You are asked to write an equation for the line of best fit for the scatter plot shown at the right without the use of a graphing calculator. What should you do first? Explain

Using the concepts of equilateral triangle, we got that 107 square feet is the total surface area of an equilateral triangular pyramid with base side lengths of 6 feet and a height of 10 feet.

We have :

Base (b) = 6 feet

Slant height (l) = 10 feet

The lateral surface area is calculated using:

L = (3/2)× Length × Breadth

So, we have:

   L = (3/2) ×6 × 10

=>L=(3×3×10)

=>L=90 square feet.

The total surface area is calculated using:

T=Lateral surface area of the wall + area of equilateral triangle

=>T=L+ (√3/4)b²

So, we have:

T = 90 + (√3/4)×(6×6)

=>T=90+(3×3×√3)

=>T=90+9√3

=>T=107 square feet (approx)

Hence, the total surface area of an equilateral triangular pyramid with base side lengths of 6 feet and a height of 10 feet is 107 square feet.

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Answer:

[tex](x+5)^{2}+(y-7)^{2} =16[/tex]

Step-by-step explanation:

The Standard Form of Circle Equation whose Center is at ( h , k) and Radius of r is given by

[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]

So for our Question

we have ( h , k ) = ( -5 , 7 )  and r = 4

By substitution

[tex](x-(-5))^{2}+(y-7)^{2} =4^{2}[/tex]

Simplify [tex](x+5)^{2}+(y-7)^{2} =16[/tex]

The calculation that is not a way to find a fraction of 5/8 is:

1 - 0.125.

A fraction is a numerical representation of the division of the two terms x and y, as follows:

Fraction = x/y.

The terms are classified as follows:

Hence the numeric value of the fraction 5/8 presented in this problem is given as follows:

5/8 = 0.625.

The calculation that is not a way to find the fraction of 5/8 is the only expression that has a different value than 5/8.

The expression with a different value is of:

1 - 0.125 = 0.875.

As the value of 0.875 is different than the value of 0.625 equivalent to the fraction of 5/8.

The complete problem is given by the image at the end of the answer.

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The new odds that the box picked is a special one is 4

Since, there are four boxes that look the same. in one box (the special one), half of the marbles are blue. but only 1/8 of the marbles in the other boxes are blue.

We will have this hypothesis:

The box the blue marble was picked from is the special box.

Prior confidence we had:

Ratio of special boxes to non special boxes=1:3

Now P(blue &special)=1/2, given that a box is selected from the special box, there is 1/2 chance that it is blue

And P(blue & not special)=1/8, given that a box is selected from a non-special box, there is 1/8 chance that it is blue

According to  Baye's factor ,we get:

P(B & S)/P(B & NS)=(1/2)/(1/8)

                               =4

Thus, 4 is the new odds that the box picked is the special one.

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The recursive definition of the arithmetic sequence -34, -21, -8 is:

It is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the rule presented as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

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

An arithmetic sequence can also be defined recursively, as follows:

In this problem, the sequence is given as follows:

-34, -21, -8.

Hence the first term and the common ratio are given as follows:

Hence the recursive definition of the sequence is:

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Answer:

y = -4x

b. y = -20.

Step-by-step explanation:

y = kx

-8 = 2k

k = -8/2

k = -4

y = -4x

y = kx

y = -4 × 5

y = -20

There is no vertex in the graph and the transformations from the parent function are

The graph represents the given parameter

As a general rule, the maximum or the minimum of a graph is the vertex

In this case, there is no maximum or minimum in the graph

This means that that there is no vertex in the graph

Here, we have:

We can see that:

The graph is 4 units to the left of the origin and 2 units below the origin

This means that the function has been shifted down and shifted to the left

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Using the concepts of statistics, we got that at least 79 is the minimum size of the sample needed in order to have a margin of error of two minutes or less, when we need to construct a 95% confidence interval for the mean length of time.

We have mean as  357.9minutes and standard deviation as 20.18 minutes.

To have the margin error 2 minutes or less than it we need to take

Z-score of the given sample distribution which is given by:

                Z=(X-μ)/σ

Here ,μ=357.9,σ=20.18,X=?,Z=95/100

=>95/100=(X-357.9)/20.18

=> -0.95×20.18=X-357.9

=>X=-357.9+0.95×20.18

=>X=-357.9+19.171

>X=-338.729

When X=-338.729,the p score is around 79.

