In a survey of women in a certain country​ (ages 20−​29), the mean height was 63.7 inches with a standard deviation of 2.75 inches. Answer the following questions about the specified normal distribution.
​(a) What height represents the 95th ​percentile?
​(b) What height represents the first​ quartile?

Answers

Answer 1

a) The height that represents the 95th percentile is approximately 68.1 inches.

b) the height that represents the first quartile is approximately 65.5 inches.

Percentile and Quartile Heights

(a) To find the height that represents the 95th percentile, we need to find the z-score that corresponds to this percentile and then use that to find the corresponding height.

The z-score for the 95th percentile can be found using a standard normal distribution table or calculator. The area to the left of the z-score is 0.95, so the area to the right is 0.05. From the standard normal distribution table, the z-score corresponding to an area of 0.05 is approximately 1.645.

Now we can use the formula for z-scores to find the corresponding height:

z = (x - mu) / sigma

where x is the height we want to find, mu is the mean height (63.7 inches), sigma is the standard deviation (2.75 inches), and z is the z-score we just calculated (1.645).

Rearranging the formula, we get:

x = mu + z * sigma

Plugging in the values, we get:

x = 63.7 + 1.645 * 2.75 ≈ 68.1

Therefore, the height that represents the 95th percentile is approximately 68.1 inches.

(b) To find the height that represents the first quartile, we need to find the z-score that corresponds to the 25th percentile and then use that to find the corresponding height.

The z-score for the 25th percentile can be found using a standard normal distribution table or calculator. The area to the left of the z-score is 0.25, so the area to the right is 0.75. From the standard normal distribution table, the z-score corresponding to an area of 0.75 is approximately 0.67.

Using the formula for z-scores and the same values for mu and sigma, we get:

x = mu + z * sigma = 63.7 + 0.67 * 2.75 ≈ 65.5

Therefore, the height that represents the first quartile is approximately 65.5 inches.

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Related Questions

What is the fourth term of the sequence:

Write the number in the blank only.

a_1 = 5
a_n = 2a_n-1 + 3

Answers

The fourth term of the sequence with the definition of functions a₁ = 5 and aₙ = 2aₙ₋₁ + 3 is 61.

Calculating the fourth term of the sequence

Given the following definition of functions

a₁ = 5

aₙ = 2aₙ₋₁ + 3

To find the fourth term of the sequence defined by a₁ = 5aₙ = 2aₙ₋₁ + 3, we can use the recursive formula to generate each term one by one:

a₂ = 2a₁ + 3 = 2(5) + 3 = 13

a₃ = 2a₂ + 3 = 2(13) + 3 = 29

a₄ = 2a₃ + 3 = 2(29) + 3 = 61

Therefore, the fourth term of the sequence is 61.

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In the image below, arc AB has a measure of 32 degrees.

What is the measure of the inscribed angle that intercepts it? (Angle ACB)

Answers

Therefore , the solution of the given problem of angles comes out to be  the engraved angle ACB is 16 degrees in size.

An angle meaning is what?

Using Cartesian coordinates, the top and bottom walls divide the circular lines that make up a skew's ends. There is a chance that two poles will meet at a junction point. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by arranging two line beams in various ways at their extremities.

Here,

A circle's inscribed angle has a measure that is half that of the interrupted arc. As a result, the inscribed angle ACB intersecting arc AB with a measure of 32 degrees will have a measure of:

=> Angle ACB = 32 / (1/2)

=> ACB = 16 degree angle

As a result, the engraved angle ACB is 16 degrees in size.

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Mr. Ed earns $15.50 per hour. His regular hours are 40 hours per week, and he receives
time-and-a-half overtime. Find his total pay for a week in which he works 45 hours.

Answers

Answer:

For the first 40 hours that Mr. Ed works, he earns his regular rate of pay, which is $15.50 per hour. So, his regular pay for the week is:

40 hours x $15.50 per hour = $620

For the additional 5 hours he works, he earns overtime pay at a rate of time-and-a-half, which is 1.5 times his regular pay rate. So, his overtime pay for the week is:

5 hours x $15.50 per hour x 1.5 = $116.25

Therefore, Mr. Ed's total pay for the week in which he works 45 hours is:

$620 (regular pay) + $116.25 (overtime pay) = $736.25.

