A boy had a packet of 320 candies with 2 different flavours. 7/16 were orange flavour and the rest were lemon. He gave his friend 30 orange candies and some lemon ones. As a result, the ratio of the number of orange candies to that of lemon became 11:15. How many lemon candies did he give his friend

Answer:

4

Step-by-step explanation:

The mean is the average of the numbers.

if you rearrange the data, you will get the order, 3,3,4,5,5.

you add all of them together to get the number twenty, then you divide 20 by the total number of data plots which is five. Then you get the number 4 which is your answer

3+3+4+5+5 = 20

20/5 = 4

Answer:

1

Step-by-step explanation:

The expression that represent the area of the cut off part is 81π / 4

The area of the cut off part can be found as follows:

Area of a circle = πr²

where

Therefore, the cut off part is like 1 / 4th of a circle.

Hence,

area of the cut off region = πr² / 4

r = 9 inches

area of the cut off region =  π9² / 4

area of the cut off region = 81π / 4

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The hypotenuse of the right triangle ABC, with legs of 5 and 12 inches is 13 inches, computed using the Pythagoras Theorem. Hence, the 3rd option is the right choice.

The Pythagoras Theorem states that in a right triangle, the square of the hypotenuse is always equal to the sum of the squares of the other two legs.

If the hypotenuse is taken as a, and the two legs are taken as b and c, then by the Pythagoras Theorem, we can write that:

a² = b² + c².

In the question, we are given that the right triangle ABC, has legs of lengths 5 and 12 inches each, and we are asked to find the length of the hypotenuse.

Thus, taking b = 5 and c = 12, in the above equation, we get:

a² = 5² + 12²,

or, a² = 25 + 144,

or, a² = 169,

or, a² = 13²,

or, a = 13.

Thus, the hypotenuse of the right triangle ABC, with legs of 5 and 12 inches is 13 inches, computed using the Pythagoras Theorem. Hence, the 3rd option is the right choice.

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The transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units

Transformation is the technique used to change the position of a figure on an xy-plane.

Given the parent function f(x) = x², the transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units

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Answer:

276 cm²

Step-by-step explanation:

    Construct a line DE  parallel to AB.

DE = 13 cm

So, ABED is a parallelogram

In ΔDEC,

     DE = a = 13 cm

    EC = AB - BE

         = 30 - 16

   EC = b = 14 cm

 DC = c = 15 cm

Use Heron's formula to find the area of triangle.

[tex]\sf s = \dfrac{a+b+c}{2}\\\\=\dfrac{13+15+14}{2}\\\\=\dfrac{42}{2}\\\\s = 21[/tex]

s-a = 21 - 13 = 8

s - b = 21 - 14 = 7

s - c = 21 - 15 = 6

 [tex]\sf \boxed{\bf Area \ of \ triangle = \sqrt{s(s-a)(s-b)(s-c)} }[/tex]

                                [tex]\sf = \sqrt{21 * 8 * 7* 6}\\\\=\sqrt{3 * 7 * 2* 2 * 2 * 7 * 2 * 3}\\\\= 3 * 7 * 2 * 2\\\\= 84 \ cm^2[/tex]

Area of ΔDEC = 84 cm²

[tex]\sf \dfrac{1}{2}*base * height = 84\\\\ \dfrac{1}{2}*14*height = 84[/tex]

           [tex]\sf height =\dfrac{84*2}{14}\\\\[/tex]

                     = 6 *2

          height = 12 cm

Now we know the height of the trapezium. h = 12 cm

The length of the parallel sides are a = 30 cm & b =16 cm

[tex]\sf \boxed{Area \ of \ trapezium = \dfrac{(a +b)*h}{2}}[/tex]

                                [tex]\sf =\dfrac{(30+16)*12}{2}\\\\=\dfrac{46*12}{2}\\\\= 23 * 12\\\\= 276 \ cm^2[/tex]

Answer:

x = 5

Step-by-step explanation:

given B is the midpoint of AC , then

AB = BC ( substitute values )

4x - 3 = 2x + 7 ( subtract 2x from both sides )

2x - 3 = 7 ( add 3 to both sides )

2x = 10 ( divide both sides by 2 )

x = 5

The number of pizza lunches sold more based on the survey is 5.

