On a different day, four song birds, six mice, one elk, and eight rabbits are present on the mountain range. If each animal is equally likely to be caught and consumed, what is the probability that the hawk will eat a song bird and then a rabbit? (Note: the elk is never consumed by the hawk.)

One possible set of values that would make the inequality true is:

g = 5

g = 0

g = -1

When we substitute these values into the inequality, we get:

4 + 5 ≥ 9 (true)

4 + 0 ≥ 9 (false)

4 + (-1) ≥ 9 (false)

Therefore, the values that make the inequality true are g = 5, g = 0, and g = -1.

Yes, if u1, u2, and u3 are linearly independent, then v1, v2, and v3 will also be linearly independent.  


To show this, assume that v1, v2, and v3 are linearly dependent. This means that there are scalars a,b, and c, such that:

a*v1 + b*v2 + c*v3 = 0

Since v1 = u1 + u2, v2 = u1 + u3, and v3 = u2 + u3, the equation above can be rewritten as:

a*(u1 + u2) + b*(u1 + u3) + c*(u2 + u3) = 0


Simplifying, this gives us:

(a + b + c)*u1 + (a + c)*u2 + (b + c)*u3 = 0


But since u1, u2, and u3 are linearly independent, the coefficients (a + b + c), (a + c), and (b + c) must all be equal to 0. This implies that a = b = c = 0, meaning that the original equation must be equal to 0. This means that v1, v2, and v3 are linearly independent.

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The inequality's solution set can be described by inspection as x <= 8.

Inequality is the unequal treatment of people based on factors such as race, gender, class, or other social characteristics. It is often seen as unfair and can lead to social and economic disparities.

This is because the inequality (x-8)^(6)<=0 is asking when the quantity (x-8) raised to the 6th power is less than or equal to zero.

Since any number raised to an even power will always be positive or zero, the only way for this inequality to be true is when (x-8) is equal to zero. This occurs when x = 8. Therefore, the solution set is x <= 8.

To summarize, the inequality's solution set is:
x <= 8

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a. The formula for the upper limit (U) is U = 220 - x, where x is the age of the person. The formula for the lower limit (L) is L = 0.65(220 - x).

b. For a 40-year-old person, the lower limit is L = 0.65(220 - 40) = 117 beats per minute and the upper limit is U = 220 - 40 = 180 beats per minute.

c. For a 60-year-old person, the lower limit is L = 0.65(220 - 60) = 104 beats per minute and the upper limit is U = 220 - 60 = 160 beats per minute.

d. Let x be the age of the younger woman and y be the age of the older woman. Since the older woman is 34 years older than the younger woman, we have y = x + 34. Since the older woman is working at the upper limit of her target heart rate zone and the younger woman is working at the lower limit of her target heart rate zone, we have U = L. Substituting the formulas for U and L, we get 220 - y = 0.65(220 - x). Substituting y = x + 34, we get 220 - (x + 34) = 0.65(220 - x). Simplifying and solving for x, we get x = 38. Therefore, the age of the younger woman is approximately 38 years and that of the older woman is approximately 72 years. Their pulse is approximately U = 220 - 72 = 148 beats per minute.

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The values of the length and angle are;

AD = 22 units

m < ADC = 106 degrees

The properties of a kite are given as;

From the information given, we have that;

AB = 8x - 2

AD = 6x + 4

Equate the sides

8x - 2 = 6x + 4

collect like terms

2x = 6

x = 3

AD = 22 units

Also,

m < ABC = m < ADC

Substitute the values

12x + 10 = 15x - 14

collect like terms

-3x = -24x

x = 8

m < ADC = 106 degrees

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Answer: AD = 22 units

Step-by-step explanation:

m < ADC = 106 degrees

AB = 8x - 2

AD = 6x + 4

Equate any sides

8x - 2 = 6x + 4

Collect terms

2x = 6

x = 3

AD = 22 units

m < ABC = m < ADC

Substitute the values

12x + 10 = 15x - 14

Collect terms

-3x = -24x

x = 8

m < ADC = 106 degrees

The length of the arc XYZ is 59.3 inches .

The radius of the circle is 10 inches. The central angle that subtend the arc is 340 degrees.

