Determine whether the point is on the graph of the equation 2x + 7y =13 (3,1) yes or no

Answer:

[tex]\dfrac{2}{169}[/tex]

Step-by-step explanation:

A standard 52-card deck comprises 4 suits (Spades, Hearts, Diamonds, and Clubs).  

Each suit comprises 10 numerical cards (numbered 2 through 10, plus an "ace") and 3 "court" cards (jack, queen and king).

Therefore:

[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]

[tex]\implies \sf P(Queen)=\dfrac{4}{52}=\dfrac{1}{13}[/tex]

[tex]\implies \sf P(King)=\dfrac{4}{52}=\dfrac{1}{13}[/tex]

Therefore, the probability of drawing a king, replacing the card, and drawing a queen is:

[tex]\implies \sf P(King)\;and\;P(Queen)=\dfrac{1}{13}\times \dfrac{1}{13}=\dfrac{1}{169}[/tex]

Similarly, the probability of drawing a queen, replacing the card, and drawing a king is:

[tex]\implies \sf P(Queen)\;and\;P(King)=\dfrac{1}{13}\times \dfrac{1}{13}=\dfrac{1}{169}[/tex]

Therefore, the probability of drawing a king then a queen, or a queen then a king is:

[tex]\implies \sf P(King\;and\;Queen)\;or\;P(Queen\;and\;King)=\dfrac{1}{169}+\dfrac{1}{169}=\dfrac{2}{169}[/tex]

The value of the constant a in f(x) = ax² such that 0 < x ≤ 3 is 0.11

The probability density function is given as

f(x) = ax²

Such that

0 < x ≤ 3

To determine the value of the constant a, we make use of the following equation

[tex]\int\limits^a_b {f(x)} \, dx = 1[/tex]

So, we have:

[tex]\int\limits^3_0 {ax^2} \, dx = 1[/tex]

Factor out the constant

[tex]a\int\limits^3_0 {x^2} \, dx = 1[/tex]

Differentiate the equation

So, we have the following representation

[tex]a\frac{x^3}3 |^3_0 = 1[/tex]

Expand the equation

a[3³ - 0³]/3 = 1

Evaluate the difference

a[3³]/3 = 1

Evaluate the quotient

9a = 1

Divide both sides by 9

a = 0.11

Hence, the variable a is 0.11

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Domain: [tex]([/tex] -∝,∝ [tex])[/tex], { [tex]x|x[/tex] ∈ R }

Range: [tex][0,[/tex] ∝ [tex])[/tex], { [tex]y|y\geq 0[/tex] }

Hope this helps!

Answer:

Step-by-step explanation:

p = 8

The equation for the polynomial in the standard form is:

P(x) = x^3 + x^2 - 2x

A polynomial of degree N with the n zeros {x₁, x₂, x₃, ..., xₙ} is written as:

P(x) = (x - x₁)*(x - x₂)*...*(x - xₙ)

That is called the factorized form of the polynomial, and we are assuming that the leading coefficient is equal to 1 just for simplicity.

In this case we have 3 zeros {-2, 0, 1}, so the polynomial is of degree 3, and we can write it as:

P(x) = (x + 2)*(x - 0)*(x - 1)

To write the polynomial in the standard form, we need to expand the product:

P(x) = (x + 2)*(x)*(x - 1)

P(x) = (x^2 + 2x)*(x - 1)

P(x) = (x^3 + 2x^2 - x^2 - 2x)

P(x) = x^3 + x^2 - 2x

That is the polynomial.

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The function d(x) = - |x - 3| + 5 is the result of using an horizontal translation, reflection about the x-axis and vertical translation on the function f(x) = |x|.

In this question we have the definition of a function (f(x)) and its image (d(x)), the latter is the result of three rigid transformations:

Horizontal translation

f'(x) = f(x - 3)

Reflection about the x-axis

f''(x) = - f'(x)

Vertical translation

d(x) = f''(x) + 5

If we know that f(x) = |x|, then the series of rigid transformations is shown below:

Horizontal translation

f'(x) = |x - 3|

Reflection about the x-axis

f''(x) = - |x - 3|

Vertical translation

d(x) = - |x - 3| + 5

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The answer is [tex]Log_{b}200 = 2[/tex]

A logarithm is the power to which a number must be raised in order to get some other number.

