If a number is added to the numerator of StartFraction 11 Over 36 EndFraction and twice the number is added to the denominator of StartFraction 11 Over 36 EndFraction ​, the resulting fraction is equivalent to one third . Find the number.

Answer:

175 balls

Step-by-step explanation:

If 12.5 percent of the balls had defects, then [tex]100-12.5=87.5[/tex]% of balls didn't have defects.

We can find 87.5 percent of 200 by converting 87.5 to a decimal.

87.5% as a decimal is 0.875.

Now we multiply this decimal by 200.

[tex]200\cdot0.875 = 175[/tex]

So, 175 balls didn't have defects.

Hope this helped!

Answer:

Step-by-step explanation:

Tom wanted to find the inverse of f(x)= 4x - 2 using the steps in the attached image.

Tom's first mistake was in Step 3.

To correct the mistake, he should not switch the variables.

The correct procedure is:

Step 1 : Given

f(x) = 4x - 2

Step 2 : Change f(x) to y

y = 4x - 2

Step 3 : Add 2 to both sides

[tex]4x=y+ 2[/tex]

Step 4:  Divide each side by 4

[tex]x=\dfrac{y+2}{4}[/tex]

Step 5: Change x to [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x)=\dfrac{y+2}{4}[/tex]

Step-by-step explanation:

Total=44,064

Host countries= 2

2nd most popular country= x

Popular country=x+8382

x+x+8,382=44,064

2x=44,064-8,382=35,682

2x=35,682

x=17,842

2nd most popular=17,842

Popular=17,842+8,382=26,224

Answer=26,224

There were students who studied abroad in the most popular host country by forming the equation is 26,224

How equations are formed?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left-hand side = right-hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. It will be regarded as a phrase.

Here, It is given:

Total number of students = 44,064

Number of Host countries= 2

Let the 2nd most popular country= x

So, the Popular country becomes x+8382

Now, According to the question:

⇒x+x+8,382=44,064

⇒2x=44,064-8,382=35,682

⇒2x=35,682

⇒x=17,842

Hence, The number of students in 2nd most popular country=17,842

And, The number of students in a popular country

= 17,842+8,382=26,224

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Answer:

A. AB

Step-by-step explanation:

Given that the musical instrument has a shape of ∆ABC, we can determine the shortest side that would be parallel to the ground by comparison of the 3 angles of the triangle corresponding to each side that is opposite each of them.

What this means is that, the larger angle would have the largest side opposite it. The medium angle will have medium length side opposite it, while the smallest angle will have the smallest side opposite it.

m < A = 59°

m < C = 57°

m < C = 180 - (59+57) (sum of angles in a triangle)

m < C = 64°

The smallest angle out of the three angles is angle C = 57°.

The side opposite it, is side AB.

Side AB is the shortest side of ∆ABC.

Therefore, AB should be parallel to the ground.

The

side

of the musical instrument that should be parallel to the ground if the

dimensions

are as given is side AB, which is option A.

Given that:

Jordon will play a

triangle

in his school’s music program.

When playing, the shortest side

is hanging down,

parallel

to the ground.

From the figure:

m∠A = 59°

m∠C = 57°

By the

angle sum

property,

m∠A + m∠B + m∠C = 180°

59° + m∠B + 57° = 180°

m∠B + 116° = 180°

m∠B = 180° - 116°

        = 64°

The

shortest side

will be the side that is opposite to the smallest angle.

So, the smallest side is the side opposite to C.

So, the side is AB.

Hence, the side is AB, which is option A.

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Triangles

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Answer:

D

Step-by-step explanation:

The chord- chord angle 105° is half the sum of the arcs intercepted by the angle and its vertical angle, thus

[tex]\frac{1}{2}[/tex](120 + x) = 105 ( multiply both sides by 2 )

120 + x = 210 ( subtract 120 from both sides )

x = 90 → D

Answer:

hello :

Step-by-step explanation:

x(x+3)(x+3)=0  means : x=0 or x+3=0 or x+3=0

x=0 or x=-3 or x=3

Answer:

[tex]Volume = 1017.36\ in^3[/tex] -- Cone

[tex]Volume = 3052.08\ in^3[/tex] -- Cylinder

[tex]Volume = 3052.08\ in^3[/tex] -- Sphere

Best Buy: Sphere Clay

Step-by-step explanation:

Given

Solid Shapes: Cone, Cylinder, Sphere

Cost of Cone Clay = $12

Cost of Cylinder Clay = $30

Cost of Sphere Clay = $28

Required

Determine the volume of each shape

Which is the best buy

The volume of a cone is calculated as thus;

