3. If the geometric mean of a and 25 is 20,
find the value of a.

If a, b and c vectors are in cyclic order , the scalar product is equals to  zero which makes Option C to be correct.

A vector  can be regarded as quantities that posses both magnitude and a direction this is the opposite to scalar quantity which posses just the magnitude without any direction.

Geometrically,  the  vector can be described as the  line segment,  having its  length as  the magnitude  with the arrow over it  showing direction.

The scalar product  can be gotten with the  multiplication  of the magnitudes of vectors .

Hence, If a, b and c vectors are in cyclic order , the scalar product is equals to  zero .

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CHECK THE COMPLETE QUESTION IN THE ATTACHMENT

Answer:

  2.57

Step-by-step explanation:

The mean absolute deviation is the mean of the absolute values of the differences from the mean.

The mean of the dataset is the sum of values, divided by their number:

  mean = (20 +16 +21 +16 +22 +16 +15)/7 = 126/7 = 18

The absolute values of the differences from 18 will have an average of ...

  mean(|differences|) = (2 +2 +3 +2 +4 +2 +3)/7 = 18/7

  mad(data) ≈ 2.57

__

Additional comment

Some calculators have the mad( ) function built-in. See the second attachment, for example.

Answer: 4096.

Step-by-step explanation:

[tex](8^3)^8\div(8^4)^5=\\8^{3*8}\div8^{4*5}=\\8^{24}\div8^{20}=\\8^{24-20}=\\8^4=\\4096.[/tex]

f(x) = 2x² + 7x + 6 and g(x) = 2^x + 5 have -

The equation of the functions are given as:

f(x) = 2x² + 7x + 6  &

g(x) = 2^x + 5

Next, we plot the graph of both functions (see attachment)

From the graph, we have the following highlights

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Answer:

Step-by-step explanation:

4x - 10 + x + 7 = 4x

5x - 3 = 4x

-3 = -x

x = 3

4(3) - 10 = 12 - 10 = 2

3 + 7 = 10

10+2 = 12

4(3)= 12

The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).

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

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

The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).

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The steps to use to construct a frequency distribution table using sturge’s approximation is as below.

The steps to construct a frequency distribution table using Sturge's approximation are as follows;

Step 1: Find the range of the data: This is simply finding the difference between the largest and the smallest values.

Step 2; Take a decision on the approximate number of classes in which the given data are to be grouped. The formula for this is;

K = 1 + 3.322logN

where;

K= Number of classes

logN = Logarithm of the total number of observations.

Step 3; Determine the approximate class interval size: This is obtained by dividing the range of data by the number of classes and is denoted by h class interval size

Step 4; Locate the starting point: The lower class limit should take care of the smallest value in the raw data.

Step 5; Identify the remaining class boundaries: When you have gotten the lowest class boundary, then you can add the class interval size to the lower class boundary to get the upper class boundary.

Step 6; Distribute the data into respective classes:

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The simplified expression of (x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6 is x^(12) y^(10/9) z^(-1/3)

The algebraic statement is given as:

(x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6

Rewrite the algebraic statement as:

[(x^0 y^2/3 z^-2y)^2/3]/[(x^2 z^1/2)^-6]

Evaluate the like factors

[(x^0 y^(2/3+1) z^-2)^2/3]/[(x^2 z^1/2)^-6]

Evaluate the sum

[(x^0 y^5/3 z^-2)^2/3]/[(x^2 z^1/2)^-6]

Expand the exponents

[(x^(0*2/3) y^(5/3 * 2/3)z^(-2*2/3)]/[(x^(2*-6) z^(1/2*-6)]

Evaluate the products

[(x^0 y^(10/9) z^(-4/3)]/[(x^(-12) z^(-3)]

Apply the quotient law of indices

x^(0+12) y^(10/9) z^(-4/3+3)

Evaluate the sum of exponents

x^(12) y^(10/9) z^(-1/3)

Hence, the simplified expression of (x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6 is x^(12) y^(10/9) z^(-1/3)

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The coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84

Binomial expansion is the expansion of two term expressions such as (a + b)ⁿ where n is a rational number.

Pascal's triangle is atriangle used in determining the coefficients of a binomial expansion.

The general term for the expansion (a + b)ⁿ = ∑ⁿCₓaˣbⁿ⁻ˣ.

So, each term is ⁿCₓaˣbⁿ⁻ˣ.

Comparing (a + b)ⁿ with (2t + s)⁷,

So, its general term is ⁿCₓ(2t)ˣsⁿ⁻ˣ = ⁷Cₓ(2t)ˣsⁿ⁻ˣ

= ⁷Cₓ(2)ˣtˣsⁿ⁻ˣ

So, the coefficient term is ⁷Cₓ(2)ˣ

Now for the term t²s⁵, x = 2.

