Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (0, 15, −9) and parallel to the line x = −1 + 4t, y = 6 − 2t, z = 3 + 9t. r(t)  = . (x(t), y(t), z(t))  = .

Answer:

Step-by-step explanation:

15x² - 2x - 1 = 0

15x² - 5x + 3x - 1 = 0

5x(3x - 1) + 3x - 1 = 0

(5x + 1)(3x - 1) = 0

x = -1/5, 1/3

8x² - 10x - 3 = 0

8x² - 12x + 2x - 3 = 0

4x(2x - 3) + 2x - 3 = 0

(4x+1)(2x-3) = 0

x = -1/4 , 3/2

16x² - 8x + 3 = 0

This question has complex answers as the D = 64 - 192 < 0

So, ignore this question. It is wrong or it has complex answers.

Use the quadratic formula for it.

9x² - 6x - 2 = 0

This also needs the quadratic formula as the answer is in roots.

8x² - 2x - 3 = 0

8x² - 6x + 4x - 3 = 0

2x ( 4x - 3) + 4x - 3 = 0

(2x + 1)(4x-3) = 0

x = -1/2 , 3/4

The correct option is option b) subjectively divide the 20 plots into 10 pairs (making the plots within a pair as similar as possible) and then, for each pair, flip a coin to assign the fertilizers to the 2 plots.

A sort of probability called subjective probability is one that is based on a person's subjective assessment or personal knowledge of the likelihood of a particular result. It doesn't use facts or formal computations; instead, it merely includes the subject's ideas and prior experience.

A subjective likelihood varies from person to person and is not based on previous facts or market data. In other words, it is not founded on reality but rather is the result of an individual's opinion.

In the majority of probability theories, quantifiable data is evaluated to ascertain the likelihood of an event occurring. However, subjective probability lacks a formal calculation, is influenced by human ideas, and is not based on quantitative data.

Therefore, The correct option is option b) subjectively divide the 20 plots into 10 pairs (making the plots within a pair as similar as possible) and then, for each pair, flip a coin to assign the fertilizers to the 2 plots.

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The answer in the form of x,y is -7x + 10y  = 118.

A Cartesian plane (named after French mathematician Rene Descartes, who formalized its use in mathematics) is defined by two perpendicular number lines: the x-axis, which is horizontal, and the y-axis, which is vertical. Using these axes, we can describe any point in the plane using an ordered pair of numbers.

from given conditions, we get,

(-4, 9) and  10  left  7 down  puts her at  (  -4 - 10 , 9  - 7)  = ( -14, 2)

So,  the points  ( -4, 9)  and (-14,2)  are on the  line

Slope of this line  =   [ 2 - 9] / [ -14 - -4 ]  =  [ -7] / [ -10]  =  7/10

Equation of the line

y  = (7/10)(x - - 4)  + 9

y  = (7/10) ( x + 4)  + 9     multiply through by 10

10y = 7 (x + 4)  + 90

10y = 7x + 28  + 90

-7x + 10y  = 118

Therefore, the answer in the form of (x , y) is -7x + 10y  = 118

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Answer:

Select all the examples of the exponential function

a) y=3x-2

b) y=3^x

c) y=(1/2)^3x

d) y=3x^2

E) y=(1/2)^x

The account balance in the bank after 5 years is $1,216.65.

An amount of $1,000 is deposited into a bank account that pays 4% annual interest. The amount in the bank account after 5 years can be calculated as follows:

Therefore,

[tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]

where

Therefore,

p = 1000 dollars

4 = 4 % = 4 / 100 = 0.04

t = 5 years

n = 1

Therefore,

A = 1000(1 + 0.04/1)¹ˣ⁵

A = 1,000(1 + 0.04)⁵

Therefore,

A = $1,216.65

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The data that is considered univariate and quantitative is Shoe size, Salary, Years of experience, Height.

What is univariate quantitative data?

Univariate quantitative data refers to a type of data that consists of only one variable and the values of that variable are numerical. This means that the data represents a single measurement or characteristic, and the values can be quantified and compared using mathematical operations. Examples of univariate quantitative data include height, weight, temperature, salary, and years of experience.

