What is the direction and magnitude of the following correlation coefficients

a. -0.81
b. 0.40
c. 0.15
d. -0.08
e. 0.29

This count is a discrete random variable (option A).

A discrete random variable is a variable that contains integers that can only be a limited number of possible values.  A discrete random variable is can contain only a finite set of numbers .

An example of discrete random variable is the number of students in the first period class. It is impossible for the number of students in the class to go on indefinitely.

Discrete random variable has the following properties:

A continous random variable is a variable that has an infinite number.

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Using a system of equations, it is found that Allison bought 2 bottles of juice and 9 bottles of soda.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are:

Allison purchased a total of 11 bottles of juice, hence:

x + y = 11 -> x = 11 - y.

These 11 bottles contain 445 grams of sugar, hence, considering the amounts of each bottle, we have that:

20x + 45y = 445

Since x = 11 - y:

20(11 - y) + 45y = 445

25y = 225

y = 225/25

y = 9.

x = 11 - y = 11 - 9 = 2.

She bought 2 bottles of juice and 9 bottles of soda.

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By using an online graphing calculator, the overall equation represented by this scenario is plotted in the image attached below.

Based on the information provided about this company with respect to its delivery and total number of miles to be covered, we would assign variables as follows:

Next, we would translate the word problem into an algebraic equation by using an inequality:

y > x/2 - 3

Also, we would determine the intercepts as follows:

When x = 0, we have;

y = 0/2 - 3

y = -3.

y-intercept = (0, -3).

For the x-intercept, we have:

When y = 0, we have;

0 = x/2 - 3

x/2 = 3

x = 6.

x-intercept = (6, 0).

By using an online graphing calculator, the overall equation represented by this scenario is plotted in the image attached below.

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Answer:

c

Step-by-step explanation:

c is the answer

[tex]\textbf{Answer:\ \ \large\boxed{\frac{12}{25} }\ or\ 0.4800}[/tex]

Step-by-step explanation:

[tex]\large\boxed{13\ green\ marbles\ and\ 13\ white\ marbles}[/tex]

After a white marble is chosen:

[tex]\large\boxed{13\ green\ marbles\ and\ 12\ white\ marbles}[/tex]

Now there are 25 (13 + 12) total marbles.

Without replacing the white marble we chose already, what is the probability of choosing another white marble?

Well, now there are 12 white marbles to choose from, out of a total of 25 marbles. This means our probability is:

[tex]\large\boxed{\frac{12}{25} }[/tex]

This in decimal form is:

0.4800

The gallons of the first brand of antifreeze should be 60 gallons.

The gallons of the second brand of antifreeze should be 90 gallons.

0.2f + 0.45s = 52.50 (0.35 x 150) equation 1

f + s = 150  equation 2

Where:

how many gallons of each brand of antifreeze must be used?

Multiply equation 2 by 0.2

0.2f + 0.2s = 30 equation 3

Subtract equation 3 from equation 2

0.25s = 22.50

s = 22.50 / 0.25

s = 90

f = 150 - 90 = 60 gallons

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The coefficient of 2(3)(6)Q is 2(3)(6)

The expression is given as:

2(3)(6)Q

For an expression

AQ

Where A is a number or product of numbers and Q is a variable

The number A represents the coefficient

By comparing:

AQ and 2(3)(6)Q

We have

A = 2(3)(6)

Hence, the coefficient of 2(3)(6)Q is 2(3)(6)

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Answer: d

Step-by-step explanation:

The graph is increasing, so the base must be more than 1.

Also, the y-intercept is 2.

This leaves d.

The values of h and r to maximize the volume are r = 4 and h = 2

From the question, we have the following equation

2r + 2h = 12

Divide through by 2

r + h = 6

Subtract r from both sides of the equation

h = 6 - r

Hence, the formula for h in terms of r is h = 6 - r

The volume of a cylinder is

V = πr²h

Substitute h = 6 - r in the above equation

V = πr²(6 - r)

Hence, the function V(r) is V = πr²(6 - r)

V = πr²(6 - r)

Expand

V = 6πr² - πr³

Integrate

V' = 12πr - 3πr²

Set to 0

12πr - 3πr² = 0

Divide through by 3π

4r - r² = 0

Factor out r

r(4 - r) = 0

Divide through by 4

4 - r = 0

Solve for r

r = 4

Hence, the single critical point on the interval [0. 6] is r = 4

We have:

V = πr²(6 - r)

and

V' = 12πr - 3πr²

Determine the second derivative

V'' = 12π - 6πr

Set r = 4

V'' = 12π - 6π* 4

Evaluate the product

V'' = 12π - 24π

Evaluate the difference

V'' = -12π

Because V'' is negative, then the single critical point is a global maximum

We have

r = 4  and h = 6 - r

Substitute r = 4  in h = 6 - r

h = 6 - 4

Evaluate

h = 2

Hence, the values of h and r to maximize the volume are r = 4 and h = 2

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A quadrilateral PQRS is a parallelogram. PQ and RS are opposite sides then the answer of this particular question is , x = 4, the parallelogram PQRS is a rhombus, QR = 31, The opposite angles are congruent. Thus, more than one answer is correct.

