FInd the rate oifd change for thgis said function . pleaser

The measure of the interior angle c is equal to 30° considering the exterior angle 156.5° of the triangle.

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

To calculate for the interior angle C°, we shall add C to the other interior angle which is also opposite the exterior angle 156.5 as follows:

C + 117.5 = 156.5

collect like terms

C = 156.5 - 117.5

C = 30°

In conclusion, the measure of the interior angle c is equal to 30° considering the exterior angle 156.5° of the triangle.

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Answer:

Therefore, the correct statements are A, B, and E.

Explanation:

Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.

To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀

.

- The component form of −4⇀

is obtained by multiplying each component of ⇀

by –4. Therefore, −4⇀

= ⟨–8, –12⟩. This means that statement A is true.

- The magnitude of −4⇀

is obtained by multiplying the magnitude of ⇀

by 4. The magnitude of ⇀

is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀

is 4√13. This means that statement B is true.

- The direction of −4⇀

is opposite to the direction of ⇀

because the scalar –4 is negative. This means that statement C is false.

- The vector −4⇀

is in the third quadrant because its components are both negative. This means that statement D is false.

- The direction of −4⇀

is 180° greater than the inverse tangent of its components because it is opposite to ⇀

. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀

is 180° + tan^(-1)(3/2). This means that statement E is true.

Therefore, the correct statements are A, B, and E.

a) The simplified ratio is 2:7.

b) 70 machines would pack approximately 245 crates of apples per day.

a) The ratio of the number of machines to the number of crates packed per day can be calculated by dividing the number of machines by the number of crates packed. In this case, there are 40 machines packing 140 crates per day. Thus, the ratio can be expressed as:

40:140

However, we can simplify this ratio by dividing both numbers by their greatest common divisor, which is 20:

40 ÷ 20 : 140 ÷ 20

2:7

So, the simplified ratio is 2:7.

b) If 40 machines pack 140 crates per day, we can use this information to determine how many crates 70 machines would pack. We can set up a proportion to solve for the unknown value:

40 machines / 140 crates = 70 machines / x crates

To solve for x, we can cross-multiply:

40 * x = 140 * 70

Dividing both sides by 40:

x = (140 * 70) / 40

x ≈ 245 crates

Therefore, 70 machines would pack approximately 245 crates of apples per day.

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[tex] {9}^{ \frac{1}{3} } \\( {3}^{3} )^{ \frac{1}{3} } \\ 3[/tex]

or

[tex] \sqrt[ 3]{9} \\ 3[/tex]

From the data given, the calculated mean of the distribution is 24.08 and the standard deviation of the binomial distribution is 3.7

Let's calculate the mean and standard deviation of a binomial distribution from the given data, we can use the formula;

Mean (μ) = n * P

Standard Deviation (σ) = √(n * P * (1 - P))

Given:

n = 56 (number of trials)

P = 0.43 (probability of success)

Calculating the mean:

Mean (μ) = n * P

Mean (μ) = 56 * 0.43

Mean (μ) = 24.08

The mean of the binomial distribution is 24.08.

Calculating the standard deviation:

Standard Deviation (σ) = √(n * P * (1 - P))

Standard Deviation (σ) = √(56 * 0.43 * (1 - 0.43))

Standard Deviation (σ) = √(24.08 * 0.57)

Standard Deviation (σ) = 3.7

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The notation "<" represents a binary relation known as the "less than" relation.

It is a fundamental concept in mathematics and is used to compare the relative magnitudes or order of two elements.

In the context of numbers, the "<" symbol indicates that one number is strictly smaller or less than another. For example, in the expression "5 < 8," it means that the number 5 is less than the number 8.

The "<" symbol can also be used to denote other types of binary relations, depending on the context.

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Answer:33, 44, 55, 66

Step-by-step explanation:

Add 11 to the number in front. Its basically 11 x table, so:

11, 22, 33, 44, 55, 66, 77, 88, 99  

Answer:

11, 22, 33, 44, 55, 66, 77, 88, 99

Step-by-step explanation:

The pattern is x+11, so you just add 11 to the previous number.

