A vector with magnitude 7 points in a direction 10 degrees counterclockwise from the positive x axis.
Write the vector in component form.
Vector
Give each value accurate to at least 1 decimal place

A reflection over the x-axis.

A vertical stretch by 11 units.

A translation left by 5 units.

A translation up 4 units.

The reflection of a function across the x- or y-axis is another transformation that may be used. In contrast to a horizontal reflection, which reflects a graph horizontally across the y-axis, a vertical reflection reflects a graph vertically across the x-axis.

An illustration of a transformation is a reflection, which flips a shape (referred to as the pre image) over a line (referred to as the line of reflection) to produce a new shape (called the image). Imagine what would happen if you flipped the form over the line in order to graph a reflection.

Here, f(x) = 1/x²

Now, reflect the graph over the x-axis to obtain the graph of:

f(x) = -1/x²

Now, stretch the graph vertically by 11 units to get the graph of:

f(x) = -11/x²

Again, translate the graph left by 5 units to obtain the graph of:

f(x) = - 11 / (x + 5)²

Now, translate the graph up by 4 units to obtain the graph of:

f(x) = 4 - {11 / (x + 5)²}

Hence,

A reflection over the x-axis. A vertical stretch by 11 units. A translation left by 5 units. A translation up 4 units.

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4 x 9 is a multiplication problem, which means 4 is being multiplied by 9. This can also be written as 4 x 9 = 36. 4 multiplied by 9 is equal to 36 because 4 is being added to itself 9 times, resulting in 36.

4 x 9 is a multiplication problem which means we are multiplying 4 and 9 together. This can also be written as 4 x 9 = 36. When multiplying two numbers together, you are adding the first number to itself the second number of times. In this case, 4 multiplied by 9 is equal to 36 because we are adding 4 to itself 9 times: 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 36. This can also be written as 4 x 9 = 36, which means that 4 times 9 equals 36.

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The length of the rectangle given the area and width is 21 inches

Area of the rectangle = 357 square inches

Width of the rectangle = 17 inches

Length of the rectangle= l

Area of a rectangle = Length × width

357 = l × 17

357 = 17l

divide both sides by 17

l = 357 / 17

l = 21 inches

In conclusion, 21 inches is the length of the rectangle.

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The blood platelet count is an illustration of normal distribution Approximately 95% of the data lies within 2 standard deviations of the mean. There are approximately 99.7% of women with platelet count between 65.2 and 431.8

The given parameters are:

μ = 248.5

[tex]\sigma = 61.1\\[/tex]

(a) The percentage within 2 standard deviation of mean or between 126.3 and 370.7

Start by calculating the z-score, when x = 126.3 and x = 370.7

[tex]Z = \frac{(x-u)}{\sigma}[/tex]

So, we have:

x = -2

Also,

x = 2

The empirical rule states that:

Approximately 95% of the data lies within 2 standard deviations of the mean.

Hence, there are approximately 95% of women with platelet count within 2 standard deviations of the mean.

(b) The percentage with platelet count between 65.2 and 431.8

Start by calculating the z-score, when x = 65.2 and x = 431.8

So, we have:

Z =-3

Also:

Z = 3

The empirical rule states that:

Approximately 99.7% of the data lies within 3 standard deviations of the mean.

Hence, there are approximately 99.7% of women with platelet count between 65.2 and 431.8

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The solution is, The value of N is 12 sq cm.

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

here, we have,

1. Find the greatest common factor of 35 and 42 to find the length (horizontal). The GCF is 7.

2. The horizontal length of the 35 and 42 sq cm is 7, and the heights are 5 and 6 respectively.

3. Moving on tot he 10 sq cm rectangle,

since the height of just that one rectangle is  and 10/5 is 2, the horizontal length is 2.

4. For n, the horizontal length is 2 and the height is 6.

2 X 6 is 12 sq cm.

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The area of the polygon is  7.5 square units

Note that the polygon given in the diagram takes the shape of a kite.

The properties of a kite are given as;

The formula for area of a kite is;

Area = pq/2

Area = 3(5)/2

Area = 15/2

Divide the values

Area = 7.5 square units.

