I need help with this question can anyone tell me ?

(a) The average rate of change of f on [−3,1] is:
f(1)-f(-3)/(1-(-3)) = (1+3)/(1-(-3)) - ((-3)+3)/(-3-(-3)) = (4/4) - (0/6) = 1 - 0 = 1

(b) The average rate of change of f on [x,x+h] is:
f(x+h)-f(x)/(x+h-x) = (x+h+3)/(x+h-8) - (x+3)/(x-8) = (x+h+3)(x-8) - (x+3)(x+h-8)/(x+h-8)(x-8) = (x^2-5x-8h-11)/(x^2-8x-8h+64)

The average rate of change of a function is the slope of the line that passes through two points on the graph of the function. It is calculated by the difference in the y-values of the two points divided by the difference in the x-values of the two points.

The average rate of change of f on [−3,1] is:
f(1)-f(-3)/(1-(-3)) = (1+3)/(1-(-3)) - ((-3)+3)/(-3-(-3)) = (4/4) - (0/6) = 1 - 0 = 1

The average rate of change of f on [x,x+h] is:
f(x+h)-f(x)/(x+h-x) = (x+h+3)/(x+h-8) - (x+3)/(x-8) = (x+h+3)(x-8) - (x+3)(x+h-8)/(x+h-8)(x-8) = (x^2-5x-8h-11)/(x^2-8x-8h+64)

Therefore, the average rate of change of f on [x,x+h] is (x^2-5x-8h-11)/(x^2-8x-8h+64).

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Michael will need to pay a total of R276,000 over the 60 months for the Mex tractor.

First, let's calculate the total amount he will need to finance:

Total amount to finance = R160,000 + 0.15 x R160,000 (VAT at 15%) = R184,000

Next, let's calculate the total interest he will need to pay over the 60 months:

Total interest = (principal x rate x time) / 100

where

Total interest = (R184,000 x 10% x 5) / 100 = R92,000

Therefore, the total amount Michael will need to pay over the 60 months is the sum of the total amount financed and the total interest:

Total amount to pay = Total amount to finance + Total interest = R184,000 + R92,000 = R276,000

So, Michael will need to pay a total of R276,000 over the 60 months for the Mex tractor.

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The vector that is perpendicular to the tangent vector of the curve at (0, 1, 0) is <1, 0, -1>, or option c

The space curve given is r(t) = sin t i + e^t j + ln(t+1) k. To find the tangent vector of the curve at a given point, we need to take the derivative of the curve with respect to t. The derivative of the curve is r'(t) = cos t i + e^t j + (1/(t+1)) k.

At the point (0, 1, 0), t = 0. So, the tangent vector at this point is r'(0) = cos 0 i + e^0 j + (1/(0+1)) k = <1, 1, 1>.

Now, we need to find which of the given vectors is perpendicular to the tangent vector. Two vectors are perpendicular if their dot product is equal to 0. So, we need to find the dot product of the tangent vector with each of the given vectors and see which one is equal to 0.

a. <1, 1, 1> • <0, 1, 0> = 0 + 1 + 0 = 1 (not perpendicular)
b. <1, 1, 1> • <-1, 0, -1> = -1 + 0 - 1 = -2 (not perpendicular)
c. <1, 1, 1> • <1, 0, -1> = 1 + 0 - 1 = 0 (perpendicular)
d. <1, 1, 1> • <1, -1, 1> = 1 - 1 + 1 = 1 (not perpendicular)
e. <1, 1, 1> • <1, 0, 1> = 1 + 0 + 1 = 2 (not perpendicular)

Therefore, the vector that is perpendicular to the tangent vector of the curve at (0, 1, 0) is <1, 0, -1>, or option c.

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The result obtained  when x^(4)-6x^(2)-x-19 is divided by x-3  using long division method is    x3 - 18x2 - 9x - 57 + 19/x-3.

The question is, "Use the long division method to find the result when x^(4)-6x^(2)-x-19 is divided by x-3".

To solve this problem using long division, we need to set up the division like this:

    x4 - 6x2 - x - 19

    ___________________      (x-3)

                      0

                           -3x3 - 18x2 - 9x - 57

Now, divide the first term of the numerator by the first term of the denominator, x4/x = x3, and write it above the division. Next, multiply the result x3 by the denominator (x-3) to get -3x3.

Now subtract -3x3 from the numerator (x4 - 6x2 - x - 19) to get -6x2 - x - 19. Divide this by the denominator (x-3) to get -18x2 - 9x - 57, and write it below the division. Now multiply the result -18x2 by the denominator (x-3) to get -54x2 - 27x - 171.

