Answer:
He will need to pay 5.4 Ghana cedis into his educational fund.
Step-by-step explanation:
We need to multiply 4 1/2 by 120 since it is a percentage. We convert 4 1/2 into a decimal which is 4.5. Now, we just need to multiply 120 by 4 1/2 to get an answer of 5.4.
First, complete the sentence to show how the figure can be decomposed into triangles and rectangles with the fewest number of pieces Then find the area of the divisions.
The figure will have a triangle and a rectangle. The area of a triangle is 10 in² and the rectangle is 80 in². Therefore, the total area is 90 in².
Area of Compound ShapesThis question requires your knowledge about the area of compound shapes. For solving this, you should:
Identify the basic shapes; Calculate your individual areas; Sum each area found. STEP 1 - Identify the basic shapes.The figure is composed of a triangle and a rectangle.
Therefore, you should sum the area of these geometric figures for determining the area of the irregular figure.
STEP 2 - Find the area of the trinagle.Area of the triangle= [tex]\frac{b*h}{2}[/tex]. The figure shows that: the base = 10 in and the height =2 in
Thus, A_triangle=[tex]\frac{b*h}{2}=\frac{10*2}{2} =10 in^{2}[/tex]
STEP 3 - Find the area of the rectangle.Area of the rectangle = bh . The figure shows that: the base = 10 in and the height =8 in
Thus, A_rectangle=bh= 10*8=80 in²
STEP 4 - Find an expression for the total area of the figure.
A_total= A_triangle + A_rectangle
A_total= 10+80=90 in²
A_total= 90 in²
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Students were asked to write an expression equivalent to the expression below:
30a+12b-6a+ 2(9b+c+15)
Their answers are as follows:
36a-30b+2c +30
Ben wrote: 36a - 30b + 2c + 30
Martin:
24a+30b+2c +30
Sara wrote: 24a + 30b + 2c + 15
Martin wrote: 24a + 30b+2c +30
Which, if any, of those students wrote expressions that are equivalent to the original expression?
In the space provided below, either prove why each student's response is equivalent, or explain and correct the student's error.
Sara
| Ben:
Allie wrote: 2(12a + 15b+c+15)
24a+30b+ac+15
Allie:
2(13a +156+c+15)
The equivalent is 24a + 30b +2c + 30
How to determine the equivalent expressionGiven the original expression as;
30a+12b-6a+ 2(9b+c+15)
First, expand the bracket, we have
30a + 12b -6a + 18b + 2c + 30
Then, collect like terms
30a -6a + 12b + 18b + 2c + 30
24a + 30b +2c + 30
The equivalent is 24a + 30b +2c + 30
From the result, we have that Martin is correct.
Sara wrote the equivalent as 24a + 30b +2c + 15
She made a mistake in expand the bracket = 2( 9b +c +15) = 18b + 2c + 30
Ben wrote 36a - 30b + 2c + 30. He made a mistake in issuing the sign for 30b = 12b + 18b = +30b
Thus, the equivalent is 24a + 30b +2c + 30
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\sqrt{27} - \sqrt{ 12} + \sqrt{48 }
Answer:
[tex]5\sqrt{3}[/tex]
Step-by-step explanation:
I'm assuming you're asking for most simplified form?
Original Equation:
[tex]\sqrt{27} - \sqrt{12} + \sqrt{48}[/tex]
Rewrite sqrt(27) using the exponent property: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex]
[tex]\sqrt{9} * \sqrt{3} -\sqrt{12} + \sqrt{48}[/tex]
Simplify sqrt(9)
[tex]3\sqrt{3} -\sqrt{12} + \sqrt{48}[/tex]
Rewrite the radical sqrt(12)
[tex]3\sqrt{3} -\sqrt{4}\sqrt{3} + \sqrt{48}[/tex]
Simplify sqrt(2)
[tex]3 \sqrt{3} -2\sqrt{3} + \sqrt{48}[/tex]
Rewrite the radical sqrt(48)
[tex]3\sqrt{3} -2\sqrt{3} + \sqrt{16}\sqrt{3}[/tex]
Simplify the sqrt(16)
[tex]3\sqrt{3} -2\sqrt{3} + 4\sqrt{3}[/tex]
You can think of sqrt(3) as x, in which case you have 3x - 2x + 4x, so you just add the coefficients and leave the sqrt(3) alone.
