NO LINKS!! Use the diagram below to answer the following questions Part 5​

The value of a³ + b³ is 64.184

Here,

a + b = 5 .........(1)

and ab = 6

a = b/6

Substitute above value of 'a' in equation(1)

b/6 + b = 5

7b/6 = 5

7b = 30

b = 30/7

b = 4.28

So, a = 5 - 4.28

a = 0.72

We know that the formula of a³ + b³

a³ + b³

= (a + b)(a² + b² - ab)

= 5 * (0.72² + 4.28² - 6)

= 5 * 12.8368

= 64.184

Therefore, the value of a³ + b³ is 64.184

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6 Boxes of colored pencils

15 Pencils in each box

Total Number of colored pencils : 15 x 6 = 90 Pencils

Step-by-step explanation:

Original prices of the office equipments

Computer = £650

Calculator = £27.75

Telephone = £69.50

45. The computer has a discount of 15%

[(100 - 15)/100]% × £650

85/100 % × £650

=£552.5

46. The calculator has a discount of 20%

[(100 - 20)/100]% × £27.75

80/100 % × £27.75

=£22.2

47. The telephone has a discount of 10%

[(100 - 10)/100] % × £69.50

90/100 % × £69.50

=£62.55

48. The saving for the computer is

= £(650 - 552.5)

= £97.5

49. The saving for the calculator is

= £(27.75 - 22.2)

= £5.55

50. The saving for the telephone is

= £(69.50 - 62.55)

=£6.95

The answer is, 1/6th cup of chocolate will she needs in order to make her cookies using fraction.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

The amount of chocolate required for this recipe is 2/3rd of a cup for a batch.

She has to make for a 1/4th of that batch.

So the amount of chocolate needed is also 1/4 for the batch which will be = 1/4*2/3 of cup.

= 1/6th of the cup.

Hence, 1/6th cup of chocolate will she need in order to make her cookies.

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The explorer stood 2.63m away from the flag pole.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

If the pole is 3m high, and his eye is 1.6 meters from the ground.

Then distance from the top of the pole and his eyes  would be 3 - 1.6 = 1.4m

The angle of elevation between the line of sight and the horizontal = 28°

so the horizontal, angle of elevation and the distance between sight and top of pole form a right angle triangle.

Let the distance of the explorer from foot of pole be x,

so that,

tan 28 = 1.4/x

by cross multiplying,

x tan28 = 1.4

x = 1.4/tan28

x = 1.4/0.5317

x = 2.63m

In conclusion, the distance of the explorer to the base of the flagpole is 2.63m

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Answer:

A

Step-by-step explanation:

Right triangle hypotenuse can be calculated using

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

Step-by-step explanation:

To find the next term or number, we'll need to keep subtracting 5. So the formula is: n-5

The graph of the given ordered pair is plotted and attached below.

Ordered pair:

Ordered pair refers the composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.

Given,

Here we have the following ordered pair.

(0, 0) (10, 125) (20, 250) (30, 375) (40, 500)

Now, we have to plot the graph for this ordered pair.

In the given question, we have to perform the following steps.

After all these steps we get the graph like the following.

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f(5)=17

Step-by-step explanation:

f(5)=3(5)+3

=15+2=17....

Area of circle of diameter with 13cm is 132.74

What is area of circle?

Given :

Diameter of circle, d = 13cm

Radius of a circle, r = d/2

=13/2

=6.5

Area of circle = πr²

= 3.142 * 6.5 * 6.5

= 132.74

Hence, the Area of circle of diameter with 13cm is 132.74.

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Answer:

slope is 3/2

Step-by-step explanation:

m = y2 - y1 / x2 - x1

m = -1 - 2 / 2 - 4

m = -3/-2 ( can be simplified )

simplified ver. = 3/2

Answer:

Slope is 3/2

Step-by-step explanation:

To find slope, subtract the y's, put that on top of a fraction. Then subtract the x's and put that on the bottom of the fraction.

(4,2) and (2,-1)

Subtract y's:

2 - -1

=3

Put it on top of a fraction:

3/something

Subtract the x's:

4 - 2

= 2, put that on the bottom of the fraction.