So, the coeficient term is  ⁷Cₓ(2)ˣ =  ⁷C₂(2)²

= 7!/2!(7 - 2)! × 4

= 7!/2!5! × 4

= 7 × 6 × 5!/(2! × 5!) × 4

= 7 × 6/2 × 4

= 7 × 3 × 4

= 84

So, the coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84

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Answer is Healthclub A costs $33 less in monthly fees than Healthclub B

The number next to the “x” is your rate.

So Healthclub A charges $33 less than B

A charges 27 monthly fee

B charges 60 monthly fee

60-27=33

Answer:

[tex]\Large\boxed{x=-3}[/tex][tex]\Large\boxed{y=6}[/tex]

Step-by-step explanation:

Given the system of equations

[tex]1)~y=3x+15[/tex]

[tex]2)~3x+3y=9[/tex]

Divide 3 on both sides of the 2) equation

[tex]3x+3y=9[/tex]

[tex]3x\div3+3y\div3=9\div3[/tex]

[tex]x+y=3[/tex]

Current system

[tex]1)~y=3x+15[/tex]

[tex]2)~x+y=3[/tex]

Substitute 1) equation into the 2) equation

[tex]x+(3x+15)=3[/tex]

Combine like terms

[tex]x+3x+15=3[/tex]

[tex]4x+15=3[/tex]

Subtract 15 on both sides

[tex]4x+15-15=3-15[/tex]

[tex]4x=-12[/tex]

Divide 4 on both sides

[tex]4x\div4=-12\div4[/tex]

[tex]\Large\boxed{x=-3}[/tex]

Substitute the x value into one of the equations to find the y value

[tex]y=3x+15[/tex]

[tex]y=3(-3)+15[/tex]

[tex]y=-9+15[/tex]

[tex]\Large\boxed{y=6}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Since Point R divides PQ in the ratio 1:3. the x-coordinate of Q is 3

The question has to do with line division

This is the division of a line into a given ratio.

Since Point R divides PQ in the ratio 1:3. If the x-coordinate of R is -1 and the x-coordinate of P is -3.

Let

Since R divides PQ in the ratio, 1:3, we have that

PR/RQ = 1/3

(x₂ - x₁)/(x₃ - x₂) = 1/3

Substituting the values of the variables into the equation, we have

(x₂ - x₁)/(x₃ - x₂) = 1/3

(-1 - (-3))/(x₃ - (-3)) = 1/3

(-1 + 3)/(x₃ + 3) = 1/3

2/(x₃ + 3) = 1/3

x₃ + 3 = 2 × 3

x₃ + 3 = 6

x₃ = 6 - 3

x₃ = 3

So, the x-coordinate of Q is 3

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The equation of the parabolic shape of the gate is:

(x - 40)² = -64(y - 25)

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

The vertex is at the middle of the parabola, that is, a width of 80/2 = 40 meters and a height of 25 meters, hence h = 40, k = 25, and the equation is:

y = a(x - h)² + k

y = a(x - 40)² + 25

When x = 0, y = 0(start of the arc), hence the leading coefficient is found as follows:

0 = 1600a + 25

a = -25/1600

a = -1/64.

Hence the equation is:

y = -1/64(x - 40)² + 25

(x - 40)² = -64(y - 25)

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Answer:

[tex]a = 8[/tex]  or [tex]a = -\frac{14}{3}[/tex]

Step-by-step explanation:

[tex]13(a+4)+24(a+5) = 3(a^{2} +9a+20)[/tex]

[tex]3a^{2} -10a-112=0[/tex]

[tex](3a+14)(a-8)=0[/tex]

[tex]a = 8[/tex]  or [tex]a = -\frac{14}{3}[/tex]

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{13}{a + 5} + \cfrac{24}{a + 4} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{13(a + 4) + 24(a + 5)}{(a + 5)(a + 4)} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{13a + 52+ 24a + 120}{a {}^{2} + 5a + 4a + 20} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ 37a + 172}{a {}^{2} +9a + 20} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3( {a }^{2} + 9a + 20) = 37a + 172[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 {a}^{2} + 27a + 60 = 37a + 172[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 {a}^{2} + 27a - 37a + 60 - 172 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 {a}^{2} - 10a - 112= 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 {a}^{2} - 24a + 14a - 112 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3a(a - 8) + 14(a - 8) = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: (a - 8) + (3a + 14) = 0[/tex]

So, required values of " a " are :

[tex]\qquad \sf  \dashrightarrow \: a = 8 \: \: \: or \: \: \: a = - \cfrac{ 14}{3} [/tex]

The value to increase is keeping A constant and decreasing the value of B

Fractions are written as a ratio of two integers. For instance a.b is a fraction where a and b are integers.