Answer:

16 months

Step-by-step explanation:

In order to find the number of months it will take for Alma's bank account to reach $145, we can plug in 145 for y and solve for x:

Step 1:  Subtract 577 from both sides:

(145 = -27x + 577) - 577

-432 = -27x

Step 2:  Divide both sides by -27 to solve for x:

(-432 = -27x) / -27

16 = x

Thus, it will take 16 months for Alma's account to reach $145.

Answer:

96

Step-by-step explanation:

There are 2021 numbers and subtracting 7 each time, we will be left with 2021/7 ≈ 289 numbers

2021/3 = remainder 2

⇒2021 = 3x + 2

2021 - 7 = 3x + 2 - 7

= 3x - 5

= 3x - 3 - 2

= 3(x - 1) - 2

adding and sub 3,

= 3(x - 1) - 2 + 3 - 3

= 3(x - 1 - 1) + 1

=3(x - 2) + 1

The remainder is 1 and hence not divisible by 3

2021 - 7 - 7 = 3(x - 1) - 2 - 7

= 3(x - 1) - 9

= 3(x - 1 - 3)

= 3 (x - 4)

Remainderis 0 and hence divisible by 3

So, every 3rd number in the 289 numbers is divisible by 3

⇒ 289/3 ≈ 96

Cog counted 96 numbers

The least score that Leon can achieve on his sixth exam and still earn an "A" is 93. He must score 93 or higher on his sixth exam to meet the requirement of accumulating at least 564 points in total.

To find the least score that Leon can achieve on his sixth exam and still earn an "A" in his Spanish course, we can set up an inequality.

Let x represent the score Leon receives on his sixth exam.

The total points Leon needs to accumulate to earn an "A" is 564.

Given his scores on the first five exams: 89, 96, 98, 95, and 93, we can add them up to find the total points earned so far:

89 + 96 + 98 + 95 + 93 = 471

To earn an "A," Leon needs a total of at least 564 points. Therefore, we can write the inequality:

471 + x ≥ 564

To solve for x, we'll isolate it on one side of the inequality:

x ≥ 564 - 471

x ≥ 93

Therefore, the least score that Leon can achieve on his sixth exam and still earn an "A" is 93. He must score 93 or higher on his sixth exam to meet the requirement of accumulating at least 564 points in total.

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The Laplace transform of the given function f(t) is

[tex]L{f(t)} = (2 / s) - (1 - 2/s) * e^(-s) + (2 / s^2) * e^(-s) + (1 / s)[/tex]

To find the Laplace transform of the given function f(t),

[tex]L{f(t)} = \int\limits[0, \infty}) e^(-st) * f(t) * dt[/tex]

where s is the complex Laplace variable.

For t < 1, f(t) = 0

[tex]L{f(t)} = \int[0, \infty) e^(-st) * 0 * dt = 0[/tex]

For t > 1, f(t) = [tex]t^2[/tex] - 2t + 2, so the integral becomes:

[tex]L{f(t)} = \int[1,\infty) e^(-st) * (t^2 - 2t + 2) * dt[/tex]

Now, integrate this expression by parts

[tex]\int[1,\infty) e^(-st) * (t^2 - 2t + 2) * dt[/tex]

[tex]= [(-t^2 + 2t - 2) / s * e^(-st)] [1,\infty) + \int[1,\infty) (2t - 2) / s * e^(-st) * dt[/tex]

[tex]= [(2 / s) * e^(-s)] - [(1 - 2/s) * e^(-s)] + [(-2 / s^2) * e^(-st)] [1,\infty)[/tex]

[tex]= [(2 / s) - (1 - 2/s) * e^(-s)] + (2 / s^2) * e^(-s)[/tex]

For t = 1, f(t) = 1, add this term to the Laplace transform

[tex]L{f(t)} = 0 + [(2 / s) - (1 - 2/s) * e^(-s)] + (2 / s^2) * e^(-s) + (1 / s)[/tex]

Hence, the Laplace transform of f(t) is given below

[tex]L{f(t)} = (2 / s) - (1 - 2/s) * e^(-s) + (2 / s^2) * e^(-s) + (1 / s)[/tex]

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The number of possible license plates that can be issued using this system is 17,576,000.

