The average of three numbers, p, q and 27 is 28.The average of five numbers p, q, r, s and 27 is 31.Find the average of r and s.

Helen is currently is 8 years old.

Endeavor to understand the question, analyze it and interpret it into equation.

Given that Helen's age is multiples of 4. Next year it'll be a multiple of 3. Helen's older brother is now 19.

This means Helen current age is multiple of 4 and next year it will be a multiple of 3. Also, Helen's age is less than 19

The two available numbers that fit this analysis and less than 19 are 8 and 9. 8 is multiple of 4. 8 + 1 = 9 which is multiple of 3

Therefore, Helen is 8 years old now

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Earth science is made of many branches of knowledge concerning all aspects of the Earth system. The main branches are geology, meteorology, climatology, oceanography, and environmental science. Astronomy uses principles understood from Earth to learn about the solar system, galaxy, and universe.

Only recently have humans begun to understand the complexity of our planet Earth. We have only known for a few hundred years that Earth is just a tiny part of an enormous galaxy, which in turn is a tiny part of an even greater universe.

An important component of experiments is the different variables involved. A variable is any parameter in the experiment that can change. This could be a parameter like temperature, weight or height, or it could be more complex, such as life expectancy or growth rate. Depending on how you set up your experiment, you will use different kinds of variables. There are three basic types to be familiar with.

The first type is the independent variable. This is the variable that is manipulated during an experiment. For example, when experimenting with how fertilisers affects plant growth, the fertiliser is the independent variable because this is the variable that you change. It might help to think of the independent variable as the cause of change in the experiment.

In contrast to this, the dependent variable is the variable that is affected during an experiment. In our experiment, our dependent variable would be plant growth since this is affected by the amount of fertiliser applied. If you think of the independent variable as the cause, then the dependent variable is the effect.

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Condition (A) P(B/A) = y is true.

To find the true condition:

If two events are independent, then:

Use formulas for conditional probabilities:

For independent events these formulas will be:

Now in your case, Pr(A) = x and Pr(B) = y.

Therefore, condition (A) P(B/A) = y is true.

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The complete question is given below:

The probability of event A is x, and the probability of event B is y. If the two events are independent, which of these conditions must be true?

a. P(B|A) = y

b. P(A|B) = y

c. P(B|A) = x

d. P(A and B) = x + y

e. P(A and B) = x/y

The exponential function represented by the points (0, 2) and (3, 686) is y = 2(7)ˣ

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

The standard form of an exponential funtion is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

At point (0, 2)

2 = ab⁰

a = 2

At point (3, 686)

686 = 2b³

b = 7

The exponential function represented by the points (0, 2) and (3, 686) is y = 2(7)ˣ

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Answer:

-7.1931540532314155

Step-by-step explanation:

-7.1931540532314155

Answer:

1

Step-by-step explanation:

The slope of a function is equal to the coefficient of x when the equation is in standard form (y=mx+c)

In this case the equation is already in standard form and thusly we can see that the coefficient of x is 1 (the constant has no effect on the slope)

The total price paid by Mr. Thapa as per the new rating will be equal to Rs 180.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Total distance traveled by Mr. Thapa = 5 km = 5000 meters.

The initial price paid for the taxi = Rs 14

Then, the meter was flagged down, then the fare went to rs 7.20 per 200 m.

Let the price paid after 5 km is x.

So, the ratio will be,

200 m = Rs 7.20

5000 m = x

Perform cross-multiplication,

200x = 5000 × 7.20

200x = 36000

x = 36000/200

x = Rs 180

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Answer:

Hey Desmariesin7587, the median of the data set that you gave is  15.9

Step-by-step explanation:

Since the amount of values in the data set was not even, I could not find a middle number. Instead, I added up all of the values and divided the total sum by the amount of values that there were; in this case, 10.

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

Have a great day,

Nish

The solutions to the quadratic equation -t² + 7t = 0 are 7 and 0.

Hence, x = 7, 0.

Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;

ax² + bx + c = 0

Where x is the unknown

To solve for x, we use the quadratic formula

x = (-b±√(b² - 4ac)) / (2a)

Given the equation;

-t² + 7t = 0

Comparing with the standard form.

