< GRADES / 2022 RATIOS AND PROPORTIONS UNIT TEST Q21
21
What percent represents the shaded part of the hundredths grid shown?

In the special right triangle, x has a value of √3/2

A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle.

To find the value of x, we should take into consideration that two of the sides of the triangle are equal to each other.

Using Pythagoras theorem;

[tex](\sqrt{3}) ^2 = x^2 + x^2\\3 = 2x^2\\x^2 = \frac{3}{2} \\x = \sqrt{\frac{3}{2} }[/tex]

The value of x in the triangle is √3/2

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The probability that every even number appears at least once before the first occurrence of an odd number is  [tex]\frac{1}{20}[/tex]

Take  [tex]A_{k}[/tex]  - the event that odd number appeared on the k-th throw,  B  - every even number appeared at least once.

Let’s find  P(B|[tex]A_{k}[/tex]) . Note that this probability is 0 for  k∈{1,2,3}  as you need  k≥4  to place all distinct even numbers before the odd one.

Now for  k≥4  we need to use the formula of inclusions and exclusions:  P(B¯|[tex]A_{k}[/tex])=P(C2+C4+C6|[tex]A_{k}[/tex])=

=P(C2|[tex]A_{k}[/tex])+P(C4|[tex]A_{k}[/tex])+P(C6|[tex]A_{k}[/tex])−P(C2C4|[tex]A_{k}[/tex])−P(C2C6|[tex]A_{k}[/tex])−P(C4C6|[tex]A_{k}[/tex])  where  Ci  is the event that the dice i is missing.

These probabilities are:

P(Ci/[tex]A_{k}[/tex])=[tex](\frac{2}{3} )^{k-1}[/tex]

P(CiCj|[tex]A_{k}[/tex])=[tex](\frac{1}{3} )^{k-1}[/tex]

So

P(B|[tex]A_{k}[/tex])=1–P(B¯|[tex]A_{k}[/tex])=1−3⋅[tex](\frac{2}{3} )^{k-1}[/tex]+3[tex](\frac{2}{3} )^{k-1}[/tex].= 1 − [tex]\frac{9}{2}[/tex].[tex](\frac{2}{3} )^{k}[/tex]+9[tex](\frac{1}{3} )^{k}[/tex]

Now as  P([tex]A_{k}[/tex])= [tex]\frac{1}{2^{k} }[/tex]we conclude that

P(B) = ∞∑k=4P(B/[tex]A_{k}[/tex])P([tex]A_{k}[/tex])=  ∞∑k=4([tex](\frac{1}{2} )^{k}[/tex]−[tex]\frac{9}{2}[/tex][tex](\frac{1}{3} )^{k}[/tex]+9.[tex](\frac{1}{6} )^{k}[/tex])=

=[tex]\frac{\frac{1}{16} }{\frac{1}{2} }[/tex]−[tex]\frac{\frac{1}{18} }{\frac{2}{3} }[/tex]+[tex]\frac{\frac{1}{144} }{\frac{5}{6} }[/tex] = [tex]\frac{1}{8}[/tex] -[tex]\frac{1}{12}[/tex] + [tex]\frac{1}{120}[/tex] =[tex]\frac{6}{120}[/tex] = [tex]\frac{1}{20}[/tex]

the probability that every even number appears at least once before the first occurrence of an odd number is  [tex]\frac{1}{20}[/tex]

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After using FOIL, the final answer will be

x2 + 3x + 2

What is the FOIL method?
The typical way of multiplying two binomials is known as the FOIL method since FOIL is a shorthand for it. The acronym FOIL stands for the following four terms that describe the item: (Each binomial "initial" term is multiplied together.) The FOIL method is a memory aid for the procedures involved in multiplying two binomials. The result of multiplying the first term, outer term, inner term, and last term is the product of two binomials: (a+b)(c+d)=ac+ad+bc+bd.

Solution explained:

A/Q we have

(x+2)(x-1)

= x * x + x + 2x + 2    (After expanding and applying distributive property)

= x2 + x + 2x + 2

= x2 + 3x + 2

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The remainder of the division of the given polynomial by (x - 3) is 966.