The information is incomplete and an overview will be given.

Let the number of pizza lunches sold be 24.

Let the number of hot dog lunches be 19.

Therefore, the number of pizza lunches sold more will be:

= 24 - 19

= 5

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Answer: C, 7

Step-by-step explanation:

Answer:

I don't know how to answer this, sorry!

Step-by-step explanation:

Answer:

24 cm^2

Step-by-step explanation:

The three sides are equal (SSS: side, side, side) so the triangles are congruent.

Answer:

A.  [tex]\frac{21}{4} \pi\ \space\ in[/tex]

Step-by-step explanation:

The formula for arc length is:

arc length = rθ

where:

r is the radius = 7 in

θ is the central angle in radians = 135  ×  [tex]\frac{ \space\ \pi\ }{180}[/tex]  = 3/4 π

Substituting these values into the formula:
arc length = 7 in × 3/4 π

                 = [tex]\frac{21}{4} \pi\ \space\ in[/tex]

The terms are as follows:

t₃ = -62

t₇ = -29.6

tₙ = 10.8n - 105.2

t₁₄ = 46

t₁₉ = 100

Therefore,

tₙ = a + (n - 1)d

where

Hence,

46 = a + 13d

100 = a + 18d

5d = 54

d = 10.8

46 - 13(10.8) = a

a = 46 - 140.4

a = - 94.4

t₃ = a + 3d = - 94.4 + 3(10.8) = -62

t₇ = a + 6d = - 94.4 + 6(10.8) = -29.6

tₙ = -94.4 + 10.8n - 10.8 = 10.8n - 105.2

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Answer:

6[tex]x^{2}[/tex] - 19x + 15

Step-by-step explanation:

(2x - 3) (3x - 5)

2x(3x-5) - 3 (3x-5)

6[tex]x^{2}[/tex] - 10x - 3 (3x - 5)

6[tex]x^{2}[/tex] - 10x - 9x + 15

6[tex]x^{2}[/tex] - 19x + 15

Answer:

6x² - 19x + 15

Step-by-step explanation:

(2x - 3)(3x - 5)

each term in the second factor is multiplied by each term in the first factor, that is

2x(3x - 5) - 3(3x - 5) ← distribute parenthesis

= 6x² - 10x - 9x + 15 ← collect like terms

= 6x² - 19x + 15

The steps used to solve the quadratic equation are

8(x2 + 2x) = –3

8(x2 + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

Given the equation;

8x² + 16x + 3 = 0

Collect like terms

8x² + 16x = -3

Take the common factors, we have

8(x² + 2x) = -3

Completing squares in the brackets and balancing the equation in the right side

8(x² + 2x + 1) = -3 + 8

Factoring the perfect square

[tex]8(x + 1)^2} = 5[/tex]

Make 'x' subject

[tex](x + 1)^2= \frac{5}{8}[/tex]

[tex](x + 1) =[/tex] ±[tex]\sqrt{\frac{5}{8} }[/tex]

[tex]x =[/tex] -1 ±[tex]\sqrt{\frac{5}{8} } }[/tex]

Thus, we can clearly see the steps used to solve the quadratic equation are

8(x2 + 2x) = –3

8(x2 + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

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Hello,

Answer:

C. (b - c)(a + b)

Step-by-step explanation:

A = (b - c)(a - c)

A = ba - bc - ac - c² ≠ ab + b² - ac - bc

B = (b + a)(b + c)

B = b² + bc + ab + ac ≠ ab + b² - ac - bc

C = (b - c)(a + b)

C = ba + b² - ca - cb

= ab + b² - ac - bc

→ That is answer C

Using translation concepts, a stretch of a decay exponential function is given by:

[tex]f(x) = 5\left(\frac{1}{5}\right)^x[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

An exponential decay function is given by:

[tex]y = ab^x[/tex]

In which |b| < 1.

A stretch means that the function is multiplied by a factor with absolute value greater than 1, hence the function would be given by:

[tex]f(x) = 5\left(\frac{1}{5}\right)^x[/tex]

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Let's take an mathematical example

Let's find the ratio of volume of a cone and cylinder if radius and height are same for both .

