we need to multiply the length and width.
Length = 2 3/4 feet = 11/4 feet
Width = 8 1/2 feet = 17/2 feet
Area = Length x Width
Area = (11/4) x (17/2)
Area = 93.5/4 sq feet
So the area of the rectangle is 23.375 sq feet (when rounded to three decimal places).
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0.1 of 60 minutes?
(pleas help me thank u)
The simplification of the given expression would be = 6
How to calculate the simplification of the given expression?60 minutes = 1 hour
But 0.1 of 60 minutes simply means the quantity of 60 minutes that is 0.1.
This can be calculated through the multiplication of 0.1 by 60 minutes.
That is;
= 0.1 ×60 = 6.
Therefore, the the quantity of 60 minutes that is 0.1 = 6.
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Define Moore’s law. How Moore’s law is associated with exponential function.
Moore's law is an observation made by Gordon Moore, co-founder of Intel Corporation, in 1965. It states that the number of transistors on a microchip doubles approximately every two years, while the cost of the chip is halved. Essentially, this means that computing power increases exponentially over time.
Moore's law is associated with exponential functions because it describes a situation in which a quantity (the number of transistors) grows at a rate proportional to its size, resulting in exponential growth. Exponential functions are often used to model phenomena in science, engineering, and other fields that exhibit this kind of behavior. In the case of Moore's law, the rate of growth is approximately 41% per year, or a doubling every 1.5 to 2 years. The formula for exponential growth is:
y = a * (1 + r)^tWhere:
y = the final amounta = the initial amountr = the annual growth ratet = the number of yearsMoore's law can be expressed using this formula as:
N = N0 * 2^(t / T)Where:
N = the number of transistorsN0 = the initial number of transistorst = the time elapsed since the initial observationT = the doubling time (approximately 2 years)For example, if a microchip had 1,000 transistors in 2000, according to Moore's law it would have 2,000 in 2002, 4,000 in 2004, 8,000 in 2006, and so on. The exponential function describes the growth of the number of transistors over time, and the formula allows us to predict future values based on past observations.
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what is solution set calculator online
A solution set calculator online is a tool used to find the set of values that satisfy an equation or system of equations.
It is useful in a variety of mathematical fields such as algebra, calculus, and linear algebra. The calculator takes in the equation(s) and returns the solution set, which is the set of values that satisfy the equation(s). These calculators can be used for both linear and nonlinear equations, and can help in finding the solutions to problems that are difficult or time-consuming to solve by hand.
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Need help ASAP!! Struggling with these word problems... D:
You invest in AAA-rated bonds, A-rated bonds, and B-rated bonds. The average yields are 4.5% on AAA bonds, 5% on A bonds, and 9% on B bonds. You invest twice as much in B bonds as in A bonds. Let x, y, and z represent the amounts invested in AAA, A, and B bonds, respectively.
x + y + z = (total investment)
0.045x + 0.05y + 0.09z = (annual return)
2y − z = 0
Use the inverse of the coefficient matrix of this system to find the amount invested in each type of bond for the given total investment and annual return. (Round your answers to the nearest cent.)
Total Investment Annual Return
$10,300 $620
The amount invested in AAA - bonds is $5353, amount invested in
A - bonds is $1681 and amount invested in B - bonds is $3369. The solution has been obtained by using matrices.
What are matrices?
The term "matrix of order m by n," sometimes known as "m × n matrix," refers to a rectangular array of m × n numbers (real or complex), organised into m rows and n columns.
Such a range is bounded by [ ] or ( ).
We are given equations as
x + y + z = $10300
0.045x + 0.05y + 0.09z = $620
2y − z = 0
From this, we get the matrix as
[tex]\left[\begin{array}{ccc}1&1&1\\0.045&0.05&0.09\\0&2&-1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}10300\\620\\0\end{array}\right][/tex]
This shows that AX = B
X = A⁻¹B
[tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex] [tex]= \left[\begin{array}{ccc}2.42&-31.57&-0.42\\-0.47&10.52&0.47\\-0.94&21.05&-0.05\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}10300\\620\\0\end{array}\right][/tex]
On solving this, we get
[tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex] [tex]=\left[\begin{array}{ccc}5353\\1681\\3369\end{array}\right][/tex]
Hence, the amount invested in AAA - bonds is $5353, amount invested in A - bonds is $1681 and amount invested in B - bonds is $3369.
