[tex]\mathbf{\frac{23}{90}}[/tex] fraction of all shapes are circles.
Given that the ratio of the number of white shapes to black shapes is 7:3
Let the number of white shapes be [tex]7n[/tex]
Then the number of black shapes be [tex]3n[/tex]
So total number of shapes [tex]=7n+3n=10n[/tex]
Now ratio of white circles to white squares is 2:7
So the fraction of circles to all white shapes [tex]=\frac{2}{2+7}=\frac{2}{9}[/tex]
Hence the number of white circles [tex]=\frac{2}{9}\times7n=\frac{14n}{9}[/tex]
Again given that the ratio of black circles to the number of black sqaures is 1:2
So the fraction of circles in all black shapes [tex]=\frac{1}{1+2}=\frac{1}{3}[/tex]
The number of black circles [tex]=\frac{1}{3}\times3n=n[/tex]
Total number of circles [tex]=\frac{14n}{9}+n=\frac{14n+9n}{9}=\frac{23n}{9}[/tex]
The fraction of all shapes are circle is [tex]=\frac{\frac{23n}{9}}{10n}=\frac{23n}{90n}=\frac{23}{90}[/tex]
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find the value of x
Answer:
x=5
\
Step-by-step explanation:
Answer:
x = 0
Step-by-step explanation:
Line segment UV and line segment VW together form line segment UW.
UV + VW = UW
(5 + x) + (6) = (2x + 11)
5 + x + 6 = 2x + 11
x + 11 = 2x + 11
x + 11 - 11 = 2x + 11 - 11
x = 2x
x - x = 2x - x
0 = x
You can also verify the result by substituting x with our result 0.
5 + x + 6 = 2x + 11
5 + (0) + 6 = 2(0) + 11
11 + 0 = 0 + 11
11 = 11
Left side of the equation is the same as the right side of the equation, therefore the result x = 0 is correct.
Brian invests £6600 into his bank
account.
He receives 0.6% per year compound
interest.
How much will Brian have after 6 years?
Give your answer to the nearest penny
where appropriate.
O
→ £ 1
Answer:
See Below
Step-by-step explanation:
The equation for this scenario would be ( compounded annually)
6600 ( 1 + .006)^6 = £ 6841.19
Answer:
Brian will have £6841.19 after 6 years.
Step-by-step explanation:
The compound interest formula is:
[tex]A = P( 1 +\frac{r}{100} )^{n}[/tex] ,
where A is the final amount, P is the initial (principal) amount invested (£6600), r is the interest rate (0.6%) and n is the number of years the money is kept for (6 years).
Using the formula:
[tex]A = 6600(1 + \frac{0.6}{100} )^{6}\\\\A = 6841.19[/tex]
Which algebraic expression represents the phrase “two times the quantity of a number minus 12”?
Answer:
The algebraic expression which represents the phrase “two times the quantity of a number minus 12” is : 2x- 12
Step-by-step explanation:
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
for example :-
3x + 4y – 7, 4x – 10, etc.
These expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three (as terms) is said to be an expression. It is to be noted that, unlike the algebraic equation, an algebraic expression has no sides or equal to sign
let the quantity mentioned in the question be 'x'
therefore according to the statement the algebraic expression which represents the phrase “two times the quantity of a number minus 12” is : 2x- 12 is
⇒2x - 12 (answer)
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which value of a and b make the equation true?
(2xy)4
An equation is formed of two equal expressions. The correct option is B.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The complete option is:
Which values of a and b make the equation true?
[tex]\dfrac{(2xy)^4}{4xy}=4x^ay^b[/tex]
A)a = 0, b = 0
B)a = 3, b = 3
C)a = 4, b = 4
D)a = 5, b = 5
The given equation can be simplified as shown below,
[tex]\dfrac{(2xy)^4}{4xy}=4x^ay^b\\\\\dfrac{2^4 \times x^4 \times y^4}{4xy}=4x^ay^b\\\\\dfrac{16x^4y^4}{4xy} = 4x^ay^b\\\\4x^{(4-1)}y^{(4-1)} = 4x^ay^b\\\\4x^3y^3 = 4x^ay^b[/tex]
Now, comparing the two sides of the equation, the value of a and b should 3 for the equation to be satisfied.
Hence, the correct option is B.
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Dose this tablet represent a function? Why or why not? {(2,1), (2,4), (3,4), (4,2), (5,5)}
Answer:
This mapping isn't a function.
Step-by-step explanation:
A mapping specifies a relation between two sets of items (input and output). For example, a mapping of the form [tex]\lbrace (x_{0},\, y_{0}),\, (x_{1},\, y_{1})\rbrace[/tex] would map the input [tex]x_{0}[/tex] to output [tex]y_{0}[/tex] and map the input [tex]x_{1}[/tex] to output [tex]y_{1}[/tex].