Subtract 2 from 3
[tex]1\sqrt{3} + 4\sqrt{3}[/tex]
Add 1 and 4
[tex]5\sqrt{3}[/tex]
Find the LCM of 10 and 25?
Distance (feet)
2
14
12
10
20
5
4
2
2
4
6
garden
Distance (feet)
12 14 15
The diagram shows a garden plot. The area of the garden is
garden is … square feet.
square feet. The length of fencing required to completely enclose the garden is … feet.
The area of a 2D form is the amount of space within its perimeter. The area of the garden is 72 feet² and the perimeter of the garden is 36 feet.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The diagram for the given garden is given below.
1.) The area of the garden is,
The area of the garden = Area of rectangle + Area of triangle
= (6 x 8) + (0.5 x 6 x 8)
= 48 + 24
= 72 feet²
2.) The perimeter of the garden is,
The perimeter of the triangle = 12 + 8 + 6 + 10 = 36 feet
Hence, the area of the garden is 72 feet² and the perimeter of the garden is 36 feet.
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What fraction of £1 is 31p?
The fraction of 1 pound to 31 penny is 31/100.
Given that, £1 and 31 p.
What is metric conversion?Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
We know that, 1 pound = 100 penny
Now, the fraction of £1 is 31 p is
31/100
Therefore, the fraction of 1 pound to 31 penny is 31/100.
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Does this graph represent a function? Why or why not?
C A. Yes, because it passes the vertical line
test.
B. No, because it is not a
straight line.
No, because it fails the vertical line test.
O D. Yes, because it passes the horizontal line test.
Answer:
A. Because it passed the y axis
Which best explains if quadrilateral WXYZ can be a parallelogram?
A quadrilateral in which opposite sides are parallel is called a parallelogram. The correct option is A.
What is a parallelogram?A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
For a parallelogram, the pair of opposite sides are equal and parallel. Therefore,
1.) For the first pair.
(x+8) = 15
x = 7
2.) For the second pair
(x+2)=(2x-5)
x + 2 = 2x - 5
2 + 5 = 2x - x
x = 7
(x+2) = (7+2) = 9
Since the measure of the pair of opposite sides is 15 units, the pair of the other two sides measure 9 units.
Hence, the correct option is A.
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in which quadrant will you find the point (-2,-2)
⊱________________________________________________________⊰
Answer:
Quadrant 3Step-by-step explanation:
Points with both negative co-ordinates are found in the third quadrant.
[tex]\boxed{\begin{tabular}{c | 1} \sf{~~Quadrant 2 (-x,y)~~& Quadrant 1~ (x,y)~~} \\ \\\\\\\\\\\\ \cline{1-2} \sf{Quadrant \ 3 (-x,-y) \ & Quadrant \ 4 (x,-y)} \\\\\\\ \\\\\\\\\\\end{tabular}}[/tex]
done !!
⊱_____________________________________________________⊰
Is the function y = –9x^8+3 linear or nonlinear?
Answer:
It is nonlinear
Step-by-step explanation:
Verbal
2. How can you tell whether an absolute value function
has two x-intercepts without graphing the function?
Without graphing an absolute value function, you can tell whether it has two x-intercepts by isolating the absolute value term to have an equation of the form |A| = B and then form two different equations.
What is an absolute value function?An absolute value function can be defined as a type of function that consist of an algebraic expression, which placed within absolute value symbols
Mathematically, the standard form of the equation for an absolute value function is given by:
y = a|x - h| +k.
Where:
h and k are the vertex of the graph.
