Calculate the length and direction of v = (2,3,1) and show that v= |v|u, where u is the direction of v. =

Answer:

the banana cost per kg is 6 and for orange it is 4

Step-by-step explanation:

The computation is shown below:

Let us assume the banana be x

And, the oranges be y

Now according to the question

There would be two equations

32x + 86y = 536.......(1)

96x + 52y = 784.........(2)

Now multiply by 3 in equation 1

96x + 258y = 1,608

96x + 52y = 784

258y - 52y = 1608 - 784

206y = 824

y = 4

And, the x would be

32x + 86(4) = 536

32x + 344 = 536

x = 6

Hence, the banana cost per kg is 6 and for orange it is 4

a. Account A has a 4% APR compounded monthly. Determine the percent change per compounding period.

i. Decimal form: 0.04/12 = 0.0033 or 0.33%

ii. Percentage form: 0.33%

b. Account B has a 6. 8% APR compounded quarterly. Determine the percent change per compounding period.

i. Decimal form: 0.068/4 = 0.017 or 1.7%

ii. Percentage form: 1.7%

c. Account A has a 3. 5% APR compounded daily. Determine the percent change per compounding period.

i. Decimal form: 0.035/365 = 0.0000957 or 0.0957%

ii. Percentage form: 0.0957%

Answer:

slope m=--3/-2=-3/2 is required slope

Answer:

m = -3, b = -2

Step-by-step explanation:

The equation is written in the form of slope-intercept, where m = slope and b = y-intercept.

The slope is the number before x. For the equation y = -3x - 2, it's -3.

The y-intercept is the constant. For the equation y = -3x - 2, it's -2.

Hence, m = -3, and b = -2.

\(\rule{350}{4}\)

\(\frak{-Dream-}\)

Answer: D. 20ft

Step-by-step explanation:

Answer:

The answer would be 20 feet.

Step-by-step explanation:

This is because square feet is referring to the area. And since the area = L * W and since the sides of the square are identical. It would be 20*20=400.

a) 7 in

b) 72 steps

Step-by-step explanation:

Angle of elevation formula:  

where  is the angle of elevation, y is the vertical distance (rise) and x is the horizontal distance.

a)  Given:

b)  Given:

1st floor = 21 feet

2nd floor = 21 feet

⇒ Total height = 21 + 21 = 42 feet

1 foot = 12 inches

⇒ 42 feet = 42 x 12 = 504 inches

Using vertical rise of 7 in per step found in part (a):

Number of steps = 504 ÷ 7 = 72

Increased accuracy

Using unrounded vertical rise of 12tan(32):

Number of steps = 504 ÷ 12tan(32) = 67 steps to the nearest step

The representation which is most appropriate for showing the change in the average hourly wage is: A. scatter plot with the title average hourly wage and the x axis labeled years since 2016 and the y axis labeled hourly wage in dollars, with points at 0 comma 9, 1 comma 9 and a half, 2 comma 10, 3 comma 11, 4 comma 12, 5 comma 13, and 6 comma 14.

In this scenario, the years would be plotted on the x-axis (x-coordinate) of the scatter plot while the hourly wage would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the years and hourly wage, an equation for the line of best fit is given by:

y = 0.8571x + 8.6429

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The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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Answer:

10g+6 is the answer

Step-by-step explanation:

Answer:

B. y = -x – 1

Step-by-step explanation:

calculate slope  =

y2-y1   =  -5- (-2)  =  -3

x2-x1   =   4 - 1     =   3

m (slope) = -3/3 =  -1

using points (1,-2) for calculating y-intercept:

y = mx + b

-2 = -1(1) + b

-2 = -1 + b

-1 = b

b = -1

answer is B   y=  -x - 1

The  surface area of the cylinder is 835.24 square centimeters

The given parameters are:

Radius= 7cm

Height= 12cm

The surface area is calculated using:

\(A = 2\pi r(h + r)\)

So, we have:

A = 2 * 3.14 * 7 * (12 + 7)

Evaluate the expression

A = 835.24

Hence, the surface area of the cylinder is 835.24 square centimeters

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If the radius of a cylinder is 7 cm and the height is 12 cm. Find the S.A (Surface Area)of a cylinder .

In this question we are provided with the radius of a cylinder that is 7 cm and it is also given that the height of the cylinder is 12 cm. We are asked to calculate the Surface Area of the cylinder.

We know,

\( \small\boxed{ \sf{ Surface \: area_{(cylinder)} = 2πr × (h + r)}}\)

Substituting the values we get

\( \small\sf{ Surface \: area_{(cylinder)} = 2 × 3.14 × 7 × (12 + 7)}\)

\( \small\rm{ Surface \: area_{(cylinder)} = 2 × 3.14 × 7 × 19}\)

\( \small\rm{ Surface \: area_{(cylinder)} = 6.28 × 133}\)

\( \small\rm{Surface \: area_{(cylinder)} = 835.24 \: {cm}^{2} } \)

Answer: 13

Explanation: To find the degree of a monomial, we need to take

the sum of the exponents of all the variables in the monomial.