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The difference quotient of quadratic equation f(x) = 5 · x² - 5 · x - 6 is equal to r = 10 · x + 5 · h.

Herein we have the quadratic equation f(x) = 5 · x² - 5 · x - 6, from which we must determine the difference quotient, defined below as:

r = [f(x + h) - f(x)] / h

Where:

First, substitute on each component of numerator of difference quotient:

f(x) = 5 · x² - 5 · x - 6

f(x + h) = 5 · (x + h)² - 5 · (x + h) - 6

f(x + h) = 5 · (x² + 2 · h · x + h²) - 5 · (x + h) - 6

f(x + h) = 5 · x² + (10 · h + 5) · x + (5 · h² - 6)

Second, substitute on difference quotient:

r = [f(x + h) - f(x)] / h

r = [[5 · x² + (10 · h + 5) · x + (5 · h² - 6)] - (5 · x² - 5 · x - 6)] / h

r = (10 · h · x + 5 · h²) / h

r = 10 · x + 5 · h

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Jamal should multiply his current balance by 1.07 to find his total balance in one year.

Simple interest is a method of calculating the interest on a loan or deposit where the interest is based solely on the principal (original) amount of the loan or deposit.

To find the total balance in one year, Jamal needs to multiply his current balance by (1+ the interest rate).

Since the interest rate is 7%, the interest rate in decimal form is 0.07

Therefore, he needs to multiply his current balance by (1+0.07) = 1.07

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An equation relating the total amount in a in Terry’s account to the number of years, t is ​A = P + P*(r/100)*t. Yes, the relationship is proportional.

An equation is a well-formed formula that connects two expressions with the equals sign to express the equality of those two expressions. For example, in French, an equation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions connected with the equals sign.

Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.

An equation relating the total amount in a in Terry’s account to the number of years, t is ​A = P + P*(r/100)*t.

Where, A is total amount,

P is amount which Terry deposit,

r is rate of interest,

and t is number of years.

Yes, the relationship is proportional.

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If you are asked to find the 85th​ percentile, you are being asked to find an area corresponding to a​ z-score of 0.8.

The term percentile in math is defined as the area to the left of a particular data value.

According to the definition of percentile, here they are asking about the 85th percentile.

As we all know that​ z-score is not an area under the normal curve and the distances along the horizontal axis are represented by​ z-scores where as the regions under the curve are represented by areas.

Therefore, in order to find the z-score is a conversion that standardizes any value from a normal distribution to a standard normal distribution.

Then we have to convert the given percent into decimal form, then we get it as,

=> 85% = 0.85

Here we need to find the value from the z table then we get the resulting value as 0.8.

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The statements that are true about the triangle f d e and its dilated counterpart f' d' e' are: (1) The center of dilation was (0, 0). (2) The coordinates of f' d' e' are (negative 3, 1), (negative 3, 3), and (negative 2, 2). (3) f' d' e' is a similar triangle to f d e.

The triangle f d e and its dilated counterpart f' d' e' have specific properties that make them similar triangles. The center of dilation for the transformation was (0, 0). This means that the distance from the center of dilation to each point before and after the dilation was the same. The coordinates of triangle f d e were (negative 9, 3), (negative 9, 9), and (negative 6, 6). In order to obtain the coordinates of f' d' e', the dilation rule one-third(x,y) (one-third x, one-third y) was used. This means that the x and y coordinates of each point were divided by three. The result is that the new coordinates of f' d' e' are (negative 3, 1), (negative 3, 3), and (negative 2, 2). These new coordinates demonstrate that the triangle f d e and its dilated counterpart f' d' e' are similar triangles.

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Answer:

A. ∠F corresponds to ∠F'.

C. The distance from point D' to the origin is 1/3 the distance of point D to the origin.

E. △DEF ~△D'E'F'

Step-by-step explanation:

got it right on edge 23

The volume of the stack affected will be 10,825.38 cubic millimeters.