In the fraction a/b, the numerator is and the denominator is b. If the value of the denominator is decreasing the fraction will increase but if the value of the denominator is increasing the fraction will decrease.

Given the expression A + 2/B, the higher the value of B provided such that that A is constant, the higher the expression. Hence the expression that will cause the value to increase is keeping A constant and decreasing the value of B

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Answer:

C

Step-by-step explanation:

The inequalities y < 4 (x-1)² - 16 written in vertex form represents the graph region.

Option C is the correct answer.

It is a statement of an ordered relationship

- greater than,

- greater than or equal to,

- less than,

- less than or equal to between two numbers or algebraic expressions.

We have,

Inequalities where we need to find the coordinates and see which inequalities represent the graph.

y < 4 (x- 1)² - 11 ____(1)

y < -4 (x-1)² - 11 _____(2)

y < 4 (x-1)² - 16 ______(3)

From (1),

y =  4 (x- 1)² - 11

x = 0, y = 4 x 1 - 11 = 4 - 11 = -7

From (2),

y = -4 (x-1)² - 11

y = -4 x 1 - 11 = -4 - 11 = -15

From (3),

y = 4 (x-1)² - 16

x = 0, y = 4 x 1 - 16 = 4 - 16 = -12

We see that,

y < 4 (x-1)² - 16  gives us the coordinates (0, -12) on the graph.

Similarly,

x = 1, y = 4 x 0  - 16 = 0 -16 = -16

x = 1, y = 4 x 1 - 16 = 4 - 16 = -12

(1, -16) and (2, -12) coordinates are on the graph.

Thus,

The inequalities y < 4 (x-1)² - 16 written in vertex form represents the graph region.

Option C is the correct answer.

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Step-by-step explanation:

-x+5+6x-7x-14

6x-8x+5-14

-2x-9

Answer:

17.2 units

Step-by-step explanation:

You would use the Pythagorean Theorem to solve. The height (a) is 4 units. The base (b) is 6 units.

4^2 + 6^2 = sqrt(52)

This would mean that the hypotenuse is 7.211102550927979 units or 7.2 units (the square root of 4^2 + 6^2).

Now you would need to just add all three sides.
6 + 4 + 7.2 = 17.2 units

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The appropriate test for a comparison a group of 10 dogs and group of 10 cats is called independent sample t-test.

In this question,

The independent samples t test (also called the unpaired samples t test) is the most common form of the T test. It helps you to compare the means of two sets of data.

The Independent samples t test compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different.

The independent sample t-test is a useful statistical method of hypothesis testing when an organization wants to determine whether there is a statistical difference between two categories, groups, or items and, furthermore, if there is a statistical difference, whether that difference is significant.

From the definition, the independent sample t-test is the appropriate test for a comparison a group of 10 dogs and group of 10 cats.

Hence we can conclude that the appropriate test for a comparison a group of 10 dogs and group of 10 cats is called independent sample t-test.

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Equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18

The correct option is C.

One or two variables make up a linear equation. Neither the numerator nor the denominator of a fraction can be a variable in a linear equation raised to a power higher than 1. The lines that connect all the points on a coordinate grid when you identify the values that make a linear equation true are congruent.

Let x stand for the number of pencils Stella purchased, and y for the number of pens Stella purchased.

Since Stella purchased a total of 18 things, the quantity of pencils and pens purchased must equal 18 or one of the following:

x + y = 18

We also know she spent $21, that a pencil costs $1, and that a pen costs $1.50. Therefore,

1x + 1.5y = 21

Thus, the set of equations that may be utilized to determine the quantity of pencils (x) and pens (y) that she purchased is as follows:

X+1.5Y = 21, and X+Y = 18

equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18

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Answer:

20

Step-by-step explanation:

To solve this you have to make a system of equations.

Since the father and son's age sum up to 60, the first equation will be:

f + s = 60

Secondly, since the father's age is 5 times the age of the son 6 years ago the equation will be:

6 - (5s) = f

Now, you have to solve the first equation to let it equal to s

f + s = 60

f = 60 - s

Plug in

6 - 5s = 60 - s

     +s          +s

6 - 4s = 60

-6         -6

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

-4s = 54

-----   -----

 -4     -4

   s ≅ 14

14 + 6 = 20

Answer:

20.

Step-by-step explanation:

x = father's age and y = son's age,

x + y = 60

x - 6 = 5(y - 6)

x - 5y = -24

Subtract this from first equation:

6y = 84

y = 14

So the son's age is 14.

Six years time son will be 20.

Answer:

Its 50

Step-by-step explanation:

60 times 4 it gives you 240.

Now minus all the numbers on the table like this

240 - 55 - 70 - 65 which equals to 50

240 would be the miles

if there was a random selection of  cartons from each of the groups to measure grams of fat. This is an example of stratified sampling

Stratified sampling can be defined as a method of sampling that involves  division of a population into smaller groups or items, these are called strata.