See

The ratio is 1:3

#Example 1

Ratio of gems=3:4

#Example 2

Ratio of ocean to continents=5:7

Note:-

Two examples are already provided on your another question .You may refer there

The radius or any additional information related to the circle to assist in calculating the length of the 40-degree arc.

To find the length of a 40-degree arc, to know the radius or diameter of the circle to which the arc belongs. Once you have that information, use the formula to find the arc length:

Arc Length = (θ / 360) × 2 ×π ×r

Where:

θ = Central angle in degrees (40 degrees in this case)

r = Radius of the circle

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1. y= 2x

2.  (0, 5)

3. y  = 3x + 12

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

1. let us take (0,0) and (1, 2)

m= 2-0/1-0

m= 2

So equation of line

y- 0 = 2(x-0)

b

2. y= 3x+5

passes through (0, 5)

3. y= 3x+5

  m = 3

We need the equation of a line with slope 3 that passes through point (0, 12).

y - y1 = m(x - x1)

y - 12 = 3(x - 0)

y - 12 = 3x

y  = 3x + 12

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Answer:

y = [tex]\frac{29}{3}[/tex]

Step-by-step explanation:

88 = 10y + 30 - 4y , that is

88 = 6y + 30 ( subtract 30 from both sides )

58 = 6y ( divide both sides by 6 )

[tex]\frac{58}{6}[/tex] = y , that is

y = [tex]\frac{29}{3}[/tex]

By applying the rigid transformations of reflection on y-axis, vertical compression and vertical translation, we find the transformed function based on f(x) = 2ˣ is f''(x) = (1/3) · 2⁻ˣ + 2.

Rigid transformations are transformations applied on functions such that their Euclidean distance is conserved. In this problem we must use the following rigid transformations to determine an expression based on f(x) = 2ˣ.

Reflection on y-axis

f'(x) = f(-x)     (1)

f'(x) = 2⁻ˣ

Vertical compression

f''(x) = k · f'(x)     (2)

f''(x) = (1/3) · 2⁻ˣ

Vertical translation

f'''(x) = f''(x) + c     (3)

f''(x) = (1/3) · 2⁻ˣ + 2

By applying the rigid transformations of reflection on y-axis, vertical compression and vertical translation, we find the transformed function based on f(x) = 2ˣ is f''(x) = (1/3) · 2⁻ˣ + 2.

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Answer:

  1 ÷ 3

Step-by-step explanation:

You want 1/3 written as a quotient.

The quotient of A and B is "A divided by B." There are two ways to write this using math symbols:

  A/B

  A÷B

The fraction 1/3 is already written as a quotient. This set of symbols can be read as either of ...

The other way to write the quotient is ...

  1 ÷ 3

__

Additional comment

When you learn about exponents, you learn another way to write the quotient of A and B is ...

  A·B⁻¹

<95141404393>

Answer: 180

Step-by-step explanation:

i got you!!!!!!! Hope u pass

Answer:

180

Step-by-step explanation:

<f and <g are on a straight line and they are supplementary angles which means their sum is equal to 180.

Step-by-step explanation:

1. -5(a - 9) = -5a + 45

2. [tex]\frac{-8.3-(+2.7)}{\frac{1}{5} } = \frac{-8.3-2.7}{0.2} =\frac{-11}{0.2}=-55[/tex]

3.13p + 13 - p = (13p - p) + 13 = 12p + 13

4. -11b - 3(-4b + 1) = -11b + 12b - 3 = b - 3

5.

[tex]-2n+\frac{1}{6}-4\frac{1}{2}n = (-2n-4\frac{1}{2}n)+\frac{1}{6} = [-\frac{4}{2} n-(\frac{8}{2}+\frac{1}{2} )n]+\frac{1}{6} = -\frac{4}{2} n- \frac{9}{2} n+\frac{1}{6} =-\frac{13}{2}n\\+ \frac{1}{6}[/tex]

6. It didn't show all the information on the question.

7. [tex]-\frac{3}{5}(20r-5)-(-6r) =-12r+3+6r = (-12r+6r)+3=-6r+3[/tex]

8. [tex]-\frac{5}{6}x+\frac{4}{9}+\frac{2}{3}x+\frac{1}{3}=(-\frac{5}{6}x+\frac{2}{3}x)+(\frac{4}{9}+\frac{1}{3})=(-\frac{5}{6}x+\frac{4}{6}x)+(\frac{4}{9}+\frac{3}{9})=-\frac{1}{6}x+\frac{7}{9}[/tex]

9.It didn't show all the information on the question.

Answer:

337.5Ft

Step-by-step explanation:

20 gallons is consumed from the first car and 25 gallons is consumed from the second car.

A mathematical statement that relates two algebraic expression using an equal sign is called an equation.

It is given that

Fuel Efficiency of the first car is 20 miles per gallon of gas

Fuel Efficiency of the second car is 40 miles per gallon of gas

Total miles travelled = 1400 miles

Total gas consumption = 45 gallons

Let the gallons consumed from the first car is x

then the gallons consumed by the second car is (45 - x)

The equation formed will be

20* x + 40 * (45 -x) = 1400

20x +1800 - 40x = 1400

-20x = -400

x = 20

Therefore 20 gallons is consumed from the first car and

45-20 = 25 gallons is consumed from the second car.

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Lets simplify the given problem,

The speed with which the plane flies = 350 mph

The direction of flight of the plane = N 40° E

The speed with which the wind blows = 40 mph

The direction in which the wind blows = S 40° E

Therefore, we have;

The resolution of the components of the motion of the plane, given as follows;

= 350 × sin(40°)·i + 350 × cos(40°)·j

The resolution of the components of the motion of the wind, given as follows;

= 40 × sin(40°)·i - 40 × cos(40°)·j

The resultant motion of the plane is given as follows;

= 262.563·i + 254.435·j

The direction of motion of the plane = tan⁻¹(262.563/254.435) ≈ N 45.9° E

Therefore, the plane's drift = Plane's Track - Plane's Heading  = N 45.9° E - N 40° E ≈ 5.9° ≈ 5.89°

Drift Angle of the plane is 5.89 degree.

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Answer: A 5.9

Step-by-step explanation:

cuz i said so

Using long division, 189 divided by 7 is 27

The picture below represent how to use long division.

Firstly, we divided 1 by 7, it can't go. Therefore, it zero. we put zero at the quotient space.

Multiply zero by 7 and subtract from 189.

We use 18 to divide 7. It will give us 2 remainder 4. we put the 2 at the quotient side and multiply it by 7 to get 14.

Then we subtract 14 from 18. And so on. This is done till we get 0.

Therefore, using long division, 189 divided by 7 is 27

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Yes it is true that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars because null hypothesis is rejected.

Given among 2049 Connecticut passenger cars, 239 had only rear license plates. Among 334 Connecticut trucks, 45 had only rear license plates.

let [tex]p_{1}[/tex] be the probability that commercial cars have rear license plates and [tex]p_{2}[/tex] be the probability that connected trucks have rear license plates.

                         Cars                     Trucks                         Total

Total                  2049                    334                             2383

x                          239                      45                                284

p                        0.1166                   0.1347                          0.1191

α=0.05

Hypothesis will be  :

[tex]H_{0}:p_{1} =p_{2}[/tex]

[tex]H_{1} :p_{1} < p_{2}[/tex]

It is a left tailed test at 0.05 significance.

Standard errors of p=[tex]\sqrt{p(1-p)/n}[/tex]

=[tex]\sqrt{(0.1191*0.8809)/2383}[/tex]

=[tex]\sqrt{0.1049/2383}[/tex]        

=0.0066

Test statistic Z=p difference/standard error

=(0.1166-0.1347)/0.0066

=-0.0181/0.0061

=-2.967

p value=0.001505<5%

Since p is less than 5% we reject null hypothesis.

We cannot calculate standard deviation so  we cannot calculate confidence interval.

Hence there is statistical evidence at 5% significance level to support that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

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Using the combination formula, it is found that there are 16,800 ways for them to do it.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, we have that:

Hence the number of ways is:

[tex]N = C_{10,1}C_{9,3}C_{6,3}C_{3,3} = \frac{10!}{1!9!} \times \frac{9!}{3!6!} \times \frac{6!}{3!3!} \times \frac{3!}{3!0!} = 16800[/tex]

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