Finally, subtract -54x2 - 27x - 171 from -6x2 - x - 19 to get the remainder, -19.

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The expression (z²+10z+25)/(z²-3z-40) in simplest form is (z+5)/(z-8), with the restriction that z cannot be equal to 8.

The expression (z²)+10z+25)/(z²-3z-40) can be simplified by factoring both the numerator and denominator.

First, factor the numerator:
(z²+10z+25) = (z+5)(z+5)

Next, factor the denominator:
(z²-3z-40) = (z-8)(z+5)

Now, the expression can be simplified by canceling out the common factor of (z+5):
(z+5)(z+5)/(z-8)(z+5) = (z+5)/(z-8)

Therefore, the expression in simplest form is (z+5)/(z-8).

There are restrictions on the variable in this expression. The denominator cannot be equal to zero, so we must exclude any values of z that would make the denominator zero.

The denominator is (z-8), so the restriction is:
z-8 ≠ 0

Solving for z, we find that the restriction is:
z ≠ 8

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A rule to represent this translation include the following (x, y)  →  (x - 9, y + 4).

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics, a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

C(3, 2) → C'(-6, 6)

3 + x = -6

x = -6 - 3 = -9.

y + 2 = 6

y = 6 - 2 = 4.

Therefore, the transformation rule is (x, y)  →  (x - 9, y + 4)

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Answer:

C.

Step-by-step explanation:

C. show the undulating forms of fabric.

The product of the number and its conjugate is 29.

The complex conjugate of a complex number is the number with the same real part and the opposite sign of the imaginary part. In other words, if a complex number is a + bi, then its complex conjugate is a - bi.

For the given number -5 - 2i:

(a) The complex conjugate is -5 + 2i. This is because the real part is the same (-5) and the imaginary part has the opposite sign (2i instead of -2i).

(b) To determine the product of the number and its conjugate, we simply multiply them together:

(-5 - 2i)(-5 + 2i) = 25 - 10i + 10i - 4i^2

Since i^2 = -1, we can simplify this to:

25 - 4(-1) = 25 + 4 = 29

So the product of the number and its conjugate is 29.

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The value of  [tex]\sum _{n=1}^{400}\:\left(2n-1\right)[/tex] is 16000.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given equation is  [tex]\sum _{n=1}^{400}\:\left(2n-1\right)[/tex]

[tex]\sum \:a_n+b_n=\sum \:a_n+\sum \:b_n[/tex]

By Applying the sum rule

[tex]=\sum \:_{n=1}^{400}2n-\sum \:_{n=1}^{400}1[/tex]

=2×2(400+1)/2 -400

=2×200×401−400

=16000

Hence, the value of  [tex]\sum _{n=1}^{400}\:\left(2n-1\right)[/tex] is 16000.

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The equation of y=x^(2) can be translated 8 units to the left and then 6 units downward by modifying the equation as follows:

y=(x+8)^(2)-6

This equation represents the same parabola as y=x^(2), but it has been shifted 8 units to the left and 6 units downward.

The translation of a function can be represented by modifying the equation in the form y=f(x-h)+k, where h is the horizontal shift and k is the vertical shift. In this case, h=-8 and k=-6, so the equation becomes:

y=f(x-(-8))+(-6)
y=f(x+8)-6

Substituting the original function f(x)=x^(2) into this equation gives:

y=(x+8)^(2)-6

Therefore, the equation of y=x^(2) when it is translated 8 units to the left and then 6 units downward is y=(x+8)^(2)-6.

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The simplified fraction is given as follows:

(2x - a)/(2x + a).

At the numerator, the fraction is simplified applying the least common factor as follows:

2 - (a/x) = (2x - a)/x.

At the denominator, the fraction is also simplified applying the common factor as follows:

2 + (a/x) = (2x + a)/x.

x is a common denominator to both of the fractions, hence it can be simplified, and then the simplified fraction is given as follows:

(2x - a)/(2x + a).

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By answering the above question, we may state that A kite has graphs perpendicular diagonals, and the larger diagonal splits the shorter diagonal in half.

Mathematicians use graphs to visually express or chart facts or values in a logical way. Usually, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph

The measurements of the numbered angles in each kite cannot be given without a reference image or particular kite. We can, however, offer some general knowledge on kites and their angles.

With two sets of neighboring congruent sides and angles, a kite is a quadrilateral with congruent sides on all four sides. A kite has perpendicular diagonals, and the larger diagonal splits the shorter diagonal in half.

Let's give a generic kite's angles the labels displayed in the accompanying diagram:

  A-------B

 /         \

D-----------C

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By answering the above question, we may infer that Hence, during the equation blizzard, snowfall totaled about 100.43 inches.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

To begin, let's calculate the amount of snow that evaporated. If 77% of the snow melted, the quantity of snow that is left is 100% - 77%, or 23%, of what was originally there.