To find the number of possible license plates that can be issued using this system, we need to determine the number of options for each character in the license plate.

For the first character, there are 26 letters in the English alphabet, so we have 26 options.

Similarly, for the second and third characters, we also have 26 options each.

For the fourth character, there are 10 possible numbers (0-9).

And for the fifth character, there are again 10 possible numbers.

To find the total number of possible license plates, we need to multiply the number of options for each character together.

Number of possible license plates = Number of options for the first character * Number of options for the second character * Number of options for the third character * Number of options for the fourth character * Number of options for the fifth character

Number of possible license plates = 26 * 26 * 26 * 10 * 10

Calculating this expression gives us:

Number of possible license plates = 17,576,000

Therefore, the number of possible license plates that can be issued using this system is 17,576,000.

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The correct statements that evaluate the report of the survey results are:A) The sample is biased because it does not represent the population. E) The question is biased towards a response of preferring to drink water after a game. Option A and E

Statement A) The sample is biased because it does not represent the population:

While the survey may have randomly selected 50 city soccer players from the soccer teams' rosters, it is important to consider whether these players truly represent the entire population of soccer players in the city.

Factors such as age, skill level, gender, and other demographic characteristics can affect the preferences of soccer players. If the sample is not diverse enough or does not adequately represent the population's composition, it may introduce bias and limit the generalizability of the survey results.

Statement E) The question is biased towards a response of preferring to drink water after a game:

The question itself introduces bias by explicitly mentioning water and a sports drink as the only options for post-game hydration. This could influence participants' responses by priming them to consider water as the default or more favorable choice.

The question should ideally be phrased in a neutral manner, allowing participants to provide their preferred choice without any suggestion or preference imposed by the question itself.

It is important to note that statements C) The sample is not biased, and D) The question is not biased, are incorrect. The sample can be considered biased due to potential limitations in its representativeness, and the question itself introduces bias by favoring one option over the other.

Option A and E

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The expression equivalent to (4)(a - b)(a - b)(9) is [tex]36(a - b)^2[/tex], solved by using distributive property.

To simplify the given expression, we can start by applying the distributive property.
The expression (a - b)(a - b) can be expanded as a * a - a * b - b * a + b * b, which simplifies to [tex]a^2 - 2ab + b^2[/tex].

Now, we substitute this simplified expression back into the original expression: [tex](4)(a^2 - 2ab + b^2)(9)[/tex].
Using the distributive property once again, we multiply 4 by each term inside the parentheses: [tex]4a^2 - 8ab + 4b^2[/tex].

Finally, we multiply this expression by 9: [tex]9(4a^2 - 8ab + 4b^2)[/tex].
Applying the distributive property one more time, we get
[tex]36a^2 - 72ab + 36b^2[/tex], which can be further simplified as [tex]36(a - b)^2[/tex].

The equivalent expression to (4)(a - b)(a - b)(9) is [tex]36(a - b)^2[/tex].

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Question: Which expression is equivalent to (4) (a-b)(a-b)(9)?

The distinguishing feature between a square and a rectangle is that all sides of a square are equal in length.

Yes, a square is a special type of rectangle because it possesses all the properties of a rectangle.

The distinguishing feature of a rhombus is that all sides are equal in length, while a parallelogram can have unequal side lengths.

Yes, a rhombus is a special type of parallelogram because it possesses the properties of a parallelogram and has all sides equal in length.

The three features used to describe 3-dimensional objects are faces, edges, and vertices.

The common properties between a square and a rectangle are that both have four sides, four right angles (90 degrees), and opposite sides that are parallel. The distinguishing feature is that all sides of a square are equal in length, while a rectangle can have unequal side lengths.

Yes, a square is a special type of rectangle. A rectangle is defined as a quadrilateral with four right angles, while a square is a specific type of rectangle where all sides are equal in length. Since a square possesses all the properties of a rectangle, including four right angles, it can be considered a special case of a rectangle.

