Complementary angles.

A) The speed of the object is 6.71 units per second.

B) , the equation of the line is y = -3x + 9

C) The magnitude of the resultant force is 4.36N

a) The position of the  object at time t is given by:

(x, y) = (4, -3) + t  (-3 , 6)

v = (dx/ dt, dy/dt) = (-3, 6)

So the velocity vector is ( -3, 6).

For speed of the object, we need to find the magnitude of the velocity vector....

|v| = √((-3)^2 + 6^2)

= √(45)

= 3 √(5)

= 6.71 units

B

The equation given  as (x, y) = (4, -3) + t (-3, 6)

Written in form of y=mx + b we have:
y = -3 t + 9
Thus,

EQuation is y = -3x + 9

C)

The angle between the two forces can be calculated as 90 ° - 30° = 60°.
To find the magnitude of the resultant force using the law of cosines, we can use the formula.....

c ² = a ² + b ² - 2ab cos(C)
In this case, we have...

a = 3N

b = 5N

C = 60 degrees

c ² = 3 ² + 5 ² - 2(3)(5) cos(60)

c ² = 9 + 25 - 30(0.5)

c ² = 19

c = √(19)

c = 4.35889894354
c ≈ 4.36

So it is right to state that  the magnitude of the resultant force is 4.36N

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Answer:

Step-by-step explanation:

Let's use variables to represent the amount of money each person had at first.

Let x be the amount of money that Theriault Luigi had.

Then, according to the problem, Faber Kozlowski had 6 times as much money as Theriault Luigi, which means Faber Kozlowski had 6x dollars.

After Faber Kozlowski spent 1/3 of his money, he had 2/3 of his money left, which is (2/3)(6x) = 4x dollars.

After Theriault Luigi spent 4/5 of his money, he had 1/5 of his money left, which is (1/5)x dollars.

Together, they had a total of $1155 left, which means:

4x + (1/5)x = 1155

Multiplying both sides by 5 to eliminate the fraction gives:

20x + x = 5775

Combining like terms gives:

21x = 5775

Dividing both sides by 21 gives:

x = 275

Therefore, Theriault Luigi had $275 at first, and Faber Kozlowski had 6 times as much, which is $1650 at first.

So, the answer to (a) is $275 + $1650 = $1925.

For (b), Theriault Luigi spent 3/4 of his remaining money on a hoodie, which means he spent (3/4)(1/5)x = 3/20 of his original amount of money on the hoodie.

Therefore, Theriault Luigi spent 3/20 of his original amount of money on the hoodie.

Answer:

(a) $1925

(b) 15%

Step-by-step explanation:

(a)

Let f = original amount of money Faber had.

Let t = original amount of money Theriault had.

"Faber Kozlowski had 6 times as much money as Theriault Luigi. "

f = 6t

"After Faber Kozlowski spent 1/3 of his money"

He has now: 2/3 f

"and Theriault Luigi spent 4/5 of his money"

He has now: 1/5 t

"they had a total of $1155 left"

2/3 f + 1/5 t = 1155

f = 6t

2/3 f + 1/5 t = 1155

2/3 (6t) + 1/5 t = 1155

4.2t = 115

t = 1155/4.2

t = 275

f = 6t = 6(275) = 1650

f + t = 275 + 1650 = 1925

Part (a) answer: $1925

(b)

Original amount: t = 275

He first spent 4/5 of the original amount, so he had 1/5 left.

275/5 = 55

He spent 3/4 of $55 on the hoodie.

3/4 × $55 = $41.25

$41.25/$275 × 100% = 15%

Part (b) answer: 15%

Sample Response: I subtracted the highest and lowest numbers. The range for new cars was 31. The range for old cars was 75. The range for used cars was much bigger.

Answer:

Without access to specific data on monthly car sales, it is impossible to determine which type of car had the largest range in monthly sales. However, one possible method for finding this information would be to gather sales data for various car models across multiple months and compare the ranges of their sales figures. Alternatively, one could use industry reports or market analysis to determine which car types tend to have the largest fluctuations in sales from month to month.

Step-by-step explanation:

Without access to specific data on monthly car sales, it is impossible to determine which type of car had the largest range in monthly sales. However, one possible method for finding this information would be to gather sales data for various car models across multiple months and compare the ranges of their sales figures. Alternatively, one could use industry reports or market analysis to determine which car types tend to have the largest fluctuations in sales from month to month.