Given that, [tex]log_{b} 8 = 0.8, log_{b} 5 = 0.6[/tex]

Using formula, [tex]log_{b} a+log_{b} b = log_{b} ab[/tex]

[tex]log_{b} 5 +log_{b} 5 = log_{b} 5*5 = log_{b} 25\\= 0.6+0.6 = 1.2\\\\[/tex]

[tex]log_{b} 200 = log_{b} 25*8\\log_{b} 25*8 = log_{b} 25 + log_{b} 25*8\\ log_{b} 25 + log_{b} 25*8 = 1.2 + 0.8 = 2[/tex]

Hence, The answer is [tex]Log_{b}200 = 2[/tex]

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Answer:

yes

By dividing the difference between each two corresponding data values, we get a constant rate of change.

y = 0.2x + 1.2

Step-by-step explanation:

1. Find the rate of change between each pair of data values in the table and compare to see if they are equal:

  (1.4-1.2)/(1-0) = 0.2/1 = 0.2

  (1.6-1.4)/(2-1) = 0.2/1 = 0.2

  (2-1.6)/(4-2) = 0.4/2 = 0.2

2. Substitute the numbers found in step 1 for m, and the y-value in the data pair (0,1.2) as b in the equation y = mx + b:  y = 0.2x + 1.2

The exponential function graphed is the one in option A.

d(x) = (0.45)^x

On the graph we can see some kind of exponential function, such that it has a vertical asymptote at x = -3

It also decreases as x increases, then the exponential function has a base that is smaller than 1 and larger than zero.

Because the y-intercept must be 1, we can discard option D where:

d(0) =4*(0.5)^0 = 4*1 = 4

Now, the only other option with a base between 0 and 1 is the first option:

d(x) = (0.45)^x

So that is the correct option.

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The result of the given terms is -2/5 as per the given question from complex numbers.

There is a multiplicative inverse for every nonzero complex number. As a result, complex numbers are a field with real numbers as a subfield. The complex numbers also form a two-dimensional real vector space with 1, I as the standard basis.

Because of this standard basis, the complex numbers form a Cartesian plane known as the complex plane. This allows for a geometric interpretation of complex numbers and operations, as well as the expression of geometric features and constructions in terms of complex numbers. Real numbers, for example, constitute the real line, which corresponds to the complex plane's horizontal axis.

=(((3/5)+(1/5)i)+((4/5)-(2/5)i) -((9/5)-(1/5)i))

=((3/5)+(4/5)-(9/5))-i((1/5)+i((1/5)-(2/5)+(1/5))

=(-2/5)+i(0)

= -2/5

Therefore, the result of the given terms is -2/5

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Considering the definition of vertex of a quadratic function, the vertex of the quadratic equation y=2x²−12x+7 is (3; -11).

A quadratic function is a variable of a polynomial function defined by f(x)=ax² + bx +c, where a≠0

The graphs of these functions correspond to vertical parabolas (symmetric axis parallel to the ordinate axis), with the particularity that:

The vertex of a quadratic equation or parabola is the highest or lowest point on the graph corresponding to that function. The vertex is calculated as:

In this case, the quadratic equation y=2x²−12x+7, where:

The value of x of the vertex is calculated as -(-12)÷(2×2)

Solving: -(-12)÷(4)= 12÷4= 3

The value of y of the vertex of the function is calculated as y=2×3²−12×3+7

Solving y= -11

Finally, the vertex in this case is (3; -11).

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Answer:

235,872

Step-by-step explanation:

Simplify:

78×7×54×8

78×69

= 235,872

Answer:

235872

Step-by-step explanation:

I hope it's useful to you

The straight-line distance between Edentown and Newberg is 90 miles. The correct option is the third option 90 miles

From the question, we are to determine the possible straight-line distance between Edentown and Newberg if the three towns form a right triangle.

Let the straight-line distance between Edentown and Newberg be x.

Now,

Assume that the straight-line distance between Martville and Newberg is the hypotenuse of the right triangle,

Then,

From the Pythagorean theorem, we can write that

150² = x² + 120²

22500 = x² + 14400

x² = 22500 - 14400

x² = 8100

x = √8100

x = 90 miles

Hence, the straight-line distance is 90 miles

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Algebraic expressions are mathematical expressions that combine a mathematical constant and variables.

What types of algebraic expressions are used in the multiplication of algebraic expressions?

The four basic mathematical operators are addition (+), subtraction (-), multiplication (), and division. Algebraic expressions are mathematical expressions that combine a mathematical constant and variables connected by one or more of the four basic mathematical operations (). Algebraic expressions include things like 4 x + 8, x - y, etc. The numbers 4 and 8 serve as the expression's given constants in the example 4 x + 8, while the word x serves as the equation's variable.

The process of multiplying two provided expressions made up of variables and constants is known as the multiplication of algebraic expressions. An expression that uses integer constants and variables together is called an algebraic expression.

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Answer:

99%

Step-by-step explanation:

Answer:No

Step-by-step explanation:

Sydney wants to make 15 rings, and each ring requires 60 beads. That means you need to multiply 60 beads by 15 rings to see how many beads she needs. 60 times 15 is 900. Sydney only has 852 beads.

The common ratio and the general term equation, a, of the geometric sequence is A. r = 1/2 , an = 16(1/2)^(n - 1).

A geometric sequence simply means the sequence of non zero numbers whereby the term after the first is simony found by multiplying the previous number by a common ratio

Based on the information, the common ratio will be:

= Second term / First term

= -8 / -16

= 1/2

The nth term will then be 16(1/2)^(n - 1).

The correct option is A.