A function is a mapping where each input is associated with exactly one output.
Note that both [tex](2,\, 1)[/tex] and [tex](2,\, 4)[/tex] are in the mapping given in this question. The input [tex]2[/tex] is mapped to more than one outputs. Thus, this mapping isn't a function.
The Law of Sines states that sin A/b = sin B/c = sin C/a
True
False
Step-by-step explanation:
hope you can understand
My rule is:y=1/3x+11/15 find x if y=6
Answer:
x=79/5 or 15.8
Step-by-step explanation:
....................
Answer:
[tex]\frac{79}{5}[/tex]
Step-by-step explanation:
Combine [tex]\frac{1}{3}[/tex] and x.
[tex]\frac{x}{3} +\frac{11}{15}=6[/tex]
Move all terms not containing x to the right side of the equation.
[tex]\frac{x}{3}=\frac{79}{15}[/tex]
Multiply both sides of the equation by 3.
3[tex]\frac{x}{3}[/tex]=3([tex]\frac{79}{15}[/tex])
Then 3 cancels out on the left side so all is left is 3.
On the right side, you need to multiply.
3 times 79 is 237.
Now simplify and you get:
79/5
Hope this helped!
simplify 26a7 + (-25a7)
Answer:
1a7
Step-by-step explanation:
26+-25=1
According to the table below, which of these is a possible taxable income for
a taxpayer filing with the Single filing status in the 33% federal income tax
bracket?
Based on the table, a possible taxable income for a taxpayer that's filing with the Single filing status in the 33% federal income tax bracket is $300,000.
What is taxation?Taxation is the involuntary fees that are levied on individuals or business firms by the government of a particular country, so as to generate revenues that can be used to fund public projects, institutions and activities.
In this scenario, we can infer and logically deduce that a possible taxable income for a taxpayer that is filing with the Single filing status in the 33% federal income tax bracket is $300,000.
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Pedro's dining room is 5 metres wide and 6 metres long. pedro wants to install a new wood floor. it will cost $2.18 per square metre. how much will pedro's new floor cost?
Answer:
65.4
Step-by-step explanation:
5 × 6 = 30 square meter
30 × 2.18 = 65.4
Identify the arc length of BD◠ in terms of π and rounded to the nearest hundredth.
The Arc Length BD from the given diagram is; 4.09π = 12.85 in
How to find the arc length?From the attached image, we are given;
m∠APC = 92°
Now, from the principle of vertical angles being congruent, we have;
m∠APC = m∠BPD = 92°
Thus;
Arc length BD = 2π * 8 * (92/360)
Arc Length BD = 4.09π = 12.85 in
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Someone please help with this !!!!!
Answer:
[tex]5^{\circ}[/tex]
Step-by-step explanation:
[tex]~~~~~~~\tan \theta = \cot 85^{\circ}\\\\\implies \tan \theta = \tan\left(90^{\circ} - 85^{\circ} \right)\\\\\implies \tan \theta = \tan 5^{\circ}\\\\\implies \theta = 5^{\circ}[/tex]
What is the slope of the line segment?
1 over 4
Negative 1 over 4
4
−4
100 Points to whoever answers
The graph below shows a company's profit f(x), in dollars, depending on the price of pencils x, in dollars, sold by the company:
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?
Part B: What is an approximate average rate of change of the graph from x = 2 to x = 5, and what does this rate represent?
Part C: Describe the constraints of the domain.
The average rate of the change from x = 2 to x = 5 is about 20 , The domain is constrained at x =0
What is a Function ?A function is a mathematical statement used to derive a relation between a dependent variable and an independent variable.
A) The vertical axis of the graph shows a company's profit f(x), in dollars, depending on the price of pencils x, in dollars, sold by the company , i.e is the x axis .
So the x-intercepts represent prices of the pencil at which the profit is 0
and The maximum value of the graph represents the maximum profit that can be obtained for any price of the pencil.
The Profit is increasing from (x = 0 to 5) and starts decreasing from x =5 to 10
B) From the graph
(f(5) -f(2))/(5 -2) = (160-100)/3 = 20
The average rate of the change from x = 2 to x = 5 is about 20.
This indicates that the profit will increase at a an average rate of $20 for each $1 increase in price in that interval.
(C)The domain is constrained at x =0 as there it cannot be concluded that if the price is 0 , the profit will be 0 , and we are obligated to sell the pencil at x =6 , as the maximum profits are booked at that point.
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Using p as the variable for the problem below, solve for p. Submit your answer
as an inequality, using "<=" for < or ">" for ≥ if necessary. Round to two
decimal places.
Hosting a dinner party for 38 people, you plan to serve peach pie for dessert.
Each pie has 8 slices. How many pies must you buy to ensure each guest
gets 1 slice?