We substitute into the quadratic formula.

x = (-b±√(b² - 4ac)) / (2a)

x = (-7±√( (7)² - ( 4 × -1 × 0) ) / (2 × -1)

x = (-7±√( 49 - 0) ) / (-2)

x = (-7±√49 ) / (-2)

x = (-7±7 ) / (-2)

x = (-7-7 ) / (-2), (-7+7 ) / (-2)

x = -14/(-2), 0/(-2)

x = 7, 0

The solutions to the quadratic equation -t² + 7t = 0 are 7 and 0.

Hence, x = 7, 0.

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Answer:

  shaded area = 9x² +10x +4

Step-by-step explanation:

The area of the shaded region is the difference between the areas of the overall rectangle and the unshaded one it contains. Each area is the product of length and width.

Overall rectangle

  A = LW

  A = (5x)(3x) = 15x² . . . . . using given dimensions

Unshaded interior rectangle

  A = (3x +1)(2x -4) = 3x(2x -4) +1(2x -4) . . . . . using given dimensions

  A = 6x² -12x +2x -4 = 6x² -10x -4

The shaded area is the difference between the area of the overall rectangle and the area of the unshaded included rectangle.

  shaded area = (15x²) -(6x² -10x -4)

  shaded area = 9x² +10x +4

Answer:

  456 kg

Step-by-step explanation:

Mass is the product of volume and density.

The product of volume and density is ...

  M = Vρ

  M = (2600 m³)(0.1755 kg/m³) ≈ 456 kg

The balloon contains about 456 kg of He.

They will both have the same amount in the bank after 10 weeks

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, we have

Nancy

Initial = 400

Rate = 10

So, the equation is

y = 400 + 10x

700

Initial = 700

Spending = 20

So, the equation is

y = 700 - 20x

When they both have the same amount of money in the bank, we have

700 - 20x = 400 + 10x

Evaluate the like terms

30x = 300

Divide by 30

x = 10

Hence, they will both have the same amount in the bank after 10 weeks

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[tex]\boldsymbol{\sf{\dfrac{4}{5}+\dfrac{9}{10} } }[/tex]

The least common multiple of 5 and 10 is 10. Convert 4/5 and 9/10 to fractions with denominators of 10.

[tex]\boldsymbol{\sf{\dfrac{4\times2}{5\times2}+\dfrac{9}{10} \ \ \to \ \ Simplify }}[/tex]

[tex]\boldsymbol{\sf{ \dfrac{8}{10}+\dfrac{9}{10} }}[/tex]

Since 8/10 and 9/10 have the same denominator, join their numerators to add them.

[tex]\boldsymbol{ \sf{\dfrac{8+9}{10} \ \to \ \ Add }}[/tex]

Simplify

[tex]\boldsymbol{\sf{ \dfrac{17}{10}= }}\boxed{\boldsymbol{\sf{1\frac{7}{10} }}}[/tex]

Answer:

-6

Step-by-step explanation:

Additive inverse is the number that when added to A gives a result of zero

A + inverse = 0

6 + inverse = 0

inverse = -6

Answer:

think its number 2 7-(3-5)=(7-3)-5

Step-by-step explanation:

The range of possible side lengths in  interval notation 41 < s < 47

What does it mean to interval notation?

Since the perimeter is four times the side, the constraints on the perimeter are immediately translated into constraints on the side-

[tex]164 < p < 188 = 164 < 4s < 188[/tex]

So, if you divide every term in the inequality by 4, you have

[tex]\frac{164}{4} < s < \frac{188}{4}[/tex]

Now simply evaluate the fractions

41 < s < 47

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Answer:

Angle symbol

Angle ACB

Angle ACE

Angle DCE

The answer choices which represents the slope of the line described by the points, (1,-1) and (5,-7) is; Choice A; -3/2.

The line in discuss as described in the task content is passing through the points; (1,-1) and (5,-7).

Hence, it follows conventionally from the slope formula that the slope of the line is;

slope, m = (-7-(-1))/(5-1)

m = -6/4

m = -3/2.

