please solve by BODMAS rule ​

The standard deviation exists as the positive square root of the variance.

So, the standard deviation = 6.819.

Given data set: 15, 17, 23, 5, 21, 19, 26, 4, 14

To calculate the mean of the data.

We know that mean exists as the average of the data values and exists estimated as:

Mean [tex]$=\frac{15+17+23+5+21+19+26+4+14}{9}[/tex]

Mean [tex]$=\frac{144}{9}[/tex]

Mean = 16

To estimate the difference of each data point from the mean as:

Deviation:

15 - 16 = -1

17 - 16 = 1

23 - 16 = 7

5 - 16 = -11

21 - 16 = 5

19 - 16 = 3

26 - 16 = 10

4 - 16 = -12

14 - 16 = -2

Now we have to square the above deviations we obtain:

1 , 1, 14, 121, 25, 9, 100, 144, 4

To estimate the variance of the above sets:

variance [tex]$=\frac{1+ 1+14+ 121+25+ 9+ 100+ 144+ 4}{9}[/tex]

Variance [tex]$=\frac{419}{9}[/tex]

Variance = 46.5

The standard deviation exists as the positive square root of the variance.

so, the standard deviation [tex]$\sqrt{46.5} =6.819[/tex] .

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The equation that Sean woul have solved using the cross multiplication would be option a.

[tex]\frac{10}{x^2-1} =\frac{15}{3x-3}[/tex]

We have to open the equation by using cross multiplication

10(3x - 3) = 15(x² - 1)

= 30x - 30 = 15x² - 15

we would have to factorize

30(x-1) = 15(x-1)(x+1)

We have to divide by 15(x-1)

2 = x + 1

take the like terms

2 -1 = x

x = 1

Hence the equation that has the extraneous solution is option a because the solution is 1.

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This exercise is about a proof in Euclidian geometry. See the explanation below.

The study of solid and flat objects using the axioms and theorems developed by the Greek mathematician Euclid is known as Euclidean geometry (c. 300 bce).

Given that S is the midpoint of [tex]\overline{QT}[/tex]:

Hence QS = TS ......................1

It is right to indicate that

PQ = TV  ........................2

And ∠RSQ is vertically opposite to ∠TSV

Hence

∠RSQ = ∠TSV.........................3

Given 1, 2, and 3,

Δ QRS ≅ ΔVTS

Therefore,

Δ QRS ≅ ΔVTS

and ∠ RSQ can be termed to be congruent to ∠TSV.

It is to be noted that the measure of an angle is the same for congruent angles. An ordinary pentagon, for instance, has five sides and five angles, each of which is 108 degrees.

The angles of a regular polygon will always be congruent, regardless of its size or scale.

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Answer:

-(10/7)

Step-by-step explanation:

See attached graphic. The slope of the Green Line is cut off in the problem photo, but can be calculated from the graph to find the slope of the Red Line. The answer options are on drugs; pick the one that looks closest.

Answer:

-4/3

Step-by-step explanation:

Answer:

4th option

Step-by-step explanation:

given

sinΘ = [tex]\frac{5}{13}[/tex] and cosΘ = [tex]\frac{12}{13}[/tex] , then

( [tex]\frac{5}{13}[/tex] )² + ( [tex]\frac{12}{13}[/tex] )²

= [tex]\frac{25}{169}[/tex] + [tex]\frac{144}{169}[/tex]

= [tex]\frac{25+144}{169}[/tex]

= [tex]\frac{169}{169}[/tex]

= 1

showing sin²Θ + cos²Θ = 1

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

In Mathematics, a mean is also referred to as an arithmetic average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the distance between the means of both classes A and B is given by:

Distance = Mean of class A - Mean of class B

Distance = 12 - 4

Distance = 8.

The mean absolute deviation (MAD) for class A is given by:

MAD A = 1/9[2(9 - 12) + (10 - 12) + (11 - 12) + (12 - 12) + (13 - 12) + (14 - 12) + 2(15 - 12)]

MAD A = 1/9[2(3) + (2) + (1) + 0 + (1) + (2) + (1) + 2(3)]

MAD A = 1/9[6 + 2 + 1 + 1 + 2 + 1 + 6]

MAD A = 1/9 × [18]

MAD A = 18/9

MAD A = 2.

Also, the mean absolute deviation (MAD) for class B is given by:

MAD B = 1/9[2(1 - 4) + (2 - 4) + (3 - 4) + (4 - 4) + (5 - 4) + (6 - 4) + 2(7 - 4)]

MAD B = 1/9[2(3) + 2(2) + (1) + (0) + (1) + (2) + 2(3)]

MAD B = 1/9[6 + 4 + 1 + 0 + 1 + 2 + 6]

MAD B = 1/9 × [18]

MAD B = 18/9

MAD B = 2.

