y = 5-3x, Darw the graph of the function. Use the find the value of y when x=4, and when x = 5​

the expression equivalent to f(p+r) is 5p + 5r.

The expression equivalent to f(p+r), where f(x) = 5x, is 5p + 5r. To understand this, we substitute (p+r) into the function f(x):

f(p+r) = 5(p+r)

Next, we distribute the 5 to both p and r:

f(p+r) = 5p + 5r

This equivalent expression arises from the definition of f(x) = 5x, where the function multiplies any given input x by 5. In this case, we substitute (p+r) into the function, resulting in 5 multiplied by the sum of p and r. Consequently, the expression 5p + 5r represents the value obtained by applying the function f to the sum of p and r. It is important to note that the function f(x) = 5x implies a linear relationship, where the function scales the input by a factor of 5.

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To compare standard deviations in two data sets, you can consider the Visual Comparison, Ratio of Standard Deviations and Coefficient of Variation.

To compare standard deviations in two data sets, you can consider the following approaches:

Visual Comparison: Plotting the data sets on a graph, such as a histogram or a box plot, can provide a visual comparison of the spread of the data. If one data set has a wider distribution, it suggests a larger standard deviation.

Ratio of Standard Deviations: Calculate the ratio of the standard deviations of the two data sets. Divide the standard deviation of one data set by the standard deviation of the other. A ratio greater than 1 indicates that the standard deviation of the first data set is larger, while a ratio less than 1 indicates that the standard deviation of the second data set is larger.

Coefficient of Variation: The coefficient of variation (CV) is another measure to compare standard deviations. It is the ratio of the standard deviation to the mean of each data set. A higher CV suggests a larger relative variability in the data.

Statistical Tests: You can perform statistical tests, such as the F-test or Levene's test, to determine if the difference in standard deviations between two data sets is statistically significant. These tests provide formal comparisons of variances between groups.

It's important to note that comparing standard deviations alone may not provide a complete understanding of the differences between data sets. It is recommended to consider other measures and conduct a comprehensive analysis to gain a more accurate and meaningful comparison.

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Answer:

The value of the function f at t = 7, will be 11.

Step-by-step explanation:

What is a function?

A statement, principle, or policy that creates the link between two variables is known as a function.

The function is given as,

f = 2t – 3

Then the value of the function f at t = 7, will be

f = 2 x 7 – 3

f = 14 – 3

f = 11

Answer:

f = 11

Step-by-step explanation:

i got it right on khan academy lol

Answer:

See below.

Step-by-step explanation:

In all triangles, the three interior angles will add up to 180°. Therefore:

\((9x+6)+(5x)+(90)=180\)

Remember that the little square means a right angle.

Now, solve for x.

\(9x+6+5x+90=180\\14x+96=180\\14x=84\\x=6\)

Now, plug x back into the equations to find each angle:

1)

\(\angle ABC = \angle B = 9(6)+6=60\textdegree\)

2)

\(\angle BCA = \angle C = 90\textdegree\)

3)

\(\angle CAB = \angle A=5(6)=30\)

Answer:

1. angle ABC = 60

2. angle BCA = 90

3. angle CAB = 30

Step-by-step explanation:

Since we know the right angle =90 degrees, we just need to do simple algebra. (We also know the all three angles added together equals 180.)

5x+9x+6+90=180.

Now let's simplify. We can simplify by adding like terms:

14x+96=180

Now we just need to do simple algebra. First we'd subtract the 96 from both sides:

14x+96=180

      -96  -96

14x = 84

Now we just need to divide 14 from both sides to separate the 14 from the x.

\(\frac{14x}{14}\) = \(\frac{84}{14}\)

x = 6

Now that we know what x equals, we just need to fill it into the equations which shouldn't be too hard. :)

Extra hint: to check your answer just add all three angles together and if you get 180 your answer is correct. :)

HOPE THIS HELPS!! <3 :D

Answer:

10

Step-by-step explanation:

14+10=24-14=10

Answer: 10

Step-by-step explanation: 14 + 10 = 24 + (-14) = 10

Answer:

The coordinates are \(Y'(x,y) = (3, 8)\) and \(Z'(x,y) = (10, 13)\).