So the degree of this monomial is 7 + 6 or 13.

So the degree of this monomial is 13.

Answer:

You did not write the options, but let's solve it in a general way.

f(x) and g(x) are quadratic functions, this means that:

f(x) = a*x^2 + b*x + c

g(x) = d*x^2 + e*x + f

now, (g + f)(x) is a linear function that goes trough the points (-3, 4), (0,1 ) and (1,0)

(g + f)(x) = s*x + k

We can find the slope of this linear function as:

S = (y2 - y1)/(x2 - x1)

i will use the first two points.

S = (1 - 4)/(0 - (-3) = -3/3 = -1

so we have: ( f + h)(x) = -1*x + k

and we can find k using one of the points, for example (0, 1)

1 = -1*0 + k

b = 1.

so we have: (f + g)(x) = -1*x + 1.

Now, (f+g)(x) = (a + d)*x^2 + (b + e)*x + (c + f) = -1*x + 1.

So we must have that:

a = -d

b + e = -1

c + f = 1.

Answer:

A. The leading coefficients of f(x) and g(x) are opposites.Step-by-step explanation:

Based on the outcomes, the estimated probability of the spinner landing on blue which has equal sections colored blue, yellow, and red is 0.22 or 22%.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

This table shows outcomes of a spinner with 3 equal sections colored blue, yellow, and red.

The total number of outcome is 100. The total number of favorable outcome to land blue is 22.

Thus, the estimated probability of the spinner landing on blue has to be found out is,

\(P=\dfrac{22}{100}\\P=0.22\\P=22\%\)

Hence, based on the outcomes, the estimated probability of the spinner landing on blue which has equal sections colored blue, yellow, and red is 0.22 or 22%.

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a) The population is all of the flights belonging to the particular airline. It's not all flights in general because the airline does not have control over a rival company's flight schedule.

------------------

b) The sample is the 5 airlines the company selected. Ideally the sample should represent the population as much as possible. The larger the sample, the more representative the sample is.

------------------

c) No, the sample is likely not representative because one day of flight does not represent the entire lifetime of all flights done so far for that company. This particular day could have been a very good day with good weather, which may explain why the 5 flights were all on time.

------------------

d) It would be better for the company to select the days at random and sample all of the flights for those particular days chosen. This is a cluster sample. Each cluster is a day. Also, I think more flights should be sampled. Five flights does not seem like enough.

Given the word problem, we can deduce the following information:

1. The diameter of the circle is 3 meters.

2. The side length of the square is 3 meters.

To determine the difference in area between a circle and a square, we note first the formulas of a circle with a diameter d and the area of a square with side length d:

where:

d=diameter

where:

d=side length

The figures are shown below:

Based on this, the difference of areas would be:

Next, we plug in d=3:

Therefore, the difference in areas is:

The equation of the line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5) is y = (-5/3)x + 5.

To find the equation of a line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5), we can use the slope-intercept form of a linear equation, which is y = mx + b. Given the point (3, 0) on the x-axis, we know that when x = 3, y = 0. This gives us one point on the line, and we can use it to calculate the slope (m).

Using the slope formula: m = (y2 - y1) / (x2 - x1)

Substituting the values (0 - 5) / (3 - 0) = -5 / 3

So, the slope (m) is -5/3. Now, we can substitute the slope and one of the given points (0, 5) into the slope-intercept form (y = mx + b) to find the y-intercept (b).

Using the point (0, 5):

5 = (-5/3) * 0 + b

5 = b

The y-intercept (b) is 5. Therefore, the equation of the line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5) is:

y = (-5/3)x + 5

To sketch the diagram, plot the points (3, 0) and (0, 5) on the x-y plane and draw a straight line passing through these two points. This line represents the graph of the equation y = (-5/3)x + 5.

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The predicted value of y when x = 3, based on the least-squares regression line equation y = 50 - 15x, is y = 50 - 15(3) = 5.

The given least-squares regression line equation y = 50 - 15x represents a linear relationship between the variables x and y. In this equation, the coefficient of x (-15) represents the slope of the line, and the constant term (50) represents the y-intercept.

To find the predicted value of y when x = 3, we substitute x = 3 into the equation and solve for y. Plugging in x = 3, we have y = 50 - 15(3). Simplifying this expression, we get y = 50 - 45 = 5.

Therefore, when x = 3, the predicted value of y based on the least-squares regression line is 5. This means that according to the regression line, when x is 3, the expected or estimated value of y is 5.

