27. Households consume much more electricity when the weather is warmer. Temperate and electricity is related as stated below. Round answers to the nearest hundredth. Questions: Temperature °F Electricity (KWH) 56 30.8 63 35.4 67 37.7 b) Determine the strength of the correlation coefficient, r. c) Determine the direction of the correlation coefficient, r. 76 a) Find the correlation coefficient round to four decimal places. d) Write the equation that best represents the data. 41.1 79 43.1 e) If the temperature was 90°F, what is the predicted electricity usage? 82 44.8 f) If a household uses 38 KwH of energy, what would be the temperature outside be?​

Answer:

Step-by-step explanation:

If she offers to 9, but 2 reject, that means she paid for 7 friends.

If each friend costs $4, multiply 4 by 7.

The answer is $28

Hope this helps! (:

Step-by-step explanation:

\( f(x) = - 3 {x}^{2} + 9x - 2\)

A) f(-2) + f(1) = -32 + 4 = -28

B) f(-2) - f(1) = -32 - 4 = -36

The correct option is a b c d.

fd = 2,809

We need to round the given answers to the nearest hundredth.

a. 150, 150, fd = 2,809

Now, we need to find 150 such that it is the same percentage as 2,809 of 150.

150 * (2,809/100) = 4.2135 ≈ 4.21

So, 150, 150, fd = 2,809 ≈ 4.21, 4.21, fd ≈ 100

b. 150, 150, fd = 2,809

Now, we need to find 150 such that it is the same percentage as 2,809 of 150.

150 * (2,809/100) = 4.2135 ≈ 4.21

So, 150, 150, fd = 2,809 ≈ 4.21, 4.21, fd ≈ 100

c. 150, 150, fd = 53

Now, we need to find 150 such that it is the same percentage as 53 of 150.

150 * (53/100) = 79.5 ≈ 79.5

So, 150, 150, fd = 53 ≈ 79.5, 79.5, fd ≈ 100

d. 150, 150, fd = 53

Now, we need to find 150 such that it is the same percentage as 53 of 150.

150 * (53/100) = 79.5 ≈ 79.5

So, 150, 150, fd = 53 ≈ 79.5, 79.5, fd ≈ 100

Therefore, the correct option is a b c d.

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Based on the fact that x has to be between 3 and 9, the value of x in interval notation is (4, 8).

The value of x in interval notation should include the two numbers. The first should be the lowers possible value of x and the second should be the highest possible value.

x has to be greater than 3 so it's lowest possible value is 4.

x has to be less than 9 so its greatest possible value is 8.

The interval notation is:

= (4, 8)

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Answer:

15

Step-by-step explanation:

The rational exponent form is 5^3/5x. Option D

We know that a rational function would be the function that does not have the radical sign in it. We can see that we have the expression that have been written for us here as; 5√125x^5.

When we open up the radical we would have;

125^1/5 * 5^5/5

But we know that;

125 = 5^3

We now have;

5^3/5 * x

This becomes;

5^3/5x

Thus we are going to end up in the rational exponent form of the expression as 5^3/5x.

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Answer:

6x^2-4xdot+5x-2dot+3

Step-by-step explanation:

correct me if im wrong i dont do this work yet

This matrix has a pivot in every column, so the set of polynomials {p1, p2, p3} is linearly independent.

There are no scalars c1, c2, c3 (not all zero) that satisfy the equation c1p1(x) + c2p2(x) + c3p3(x) = 0 for all x.

To test the linear independence of the set of polynomials, we can make each coordinate vector a column of the matrix and perform row operations to transform the matrix to row-echelon form.

If the resulting matrix has a pivot in every column, then the set of polynomials is linearly independent.

If there is a column without a pivot, then the set of polynomials is linearly dependent.

To demonstrate, let's consider the set of polynomials {p1, p2, p3}.

where:

p1(x) = x2 - 3x + 2p2(x)

= -x2 + 2xp3(x)

= 3x2 - 4x - 1

We will create a matrix with the coordinate vectors of each polynomial as columns:

\($$\begin{pmatrix}1 & -1 & 3\\-3 & 2 & -4\\2 & 0 & -1\end{pmatrix}$$\)

Now, we will perform row operations to transform the matrix to row-echelon form:

\($$\begin{pmatrix}1 & -1 & 3\\0 & -1 & 5\\0 & 0 & 1\end{pmatrix}$$\).

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Step-by-step explanation:

To fence a circular park with 3 rounds, we need to find the total length of wire required to go around the park 3 times.

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, π is the constant pi, and d is the diameter.

Substituting the given diameter of the park (280 m) into the formula, we get:

C = π * 280 m

≈ 879.65 m

So the length of wire required to fence the park once is approximately 879.65 m.

To fence the park three times, we need to multiply this length by 3:

3 rounds of wire = 3 * 879.65 m

= 2638.95 m

Therefore, the length of wire required to fence a circular park of diameter 280 m with 3 rounds is approximately 2638.95 m.