From the question, we have

f(x) = 4x^5 - x - 3

The remainder of the division is the f(x) at x= 3

f(3) = 4*3^5 - 3 - 3

=972-6

=966

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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Answer:

seven and two thirtieths

Step-by-step explanation:

3 2/5 + 3 4/6 find an equal value between 5 and 6

3 12/30 + 3 20/30

12+20=32

32/30=1 2/30

3+3+1=7

7 2/30

Answer:

0.2

Step-by-step explanation:

1/5 is equvalent with 10/5=0.2

Using the percentage of money the group gave out to the youth program, the amount of money the group raised is 6200 dollars.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.

The group gives 50% of the money they raised to youth programs. This year the team gave $3,100 to youth programs.

Therefore, the amount of money the group raised can be calculated as follows:

let

x = amount of money raised by the group

Hence,

50% of x = 3100

50 / 100 × x = 3100

50x / 100 = 3100

cross multiply

50x = 3100 × 100

50x = 310000

divide both sides by 50

50x / 50 = 310000 / 50

x = 6200

Therefore, the group raised 6200 dollars this year.

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The common difference 9 will make 5, x, y, 32 an arithmetic sequence of 5, 14, 23, 32.

It is given that the arithmetic sequence is

5, x, y, 32

We know that for any arithmetic sequence the term aₙ is

aₙ = a + (n - 1)d

where,

a = first term

n = order of the value in the sequence

Since x is the second term

x = 5 + (2 - 1)d

or, x = 5 + d

Similarly,

y = 5 + 2d

32 = 5 + 3d

or, 3d = 27

or, d = 9

Hence, x = 14

y = 5 + 18

= 23

Hence, the common difference is 9

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The statements that is true are "6 + 3 = 9 and 4 x 4 = 16" , the true statement is (2) .

In the question ,

four statements are given ,

we need to find which statement is true ,

Option(1) ,

if 6 > 10, then 8 x 3 = 24

we know , that 10 > 6 , but it is given that 6 > 10 ,

hence the statement is false  .

Option(2)

6 + 3 = 9 and 4 x 4 = 16

we know , that 6+3=9 and 4×4=16

so , the statement is true .

Option(3)

if 6 x 3 = 18 then 4+8=20

we know , that 4+8 = 12 , but it is given that 4+8=20

So , the statement is false ,

Option(4)

5x3=15 or 7+5 = 20

we know , that 7+5 = 12 , but it is given that 7+5=20

So , the statement is false .

Therefore , The statements that is true are "6 + 3 = 9 and 4 x 4 = 16" , the true statement is (2) .

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Answer:

Since angle 8 is 95 degrees, we will have to either subtract or use the rules to solve this!

Lets find angle 1 first!

Since opposite angles are the same, angle 1 will be 95 degrees!

Angle 2 will wave subtracting used to find it!

180 - 95 = 85

Angle 2: 85 degrees

Angle 3 is the same as angle 2 so 85 degrees!

Angle 4 is the same as angle 8 and 1 so 95 degrees!

Angle 5 is the same as 8, 4, and 1 so 95 degrees!

Angle 6 is the same as angle 3 and 2 degrees!

Angle 7 will be 85 by subtraction!

Angle 8 is given and it is 95!

Have an amazing day!!

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In the given triangle LMN, measure of side LM = 18in. and measure of angle MLN is 28° then the measure of side LN = 18in. , m ∠M = 76° and

m ∠N = 76°.

As given in the question,

In the given triangle LMN,

Measure of side LM = 18in.

Measure of angle MLN is equal to 28°

It is given that side LM ≅ LN

LM = 18 in.

LN = 18in.

In a triangle  LMN ,

In a triangle opposite sides are congruent to each other then angle opposite to them also congruent to each other.

LM ≅LN

⇒m ∠N = m ∠M

In a ΔLMN,

Let x° be the measure of angle M and N each.

m ∠M + m ∠N + m ∠L = 180°

⇒ x° + x° + 28° = 180°

⇒ 2x° = 180° -28°

⇒2x° = 152°

⇒ x = 76°

Therefore, in the given triangle LMN, measure of side LM = 18in. and measure of angle MLN is 28° then the measure of side LN = 18in. , m ∠M = 76° and m ∠N = 76°.