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Jessica makes $48,960.00 per year. She has a clothing budget of 5 % of her monthly budget. What was the average amount of money that Jessica's budget allowed for clothing the first six months of 2001?
Answer: Jessica's average clothing budget for the first six months of 2001 was $102.
Explanation: To calculate the average amount of money that Jessica's budget allowed for clothing in the first six months of 2001, we first need to find her monthly budget.
We can do this by dividing her annual salary by 12 (the number of months in a year):
$48,960 / 12 = $4,080 per month
Next, we need to find her clothing budget for one month. We're told that her clothing budget is 5% of her monthly budget, so we can calculate this as follows:
5% of $4,080 = (5/100) x $4,080 = $204
Therefore, Jessica's clothing budget for one month is $204.To find her average clothing budget for the first six months of 2001, we simply need to multiply her monthly clothing budget by the number of months (i.e., 6):
$204 x 6 = $1,224
Finally, we divide this total by the number of months to find the average: $1,224 / 6 = $102
Find the sum: 1/10 + 5/100
A: 15/100
B: 15/10
C:6/100
D:15/110
15/100
1/10+5/100
step1: di LCM si nye denominator si nye 100..emegbe zã denominator la nàtsɔ ama LCM la ..le ema megbe la, èdzinɛ ɖe edzi kple numerator
10+5/100
afɔɖeɖe 2: ƒo xexlẽdzesifianu la nu ƒu
15/100
ale,1/10+4/100 ƒe ƒuƒoƒo nye 15/100
What is the slope of a line perpendicular to a line with a slope of five
Answer: It is undefined
Step-by-step explanation:
Hope this helps-just had a test on this!
Evaluate the expression (12)2•(3•5−3)+13
The Evaluate the expression (12)2•(3•5−3)+13 is [tex]{7\frac{1}{2}[/tex]
Multiply the numerator by the reciprocal of the denominator:
[tex]5(\frac{3}{2} )[/tex]
Multiply [tex]5(\frac{3}{2} )[/tex]:
Combine [tex]5[/tex] and [tex]\frac{3}{2}[/tex]:
[tex]\frac{5⋅3}{2}[/tex]
Multiply [tex]5[/tex] by [tex]3[/tex]:
[tex]\frac{15}{2}[/tex]
The result can be shown in multiple forms.
Exact Form:
[tex]\frac{15}{2}[/tex]
Decimal Form:
[tex]7.5[/tex]
Mixed Number Form:
[tex]{7\frac{1}{2}[/tex]
Hence, The Evaluate the expression (12)2•(3•5−3)+13 is [tex]{7\frac{1}{2}[/tex]
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Answer:
Step-by-step explanation:
66666
I missed a few days in geometry class and now I’m absolutely clueless about how to go about this problem, someone please help
The value of b is given as follows:
b = 18.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.The bisection, represented by the altitude segment in this triangle, divides the triangle into two similar triangles, hence the equivalent side lengths are given as follows:
b and 28 - b.27 and 15.Then the proportional relationship for these side lengths is given as follows:
b/(28 - b) = 27/15
Applying cross multiplication, the value of b is obtained as follows:
15b = 27(28 - b)
42b = 27 x 28
b = 27 x 28/42
b = 18.
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At Silver Gym, membership is $45 per month, and personal training sessions are $25 each. At Fit Factor, membership is $75 per month, and personal training sessions are $15 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Answer:
3
Step-by-step explanation:
Set the equations. Let the variable x denote the amount of months that are needed.
Silver Gym:
In Silver Gym, the membership is a flat fee (constant) of $45, and training sessions are $25 for each session (25x, x denoting the amount of sessions).
Therefore, total cost is:
Total Cost (c) = Training session x Training cost per session + Flat Fee
or
c = 25x + 45
Fit Factor:
In Fit Factor, the membership is a flat fee (constant) of $75, and training sessions are $15 for each session (15x, x denoting the amount of sessions).
Therefore, the total cost is:
Total Cost (c) = Training session x Training cost per session + Flat Fee
or
c = 15x + 75
~
You are trying to solve for the amount of training sessions that have to be bought in which both prices will be the same. Note that both equations are equal to c. Based on the transitive property of equality, if a = b and b = c, then a = c. Therefore:
c = 25x + 45
c = 15x + 75
15x + 75 = c = 25x + 45
15x + 75 = 25x + 45
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 25x and 75 from both sides of the equation:
15x (-25x) + 75 (-75) = 25x (-25x) + 45 (-75)
15x - 25x = 45 - 75
-10x = -30
Next, divide -10 from both sides of the equation:
(-10x)/-10 = (-30)/-10
x = -30/-10 = 3
3 personal training sessions is your answer.