According to the question,

PQ = 7x+12; RS = 5x -20 and QR = 31

Solving PQ and RS we get x = 4. Thus, PQ = 40 and RS = 40.

A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and congruent.  A quadrilateral that has all sides equal and opposite sides parallel is called Rhombus.

Thus, the parallelogram PQRS is a rhombus.

Hence,  a quadrilateral PQRS is a parallelogram. PQ and RS are opposite sides then the answer of this particular question is , x = 4, the parallelogram PQRS is a rhombus, QR = 31, The opposite angles are congruent. Thus, more than one answer is correct.

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:x + 4x + 12 + x=180°[/tex]

( Angle EBA= Angle DBC, and the three angles sum upto 180° due to linear pair property )

[tex]\qquad❖ \: \sf \:6x + 12 = 180[/tex]

[tex]\qquad❖ \: \sf \:6x = 180 - 12[/tex]

[tex]\qquad❖ \: \sf \:6x = 168[/tex]

[tex]\qquad❖ \: \sf \:x = 28 \degree[/tex]

Next,

[tex]\qquad❖ \: \sf \: \angle C + \angle D + x = 180°[/tex]

[tex]\qquad❖ \: \sf \: \angle C +3x + 5 + x = 180°[/tex]

[tex]\qquad❖ \: \sf \: \angle C +4x = 180 - 5[/tex]

[tex]\qquad❖ \: \sf \: \angle C +4(28) = 175[/tex]

( x = 28° )

[tex]\qquad❖ \: \sf \: \angle C +112 = 175[/tex]

[tex]\qquad❖ \: \sf \: \angle C = 175 - 112[/tex]

[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]

Answer:

  y = x +5

Step-by-step explanation:

The equation of a parallel line will have the same x- and y-coefficients, but a different constant. You need to find the constant that makes the line go through the given point.

The given line is y = x +1. The equation you're looking for is

  y = x +c . . . . . . for some new constant c

We want this equation to be true for (x, y) = (-2, 3). Putting these values into the equation, we can solve for c.

  3 = -2 +c

  5 = c . . . . . . add 2

The desired equation is y = x +5.

Jet 1 moves with a speed of  672 mi/h, while jet 2 moves with a speed of  672 mi/h + 80mi = 752 mi/h.

Let's say that the rate (or speed) of the slower jet is R, then the rate of the faster jet is:

R + 80mi/h

Now, if we step on any of the two jets (such that we view it as if it doesn't move) the other jet will move with a speed equal to:

S = R + R + 80mi/h

We know that after 8 hours, the to jets are 11,392 mi apart, then we know that:

(R + R + 80mi/h)*8h = 11,392 mi

Now we can solve that for R:

2*R + 80mi/h = 11,392 mi/8h = 1,424 mi/h

R = 1,424 mi/h - 80mi/h)/2 = 672 mi/h

So Jet 1 moves with a speed of  672 mi/h, while jet 2 moves with a speed of  672 mi/h + 80mi = 752 mi/h.

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Answer:

39916800

Step-by-step explanation:

1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10 × 11

Answer:

S = √( 1009)

Step-by-step explanation:

S = √( h² + 1/2)²)

S = √(28² + 15²)

S = √( 1009)

Hope this helps u!

The given geometric sequence has the common ratio, r = -2/3, and the value of the 4th term, a₄ = -8/3.

A geometric sequence is a special series where every term is the product of the previous term and a common ratio.

The first term of a geometric sequence is represented as a, the common ratio as r, and the n-th term as aₙ, which is calculated as, aₙ = a.rⁿ⁻¹.

In the question, we are asked to find the common ratio and the 4th term of the geometric sequence, 9, -6, 4, ........

The first term of the sequence, a = 9.

The second term of the sequence, a₂ = -6.

By the formula of the n-th term, aₙ = a.rⁿ⁻¹, we can show that:

a₂ = a.r²⁻¹.