Let r be the radius and h be the height of the cylinder.

Then the volume of the cylinder will be

V = π r²h cubic units

The table holding Juanita's pennies gets bumped, and the stack becomes slanted.

The radius of the cylinder is given as,

r = 19.05 / 2

r = 9.525 mm

Then the volume of the cylinder is calculated as,

V = π x (9.525)² x 38

V = 3.14 x 90.725 x 38

V = 10,825.38 mm³

The volume of the stack affected will be 10,825.38 cubic millimeters.

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Answer:

The volume of the stack affected will be 10,825.38 cubic millimeters.

Step-by-step explanation:

Answer:

First brand: 98 gallons

Second brand: 42 gallons

Step-by-step explanation:

x + y = 140

.4x + .9y = .55*140

x=140-y

.4(140-y) + .9y = 77

56 - .4y + .9y = 77

.5y = 21

y = 42

x + 42 = 140

x = 98

The equation of the line that passes through (4, 5) and is parallel to x = 0 is expressed as: x = 4.

Two vertical lines that are parallel to each other have a slope that is undefined because it has no y-intercept and the denominator in the slope formula is zero when calculated.

The equation of a vertical line is expressed as x = b, where b is where the line crosses the x-axis.

Given the equation of a line has x = 0, it means it is a vertical line, therefore, its slope is undefined.

Therefore, the line that is parallel to x = 0 will be undefined. Since the line passes through the point (4, 5), the equation of the line will be written by substituting b = 4 into x = b:

x = 4.

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Answer:

12. <4 = 100°

Step-by-step explanation:

For number 12. angle m<2 is a corresponding angle to angle m<6 . So the equations, (3x+20) and (5x-20) are equal to each other.

So lets set them equal to each other:

(3x+20) = (5x-20)

40 = 2x

x = 20

Now we need to plug in the value of x into the equation of angle m<2, to find its angle.

(3x+20) = ?

(3(20)+20) = ?

= 80 degrees

m<2 = 80 degrees

We need to find <4

Since <4 and <2 share the same line and are supplementary angles (they add up to 180) we can subtract the value of <2 from 180 to find <4

180 - 80 = 100

So <4 is 100 degrees.

Two -dimensional shape is formed if a plane intersects the cylinder shown, perpendicular to the base is a rectangle. Hence option C is the correct option.

What is the two-dimensional shape?

Plane figures are two-dimensional figures. Three-dimensional figures are solid shapes.

A cross-section is a shape formed by the intersection of a solid object and a plane. A three-dimensional shape's cross-section is a two-dimensional geometric shape.

Cross-Sectional Shapes

Cross-sections are classified into two types:

* Horizontal cross-sections and

* Vertical cross-sections.

The shape is a circle if the cylinder has a horizontal cross-section. If the plane of the cylinder's base is perpendicular to its base, the shape is a rectangle.

When the plane intersects the cylinder parallel to the base with a variable angle, an oval shape is formed.

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The biggest difference between an installment loan and revolving credit is that Installment loans have a fixed term and monthly payment, revolving credit is a credit line that is paid off and used again. That is option B.

An installment loan is defined as the type of loan an individual obtains from the bank which can be paid back in installments.

Revolving credit is defined as the type of loan that allows the borrower to spend the money they have borrowed, repay it, and borrow again as needed.

Therefore, the difference between an installment loan and revolving credit is that Installment loans have a fixed term and monthly payment, revolving credit is a credit line that is paid off and used again.

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Answer: why is the question?

Step-by-step explanation: also the integer is the whole number whether if its negative or positive number e.g. -12 or 5

Integers = {...,−4, −3, −2, −1, 0, 1, 2, 3, 4, ... }

Negative Integers = { ..., −4, −3, −2, −1 }

Positive Integers = { 1, 2, 3, 4, ... }

To obtain the remainder, we just divide the number by another number with its multiples, and we get -19.

f(x) = 4X x 3 + 1,

f(-5) = 4(-5) x + 1

f(-5) = -20 + 1

f(-5) = -19.