Hence, when I want to construct a 95% confidence interval for the mean length of time of the flight in 2018 based on a sample of flights in 2018., the minimum size of the sample needed in order to have a margin of error of two minutes or less is 79.

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For the given figure, angle 3 will be equal to angle 2.

According to the question,

We have the following information:

We have a figure where some angles are marked in form of numbers and  the measure of angle 3 is equal to the sum of the measures of angle 6.

Now, we know that vertically opposite angles are equal and angle 1 and angle 4 are vertically opposite angles like angle 2 and angle 3.

(More to know: the sum of three angles of a triangle is equal to 180°.)

Hence, for the given figure, angle 3 will be equal to angle 2.

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[tex]\huge\mathcal{♨Answer♥}[/tex]

Answer is on the attachment...

☆...hope this helps...☆

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The equation p=5xy+q can be expressed in terms of p,q, and x as y = (p-q)/5x.

The equation p=7x+4q can be expressed in terms of p and q as x = (p-4q)/7x.

Given in the first equation, p = 5xy+q

p-q=5xy

y=(p-q)/5x

Here we need to express y in terms of p,q, and x so we need all these three variables on one side of the equation and y on the other side. Initially we more q to the left-hand side of the equation which makes it p-q=5xy. Now we divide the left-hand side and the right-hand side by 5x making the equation y = (p-q)/5x.

Similarly in the second equation, p = 7x+4q

p-4q = 7x

x = (p-4q)/7

Here we need to express x in terms of p and q so we need all these two variables on one side of the equation and the term x on the other side. First, we will move 4q to the left-hand side of the equation which will make it p-4q=7x. Now, we will divide the whole equation by 7 which will make the equation x = (p-4q) / 7.

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There were 58 cars sold with exactly two of the given options.

1. There were 90 cars sold with air conditioning.

2. There were 102 cars sold with automatic transmission.

3. There were 72 cars sold with power steering.

4. There were 7 cars sold with all three options.

5. There were 22 cars sold with none of the options.

6. There were 25 cars sold with only air conditioning.

7. There were 61 cars sold with only automatic transmission.

8. There were 33 cars sold with only power steering.

9. There were 11 cars sold with both automatic transmission and power steering.

Let's just count the number of cars that have exactly two of the given options:

Air Conditioning & Automatic Transmission: 25

Air Conditioning & Power Steering: 22

Automatic Transmission & Power Steering: 11

So there are 25 + 22 + 11 = 58 cars that have exactly two of the given options.

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For the given triangle and the measures of the given angle the value of x is equal to -11° .

As given in the question,

For the given triangle,

Let us consider the triangle name ABC,

Where,  m ∠A = x + 51° ,

m ∠ABC = 80° ( vertically opposite angle of given 80° angle.)

m ∠ACB = 60° ( vertically opposite angle of given 60° angle.)

To get the value of x we have,

Sum of all the interior angles of a triangle is equal to 180°

m ∠A + m ∠B + m ∠C = 180°

⇒ x + 51° + 80° + 60° = 180°

⇒ x + 191° =  180°

⇒ x = 180° - 191°

⇒ x = - 11°

Therefore, for the given triangle and the measures of the given angle the value of x is equal to -11° .

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Answer:

-1/4 * x + 2

Step-by-step explanation:

first figure out the slope. You can easily read the point where the graph is crossing the y axis. From there, more right and read how much the graph goes up wor down. You see the graph goes down, so you know the slope must be a negative value. To get the full value of the slope, you need to work out how much the graph goes down if you go 1 right. So when you move 1 right from the point 2 on the y axis, you can't easily read how much it went down. But you can see that the graph passes the pont of x = 4 and y = 1. So it went 4 right and 1 down. To only got 1 down you divide y/x -> 1/4
So the slope is -1/4
and because the graph hits the y axis at 2 and not at 0, you need to add +2 to the equation.

There are 24,024 different ways to choose a President, Vice President, Treasurer, and Secretary from a group of 14 students.

Permutation is the arrangement of objects in a specific order. It is the number of different ways in which a set of objects can be arranged in a specific order. The formula to calculate permutation is:

[tex]P(n, r) = n! / (n - r)![/tex]

Permutations are commonly used in mathematics, science, and engineering, and are useful for solving problems that involve counting the number of possible arrangements of objects or events.

