4. find the equation, in parametric scalar form, for the line that passes through the points (5,2,7) and (8,–6,1) then determine whether the point (17,–30,31) is on the line.

Answer: exponential

Step-by-step explanation:

its exponential

count the squares in each one

first is 2 squares

second is 4 squares

third is 8 squares

this is going up exponentially because the first one would be 2^1 the second would be 2^2 and the third would be 2^3

the are of rectangle=x2+3x-10

Answer:

Step-by-step explanation:

\((1 - Cos \ x)*(1+\dfrac{1}{Cos \ x})=(1- Cos \ x)* \left(\dfrac{Cos \x }{Cos \ x}+\dfrac{1}{Cos \ x} \right)\)

                                         \(= (1-Cos \ x)*\left(\dfrac{Cos \ x + 1}{Cos x}\right)\\\\=\dfrac{(1-Cos \ x)(1+Cos \ x)}{Cos \ x}=\dfrac{1^{2}-Cos^{2} \ x}{Cos \ x}\\\\=\dfrac{1 -Cos^{2} \ x}{Cos \ x}\\\\=\dfrac{Sin^{2} \ x}{Cos \ x}\\\\=Sin \ x * \dfrac{ Sin \ x}{Cos \ x}\\\\\)

                                         = Sin x * Tan x

Hence proved

The number that Bethany thinks of is 104, and 1/13 of that number is 8.

Word problems in mathematics involve arithmetic operations and the use of variables to solve those problems. Word problems are problems we encounter in our daily life and with the use of correct mathematical interpretation, we can provide accurate solutions to them.

Let the number that  Bethany thinks of be (x) for example. So, 6/13 of x is equal to 48.

i.e.

(6/13) * (x) = 48

By dividing both sides with (6/13), we have:

x = 48 ÷ (6/13)

x = 48 × (13/6)

x = 8 × 13

x = 104

Thus, 6/13 of the number that Bethany thinks of that gives us 48 is 104. Now, to find 1/13 of 104, we have:

1/13 × 104

= 8

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There are 210 different ways for the club to fill the positions of president, vice-president, and secretary if the club consists of 7 members.

To calculate the different ways for the club to fill the positions of president, vice-president, and secretary if the club consists of 7 members, we need to use the permutation formula.

The permutation formula helps in counting the number of ways an event can occur.

Here, we need to select 3 members out of 7 members and arrange them for the 3 positions of the club.

Hence, we can use the permutation formula as:

P(7,3) = 7! / (7 - 3)! = 7! / 4! = 7 x 6 x 5 = 210

Therefore, there are 210 different ways for the club to fill the positions of president, vice-president, and secretary if the club consists of 7 members.Hope this helps!

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Answer:

50 is the sum

Step-by-step explanation:

-10+20=10

10+-40=-30

-30+80=50

Answer:

540 meters per minute, or 9 meters per second

Step-by-step explanation:

Since 80 out of 100 free throws were successful, the standard deviation of the success rate would be 8, and the standard deviation of a binomial distribution is the square root of (p*q)/n, where p is the probability of success, q is the probability of failure (1-p), and n is the total number of trials.

Standard deviation is calculated as follows:

p*q/n = 0.8*0.2/100 = 0.0016 = 0.04 = 8

Since 80% of 100 equals 80 successful free throws, the standard deviation of the successes from 100 free throws would be 8. The dispersion in a set of data is measured by standard deviation. A binomial distribution's standard deviation is equal to the square root of (p*q)/n, where p is the success probability, q is the failure probability (1-p), and n is the number of trials. Since the success rate in this instance is 80%, p = 0.8, q = 0.2, and n = 100. The standard deviation is then equal to the square root of (p*q/n): (0.8*0.2/100) = (0.0016) = (0.04), which equals 8. Therefore, the standard deviation of the successes from 100 free throws for a basketball player who makes 80% of them would be 8.

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Answer:

d= 8.6 ft

Step-by-step explanation:

In similar triangles, the corresponding sides are in proportion.

\(\boxed{\dfrac{AW}{MZ}=\dfrac{AJ}{MJ}=\dfrac{WJ}{ZJ}}\)

To find the value of x,

\(\dfrac{AJ}{MJ}=\dfrac{WJ}{ZJ}\\\\\\\dfrac{6}{7}=\dfrac{d}{10}\\\\\\\dfrac{6}{7}*10=d\)

d = 8.6 ft

The required problem can be stated as the sum of a number and 4 is 10.

the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
To write a word a problem can be translated into the equation x + 4 = 10. So, the problem can be given as " the required problem can be stated as the sum of a number, and 4 is 10."

Thus, the required problem can be stated as the sum of a number, and 4 is 10.