Thus, the value is  7.5 square units

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Answer:

Value of account after t years is
[tex]A = \boxed{190( 1.0178)^{4t}}[/tex]

Percentage of growth per year

CAGR = [tex]\boxed{7.31\%}[/tex]

Step-by-step explanation:

The generalized equation for the accrued value of an amount P(the principal) deposited at i% annual interest compounded n times a year for t years is

[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}[/tex]

where r = i/100, the interest rate expressed as a decimal

Given P = $190
i = 7.1% ==> r = 7.1/100 = 0.071

Since the interest is compounded quarterly and there are 4 quarters in a year, the interest is compounded 4 times a year so n = 4

[tex]A = 190 \left(1 + \dfrac{0.071}{4}\right)^{4t}[/tex]

[tex]A = 190\left(1 + 0.01775\right)^{4t}}\\\\A = 190( 1.01775)^{4t}[/tex]\

Rounding the annual growth rate to 4 decimal places gives

[tex]A = P(1.0178)^{4t}[/tex]

In one year, the investment of $190 will grow to
[tex]A = 190(1.0178)^{4}[/tex]

[tex]A = $203.89[/tex]

Compound Annual Growth = = 203.89 - 190 = $13.89

Compound Annual Growth Rage(CAGR) = $13.89/$190 = 0.073105

As a percentage, CAGR Percent = 0.073105 x 100 = 7.3105% or rounded to nearest hundredth it would be 7.31%

The equation is y = (-0.5)x + 34 and it will take 16 days for the water level to be 26 feet.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let the number of days = x, and the water level = y.

Given that,

Water level of river = 34 ft (initial value/y-intercept)

Rate of change = -0.5 ft per day (slope)

The equation of the line is given as:

y = mx + c

where, m is the slope

c is the y-intercept.

Substituting the values we have:

y = (-0.5)x + 34

The number of days in which the water level will reduce to 26 ft is:

26 = (-0.5)x + 34

26 - 34 = -0.5x

x = 16 days.

Hence, it will take 16 days for the water level to be 26 feet.

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The length of the rectangular classroom will be 8 inches on the scale drawing.

What is a rectangle defined as?

Rectangles are four-sided polygons having internal angles of 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from the square in that its opposite sides are of equal length.

If one side of a rectangle is 20 cm long, the other side must be 20 cm long as well.

Two diagonals cross form a rectangle. Both diagonals are the same length.

P = 2 (Length + Width) defines the perimeter.

Rectangle Area=Length*Breadth

Now,

As total length of room =36 feet

and 9 feet = 2 inch on drawing scale

then length of classroom on  drawing scale is = 36/9*2

=8 inch

Hence,

            The length of the rectangular classroom will be 8 inches on the scale drawing.

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The value of the equation is 35 = 15 + 2y , where y is the number of years and the y = 10 years

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the initial height of the weeping willow be = 15 feet

Let the final height of the weeping willow be = 35 feet

The height in feet the weeping willow grows each year = 24 inches = 2 feet

Let the number of years be = y

On simplifying the equation , we get

35 = 15 + 2y

Subtracting 15 on both sides of the equation , we get

2y = 20

Divide by 2 on both sides of the equation , we get

y = 10 years

Hence , the equation is y = 10 years

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The table is

x = 0            5         8            10           30.

y = 300       250    220        200         0

The height of the airplane decreases with time. Thus airplane landed in the time interval.

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.

Given equation is y = -10x + 300.

Putting x = 0 in the equation:

y = -10×0 + 300

y = 300

Putting x = 5 in the equation:

y = -10×5 + 300

y = -50 + 300

y = 250

Putting x = 8 in the equation:

y = -10×8 + 300

y = -80 + 300

y = 220

Putting x = 10 in the equation:

y = -10×10 + 300

y = -100 + 300

y = 200

Putting x = 30 in the equation:

y = -10×30 + 300

y = -300 + 300

y = 0

The height of the airplane after 5 minutes is 250 feet.

The height of the airplane after 30 minutes is 0 feet.

The altitude of the airplane decreases with time. The altitude of the airplane decreases with time. The airplane is landing in the time interval.

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In mathematics, a line is a set of points that extend indefinitely in two directions.

Points on the line: These are points that lie exactly on the line. They are equidistant from the two endpoints of the line and are considered to be part of the line itself.

Points above the line: Points that are vertically above the line are referred to as points above the line. These points are located higher than the line and have a greater y-coordinate than any point on the line.