3/2

Slope is 3/2.

The graph of f(x) is transformed 6 units horizontally to get the graph g(x). g(x) is a transformation form of the graph of f(x).

What is the reciprocal function?

The typical instance of reciprocal functions that we might run into is y = a/x, where a is a real number. Accordingly, reciprocal functions are those that have an algebraic expression in the denominator and a constant on the numerator.

Given functions are:

f(x) = -1/(2x-5)

g(x) = f(x-3)

The points on the graph f(x) = -1/(2x-5) are:

When x = 0, f(x) = 1/5

When x = 1, f(x) = 1/3

When x = -1, f(x) = 1/7

The graph of f(x) is added.

Putting x = x-3 in f(x) = -1/(2x-5) to find the function g(x):

g(x) = -1/(2x-6-5)

g(x) = -1/(2x-11)

The points on the graph g(x) = -1/(2x-11) are:

When x = 0, g(x) = 1/11

When x = 1, g(x) = 1/9

When x = -1, g(x) = 1/13

The graph of g(x) is added.

The graph g(x) is translated  6 units  horizontally.

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The expression that can used to determine the total number of credit cards opened at the two locations can be written as Option A.

( A + B ) ( t ) = 35 + t

What is an Equation?

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.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The equation of function for number of credit cards at location A at t months is given by A( t ) = 10 + 2t

The equation of function for number of credit cards at location B at t months is given by B( t ) = 25 - t

Now , A function assigns the value of each element of one set to the other specific element of another set.

So ,

The total number of credit cards that are opened at both the location A and B is given by the equation =
Number of credit cards at location A at t months + Number of credit cards at location B at t months

The total number of credit cards that are opened at both the location A and B is given by the equation = A( t ) + B( t )

                                                   = ( A + B ) ( t )

                                                   = 10 + 2t + 25 - t

                                                   = 35 + t

Hence , the equation for the function of total number of credit cards opened at the two locations is given as ( A + B ) ( t ) = 35 + t

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After 15 years, Zephan will have a balance of $13181.07 in his savings account.

Given,

In the question:
Compound Interest is given by the formula.

A = P(1 + r)^t

Zephan invested $5500 in a savings .

Rate of interest is 6%

Time = 15 years

Now, According to the question:

We know that :

P = 5500

r = 6%

n = 1

t = 15

Compound Interest is given by the formula.

A = P(1 + r)^t

Substitute the values in above formula.

A = 5500. [tex](1+\frac{6}{100}/1 )^1^5[/tex]

Evaluate the equation/expression:
A = 13181.070062

Round 13181.070062 to the required place

= 13181.07

Hence, After 15 years, Zephan will have a balance of $13181.07 in his savings account.

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The probability that both male and female are non-smokers is 0.56.

Given that, at a local college, 198 of the male students are smokers and 792 are non-smokers.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes

Number of male smokers=198

Number of male non-smokers=792

Total number of male smokers=198+792

= 990

Number of female smokers=330

Number of female non-smokers=770

Total number of female smokers=330+770

= 1100

Probability that both are non-smokers is given by

P(both are non-smokers ) = P(Male non-smoker) × P(female non-smoker)

= 792/990 × 770/1100

= 0.8 × 0.7

= 0.56

Therefore, the probability that both male and female are non-smokers is 0.56.

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The probability that they two people are chosen and travel by different transport is 47/144

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.

Probability is given as sample space / total outcome

Probability to travel by car p(C)= 5/12

Probability to travel by bus P(B)= 4/12=1/3

Probability to travel by train P(T)= 3/12= 1/4

for two people chosen at random

P(C ×B)= 5/12×1/3= 5/36

P(B×T)= 1/3×1/4= 1/12

P(C×T)= 1/4×5/12= 5/48

Therefore the probability that the two chosen travel by different car is

P(C ×B)+P(B×T)+P(C×T)= 5/36+1/12+5/48

= 141/432

divide through by 3

= 47/144

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The value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.

It is given that the expression is,

x + 20 ≤ -10

Rearrange the expression as

x≤ -10-20

x≤ -30

Thus, the value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.