Without graphing an absolute value function, you can tell whether it has two x-intercepts by isolating the absolute value term to have an equation of the form |A| = B and then form two different equations.
Lastly, solve each equation for the two x-intercepts.
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Pleaseeee helppppppp
Answer:
The second choice (-6, -5 2/5, -4 1/5)
Step-by-step explanation:
1) Find the nth term by using the rule given. Foil them out.
A(n) = -6 + 1/5n - 1/5
A(n) = 1/5n - 31/5
2) Find the first term by substituting 1 into n.
a1 = 1/5(1) - 31/5
a1 = -6
3) Find the fourth term by substituting 4 into n.
a4 = 1/5(4) - 31/5
a4 = -27/5 or -5 2/5
4) Find the tenth term by substituting 10 into n.
a10 = 1/5(10) - 31/5
a10 = -21/5 or -4 1/5
Therefore, the second choice (-6, -5 2/5, -4 1/5) is correct.
Which ordered pair below is a solution to the following system of equations?
-x + 2y = 5
x + y = 1
Answer:
The correct option is OPTION (A) .
Solve 4(5)^x= 500.
help please
Answer:
x=3
Step-by-step explanation:
Isolate x.
[tex]4(5)^x=500[/tex] Divide both sides by four
[tex]5^x=125[/tex] Take [tex]log_{5}[/tex] of both sides. In other words, what power must you raise 5 to in order to get 125? ([tex]5^3=125[/tex])
x=3
Please Help Asap Please And Thank You.
Answer:
m (slope) = -1/10; the slope means that every 1/10 minute the candle goes down 1/100 centimeters OR every 10 minutes the candle goes down 1 centimeter; the y intercept is how tall the candle is at the beginning
Step-by-step explanation:
to find the slope of this line we can simply use the (y2 - y1) / (x2 - x1) formula
that gives us
(0 - 25) / (250 - 0)
or
-25/250
or
-1/10
the slope means that every 1/10 minute the candle goes down 1/100 centimeters OR every 10 minutes the candle goes down 1 centimeter
the y intercept is how tall the candle is at the beginning
By what percent will the fraction increase if its numerator decreased by 30% and the denominator decreased by 50%
Answer:
140%
Step-by-step explanation:
So a fraction can be expressed as: [tex]\frac{a}{b}[/tex] and if a number decreases by x%, the new number is (100-x)% the original value. So since the numerator decreases by 30%, it's not 70% the original value, and it's very similar with the denominator, with it only retaining 50% of it's original value. This gives you the formula: [tex]\frac{0.70a}{0.50b}[/tex]. You can rewrite the fraction as: [tex]\frac{1.4 * 0.5 * a}{0.5 * b}[/tex] in doing so it's easy to see that you can cancel out the 0.5 and get: [tex]1.4\frac{a}{b}[/tex]. This means the value is increasing by 1.4 or 140%
Answer:
140%
Step-by-step explanation:
since the numerator decreases by 30%, it isnt 70% the original value, This gives a formula: . You can rewrite the fraction as so, in doing so it's easy to see that you can cancel out the 0.5 and get: . This means the value is increasing by 1.4 or 140%.
Random assignment to treatments helps control for lurking variables ? true ? false.
It is true that Random assignment to treatments helps control for lurking variables
The main purpose for using randomization in an experiment is to create sure that the results are accurate. you wish to avoid biasis and lurking variables. Having a randomized experiment will facilitate your to create sure that your information is correct
The main purpose for using randomization in an experiment is to manage the lurking variable and establish a cause and effect relationship. Also, by randomizing an experiment the evidence is more supported
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Discuss the implications of an infinite-dimensional space in generalization ability of the hard-margin SVM. What are the strategies we can use to improve generalization
The SVM classifier's generalization performance is improved by decreasing the VC dimension.
What is SVM ?SVM stands for Support Vector Machine .
A potent machine learning technique for classification and regression is called a Support vector machine. The selection of a margin type is crucial if we want to use it to solve an issue.