Sue deposited $1,500 into two different accounts.
- She deposited $600 into an account that pays 7.5% simple interest.
- She deposited $900 into an account that pays 6% compounded annually.
If Sue does not deposit additional money into the accounts and she doesn't withdraw any
money from the accounts, which is closest to the total balance she will have in the two
accounts at the end of 5 years?
F $2,029.40
G $2,005.68
H $529.40
J $1,995.00

Answers

The total balance that Sue will have in the two accounts after 5 years can be calculated as follows:

Balance of the first account with simple interest:

FV = P(1 + rt)

FV = $600(1 + 0.075 x 5)

FV = $825

Balance of the second account with compounded interest:

FV = P(1 + r)^n

FV = $900(1 + 0.06)^5

FV = $1,286.87

Total balance = $825 + $1,286.87

Total balance = $2,111.87

The closest answer choice to this amount is F) $2,029.40, which is only off by a small margin. Therefore, the answer is F) $2,029.40.


[tex]65y - 147y[/tex]
Math problem.
I need help. ​

Answers

Answer: 82y

Step-by-step explanation:

147y - 65y = 82y

Just perform simple subtraction

You went out to dinner and your meal $22.00. If you want to leave a 20% tip, how much will you pay total?

Answers

You will pay a total of $26.40 including the 20% tip.

To calculate the total amount including the 20% tip, you need to add 20% of the meal cost to the original meal cost:

A gratuity or a small amount of money given to someone for their service, such as a waiter or a hairdresser.

A piece of advice or a suggestion given to someone to help them do something better or more efficiently.

A pointed or tapered end of an object, such as the tip of a pen or a needle.

Tip amount = 20% of $22.00 = 0.2 x $22.00 = $4.40

Total amount including tip = $22.00 + $4.40 = $26.40

Therefore, you will pay a total of $26.40 including the 20% tip.

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Find the missing length indicated. * A) 12 C) 8 A OB D 16 24 36 B) 18 D) 15​

Answers

Answer:

Is D

Step-by-step explanation:

Find the derivative of f(x) 5/x + 7/x^2​

Answers

Answer:

[tex] \rm \: f(x) = \dfrac{5}{x} + \dfrac{7}{ {x}^{2} } [/tex]

Differentiating both sides with respect to x

[tex] \rm \dfrac{d}{dx} ( {f}( x) = \dfrac{d}{dx} \bigg( \dfrac{5}{x} + \dfrac{7}{ {x}^{2} } \bigg)[/tex]

Using u + v rule

[tex] \rm \: {f}^{ \prime} x = \dfrac{d}{dx} \bigg( \dfrac{5}{x} \bigg) + \dfrac{d}{dx} \bigg( \dfrac{7}{ {x}^{2} } \bigg)[/tex]

[tex] \rm \: {f}^{ \prime} x = 5. \dfrac{d}{dx} ( {x}^{ - 1} ) + 7. \dfrac{d}{dx} ( {x}^{ - 2} )[/tex]

[tex] \rm \: {f}^{ \prime} x = 5.( - 1. {x})^{ (- 1 - 1)} + 7.( - 2. {x})^{ - 2 - 1} [/tex]

[tex] \rm \: {f}^{ \prime} x = { - 5x}^{ - 2} { - 14x}^{ - 3} [/tex]

[tex] \rm \: {f}^{ \prime} x = - \dfrac{5}{ {x}^{2} } - \dfrac{14}{ {x}^{3} } [/tex]

[tex] \rm \: {f}^{ \prime} x = - \bigg(\dfrac{5}{ {x}^{2} } + \dfrac{14}{ {x}^{3} } \bigg)[/tex]

Hense The required Derivative is answered.