Start by putting the possible integers your friend can select

[tex]\text{S}=\{1,2,3,4,5,6,7,8,9,10\}[/tex]

Then, call the 2 possible events as A and B, and what are the possible integers in each event:

A = Be more than 6

B = The number is odd

 [tex]\text{A}=\{7,8,9,10\}[/tex]

 [tex]\text{B}=\{1,3,5,7,9\}[/tex]

The probability of the union of two events can be calculated as:

[tex]\text{P}(\text{A}\cup\text{B})=\text{P(A)}+\text{P(B)}-P(\text{A}\cap\text{B})[/tex]

Then,

         [tex]\text{P(A)}=\dfrac{\text{number of elements in A}}{\text{number of elements in S}}[/tex]

                             [tex]\text{P(A)}=\dfrac{4}{10}[/tex]

         [tex]\text{P(B)}=\dfrac{\text{number of elements in B}}{\text{number of elements in S}}[/tex]

                              [tex]\text{P(B)}=\dfrac{5}{10}[/tex]

[tex]\text{P(A}\cap\text{B})=\dfrac{\text{number of elements in A and B}}{\text{number of elements in S}}[/tex]

                        [tex]\text{P(A}\cap\text{B})=\dfrac{2}{10}[/tex]

Finally,

[tex]\text{P(A}\cup\text{B})=\dfrac{4}{10}+\dfrac{5}{10}- \dfrac{2}{10}[/tex]

          [tex]\text{P(A}\cup\text{B})= \dfrac{7}{10}[/tex]

Answer:

the probability that the number will be more than 6 or odd is: 7/10

Start by putting the possible integers your friend can select

[tex]\text{S}=\{1,2,3,4,5,6,7,8,9,10\}[/tex]

Then, call the 2 possible events as A and B, and what are the possible integers in each event:

A = Be more than 6

B = The number is odd

 [tex]\text{A}=\{7,8,9,10\}[/tex]

 [tex]\text{B}=\{1,3,5,7,9\}[/tex]

The probability of the union of two events can be calculated as:

[tex]\text{P}(\text{A}\cup\text{B})=\text{P(A)}+\text{P(B)}-P(\text{A}\cap\text{B})[/tex]

Then,

         [tex]\text{P(A)}=\dfrac{\text{number of elements in A}}{\text{number of elements in S}}[/tex]

                             [tex]\text{P(A)}=\dfrac{4}{10}[/tex]

         [tex]\text{P(B)}=\dfrac{\text{number of elements in B}}{\text{number of elements in S}}[/tex]

                              [tex]\text{P(B)}=\dfrac{5}{10}[/tex]

[tex]\text{P(A}\cap\text{B})=\dfrac{\text{number of elements in A and B}}{\text{number of elements in S}}[/tex]

                        [tex]\text{P(A}\cap\text{B})=\dfrac{2}{10}[/tex]

Finally,

[tex]\text{P(A}\cup\text{B})=\dfrac{4}{10}+\dfrac{5}{10}- \dfrac{2}{10}[/tex]

          [tex]\text{P(A}\cup\text{B})= \dfrac{7}{10}[/tex]

Answer:

the probability that the number will be more than 6 or odd is: 7/10

Answer:

r/p = 2

Step-by-step explanation:

The proportional relationship between the amount of raisins and the amount of peanuts can be expressed as:

r/p = k

where k is the constant of proportionality.

To find an equation with a constant of proportionality greater than 1, we simply need to choose a value of k that is greater than 1. For example, if we choose k = 2, the equation becomes:

r/p = 2

To check that this equation is correct, we can use the original ratio of 4 cups of raisins for every 6 cups of peanuts:

4/6 = 2/3

This confirms that the constant of proportionality is indeed 2, and that the equation for the relationship with a constant of proportionality greater than 1 is:

r/p = 2

That's correct. An observation is considered an outlier if it is more than 1.5 times the interquartile range (IQR) above the third quartile (Q3) or below the first quartile (Q1).

The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

In this case, the first quartile Q1 is 5 and the third quartile Q3 is 16. So the IQR is:

IQR = Q3 - Q1 = 16 - 5 = 11

An observation is considered an outlier if it is more than 1.5 times the IQR above Q3 or below Q1.

To find the upper outlier bound, we add 1.5 times the IQR to Q3:

Upper outlier bound = Q3 + 1.5(IQR) = 16 + 1.5(11) = 32.5

So any observation above 32.5 is considered an outlier.

To find the lower outlier bound, we subtract 1.5 times the IQR from Q1:

Lower outlier bound = Q1 - 1.5(IQR) = 5 - 1.5(11) = -11.5

So any observation below -11.5 is considered an outlier.

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Therefore the 95% confidence interval is,

(219.25, 534.75)

Here sample standard deviation is given but the sample size is large. Therefore we use z table to find the critical value.