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Answer:

The graphs are parallel

Step-by-step explanation:

Equation one and equation two has the same gradient therefore their graphs are parallel

(a)

Let X be the percentage of students who passed in both Nepali and English. Then the percentage of students who failed in at least one of the subjects would be:

Percentage of students who failed in Nepali = 30%

Percentage of students who failed in English = 27%

Percentage of students who failed in both subjects = 15%

Therefore, the percentage of students who failed in at least one of the subjects would be:

30% + 27% - 15% = 42%

This means that the percentage of students who passed in both subjects would be:

100% - 42% = 58%

Therefore, 58% of students passed in both Nepali and English.

    ____________

   /            \

  /              \

 /      NE        \

/                  \

/____________________\

       EN

NE: Nepali

EN: English

The left circle represents Nepali, the right circle represents English, and the overlap represents students who failed in both subjects. The percentage values can be added to each section of the Venn diagram to make it clearer.

Answer:

B(3,3)

Step-by-step explanation:

Midpoint = (2,5)

A = (x₁,y₁) = (1,7)

M(x,y) = \((\frac{x1+x2}{2} , \frac{y1+y2}{2})\)

M(2,5) = \((\frac{1+x2}{2} , \frac{7+y2}{2} )\)

Writing the equations separately for convenience

1) \(\frac{1+x2}{2} = 2\)  

=> 1+x2 = 4

=> x₂ = 3

2) \(\frac{7+y2}{2} =5\)

=> 7+y2 = 10

=> y₂ = 3

So, the coordinate is,

B = (x₂,y₂) = (3,3)

Answer:

(3,3)

please see the attached picture for full solution

hope it helps..

Good luck on your assignment

Answer:

Answer below

Step-by-step explanation:

The coordinates of vertex in triangle 1 - A = 4, 2   B= 6, 8   C= 8, 4

The coordinates of vertex in triangle 2- A= -4, 2   B= -6, 8   C= -8, 4

To do this you write the coordinates of the vertex ( corners of the the triangle )

HOPE IT HELPED

Answer:

Shape #1:

A (4,2)

B (6,8)

C (8,5)

Shape #2:

A' (-4, 2)

B' (-6, 8)

C' (-8, 5)

Hope this helps :)

Answer. 1/36

Step-by-step explanation:

1/6 chance 6 sides 6^2 cause gotta hit 1 twice so 6 Squared is 36 so 1 in 36 chance

Step 1:

Given data

The average mass of a cow = 410 kg

Step 2:

To find the mass of 150 cows, you will multiply 150 cows by 410 kg.

Therefore

Final answer

Write the total weight in scientific notation

The type of function that fits the given description is D. Exponential decay.

In an arithmetic sequence, the difference between consecutive terms remains constant. If the y-values of a function form an arithmetic sequence that decreases in value, it means that the difference between consecutive terms is negative.
Exponential decay functions exhibit a constant ratio between consecutive terms, resulting in a decreasing sequence. As the x-values increase, the y-values decrease at a consistent rate. This is represented by the formula y = ab^x, where b is a constant between 0 and 1.
In contrast, linear functions have a constant difference between consecutive terms, resulting in an arithmetic sequence. However, since the y-values are decreasing, the function cannot be linear.
Exponential growth functions, on the other hand, have a constant ratio between consecutive terms, but they result in an increasing sequence. The y-values of an exponential growth function increase as the x-values increase.

Therefore, based on the given information, the most appropriate type of function is D. Exponential decay.

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The geom_jitter() function is the function creates a scatterplot and then adds a small amount of random noise to each point in the plot to make the points easier to find

Given that,

In order to make the points in the plot easier to find, function first creates a scatterplot and then adds a small amount of random noise to each point in the plot.

Generally, To make the points in the scatterplot easier to find, the geom jitter() method first builds a scatterplot and then adds a little amount of random noise to each point in the plot.

What is the purpose of the Geom jitter () function? Description. The geom point (position = "jitter") shortcut is the jitter geom. It is a practical method of managing overplotting brought on by discreteness in smaller datasets by adding a little degree of random variation to the location of each point.

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The geom_jitter() function is a funcreates a scatterplot and then adds a small amount of random noise to each point in the plot to make the points easier

Given that,

Function first makes a scatterplot, then adds a small amount of random noise to each point in the plot to make the points in the field easier to find.

The geom jitter() method often produces a scatterplot first, then adds a small amount of random noise to each point in the plot to make the points in the field easier to find.

What does the Geom jitter () function do? The jitter geom is the shortcut geom point with a position equal to "jitter". It is a helpful technique for controlling overplotting caused by discreteness in smaller datasets by giving each point's location a small amount of random variation.

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The number of ways pets can be arranged in group according to the species is  in a row 288 ways.