This can be represented as:

Snow remaining equals 0.23x.

Assume that x inches of snow were present at the start. Thus, we may construct the equation shown below:

0.23y = 30

By finding y, we obtain:

y = 30 / 0.23 ≈ 130.43

Hence, the initial snowfall measured about 130.43 inches.

We may use the difference between the present depth of snow and the original depth of snow to calculate how much snow fell during the blizzard:

130.43 - 30 = 100.43

Hence, during the blizzard, snowfall totaled about 100.43 inches.

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The possible length of the third side of a triangle is l < 25

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

Given that, we need to find the possible lengths to complete a triangle with side lengths of 11 in. and 14 in.

We know that, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

Therefore,

11 + 14 = 25

Let the third side be l,

Therefore,

l < 25

Hence, the possible length of the third side of a triangle is l < 25

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Answer:

To simplify the expression, we can combine the like terms.

(3x + 1/2) + (7x - 4 1/2)

= 3x + 7x + 1/2 - 4 1/2 (distributing the addition)

= 10x - 4 (combining the like terms)

Therefore, (3x + 1/2) + (7x - 4 1/2) simplifies to 10x - 4.

The expression ((-8x⁵)(x⁻³))/(20x²) when simplified, making all exponents positive, will become -2/5.

To simplify the expression ((-8x⁵)(x⁻³))/(20x²), we need to apply the rules of exponents and simplify the coefficients.

First, let's simplify the coefficients:
-8/20 = -2/5

Next, let's apply the rules of exponents:

Product Rule: When multiplying two exponential expressions with the same base, you can add the exponents. That is, xᵃ · xᵇ = xᵃ⁺ᵇ

Quotient Rule: When dividing two exponential expressions with the same base, you can subtract the exponents. That is, xᵃ / xᵇ = xᵃ⁻ᵇ

(x⁵)(x⁻³) = x⁵⁺⁽⁻³⁾ = x²
x²/x² = x²⁻² = x⁰ = 1

So the expression simplifies to:
(-2/5)(1) = -2/5

Therefore, the simplified expression is -2/5.

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a) P (20 < or = X) =  0.8617: This is the probability that 20 or more of the 30 patients will be helped by the medicine.

b) P (18 < or = X < 25) = 0.8557: This is the probability that between 18 and 25 of the 30 patients will be helped by the medicine.

c) P ( X < 16) = 0.0266: This is the probability that less than 16 of the 30 patients will be helped by the medicine.

The given situation can be modeled using a binomial distribution, where the number of trials is 30, and the probability of success is 0.75. We can use the binomial probability formula to find the probabilities for each of the given conditions. The binomial probability formula is:

P(X = x) = (n choose x) * p^x * (1-p)^(n-x)
where n is the number of trials, x is the number of successes, p is the probability of success, and (n choose x) is the binomial coefficient.

a) P (20 < or = X) = 1 - P (X < or = 19) = 1 - sum_{x=0}^{19} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.8617

b) P (18 < or = X < 25) = P (X < or = 24) - P (X < or = 17) = sum_{x=18}^{24} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.8557

c) P ( X < 16) = sum_{x=0}^{15} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.0266

Therefore, the probabilities are 0.8617, 0.8557, and 0.0266 for the conditions a), b), and c) respectively.

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The distance of the mall from the pet shop, based on the graphic given, is 2 miles.

The distance between the Pet Shop, the School, the Mall and the Park are all shown on the graphic. The intervals between the distance given is shown to be 1 / 2 miles.

The number of distance marks between the Pet Shop and the Mall is 4 marks which means that distance between the Pet Shop and the Mall would be :

= 4 x 1 / 2

= 4 / 2

= 2 miles

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0.142857.

To convert the rational number 1/7 to its decimal form and round to the nearest thousandth, let's start by converting the fraction into a long division problem.

Enter the numerator of the fraction, 1, into the division box, and then divide it by the denominator of the fraction, 7.

The result of this long division is 0.142857. Finally, round this decimal to the nearest thousandth, which gives us 0.143.

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Based on the calculation, we find that:

(fog)(x) = (15Vx)¹⁵
(gof)(x) = 15V(x¹⁵)
(fog)(x) ≠ (gof)(x)

Function composition can be meant as an operation that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.

To find (fog)(x), we need to substitute g(x) into f(x). This means that we will replace every x in f(x) with 15Vx. So, (fog)(x) = f(g(x)) = f(15Vx) = (15Vx)¹⁵.