Therefore the 90% confidence interval for the mean GPA for students at the University who are employed and who are not employed is,

(0.112, 0.308)

For the next problem,

We follow the same procedure as we have done in the first problem.

And here the data is different and we construct 95% confidence interval.

Therefore the 95% confidence interval is,

(219.25, 534.75)

And we interpret this confidence interval as,

We are 95% confident that the true difference in the mean daily caorie intake for teens who do eat fast food on a typical day and those who do not falls within this interval.

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The area of the rhombus by decomposition is

The rhombus is decomposed into simpler elements which are

Area of 2 triangles

= 2 * 1/2 * base * height

= 2 * 1/2 * x * h

= 2 * 1/2 * 3 * 4

= 12 square units

Area of a parallelogram

= base x height

= y * h

= 5 * 4

= 20 square units

Area of the rhombus

= 20 square units + 12 square units

= 32 square units

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Answer:b

Step-by-step explanation:

Answer:

Step-by-step explanation:

In the given figure, the triangle ABC is a right triangle with a right angle at C. We need to find the length of the side AB.

Using the Pythagorean theorem, we know that in a right triangle with sides of length a, b, and c (where c is the hypotenuse), we have c^2 = a^2 + b^2.

In this case, we have AC = 4 and BC = 3. So, applying the Pythagorean theorem, we get:

AB^2 = AC^2 + BC^2

AB^2 = 4^2 + 3^2

AB^2 = 16 + 9

AB^2 = 25

Therefore, AB = 5.

Answer:

D. The data has an outlier, therefore the range will be much greater than it would be without the outlier.

Step-by-step explanation:

The given data consists of six values, ranging from 187 to 1984. The numbers are not listed in order. There is an obvious outlier value, 1984, which is potentially impacting the spread and central tendencies of the data. However, without calculating the range or interquartile range, it is difficult to determine the extent of its impact.

Answer:

d got it right in edge.

Answer:

Step-by-step explanation:arcsin(1) = pi/2

The expressions B and C are equivalent to the given expression:

A logarithmic function is the inverse of an exponential function. In other words, if we have an exponential function that takes a base, b, and raises it to a power, x, to get a result, y, then the logarithmic function is the inverse of that process.

Simplify the expression using logarithmic property,

log m + log n = log (m.n)

Expression can be written as,

log₂(2) + log₂(8) = log₂(2x8)

                         = log₂ 16

simplify further,

log₂16 = log₂(2)⁴

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The equation sin(4x) = 1/2 has two solutions on the interval (0, 2π]: x = π/24 and x = 5π/24.

The equation sin(4x) = 1/2 has two solutions on the interval (0, 2π].

The first solution occurs when 4x = π/6, or x = π/24. This corresponds to an angle of π/24 radians, or 7.5°.

The second solution occurs when 4x = 5π/6, or x = 5π/24. This corresponds to an angle of 5π/24 radians, or 112.5°.

Therefore, the equation sin(4x) = 1/2 has two solutions on the interval (0, 2π]: x = π/24 and x = 5π/24.

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Answer:

To find the gross profit, we need to subtract the cost of the dolls sold from the gross sales revenue (after returns have been deducted).

First, we need to calculate the net sales revenue, which is the gross sales revenue minus the returns:

Net sales revenue = Gross sales revenue - Returns

Net sales revenue = ₱42,356 - ₱3,479

Net sales revenue = ₱38,877

Next, we can calculate the gross profit:

Gross profit = Net sales revenue - Cost of goods sold

Gross profit = ₱38,877 - ₱27,212

Gross profit = ₱11,665

Therefore, the gross profit from the sale of the dolls is ₱11,665.

[ rate 5 stars po and thanks if this helps u po! welcome! ]

Answer:

[tex] a_{old} = \frac{1}{2} (x)(4x) = 2 {x}^{2} [/tex]

[tex] a_{new} = \frac{1}{2} (x + 9)(4x + 2)[/tex]

[tex] = (x + 9)(2x + 1)[/tex]

[tex] = 2 {x}^{2} + 19x + 9[/tex]

Answer:

V = 16155.3 cubic feet

Step-by-step explanation:

The formula for volume (V) of a cone is

[tex]V=1/3\pi r^2h[/tex], where r is the radius and h in the height.