Therefore, the length of the arc xyz can be found as follows:

length of an arc = ∅/ 360 × 2πr

where

length of an arc(xyz) = 340 / 360 × 2 × 3.14 × 10

length of an arc(xyz) = 21352 / 360

length of an arc(xyz) = 59.3111111111

length of an arc(xyz) = 59.3inches

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Method of inverse of matrix is given:  

To obtain the inverse of the given matrix, M, without using the Matlab inv() command, you can use the following steps:

1. Compute the determinant of M, which is equal to 2.

2. Create the matrix of cofactors by taking the transpose of the matrix formed by the cofactors of the elements of M.

3. Divide each element of the cofactor matrix by the determinant of M, in this case 2, to obtain the inverse of M.

Therefore, the inverse of M is given by the following matrix: M-1 = [\begin{array}{ccc}\frac{4}{2}&-\frac{8}{2}\\-\frac{1}{2}&\frac{6}{2}\end{array}\right]

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Answer:

13,860 egyptian pounds

Answer:

Step-by-step explanation:

1 USD = 18.48 Egyptian pounds

∴ 750 USD = 750 × 18.48 Egyptian pounds

                  = 13860 Egyptian pounds

The solution to the equation |9a+5|=68 is a = 7, -8.111. To solve the equation |9a+5|=68, we can use the property of absolute value that states that |x| = x or |x| = -x. This means that we can set up two equations to solve for a:

9a+5 = 68 or 9a+5 = -68

Now we can solve each equation separately:

9a+5 = 68
9a = 63
a = 7

9a+5 = -68
9a = -73
a = -8.111

So the solutions are a = 7 and a = -8.111. We can write these solutions separated by a comma as follows:

a = 7, -8.111

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Answer:

false

Step-by-step explanation:

the pothagirum therum say that theres many reason its false

Answer: True

Step-by-step explanation:

True because we do not know the letters value, so in this case you only add the numbers 14 and 2. You will end up with the answer 16x after adding the letter/valuable.

The equations that represent functions are:

  1) 2x + 3y = 10

  2) 3y = 18

Functions are relations which give a particular output for each input.  The characteristic that every input is associated with exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. Specific input is supplied to a function in order to produce a specific result. To determine if a curve is a function or not, apply the vertical line test. Any curve that intersects a vertical line at more than one point is not a function.

Let us look into each equation.

1)  2x + 3y = 10

Here for each input of x, we get only one output y.

So this is a function.

2)  4x = 16

 This is not a function because there can be multiple values of y for a single value of x.

3) 2x − 3 = 14

 This is also not a function because there can be multiple values of y for a single value of x.

4)  3y = 18

 This is a function because there is only one value of y for exactly one value of x. Also, considering the vertical line test, the curve is a straight horizontal line which intersects with a given vertical line only once. So it is a function.

5)14.6 = 2x

  This is also not a function because there can be multiple values of y for a single value of x.

Therefore the equations that represent functions are:

  1) 2x + 3y = 10

  2) 3y = 18

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The measure of <TAV is [tex]92^{o}[/tex].

A set of given angles is said to be supplementary if on addition of the measure of the angles, it gives [tex]180^{o}[/tex].

In the given diagram, given that PQ is parallel to RS, it can be observed that;

<SCU ≅ <ACB (definition of vertically opposite angles)

Thus, <ACB = [tex]18^{o}[/tex]

<QAC = <BCA     (alternate angle property)

So that,

<QAC = [tex]18^{o}[/tex]

But,

<TAP ≅ <QAC  (definition of vertically opposite angles)

So that;

<BAP + <PAT + <TAV = [tex]180^{o}[/tex]  (sum of angles on a straight line)

Then,

70 + 18 + <TAV = 180

<TAV = 180 - 88

         = 92

<TAV = [tex]92^{o}[/tex]

The measure of <TAV = [tex]92^{o}[/tex].

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[tex](f+g)(x)= f(x) .g(x)[/tex][tex](f+g)(0) = f(0)+g(0) = 1+\frac{1}{2} = \frac{3}{2}[/tex][tex]g(0) = \frac{1}{2-0} =\frac{1}{2}[/tex]Answer:

Step-by-step explanation:

We are given:

[tex]f(x) = x^{2} +1\ ;g(x) = \frac{1}{2-x}[/tex]

We need to find:

a) [tex](f+g)(0)[/tex]

b) [tex](f.g)(0)[/tex]

[tex]f(0) = 0^{2} +1 = 1[/tex]

[tex]g(0) = \frac{1}{2-0} =\frac{1}{2}[/tex]

a) we know that

[tex](f+g)(x)= f(x) +g(x)[/tex]

[tex](f+g)(0) = f(0)+g(0)[/tex]

Using the value of f(0) and g(0)

we get

b) we know that

[tex](f+g)(x)= f(x) .g(x)[/tex]

[tex](f+g)(x)= f(x) .g(x) = (1)(\frac{1}{2}) =\frac{1}{2}[/tex]