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a property has a back yard 125 x 150 feet and a side yard of 195 x 25 feet. then 23625  is the combined square footage of the side and back yard

125*150 and 195*25

total 23625

The area covered with grass, in square feet, is the area of the shape of the yard.

What is the Area of a Yard?

The area of a yard can be calculated by determining the shape of the yard, and using the appropriate area formula of the shape to find the area of the yard.

Image of the yard is missing. However, assuming the yard is a rectangular shape with a dimension of 10 ft by 6 ft, therefore:

The square feet of grass Russell has = area of rectangle = (10)(6) = 60 ft²

In summary, the area covered with grass, in square feeet, is the area of the shape of the yard.

a property has a back yard 125 x 150 feet and a side yard of 195 x 25 feet. then 23625  is the combined square footage of the side and back yard

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Answer:

Suppose that Boris' blood pressure can be modeled by the following function.

p(t)=85+18 sin (73mt)

Boris' blood pressure increases each time his heart beats, and it decreases as his heart rests in between beats. In this equation, p (t) is the blood pressure in

mmHg (millimeters of mercury), and t is the time in minutes.

Find the following. If necessary, round to the nearest hundredth.

The margin of error is 1.6393 for the supplied values of  c, s, and n, which are 0.98, 3.3 and 22respectively.

what is margin ?

Margin is the term used to describe the equity that a trader has in their account. Using funds borrowed from a broker to buy stocks is referred to as "marging" or "buying on margin." Instead of a typical brokerage account, you must have a margin account to execute this. Beginning with your gross profit, which is the distinction between revenue and COGS, you may compute profit margin. Find the percentage of revenue that represents gross profit next. Calculate it by dividing your gross profit by your revenue. You can calculate your margin % by multiplying the sum by 100.

Given that,

standard deviation = s =  3.3

z is the 98% =  z score = 2.33

Sample size = n =22

Margin of error is expressed using the formula;

M = z * √s²/n

M = 2.33* √3.3²/22

M = 2.33* 0.7035

M = 1.6393

Therefore, the margin of error is 1.6393 for the supplied values of  c, s, and n, which are 0.98, 3.3 and 22respectively.

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The 9 characteristics of system are Inputs, Outputs, Processes, Control, Interface, Storage, Feedback, Boundaries, and Environment.

1. Inputs: This is data received from external sources, such as user input, sensors, or other systems. This data is used to initiate the system's operations and can include commands, parameters, and other information.

2. Outputs: This is the result of the system's operations, such as responding to user input or displaying results. Outputs can be in the form of data, reports, or graphical displays.

3. Processes: This is how data is transformed from inputs into outputs. Processes may involve calculations, sorting, or other operations.

4. Control: This is how the system's operations are managed. It can include scheduling, sequencing, and coordinating processes.

5. Interface: This is how the system interacts with its environment. This includes receiving inputs, producing outputs, and communicating with other systems.

6. Storage: This is where data is stored for later use. This can include databases, files, and other types of storage.

7. Feedback: This is how the system monitors its performance and adjusts accordingly. This can include error checking, logging, and analyzing data.

8. Boundaries: This is how the system's scope is defined. It can include limiting the system's access to certain data or operations.

9. Environment: This is the external conditions in which the system operates. This includes the hardware, software, and other systems the system interacts with.

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For the graph of data given option C: The median 300 is the middle number is correct.

What is median?

In mathematics, the middle number in a sorted list of numbers is referred to as the median. By arranging the numbers, the middle number can be discovered. Ascending order is used to arrange the numbers. The middle number in the ordered set of numbers is referred to as the data set's median.

Draw the median table for the graph of values given -

Number    Frequency    ∑f

100            14                   14

200            6                    20

300            18                  38

400            12                  50

500            2                    52

600            12                  64

700             8                   72

The formula for median is -

Median = [n/2 + (n/2 + 1)] / 2

Median = [72/2 + (72/2 + 1)] / 2

Median = [36 + (36 + 1)] / 2

Median = 73/2

Median = 36.5

According to the table the ∑f value 36.5 corresponds to 300.