[tex]Volume = \frac{1}{3}\pi r^2h[/tex]

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and [tex]\pi = 3.14[/tex]

Substitute these values in the above formula;

[tex]Volume = \frac{1}{3} * 3.14 * 9^2 * 12[/tex]

[tex]Volume = \frac{3052.08}{3}[/tex]

[tex]Volume = 1017.36\ in^3[/tex]

The unit cost of the cone is calculated as thus;

[tex]Volume:Price = \frac{Volume}{Total\ Cost}[/tex]

Where

[tex]Volume = 1017.36\ in^3[/tex]

[tex]Total\ Cost = \$12[/tex] (Given)

[tex]Volume:Price = \frac{1017.36\ in^3}{\$ 12}[/tex]

[tex]Volume:Price = 84.78 in^3/\$[/tex]

[tex]Volume:Price = 84.78 in^3:\$1[/tex]

The volume of a cylinder is calculated as thus;

[tex]Volume = \pi r^2h[/tex]

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and [tex]\pi = 3.14[/tex]

Substitute these values in the above formula;

[tex]Volume = 3.14 * 9^2 * 12[/tex]

[tex]Volume = 3052.08\ in^3[/tex]

The unit cost of the cone is calculated as thus;

[tex]Volume:Price = \frac{Volume}{Total\ Cost}[/tex]

Where

[tex]Volume = 3052.08\ in^3[/tex]

[tex]Total\ Cost = \$30[/tex] (Given)

[tex]Volume:Price = \frac{3052.08\ in^3}{\$ 30}[/tex]

[tex]Volume:Price = 101.736\ in^3/\$[/tex]

[tex]Volume:Price = 101.736\ in^3:\$1[/tex]

The volume of a sphereis calculated as thus;

[tex]Volume = \frac{4}{3}\pi r^3[/tex]

From the attached diagram

Radius, r = 9 inches; and [tex]\pi = 3.14[/tex]

Substitute these values in the above formula;

[tex]Volume = \frac{4}{3} * 3.14 * 9^3[/tex]

[tex]Volume = \frac{9156.24}{3}[/tex]

[tex]Volume = 3052.08\ in^3[/tex]

The unit cost of the cone is calculated as thus;

[tex]Volume:Price = \frac{Volume}{Total\ Cost}[/tex]

Where

[tex]Volume = 3052.08\ in^3[/tex]

[tex]Total\ Cost = \$28[/tex] (Given)

[tex]Volume:Price = \frac{3052.08\ in^3}{\$ 28}[/tex]

[tex]Volume:Price = 109.003\ in^3/\$[/tex]

[tex]Volume:Price = 109.003\ in^3:\$1[/tex]

Comparing the Volume:Price ratio of the three clay;

The best buy is the sphere because it has the highest volume:price ratio.

Having the highest volume:price ratio means that with $1, one can get more clay from the sphere compared to other types of clay

Answer:

x = - [tex]\frac{96}{23}[/tex]     or   x=  4.1739

Step-by-step explanation:

[tex]\frac{3x}{8}[/tex]  -  [tex]\frac{4x}{3}[/tex]  =  4

I will show  two methods  of solving this equation

First method

We will follow the steps below:

First find the LCM of 8 and 3

The LCM of 8 and 3 is 24

Next is to multiply through by 24

Our equation becomes

24 ×[tex]\frac{3x}{8}[/tex]  - 24× [tex]\frac{4x}{3}[/tex]  = 24× 4

3×3x    -  8×4x    =24×4

9x  -  32x   = 96

-23x = 96

Divide both-side of the equation by - 23

-23x/-23= 96/-23

x=-[tex]\frac{96}{23}[/tex]        or      x=4.1739

second method

[tex]\frac{3x}{8}[/tex]  -  [tex]\frac{4x}{3}[/tex]  =  4

[tex]\frac{9x - 32x}{24}[/tex]   =   4

multiply both-side of the equation by 24   or cross multiply

9x - 32x = 96

-23x = 96

divide both-side of the equation by -23

x = - [tex]\frac{96}{23}[/tex]     or   x=  4.1739

Answer:

x² - 20 = 0

Using the quadratic formula

[tex]x = \frac{ - b± \sqrt{( {b})^{2} - 4ac } }{2a} [/tex]

a = 1 b = 0 c = -20

So we have

[tex]x = \frac{ - 0 ± \sqrt{ {0}^{2} - 4(1)( -20)} }{2(1)} \\ \\ x = \frac{± \sqrt{80} }{2} \\ \\ x = \frac{±4 \sqrt{5} }{2} \\ \\ \\ x = ±2 \sqrt{5} \\ \\ \\ x = 2 \sqrt{5} \: \: \: or \: \: \: x = - 2 \sqrt{5} [/tex]

Hope this helps you.