Substituting the values, we get:

-6 = 9(r²⁻¹),

or, r²⁻¹ = -6/9,

or, r = -2/3.

Thus, the common ratio of the given geometric sequence is -2/3.

The 4th term can be calculated using the formula of the n-th term, aₙ = a.rⁿ⁻¹ as:

a₄ = a.r⁴⁻¹ = a.r³.

Substituting the values, we get:

a₄ = 9(-2/3)³,

or, a₄ = 9.(-8/27),

or, a₄ = -8/3.

Thus, the 4th term of the given geometric sequence is -8/3.

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Answer:

Step-by-step explanation:

You want to begin by making each fraction have  the same common denominator. The LCF (least common factor) is 77. So, knowing this, we can now multiply the fractions that need to have a denominator of 77.

1. 5/7*11/11=55/77

2. 9/11 * 7/7 =63/77

Now we can add

55/77 + 63/77 + 21/77 = 139/77 or 1.805194805

Trigonometry functions are functions that relate two sides of a given triangle with one of its included angles.

The expression that shows the distance that he walked = x + y + 100

                                                                 = 87 + 50 + 100

                                                                 = 237 yards

Trigonometry functions are functions that relate two sides of a given triangle with one of its included angles. The required function may be a sine function, a cosine function, or a tangent function.

Such that;

The given question can be solved by applying the appropriate trigonometric function.

So that to determine the value of x, we have:

Cos θ = [tex]\frac{Adjacent}{Hypotenuse}[/tex]

Cos 30 = [tex]\frac{x}{100}[/tex]

⇒ x = 100 cos 30

      = 100 x 0.866

x = 86.60

Thus, the start of the sidewalk is approximately 87 yards.

To determine the value of sidewalk y, we have:

Sin θ = [tex]\frac{Opposite}{Hypotenuse}[/tex]

Sin 30 = [tex]\frac{y}{100}[/tex]

⇒ y = 100 x Sin 30

      = 100 x 0.5

   y = 50

Thus the sidewalk which represents the end of the path is 50 yards.

Therefore, the total distance that he walked = 100 + 87 + 50

                                                                 = 237 yards

The expression that shows the distance that he walked = x + y + 100

                                                                 = 87 + 50 + 100

                                                                 = 237 yards

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The number of loaves of bread can the baker make with a 10 lb-bag of flour is 20 loaves of bread.

Ratio of flour to loaves of bread = 3 cups : 2 loaves

Number of loaves of bread can the baker make with a 10 lb-bag of flour

3 : 2 = 30 : x

3/2 = 30/x

3 × x = 2 × 30

3x = 60

x = 60/3

x = 20 loaves of bread

Therefore, the number of loaves of bread can the baker make with a 10 lb-bag of flour is 20 loaves of bread.

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Answer:

$78.60

Step-by-step explanation:

0.14x + 31 = 0.14*340 + 31 = 78.6

Answer:

2

Step-by-step explanation:

If he sells and makes x paintings, his expenses will he 10+45x and his revenue will be 50x.

The break-even point is the point at which total cost and total income are equal. For breakeven, Lamar needs to sell 2 paintings.

In economics, business, and especially cost accounting, the break-even point is the point at which total cost and total income are equal, i.e. "even."

Let the number of paintings that Lamar makes and sells at the break-even point be represented by x.

Given that Lamar bought some brushes for $10, and paint and canvas for each painting cost $45. Therefore, the total cost of making x number of paintings is,

Total cost of x painting = $10 + $45(x)

Also, the selling price of each painting is $50. Therefore, the revenue generated from x paintings is,

Revenue generated = $50(x)

Further, at the breakeven point, the total cost of production of any product is equal to the revenue generated by the product. Therefore, we can write,

Total cost of x painting = Revenue generated

$10 + $45(x) = $50(x)

10 + 45x = 50x

10 = 50x - 45x

10 = 5x

x = 10/5

x = 2

Hence, For breakeven Lamar needs to sell 2 paintings.

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Assuming you mean

[tex]\displaystyle \sum_{i=0}^n {}_nC_{i}[/tex]

where

[tex]{}_n C_i = \dbinom ni = \dfrac{n!}{i! (n-i)!}[/tex]

we have by the binomial theorem

[tex]\displaystyle (1 + 1)^n = \sum_{i=0}^n {}_nC_{i} \cdot 1^i \cdot 1^{n-i}[/tex]

so that the given sum has a value of [tex]\boxed{2^n}[/tex].

The answer is -7.