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The length of HG is also equal to 23, which is the length of EH because the line DF bisects EG in the parallelogram DEFG.

A parallelogram is a quadrilateral, and the diagonals always bisect each other. However, diagonals only form right angles if the parallelogram is a rhombus or a square.

For the given parallelogram DEFG; the lines DF and EG are its diagonals, and the both bisect each other, that is the cut each other to form two equal parts.

So EH and HG are equal halves of the line EG

Therefore, since EH = 23 then HG = 23 because they form a diagonal of the parallelogram DEFG bisected by the diagonal DE.

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If Percent of Sales Method At the end of the current year, Accounts Receivable has a balance of $805,000.  the amount of the adjusting entry for uncollectible accounts is  $27,150.

a. Amount of bad  debts

Amount of bad  debts = Sales × Bad debts rate

Amount of bad  debts = $3,620,000×0.75%

Amount of bad  debts= $27,150

b. Adjusted balances

Accounts Receivable           $805,000

Allowance for Doubtful Accounts    $20,150

( $27,150- $7,000)

Bad Debt Expense                            $27,150

c. Net realizable value of accounts receivable

Net realizable value of accounts receivable = Balance of accounts receivables  - Allowance for Doubtful Accounts

Net realizable value of accounts receivable =  $805,000-  $20,150

Net realizable value of accounts receivable = $784,850

Therefore the amount of bad  debts is $27,150.

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Answer:

Maximum value of the objective function is 15

This occurs at x = 3, y = 0

Step-by-step explanation:

Attached is a plot of the two inequalities. The feasible region is the dark shaded area bounded by the points O, A, B and C

The maximum value of the objective function will occur at one of the corner points

The four corner points are

O (0,0)

A(0,3)

B(2,2)

C(3,0)

Plug in each of these values into the objective function, see which of the corner points will yield the maximum value and those will be the optimal values of x and y

Corner point  (x, y)                      O.F Value (5x + 2y)

(0, 3)                                             5(0) + 2(3) = 6

(2, 2)                                             5(2) + 2(2) = 14

(3, 0)                                              5(3) + 2(0)  = 15   (Maximum value)

Answer:

[tex]y=53.75x+70[/tex]

Step-by-step explanation:

From inspection of the given graph with added trendline:

Find the slope of the trendline by substituting the identified points into the slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{500-70}{8-0}=53.75[/tex]

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the trendline:

[tex]\implies y=53.75x+70[/tex]

We are given the following:

Solve for y.

[tex]-y+28+y^2=2y+2y^2[/tex]

This being said, lets begin.

~~~~~~~~~~~~~~~~~~~~~~~

1. First, move [tex]2y^2[/tex] to the left side.

[tex]-y+28-y^2=2y[/tex]

2. Move [tex]2y[/tex] to the left side.

[tex]-y^2-3y+28=0[/tex]

3. Solve with the quadratic formula.

[tex]y_{1,2} = \frac{-(-3) -+ \sqrt{(-3)^2-4(-1)*28} }{2(-1)}[/tex]

4. [tex]\sqrt{(-3)^2-4(-1)*28}=11[/tex]

   [tex]y_{1,2} =\frac{-(3)-+11}{2(-1)}[/tex]

5. Separate the solutions.

[tex]y=\frac{-(-3)+11}{2(-1)} , y_{2} =\frac{-(-3)-11}{2(-1)}[/tex]

6.

[tex]y=\frac{-(-3)+11}{2(-1)}[/tex] [tex]=-7[/tex] ← First Solution

7.

[tex]y=\frac{-(-3)-11}{2(-1)} =4[/tex]   ←Second Solution

Final Solution:

[tex]y=-7,y=4[/tex]

Hope this helps!

Answer:22

Step-by-step explanation:

Answer: h(5)=22

Step-by-step explanation:

h(5) is saying that x is equal to 5

replace x with 5

h(5)=4(5)+2

h(5)=20+2

h(5)=22

Answer: x=9

Step-by-step explanation:

To get the answer, just divide, but you must not count in the rows that have less or more than 42 projects. 405/42=xThere are 9 rows that have exactly 42 projects because 42 x 9 = 378, which is the closest we can get to 405. 

Answer:

Step-by-step explanation:

94.25 days

Answer:

square

Step-by-step explanation:

need more information

Answer:

-4/9x - 16.22222

Step-by-step explanation:

Use slope formula

(-5) - (-1) = -4

4 - (-5) = 9

Remember -(-) cancel out to become positive!

The answer is

-4/9x - 16.22222

I can't approximate the 16.222, it is literally that. I did trial and error.

The value of x in the statement negative 3 less than 4.9 times a number x is the same as 12.8 is 2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given a statement negative 3 less than 4.9 times a number, x, is the same as 12.8 this can be numerically expressed as,

4.9x - (- 3) = 12.8.

4.9x + 3 = 12.8

4.9x = 12.8 - 3.

4.9x = 9.8.

x = 9.8/4.9.

x = 2.

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