Derivative Formulae:-

[tex]\boxed{\begin{array}{c|c} \rm \: \underline{function}& \rm \underline{Derivative} \\ \\ \rm \dfrac{d}{dx} ({x}^{n}) \: \: \: \: \: \: \: \: \: \ & \rm nx^{n-1} \\ \\ \rm \: \dfrac{d}{dx}(constant) &0 \\ \\ \rm \dfrac{d}{dx}( \sin x )\: \: \: \: \: \: & \rm \cos x \\ \\ \rm \dfrac{d}{dx}( \cos x ) \: \: \: & \rm - \sin x \\ \\ \rm \dfrac{d}{dx}( \tan x ) & \rm \: { \sec}^{2}x \\ \\ \rm \dfrac{d}{dx}( \cot x ) & \rm- { \csc }^{2}x \\ \\ \rm \dfrac{d}{dx}( \sec x ) & \rm \sec x. \tan x \\ \\\rm \dfrac{d}{dx}( \csc x ) & \rm \: - \csc x. \cot x\\ \\ \rm \dfrac{d}{dx}(x) \: \: \: \: \: \: \: & 1 \end{array}}[/tex]

Please help. Deeply appreciated​

Answers

By using the Pythagorean theorem we know that the given triangle is not a right triangle.

What is the Pythagorean theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Pythagorean triples consist of the three positive numbers a, b, and c, where a2+b2 = c2.

The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular.

The smallest and most well-known triplets are (3,4,5).

So, we have the values already,

Now, calculate as follows:

3² + 4² = 6²

9 + 16 = 36

25 ≠ 36

Hence, the given triangle is not a right triangle.

Therefore, by using the Pythagorean theorem we know that the given triangle is not a right triangle.


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Rachel ran 3 miles when she was training for a race. How many feet did she run?
15,840 feet
5,280 feet
10,560 feet
14,840 feet

Answers

To convert miles to feet, we need to multiply the number of miles by the number of feet in one mile. There are 5,280 feet in one mile. So, to find out how many feet Rachel ran, we can multiply 3 miles by 5,280 feet/mile:

3 miles x 5,280 feet/mile = 15,840 feet

Therefore, Rachel ran 15,840 feet. Answer: 15,840 feet.

Need help pls
geometry
#23

Answers

Answer: I think its C

Answer:

Step-by-step explanation:

C is false. [tex]\angle BEC = \angle AED=126[/tex]   (vertically opposite).

The rest are correct.

View the photo and solve the probability

Answers

Therefore, the probability that at least one of the next six births is a girl is 1 - 0.033 = 0.967 (rounded to three decimal places).

What is Probability?

Probability is a measure of the likelihood that an event will occur. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

To calculate the probability of an event, you divide the number of ways that event can occur by the total number of possible outcomes. For example, if you flip a fair coin, there are two possible outcomes - heads or tails - and each has an equal probability of 0.5 (or 50%) of occurring.

Given by the question.

To find the probability that at least one of the next six births is a girl, we can find the probability that all six of them are boys and subtract it from 1.

The probability that one birth is a girl is 1 - 0.513 = 0.487.

The probability that all six births are boys is. [tex]0.513^{6}[/tex] = 0.033.

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The function S=m^(2)+6m+8 models the growth of book sales in m months, where S is an amount in thousands of dollars. In how many months do book sales reach $80,000 ?

Answers

Answer:

We are given the function S = m^2 + 6m + 8 which models the growth of book sales in m months, where S is an amount in thousands of dollars. We want to find in how many months book sales reach $80,000.

We can set up an equation as follows:

S = m^2 + 6m + 8 = 80

Subtracting 80 from both sides, we get:

m^2 + 6m - 72 = 0

We can factor this quadratic equation as:

(m + 12)(m - 6) = 0

This gives us two possible solutions:

m + 12 = 0 or m - 6 = 0

Solving for m in each case, we get:

m = -12 or m = 6

Since we are looking for a number of months, we can discard the negative solution.

Therefore, book sales reach $80,000 in 6 months.

So, the answer is: 6 months.

A pyramid has a height of 5 inches and a volume of 60 cubic inches. Which of the following figures could be the base for this pyramid?
Select 3 answers that apply.
A a hexagon with an area of 36 square inches
11 a right triangle with one leg 5 inches and the hypotenuse 13 inches
ca circle with radius 4 inches
Da 4-inch by 9-inch rectangle
a 3-inch by 4-inch rectangle
a square with side length 6 inches
E

Answers

The 3 correct answers of the figures that could be the base for the pyramid that has a height of 5 inches and a volume of 60 cubic inches are:

A hexagon with an area of 36 square inches (option A)A 4-inch by 9-inch rectangle (option D)A 3-inch by 4-inch rectangle (option E)

How do we calculate?