A soft margin or a hard margin can be chosen on the basis of the data , If the data is linearly separable , hard margin is used , If the data is not separable linearly and misclassifications can be allowed then soft margin is used.
The hard margin SVM's capacity for generalization is significantly influenced by VC.
the SVM classifier's generalization performance is improved by decreasing the VC dimension.
We contend that by using dimensionality reduction and bootstrapping techniques, the VC dimension of an SVM classifier can be decreased.
The SVM classifier's performance was now enhanced by bootstrapping both the original data and the projected data that is dimensionally reduced .
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Find m/CDU if m/CDE-154° and m/UDE = 108°.
U
E
D
C
Answer: [tex]46^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle CDE=m\angle UDE+m\angle CDU\\\\154^{\circ}=108^{\circ}+m\anlge CDU\\\\m\angle CDU=46^{\circ}[/tex]
Flo has two equations that she found to be valuable models for her research. She thinks that if she can find the solution of the two graphs, she will be able to identify a key point to her studies. What can Flo expect to be her outcome for the solutions of these two graphs?
The point of intersection is (-2,1) and this is the solution of the two graphs and the correct option is A.
What is a System of Equations?The system of equations is the set of equations that have a common solution.
The solution to the graph given is the answer to the Flo's model
The intersection point of the line of the two-equation is the solution to the two equations.
The point of intersection is (-2,1) and so the correct option is A.
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The graphs below have the same shape. What is the equation of the blue
graph?
G(x) =
―
F(x)=x3
-6
O A. G(x) = (x+1)³
OB. G(x) = x³-1
OC. G(x) = (x-1)³
OD. G(x)= x³ +1
GX) = ?
Using translation concepts, it is found that the equation of the blue graph is given by:
C. G(x) = (x - 1)³.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the function G(x) is a shift of one unit right of F(x) = x³, hence it's equation is:
G(x) = F(x - 1) = (x - 1)³.
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There are 4 circles and 6 triangles. What is the simplest ratio of circles to triangles?
Answer:
2/3
Step-by-step explanation:
Since there are 4 circles and 6 triangles, and they are asking for the ratio of circles to triangles, the fraction would be 4/6
4/6 when divided by two = 2/3 which is the simplest form of the fraction 4/6
The simplest ratio of circles to triangles would be; 2/3
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that there are 4 circles and 6 triangles.
Since there are 4 circles and 6 triangles, and they are asking for the ratio of circles to triangles, the fraction would be as given;
4/6
when divided by two we get;
2/3
This is the simplest form of the fraction 4/6
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Which expression is equivalent to (4 + 6)²?
Answer:
A) -20+48i
Step-by-step explanation:
[tex](4+6i)^2\\(4+6i)(4+6i)\\16+24i+24i+36i^2\\**i^2=-1*\\16+48i+36i^2(-1)\\16+48i-36\\-20+48i[/tex]
How many positive three-digit numbers are evenly
divisible by 33?
Answer:
27
Step-by-step explanation:
smallest multiple of 33 that is 3 digits is 132 (33*4), and largest is 990 (33*30)
then all the numbers between 4 and 30 would also be 3 digits
including 4 and 30, that makes 27 number in total
Simplify, state all restrictions.
The simplified expression is [tex]\frac{1 - x - y}{x + y}[/tex]and the restriction is [tex]y \ne -x[/tex]
How to simplify the expression?The expression is given as:
[tex]\frac{x - y}{4x^2 - 8xy + 3y^2} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{x^2 - y^2} -1[/tex]
Express x^2 - y^2 as (x + y)(x - y) and factorize other expressions
[tex]\frac{x - y}{(2x - y)(2x - 3y)} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1[/tex]
Rewrite the expression as products
[tex]\frac{x - y}{(2x - y)(2x - 3y)} \times \frac{2x - 3y}{2x + y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1[/tex]
Cancel out the common factors
[tex]\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{4x^2 - y^2}{(x + y)} -1[/tex]
Express 4x^2 - y^2 as (2x - y)(2x + y)
[tex]\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{(2x - y)(2x + y)}{(x + y)} -1[/tex]
Cancel out the common factors
[tex]\frac{1}{x + y} -1[/tex]
Take the LCM
[tex]\frac{1 - x - y}{x + y}[/tex]
Hence, the simplified expression is [tex]\frac{1 - x - y}{x + y}[/tex]and the restriction is [tex]y \ne -x[/tex]
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The ratio of the area of the shaded part to the unshaded part is______.