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Answer:

B

Step-by-step explanation:

point T is on the y-axis with x- coordinate 0 and y- coordinate 5, then

the ordered pair for point T is (0, 5 )

Answer:

49 leaves

Step-by-step explanation:

7 days x 7 leaves per day = 49 leaves in total

The probability that the animal patient is NOT a bird as a simplified fraction is 11/13.

What is probability?

The study of probabilities, which are determined by the ratio of favorable occurrences to probable cases, is known as probability.

As given in the question,

Number of dog patients is 5,

Number of cat patients is 6, and

Number of bird patients is 2.

So,

Total number of animal patients = 5 + 6 +2 = 13

Total number of ways of picking 1 animal patient = 13C1 = 13

Number of patients that are NOT birds = 11

So,

probability that the animal patient picked is not a BIRD = 11C1 / 13C1 = 11/13

Therefore, the probability that the animal patient is NOT a bird is 11/13.

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Answer:30

Step-by-step explanation:

The solution of the differentiated equation is dy/dx = 40x³+ 3

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

Y=10 x^4+3 x+50

Rewrite properly

So, we have

y = 10x⁴ + 3x + 50

The rule of first principle of differentiation is represented as

If y = axⁿ, then dy/dx = naxⁿ⁻¹

Using the above as a guide, we have

dy/dx = 4 * 10x⁴⁻¹ + 1 * 3x¹⁻¹ + 0 * 50

Evaluate

dy/dx = 40x³+ 3

Hence, the equation result is dy/dx = 40x³+ 3

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Answer:

Step-by-step explanation:

You want Elga's age, given that Alvin is 15 years younger and the sum of their ages is 43.

Let e represent Elga's age. Then (e-15) is Alvin's age, and the sum of their ages is ...

  e +(e -15) = 43

  2e = 58 . . . . . . . add 15

  e = 29 . . . . . . . divide by 2

Elga's age is 29.

  e -15 = 29 -15 = 14 . . . . Alvin's age

The required amount after 3 years is $1090, but when compounded annually the amount becomes $1092.72.

Given that,
$1000 become in a saving account at 3% per year for 3 years when the interest is not compounded.

Simple interest is defined as the percentage of earning on the lending for a period of time

Here,
Simple interest earned = P × r × t /100
                                      = 1000 × 3 × 3 /100 = 90
Amount = P + SI = 1000 + 90 = $90
Now, when interest is compounded annually,
Amount =  1000(1.03)³
Amount = $1092.72

Thus, the required amount after 3 years is $1090, but when compounded annually the amount becomes $1092.72.

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========================================================

Work Shown:

A = set of multiples of 3 between 1 and 16

A = {3, 6, 9, 12, 15}

B = set of even natural numbers up to and including 20

B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

A u B = {3, 6, 9, 12, 15,       2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

A u B = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20}

---------------

Explanation:

The U stands for "set union". It's where we combine two or more sets together to form a larger set. The duplicates are tossed out. This is what your teacher meant when writing "Make sure each element is only listed once". Writing A u B indicates "the set of values in either set A, set B, or both".

In this case, the duplicates are "6" and "12" since they are found in set A and B simultaneously. They are in the overlapped area of both sets. It might help to draw out a Venn Diagram.

Common convention is to sort the items in the set. Though technically a set like {1,2,3} is the same as {3,1,2}.

Don't forget about the curly braces to indicate to the reader that this is a set of values.

The probability of getting both these numbers correctly is of:

0.028%.

The probability of an event in an experiment is obtained as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.

In this problem, the probabilities are presented as follows:

The probability of getting both these numbers correctly is given by the multiplication of the probabilities of getting the correct number on each trial, hence:

p = 1/60 x 1/59 = 0.00028 = 0.028%.

The problem states that two numbers are selected from a set of 60, and it asks for the probability that both are guessed correctly.

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Answer:

96% rounded to the nearest percent.

Step-by-step explanation:

Divide 100 by 23 which is approximately 4.35

Multiply 4.35 by 22 which is 95.7%.

If you round 95.7 to the nearest percent, it would be 96%.

Answer:

95.6521739%

explanation:

22 is 95.6522% of 23