So we have answer for a) 3/2 and for b) 1/2

Using the expressions to evaluate each function we are left with the following:

To evaluate the expressions, we simply need to substitute the value of x with 0 in the given functions and then perform the indicated operations. For part a, we need to add the functions f and g, and for part b, we need to multiply them:

(f + g)(0) = f(0) + g(0) = (0² + 1) + (1 / (2 - 0)) = 1 + (1 / 2) = 1.5

(f · g)(0) = f(0) * g(0) = (0² + 1) * (1 / (2 - 0)) = 1 * (1 / 2) = 0.5

In conclusion, we have that (f + g)(0) = 1.5 and (f · g)(0) = 0.5.

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Answer:

too blurry

Step-by-step explanation:

The weighted mean is a type of average that takes into account the relative importance of each data point. In this case, each unit has a different weighting, so we need to take that into account when calculating the weighted mean. Here is how to calculate the weighted mean:

1. Multiply each unit's weighting by its corresponding value.

2. Add up all of the products from step 1.

3. Divide the sum from step 2 by the sum of all the weightings.

Using the chart provided, here is how to calculate the weighted mean for this question:

Unit Weighting Value Product

Trigonometry 25% x 0.25x

Algebra 15% y 0.15y

Statistics 10% z 0.1z

Financial Math 12% a 0.12a

Linear Functions 20% b 0.2b

Quadratic Functions 18% c 0.18c

Weighted mean = (0.25x + 0.15y + 0.1z + 0.12a + 0.2b + 0.18c) / (0.25 + 0.15 + 0.1 + 0.12 + 0.2 + 0.18)

Weighted mean = (0.25x + 0.15y + 0.1z + 0.12a + 0.2b + 0.18c) / 1

Weighted mean = 0.25x + 0.15y + 0.1z + 0.12a + 0.2b + 0.18c

So the weighted mean is a combination of the values of each unit, weighted by their relative importance.

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To obtain 40g of active ingredient from a 100:1000 solution, you would need 400mL of the solution. The correct answer is option c. 400mL. A 100:1000 solution means that there are 100g of active ingredient in 1000mL of the solution. To find out how many milliliters of the solution you need to obtain 40g of active ingredient, you can use the following proportion:

100g/1000mL = 40g/x mL

Cross-multiplying gives:

100g * x mL = 40g * 1000mL

Simplifying and solving for x gives:

x = (40g * 1000mL)/100g

x = 400mL

Therefore, you would need 400mL of the 100:1000 solution to obtain 40g of active ingredient.

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The correct answer is E) approximately normal.

When the process of rolling a fair 20-sided die 60 times and computing the value of chi-square using expected counts of 3 for each face is repeated many times, the distribution of the values of chi-square should be approximately normal. This is because the chi-square distribution is a special case of the gamma distribution, and as the degrees of freedom increase, the chi-square distribution approaches a normal distribution. In this case, the degrees of freedom are 19 (20-1), which is a relatively large number, so the distribution should be approximately normal.

To summarize, the repeated process of rolling a fair 20-sided die 60 times and computing the value of chi-square using expected counts of 3 for each face will result in an approximately normal distribution of the values of chi-square.

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The common tangent of the compound curve is parallel to its long chord. This means that the angle between the common tangent and the long chord is 0°. The long chord makes an angle of 18° with the shorter tangent and 12° with the longer tangent. We can use the law of sines to determine the length of the common tangent.

Let's call the length of the common tangent x, the length of the long chord L, the angle between the common tangent and the long chord θ, the angle between the long chord and the shorter tangent α, and the angle between the long chord and the longer tangent β.

Using the law of sines, we have:

x/sin(θ) = L/sin(α+β)

Substituting the given values, we have:

x/sin(0°) = 546/sin(18°+12°)

Simplifying the equation, we get:

x = 546*sin(0°)/sin(30°)

Since sin(0°) = 0 and sin(30°) = 0.5, we have:

x = 546*0/0.5

x = 0

Therefore, the length of the common tangent is 0m.

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The is no solution of the  equation  (1)/(x-1)-1=(x)/(x-1).

To solve for all values of x in the equation (1)/(x-1)-1=(x)/(x-1), we can follow these steps:

1. Multiply both sides of the equation by (x-1) to eliminate the denominators:
1 - (x-1) = x

2. Simplify the left side of the equation:
- x + 2 = x

3. Add x to both sides of the equation to isolate the variable on one side:
2 = 2x

4. Divide both sides of the equation by 2 to solve for x:
x = 1

Therefore, the solution for x is 1.