Therefore, distance between the means = four (4) times the MAD.

Distance = Means × MAD

8 = 4 × 2.

In conclusion, we can infer and logically deduce that there is no overlap and the distance between the means of both classes A and B is between one (1) times the MAD and five (5) times the MAD.

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Using the normal distribution, it is found that the standard deviation is of 26.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, we have that the mean is of [tex]\mu = 95[/tex], while X = 110 has a p-value of 0.75, hence X = 110, Z = 0.575, and then we solve for [tex]\sigma[/tex] to find the standard deviation.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.575 = \frac{110 - 95}{\sigma}[/tex]

[tex]0.575\sigma = 15[/tex]

[tex]\sigma = \frac{15}{0.575}[/tex]

[tex]\sigma = 26[/tex]

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Answer:

Below in bold.

Step-by-step explanation:

a) 0.04, 0.1, 0.16

You  add 0.06 to get the next term:

The next 2 are: 0.22, 0.28.

b) 3, 9, 27

You multiply by 3 to get next term

Next 2 are: 81, 243.

c)  0.3, 1/3, 11/30

1/3 - 0.3 = 1/30

11/30 - 1/3 = 1/30

So common difference = 1/30

The next 2 terms are 12/30 and 13/30

= 2/5 , 13/30.

The description of this graph tells us that the equation 2x + 3y ≤ 15 was shaded to the bottom while x + y ≥ 3 was shaded to the top as shown in the diagram.

a. The first equation of the graph when it was drawn was shaded to the bottom, while the upper part of the shading has is that of the equation x + y ≥ 3.

b. (5,1) are the solutions for the equation 2x+3y<15. This is given that when x and y are substituted we would still have less than 15.

C The point in the graph would be 2,3. At this point, Michael would be able to buy 2 sandwiches and 3 hot lunches. This is still within his budget for 3 students.

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Answer:

Step-by-step explanation:

2,3 is the anwser

The slope of a line is -2.

The slope of a line can be described as follows:

The slope of a line is a measure of its steepness

Slope = rise / run

slope = y₂ - y₁ / x₂ - x₁

using (0, -4)(-1, -2)

x₁ = 0

x₂ = -1

y₁ = -4

y₂ = -2

Therefore,

slope = -2 - (-4) / -1 - 0

slope = -2 + 4 / -1

slope = 2 / -1

slope = -2

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After some algebraic handling, the algebraic expression for x in terms of r is x = 1 / r + 1 .

In this question we must make use of algebra properties to clear a variable within a formula only formed by algebraic form, there are no trascendent functions herein. Clearing variables consists in leaving such variables alone in one side of the equivalence. Now we proceed to present the procedure in detail:

The statement presents a typing omission, correct form is shown below:

Solve the equation r = 1 / (x - 1) for x in terms of r.

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The steps to solve a quadratic formula include:

In algebra, a quadratic equation is a equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0.

A quadratic equation is an equation that could be written as ax² + bx + c = 0

when a 0. The factoring method is illustrated:

To solve a quadratic equation by factoring, put all terms on one side of the equal sign, leaving zero on the other side.

Set each factor equal to zero.

Solve each of these equations.

Check by inserting your answer in the original equation.

Example 1

Solve x² – 6 x = 16.

Following the steps,

x² – 6 x = 16 becomes x² – 8x + 2x – 16 = 0

Factor.

( x – 8)( x + 2) = 0

Therefore, x = 8 and -2.

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The resultant of subtractions of u = <-8, 4> and v = <2, 7> are

-u-v = <6, -11>,

u-v = <-10, -3>,

and v-u= <10,3>.

What is a vector in simple definition?

The resultant of subtractions of u = <-8, 4> and v = <2, 7> are

-u-v = <6, -11>,

u-v = <-10, -3>,

and v-u= <10,3>.

Given that,

The results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.

We have to determine,

The value of -u-v, u-v, and v-u.

According to the question,

The results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.

The value of -u-v is,

-u -v = - < -8 ,4 > - <2,7>

-u -v = <8, -4> - < 2, 7 >

-u - v = < 8 - 2 , -4 - 7 >

-u -v =  < 6 , - 11 >

The value of u-v is,

u -v = < -8 ,4 > - < 2,7 >

u - v = < - 8  - 2, 4 - 7 >

u - v = < 10 ,3>

The value of v - u is,

v - u = < 2 , 7>  - < - 8,4 >

v - u = <  2 + 8 ,  7 - 4 >

v - 4 = <  10 , 3 >

Hence, The resultant of subtractions of u = <-8, 4> and v = <2, 7> are

-u-v = <6, -11>,

u-v = <-10, -3>,

and v-u= <10,3>.