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I assume [tex]C[/tex] is oriented counterclockwise. If [tex]C[/tex] is the closed rectangle, then by Green's theorem we have

[tex]\displaystyle \int_C F\cdot dr = \int_0^3 \int_0^9 \frac{\partial (x-y)}{\partial x} - \frac{\partial (x^2+y^2)}{\partial y} \, dy \, dx \\\\ ~~~~~~~~~~~~ = \int_0^3 \int_0^9 (1 - 2y) \, dy \, dx = 3 \int_0^9 (1-2y)\, dy = \boxed{-216}[/tex]

It seems unlikely, but if you actually are omitting the integral along the line segment joining (0, 9) and (0, 0), let [tex]x=0[/tex] and [tex]y=9-t[/tex] with [tex]0\le t\le9[/tex]. Then the integral along this line segment would be

[tex]\displaystyle \int_{(0,9)\to(0,0)} F\cdot dr = \int_0^9 \bigg((0^2 + (9-t)^2) i + (0 - (9-t)) j\bigg) \cdot (0i - j) \, dt \\\\ ~~~~~~~~  = \int_0^9 (9-t) \, dt = \frac{81}2[/tex]

so that the overall integral would instead have -216 - 81/2 = -513/2.

Answer:

D

Step-by-step explanation:

This function passes the vertical line test.

The vertical line test test is done by drawing a vertical line anywhere on the graph. If the line goes through two points or more then it isn't a function.

The LCM of 18 and 24 using the prime-factorization method is 72.

The LCM of 27, 81, and 54, using the division method is 162.

In the first question, we are asked to find the LCM of the given numbers using the prime factorization method.

(i) 18, 24.

Prime factorization gives:

18 = 2*3², and 24 = 2³*3.

The LCM is the product of the highest power of each prime factor.

Thus, LCM = 2³*3² = 8*9 = 72.

Thus, the LCM of 18 and 24 using the prime-factorization method is 72.

Doing similarly for other sub-parts, The LCM of:

(ii) 16, 40 is 80.

(iii) 30, 36 is 180.

(iv) 28, 44 is 308.

(v) 20, 32 is 160.

(vi) 20, 135 is 540.

(vii) 45, 75 is 225.

(viii) 36, 84 is 252.

(ix) 12, 18, 24 is 72.

(x) 25, 35, 45 is 1575.

(xi) 9, 15, 21 is 315.

(xii) 25, 50, 75 is 150.

In the second question, we are asked to find the LCM of the given numbers, using the division method.

(i) 27, 81, 54.

The division method gives:

[tex]\underline{2|27,81,54}\\\underline{3|27,81,27}\\\underline{3|9,27,9}\\\underline {3|3,9,3}\\\underline{3|1,3,1}\\{1|1,1,1}[/tex]

The LCM is the product of all the numbers used for division.

LCM = 2*3*3*3*3*1 = 162.

Thus, the LCM of 27, 81, and 54, using the division method is 162.

Doing similarly for other sub-parts, The LCM of:

(ii) 18, 45, 63 is 630.

(iii) 35, 55, 100 is 7700.

(iv) 210, 140, 315 is 1260.

(v) 112, 120, 150 is 8400.

(vi) 144, 180, 300 is 3600.

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See below for the combination of the arithmetic operations and exactly five 3's

The conditions are given as:

There are no direct rules to this, except by trial and error.

After several trials, we have the following operations:

(3 * 3 - 3 * 3)/3 = 0

3 - 3/3 - 3/3 = 1

(3 + 3 - 3 / 3)-3 = 2

(3 * 3 - 3 + 3)/3 = 3

3 *3/3 + 3/3 = 4

3 +3/3 + 3/3= 5

3 + 3 + (3 - 3)/3 = 6

(3^3 - 3 - 3)/3 = 7

3 + 3 + (3 + 3)/3 = 8

3 + 3 + 3+ 3 -3 =9

3 + 3 + 3 + 3/3 = 10

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Answer:

a(1) = 2

a(n) = a(n-1)+4

Step-by-step explanation:

Using the given arithmetic sequence,

a1 is 2

a2 is 6

a3 is 10

a4 is 14

a5 is 18

and to get from a1 to a2 you have to +4, to get from a2 to a3 you have to +4 and so on.