The coefficient is the part of the variable that does not change with respect to the variable.

Hence, in the monomial -7x²y⁴, the coefficient is -7.

(a) The half-life of the unknown radioactive element is 250.28 days.

(b) The time taken for a sample of 100 mg to decay to 81 mg is 76.1 days.

N(t) = N₀(0.5)^t/h

where;

in 340 days; N(340) = N₀(0.39);

1 - 0.61 = 0.39

N(340) = N₀(0.5)^340/h

N(340)/N₀ = 0.5^340/h

0.39 = 0.5^340/h

log(0.39) = 340/h x log(0.5)

log(0.39) /log(0.5) = 340/h

1.358 = 340/h

h = 340/1.358

h = 250.28 days

81 = 100(0.5)^t/250.28

81/100 = (0.5)^t/250.28

0.81 = (0.5)^t/250.28

log(0.81) = t/250.28 x log(0.5)

log(0.81) / log(0.5) = t/250.28

0.304 = t/250.28

0.304(250.28) = t

76.1 days = t

Thus, the half-life of the unknown radioactive element is 250.28 days and the time taken for a sample of 100 mg to decay to 81 mg is 76.1 days.

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Answer:

x = 4 and x = 6

Step-by-step explanation:

Considering the vertex of the quadratic equation, the maximum height that the object will reach is of 80 feet.

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

Considering the coefficient a, we have that:

In this problem, the equation is:

f(t) = -16t² + 64t + 16.

Hence the coefficients are:

a = -16, b = 64, c = 16.

The maximum value is found as follows:

[tex]y_v = -\frac{64^2 - 4(-16)(16)}{4(-16)} = 80[/tex]

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Check the picture below.

Answer:

See below

Step-by-step explanation:

Salary (y)       =    30 000   +  50 x        

y = 30 000 + 50x     where x is the number of sales

How many sales for 50 000 ?

50 000 = 30 000 + 50 x

20 000 = 50 x

x = 400 sales

I. Model Problems

A linear model is a linear equation that represents a real-world

scenario. You can write the equation for a linear model in the same way

you would write the slope-intercept equation of a line. The y-intercept

of a linear model is the quantity that does not depend on x. The slope is

the quantity that changes at a constant rate as x changes. The change

must be at a constant rate in order for the equation to be a linear model.

Example 1 A machine salesperson earns a base salary of $40,000 plus

a commission of $300 for every machine he sells. Write an equation

that shows the total amount of income the salesperson earns, if he sells

x machines in a year.

The y-intercept is $40,000; the salesperson earns a $40,000 salary in a

year and that amount does not depend on x.

The slope is $300 because the salesperson’s income increases by $300

for each machine he sells.

Answer: The linear model representing the salesperson’s total income

is y = $300x + $40,000.

Linear models can be used to solve problems.

Example 2 The linear model that shows the total income for the

salesperson in example 1 is y = 300x + 40,000. (a) What would be the

salesperson’s income if he sold 150 machines? (b) How many

machines would the salesperson need to sell to earn a $100,000

income?

(a) If the salesperson were to sell 150 machines, let x = 150 in the linear

model; 300(150) + 40,000 = 85,000.

Answer: His income would be $85,000.

(b) To find the number of machines he needs to sell to earn a $100,000

income, let y = 100,000 and solve for x:

The trigonometric identity cos x + cos y = 2 cos (x + y/2) cos (x - y/2), is derived using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

In the question, we are asked to derive the trigonometric identity, cos x + cos y = 2 cos (x + y/2) cos (x - y/2), using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

We are given the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

Substituting a = x + y/2 and b = x - y/2 in this, we get:

cos (x + y/2) cos (x - y/2) = 1/2[cos (x + y/2 + x - y/2) + cos (x + y/2 - x - y/2)],

or, cos (x + y/2) cos (x - y/2) = 1/2[ cos (2x/2) + cos (2y/2) ],

or, 2 cos (x + y/2) cos (x - y/2) = cos x + cos y, which on inter-changing the sides, gives us:

cos x + cos y = 2 cos (x + y/2) cos (x - y/2), which is the required trigonometric identity.

Thus, the trigonometric identity cos x + cos y = 2 cos (x + y/2) cos (x - y/2), is derived using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

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The provided question is incorrect. The correct question is:

"Use cos a cos b=1/2 [cos (a + b) + cos (a-b)]to derive cos x + cos y = 2 cos (x + y/2) cos (x - y/2) ."

Answer:

22.34021442

Step-by-step explanation:

22.34021442