Answer:
Step-by-step explanation:
As host, we want to insure each guest has at least one slice of pie. We can say (1 Slice/Guest) and use this as a conversion factor. We also know each pie has 8 slices: (8 Slices/1 Pie). Since this is a conversion factor, we can invert it to (1 Pie/8 Slices). We expect 38 people and want to convert that number of people to the number of pies, p, we need.
p (pies) [tex]\geq[/tex] (38 Guests)*(1 Slice/Guest)*(1 Pie/8 Slices)
We use the [tex]\geq[/tex] sign to note that we need a minimum of pies to be sure everyone is served.
p (pies) [tex]\geq[/tex] (38 )*(1 /)*(1 Pie/8 )
Note how the units cancel:
Guests and Slices both cancel and we are left with pies as the only remaining unit, as we hoped we'd see.
p [tex]\geq[/tex] (38/8) pies
p = 4 +(6/8) pies
Since we cannot purchase 6/8 of a pie, we need to round up to 5 pies.
5 pies, at 8 slices per pie, will provide 40 servings, enough for the 38 guests.
Which is a rational function?
A. Y=5
B. Y=√x-3
C. Y=x²-3x+5
D.Y = x-5/x
Does this graph represent a function? Why or why not?
10.
8
6
4
2
-10 8 6 4 2
88
-8
10
2468 10
A. No, because it fails the vertical line test.
O B. No, because it is not a straight line.
OC. Yes, because it passes the horizontal line test.
OD. Yes, because it passes the vertical line test.
Answer:
D.) Yes, because it passes the vertical line test.
Step-by-step explanation:
For a function to be a function, there must be one output for every input. IN other words, there must be one "y" value for every "x" value. One can see if a graph passes this test by performing the vertical line test.
In this case, the line on the graph passes the test and represents a function. Again, this is because each "x" value has only one "y" value.
Yes, The graph is function because it passes the vertical line test.
We have to given that,
A graph of function is shown in image.
Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
And, The vertical line test is used to determine if a graph of a relationship is a function or not. if you can draw any vertical line that intersects more than one point on the relationship, then it is not a function.
Hence, By given graph,
it passes the vertical line test.
So, Graph shown is a function.
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Yui makes a list of the balances in her savings account at the end of each month. She notices that each month’s total is 5% greater than the previous month’s total. She writes a recursive formula to describe the account balances.
The Common Ratio is 1.05 . Option C is the answer.
The complete question is
Which value should she use as the common ratio?
0.05
0.5
1.05
5.0
What is common Ratio ?In a Geometric Sequence the ratio between each if the consecutive number is called the common Ratio.
Let Yui saving at the end of first month is Rs.x .
As given in the question
each month’s total is 5% greater than the previous month’s total.
Saving after second month is = First Month Total + 5% of First Month Total
= x + (5 % of x )
= x + (5*x/100)
= x + 0.05x
= 1.05x.
Yui balance is 1.05 times of Previous Month balance
Common Ratio = {Next Month }/ {Previous Month}
Common Ratio = 1.05 x / x
Common Ratio = 1.05
Therefore Common Ratio is 1.05 . Option C is the answer.
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Triangle N P O is shown. Line O N extends through point M to form exterior angle P N M. Angle N P O is 38 degrees. Angle P O N is 39 degrees. Exterior angle P N M is x degrees.
Which statement about the value of x is true?
x > 38
x < 39
x < 77
x > 103
The measure of the exterior angle PNM will be x < 77. Then the correct option is C.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
Triangle NPO is shown.
Line ON extends through point M to form exterior angle PNM.
Angle NPO is 38 degrees.
Angle PON is 39 degrees.
Let the exterior angle PNM is x degrees and the interior angle PYO be y.
Then we have
38 + 39 + y = 180°
y = 103°
And we know that the sum of interior and exterior angle is a triangle is 180 degrees.
x + y < 180
103 + x < 180
x < 77
Then the correct option is C.
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Quentin currently owes a total of $1,551.42 on his revolving credit accounts. What is Quentin's debt-to-credit ratio if his total revolving credit limit is $8,619.00? (4 points)
18%
23%
29%
31%
Answer:
(a) 18%
Step-by-step explanation:
The debt to credit ratio is found by dividing his debt by his credit limit.
__
using the definitionratio = debt/credit limit = $1551.42/$8619.00 ≈ 0.18 = 18%
Quentin's debt to credit ratio is 18%.
Identify the value of a and the length of each secant segment.
x= 10, NL= 8 , NP = 12
What is secant?A secant is a line that intersects a curve at a minimum of two distinct points.
Using secant theorem,
NL* NM = NP* NO
(3+5)*3 = (2+x)*2
24= (2+x)*2
12= 2+x
x= 12-2
x= 10
So, NP= 2+x
NP = 12
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i need a little help -
Write the algebraic expression for the following statement.