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Answer:

Asymptote: x= -8
Two points: (-7,0) and (-6,-1)

Step-by-step explanation:

1. Convert log form to exponential form.
y = -2log_4(x+8)
-y/2=log_4(x+8)
4^(-y/2)=x+8
x=4^(-y/2)-8

Note: from here, you can choose to find the inverse of the graph, solve f(x)^-1, and then revert the x and y coordinates to find the f(x) (but I won't be going over that because the question is not asking for the inverse).

2. Make a table by plugging in points.
At this point, all you need to do is to plug in y-values into the equation: x=4^(-y/2)-8
If we plug in y as 0, we get x as -7, and plug in y as -1, we get x as -6, so (-7,0) and (-6,-1) will be your two points.

3. Find the asymptote

An asymptote is a line in which the log function will approach infinitely close to, but never touch. Same deal, we can try to plug in more numbers into our graph -- y as 1 and we will get x as -15/2 (-7.5); y as 3 and we will get x as -63/8 (-7.875); y as 5 and we will get x as-255/32 (-7.96875). At this point, it's pretty clear that our graph is approaching -8. Hence, x= -8
We use vertical asymptote (x=) when graphing log and we use horizontal asymptote (y=) when graphing exponential.

The vertical asymptote is x = -8.

One point on the graph is (-7, 0).

Another point on the graph is (-6, -1).

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

To graph the function [tex]f(x) =-2 \log _{4}(x+8),[/tex]

we need to first find the vertical asymptote, which is the value of x that makes the argument of the logarithm equal to zero.

x + 8 = 0

x = -8

So the vertical asymptote is x = -8.

Next, we can choose two integer values of x and find their corresponding values of f(x).

Let's choose x = -7 and x = -6.

When x = -7:

[tex]f(-7) = -2 \log _{4}(-7+8) = -2 \log _{4}(1) = 0[/tex]

So one point on the graph is (-7, 0).

When x = -6:

[tex]f(-6) = -2 \log _{4}(-6+8) = -2 \log _{4}(2) = -2(1/2) = -1[/tex]

So another point on the graph is (-6, -1).

Now we can plot the points and draw the vertical asymptote at x = -8.

Thus,

The vertical asymptote is x = -8.

One point on the graph is (-7, 0).

Another point on the graph is (-6, -1).

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The radius of the cone is 16.33, the height of the cone is 11.55, and the maximum volume of the cone is 1,026.67[tex]\pi[/tex].

How to find volume of the cone?

Given

metal radius = R = 20

cone base radius = r

cone height = h

First, we can use Pythagoras theorem

R^2 = r^2 + h^2

r^2 = R^2 - h^2

r^2 = 400 - h^2

Then, we use volume of cone formula

V = 1/3[tex]\pi[/tex] * r^2 * h

V = 1/3[tex]\pi[/tex] * (400 - h^2) * h

V = 1/3[tex]\pi[/tex] * 400h - h^3

To get maximum volume of cone, V'(h) must be 0. So,

1/3[tex]\pi[/tex] * 400 - 3h^2 = 0

400 - 3h^2 = 0

3h^2 = 400

h^2 = 400/3

h = [tex]\frac{20}{\sqrt{3}}[/tex] or 11.55

Next, we find the r with substitution method. So,

r^2 = 400 -  ([tex]\frac{20}{\sqrt{3}}[/tex]    )^2

r^2 = 400 - [tex]\frac{400}{3}[/tex]

r^2 = [tex]\frac{800}{3}[/tex]

r = [tex]\frac{20\sqrt{2}}{\sqrt{3}}[/tex] or 16.33

Now, we can get maximum volume of cone.

V = 1/3[tex]\pi[/tex] *  16.33^2 * 11.55

V = 1,026.67[tex]\pi[/tex]

Thus, the radius of the cone is 16.33, the height of the cone is 11.55, and the maximum volume of the cone is 1,026.67[tex]\pi[/tex].

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Answer:

Step-by-step explanation:

f/4 = 3

The height of the cylinder whose surface area and radius are as given in the task content is; 67 ft.

It follows from the task content that the height of the cylinder as described by the surface area and radius above be determined.

On this note, recall that the surface area of a cylinder is given by the formula;

Surface area = 2πrh

Therefore;

6732.16 = 2 × 3.14 × 16 × h

h = 6732.16/100.48

h = 67.

Consequently, the height of the cylinder which is as described is; 67 ft.