Answer: 1 : 3
Shaded area:
[tex]\Longrightarrow \sf Length \ \times \ Breadth = \dfrac{x}{4} \ \times \ x \ = \ \dfrac{1}{4}x^2[/tex]
Unshaded area:
[tex]\Longrightarrow \sf Length \ \times \ Breadth = (x - \dfrac{x}{4}) \ \times \ x \ = \ \dfrac{3}{4}x^2[/tex]
Ratio of shaded to unshaded:
[tex]\Longrightarrow \sf \dfrac{1}{4} x^2 \ : \ \dfrac{3}{4} x^2 = 1 : 3 \quad (simplified)[/tex]
Two similar triangles have areas 16 and 4. if a side of the smaller triangle measures 2, find the length of the corresponding side in the larger triangle.
Answer: 4
Step-by-step explanation:
The ratio of the areas of similar figures is the square of the side length.
Since the ratio of the areas is 16:4 = 4:1, the ratio of the side lengths is 2:1.
So, the length of the corresponding side is 2(2) = 4.
A given gas powered water pump delivers 42.50 gallons of water per minute. This value can also be expressed as _____________ L/s (Liters per second).
The rate at which the gas powered pump deliver water is 160.9 litres per seconds
How to convert rate?The gas powered water pump delivers 42.50 gallons of water per minute.
Therefore,
1 gallon = 3.78541 litres
42.50 gallons = ?
cross multiply
volume = 42.50 × 3.78541 = 160.879925 litres
Hence,
60 seconds = 1 minutes
1 second = ?
time = 1 / 60 = 0.01666666666 seconds
Hence,
rate = 160.9 litres per second
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Factorise the following:
a) x² + 10x + 16 answer
Factoring polynomials is breaking them down to the products of other smaller polynomials. Identifying the greatest common divisor (GCF) is an important first step because it will reduce the number of factors in each term and thus make factoring easier. In addition to polynomials, it can be factored by decomposition of the intermediate term or by difference of squares. Then, the Zero Product Property can be applied to solve the equation.
x² + 10x + 16Use the sum-product pattern.
x² + 8x + 2x + 16Extract the common factors.
x (x + 8) + 2(x + 8)Rewrite factored
( x + 2 ) ( x + 8 ) ===> Answer{ Pisces04 }Answer:
(x+2)(x+8)
Step-by-step explanation:
two numbers that multiply to 16 and add up to 10 is 2 and 8. You just plug both numbers in this factored form (x+ n1)(x+n2). if you chech the answer by multiplying the binomials, you will find out that the answer is the original question (x^3 +10x+16).
Given that A varies directly as B and inversely as C and that; A=12 when B=3 and C=2. Find B when A=10 and C=1.5
Answer:
B = 1.875
Step-by-step explanation:
given that A varies directly as B and inversely as C then the equation relating them is
A = [tex]\frac{kB}{C}[/tex] ← k is the constant of variation
to find k use the condition A = 12 when B = 3 and C = 2 , then
12 = [tex]\frac{3k}{2}[/tex] ( multiply both sides by 2 to clear the fraction )
24 = 3k ( divide both sides by 3 )
8 = k
A = [tex]\frac{8B}{C}[/tex] ← equation of variation
when A = 10 and C = 1.5 , then
10 = [tex]\frac{8B}{1.5}[/tex] ( multiply both sides by 1.5 )
15 = 8B ( divide both sides by 8 )
1.875 = B