In a reclusive formula you need to find two pieces of information:

1. The first term of the sequence

2. The pattern rule to get any term from the term that comes before it

Using the given sequence, the first term is 2 and the rule to get any term from its previous term is +4.

So, putting that information in the form of a recursive formula will read as the following:

an+1 = an+4

a1 = 2, n is greater or equal to 1 (n is an interger)

Which can be rearranged to

a(1) = 2

a(n) = a(n-1)+4

The scale factor of the given dilation transformation is calculated as; 1/2

We know that from transformation that  a dilation is a non - rigid transformation that produces similar figures.

If two lines are similar, then the lines are parallel and parallel lines always have the same slope.

Thus;

Line A has the formula; 2y = x + 8

Writing it in slope intercept form gives us;

y = 0.5x + 4   ------(1)

Thus;

slope of the line A is m = 0.5

y-intercept of the line A is b = 4

Line B has the equation;

y - ¹/₂x = 2

Rearranging in Slope Intercept form gives us;

y = ¹/₂x + 2

Thus;

slope of the line B is m = 0.5

y-intercept of the line B is b = 2

Now, it should be noted that the y-intercept of line A multiplied by the scale factor k must be equal to the y-intercept of line B. Thus;

4k = 2

k = 2/4

k =  ¹/₂

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Using derivatives, it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval:

(-15,-10).

It is given by the derivative at x = x0, that is:

[tex]m = f^{\prime}(x_0)[/tex].

In this problem, the function is:

[tex]f(x) = 0.2x^2 + 5x - 12[/tex]

Hence the derivative is:

[tex]f^{\prime}(x) = 0.4x + 5[/tex]

For a slope of -1, we have that:

0.4x + 5 = -1

0.4x = -6

x = -15.

For a slope of 1, we have that:

0.4x + 5 = 1.

0.4x = -4

x = -10

Hence the interval is:

(-15,-10).

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The sum of the first 40 terms of the geometric sequence is:

22,114,662.64

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The sum of the first n terms of a sequence is:

[tex]S_n = \frac{a_1(1 - q^n)}{1 - q}[/tex]

For this problem, the parameters are:

a1 = 1, q = 1.5, n = 40.

Hence the sum is:

[tex]S_{40} = \frac{1 - 1.5^{40}}{1 - 1.5} = 22,114,662.64[/tex]

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There would not be enough time to reach the half marathon distance.

The distance run in a week can be represented with a linear equation. A linear equation is an equation that has a single variable raised to the power of 1.

The linear equation that would be used to represent the distance run would be in the form:

Miles run in a week = miles run the previous week - increase in miles

Increase in miles = 6 - 4.5 =  1.5 miles

Miles run in the fourth week = 1.5 + 6  = 7.5 miles

Miles run in the fifth week = 7.5 miles + 1.5 miles = 9 miles

Miles run in the sixth week = 9 + 1.5 = 10.5 miles

There would not be enough time to reach the half marathon distance because in the sixth week she would be able to run 10.50 miles

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The two positive numbers satisfying the given requirements are 15.56 and 15.56

For given question,

Let x and y be  two positive numbers satisfying the given requirements.

⇒ xy = 242             .............(1)

The sum of given two positive numbers is a minimum.

Let the sum of given two positive numbers is S.

⇒ x + y = S             ............(2)

From equation(1),

⇒ y = 242/x

Substitute above value of y in equation (2),

⇒ x + y = S  

⇒ S = x + (242 / x)    

Now, for above equation we find the derivative of x with respect to x.

⇒ 0 = 1 - [tex]\frac{242}{x^{2} }[/tex]

⇒ 242/x² = 1

⇒ x² = 242

⇒ x = ±15.56

Since the numbers are positive, x = 15.56

For x = 15.56

⇒ y = 15.56

Therefore, the two positive numbers satisfying the given requirements are 15.56 and 15.56

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