Answer:

r = 1.59inch

the radius of the cylinder is

1.59inch

Step by step Explanation

lateral surface of a cylinder can be calculated using the below formula

Surface Area= 2 πr h

We were given area as 400inch^2 and height as 40inch then substitute we have

400 = 2 ×π × r ×40

400= 2×22/7×40

Then do the calculation, where, π

=22/7

400 = r × 251.2

Make r subject of formula we have

r = 400 / 251.2

r = 1.59inch

Therefore, the radius of the cylinder is

1.59inch

CHECK THE ATTACHMENT FOR THE FIGURE

Answer:

The solution is (2,5)

Step-by-step explanation:

The solution to the system of equations is where to the two graphs intersect

The two lines intersect at x=2 and y = 5

The solution is (2,5)

Answer:

Hey there!

The solution for a system of equations (simultaneous equations), is where the two lines intersect.

We see that the lines intersect at (2,5), making (2,5) the solution to the system of equations.

Let me know if this helps :)

Answer::

SSS: When all three sides are equal to each other on both triangles, the triangle is congruent. AAS: If two angles and a non-included (you can think of it as outside) side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Therefore let's solve according to the statement..

1) yes..all three sides are equal

2)no..all sides aren't equal

3)yes..all sides are equal

4)no..all sides aren't equal

Hope this helped u..

Answer:

1) No 2) No 3) Yes; SAS 4) Yes; AAS

Step-by-step explanation:

In the first triangle, you see two sides are congruent to each other, and there is an angle but it is not in between. An Angle-Side-Side-Postulate doesn't exist, so this will be a no. For number 2, you see one angle and two sides are congruent. The angle isn't between the triangles, so this is not congruent. Again, an Angle-Side-Side Postulate doesn't exist. For number three, we see two sides are given, and the two triangles intersect. This gives us a vertical angle, and vertical angles are congruent. We can conclude these triangles are congruent by the Side-Angle-Side Postulate. Lastly, we're given one side and one angle. We can also infer that the vertical angles are congruent, so this will be the result of Angle-Angle-Side.

Answer:

9120(b)

Step-by-step explanation:

95×96

(90+5)×(90+6)

(90×90)+(5+6) (90)+(5)(6)

(90) square+(5+6) (90)+(5)(6)

I am using identity 4

=8100+990+30=9120

Answer:

length = 1273.2 cm or 12.73 m

Step-by-step explanation:

Assume no loss.

diameter of wire, d = 2 mm

radius of wire, r = 1 mm = 0.1 cm

Volume of block, V = 5*4*2 = 40 cm^3

cross sectional area of wire, A = pi (r^2) = pi 0.1^2 = 0.01pi cm^2

Length of wire

= V/A  

= 40 cm^3 / 0.01pi cm^2

= 4000/pi cm

= 1273.2 cm

= 12.73 m

Answer:

y = 4x

Step-by-step explanation:

A direct variation is written in the form

y = kx where k is the constant of variation  ( or the slope)

y = 4x

Answer:

d. y = 4 x

Step-by-step explanation:

A direct variation

1. has no y-intercept

2. has a constant positive slope.

Out of

y = 4 x + 1   [has y-intercept of +1]

y = 1/4 x       [direct variation with a slope of 1/4, not 4]

y = -4 x        [has a negative slope]

y = 4 x         [direct variation with slope of 4]

Answer:

For f(x)+2, it goes along the y axis, 2 units.

For f(x+2), it goes along the x axis, -2 untis.

Step-by-step explanation:

Answer:

72%

Step-by-step explanation:

First find the number of mangoes

200 -56 = 144

Take the number of mangoes over the total

144/200

.72

Change to percent by multiplying by 100

72%

Answer:

72%

Step-by-step explanation:

If 56 of the 200 fruits were durians, then [tex]200-56[/tex] of the fruits were mangoes. Therefore, 144 of the fruits were mangoes.

Now we can set up a percentage proportion to find what percent of 200 144 is.

[tex]\frac{144}{200} = \frac{x}{100}[/tex]

Multiply the cross values and divide by the value thats diagonal to the variable.

[tex]144\cdot100=14400\\14400\div200=72[/tex]

So, the answer is 72%

Hope this helped!

Answer:

Largest prime factor of the given expression is 379.

Step-by-step explanation:

Given the expression:

[tex]15^6 - 7^6[/tex]

To find:

The largest prime factor of the given expression.

Solution:

First of all, let us factorize the given expression.