Step-by-step explanation:

First, we have to derive an expression for translation under the assumption that each point of XYZ experiments the same translation. Vectorially speaking, translation from X to X' is defined by:

\(X'(x,y) = X(x,y) + T(x,y)\) (1)

Where \(T(x,y)\) is the vector translation.

If we know that \(X(x,y) = (2,3)\) and \(X'(x,y) = (4,7)\), then the vector translation is:

\(T(x,y) = X'(x,y)-X(x,y)\)

\(T(x,y) = (4,7) - (2,3)\)

\(T(x,y) = (2, 4)\)

Then, we determine the coordinates for Y' and Z':

\(Y'(x,y) = Y(x,y) + T(x,y)\)

\(Y'(x,y) = (1,4) + (2,4)\)

\(Y'(x,y) = (3, 8)\)

\(Z'(x,y) = Z(x,y) + T(x,y)\)

\(Z'(x,y) =(8,9) + (2,4)\)

\(Z'(x,y) = (10, 13)\)

The coordinates are \(Y'(x,y) = (3, 8)\) and \(Z'(x,y) = (10, 13)\).

The point (3/5,4) would lie on the circle if it makes the equation of the circle to be true

Latansha's equation of the circle is wrong

The given parameters are:

Center = (a,b) = (0,-2)

Radius, r = 7

The equation of a circle is:

\((x - a)^2 + (y - b)^2 = 0\)

This gives

\((x - 0)^2 + (y + 2)^2 = 0\)

Rewrite as:

\(x^2 + (y + 2)^2 = 0\)

In Latanya's first step, we have:

\(x^2 + (y - 2)^2 = 0\)

By comparing her first step with x^2 + (y + 2)^2 = 0, we can see that her equation is wrong

Hence, Latansha's error is that she determine the equation of the circle, wrongly.

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The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.

Total number of fruits Amy has = 10

Number of Apples = 7

Number of Oranges = 3

First random pieces of fruits chosen:

Probability of choosing Apples = 6/9

Probability of choosing Oranges = 3/9

Second random pieces of fruits chosen:

Probability of choosing Apples = 6/8

= 3/4

Probability of choosing Oranges = 2/8

= 1/4

Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.

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Answer:

BDE

or

EDB

Step-by-step explanation:

Make the marked angle, D, your center point. Find the two other points of the angle, E and B. write them in order, forwards and backwards.

Answer: B is the correct answer -23.801505

Step-by-step explanation: A, C, & D all have two negatives and when you multiply 2 negatives, you get a positive. B has 3 negatives which will give you a negative answer.

The required unit of the measure of the mean is given in Dollars. Option A is correct.

Given that:

The distribution of prices for a certain car model is approximately normal with a mean of $21,800 and a standard deviation of $400. A random sample of 4 cars of the model will be selected.

The correct unit of measure for the mean of the sampling distribution of the price of the car is to be determined,

The mean of the values is the ratio of the total sum of values to the number of values.

Since the given data is of price in dollars so the measure of the mean will also be taken in Dollars because the mean is defined as the sum of all the values in a particular unit divided by the total number of different quantities.

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Answer:

The value is -10

Step-by-step explanation:

Answer:

Step-by-step explanation: 7 more workers

Pat's company used 7 more workers each day than Bob's company.

Division is breaking a number up into an equal number of parts.

Given that, The number of days, d, to build a house is given by d = 780 / w

where w is the number of workers used each day on site. Bob's company will take 60 days to build the house. Pat's company will take 39 days to build the house.

Rearranging the given equation to find the number of workers,

w = 780 / d

Number of workers in Bob's company = 780 / 60 = 13

Number of workers in Pat's company = 780 / 39 = 20

Therefore, number of workers in Pat's company is (20-13) = 7 more that Bob's company

Hence, Pat's company used 7 more workers each day than Bob's company.