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Answer:

1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

3/8*4/3

The 3 can be cancel out

you can also cancel out 8 and 4

leaving you with 1/2

The expressions represent the service fee charge on her account balance is 4x+3.

Given that,

Every time money is withdrawn from an ATM run by a different bank, Marley's Bank levies a $3 service fee. Marley needs to make four ATM withdrawals from a different bank while she is abroad.

We have to find which expressions represent the service fee charge on her account balance.

The expression we can write as,

4x+3

Because 4 times he has taken from ATM money and adding the service fee $3.

Therefore, The expressions represent the service fee charge on her account balance is 4x+3.

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The equation which can be used to determine p is 7.75 + 27.25p = 89.50, then the number of people who can go to the amusement park is 3

The total amount that they have to spend on parking and admission = $89.50

The parking cost = $7.75

The ticket cost including tax = $27.25

Consider the number of people who can go to amusement park as p

Then the equation will be

7.75 + 27.25p = 89.50

Subtract both side of the equation by 7.75

27.25p + 7.75 - 7.75 = 89.50 - 7.75

27.25p = 81.75

Divide both side of the equation by 27.25

27.25p / 27.25 = 81.75 / 27.25

p = 3

Hence, the equation which can be used to determine p is 7.75 + 27.25p = 89.50, then the number of people who can go to the amusement park is 3

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Answer:

16.80

Step-by-step explanation:

The ratio is 1:5.60. Where 1 is the amount of friends and 5.60 is the amount owed. Since there are 3 friends, multiply 5.60 by 3.

Answer: 16.8

Step-by-step explanation: basically multiply 5.60 by 3 (5.60 x 3 = 16.8) or add 5.60 3 times (5.60 + 5.60 + 5.60 = 16.8)

Answer:

18%

Step-by-step explanation:

[tex]x = y*\frac{60}{100} =y*0.6=0.6y\\x=0.6y[/tex]

[tex]y = z*\frac{30}{100} =z*0.3=0.3z\\y=0.3z[/tex]

x is what percent of z?

Since x = 0.6y and y = 0.3z:

[tex]\%=\frac{x}{z} *100\\\\\%=\frac{0.6y}{z}*100\\ \\\%=\frac{0.6(0.3z)}{z} *100\\\\\%=\frac{0.18z}{z} *100\\\\\%=0.18*100\\\\\%=18[/tex]

The linear equation is z = 450 - 30 x, where z is the number of pages Lourdes has left to read after x days

We need to write a linear equation to represent the number of pages

Lourdes has left the number of pages to read after x days

Lourdes reads 30 pages each day

Lourdes will read for x days

The number of pages Lourdes will read in x day = 30 x

The left pages will be the difference between the total pages of the

book and the pages Lourdes read.

After 9 days Lourdes completes 3/5 of the total number of pages.

So the  number of pages Lourdes reads after 9 days = 30×9 = 270 pages.

Let The total number of pages in the book = y

Therefore 3/5 × y = 270.

So y = 270 × (5/3) = 450 pages.

The total number of pages in the book = 450 pages.

Lourdes will read 30 x in x days

The number of pages left = 450 - 30 x

Assume that z represents the number of pages Lourdes has left to read after x days

z = 450 - 30 x

The linear equation is z = 450 - 30 x, where z is the number of pages Lourdes has left to read after x days

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Using the concepts of equilateral triangle, we got that  2.113 is the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles.

Firstly we find the side length of equilateral triangle , G is the midpoint of side FE.

Let GE=x, since G is the midpoint due to that DE=GB.

So, using basic trigonometry=DG^GB=x√3.

Thus DB=2x√3.

Since DB is the diagonal of ABCD, it has length 10√2 Then we can set up the equation 2x√3=10√2. So the side length of the triangle is

2x=(10√2)/√3.

Now look at the diagonal AC it is made up of twice the diagonal of the small square plus the side length of the triangle. Let the side length of the small square be y:

Let the side length of the small square be y:

AC=y√2 + [(10√2)/√3]+y√2=10√2.