When we plug x = 1 back into the original equation, we get a denominator of 0, which is undefined. This means that there are actually no solutions for this equation.

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Answer:

area=66

perimeter=42

Step-by-step explanation:

area = (12 x 3) + (5 x 6)

=36 + 30

=66

perimeter = 12 +9 +5 +6 +7 +5

=42

1. 9 months 2) $163.06, because it is the remaining balance after paying off the principal and interest accrued for that month. 3) $348.16, because it is the balance remaining on the lower interest card after paying off the higher interest card and making the monthly payment for that month. 4) 9 months 5) $168.79, because it is the difference between the total amount paid to each card when paying off the higher interest card first versus paying off the lower interest card first.

Interest is the fee paid for the use of borrowed money, usually expressed as a percentage of the borrowed amount.

Therefore, 1. 9 months 2) $163.06, because it is the remaining balance after paying off the principal and interest accrued for that month. 3) $348.16, because it is the balance remaining on the lower interest card after paying off the higher interest card and making the monthly payment for that month. 4) 9 months 5) $168.79, because it is the difference between the total amount paid to each card when paying off the higher interest card first versus paying off the lower interest card first.

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The system of three inequalities that describes this region is:x > 0y > 0x + y < 5

In a coordinate plane, the region that consists of all points that have positive x-and y-coordinates whose sum is less than 5 is the triangular region in the first quadrant bounded by the x-axis, y-axis, and the line x + y = 5. The system of three inequalities that describes this region is:x > 0y > 0x + y < 5Explanation:To find the region that consists of all points that have positive x-and y-coordinates whose sum is less than 5, we need to first graph the line x + y = 5 on a coordinate plane. This line has a slope of -1 and passes through the points (0,5) and (5,0). The region that we are looking for is the triangular region in the first quadrant bounded by the x-axis, y-axis, and this line.To write a system of three inequalities that describes this region, we need to consider the following facts:- All points in this region have positive x-coordinates, so x > 0.- All points in this region have positive y-coordinates, so y > 0.- All points in this region have x-and y-coordinates whose sum is less than 5, so x + y < 5.Therefore, the system of three inequalities that describes this region is:x > 0y > 0x + y < 5

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The multiplied the binomials of

Multiplying binomials involves using the distributive property to multiply each term in one binomial by each term in the other binomial.

(i) 2a-9 and 3a+4
(2a-9)(3a+4) = 2a(3a) + 2a(4) - 9(3a) - 9(4) = 6a²+ 8a - 27a - 36 = 6a² - 19a - 36

(ii) x-2y and 2x-y
(x-2y)(2x-y) = x(2x) + x(-y) - 2y(2x) - 2y(-y) = 2x² - xy - 4xy + 2y² = 2x^(2) - 5xy + 2y²

(iii) kl+lm and k-l
(kl+lm)(k-l) = kl(k) + kl(-l) + lm(k) + lm(-l) = k^(2)l - kl²+ lmk - l²m = k²l - l²m - kl² + lmk

(iv) m²-n² and m+n
(m²-n²)(m+n) = m²(m) + m²(n) - n²(m) - n²(n) = m³ + m²n - mn² - n²

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The equation of the graph of the function g(x) is -√(x-7).

Turns are frequently used to refer to reflection, which is when an object is flipped over a line without affecting its size or shape. The preimage is flipped over a line in a rigorous transition known as a reflection, but its size and shape are left unchanged. Flips is another name for reflections.

A figure can be translated if it is moved in any direction without altering its size, form, or orientation. A hard transformation called a translation alters the preimage's position but not its size, shape, or orientation. Slides are another name for translations.

Given that, f(x)= square root of x, that is:

f(x) = √x

Reflect the graph over x-axis we have:

Reflecting f(x) across the x-axis gives us -f(x) = -√x.

Translating -f(x) = -√x 7 units to the right gives us -f(x-7) = -√(x-7).

Hence, the equation of the graph of the function g(x) is -√(x-7).

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The solutions to the cosine functions are x = π/3 + 2nπ or x = 5π/3 + 2nπ, where n is an integer and x = 3π/4 + 2nπ or x = 5π/4 + 2nπ, where n is an integer.

1. 2 cos x - 1 = 0

Adding 1 to both sides and dividing by 2, we get:

cos x = 1/2

This equation has solutions for x of π/3 and 5π/3 (plus any integer multiple of 2π, since the cosine function is periodic with period 2π).

Therefore, the solutions are:

x = π/3 + 2nπ or x = 5π/3 + 2nπ, where n is an integer.