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The expression that is an element of AxBxB is (1,2,3)

The given data is A= (a, b}, B = {1,2,3}

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. If both A and B are square matrices of the same order, then both AB and BA are defined.

\(& \ A \times B=\left\{\begin{array}{c}(a, 1),(a, 2),(a, 3),(b, 1) \\(b, 2),(b, 3)\end{array}\right. \\\)

\(& A \times B \times B=\left\{\begin{array}{l}(a, 1,1),(a, 1,2),(a, 1,3), \\(a, 2,1),(a, 2,2),(a, 2,3),\end{array}\right. \\& (a, 3,1),(a, 3,2),(a, 3,3) \\ & (b, 1,1),(b, 1,2),(b, 1,3) \\& \left.\begin{array}{l}(b, 2,1),(b, 2,2),(b, 2,3) \\(b, 3,1),(b, 2),(b, 3,3)\end{array}\right\} \\\)

\(& \therefore(b, 2,3) \in D \times B \times B \\\\& (a, a, 1) \notin A \times B \times B \\\\& \left(b, 2^2\right) \quad \forall A \times B \times B \\\\& (2,1,1) \notin A \times B \times B \\\\&=(b, 2,3) \in \cap \times B \times B \\&\end{aligned}\)

The union of two sets X and Y is equal to the set of elements that are present in set X, in set Y, or in both the sets X and Y.

The intersection of sets can be denoted using the symbol ‘∩’. As defined above, the intersection of two sets A and B is the set of all those elements which are common to both A and B. Symbolically, we can represent the intersection of A and B as A ∩ B.

Therefore, the expression that is an element of AxBxB is (1,2,3).

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Answer:

Yes, the lines on the graph at 3 and -3 a part  of the solution,

Step-by-step explanation:

The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.

Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.

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A polynomial function of degree n has at most n real zeros and at most n - 1 turning points.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

A polynomial function

Now,

Because of the Fundamental Theorem of Algebra states that a polynomial function of degree n has exactly n complex roots (or zeros), some of which may be repeated or non-real. The number of real roots is equal to or less than the number of complex roots.

A turning point is a point where the graph of the polynomial function changes direction from increasing to decreasing or vice versa. The number of turning points is equal to or less than one less than the degree of the polynomial function. This is because each turning point corresponds to a change in the sign of the first derivative of the function, and the first derivative is a polynomial function of degree n - 1.

Therefore, by the function the answer will be n - 1.

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The surface area of the right rectangular prism is 87.88 square units.

The surface area of ​​a rectangle is the total area or area of ​​six faces. A prism is a solid with straight parallelogram sides and a base of the same polygon. There are many types of prisms such as triangular prism, square prism, cartesian prism, penta prism, and hexagonal prism.

Given that:

from the set of information :

Length(l) = 5.2

Breadth (b) = 2.6

Height(h) = 3.9

Area of the rectangular prism = 2(lb + bh + lh)

                                                 = 2(5.2×2.6 + 2.6×3.9 + 3.9×5.2)

                                                 = 2(43.94)

                                                 = 87.88

Therefore, the surface area of the right rectangular prism is 87.88 square units.

Complete Question:

The net of a right rectangular prism is shown 2.6 3.9 5.2

What is the surface area of the right rectangular prism? Enter the answer as a decimal in the box unit².

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we have the expression

we have that

Using the Quotient of Powers Rule to simplify the problem. This rule states that when you are dividing terms that have the same base, just subtract their exponents to find your answer.

so

The correct description of the function f: Z → Z, given by f(x) = x + 3, is "Neither one-to-one nor onto."

To determine if the function f is one-to-one, we need to check if each input value (x) has a unique output value (f(x)). In this case, for any integer x, f(x) = x + 3. Since the value of f(x) depends solely on the input value x, different input values can yield the same output value. For example, f(1) = 4 and f(2) = 5, indicating that the function is not one-to-one.