~
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Does (2, –2) make the equation y = –5x + –2 true? yes or no
(2, -2) does not make the equation y = -5x - 2 true.
Why it is and what is an equation ?
We can check if the point (2, -2) satisfies the equation y = -5x - 2 by plugging in the values of x and y and seeing if the equation is true:
y = -5x - 2
-2 = -5(2) - 2
-2 = -12
Since -2 is not equal to -12, the equation is not true for the point (2, -2). Therefore, (2, -2) does not make the equation y = -5x - 2 true.
An equation is a mathematical statement that shows that two expressions are equal.
It typically consists of one or more variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.
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Which get the tens digit of x. Ex: If x = 693, which yields 9?
a. x % 10
b. x % 100
c. (x / 10) % 10
The correct answer is (c) x's tens digit. , if x = 693, that yield 9 is (x / 10) % 10
Here's how we have to evaluate the expression:
Substitute x = 693 into the expression to get:
(693 / 10) % 10
Perform the division first:
693 / 10 = 69 with a remainder of 3.
Substitute the result of the division into the expression:
(69 % 10)
To Evaluate the remainder use the modulo operator (%):
69 % 10 = 9
The result, 9, is the tens digit of 693.
=(x / 10) % 10.
The tens digit of a number refers to the digit in the second place from the right, or the digit that represents the multiple of 10. For example, in the number 365, the tens digit is 6 because it represents 6 tens or 60.
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How do you know if a quadratic equation can be solved by factoring?
A quadratic equation can be solved by factoring if its coefficients are rational numbers and its discriminant, which is the expression under the square root in the quadratic formula, is a perfect square.
To determine if a quadratic equation can be solved by factoring, you must first ensure that its coefficients are rational numbers, meaning that they can be expressed as a ratio of two integers. Once you have confirmed this, you can calculate the discriminant of the quadratic equation, which is the expression b²-4ac, where a, b, and c are the coefficients of the quadratic equation in standard form.
If the discriminant is a perfect square, then the quadratic equation can be solved by factoring. If the discriminant is not a perfect square, then the quadratic equation cannot be solved by factoring using rational numbers, but may still be solvable using other methods, such as completing the square or the quadratic formula.
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A big ship drops its anchor. E represents the anchor's elevation relative to the water's surface (in meters) as a function of time t (in seconds).
E=−2.4t+75
How far does the anchor drop every 5 seconds?
Answer:12
Distance for the anchor drop every 5 seconds is,
⇒ E = 63 meters
What is mean by Multiplication?Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.
Given that;
A big ship drops its anchor.
Here, E represents the anchor's elevation relative to the water's surface (in meters) as a function of time t (in seconds).
E = - 2.4t + 75
Now, Distance for the anchor drop every 5 seconds is,
Put t = 5;
E = - 2.4t + 75
E = - 2.4 × 5 + 75
E = - 12 + 75
E = 63 meters
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An angle measures 63.4° less than the measure of its supplementary angle. What is the measure of each angle?
The measure of the angles required are,
Angle A = 58.3deg
Angle B = 121.7deg
What are Supplementary Angles?If two angles sum up to 180 degrees, they are referred to as supplementary angles. When paired, supplementary angles result in a straight angle (180 degrees). In other words, if angle 1 plus angle 2 equals 180 degrees, angle 1 and angle 2 are supplementary. In this case, Angles 1 and 2 are referred to as "supplements" of one another.
Supplementary angles, by definition, add to to a sum of 180deg.
So what we know is:
Angle B + Angle A = 180deg
Angle B - 63.4deg = Angle A
By substitution:
Angle B + (Angle B - 63.4deg) = 180deg
Using the commutative property of addition, we can re-write the equation as:
(Angle B + Angle B) - 63.4deg = 180deg
We can add 63.4deg to both sides of the equation:
(Angle B + Angle B) - 63.4deg + 63.4deg = 180deg + 63.4deg
By simplifying, that gives us:
2(Angle B) = 243.4deg
Dividing both sides of the equation by 2, we can determine the measure of Angle B:
Angle B = 243.4deg/2 = 121.7deg
Now we have the measure of one of the angles, which we can plug back into our first equation:
Angle B + Angle A = 180deg
121.7deg + Angle A = 180deg
Subtracting 121.7deg from both sides, we get:
Angle A = 180deg - 121.7deg = 58.3deg
There’s your answer:
Angle A = 58.3deg
Angle B = 121.7deg
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Consider the following function. g ( x ) = x 3 − 6 A) Find its average rate of change over the interval [ − 2 , 2 ] . B) Compare this rate with the instantaneous rates of change at the endpoints of the interval.