The common properties between a rhombus and a parallelogram are that both have four sides and opposite sides that are parallel. The distinguishing feature of a rhombus is that all sides are equal in length, while in a parallelogram, the opposite sides are equal in length.

Yes, a rhombus is a special type of parallelogram. A parallelogram is defined as a quadrilateral with opposite sides that are parallel. A rhombus possesses this property, but it also has the additional feature of having all sides equal in length. Therefore, a rhombus can be considered a special case of a parallelogram.

The three features used to describe 3-dimensional objects are:

Faces: The flat surfaces that make up the object.

Edges: The lines where two faces intersect.

Vertices: The points where multiple edges meet.

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Answer:

The slope of the line in the graph is 3/4.

-5 = (3/4)(8) + b

-5 = 6 + b, so b = -11

y = (-3/4)x - 11

The correct answer is B.

Answer:

is this right i mean im not very good at it but i hope this helped!

Step-by-step explanation:

:)

The value of K is 4.

In a regular polygon, all interior angles are congruent, which means they have the same measure. Let's denote the measure of each interior angle as A.

The sum of the interior angles of a polygon with (2x + 1) sides can be found using the formula:

Sum of interior angles = (2x + 1 - 2) * 180°

Since the polygon is regular, each interior angle has the same measure A. Therefore, we have the equation:

(2x + 1 - 2) * 180° = (2x + 1) * A

Simplifying the equation:

(2x - 1) * 180° = (2x + 1) * A

Now, we are given that the size of each interior angle is 140°. Substituting this value into the equation:

(2x - 1) * 180° = (2x + 1) * 140°

Solving for x:

360x - 180° = 280x + 140°

80x = 320°

x = 4

Therefore, the value of K is 4.

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A point with a positive x-coordinate and a negative y-coordinate will lie in Quadrant IV.

option D is the correct answer.

The bottom right quadrant is the fourth quadrant, denoted as Quadrant IV. In this quadrant, the x-axis has positive numbers and the y-axis has negative numbers.

So for coordinate plane in which Quadrant 1 is the top right quadrant, quadrant 2 is the top left, quadrant 3 is the bottom left, and quadrant 4 is the bottom right, a point with a positive x-coordinate and a negative y-coordinate will lie in Quadrant IV.

Thus, Quadrant IV is the correct answer because the x-axis has positive numbers and the y-axis has negative numbers.

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Answer:

Average rate of change = 4/3

Step-by-step explanation:

The formula for the average rate of change (AROC) is given by:

AROC = f(b) - f(a) / b - a

Thus, we have f(5) - f(2) / 5 - 2

The y-coordinate when x = 5 is 7 so this is our f(5) value.

The y-coordinate when x = 2 is 3 so this is our f(2) value.

Now we can find the AROC:

AROC = (7 - 3) / (5 - 2)

AROC = 4 / 3

Thus, the average rate of change from x = 2 to x = 5 is 4/3.

The measure of each angle indicated in the given triangle above would be given below as:

1.) ∅ = 21°

For question 1.

Using the Pythagorean formula such as:

C² = a²+b²

13² = a²+12²

a² = 169-144

= 25

a = √25 = 5

Using sine rule formula:

a/sinA = c/sinC

where;

a = 5

A = ?

c = 13

C = 90°

5/sin A = 14/sin 90

SinA = 5×1/14

SinA = 0.3571

A = Sin-1 (0.357142857)

= 21°

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The second coordinate of the given first coordinate is determined as;

f(0) = 1 and (1) = 0.7.

The second coordinate of the given first coordinate is calculated by applying the following method as follows;

The given function;

F(x) = 0.7ˣ

The value of f(0) is calculated as;

f (0) = 0.7⁰  = 1

The value of f(1) is calculated as;.

f (1) = 0.7¹ = 0.7

Thus, the second coordinate of the given first coordinate is determined by applying the appropriate substitute of the function as shown above.

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Answer: 18 meters

Let L be the length, w the width (all in meters).