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The answer is B.

Since ΔQRS ~ ΔXYZ, the value of tan(Q) is :

The experimental probability the placebo pill induced better concentration on the student exams is 0.64

The question has to do with probability.

Probability is the likelihood of an event occurring.

The probability of an event A is given by

P(A) = number of occurrences of event A/total number of occurrences of all events.

Given that in the study on the placebo effect on 100 students, 64 were found to perform better on tests after taking a fake pill to improve concentration.

The event A = students performing better.

Since 64 students performed better, the number of occurrences of event A = 64.

Since there were 100 students, the total number of occurrences = 100.

So, P(A) = P(students perform better)

= number of occurrences of event A/total number of occurrences of all events.

= 64/100

= 0.64

So, the experimental probability the placebo pill induced better concentration on the student exams is 0.64

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Answer:

x = 10°

Step-by-step explanation:

If the two lines are parallel then the two marked angles will be equal.

8x = 2x + 60

Subtract 2x to combine like terms.

6x = 60

Divide by 6.

x = 10

Answer:

[tex] {x}^{4} [/tex]

Step-by-step explanation:

[tex] { {( - x}^{2} )}^{2} = ( - {x}^{2} )( - {x}^{2} ) = {x}^{4} [/tex]

An expression is defined as a set of numbers, variables, and mathematical operations. The value of the given expression when simplified is equal to x⁴.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression can be simplified as shown below,

(-x²)²

= (-x × -x)²

Since the product of two negatives is always positive, therefore, we can write,

= -x² × -x²

As per the rule of exponents, the expression can be written as,

= x⁴

Hence, the value of the given expression when simplified is equal to x⁴.

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Answer:

look at attached image for the step-by-step proof. thanks for reposting this lol

Answer:

a) horizontal compression with a factor of 0.5 and a horizontal reflection over the y-axis.

b) Pick one the two correct answers:

translation of 2 units right

translation of 2 units down

Step-by-step explanation:

If function f(x) is transformed into f(ax) then it is stretched or compressed horizontally.

If |a| > 1 it is compressed horizontally.

If 0 < |a| < 1, it is stretched horizontally.

If a is negative, then it is reflected over the y-axis.

a) Compare y = -2x with y = x.

The change is in that x became -2x.

Here, a = -2.

Since |-2| = 2, and 2 > 1, it has a compression of a factor of 2 horizontally.

Also, since -2 is a negative number, it is reflected over the y-axis.

Answer: horizontal compression with a factor of 0.5 and a horizontal reflection over the y-axis.

If function f(x) is transformed into f(x) + b then it is translated vertically b units. If b > 0, the translation is b units up. If b < 0, the translation is b units down.

b) y = x - 2

This can be thought of the function f(x) becoming f(x) - 2.

It is a translation of 2 units down.

Interestingly, in this case, this can also be thought of x being replaced by x - 2 which is a translation of 2 units to the right.

Answer:

There are two correct answers (use only one of the two below):

translation of 2 units right

translation of 2 units down

Answer:

about 1800 im sorry if im wrong

Step-by-step explanation:

The missing dimension in the figure given in the question is 9 ft

Diameter of small circle / Diameter of big circle = Height of small / Height of Big

24 / d = 8 / 36

Cross multiply

d × 8 = 24 × 36

d × 8 = 864

Divide both sides by 8

d = 864 / 8

d = 108 in

Divide by 12 to express in feet

d = 108 / 12

d = 9 ft

Thus, the missing dimension is 9 ft

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If the solids are similar, then their lengths/dimensions are proportional.

24 inches / 8 inches = d / 3 feet

---Cross Multiply

8d = 72

d = 9 feet

Hope this helps!

Answer:

The frame will be 4 inches in width

Step-by-step explanation:

The length of the outside is 24+2x

The width of the outside is 20+2x

(24+2x)(20+2x) - 20(24) = 416

480 + 40x + 48x + 4x2 - 480 = 416

4x2 + 88x - 416 = 0

x2 + 22x - 104 = 0

(x+26)(x-4) = 0

x = -26 or x=4

The frame will be 4 inches in width

The lengths of the sides of the rectangles are;

a. (2•x + 3) and (x + 2)

b. (6•x + 2) and (x + 1)

c. (x + (2 + √3)) and (x + (2-√3))

The given functions are presented as follows;

a. 2•x² + 7•x + 6

By factoring of the above function we have;

2•x² + 7•x + 6 = (2•x + 3) × (x + 2)

The lengths of the sides of the rectangle are therefore;

b. 6•x² + 7•x + 2

The above function can be factored as follows;

6•x² + 7•x + 2 = (6•x + 2) × (x + 1)

The rectangle side lengths are;

c. x² + 4•x + 1

Using the quadratic formula, the above function can be factored to give;

x² + 4•x + 1 = (x + (2 + √3)) × (x + (2-√3))

The sides of the rectangle are therefore;

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He has thrown 425 free throws if he missed 17

The given parameters are:

Proportion of free throw missed, p = 4%

Number of free throw missed, n = 17

Let the total number of throws be N.