[tex]15^6 - 7^6\\\Rightarrow (15^3)^2 - (7^3)^2\\\\\text{Using } x^{2} -y^2 = (x+y) (x-y)\\\\\Rightarrow (15^3+7^3)(15^3-7^3)[/tex]

Let us learn two formula:

[tex]x^3+y^3 = (x+y)(x^2+y^2-xy)[/tex]

[tex]x^3-y^3 = (x-y)(x^2+y^2+xy)[/tex]

Applying the above formula in the expression written above:

[tex](15^3+7^3) = (15+7)(15^2+7^2-15\times 7)\\\Rightarrow 22(225+49-105 ) = 2 \times 11 \times 169 \\\Rightarrow 2 \times 11\times 13\times 13\\\Rightarrow 2 \times 11\times 13^2[/tex] ...... (1)

Similarly:

[tex](15^3-7^3) = (15-7)(15^2+7^2+15\times 7)\\\Rightarrow 8(225+49+105 ) = 2^3 \times 379[/tex]........ (2)

Multiplying the expressions from (1) and (2) to get the result:

[tex]\therefore 15^6 - 7^6 = 2^4 \times 11 \times \underline{\bold{379}} \times 13 ^2[/tex]

So, largest prime factor of the given expression is 379.

The largest prime divisor of the expression is 379.

The expression will be factorized. This will be:

= (15³)² - (7³)²

= (15 + 7)³(15 - 7)³

This can be illustrated as:

(15 + 7)³ = 2 × 11 × 13²

(15 - 7)³ = 2³ × 379

In conclusion, the largest prime divisor of the expression is 379.

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Answer:

x ≈ 5.7

Step-by-step explanation:

Using the Sine rule in Δ WXY

[tex]\frac{WY}{sinX}[/tex] = [tex]\frac{XY}{sinW}[/tex] , substitute values

[tex]\frac{x}{sin33}[/tex] = [tex]\frac{10}{sin107}[/tex] ( cross- multiply )

x sin107° = 10 sin33° ( divide both sides by sin107° )

x = [tex]\frac{10sin33}{sin107}[/tex] ≈ 5.7 ( to the nearest tenth )

Answer:

4/5

Step-by-step explanation:

Slope(m) = (y2-y1)/(x2-x1)

Pick two points on your graph that are closest to clear values. (By that I mean you shouldn't pick points that aren't obvious unless you have to.)

For instance, I see the points (-2,0) and (3,4) to be clear; so we don't have to approximate anything.

You could plug these in in a any order but I'm going to let Point 1=(-2,0) and Point 2=(3,4). So:

m=(4-0)/(3--2)=(4/5)

Slope=4/5

Answer:

2

Step-by-step explanation:

Five and above, round up. Four and below, round down.

Answer:

2

Step-by-step explanation:

anything less then five is rounded down anything above 5 is rounded to the higher number

Answer:

Equation of the circle

(x - 0.7)² + (y - 1.3)² = 12.58

Step-by-step explanation:

The formula for the equation of a circle is given as:

(x - a)² + (y - b)² = r²,

where(a, b) is the center of the circle and r = radius of the circle.

a) We are told in the question that the equation of the circle passes through point(2, -2)

Hence,

Substituting 2 for x and -2 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

(2 - a)² +(-2 - b)² = r²

Expanding the bracket

(2 - a) (2 - a) + (-2 - b)(-2 - b) = r²

4 - 2a - 2a +a² +4 +2b +2b +b² = r²

4 - 4a + a² + 4 + 4b + b² = r²

a² + b² -4a + 4b + 4 + 4 = r²

a² + b² -4a + 4b + 8 = r²............Equation 1

We are also told that the equation of the circle also passes through point (3,4) also, where 3 = x and 4 = y

Hence,

Substituting 3 for x and 4 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

(3 - a)² +(4 - b)² = r²

Expanding the bracket

(3 - a) (3 - a) + (4 - b)(4- b) = r²

9 - 3a - 3a +a² +16 -4b -4b +b² = r²

9 -6a + a² + 16 -8b + b² = r²

a² + b² -6a -8b + 9 + 16 = r²

a² + b² -6a -8b + 25 = r²..........Equation 2

The next step would be to subtract Equation 1 from Equation 2

a² + b² -4a + 4b + 8 - (a² + b² -6a -8b + 25) = r² - r²

a² + b² -4a + 4b + 8 - a² - b² +6a +8b - -25= r² - r²

Collecting like terms

a² - a² + b² - b² - 4a + 6a + 4b + 8b +8- 25 = 0

2a + 12b -17 = 0

2a + 12b = 17...........Equation 3

Step 2

We are going to have to find the values of a and b in other to get our equation of the circle.