Solving  for y:

=>y√2+y√2 + (10√2√3)/3=10√2

=>y√2+y√2 + (10√6)/3=10√2

=> [3y√2+3y√2 + (10√6)] /3=10√2

=>6y√2+10√6=30√2

=>6y√2 = 30√2-10√6

=>y√2 = (30√2-10√6)/6

=>y = (30√2-10√6)/6√2

=>y = (60-20√3)/12

=>y= 5(3−√3)3  or 2.113

Hence, inside a square with side length 10, two congruent equilateral triangles are drawn such that they share one side and each has one vertex on a vertex of the square. the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles is to be 2.113.

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if n decreases then the value of level of significance of each samples [tex]\alpha[/tex] decreases

1. Critical Value: The value of the statistic for which the test just rejects the null hypothesis at the given significance level.

2. Power of the Test: The probability that the test correctly rejects the null hypothesis when the alternative is true.

3. Significance Level: The prescribed rejection probability of a statistical hypothesis test when the null hypothesis is true.

4. Size of the test: The probability that the test incorrectly rejects the null hypothesis when it is true.

if n decreases then the value of level of significance of each samples [tex]\alpha[/tex] decreases and hence 1- [tex]\alpha[/tex] increases which are called the rejection of test sample increases

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Answer:

Each interior angle of a regular polygon is 174°

To find The number of sides of the polygon.

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the number of sides of the polygon)

Now, the sum of an interior angle and an exterior angle of a regular polygon is always equal to 180°.

So, the exterior angle of the given regular polygon :

= (Sum of an interior angle and an exterior angle) - (An interior angle)

= 180° - 174°

= 6°

Let, the number of sides of the regular polygon = n

Now, the value of an exterior angle of a regular polygon = (360° / Number of sides)

So, the exterior angle of the given regular polygon :

= (360°/n)

By, comparing the two values of an exterior angle of the given regular polygon, we get :

360/n = 6

n × 6 = 360

n = 360/6

n = 60

Number of sides of the regular polygon = n = 60

(This will be considered the final result.)

Hence, the number of sides of the regular polygon is 60.

The values of the variables s and c are 13 and 17, respectively.

We are given a system of two equations. The equations are linear in nature. Each equation represents a straight line. We need to find the solution to the system of linear equations. The coordinates of the intersection point of the straight lines are the solution. The equations are given below.

s + 2c = 47

5s + 8c = 201

We will substitute the value of s from the first equation into the second equation.

s = 47 - 2c

5s + 8c = 201

5(47 - 2c) + 8c = 201

235 - 10c + 8c = 201

235 - 2c = 201

2c = 235 - 201

2c = 34

c = 17

We will substitute the value of c into the first equation to find the value of s.

s = 47 -2c

s = 47 - 2(17)

s = 47 - 34

s = 13

Hence, the values of s and c are 13 and 17, respectively.

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Answer:

no

Step-by-step explanation:

the conditional p-> r is the basically both of the beginning 2 conditionals combined

Answer:

7x 3,012=7(__3000__+__12_) = 21084

Answer:

r = 2[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using the rules of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

([tex]\sqrt{x}[/tex] )² = x

substitute the given values of w and h into the equation

r = [tex]\sqrt{w^2-h^2}[/tex]

  = [tex]\sqrt{(9\sqrt{2})^2-(5\sqrt{6})^2 }[/tex]

  = [tex]\sqrt{162-150}[/tex]

  = [tex]\sqrt{12}[/tex]

  = [tex]\sqrt{4(3)}[/tex]

  = [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]

  = 2[tex]\sqrt{3}[/tex]

1(3x+9)/3 = -3x + 11,  3x/3 + 9/3, x + 3, 8 and 2 should be entered in each blank space respectively

Given: the algebraic equation, 4(3x+9)/12 = -3x + 11

4(3x+9)/12 = -3x + 11      

Divide the Right-Hand Side (RHS) by 4 to get:

1(3x+9)/3 = -3x + 11

Then, on the RHS divide 3x and 9 separately by 3:

3x/3 + 9/3  = -3x + 11

x + 3  = -3x + 11

Take -3x to the Left and take 3 to the right (Note that, this will change their signs):

x + 3 + 3x = 11

x+3x = 11-3

Add/subtract like terms:

4x = 8

Divide both sides by 4:

x = 8/4

x = 2

Therefore, 1(3x+9)/3 = -3x + 11,  3x/3 + 9/3, x + 3, 8 and 2 should be entered in each blank space accordingly. The solution of the equation is x =2

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