Answer:

1239 it is 1239 I think I have same test

Answer: \(\huge\boxed{\ x^2+3x-40}\)

My step-by-step explanation:

1. First thing we do is: Distribute

(x+8)(x−5)x

(x−5)+8(x−5)

2. Second thing:Distribute

x(x−5)+8(x−5)

x^2−5x+8(x−5)

3.Third thing: Distribute

x^2−5x+8(x−5)

x^2−5x+8x−40

4. Fourth thing: Combine like terms

x^2−5x+8x−40

x^2+3x−40

5.And finnaly we find: The solution

x^2+3x−40

Good Luck!

From the question, the sum of each of the geometric sequence are;

1)  31 3/4

2) 340

3) 11/16

4) -6, 12, -24

We have that;

Sn = a(1 -\(r^n\))/1 - r

Sn = 16(1 \(- (1/2)^7\))1 - 1/2

Sn = 16(1 - 1/128)/1/2

Sn = 16(127/128) * 2

Sn = 31 3/4

2) Un = a\(r^n\) -1

256 = \(4(4)^n-1\)

64 =\(4^n-1\)

\(4^3 = 4^n-1\)

n = 4

Sn= \(4(4^4 - 1)\)/4 - 1

Sn = 340

3) Since we have a5 then n = 5

Sn = 1(1 - (\(-1/2)^5\))/1 -(-1/2)

Sn = 33/32 * 2/3

= 11/16

4) 30= a(1 -\((-2)^4\))/1 - (-2)

30 = a(-15)/3

30 = -5a

a = 30/-5

a = -6

Then the first three terms are;

-6, 12, -24

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Answer:

(5x+4)(x-3)

Step-by-step explanation:

Answer:

(x - 3)(5x + 4)

Step-by-step explanation:

5x² - 11x - 12

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 5 × - 12 = - 60 and sum = - 11

the factors are - 15 and + 4

use these factors to split the x- term

5x² - 15x + 4x - 12 ( factor first/second and third/fourth terms )

= 5x(x - 3) + 4(x - 3) ← factor out (x - 3) from each term

= (x - 3)(5x + 4)

The correlation coefficient goes from -1 to 1 and measures the degree and direction of a linear link between two variables. A correlation value of 1 or -1 shows a perfect positive or negative correlation, where all data points lie on a straight line. Zero means that there is no linear association between the variables. So, it is accurate.

The correlation coefficient quantifies the magnitude and direction of a linear link between two variables. When there is a perfect positive correlation between two variables, it means that as one variable increases, the other variable similarly increases in a linear fashion.

This causes every data point to lie precisely on a straight line with a positive slope. When two variables have a perfect negative correlation, it indicates that when one variable increases, the other variable drops in a straight-line connection, resulting in all the data points resting exactly on a straight line with a negative slope.

The correlation coefficient spans from -1 to 1 to represent the linear relationship between variables, where 1 or -1 represent a perfect correlation and 0 shows no linear correlation.

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The answer is: 2(5a + 3)

hope this helps :)

Answer:

B. 2(5a + 3)

Step-by-step explanation:

Using the distributive property, we know that we can distribute to polynomial within parenthesis. So, following this, we can multiple 2*5a and 2*3. This gives us the expression, 10a+6. Showing that these two expressions are equivalent.

Additionally, the expression 2(5a+3) is an example of factoring. The GCF, 2, was factored out of the original expression 10a+6. Since 2(5a+3) is a factored form of 10a+6, they must be equivalent.

The parabola y = -16x^2 + 32x opens downward and the y value of the vertex is 16

The equation of the function is given as:

y = -16x^2 + 32x

Factor out -16

y = -16(x^2 - 2x)

In the above equation, the factor -16 is negative,

This means that the parabola opens downward

We have:

y = -16(x^2 - 2x)

Set to 0

-16(x^2 - 2x) = 0

Divide by -16

x^2 - 2x = 0

Factor out x

x(x - 2) = 0

Split

x = 0 or x - 2 = 0

Solve for x

x = 0 or x = 2

Hence, the roots are 0 and 2, and the x-intercepts are (0,0) and (2,0)

We have:

y = -16x^2 + 32x

Differentiate

y' = -32x + 32

Set to 0

-32x + 32= 0

Divide through by -32

x - 1 = 0

Add 1 to both sides

x = 1

Hence, the x value of the vertex is 1

In (c), we have:

x = 1

Substitute x = 1 in y = -16x^2 + 32x

y = -16(1)^2 + 32(1)

Evaluate

y = 16

Hence, the y value of the vertex is 16

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ANSWER: dA/dt=0.17A A(0)=950

The correct differential equation and initial condition for the continuous compounding of a sum of 950$ at 17% interest are given by dA/dt = 0.17A and A(0) = 950. This represents the rate of change of the amount A(t) with respect to time and the initial investment value, respectively.

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Answer:

1/3

Step-by-step explanation:

The given two-way Frequency table, there are 33 left-handed students who are not in the music program.

The number of left-handed students who are not in the music program, we need to examine the data presented in the two-way frequency table.