In the diagram, we're shown that the radius is 21 feet and the height is 35 feet.  Thus, we can plug everything into the formula including 3.14 instead of the entire pi number:

[tex]V=1/3(3.14)(21)^2(35)\\V=16155.3[/tex]

Answer:

i'm pretty sure its c, but if not then sorry

Step-by-step explanation:

Answer:

The equation of the line in the point-slope form is y+3=2/3(x−5)

Step-by-step explanation:

B

The value of the quotient of 4 1/2 ÷ 2/3 is,

⇒ 27/4

We have to given that;

The expression is,

⇒ 4 1/2 ÷ 2/3

Now, We can simplify as;

⇒ 4 1/2 ÷ 2/3

⇒ 9/2 × 3/2

⇒ 27/4

Thus, The value of the quotient of 4 1/2 ÷ 2/3 is,

⇒ 27/4

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The standard form equation of the ellipse as described in the task content is;

It follows from the task content that the standard form equation of the ellipse is to be determined.

Recall, the equation of an ellipse takes the form;

(x - h)²/a² + (y - k)²/b² = 1

where (h, k) is the center and a represents the distance of the center to each vertex on the major axis and b represents the distance from the center to each vertex on the minor axis.

Therefore, for the given scenario where center is at the origin; the equation of the ellipse is;

x²/4² + y²/(5/2)² = 1

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Answer:

Part A: ∠A ≈ 27.7 °

Part B: c ≈ 8.75

Step-by-step explanation:

Part A:

Use the Law of Cosines.

Cosθ =

[ a² + b² - c² ] / [ 2ab ]

Sub in all the information where θ is A.

A = cos⁻¹ { [10² + 7² - 5²] / [2×10×7]

A ≈ 27.7 ° (1 decimal place)

Part B:

Use the Law of Cosines, but instead the unknown is the side c.

Rearrange to isolate c:

c² = a² + b² - 2ab×cosθ

c = √(5² + 6² - 2×5×6×cos(105°))

c ≈ 8.75 (2 decimal places)

Answer:

Since the given quadratic function has zeros of -8 and 4, we know that the factors of the quadratic equation are (x + 8) and (x - 4).

The maximum of the function occurs at the midpoint between the zeros, which is (-8 + 4)/2 = -2. So, the x-coordinate of the vertex is -2.

We also know that the y-coordinate of the vertex is 18. So, the vertex of the quadratic function is (-2, 18).

Using the vertex form of the quadratic function, we can write:

F(x) = a(x + 2)^2 + 18

Since the function has zeros of -8 and 4, we can write:

F(x) = a(x + 8)(x - 4)

a(x + 2)^2 + 18 = a(x + 8)(x - 4)

ax^2 + 6ax - 128a - 576 = ax^2 + 16ax - 32a

10ax - 96a - 576 = 0

10a(x - 6) = 0

a = 0 or x = 6.

Since the vertex is a maximum and the coefficient of the x^2 term is positive, we know that a > 0. Therefore, we can conclude that x = 6 and a = 3.

Hence, the value of "a" in the function equation is 3.

The solution of the graph is approximately

The solution of a graph depends on the type of graph and the problem being represented. In general, a solution of a graph refers to a point or set of points that satisfy the conditions or constraints of the problem.

For the problem, the solution of the graph is the point where the two graphs intersects.

Deducing from the graph this is at point x approximately 4.455 the closest value to this point in the option is x = 71/16

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Part A: The Table for the data set above and it's title are attached accordingly.

Part B:

1) The shortest marker in the data set is Marker 1, which has a length of 4.00 inches.

2) The longest marker in the data set is Marker 14, which has a length of 6.75 inches.

3) The range of the data set is 2.75 inches, calculated by subtracting the shortest marker (4.00 inches) from the longest marker (6.75 inches).

4) To find the median, we need to arrange the data set in order from smallest to largest:

4.00, 4.25, 4.75, 5.00, 5.00, 5.25, 5.50, 5.50, 5.625, 6.00, 6.25, 6.25, 6.25, 6.50, 6.75

The median is the middle value, which is 5.50 inches.

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The length of the shorter leg is 6 centimeters, and the length of the longer leg is x + 14 = 20 centimeters.

Explanation:

Let x be the length of the shorter leg of the right triangle.

According to the problem, the longer leg is 14 centimeters longer than the shorter leg, so its length is x + 14.

We also know that the length of the hypotenuse of the right triangle is 26 centimeters.By the Pythagorean theorem, we have:

x^2 + (x + 14)^2 = 26^2

Simplifying the left side:

x^2 + x^2 + 28x + 196 = 676

Combining like terms:

2x^2 + 28x - 480 = 0

Dividing by 2:

x^2 + 14x - 240 = 0

Factoring:

(x + 20)(x - 6) = 0

Therefore, x = -20 or x = 6.

Since the length of a side cannot be negative, we reject x = -20 and conclude that x = 6.

So the length of the shorter leg is 6 centimeters, and the length of the longer leg is x + 14 = 20 centimeters.