2. 5 cos x + 3√2 = 3 cos x + 2√2

Subtracting 3 cos x and 2√2 from both sides, we get:

2 cos x = -√2

Dividing by 2, we get:

cos x = -√2/2

This equation has solutions for x of 3π/4 and 5π/4 (plus any integer multiple of 2π).

Therefore, the solutions are:

x = 3π/4 + 2nπ or x = 5π/4 + 2nπ, where n is an integer.

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This would give us a modified statement of the limit, which would be "the limit of the rational function as x approaches 4".

A rational function is a type of mathematical function that can be expressed as the ratio of two polynomials. It can be written in the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomials with q(x) not equal to zero. Rational functions are used to model many real-world phenomena, such as the rate of change of a quantity with respect to another. They can also be used to solve complex equations and to analyze the behavior of a system.

The statement of the limit of a rational function can be modified by substituting different values for the variable and determining the resulting limit. For example, if the limit of the rational function is as x approaches 3, then we can substitute x = 4 and determine the resulting limit. This would give us a modified statement of the limit, which would be "the limit of the rational function as x approaches 4".

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Answer: I believe its A.

Step-by-step explanation:

The polynomial is  (x - 4)(x - 7)/(x + 4)(x + 5).

The question asks to add the two fractions (x^(2)-4x+9)/(x^(2)+9x+20) and (x-37)/(x^(2)+9x+20). To solve this problem, we can first simplify the denominator by factoring the polynomial:

Denominator: (x^(2)+9x+20) = (x + 4)(x + 5)


Now, we can rewrite the two fractions with this new denominator:

(x^(2)-4x+9)/(x + 4)(x + 5) + (x-37)/(x + 4)(x + 5)


Then, we can use the distributive property to expand the fractions and combine like terms:

(x^(2)-4x+9 + x-37)/(x + 4)(x + 5)

= (x^(2) - 3x - 28)/(x + 4)(x + 5)


Finally, we can simplify the numerator by combining like terms:

= (x^(2) - 3x - 28)/(x + 4)(x + 5)

= (x - 4)(x - 7)/(x + 4)(x + 5)

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The solution of the equation 1/2x² + 3/8x - 2 using completing the square method are: 1.66 or -2.41.

To solve the equation 1/2x² + 3/8x -2 using completing the square method, follow these steps:

Step 1: Move the constant term to the right-hand side

1/2x² + 3/8x = 2

Step 2: Multiply both sides by 2 to clear the fraction

x² + 3/4x = 4

Step 3: Add the square of half of the coefficient of x to both sides of the equation

x² + 3/4x + (3/8)² = 4 + (3/8)²

The left-hand side is now a perfect square, specifically (x + 3/8)².

Step 4: Simplify the right-hand side of the equation

x² + 3/4x + 9/64 = 256/64 + 9/64

x² + 3/4x + 9/64 = 265/64

Step 5: Take the square root of both sides

x + 3/8 = ±√(265)/8

Step 6: Solve for x

x = -3/8 ± √(265)/8

x = 1.66 or - 2.41

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[tex]x=\textit{kgs of solution at 30\%}\\\\ ~~~~~~ 30\%~of~x\implies \cfrac{30}{100}(x)\implies 0.3 (x) \\\\\\ y=\textit{kgs of solution at 15\%}\\\\ ~~~~~~ 15\%~of~y\implies \cfrac{15}{100}(y)\implies 0.15 (y) \\\\\\ \textit{60 kgs of solution at 20\%}\\\\ ~~~~~~ 20\%~of~60\implies \cfrac{20}{100}(60)\implies 0.2 (60)\implies 12 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{lcccl} &\stackrel{kgs}{quantity}&\stackrel{\textit{\% of kgs that is}}{\textit{nitrogen only}}&\stackrel{\textit{kgs of}}{\textit{nitrogen only}}\\ \cline{2-4}&\\ \textit{1st Fert.}&x&0.3&0.3x\\ \textit{2nd Fert.}&y&0.15&0.15y\\ \cline{2-4}&\\ mixture&60&0.2&12 \end{array}~\hfill \begin{cases} x + y = 60\\\\ 0.3x+0.15y=12 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{x+y=60}\implies y=60-x \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 2nd equation}}{0.3x+0.15y=12}\implies \stackrel{\textit{substituting from above}}{0.3x+0.15(60-x)=12} \\\\\\ 0.3x+9-0.15x=12\implies 0.15x=3\implies x=\cfrac{3}{0.15} \\\\\\ \boxed{x=20}\hspace{5em}\stackrel{ 60~~ - ~~20 }{\boxed{y=40}}[/tex]