Points below the line: Points that are vertically below the line are referred to as points below the line. These points are located lower than the line and have a smaller y-coordinate than any point on the line.

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Option C. the least squares method is a procedure for using sample data to find the estimated regression equation.

The procedure for using sample data to find the estimated regression equation is called the least squares method. This method involves finding the line that minimizes the sum of the squared vertical distances between the observed data points and the line. The estimated regression equation is used to predict the value of the dependent variable based on the value of the independent variable. This method is commonly used in regression analysis to model the relationship between two variables. It is a useful tool for making predictions and understanding the relationship between variables.

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Raoul and Sven are at an angle of = cos1 (cos a cos 43° + sin a sin 43°). The sled is being moved by a force with a magnitude of [(105 cos a + 122 cos 43°)2 + (105 sin a + 122 sin 43°)2].

The outcome of two vectors is determined by the parallelogram law of vector addition. The resultant vector, R=(A2+B2+2ABcos), follows this law. A and B are the two vectors in this situation, and is the angle between them.

The component in the direction of the sled's path is:

105 cos a

The component perpendicular to the path is:

105 sin a

Similar to this, Sven's force may be broken down into two parts: one that is parallel to the sled's course and one that is perpendicular to it. The element pointing in the sled's direction is:

122 cos 43°

The component perpendicular to the path is:

122 sin 43°

The net force on the sled is the vector sum of these four components:

Net force = (105 cos a + 122 cos 43°) i + (105 sin a + 122 sin 43°) j

The magnitude of the net force is:

|Net force| = √[(105 cos a + 122 cos 43°)² + (105 sin a + 122 sin 43°)²]

To find the angle between Raoul and Sven, we can use the dot product of their forces:

Raoul · Sven = |Raoul| |Sven| cos θ

We can solve for θ as follows:

cos θ = (Raoul · Sven) / (|Raoul| |Sven|)

cos θ = [(105)(122) cos a cos 43° + (105)(122) sin a sin 43°] / (105)(122)

cos θ = cos a cos 43° + sin a sin 43°

θ = cos⁻¹(cos a cos 43° + sin a sin 43°)

a. The angle between Raoul and Sven is θ = cos⁻¹(cos a cos 43° + sin a sin 43°).

b. The magnitude of the force moving the sled is |Net force| = √[(105 cos a + 122 cos 43°)² + (105 sin a + 122 sin 43°)²].

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5050 flips expect to make before running out of coins .

Let's approach this problem using the concept of geometric distribution.

The probability of getting heads on any given coin flip is 1/2, assuming a fair coin.

So the probability of getting tails on a given flip is also 1/2.

The number of flips it takes to get the first head is a geometric distribution with a probability of success p = 1/2.

The expected number of flips until the first head appears is 1/p = 2 flips.

After the first head appears, there will be 99 coins left to flip.

The expected number of flips until the next head appears is still 2, since the probability of getting heads on any given flip is still 1/2.

So the expected number of flips until the second head appears (and the number of coins remaining drops to 98) is 2+1 = 3 flips.

Similarly, the expected number of flips until the third head appears (and the number of coins remaining drops to 97) is 2+1+1 = 4 flips.

We can generalize this pattern: after k heads have been obtained, the expected number of additional flips until the next head appears (and the number of coins remaining drops to 100-k) is k+1 flips.

Using this formula, we can calculate the expected number of flips to obtain all 100 heads:

E(number of flips) = (2 + 3 + 4 + ... + 101)

= (1 + 2 + 3 + ... + 100) + 100

= (100 x 101 / 2) + 100

= 5050

Therefore, we expect to make 5050 flips before running out of coins to flip and obtaining all 100 heads.

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Answer:

Step-by-step explanation:

According to question

    [tex]4ax^{2} +9x+c < 0[/tex]

This means that the coefficient of the highest degree term

([tex]4ax^{2}[/tex]) must be positive

And the constant term (c) must be negative

So, the according to condition

   4a must be positive,

    which means a must be positive

And, c must be negative

          [tex]a > 0\\c < 0[/tex]

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1. In his newspaper, Peter Zenger published articles criticizing the Governor's use of arbitrary power

2. Because it was against the law to criticize the king or his appointees, the Attorney General accused Peter Zenger of committing" libel.