We can use the formula for permutations to find the number of ways to choose the four officers from a group of 14 students.

The number of permutations of n objects taken r at a time is given by:

[tex]^nP_r = n! / (n - r)![/tex]

where n! denotes n factorial, which is the product of all positive integers up to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

In this case, we want to choose 4 students from a group of 14, and the order in which they are chosen matters (since we are electing them to specific positions). So we have:

n = 14

r = 4

The number of ways to choose the four officers is therefore:

[tex]^1^4P_4 = 14! / (14 - 4)! = 14 \times 13 \times 12 \times 11 = 24,024[/tex]

Therefore, there are 24,024 different ways to choose a President, Vice President, Treasurer, and Secretary from a group of 14 students.

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Answer:

slope=5/4 y intercept=-3/4

Step-by-step explanation:

put it into slope intercept form y=5/4x-3/4

pull out 5/4 as slope and -3/4 as y intercept

The equation of straight line having

(a) gradient -4 and coordinates (-2,1) is  4x + y [tex]=[/tex] -7

(b) gradient 0 and coordinates (-1,21) is y = 21 .

In the question ,

the gradient and coordinates of the point on the line is given .

we have to find the equation of the straight line .

Part(a)

the gradient of the line [tex]=[/tex] -4 ,

the coordinates of a point on the line = (-2,1)

So , the equation of the line is

(y - 1) = (-4)*(x -(-2))

y - 1 = -4(x + 2)

y - 1 = -4x - 8

4x + y = -8 + 1

4x + y = -7

the equation is 4x + y = -7  .

Part(b)

the gradient of the line = 0 ,

the coordinates of a point on the line = (-1 , 21)

So , the equation of the line is

(y - 21) = 0(x-(-1))

y - 21 = 0

y = 21

the equation of the line is y = 21  .

Therefore , The equation of straight line having  (a) gradient -4 and coordinates (-2,1) is 4x + y [tex]=[/tex] -7  and (b) gradient 0 and coordinates (-1,21) is  y = 21  .

The given question is incomplete , the complete question is

Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.

(a) -4, (-2 , 1)

(b) 0, (-1, 21)

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Answer:

150/512 < 64/125

Step-by-step explanation:

5/8 * 6/8 * 5/8 = 150/512 = 0.295

4/5 *4/5 * 4/5 = 64/125 = 0.512

Therefore: 0.295 < 0.512 or 150/512 < 64/125

Answer:

5/8 - 1/4 = 3/8

Step-by-step explanation:

1 x 2 = 2, 4 x 2 = 8, so we're left with 2/8

Answer:

3/8

Step-by-step explanation:

5/8 - 1/4

to be able to compare fractions or add/subtract them directly, we need to bring them all to the same denominator (the bottom part of the fractions).

it is usually easier to bring the smaller to a larger number than the other way around, because of the existing numerators (the top part of a fraction).

since we are dealing with fractions (divisions !), the best way to manipulate them is by multiplying or dividing them by a factor.

so, what do we need to multiply with 4 to get 8 (the other denominator) ?

2, as 4×2 = 8.

aha.

but now careful, we cannot just multiply the denominator by 2. that would change the value of the whole original fraction.

we have to multiply denominator AND numerator by the same factor. that way the original value of the fraction remains the same, because we are essentially multiplying the whole fraction just by 1.

so,

1/4 × 2/2 = 2/8

and now we can easily use it in a calculation with other 8ths :

5/8 - 2/8 = 3/8

The points (2, 3)  (6, 3), and  (2, 7) sides corresponds to length of 4 : 4 : 5 and do not form Pythagorean triple hence they do not form a right angle

The distance between the points is calculated and Pythagoras theorem is used to determine if the triple  forms a right angle

let the points be

A (2, 3)  B (6, 3), and  C (2, 7)

using the equation

d = √{(x₁ - x₂)² + (y₁ - y₂)²}

AB = √{(2 - 6)² + (3 - 3)²} = 4

BC = √{(6 - 2)² + (3 - 7)²} = 5

CA = √{(2 - 2)² + (3 - 7)²} = 4

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the company uses 37 screws to make each table and 14 screws to make each chair. The company needs to order screws for 12 tables and 48

Step-by-step explanation:

3 units right = x + 3

12 units down = y - 12

E = (-5, 4) -> E' (-2, -8)

F = (-5, 9) -> F' (-2, -3)

G = (1, 9) -> G' (4, -3)

H = (1, 4) -> G' (4, -8)

Answer:

x=6

Step-by-step explanation:

-2x-6=-18

     +6. +6

-2x=-12

/-2. /-2

x=6

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If the matrix C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex], then the determinant of the matrix |C| = -12

The given matrix is

C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex]

The matrix is defined as the set of numbers that arranged in rows and columns to form a rectangular array. The numbers in the matrix are called the elements of the matrix.