So we have

n = p * N

Substitute the known values in the above equation

17 = 4% * N

Divide both sides by 4%

N = 425

Hence, he has thrown 425 free throws if he missed 17

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From the attached speed versus time graph, it can be seen that the orange or first or car is speeding up. The third or green car is slowing down, and the blue or second car is maintaining a constant speed.

Speed Analysis from the Graph

The graph in the attachment shows the linear increase in speed of the first car over time. Therefore, we can say that it is accelerating at a certain rate.

The graph shows how the speed of the third car is decreasing with time. This demonstrates that the green vehicle is de-accelerating.

The graph shows a straight line for the second car. It displays that the speed does not alter as seconds or minutes pass. We might infer that the blue car is continuing to travel at its current pace as a result.

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Answer:

A C B

Step-by-step explanation:

Which of the cars is speeding up?  

A

Which of the cars is slowing down?  

C

Which of the cars is maintaining a constant speed?  

B

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.

In this exercise, you're required to plot a graph for the data (velocity and time) recorded for an object that is falling from rest.

Based on the graph for the data (see attachment), we can logically deduce the following points:

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Complete Question:

Plot a graph for the following data recorded for an object falling from rest

a. What kind of a curve did you obtain?

b. What is the relationship between the variables?

c. What do you expect the velocity to be after 4.5 s?

d. How much time is required for the object to attain a speed of 100 ft/s?

Let's try solving the problem using the order of operations method, otherwise known as PEMDAS.

[tex]\begin{tabular}{c | l}Order of Operation & Required Operation \\\cline{1-2}1 & Parentheses () \\2 & Exponents e^{x} \\3 & Multiplication \times \\4 & Division \div \\5 & Addition + \\6 & Subtraction -\end{tabular}[/tex]

We are given this question :

[tex]\mathrm {\frac{7}{4} - 9 \div .08 + \frac{4}{5} - 7 \times .8}[/tex]

Since there are no parentheses or exponents, let's multiply.

[tex]\mathrm {\frac{7}{4} - 9 \div .08 + \frac{4}{5} - 5.6}[/tex]

The next step is to divide.

[tex]\mathrm {\frac{7}{4} - 112.5 + \frac{4}{5} - 5.6}[/tex]

After that, add.

[tex]\mathrm {\frac{7}{4} - 112.5 + 0.8 - 5.6}[/tex]

[tex]\mathrm {\frac{7}{4} - 111.7 - 5.6}[/tex]

Finally, subtract the remaining terms.

[tex]\mathrm {1.75 - 111.7 - 5.6}[/tex]

[tex]\mathrm {-109.95 - 5.6}[/tex]

[tex]\mathrm {-115.55}[/tex]

The final answer is -115.55.

I hope this helped solve the problem.

Good luck on your studies!

Answer:

-115.55

Step-by-step explanation:

7/4 -9÷ .08 + 4/5 -7 * .8

I would change fractions to decimals

1.75 - 9 ÷ .08  +.8 -7 * .8

Now using pemdas, multiply and divide from left to right

1.75 -112.5 +.8 -7 * .8

1.75 -112.5 +.8 -5.6

Now add and subtract from left to right

-110.75+.8 -5.6

-109.95-5.6

-115.55

It is true that the graph represents a function

For a graph to represent a function, the following must be true

Each x value on the graph must point to exactly one

The above means that the function must pass the vertical line test

The given graph would pass the vertical line test

This is so because:

Each x value on the graph points to exactly one

Hence, the graph represents a function

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Based on the data given, the conclusion that can be drawn from the correlation coefficient associated with the linear equation is C. There's a weak negative correlation between the variables.

From the information given, it can be seen that the value of y is increasing with the increase in the value of x.

This implies that the correlation is positive. Also, the change in the values of y with x are scattered a lot.

Therefore, the conclusion that can be drawn from the correlation coefficient associated with the linear equation is that there's a weak negative correlation between the variables

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2461,8

hope this helps!! just use the formulas and substitute