Then you have L = 2w - 4, and 2l+2w =100. or L + w = 50. But L from the first relation into the second and simplify: 3w = 54 or w = 18.

Therefore, the width is 18 meters.

Happy to help; have a great day! :)

As per the given statement -

Let's assume that-

Formula used,

Substituting the values,

[tex] \longrightarrow[/tex] 2 (x + 2x - 4 ) = 100

[tex] \longrightarrow[/tex] 2(3x - 4) = 100

[tex] \longrightarrow[/tex] 3x - 4 = 100/2

[tex] \longrightarrow[/tex] 3x - 4 = 50

[tex] \longrightarrow[/tex] 3x = 50 + 4

[tex] \longrightarrow[/tex] 3x = 54

[tex] \longrightarrow[/tex] 3x = 54/3

[tex] \longrightarrow[/tex] x = 18

Since we have assumed width of the rectangle as 'x'.

So, The width of the rectangle is 18 m

The amount of money in the account after 9years to the nearest cent is $4826.69

Compound interest is the interest you earn on interest.

For example,if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

V = Pe^{rt}

V = 3980 e^{0.021 ×9}

V = 3989 e^{0.189}

V = 3989 × 1.21

V = $4826.69

Therefore the amount of money in the account after 9 years is $4826.69

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I think 5x but I'm not sure

Answer:

-5

Step-by-step explanation:

Simplify f(x)

[tex]f(x)=x^5-5x^4-17x^3+85x^2+16x-80\\f(x)=x^4(x-5)-17x^2(x-5)+16(x-5)\\f(x)=(x^4-17x^2+16)(x-5)\\f(x)=(x^2-16)(x^2-1)(x-5)\\f(x)=(x-4)(x+4)(x+1)(x-1)(x-5)[/tex]

Therefore, [tex]x=4,-4,-1,1,5[/tex] are the roots of the polynomial [tex]f(x)[/tex], which makes option 3 the best choice.

The formula for each transformation are

a) y = - √x

b) y = √|-x|

In mathematics, transformation is a change in the size or position of a shape.

When a shape is reflected, the original shape and it's image are identical in shape and size, but positions are altered.

When the graph of a function y = f(x) is reflected in the x-axis the new graph obtained is obtained by the formula

• y = – f(x)

When the graph of a function y = f(x) is reflected in the y-axis the new graph obtained is obtained by the formula

• y = f(-x)

From the given graphs,

• y = f(x) = √x

(a) When f(x) = √x is reflected in the x-axis, the image formed is the graph of

• y = -f(x) = –√x

(b) When f(x) = √x is reflected in the y-axis, the image formed is the graph of

• y = f(-x) = √|-x|

The modulus sign has to be introduced to avoid complex values for y.

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The values of x from the graph for which y = 0 are -3 and 4

From the question give above, we obtained the following:

The value of x from the graph can be obtained as follow:

y = x² - x - 12

but

y = 0

Thus, we have

x² - x - 12 = 0 (a quadratic function)

Thus, the vales of x will be the solutions of the equation x² - x - 12 = 0.

From the graph, the values of x when y = 0 will be the point when the line cuts across the x-axis.

From the graph, the line cuts across the x-axis at -3 and 4.

Thus, we can conclude that the value of x from the graph is -3 and 4.

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Answer:

[tex]\huge\boxed{\sf 60}[/tex]

Step-by-step explanation:

10 • √64 – 5 • 4

We know that, √64 = 8

So,

= 10 × 8 - 5 × 4

In an expression, we follow the order of DMAS:

D => Division

M => Multiplication

A => Addition

S => Subtraction

So, here we will multiply first.

= 80 - 20

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

The answer is **-4**.

The number line shows that 2 is to the right of 6 on the number line. This means that 2 is greater than 6. To find the difference between 2 and 6, we can subtract 6 from 2. 2 - 6 = **-4**.

The other choices are incorrect. A is incorrect because 2 is greater than 6, so the difference between them cannot be 8. B is incorrect because 4 is the sum of 2 and 6, not the difference. C is incorrect because -3/4 is not a real number.