This groups or strata are then arranged or organized based on the shared characteristics or attributes of the members in the group of the given population.

Stratification is the process of classifying the population into groups.

Features of  stratified sampling are;

From the information given, we can see that it is an example of stratified sampling.

Thus, if there was a random selection of cartons from each of the groups to measure grams of fat. This is an example of stratified sampling

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Universities A had an income under $20,000 25% graduates.

A two way table is a way to display frequencies or relative frequencies for two categorical variables. One category is represented by rows and a second category is represented by columns.

Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey.

A had an income under $40,000 25% graduates.

We have to add 30 45 together and get 75 because those are the students that have income under $40,000 dollars in both Universities

Then u convert have to convert it to a percentage and get 25%.

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The above question is not complete:

Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey.

How many graduates from University A had an income under $40,000?

________graduates.

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The answer is 25%

its what khan says :>

The area of the resulting surface of this infinite curve is π units.

In this question,

The infinite curve is y = e^−2x, x ≥ 0.

The curve is rotated about x-axis.

Since x ≥ 0, the limits will be 0 to ∞.

Then the area of the resulting surface is,

[tex]A= 2\pi \lim_{b\to \infty} (\int\limits^\infty_0{e^{-2x} } \, dx )[/tex]

Now substitute,

u = -2x

⇒ du = -2dx

⇒ dx = [tex]-\frac{1}{2} du[/tex]

Then,

[tex]\int\limits{-\frac{1}{2}e^{u} } \, du =-\frac{1}{2}\int\limits{e^{u} } \, du[/tex]

Now substitute u and du, we get

⇒ [tex]-\frac{1}{2} \int\limits {e^{-2x} }(-2) \, dx[/tex]

⇒ [tex]-\frac{-2}{2} \int\limits {e^{-2x} } \, dx[/tex]

⇒ [tex](1) \int\limits {e^{-2x} } \, dx[/tex]

⇒ [tex]\int\limits {e^{-2x} } \, dx[/tex]

Thus the area of the resulting surface is

[tex]A= 2\pi \int\limits^\infty_0{e^{-2x} } \, dx[/tex]

⇒ [tex]A= 2\pi [{e^{-2x}(\frac{1}{-2} ) } \,]\limits^\infty_0[/tex]

⇒ [tex]A= \frac{2\pi}{-2} [{e^{-2(\infty)}-e^{-2(0)} } \,]\\[/tex]

⇒ [tex]A= -\pi [0-1} \,]\\[/tex]

⇒ [tex]A= \pi[/tex]

Hence we can conclude that the area of the resulting surface is π units.

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The measures of variation that can be used by Paul are interquartile range and mean absolute deviation.

The interquartile range is the difference between the third quartile and the first quartile.

Third quartile = 3/4(n + 1)

First quartile = 1/4 x (n + 1)

The mean absolute deviation is the average of the distance of a data set from its mean.

Mean absolute deviation =  ∑ l x - m(x) l

Mean, median and mode are measures of tendency. They are used to measure the number at the center of a dataset.

Here are the options:

Mean absolute deviation

mean

interquartile range

median

mode

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mean absolute deviation
mean

median

interquartile range

mode

Answer:

[tex]4x^{6} y^{10}[/tex]  A.

The identity Sin(α)/Tan(α) = Cos(α) is valid

Trigonometry is study of triangles. All trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side. Three major of them are as follows :-

Sine Function:

sin(θ) = Opposite / Hypotenuse

Cosine Function:

cos(θ) = Adjacent / Hypotenuse

Tangent Function:

tan(θ) = Opposite / Adjacent

Lets prove this identity by proceeding with the LHS

= Sin(α)/Tan(α)

= Sin(α)/ (Sin(α)/Cos(α)) (Tan(α) = Sin(α)/Cos(α))

= Sin(α)xCos(α) / Sin(α)

= Cos(α)

Hence verified

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The value of tan(X) in fraction is 7.2/6.4 and in decimal is 1.13

The complete question is added as an attachment

From the question, the given parameters are as follows:

Hypotenuse = XZ

Hypotenuse XZ = 9.6

Leg ZY = 7.2

Leg YX = 6.4

The tangent of X is then calculated as:

tan(X) = ZY/YX

Substitute the known values in the above equation

tan(X) = 7.2/6.4

Evaluate the above quotient

tan(X) = 1.125

Approximate the above result

tan(X) = 1.13

Hence, the value of tan(X) in fraction is 7.2/6.4 and in decimal is 1.13

So, the complete parameters are:

Hypotenuse = XZ

Hypotenuse XZ = 9.6

Leg ZY = 7.2

Leg YX = 6.4

tan(X) = 7.2/6.4

tan(X) = 1.13

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