The formula to find the base of a pyramid given its height and volume,

Volume of pyramid = (1/3) * Base area * Height

Substituting in the given values, we have:

60 = (1/3) * Base area * 5

Base area = 36 square inches

In conclusion, any figure with a base area of 36 square inches could be the base for this pyramid.

The following figures have a base area of 36 square inches:

A hexagon with an area of 36 square inches A 4-inch by 9-inch rectangle A 3-inch by 4-inch rectangle

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You deposit $1000 each year into an account earning 8% compounded annually.How much will you have in the account in 10 years?

Answers

Answer:

If you deposit $1000 each year into an account earning 8% compounded annually, you will have $13,366.37 in the account in 10 years. Using the compound interest formula A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years, we can calculate the amount. Plugging in the values, we get A = 1000(1 + 0.08/1)^(1*10) = $2,159.15. Therefore, the total amount after 10 years will be $13,366.37, which is the sum of the principal and the interest earned.

Given,

Annual deposit = $1000

Rate = 8% compounded annually

Time(n) = 10 year

Amount = ?

As we know the formula ,

Amount = P(1+r/100)ⁿ

Amount = 1000(1+8/100)¹⁰

Amount = 1000(1+0.08)¹⁰

Amount =1000(1.08)¹⁰

Amount = 1000 × 2.15892

Amount = $2158.92

Hence, amount in 10year will be $2158.92

Suppose

cos()=3/4

.

Using the formulas



Determine



cos(

Answers

Answer:

Step-by-step explanation:

I'm sorry, but there seems to be some information missing from your question. Specifically, it is unclear what quantity or angle you want to determine the cosine of.

If you meant to ask for the value of the cosine of an angle given that its sine is 3/4, then we can use the Pythagorean identity to determine the cosine:

sin^2(x) + cos^2(x) = 1

Plugging in sin(x) = 3/4, we get:

(3/4)^2 + cos^2(x) = 1

Simplifying, we have:

9/16 + cos^2(x) = 1

Subtracting 9/16 from both sides, we get:

cos^2(x) = 7/16

Taking the square root of both sides, we get:

cos(x) = ±sqrt(7)/4

Since the sine is positive (3/4 is in the first quadrant), we know that the cosine must also be positive. Therefore:

cos(x) = sqrt(7)/4

I hope this helps! Let me know if you have any further questions.

The proof shows that ABCD is a rhombus. Which of the following is the
missing reason?
A. Reflective property
B. Symmetric property
C. Transitive property
D. Addition property

Answers

The correct answer is B. Symmetric property.

The symmetric property states that if a = b, then b = a. In the context of geometry, this property can be used to show that if one side of a figure is congruent to another side, then the second side is also congruent to the first. In the case of the given proof, it is possible that the symmetry of the figure is used to show that opposite sides of the rhombus are congruent.

The reflective property (A) is not typically used to prove that a figure is a rhombus, as it relates to the reflection of a figure across a line. The transitive property (C) and the addition property (D) are also unlikely to be used in this context, as they relate to the properties of equality and addition, respectively, rather than geometric properties of figures.

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In a restaurant, there are 5 managers, 15 servers, 10 cooks and 15 other personnel. If a person is selected at random, what is the probability that the person is either a manager or a cook?​

Answers

Answer:

0.33

Step-by-step explanation:

There are a total of 5 + 15 + 10 + 15 = 45 people in the restaurant.

The probability of selecting a manager or a cook is the sum of the probabilities of selecting a manager and selecting a cook, since these events are mutually exclusive (a person cannot be both a manager and a cook at the same time).

The probability of selecting a manager is 5/45, since there are 5 managers out of 45 people in total.

The probability of selecting a cook is 10/45, since there are 10 cooks out of 45 people in total.

Therefore, the probability of selecting either a manager or a cook is:

P(manager or cook) = P(manager) + P(cook)

P(manager or cook) = 5/45 + 10/45

P(manager or cook) = 15/45

P(manager or cook) = 1/3

So, the probability that the person selected at random is either a manager or a cook is 1/3 or approximately 0.333

leave a comment

Domain is now called the ____________ which means before a change

Answers

Answer:

Step-by-step explanation:

Domain is now called the "source" which means before a change or transformation. In mathematics, the term "source" is often used to refer to the set of all possible inputs or values that can be fed into a function or transformation, before any changes or transformations take place. The set of all possible outputs or resulting values from the function or transformation is called the "range" or "codomain".