Therefore, the median 300 is the middle number.

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According to the given vector, the value of the orthogonal projection of y onto u is <16, -8>

Here we have the vector values that is as follows:

Y= [8 -24],

u=[4 -2]

Now, based on the formula of the vector projection is written as,

=> [(y x u) / |u²| ] x u

Now, we have to calculate the value of the vector and it can be obtained by what we need to do is multiply the corresponding coordinates and then add up the results:

=> ⟨8,−24⟩⋅⟨4,−2⟩

=> (8)⋅(4)+(−24)⋅(−2)

When we simplify this one then we get the value as,

=>80.⟨8,−24⟩⋅⟨4,−2⟩

=> (8)⋅(4)+(−24)⋅(−2) = 80.

Similarly, now we have to calculate the value of  |u²| is written as,

Here we have the sum of squares of the absolute values of the coordinates is 

=> ∣4∣² + ∣−2∣² = 20.

Therefore, the magnitude of the vector is

=> √20 =  2√5

Thus the vector projection is written as,

=> [tex]\frac{8}{2\sqrt{5} }\times < 4,-2 >[/tex]

When we simplify this one then we get the resulting value of projection as <16, -8>

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Answer:

.18B = 4.5

B = 4.5/.18 = 450/18 = 50/2 = $25 bill

The area of the octagon ABCDEFGH is 119 cm².

The figure is attached below for reference.

AP = 4 cm

HC = CD = 11 cm

Area of trapezium ABCH = Area of trapezium GDEF

Now, Area of a trapezium = [tex]\frac{1}{2} (a+b)h[/tex]

Area of trapezium ABCH = Area of trapezium GDEF  = [tex]\frac{1}{2} (5+11)4 = 32[/tex] cm².

So, Area of trapezium GDEF = 32 cm².

Area of rectangle MCDG = l x b = 11 x 5 = 55 cm²

Area of the Octagon ABCDEFGH = Area of the two trapeziums + Area of the rectangle

= (2 x 32) + 55 = 119 cm².

Hence, the area of the octagon ABCDEFGH is 119 cm².

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Answer:

Step-by-step explanation:

a. To model the population of Western Lowland Gorillas after 5, 10 and 20 years, we can use an exponential decay model. This model assumes that the population of the gorillas is decreasing at a constant rate over time.

Let y equal the population of the gorillas and x represent the number of years since 2022.

The exponential decay model is represented by the equation:

y = a*e^(-rt)

Where a is the initial population, r is the decay rate and t is the number of years.

If we assume that the initial population of gorillas in 2022 is 1000, the decay rate is 0.1, and we can calculate the population of gorillas after 5, 10, and 20 years.

For 5 years after 2022:

y = 1000e^(-0.15) = 810 gorillas

For 10 years after 2022:

y = 1000e^(-0.110) = 648 gorillas

For 20 years after 2022:

y = 1000e^(-0.120) = 404 gorillas

b. Table:

Years Gorilla Population

5            810

10            648

20            404

c. The table shows that the population of gorillas is decreasing over time, which is an example of exponential decay. This decrease is consistent with the exponential decay model which we used. Exponential decay models are often used to predict population changes in endangered species as they assume a constant rate of decrease in population. Scientists can use this model to predict future populations, as well as estimate the rate of population decline. Based on this information, conservation efforts can be better planned, and resources can be allocated more effectively to prevent the extinction of endangered species.

The requried average weight of 15 weights is given as 24 pounds.

The average of the values is the ratio of the total sum of values to the number of values.

Here,
The average of the first 3 weights was 20 pounds. the average of the next twelve was 25 pounds.

overall average = total weight of 3 + total weight of 12 / [3 + 12]

overall average = 360 / 15 = 24 pounds

Thus, the requried average weight of 15 weights is given as 24 pounds.

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Answer:

Area = 1/2 *base * height

24 = 1/2 * b* 4

24 = 2b

b= 12cm