To determine if the function f is onto, we need to check if every possible output value has a corresponding input value. In this case, since f(x) = x + 3, any integer y can be obtained as an output value by choosing x = y - 3. Therefore, every possible integer output has a corresponding input value, making the function onto.

As a result, the function f: Z → Z, defined by f(x) = x + 3, is neither one-to-one nor onto.

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f:Z→Z.f(x)=x+3f:Z→Z.f(x)=x+3

Select the correct description of the function f.

One-to-one and onto

One-to-one but not onto

Onto but not one-to-one

1.- The sum of the internal angles in a triangle equals 180°.

8x + 5x + 6x = 180°

19x = 180

x = 180/19

x = 180/19

2.- Calculate angle ABC

ABC = 8x

ABC = 8(180/19)

ABC = 1440 / 19

ABC = 75.8°

Answer:

4

Step-by-step explanation:

Four people will play basketball, so 10 - 4 = 6.

Half as many people will play baseball, and half of 4 is 2, so 6 -2 = 4.

The rest will play soccer, which is 4.

Answer:

12+y

Step-by-step explanation:

Given,

a=6

b=6

c=y

Perimeter of triangle= sum of all sides of triangle

= 6+6+y

= 12+y

Answer:

Step-by-step explanation:

Perimeter is the length of any closed figure. So for a triangle, the Perimeter is equal to P = a + b + c.

You are told that the triangle is isosceles which means it has 2 equal. You are to presume that the third side is not equal to the other 2.

a=  6

b = 6

c = y

Perimeter = a + b + y

Perimeter = 6 + 6 + y

Perimeter = 12 + y

You cannot go any further. There is no way to reduce it any further.

The total electric force on the 7.00−μC charge is 0.872 N at an angle of 330°.

The force exerted on the 7.00−μC charge by the 2.00−μC charge is

F₁​ ​= \(k_{e}\)q₁q₂​​/r₂ r^

= [(8.99×10⁹N.m²/C²)(7.00×10^−6C)(2.00×10^−6C) ×(cos60°i^+sin60°j^​)]/ (0.500m)²

F₁ ​= (0.252i^+0.436j^​)N

Similarly, the force on the 7.00μC charge by the −4.00−μC charge is

F₂​ ​= \(k_{e}\)q₁​q₃/​r² ​​r^

= [(8.99×10⁹N.m²/C²)(7.00×10^−6C)(−4.00×10^−6C)​×(cos60°i^−sin60°j^​)]/(0.500m)²

F₂​ ​=(0.503i^−0.872j^​)N

Hence, the total force on the charge 7.00−μC  is

F = F₁​​+F₂​

​=(0.755i^−0.436j^​)N

We can also note the total force as:

F = (0.755N)i^−(0.436N)j^​ = 0.872N

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--This question is incomplete; the complete question is

"Three charged particles are located at the corners of an equilateral triangle, as shown in Figure. Calculate the total electric force on the 7.00−μC charge."--

Answer:

5 weeks

Step-by-step explanation:

is she recycles 12 in 6 weeks that's 2 per week. So 2x5=10

The equation of a plane in vector form is r. (n * a) = d, where a is a point on the plane, n is the normal, r is the position vector, and d is the distance from the origin. The line passes through (0,-5,-4) and has a direction vector of d = (1,0,0).

Given:Point through which the line passes (0,−5,−4)Normal to the surface at (0,−5,−4)The equation of a plane in vector form is given byr. (n * a) = dwhere, a is a point on the plane, n is the normal to the plane, r is the position vector and d is the distance of the plane from the origin.For the given point and normal vector,n = (0,-1,0)and a = (0,-5,-4)respectively.

So, the plane equation can be written as

r.(0,-1,0) = - 5

So, the equation of the plane can be given by y = - 5 It is given that the line passes through the point (0,-5,-4) which is normal to the surface at (0,-5,-4).As the given normal vector is in y-direction, the line will be parallel to x-z plane and perpendicular to the y-axis.