From the table, we can see that the number of left-handed students in the music program is 15, and the total number of left-handed students is 48.

the number of left-handed students not in the music program, we subtract the number of left-handed students in the music program from the total number of left-handed students.

Number of left-handed students not in the music program = Total number of left-handed students - Number of left-handed students in the music program

Number of left-handed students not in the music program = 48 - 15

Calculating this, we find that the number of left-handed students not in the music program is 33.

Therefore, there are 33 left-handed students who are not in the music program, based on the data provided in the two-way frequency table.

In conclusion, based on the given two-way frequency table, there are 33 left-handed students who are not in the music program.

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The coordinates as required to be written are as follows;

It follows from the task content that the coordinates of the points as described are to be determined.

It is important to note that a point which lies on the y-axis would have an x-coordinate of 0 while a point which lies on the x-axis would have a y-coordinate of 0.

Consequently since the right corresponds to positive x and upward corresponds to positive y;

i). Above the x-axis, lying on y-axis at a distance of 3 units corresponds to; (0, 3).

(ii) Below the x-axis, lying on y-axis at a distance of 8 units corresponds to; (0, -8)

(iii) Right of the origin and on the x-axis at a distance of 2 units. corresponds to; (2,0).

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Mr. Titus travels a total of 7476 miles annually between Charlotte, North Carolina, and New York City.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that twelve times a year, Mr. Titus makes the trip from Charlotte to New York City and back. Each round trip covers a total distance of 623 miles.

The total distance will be calculated as:-

Distance = 12 x 623

Distance = 7476 miles

Therefore, Mr. Titus' annual mileage between Charlotte, North Carolina, and New York City is 7476 miles.

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Using rates and ratio concept, Martine received €175.44 after converting 200 Swiss francs (CHF)

A rate is a ratio that compares two different quantities which have different units. The unit rate is different from that of a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity. In other words, we can say that the second quantity in the comparison is always 1.

To calculate the amount Martine received, we have to use the rate given in the question.

€1 = 1.14 CHF

x € = 200

Cross multiply both sides and solve for x

1 * 200 = 1.14 * x

200 = 1.14x

Divide both sides by the coefficient of x

200 / 1.14 = 1.14x / 1.14

x = 175.44

Martine received €175.44

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The major milestones in mathematics from Euclid to Euler are shown below.

Here are some major milestones in mathematics from Euclid to Euler:

1. Euclid (circa 300 BCE):

Euclid's Elements: Euclid wrote a comprehensive mathematical treatise called "Elements.

2. Archimedes (circa 287 BCE - 212 BCE):

Archimedes' Principle: He formulated the principle of buoyancy, known as Archimedes' Principle, which states that an object submerged in a fluid experiences an upward force equal to the weight of the displaced fluid.

3. Leonardo Fibonacci (1170 - 1250):

Fibonacci Numbers: Fibonacci introduced the concept of Fibonacci numbers, a sequence in which each number is the sum of the two preceding ones (e.g., 0, 1, 1, 2, 3, 5, 8, ...).

4. René Descartes (1596 - 1650):

Cartesian Coordinate System: Descartes developed the Cartesian coordinate system, which allows for the representation of geometric figures and algebraic equations using a set of axes.

5. Isaac Newton (1642 - 1727) and Gottfried Wilhelm Leibniz (1646 - 1716):

Calculus: Newton and Leibniz independently developed calculus, a branch of mathematics that deals with rates of change and the calculation of areas and volumes.

6. Leonhard Euler (1707 - 1783):

Euler's Formula: Euler made numerous contributions to mathematics, including the development of graph theory and the discovery of many important mathematical relationships. One of his notable achievements is Euler's formula, which relates the number of vertices, edges, and faces of a polyhedron.

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Answer:

A) -1.7 x 10^-4 D)-0.00017

Step-by-step explanation:

Since its negative in the base B and C wont work. The negative in the exponent means the decimal moves left which exclude E.

Answer:

A) -1.7 x 10^-4 D)-0.00017

Step-by-step explanation:

Since its negative in the base B and C wont work. The negative in the exponent means the decimal moves left which exclude E.

Step-by-step explanation:

Answer:

24v+8

Step-by-step explanation:

Calculations

Answer:

24v+8

Step-by-step explanation:

-8(-1 - 3v)

-8(-3v -1)

distribute

24v+8

Step-by-step explanation:

At the bottom, there is a hint to solve (-9) x (-9)

Negative times negative is positive

Meaning that -1 x -1 would equal to 1

-9 x -9 = ?

Isolate the negatives

(- -)(9x9)

Open parenthesis

You can answer the rest on your own.

Hope this helps :)

Have a great day!

\( {\qquad\qquad\huge\underline{{\sf Answer}}} \)

Here's the explanation ~

Zeros or roots of a function is the value of independent variable (usually x - coordinate or absicca) where the value of dependent variable (y - coordinate or ordinate) is 0.

That is :

The point where it cuts the x - axis, it has an x - coordinate = -6

Therefore, we can conclude that The zero of given function is -6

Answer:

x = -6.

Step-by-step explanation:

It is where the graph cuts the x-axis  (where the function is zero).

That is -6.