I will mark you brainiest!

The value of M is
A) 14
B) 18
C) 20
D) 28

Answers

Answer:

I got 28

Step-by-step explanation:

use the formula k=y/x. 6/8=0.75

21/0.75=

-15>-11+w solve inequality for W

Answers

Answer:

Starting with:

-15 > -11 + w

Add 11 to both sides:

-15 + 11 > w

Simplifying:

-4 > w

Therefore, the solution for the inequality -15 > -11 + w, when solved for w, is:

w < -4

CAN SOMEONE HELP WITH THIS QUESTION?

Answers

Answer:

a. Since the half-life of the isotope is 8 hours, we know that the decay rate is exponential and we can use the formula:

A(t) = A0 * (1/2)^(t/8)

where A0 is the initial amount of the substance, t is the time elapsed, and A(t) is the amount of substance remaining after t hours.

Substituting the given values, we get:

A(t) = 7 * (1/2)^(t/8)

b. To find the rate at which the substance is decaying, we need to take the derivative of A(t) with respect to t:

A'(t) = -7/8 * (1/2)^(t/8) * ln(1/2)

Simplifying, we get:

A'(t) = -ln(2) * (7/8) * (1/2)^(t/8)

c. To find the rate of decay at 14 hours, we can plug in t=14 into the equation we found in part b:

A'(14) = -ln(2) * (7/8) * (1/2)^(14/8) ≈ -0.4346 grams per hour (rounded to four decimal places)

please please please help i’ll give brainlist

Answers

The scale factor of PQRS to JKLM is 4/5.

The scale factor of JKLM to PQRS is 5/4.

The value of w, x, and y are 20, 12.5, and 20 respectively.

The perimeter ratio is 4:5.

What is scale factor?

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor of PQRS to JKLM = 15/12

Scale factor of PQRS to JKLM = 5/4 or 1.25.

Scale factor of JKLM to PQRS = 12/15

Scale factor of JKLM to PQRS = 4/5 or 0.8.

For the value of w;

15/12 = 25/w

15w = 12 × 25

w = 20

For the value of x;

15/12 = x/10.

12x = 150

x = 12.5

For the value of y:

15/12 = y/16

12y = 15 × 16

y = 20

Perimeter ratio = 12 : 15 = 4:5

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A particle moves along the x-axis so that its velocity at any time t ≥ 0 is given by
v(t) = (2(pi) − 5)t − sin(t(pi))
A. Find the acceleration at any time t.
B. Find the minimum acceleration of the particle over the interval [0, 3].
C. Find the maximum velocity of the particle over the interval [0, 2].

Answers

Answer:

A. To find the acceleration, we need to take the derivative of the velocity function with respect to time:

a(t) = v'(t) = 2(pi) - cos(t(pi))

B. To find the minimum acceleration, we need to find the critical points of the acceleration function in the interval [0, 3].

a'(t) = sin(t(pi))

The critical points occur when sin(t(pi)) = 0, which means t = 0, 1, 2, 3. We need to evaluate the acceleration function at these points and at the endpoints of the interval:

a(0) = 2(pi) - cos(0) = 2(pi)

a(1) = 2(pi) - cos(pi) = pi + 2

a(2) = 2(pi) - cos(2pi) = 2(pi)

a(3) = 2(pi) - cos(3pi) = pi - 2

The minimum acceleration occurs at t = 3, with a minimum value of pi - 2.

C. To find the maximum velocity, we need to find the critical points of the velocity function in the interval [0, 2].

v'(t) = 2(pi) - cos(t(pi)) = 0

The critical points occur when cos(t(pi)) = 2(pi). We can solve for t as follows:

cos(t(pi)) = 2(pi)

t(pi) = arccos(2(pi))

t = arccos(2(pi))/pi ≈ 1.58

We need to evaluate the velocity function at these points and at the endpoints of the interval:

v(0) = -sin(0) = 0

v(1.58) ≈ 1.69

v(2) = (2(pi) - 5)(2) - sin(2(pi)) = 4(pi) - 10

The maximum velocity occurs at t = 1.58, with a maximum value of approximately 1.69.

Can someone please help me!!!