A- The average rate of change of g(x) over the interval [-2, 2] is 4, B- the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.
A) To find the average rate of change of the function g(x) over the interval [-2, 2], we need to compute the difference quotient:
average rate of change = [g(2) - g(-2)] / [2 - (-2)]
First, we find the values of the function at the endpoints of the interval:
g(-2) = [tex]-2^{3}[/tex] - 6 = -14
g(2) = [tex]2^{3}[/tex] - 6 = 2
Substituting these values into the
average rate of change = (2 - (-14)) / (2 - (-2)) = 16 / 4 = 4
Therefore, the average rate of change of g(x) over the interval [-2, 2] is 4.
B) To compare this rate with the instantaneous rates of change at the endpoints of the interval, we need to find the derivatives of the function at x=-2 and x=2 using the power rule of differentiation:
g'(x) = 3[tex]x^{2}[/tex]
g'(-2) = 3[tex]-2^{2}[/tex] = 12
g'(2) = 12
The instantaneous rate of change at x=-2 is 12, and the instantaneous rate of change at x=2 is also 12. These values are equal to the average rate of change over the interval [-2, 2], which is 4.
This means that the function g(x) is not a linear function over the interval [-2, 2], and the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.
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step to calculate determine equilibrium concentration ?
The steps to calculate the equilibrium concentration have been explained below.
Equilibrium concentration is a state in a chemical reaction, at which the rate of forward reaction becomes the same as the rate of backward reaction.
Calculating equilibrium concentration requires several steps depending on the type of equilibrium you are dealing with which are,
1)Write the balanced chemical equation for the reaction.
2)Write the equilibrium expression that describes the relationship between the concentrations of the reactants and products at equilibrium.
3)Determine the initial concentrations of the reactants and/or products
4)Determine the direction of the reaction by comparing the initial concentrations of the reactants and products with the equilibrium constant (Keq).
5)Calculate the change in concentration between the equilibrium concentration and the initial concentration.
6)Calculate the equilibrium concentration by adding the change in concentration to the initial concentration.
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how to convert 1gb to mb?
Answer:
To convert GB to MB multiply the value of a GB by 1000 to get mb.
1gb x 1000 equals 1000 mb
what is a shape with 7 sides?
The shape with 7 sides is called a heptagon.
There a several shapes which has more number of sides than the usual shapes like square, circle or triangle.
As the number of the sides in the shape increases the propertied of the shape also changes. If the shape has 7 sides it is called a heptagon and if it has 6 sides than it is called a hexagon, it it has a 5 sides it is called a pentagon.
If all the 7 sides of the pentagon are equal in magnitude then the heptagon is said to be a regular heptagon but is not equal then they are called heptagon with different features.
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How to convert 112 kg to lbs?
The required value of 112 kilograms into pounds using standard conversion relation is equal to 112 kilograms = ( 246. 92 ) pounds ( round up to two decimal places )
Units pounds and kilograms are used to measure the mass of a given things.One kilograms is equal to 2.20462 pounds.
We need to convert 112 kilograms into pounds :
This implies :
⇒ 112 kilograms = ( 112 × 2.20462 ) pounds
⇒ 112 kilograms = ( 246.91744 ) pounds
⇒ 112 kilograms = ( 246. 92 ) pounds ( round up to two decimal places )
Therefore, the converting value of kilogram to pounds is given by :
112 kilograms = ( 246. 92 ) pounds ( round up to two decimal places ) .
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I need some help with this I don't really understand this.
Answer: 31.5
Step-by-step explanation:
6*4=24 (Shaded Rectangle)
3*5=15 15/2=7.5 (Shaded Triangle)
7.5 + 24 = 31.5
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use familiar figures to find the area of the figure shown. Show all work.