3. Hamilton believed Zenger was not guilty of this charge because in Zenger's newspaper articles the "truth is told

4. Hamilton felt that more than just Peter Zenger was on trial. He felt that the larger concept of American" liberty was at stake.

Hamilton and Morris agreed that the trial of Peter Zenger was important for American freedom and the defense of liberty.

As for the question about television and newspaper reporters, it is a matter of opinion. Some people believe that the freedom of the press is an important part of democracy, and that reporters should be able to criticize anyone in power, including the president. Others believe that criticism of the president should be limited to protect the dignity and stability of the office. In either case, it is important to strike a balance between free speech and responsible journalism.

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The total number of red blood cells produced by human body in each minute is given by [ 1.2 × 10^8​ ] red blood cells

Number of red blood cells produced by human body = 4. 8 × 10^6

Time taken by human body to produce 4. 8 × 10^6 red blood cells

= 4×10^(−2)​ minute

Number of red blood cells produced by human body in one minute are :

4 × 10^(−2)​ minute = 4. 8 × 10^6 red blood cells

⇒ 1 minute =  [ 4. 8 × 10^6 / 4 × 10^(−2)​ ] red blood cells

⇒ 1 minute =  [ 1.2 × 10^( 6 - (−2) )​ ] red blood cells

⇒ 1 minute =  [ 1.2 × 10^( 6 + 2) )​ ] red blood cells

⇒ 1 minute =  [ 1.2 × 10^8​ ] red blood cells

Therefore, total number of red blood cells produced by human body in one minute is equal to [ 1.2 × 10^8​ ] red blood cells.

The above question is incomplete, the complete question is:

The human body produces about4. 8×10^6​ red blood cells in 4×10^(−2)​ minute. How many red blood cells does the body produce each minute? Write your answer in scientific notation and in standard form.

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The m values that allow the quadratic equation [tex]x^2 + mx + 4[/tex] to have two independent real roots are m in the open range (-∞ , -4) (4 , ∞). This may be expressed in interval notation as:

m ∈ (-∞, -4) ∪ (4, ∞).

The quadratic formula tells us that the quadratic equation's roots

[tex]x^2 + mx + 4 = 0[/tex]

are provided by:

[tex]x = (-m[/tex] ± [tex]sqrt(m^2 - 16))/2[/tex]

The discriminant [tex](m^2- 16)[/tex]must be positive, i.e., [tex]m^2[/tex] > 16, for the quadratic to have two separate real roots. As a result, we have two instances to consider:

Case 1: m > 4. Because [tex](-m + sqrt(m^2 - 16)/2[/tex]and[tex](-m - sqrt(m^2 - 16)/2[/tex]are both real and unique in this case, the quadratic has two separate real roots.

Case 2: m < -4. In this situation, [tex](-m + sqrt(m^2 - 16)/2[/tex] is negative, whereas[tex](-m - sqrt(m^2 - 16)/2[/tex] is positive, indicating that the quadratic has two separate real roots.

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Answer:

x = 4

Step-by-step explanation:

Move the x to the left-hand side and change its sign

2x - x = 9 - 5

x = 9 - 5

Answer:

x=4

Step-by-step explanation:

Subtract 1x from both sides

Subtract 5 from both sides to isolate the variable

x=4

Answer: this app should be freer

Step-by-step explanation:

After 5 hours of snow falling, Kaj would have 9.5 inches of snow on her lawn.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

After 3 hours of snow falling, Kaj would have:

7 + 0.5(3) = 8.5 inches of snow on her lawn.

To find how much snow Kaj would have on her lawn after t hours of snow falling, we can use the following formula:

S = 7 + 0.5t

where S is the amount of snow on Kaj's lawn in inches and t is the time in hours since the beginning of the snowstorm.

For example, if we wanted to find how much snow Kaj would have on her lawn after 5 hours of snow falling, we could substitute t = 5 into the formula:

S = 7 + 0.5(5) = 9.5

Therefore, After 5 hours of snow falling, Kaj would have 9.5 inches of snow on her lawn.