Answers

The graph of f(x) is a parabola that opens downward and has a vertex at (-3/2, 3/4), while the graph of g(x) is a parabola that opens upwards and has a vertex at (-1/2, 7/4). They both intersect at the point (-3/2, -5/4).

What is vertex?

Vertex is a mathematical term used to describe the point where two lines or line segments meet. It is the point of intersection for two or more lines. In a two-dimensional plane, a vertex is the point that marks the beginning and end of a line segment. In a three-dimensional plane, a vertex is the point of intersection of three or more lines. A vertex can also refer to a corner, such as the vertex of a triangle or a cube. In graph theory, a vertex is a node, or point, in a graph. Vertex can also refer to the highest point of a graph, such as the vertex of a parabola.

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Set up and solve a proportion for the following application problem. If 5 pounds of grass seed cover 355 square​ feet, how many pounds are needed for 6035 square​ feet?

Answers

Let x be the number of pounds needed for 6035 square feet.

We can set up a proportion between the pounds of grass seed and the square feet covered:

5 pounds / 355 square feet = x pounds / 6035 square feet

To solve for x, we can cross-multiply and simplify:

5 pounds * 6035 square feet = 355 square feet * x pounds

30175 = 355x

x = 30175 / 355

x ≈ 85.07

Therefore, approximately 85.07 pounds of grass seed are needed for 6035 square feet

How many total blocks does Ben need to walk north and east to get from his home to the playground and home again?

Answers

He needs to walk 13 blocks to his home and playground

Determina analítica y geométricamente el vector que inicia en el punto P(3,3) y termina en el punto
Q(-2,2), da el vector de igual magnitud y sentido contrario al vector anterior.

Answers

After answering the presented question, we can conclude that The vector expression of equal magnitude and opposite direction to  [tex]\vec{PQ}[/tex] is the same arrow but pointing in the opposite direction: QP vector

What is expression?

An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression.

Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form.

They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

To find the vector that starts at [tex]P[/tex]  [tex](3,3)[/tex] and ends at  [tex]Q(-2,2)[/tex] , we can subtract the coordinates of the starting point from the coordinates of the ending point:

[tex]$\vec{PQ} = \begin{pmatrix} -2 \ 2 \end{pmatrix} - \begin{pmatrix} 3 \ 3 \end{pmatrix} = \begin{pmatrix} -5 \ -1 \end{pmatrix}$[/tex]

So the vector that starts at P(3,3) and ends at  [tex]Q(-2,2) is $\vec{PQ} = \begin{pmatrix} -5 \ -1 \end{pmatrix}$.[/tex]

To find the vector of equal magnitude and opposite sense to  , we can simply multiply   [tex]$\vec{PQ}$[/tex] by  [tex]-1:[/tex]

[tex]$-\vec{PQ} = -1 \begin{pmatrix} -5 \ -1 \end{pmatrix} = \begin{pmatrix} 5 \ 1 \end{pmatrix}$[/tex]

So the vector of equal magnitude and opposite sense to [tex]$\vec{PQ}$[/tex]   is [tex]$\begin{pmatrix} 5 \ 1 \end{pmatrix}$.[/tex]

Geometrically, we can represent the vectors graphic[tex]$\vec{PQ}$[/tex]ally by drawing them as directed line segments on a coordinate plane. The vector that starts at [tex]P(3,3)[/tex] and ends at [tex]Q(-2,2)[/tex] is represented by the line segment connecting [tex]P[/tex] to  [tex]Q[/tex].

Therefore, The vector of equal magnitude and opposite sense to  [tex]$\vec{PQ}$[/tex][tex]$\vec{PQ}$[/tex] is represented by the line segment starting at  [tex]Q[/tex] and ending at the point R, which is  [tex]5[/tex] units to the right and [tex]1[/tex] unit up from  [tex]Q[/tex].

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I need help with a problem on my test.

Write an exponential function to model the situation. Tell what each variable represents. A price of $115 increases 9% each month.


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Answer: 1050$

Step-by-step explanation:

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A bank account gathers compound interest at a rate of 5% each year. Another bank account gathers the same amount of money in interest by the end of each year, but gathers compound interest each month. If Abraham puts £4300 into the account which gathers interest each month, how much money would be in his account after 2 years and 5 months? Give your answer in pounds to the nearest 1p.​

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Answer:

$6235 1

' 1 . ' 8

Answer:

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