Since the center of the circle(a, b) lies on x + y = 2

Therefore, we have

a + b = 2

a = 2 - b

2a + 12b = 17 ..........Equation 3

Substituting 2 - b for a in

2(2 - b) + 12b = 17

4 - 2b + 12b = 17

4 + 10b = 17

10b = 17 - 4

10b = 13

b = 13/10

b = 1.3

Substituting 1.3 for b in

a + b = 2

a + 1.3 = 2

a = 2 - 1.3

a = 0.7

hence, a = 0.7, b = 1.3

Step 3

We have to find the value of r using points (2, -2)

(x - a)² + (y - b)² = r²

Where x = 2 and y = -2

(-2 - 0.7)² + (-2 - 1.3)² = r²

(-2.7)² + (-3.3)² = r²

1.69 + 10.89 = r²

r² = 12.58

r = √12.58 = 3.55

Step 4

The formula for the equation of a circle is given as:

(x - a)² + (y - b)² = r²,

where(a, b) is the center of the circle and r = radius of the circle

a = 0.7

b = 1.3

r² = 12.58

Equation of the circle =

(x - 0.7)² + (y - 1.3)² = 12.58

Answer:  3.2 yd

Step-by-step explanation:

Notice that TWV is a right triangle.  

Segment TU is not needed to answer this question.

∠V = 32°, opposite side (TW) is unknown, hypotenuse (TV) = 6

[tex]\sin \theta=\dfrac{opposite}{hypotenuse}\\\\\\\sin 32=\dfrac{\overline{TW}}{6}\\\\\\6\sin 32=\overline{TW}\\\\\\\large\boxed{3.2=\overline{TW}}[/tex]

Answer:

Yes, it can.

Step-by-step explanation:

Looking at this table, we can see that each type of hat is ALWAYS next to the same type of flower.

Berets are ALWAYS next to Daffodils.

Panamas are ALWAYS next to Sunflowers.

Cloches are ALWAYS next to Violets.

Bowlers are ALWAYS next to Irises.

Fedoras are ALWAYS next to Narcissuses.

If we assume that every type of FLOWER is a number and every type of HAT is also a number, these will all match up.

So, they are consistent.

This means that the type of flower can be represented as a function of the type of hat.

Hope this helped!

Answer:

No

Step-by-step explanation:

There is not a known causation or correlation between the two variables.

Answer:

Which of the following numbers is a composite number that is divisible by 3? A. 49 B. 103 C. 163 D. 261 Answer: B) 245

Step-by-step explanation:

Answer:

x < 7

Step-by-step explanation:

-6x > -42

Divide each side by -6, remembering to flip the inequality

-6x/-6 < -42/-6

x < 7

Answer:

[tex]\boxed{x<7}[/tex]

Step-by-step explanation:

[tex]-6x > -42[/tex]

Divide both sides by -6 (flip sign).

[tex]\displaystyle \frac{-6x}{-6} < \frac{-42}{-6}[/tex]

[tex]x<7[/tex]

Answer: The answer is D.

Step-by-step explanation: Ok, we start by simplifing the equation to 3√x^2 - 3√x=2. Now, by plugging the possible options in, we can find the answer. You find that -1 is a possible answer for x, so that eliminates E. Since there is no cube root for 2, we elimate A and B. By plugging in C and D, you find that C=6, not C=2. So D must be the answer.

Answer:

2) 30, 70, 80

Step-by-step explanation:

Well there has to be 3 angles that all add up to 180°.

1)

100+130+130

=360

2)

30+70+80

= 180

3)

25+3+35

=63

4)

45 + 105 + 120

=150

150+120

270

Answer:

6√5

Step-by-step explanation:

We have to solve the expression [tex]\sqrt{180}[/tex]

Break 180 into its factors which are in the perfect square form.

Since, 180 = 9 × 4 × 5

                 = 3² × 2² × 5

Therefore, [tex]\sqrt{180}=\sqrt{3^{2}\times 2^{2}\times 5}[/tex]

                           = [tex]\sqrt{3^2}\times \sqrt{2^{2}}\times \sqrt{5}[/tex] [Since [tex]\sqrt{ab}=\sqrt{a}\times \sqrt{b}[/tex]]

                           = 3 × 2 × √5

                           = 6√5

Therefore, solution of the given square root will be 6√5.

Answer:

Step-by-step explanation:

The area of a parallelogram is equal to the product of the length of its side and the height of the parallelogram perpendicular to that side.

H = 9 cm

S = 21 cm

A = S•H = 21 cm • 9 cm = 189 cm²