A number plus 15.
Answer:
the algebraic expression is; x+15
−3x−6+(−1) What is it evaluated
Answer:
-3x-7
Step-by-step explanation:
Remember this in mind while solving.
negative + negative = negative.
= −3x−6+(−1)
= -3x-7
Therefore when −3x−6+(−1) is evaluated it is
-3x-7
A store selling school supplies advertises a bundle deal. The consumer can
pick a backpack, a binder, a pack of pencils, and notebook paper for a set
price. There are 6 types of backpacks, 4 types of binders, 5 types of pencils,
and 2 types of notebook paper. How many outcomes are possible in this
bundle?
Answer:
D. 240
Step-by-step explanation:
6 types of backpacks = 6
4 types of binders = 4
5 types of pencils = 5
2 types of notebook paper= 2
6×4×5×2=
24×10=
240
The number of possible outcomes will be 240. The correct option is D.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
Given that there are 6 types of backpacks, 4 types of binders, 5 types of pencils, and 2 types of notebook paper.
6 types of backpacks = 6
4 types of binders = 4
5 types of pencils = 5
2 types of notebook paper= 2
The number of possible outcomes will be calculated as:-
N = 6×4×5×2
N = 24×10
N = 240
Therefore, there will be 240 possible outcomes. The correct answer is D.
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Find the area of following quadrilateral
Answer:
[tex]222cm^{2}[/tex]
Step-by-step explanation:
First we will find the length of BD.
By Pythagoras' Theorem,
[tex]c^{2} =a^{2} +b^{2} \\BD^{2} = AD^{2} +AB^{2} \\BD^{2} =12^{2} +16^{2} \\BD^{2} = 144+256\\BD^{2} =400\\BD = \sqrt{400} \\=20cm[/tex]
Now we will find Angle ADB.
[tex]\frac{AB}{sin(Angle ADB)} =\frac{BD}{Sin(AngleBAD)} \\\frac{16}{sin(AngleADB)} =\frac{20}{sin(90)} \\20sin(AngleADB)=16sin(90)\\20sin(AngleADB)=16\\sin(AngleADB)=\frac{16}{20} \\sin(AngleADB)=0.8\\AngleADB=sin^-1(0.8)\\=53.130deg\\[/tex]
Now we will find Area of triangle BCD
[tex]Angle BDC = 90 - Angle ADB = 90 - 53.130 = 36.87deg\\\\\\Area of Triangle BCD \\= \frac{1}{2} (BD)(CD)sin(AngleBDC)\\=\frac{1}{2} (20)(21)sin(36.87)\\= 126cm^{2}[/tex]
Then we will find the area of triangle BAD
[tex]=\frac{1}{2} (16)(12)\\= 96cm^{2} \\[/tex]
Area of quadrilateral = Area of Triangle BCD + Area of Triangle BAD
= 126+96
= [tex]222cm^{2}[/tex]
Answer:
A = 222 cm²Step-by-step explanation:
it is a trapezoid
so
A = ½ (a + b) h
A = ½ (16 + 21) × 12
A = ½ 37 × 12
A = ½ 444
A = 222 cm²
Find the range of the function f(x) = 3x² - 2x for the domain (1, 2, 3).
Answer:
Step-by-step explanation:
4x² + 6x = 12
Solve by completing square
4x² + 6x = 12
We move all the terms to the left:
a = 4; b = 6; c = -12;Δ = b² - 4acΔ = 6² - 4 · 4 · ( -12 )Δ = 228The value of Δ is greater than zero, so the equation has two solutions
We use the following formulas to compute our solutions:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x_{1}=\dfrac{-b-\sqrt{\Delta} }{2a }| \ x_{2}=\dfrac{-b+\sqrt{\Delta} }{2a } } \end{gathered}$}[/tex]
The end solution:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57} } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x_{1}=\dfrac{-b-\sqrt{\Delta} }{2a}=\dfrac{-(6)-2\sqrt{57} }{2*4}=\dfrac{-6-2\sqrt{57} }{8} } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x_{1}=\dfrac{-b+\sqrt{\Delta} }{2a}=\dfrac{-(6)+2\sqrt{57} }{2*4}=\dfrac{-6+2\sqrt{57} }{8} } \end{gathered}$}[/tex]
{ Pisces04 }
What is the value of the expression 4 x (2a - 1) if a = 3?
16
20
23
25
Answer:
20
Step-by-step explanation:
⇒ Multiply 2 by 3
2 * 3 = 6
4 (6 - 1)
⇒ Distribute terms
4 * 5
20
Hence, the answer is 20.
Which is a perfect square?
61
62
63
65
Answer:
So none of these would be a perfect square but the closet one to it would be 65
Step-by-step explanation:
