If a /b=p/q, then (a + b)/b=
b/(a+d)

The set containing all the colors of the marbles is given as follows:

{blue, yellow, purple, green, pink}.

A set of elements is composed by elements that respect a given characteristic, or are present in an experiment.

In this problem, we need to find the colors present in each marble, which are given as follows:

Then we have to list all these colors in a set, which are opened and closed by the brackets {}.

The color blue appears in both sets, however, it will appear only once in the set of the colors, as the elements are not repeated.

Thus, the set containing all the colors of the marbles is given by the set presented as follows:

{blue, yellow, purple, green, pink}.

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Answer:

The entire clock measures 360 degrees. As the clock is divided into 12 sections. The distance between each number is equivalent to 30 degrees (360/12)

I hope this helps you!

Answer:

The best buy is the 16-ounce drink

Step-by-step explanation:

here, we see that,

12 ounce = 3/4 (16 ounce)

So, the price should reflect that,

i.e,

price of 12 ounce drink = 3/4 (price of 16 ounce drink)

By this metric,

Price of 12 ounce drink = 3/4 ( 1.19)

Price of 12 ounce drink = $0.8925

So, 12-ounce drink should cost $0.8925 but the actual drink costs $0.99,

So, it is more expensive than it should be,

So, the best buy is the 16-ounce drink

Answer:

Here is the picture

Step-by-step explanation:

The number lies between x-values 4 and 6 and y-values 6 and 9.

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

Given that scatter plot lies in quadrant 1 of a coordinate plane, and the 14 points are plotted in the first quadrant.

We need to find the range of x and y values for this scatter plot.

The x values of the 14 points are given as;

2, 4, 4,1, 5, 5, 5, 5, 6, 6, 7, 8, 9.5, 9.5

The y values of the 14 points are given as;

5, 6, 9, 7.2, 6, 6.8, 8, 9, 7, 8.5, 10, 10.5, 9.5, 11.4

We can conclude that that most of the points are clustered between x-values 4 and 6 and y-values 6 and 9.

Therefore, the points are clustered between the x-values 4 and 6 and y-values 6 and 9.

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The complete question is

Select the correct answer. Scatter plot in quadrant 1 of a coordinate plane. 14 points are plotted at (2, 5), (4, 6), (4, 9), (4.1, 7.2), (5, 6), (5, 6.8), (5, 8), (5, 9), (6, 7), (6, 8.5), (7, 10), (8, 10.5), (9.5, 9.5), and (9.5, 11.4). Between which x-values and y-values does the cluster in this scatter plot lie? A. It lies between x-values 2 and 4 and y-values 4 and 6. B. It lies between x-values 4 and 6 and y-values 9 and 10. C. It lies between x-values 4 and 6 and y-values 6 and 9. D. It lies between x-values 7 and 9 and y-values 10 and 11.

The missing dimensions of the triangular plot of land are:

i. b = 2.45

ii. A = 69.5

iii. C = 75.5^o

A cosine rule is a trigonometric function that can be used to determine the length of side, or measure of the internal angles of a none right angled triangle.

Cosine rule states that;

\(b^{2}\) = \(a^{2}\) + \(c^{2}\) -2acCos B

To determine the missing values of the triangle in the attached diagram, we have;

\(b^{2}\) = \(a^{2}\) + \(c^{2}\) -2acCos B

  = 4^2 + 7^2 - 2(4*7)Cos35^o

  = 16 + 49 -2(36*0.8192)

  = 65 - 58.9824

  = 6.0176

b = (6.0176)^1/2

  = 2.4531

b = 2.45

From sine rule,

a/ Sin A = b/Sin B = c/ Sin C

a/ Sin A = b/Sin B

4/Sin A = 2.45/ Sin 35

Sin A = 4* Sin 35/ 2.45

        = 0.9365

A = Sin^-1 0.9365

  = 69.47

A = 69.5

So to determine the value of C, we have;

A + B + C = 180^o

69.5 + 35 + C = 180

104.5 + C = 180

C = 180 - 104.5

   = 75.5

C = 75.5^o

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Answer:

A, B, C

It is a rational number, whole number, integer.

Step-by-step explanation:

\( - \sqrt{16} \\ = - 4\)

Answer:

d=13

Step-by-step explanation:

12d -37 +37 =119 +37 (getting rid of -37 to get 12d alone )

12d =156

12d/12=156/12 (getting rid of 12cto get d alone and/ means divide)

d=13

we need to find d so , we need to make a d as a subject . Just bring the 37 to the right hand side and it will be from -37 to +37 so 119 + 37. Total it and we get 156 and then bring the 12 to the right hand side to leave d alone. The symbol will be divide , we devide the 156 with 12 to get d and we get 13. That's the answer !

The coefficient of the term x²y in the binomial expansion of (2x − y)³ is -12.

The expression (2x − y)³ can be simplified as

8x³−12x²y+6xy²−y³ .

Thus the coefficient of the binomial expansion is  -12.

Of the use of the binomial theorem, it is possible to determine the expanded value of either formula with the form (x + y)ⁿ.

The values of (x + y)², (x + y)³, and (a + b + c)² can be easily determined by adding the integers algebraically in accordance with the exponent value.  

The binomial theorem was first mentioned by a well-known Greek mathematician by the name of Euclid in the fourth century BC.

According to the binomial theorem, which represents it as a sum of terms using distinct exponents of the variables x and y, the algebraic statement (x + y)ⁿ can be expanded. A coefficient, or numerical value, is assigned to each word in a binomial expansion.

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The inequality tha calculates the possible values of x is x < 2

From the question, we have the following parameters that can be used in our computation:

The figure

Where, we have

3x + 2 < 10

And, we have

2x + 6 < 10

Evaluate the expressions

So, we have

3x < 8 and 2x < 4

Evaluate

x < 8/3 and x < 2

Hence, the inequality tha calculates x is x < 2

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Answer:

Step-by-step explanation:

67

Alijah's taxable income puts him in the first tax bracket, over $8,350 but not surpassing $33,950. Hence, his tax due is a base of $835 plus 15% of the income that exceeds $8,350. This results in a total tax payable of $850. Option B is the correct answer.

Alijah's taxable income falls within the first bracket of the tax table given, being over $8,350 but not over $33,950.

This bracket requires him to pay a tax of $835.00 plus 15% of the amount over $8,350.

He has a surplus of $100 over the $8,350 threshold (i.e., $8,450 - $8,350), and 15% of $100 equals $15.

Therefore, the total tax he owes would be the fixed amount of $835.00 plus the $15.00 calculated, which sums up to $850.00.

Thus, looking at the provided options, option B ($850.00) would be the correct answer.

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The value of the logarithm of 0.81 for logarithm properties is equal to - 0.1.

Herein we must use logarithm properties to simplify a given logarithm and solve the resulting expression. The properties to be used in this question are described below:

㏒ (a / b) = ㏒ a - ㏒ b

㏒ aᵇ = b · ㏒ a

First, write the logarithmic equation:

㏒ 0.81

㏒ 81 / 100

Second, use the logarithmic property for a division:

㏒ 81 - ㏒ 100

Third, use the logarithmic property for a power:

㏒ 3⁴ - ㏒ 10²

4 · ㏒ 3 - 2 · ㏒ 10

4 · ㏒ 3 - 2

4 · 0.477 - 2

- 0.092

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Answer:

Image of the graph attached

Step-by-step explanation:

STEP 1: Write the given function

Taking the x in the given question to be an absolute value, the function is:

\(y = 3 |x| + 4\)

STEP 2: Plot the given function

Answer:

5 kittens and 6 children

Step-by-step explanation:

We can use variables to find the number of kittens (K) and children (C)

each kitten will have 4 legs and each child will have 2.

You can make two equations like so:

4k+2c=32

k+c=11

You then can use the substitution method to solve for both variables:

k+c=11

Subtract k from each side:

c=11-k

Substitute this into the other equation:

4k+2(−k+11)=32

Solve for k:

4k-2k+22=32

2k=10

k=5

Then use this in one of the equations to find the other variable:

k+c=11

5+c=11

Rewrite this to make it easier:

11-5=c

c=6

k=5 and c=6

you can check this by substituting each of these value to make sure the equations are true:

k+c=11

5+6=11

11=11

4k+2c=32

4(5)+2(6)=32

20+12=32

32=32

They both check right, so

c=6 and k=5

are your answers.

There are 5 kittens and 6 children in the backyard

There is your answer

Hope this helps!

Answer:

0.7

Step-by-step explanation:

Answer:

0.7

Step-by-step explanation:

e2020

The volume of the composite figure is 228 ft³.

To calculate the volume of a composite figure, we need to break it down into its individual components and then sum up the volumes of each component.

From the given dimensions, it seems that the composite figure consists of multiple rectangular prisms. Let's calculate the volume of each prism and then add them together.

First prism:

Length = 8 ft, Width = 4 ft, Height = 6 ft

Volume = Length * Width * Height = 8 ft * 4 ft * 6 ft = 192 ft³

Second prism:

Length = 3 ft, Width = 2 ft, Height = 6 ft

Volume = Length * Width * Height = 3 ft * 2 ft * 6 ft = 36 ft³

Now, let's add the volumes of both prisms:

192 ft³ + 36 ft³ = 228 ft³

Therefore, the volume of the composite figure is 228 ft³.

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What is the volume of the composite figure? 8 ft 4 ft 6 ft 3 ft 2 ft

Answers 96 ft³3 76 ft³ 228 ft³ 192 ft³ ​

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Parabola: y=2x²

Let say (a,b) the focus and y=k the directrix.

\(formula\ to\ use:\ \boxed{y=\dfrac{(x-a)^2}{2(b-k)} +\dfrac{b+k}{2} }\\\\\left \{\begin {array}{ccc}a&=&0\\2&=&\dfrac{1}{2(b-k)} \\\dfrac{b+k}{2} &=&0\\\end {array} \right.\\\\\\\left \{\begin {array}{ccc}a&=&0\\b-k&=&\dfrac{1}{4} \\b+k &=&0\\\end {array} \right.\\\\\\\left \{\begin {array}{ccc}a&=&0\\b&=&\dfrac{1}{8} \\k &=&\dfrac{-1}{8} \\\end {array} \right.\\\\\\focus=(0,\dfrac{1}{8} )\\\\directrix:\ y=\dfrac{-1}{8}\)

Answer:

\(r = 1.34\)

Step-by-step explanation:

Given

Solid = Cylinder + 2 hemisphere

\(Volume = 10cm^3\)

Required

Determine the radius (r) that minimizes the surface area

First, we need to determine the volume of the shape.

Volume of Cylinder (V1) is:

\(V_1 = \pi r^2h\)

Volume of 2 hemispheres (V2) is:

\(V_2 = \frac{2}{3}\pi r^3 +\frac{2}{3}\pi r^3\)

\(V_2 = \frac{4}{3}\pi r^3\)

Volume of the solid is:

\(V = V_1 + V_2\)

\(V = \pi r^2h + \frac{4}{3}\pi r^3\)

Substitute 10 for V

\(10 = \pi r^2h + \frac{4}{3}\pi r^3\)

Next, we make h the subject

\(\pi r^2h = 10 - \frac{4}{3}\pi r^3\)

Solve for h

\(h = \frac{10}{\pi r^2} - \frac{\frac{4}{3}\pi r^3 }{\pi r^2}\)

\(h = \frac{10}{\pi r^2} - \frac{4\pi r^3 }{3\pi r^2}\)

\(h = \frac{10}{\pi r^2} - \frac{4r }{3}\)

Next, we determine the surface area

Surface area (A1) of the cylinder:

Note that the cylinder is covered by the 2 hemisphere.

So, we only calculate the surface area of the curved surface.

i.e.

\(A_1 = 2\pi rh\)

Surface Area (A2) of 2 hemispheres is:

\(A_2 = 2\pi r^2+2\pi r^2\)

\(A_2 = 4\pi r^2\)

Surface Area (A) of solid is

\(A = A_1 + A_2\)

\(A = 2\pi rh + 4\pi r^2\)

Substitute \(h = \frac{10}{\pi r^2} - \frac{4r }{3}\)

\(A = 2\pi r(\frac{10}{\pi r^2} - \frac{4r }{3}) + 4\pi r^2\)

Open bracket

\(A = \frac{2\pi r*10}{\pi r^2} - \frac{2\pi r*4r }{3} + 4\pi r^2\)

\(A = \frac{2*10}{r} - \frac{2\pi r*4r }{3} + 4\pi r^2\)

\(A = \frac{20}{r} - \frac{8\pi r^2 }{3} + 4\pi r^2\)

\(A = \frac{20}{r} + \frac{-8\pi r^2 }{3} + 4\pi r^2\)

Take LCM

\(A = \frac{20}{r} + \frac{-8\pi r^2 + 12\pi r^2}{3}\)

\(A = \frac{20}{r} + \frac{4\pi r^2}{3}\)

Differentiate w.r.t r

\(A' = -\frac{20}{r^2} + \frac{8\pi r}{3}\)

Equate A' to 0

\(-\frac{20}{r^2} + \frac{8\pi r}{3} = 0\)

Solve for r

\(\frac{8\pi r}{3} = \frac{20}{r^2}\)

Cross Multiply

\(8\pi r * r^2 = 20 * 3\)

\(8\pi r^3 = 60\)

Divide both sides by \(8\pi\)

\(r^3 = \frac{60}{8\pi}\)

\(r^3 = \frac{15}{2\pi}\)

Take \(\pi = 22/7\)

\(r^3 = \frac{15}{2 * 22/7}\)

\(r^3 = \frac{15}{44/7}\)

\(r^3 = \frac{15*7}{44}\)

\(r^3 = \frac{105}{44}\)

Take cube roots of both sides

\(r = \sqrt[3]{\frac{105}{44}}\)

\(r = \sqrt[3]{2.38636363636}\)

\(r = 1.33632535155\)

\(r = 1.34\) (approximated)

Hence, the radius is 1.34cm

The radius of the cylinder that produces the minimum surface area is 1.34cm and this can be determined by using the formula area and volume of cylinder and hemisphere.

Given :

The volume of a cylinder is given by:

\(\rm V = \pi r^2 h\)

The total volume of the two hemispheres is given by:

\(\rm V' = 2\times \dfrac{2}{3}\pi r^3\)

\(\rm V' = \dfrac{4}{3}\pi r^3\)

Now, the total volume of the solid is given by:

\(\rm V_T = \pi r^2 h+\dfrac{4}{3}\pi r^3\)

Now, substitute the value of the total volume in the above expression and then solve for h.

\(\rm 10 = \pi r^2 h+\dfrac{4}{3}\pi r^3\)

\(\rm h = \dfrac{10}{\pi r^2}-\dfrac{4r}{3}\)

Now, the surface area of the curved surface is given by:

\(\rm A = 2\pi r h\)

Now, the surface area of the two hemispheres is given by:

\(\rm A'=2\times (2\pi r^2)\)

\(\rm A'=4\pi r^2\)

Now, the total area is given by:

\(\rm A_T = 2\pi rh+4\pi r^2\)

Now, substitute the value of 'h' in the above expression.

\(\rm A_T = 2\pi r\left(\dfrac{10}{\pi r^2}-\dfrac{4r}{3}\right)+4\pi r^2\)

Simplify the above expression.

\(\rm A_T = \dfrac{20}{r} + \dfrac{4\pi r^2}{3}\)

Now, differentiate the total area with respect to 'r'.

\(\rm \dfrac{dA_T}{dr} = -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}\)

Now, equate the above expression to zero.

\(\rm 0= -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}\)

Simplify the above expression in order to determine the value of 'r'.

\(8\pi r^3=60\)

r = 1.34 cm

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Answer:

The answer is - 4/5

Step-by-step explanation:

Because the "opposite" of a number is its inverse operation, therefore it is negative 4/5

(i) Probability is a notion in Mathematics which describes the likelihood of an event or a set of events occurring. It is a measure of uncertainty when estimating the outcome of an experiment or an observation.

(ii) The axioms of probability are:

the non-negativity (that the probability of an event is greater than or equal to zero), and

the additivity (that the probability of the union of two or more mutually exclusive events is equal to the sum of their individual probabilities).

(iii) When two fair dice are thrown the probability of getting:

a) The sum of 9 = 1/9

b) Two odd numbers = 1/4

c) two prime numbers = 1/9

d)  two factors of 12 = 1/9

(iv) Statistics is a branch of mathematics that deals with data collection, analysis, interpretation, presentation, etc.

To find probability when two dice are thrown, we have:

(a) The sum of 9:

We will estimate the number of ways to get a sum of 9: (3,6), (4,5), (5,4), and (6,3) = 4 ways

A die has 6 possible outcomes, the total number of possible outcomes is 6x6=36 = 4/36 = 1/9.

(b) Two odd numbers:

We count the number of ways to get two odd numbers: (1,3), (1,5), (1,7), (3,1), (3,5), (3,7), (5,1), (5,3), and (5,7).

possible outcomes = 9,

So, the total possible outcomes = 6x6=36 = 9/36 = 1/4.

(c) Two prime numbers

We estimate the number of ways we can get two prime numbers: (2,3), (3,2), (5,2), and (2,5)

possible outcomes = 4,

So, the total possible outcomes = 6x6 =36 = 4/36, = 1/9.

(d) Two factors of 12:

We count the number of ways and divide by the total possible outcomes.

The factors of 12 are 1, 2, 3, 4, 6, and 12: (2,6), (3,4), and (4,3) = 3 ways

possible outcomes = 6

Therefore, the total number of possible outcomes = 6x6=36 = 3/36, = 1/12

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Answer: 1 & 4 4&5 6&7

Step-by-step explanation:

The probability of this occurring is around 0.0714.

In order to determine the likelihood that an adolescent would play the lead role in each of Britney's four films, we must take into account both the total number of possible outcomes and the number of favourable possibilities.

There are 8 films scheduled in total.

Five films have had a teenager as the primary character.

Calculating the ratio of the number of favourable outcomes—all four films with teenagers—to the entire number of possible outcomes—any four films—will help us determine the probability.

The combination formula, sometimes referred to as "n choose r," shows how many different methods there are to choose 4 films from the available 8 options:

\(C(n, r) = n! / (r! * (n - r)!)\)

In this case, we want to select 4 movies out of the 5 movies featuring a teenager:

\(C(5, 4) = 5! / (4! * (5 - 4)!) = 5\)

The total number of ways to select any 4 movies out of the 8 total movies is:

\(C(8, 4) = 8! / (4! * (8 - 4)!) = 70\)

Therefore, the likelihood that a teenager will play the lead role in each of the four films that Britney cleans up after is:

Probability is calculated as follows: 5 / 70 (rounded to four decimal places) = 0.0714 (Number of favourable outcomes / Total number of probable outcomes).

Therefore, the chance is around 0.0714.

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The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively

Given the function :

Substitute the given value of x to obtain the corresponding f(x) values :

x = -0.6

f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358

x = -0.51

f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350

x = -0.501

f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967

x = -0.5

f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959

x = -0.4999

f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958

x = 0.499

f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951

x = -0.49

f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188

x = -0.4

f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125

Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013

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Answer:

5

Step-by-step explanation:

6+9=15

15/3=5

Triangle ABC and ADE are similar triangles

Similar triangles have the same corresponding angle measures and proportional side lengths.

This means that for two triangles to be similar, the corresponding angles must be equal and the ratio of corresponding sides of similar triangles are equal.

It has been shown that angles in ABC and ADE are equal.

To show that the ratio of corresponding sides are equal

6/12 = 8/16 = 10/20

The ratios all give a value of 1/2

Therefore we can say that the triangles ABC and ADE are similar.

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Answer:

From the table, we observe that the domain of the function is {Mon, Tues, Wed, Thurs, Fri} and the range is {1, 2, 3, 4, 0}

So, S(Mon) = 1

S(Tues) = 2

S(Wed) = 3

S(Thurs) = 4

S(Fri) = 0

Hence,

Step-by-step explanation:

Answer:

a rotation of 90° clockwise about the origin followed by translations down 1 unit and left 10 units

Step-by-step explanation:

Rotation of 90° clockwise about the origin followed by translations down 1 unit and left 10 units is the required transformation.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

We have to show that  triangle ABC could be transformed by which movement(s) to fit exactly on triangle XYZ.

Rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size

So if triangle ABC is rotated about 90 degrees clockwise about the origin followed by translated down 1 unit and left 10 units we get XYZ.

Hence,  rotation of 90° clockwise about the origin followed by translations down 1 unit and left 10 units is the required transformation.

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The complete factorisation of the polynomial given; x³ + 2x² + 4x + 8 as in the task content can be factorised and determined as; Choice D; (x+2)(x+2i)(x-2i).

It follows from the given task content that the polynomial whose factors are to be determined by means of factorisation is; x³ + 2x² + 4x+8.

It follows from observation that one of the zeros of the polynomial expression is at; x = -2.

Consequently, one of the factors of the polynomial in discuss is; (x+2).

x³ + 2x² + 4x+8 = (x+2) (x² - 4i²)

= (x+2)(x+2i)(x-2i)

Consequently, it follows that the complete factorisation of the polynomial is; (x+2)(x+2i)(x-2i).

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