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Answer: 4

Step-by-step explanation:

u+3=7

u=7-3

u=4

The equation of line in point slope form is y = ( -7/8 )x - 1/4

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the point passes through the point P ( -14 , 12 )

And , the slope of the line is m = -7/8

where , y - y₁ = m ( x - x₁ )

y - 12 = ( -7/8 ) ( x - ( -14 ) )

y - 12 = ( -7/8 ) ( x + 14 )

On simplifying , we get

y - 12 = ( -7/8 )x - 12.25

Adding 12 on both sides , we get

y = ( -7/8 )x - 0.25

Hence , the equation of line is y = ( -7/8 )x - 1/4

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By the compare to y =mx + b, the value of slope (m) is 1/10 and value of y - intercept is 0.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

The expression is,

⇒ v = 1/10u

Now, We can write as;

⇒ v = 1/10u

⇒ v = 1/10u + 0

By compare with y = mx + b, we get;

⇒ slope (m) = 1/10

⇒ y - intercept (b) = 0

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Answer:

Step-by-step explanation:

I think is x-1

It is because you need to find f(1) and the formula of x-1 when x is greater and equal to 1.

The possible number of minutes he has used his phone for a month is 1205.

Phone Service refers to the routing of calls and telephone services across an IP-based telecommunications network that you access using permitted electronic equipment and/or device(s).

Shen pays a monthly cost of $20 for his phone service.

He also has to pay $0.09 each minute of use.

The smallest amount he has been charged in a month is $128.45.

In this case,

128.45 = ( 20 + 0.09m )

We must find a solution for m.

128.45 = ( 20 + 0.09m )

Take 20 off both sides.

128.45 -20 = 0.09 m

108.45 = 0.09 m

Dividing both the sides of the equation by 0.09,

m = 108.45/0.09= 1205 minutes

The possible number of minutes he has used his phone for a month is 1205.

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The possible combinations of the number of samples and sample sizes she could use to gather data for 200 students will be:

8 samples of 25 students

10 samples of 20 students

5 samples of 40 students

The possible combinations of the number of samples and sample sizes she could use to gather data for 200 students:

8 samples of 25 students

= 8 × 25.

= 200

10 samples of 20 students = 200

5 samples of 40 students = 200

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11 4/10

eleven and four tenths

i hope this is correct.

Answer:

11 4/10

Step-by-step explanation:

first you have to plus 4+6-=10 and then add 6/10 + 8/10=14/10, 14/10 is a improper fraction, 14/10=11 4/10

The decay factor of the exponential decay function describing the value of construction equipment is 0.25.

A percentage is used to represent the degradation rate.

Simply decreasing the percent and dividing it by 100 yields the decimal equivalent.

The decay factor b = 1-r can therefore be calculated.

For instance, the exponential function's decay rate is 0.25, and the decay factor b = 1- 0.25 = 0.75 if the rate of decay is 25%.

A percentage is used to represent the degradation rate.

Simply decreasing the percent and dividing it by 100 yields the decimal equivalent.

The decay factor b = 1-r can therefore be calculated.

For instance, the exponential function's decay rate is 0.25, and the decay factor b = 1- 0.25 = 0.75 if the rate of decay is 25%.

So, we know that the depreciation rate is 25%.

Then, the decay rate:

.025

Therefore, the decay factor of the exponential decay function describing the value of construction equipment is 0.25.

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Answer:

b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I did this.

Answer:

Step-by-step explanation:

x^2+64=(x+8i)(x-8i)

16x^2+49=(4x+7i)(4x-7i)

Answer:

The only single-digit prime numbers are: 2, 3, 5, and 7.

Answer:

2, 3, 5, 7

Step-by-step explanation:

1) Prime numbers are numbers that can only be multiplied by themselves and one; therefore, they only have two factors.

Hope this helps!

Answer:

Each journal costs $2.48

Step-by-step explanation:

Let X be the cost of a single journal.

You can write this equation to represent the problem:

26x = 64.48

(26 times the cost of the journal is $64.48)

Then just solve for x by dividing both sides by 26:

\(26x=64.48\\\frac{26x}{26} =\frac{64.48}{26}\\x=2.48\)

Each journal costs $2.48

This function can be represented as a the rational function y = 2 /x+2 that is option A.

In mathematics, a function is a relationship between two sets of elements, where each element of the first set (the domain) is associated with exactly one element of the second set (the range). In other words, a function is a rule that assigns to each input value from the domain a unique output value from the range.

Here,

To show that the given function can be represented as a rational function in the form y = A/(x+B), where A and B are constants, we need to perform partial fraction decomposition. Starting with the given function:

y = 2/(x+2)

We can write this as:

y = A/(x+2) + B

Where A and B are constants to be determined.

To solve for A and B, we can multiply both sides of the equation by the denominator of the first term, (x+2):

y(x+2) = A + B(x+2)

Now, we can substitute in values of x to solve for A and B.

Let x = -2:

y(-2+2) = A + B(-2+2)

y(0) = A

A = 2

Let x = 0:

y(0+2) = A + B(0+2)

y(2) = 2B + A

Substitute A = 2:

y(2) = 2B + 2

Solve for B:

y(2) - 2 = 2B

y(2) - 2 = 2/(2+2)

y(2) - 2 = 1/2

2B = (1/2) - 2

B = -3/4

Therefore, we have found that:

y = 2/(x+2) - 3/4

which can be written as:

y = (8-3x)/(4(x+2))

So the answer is (a) x+2.

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