Here we have to find the determinant of the matrix C

The determinant of the matrix is defined as the scalar value calculated for a given square matrix.

The determinant of C is represented by |C|

Then,

C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex]

|C| = -6×4 - 6×-2

= -24 -(-12)

= -24 + 12

= -12

Hence, if the matrix C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex], then the determinant of the matrix |C| = -12

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Answer:

4x

Step-by-step explanation:

the quotient of x and 2 is [tex]\frac{x}{2}[/tex] , then

8 × [tex]\frac{x}{2}[/tex] ( cancel 8 and 2 by 2 )

= 4 × x

= 4x

Using the simplification, the solution of the given expression for x is 107.5.

In the given question we have to solve the given expression.

The given expression is x-12.5=95.

Now solving the expression.

x-12.5=95

To solve the expression we add 12.5 on both side

x-12.5+12.5=95+12.5

x=107.5

The solution of the given expression for x is 107.5.

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297 children like at most one kind of ice cream.

Total number of children = 397

Let C and P be the number of children like chocolate and pistachio ice cream respectively.

n(C) = 175

n(P) = 225

The number of student do not like chocolate or pistachio ice cream is,

n(P' and C') = 97

n(P or C)' = 97, by De Moivre's theorem

n(P or C) = 397-97 = 300

n(P) + n(C) - n(P and C) = 300

175 + 225 - n(P and C) = 300

400 - n(P and C) = 300

n(P and C) = 100

So the required number of children like at most one kind of ice cream = 397-n(P and C) = 397-100 = 297

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Answer:

5

Step-by-step explanation:

divide.

From the given table which represents the two system of linear function is given by y = -4x +10 and y = -3x +2 , the solution of the system of linear function is (x, y) = (8 , -22).

As given in the question,

Table which represents the system of linear function are as follow:

table 1:

x:      -4       -2        0       2

y:     26       18       10     2

table 2:

x:      -4       -2        0       2

y:     14       8         2      -4

For table1 :

System of linear function:

(x₁ , y₁) = (0,10)

(x₂ , y₂) = (2, 2)

Equation of linear function:

(y -y₁)/ (x-x₁) =(y₂ -y₁)/(x₂ -x₁)

⇒(y -10)/ (x-0) =(2-10)/(2-0)

⇒y-10 =-4(x)

⇒ y = -4x +10     __(1)

For table2 :

System of linear function:

(x₁ , y₁) = (0,2)

(x₂ , y₂) = (2, -4)

Equation of linear function:

(y -y₁)/ (x-x₁) =(y₂ -y₁)/(x₂ -x₁)

⇒(y -2)/ (x-0) =(-4-2)/(2-0)

⇒y-2 =-3(x)

⇒ y = -3x +2     __(2)

Solve system of linear function (1) and (2) we get,

-4x +10 = -3x +2

⇒4x -3x =10 -2

⇒x =8

⇒y = -4(8) +10

     = -22

(x, y) = (8 ,-22)

Therefore, from the given table which represents the two system of linear function is given by y = -4x +10 and y = -3x +2 , the solution of the system of linear function is (x, y) = (8 , -22).

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Answer:

D

Step-by-step explanation:

trust

Answer:

33

Step-by-step explanation:

evaluate f(- 3) by substituting x = - 3 into f(x)

f(- 3) = 3(- 3)² - (- 3) + 5 = 3(9) + 9 + 5 = 27 + 14 = 41

evaluate f(4) by substituting x = 4 into f(x)

f(4) = 3(4)² - 4 + 5 = 3(16) + 1 = 48 + 1 = 49

Then

2f(- 3) - f(4) = 2(41) - 49 = 82 - 49 = 33