Answer: 10in
Step-by-step explanation: It's been awhile since I have done a problem like this but what you would do first is LxHxW of coarse. I believe you would multiply 5x2=10 3x10=30 30+10=40 40 divided by 4= 10. I'm sorry if it's wrong like I said it's been awhile.
Find the area of the square ABCD. A D BE IC 14 m- [?] m[ ]
Answer:
196 m²
Step-by-step explanation:
area = side × side
area = 14 m × 14 m
area = 196 m²
Find the orthogonal trajectories for the family of curves. (enter your solution in the form f(x, y) = c or y = f(x, c) where c is a needed constant. ) y = ce5x
Refer to the attached image.
What would be the cosine for sin 55 ?
Answer:
0.5735764
Step-by-step explanation:
sin(55°) = √(1-cos²(55°))
Answer:
The answer is 0.5735764
Step-by-step explanation:
sin(55°) = √(1-cos²(55°)
Hope this helped! Have a GOOD DAY!
Please Help! Thank you
The side of the small square is equal to the length of the rectangles, which is 16cm.
What is area?Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.
We can calculate the area of the small square by using the formula A = side² where A is the area and side is the length of the side of the square. Thus, A = 16² = 256 cm².
Now, the area of the large square is equal to the area of the small square plus the area of the four rectangles. The area of each rectangle is equal to 16 x 4 = 64 cm² Thus, the total area of the large square is 256 + 4(64) = 512 cm²
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Please help me for 30 points!!.
Answer: Correct option is B
Step-by-step explanation: 3/6 + 2/6 = 5/6
What is 729 cube rooted?
The value of 729 cube root is 9.
The cube root function is important in various mathematical applications, including calculus, geometry, and physics.
The cube root of 729 is the number that when multiplied by itself three times, results in 729. This number is often represented as the symbol ³√729.
In other words, if we cube the cube root of 729, we get back the original number 729. The cube root of 729 is 9, since 9 x 9 x 9 = 729.
In mathematical terms, the cube root of 729 can be expressed as: ³√729 = 9.
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find the missing side x 4 13
The length of missing side of the given right triangle by using pythagoras theorem is x = 12.369 .
Pythagoras Theorem :The hypotenuse side of a right-angled triangle's square is equal to the sum of the squares of the other two sides, according to Pythagoras' Theorem. The Perpendicular, Base, and Hypotenuse of this triangle are its three sides. Because to its position opposite the 90° angle, the hypotenuse in this case is the longest side. A right triangle's positive integer sides (let's say sides a, b, and c) are squared to obtain a Pythagorean triple equation.
Formula for Pythagoras' Theorem :Consider about the triangle given above:
the perpendicular to "a,"
B stands for base,
The letter "c" stands in for the hypotenuse.
The definition provides the following as the Pythagoras Theorem formula:
[tex]Hypotenuse^2 = Base^2 + Perpendicular^2\\\\c^2 = a^2 + b^2[/tex]
The right triangle's sides are as follows:
Perpendicular ( p ) = x
Base ( b ) = 4
Hypotenuse ( h ) = 13
Finding the length of missing side
Using Pythagoras theorem
[tex]p^2 +b^2=h^2[/tex]
plug the values
[tex]x^2+4^2=(13)^2[/tex]
Evaluate the power
[tex]x^2+16=169\\\\x^2=169-16\\\\x^2=153\\\\x=\sqrt{153}\\\\x= 12.369[/tex]
The length of missing side x = 12.369
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The complete question is ,
Find the missing side of the given right triangle whose sides are given as base = 4 units , hypotenuse = 13 units .
Given the functions f(x) and g(x) below, find all solutions to the equation
f(x) = g(x) to the nearest hundredth.
f(x) = 0.15x³ 2x² + 7x - 3.3
g(x) = 1.5|x - 7.3
The solutions to the equation f(x) = g(x) to the nearest hundredth are: x = -8.85, -5.1 and x = 0.6
What is the solution of the function?
To find the solutions to the equation f(x) = g(x), we need to solve for x such that:
0.15x³ + 2x² + 7x - 3.3 = 1.5x - 7.3
We can simplify this equation by bringing all the terms to one side:
0.15x³ + 2x² + 5.5x - 4 = 0
To find the solutions to the nearest hundredth, we can use a graphing calculator or software to graph the functions f(x) and g(x) and find their points of intersection.
Using a graphing calculator , we can plot the two functions and find that they intersect at two points;
approximately x = -8.85, -5.1 and x = 0.6
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