So, the direction vector of the line can be given byd = (1,0,0)Now, as the line passes through (0,-5,-4), we can get the vector equation of the line as

r = a + td

where, t is the parameter.So, the vector equation of the line can be givend = (0,-5,-4) + t(1,0,0)Thus, the vector equation of the line through point (0,−5,−4) which is normal to the surface at (0,−5,−4) isr = (t, - 5, - 4) where t is any real number.

Note: In the given question, it was not mentioned about the surface. But it is given that the line is normal to the surface. So, the equation of the surface is taken as the plane equation.

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The last step in evaluating the expression r is D) 120-48.

BODMAS is an acrοnym used tο remember the οrder οf οperatiοns in mathematics. It stands fοr Brackets, Order (expοnents), Divisiοn and Multiplicatiοn (left-tο-right), and Additiοn and Subtractiοn (left-tο-right).

Tο evaluate the expressiοn, yοu need tο fοllοw the οrder οf οperatiοns, which is Parentheses, Expοnents, Multiplicatiοn and Divisiοn, and finally Additiοn and Subtractiοn (PEMDAS).

(9+4-1) X 10'- 3 X2 (4x2)

First, simplify the parentheses:

(9+4-1) X 10'- 3 X 2 (4x2) = (12) X 10' - 3 X 2 (8)

Next, evaluate the expοnents:

(12) X 10' - 3 X 2 (8) = (12) X 1 - 3 X 2 (8)

Then, perfοrm the multiplicatiοn and divisiοn οperatiοns:

(12) X 1 - 3 X 2 (8) = 12 - 3 X 16

Finally, perfοrm the additiοn and subtractiοn οperatiοns:

12 - 3 X 16 = 12 - 48 = -36

Therefοre, the answer is D) 120-48.

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The equation 2/3 - x + 1/6 = 6x - x has the same solution set as the equation x = 5/36.

To determine which equations have the same solution set as the given equation, let's simplify and rearrange the terms.

Starting with the given equation:

2/3 - x + 1/6 = 6x - x

We can simplify the left side by finding a common denominator for 2/3 and 1/6, which is 6:

(4/6) - x + (1/6) = 6x - x

Combining like terms on the left side gives us:

(5/6) - x = 6x - x

Further simplifying, we can combine the x terms on the right side:

(5/6) - x = 5x

To isolate the x term on one side, we can add x to both sides:

(5/6) = 6x

Next, we can divide both sides by 6 to solve for x:

5/36 = x

Therefore, the equation 2/3 - x + 1/6 = 6x - x has the same solution set as the equation x = 5/36. Any equation that simplifies and rearranges to x = 5/36 will also have the same solution set as the given equation.

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We can calculate the number of individuals likely to fall within two standard deviations above the mean by finding 2.5% of 1000

individuals: 25.

What is mean?

In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.

If the IQ data for 1000 individuals are normally distributed, approximately 95% of the individuals will fall within two standard deviations above or below the mean. This is known as the empirical rule or the 68-95-99.7 rule.

So, to find out how many of the 1000 individuals are likely to fall within two standard deviations above the mean, we can use this rule. We know that 95% of the data fall within two standard deviations of the mean, which means that 2.5% of the data fall above two standard deviations above the mean.

Therefore, we can calculate the number of individuals likely to fall within two standard deviations above the mean by finding 2.5% of 1000 individuals:

2.5% of 1000 = (2.5/100) x 1000 = 25

So, approximately 25 of the 1000 individuals are likely to fall within two standard deviations above the mean.

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Complete Question:

IQ data is collected for one thousand individuals. If the data are normally distributed, how many of these individuals are likely to fall within two standard deviations above the mean?

Answer:

Step-by-step explanation:

Let the scale factor be k, then

Considering this we have:

The value of x is

Finding the scale factor

So the answer is