Similarly, to find (gof)(x), we need to substitute f(x) into g(x). This means that we will replace every x in g(x) with x¹⁵. So, (gof)(x) = g(f(x)) = g(x¹⁵) = 15V(x¹⁵).

Now, to determine whether (fog)(x) = (gof)(x), we need to compare the two expressions.

(fog)(x) = (15Vx)¹⁵ and (gof)(x) = 15V(x¹⁵). These two expressions are not equal, so (fog)(x) ≠ (gof)(x).

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Answer:

$3.30

Step-by-step explanation:

66 times 0.05

The probability of selecting a red pencil and a green M&M is calculated as follows:

p = [number of red pencils / number of pencils] x [number of green M&Ms / number of M&M's].

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The pencil and the M&M are independent events, hence we calculate the probability of each event and then multiply then, as follows:

p = [number of red pencils / number of pencils] x [number of green M&Ms / number of M&M's].

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The surface area, in square centimeters, of the toy box is 370 cm²

The quantity of space enclosing a three-dimensional shape's exterior is its surface area. Surface area is measured in cm².

Given, the lengths are 9 cm, 5 cm, and 10 cm.

To calculate the surface area, the formula is2(h × W) + 2(h × L) + 2(W × L)

2 x 9 x 5 + 2 x 9 x 10 + 2 x 5 x 10

90 + 180 + 100

370

Therefore, the surface area of the box is 370 cm²

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The question is incomplete, the image of the box is attached below:

Answer:

Step-by-step explanation:

45 points for signing up.

2.5 points for each visit [tex]=2.5v[/tex]

Needs to total 75 points.

So [tex]45+2.5v=75[/tex] is the solution.

This is shown by option [tex](D)[/tex].

The number of balloons which will not be used by Anissa is 4 balloons.

To make all 5 hats the same, Anissa needs to use the same number of balloons for each hat.

Let us call the number of balloons she uses for each hat "x". Since she's making 5 hats, she'll use a total of 5x balloons. We know that she has 54 balloons in total, so we can set up an equation:

5x = 54

To solve for x, we can divide both sides by 5:

x = 54 / 5

x = 10.8

Since she can't use a fraction of a balloon, she'll need to use 10 balloons for each hat.

= 5 hats x 10 balloons/hat

= 50 balloons used

So Anissa will not use:

= 54 - 50

= 4 balloons.

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Option B, On a coordinate plane, the locations of the points (9, -5) and (9, 5) related reflection across the x-axis.

The two locations (9, -5) and (9, 5) have the same x-coordinate, but their y-coordinates are different. We need to see how the coordinates of two points change as they undergo various transformations to understand their relationship.

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Answer:

See image attached for complete answer

Step-by-step explanation:

The attached image shows the calculation of probabilities for each branch

I believe it is self-explanatory

Since P(bus to shops) = 0.4, P(walk to shops ) = 1- 0.4 = 0.6

Since P(bus from shops) = 0.7, P(walk from shops) = 1- 0.7 = 0.3

The probabilities at the leaves of the tree(rightmost entries) show the combined probabilities of to and from

For example if she takes a bus to the shops and takes a bus from the shops, the combined probability = 0.4 x 0.7 = 0.28

If she walks to the shops and takes a bus from the shops the combined probability = 0.6 x 0.7 = 0.42

The other two probabilities can be computed the same way

The probability that she walks at least one way
= P(walking to shop) or P(walking from shop)

= sum of the probabilities in the yellow shaded boxes

= 0.12 + 0.42 + 0.18

= 0.72

Answer:

When dividing a whole number by a decimal, you can use long division to find the quotient (the answer to the division problem). Here's how to divide 9 by 0.85 using long division:

.        __________

0.85 | 9.00

        8.50    (0.85 goes into 9.00 one time)

      -----

        1.50    (subtract 8.50 from 9.00)

        1.27    (0.85 goes into 1.50 one time)

      -----

        0.23    (subtract 0.85 from 1.50)

When dividing a whole number by a decimal, you can use long division to find the quotient (the answer to the division problem). Here's how to divide 9 by 0.85 using long division:

sql

Copy code

.        __________

0.85 | 9.00

        8.50    (0.85 goes into 9.00 one time)

      -----

        1.50    (subtract 8.50 from 9.00)

        1.27    (0.85 goes into 1.50 one time)

      -----

        0.23    (subtract 0.85 from 1.50)

The quotient is the number above the division line, which is 10 with a remainder of 23/100. Therefore:

9 / 0.85 = 10 with a remainder of 23/100, or 10.5882 (rounded to four decimal places)

So, 9 divided by 0.85 is approximately 10.5882.

Answer:

2 hours

Step-by-step explanation:

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