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The required answers are

a) b = -4

b) x = 23.45

c) p = 201

The distributive property implies that multiplying a number by the sum of two or more addends yields the same result as dividing the multiplier, multiplying each addend individually, and combining the products . It can be given as,

a (b+c) = d

[tex](a*b) + (a*c) = d[/tex]

Now in the given question,

a) −1/2(b−6)= 5

by distributive property , we have

[tex](\frac{-1}{2} *b)-(\frac{-1}{2}*6 )=5\\\frac{-1}{2}b+3=5\\\frac{-1}{2}b=2\\b=-4[/tex]

b) 0.4(x−0.45)= 9.2

by distributive property , we have

0.4x - 0.4(0.45) =9.2

0.4x -0.18 = 9.2

0.4x = 9.38

x = 23.45

c) −4(p−212)=44

by distributive property , we have

-4p +4 (212) = 44

-4p + 848 =44

-4p = 44 - 848

-4p = -804

p = 201

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Answer:

The distance to the nearest exit door is at most 100 feet can be written as an inequality as:

d ≤ 100

Step-by-step explanation:

2y+57=180

2y=180-57

2y=123

y=123/2=61.5°

y=61.5

Answer:

61.5

Step-by-step explanation:

As the lines are parallel you can use the alternate angle rule.

So within the triangle you have 57 + x + x ( y is equal to the other angle because the lines are the same length and angle highlighted by the double lines )

And so...

180 - 57 = 123

123/2 = 61.5

a. It should be noted that c(10) represents the number of cars sold in the 10th month.

b. c(16) - c(8) represents the number of cars sold in the 16th month minus the number of cars sold in the 8th month. This difference could represent the net change in the number of cars sold between those two months.

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. The process of evaluating a function is typically straightforward when we have the function in the form of a formula.

In this case, c(10) represents the number of cars sold in the 10th month.

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The probability of having more than the expected number of failures (i.e., at least five failures) in a set of nine Bernoulli trials is 0.2461, assuming that the probability of failure is 0.5.

In the field of probability, it is essential to understand the expected number of successes or failures in a given set of trials. However, what happens when we observe more or fewer outcomes than expected? In this scenario, we need to calculate the probability of observing a specific number of failures in a set of Bernoulli trials.

Let's assume that the probability of failure is denoted by "p," and the probability of success is denoted by "q." Thus, the expected number of failures in nine Bernoulli trials is given by:

E(X) = np

where n is the number of trials, and p is the probability of failure. In this case, n = 9, and we need to determine the probability of having more than the expected number of failures. This means we are interested in finding the probability of observing at least five failures since the expected number of failures is given by:

E(X) = 9p

If we assume that the probability of failure is 0.5 (i.e., p = 0.5), then the expected number of failures is 4.5 (i.e., E(X) = 9 * 0.5 = 4.5). Therefore, we are interested in finding the probability of observing at least five failures in nine Bernoulli trials.

To calculate this probability, we need to use the binomial distribution formula, which is given by:

[tex]P(X = k) = (^n_k) \times p^k \times q^{n-k}[/tex]

where P(X = k) is the probability of observing k failures in n trials, (n choose k) is the binomial coefficient, which is calculated as n! / (k! (n-k)!), p is the probability of failure, q is the probability of success (i.e., q = 1 - p), and k is the number of failures we are interested in observing.

Using this formula, we can calculate the probability of observing at least five failures in nine Bernoulli trials as follows:

P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)

= (9 choose 5) x 0.5⁵ x 0.5⁴ + (9 choose 6) x 0.5⁶ x 0.5³ + (9 choose 7) x 0.5⁷ x 0.5² + (9 choose 8) x 0.5⁸ x 0.5¹ + (9 choose 9) x 0.5⁹ x 0.5⁰

= 0.2461

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The set builder form of the set b = {1/10, 1/00, 1/1000} is b = {x | x = 1/10ⁿ, where n is a positive integer}

In mathematics, set builder notation is a concise way of describing a set using a rule or a formula.

Let's explore how we can use set builder notation to write the set b={1/10, 1/100, 1/1000}.

To begin, we need to identify the common property that these elements share. In this case, we can observe that each element is a rational number with a power of ten as the denominator. So, we can write the set b as follows:

b = {x | x = 1/10ⁿ, where n is a positive integer}

In this notation, the vertical bar represents "such that" and separates the description of the element from the rule that defines the set. The letter x is a variable that represents any element that satisfies the rule. We use the power of ten as a common property to describe the set b.

In this set builder form, we can see that b is a set of elements that can be expressed as 1/10 to the power of a positive integer. We can also use set builder notation to define other sets with different properties, such as sets of even numbers or sets of prime numbers.

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