Pets can be grouped by permutation concept as follows.

Total number of pets = 10

Number of dogs = 4

Number of cats = 3

Number of alpacas = 2

Number of bunny = 1

The number of ways pets can be arranged in group according to the species in a row as,

⇒ (4!)(3!)(2!)(1!)

⇒ (24)(6)(2)(1)

⇒ 288

Hence we can conclude that the number of ways pets can be arranged in group according to the species in a row is 288 ways.

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Answer:

the answers below:

1: (3,-2)

2: ( -3,2)

The effective interest rate on the operating lease is 12.45%

Under the straight-line method of depreciation, the annual depreciation for the computers can be determined as follows:

Depreciation expense = (Cost - Residual value) / Useful life

Depreciation expense = ($120,000 - $0) / 6 years = $20,000 per year

Hence, semi-annual depreciation is $10,000 ($20,000 / 2) per payment.

The operating lease payments are $15,000 per semi-annual payment. The total amount of the lease payments for the 2-year term is $60,000 ($15,000 x 4).

Thus, the present value of the operating lease payments can be computed as follows:PV of lease payments = ($10,000 / 0.0609) x [1 - (1 / 1.0609^8)]PV of lease payments = $47,907.29

The implicit interest rate on the lease is 0.0609 or 6.09% (computed by dividing the lease interest by the present value of the lease payments).

The effective interest rate is 12.45% (computed by doubling the implicit interest rate).

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The equation of the line that is parallel to y = 2/5x + 2 and passes through (-5, 6) is y = (2/5)x + 8.

Perpendicular line slopes are the negative reciprocals of one another. In other words, any line that is perpendicular to a line with a slope of m will have a slope of -1/m. If lines are parallel if they have the same slope.

The slope of the given line is 2/5.

We know that, any line perpendicular to it will have a slope that is the negative reciprocal of 2/5, which is -5/2.

Using the point-slope form of a line:

y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Substituting the values we know:

y - 6 = (-5/2)(x - (-5))

y - 6 = (-5/2)x - (25/2)

y = (-5/2)x + 17.5

Therefore, the equation of the line perpendicular to y = 2/5x + 2 and passes through (-5, 6) is y = (-5/2)x + 17.5.

The slope of parallel lines are same. Thus, using point slope form:

y - 6 = (2/5)(x - (-5))

y - 6 = (2/5)x + 2

y = (2/5)x + 8

Therefore, the equation of the line that is parallel to y = 2/5x + 2 and passes through (-5, 6) is y = (2/5)x + 8.

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The point where the line intersects the plane is (-8/3, 11/3, 8/3).

To find the point where the given line intersects the plane, we need to find values of t that satisfy both the equation of the line and the equation of the plane.

First, we can substitute the equations of  line into the equation of the plane to get:

3(-1-t) + (2+t) + 3(1+t) = 1

Simplifying this equation gives:

-3t + 6 = 1

-3t = -5

t = 5/3

Now that we have found a value of t that satisfies both equations, we can substitute it back into the equation of the line to get the point of intersection:

x = -1 - (5/3) = -8/3

y = 2 + (5/3) = 11/3

z = 1 + (5/3) = 8/3

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The given question is incomplete, the complete question is:

How to find the point where the line x = –1 – t, y = 2 + t, z = 1+ t intersects the plane 3x + y + 3z = 1 ?

The taxpayer’s gross annual salary is $98500

The given parameters in the question are

Social Security tax = $6,107

Social security tax = 6.2%.  

Also, we have the following formula for tax

Tax rate = tax amount / gross income

Substitute the known values in the above equation, so, we have the following representation

6.2% = 6107/gross income

Make gross income the subject

gross income = 6107/6.2%

Evaluate

gross income = 98500

Hence, the gross income is 98500

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The clinic should hire at least 7 doctors in order to serve 122 patients per day.

To determine how many doctors the clinic should hire in order to serve 122 patients per day, we need to calculate the number of patients each doctor can see within their working hours.

Let's start by calculating the total number of minutes each doctor works per day. Since each doctor works 8 hours per day and there are 60 minutes in an hour, the total minutes worked by a doctor per day would be 8 hours × 60 minutes = 480 minutes.

Next, we need to find out how many patients a doctor can see within their working hours. Given that each patient requires an average of 27 minutes with a doctor, the number of patients a doctor can see per day would be 480 minutes ÷ 27 minutes per patient = 17.7778 patients.

Since we can't have a fractional number of patients, we need to round this number up to the nearest whole number to ensure that each patient gets the required attention. Therefore, each doctor can see approximately 18 patients per day.

To serve 122 patients per day, we divide the total number of patients by the number of patients each doctor can see per day: 122 patients ÷ 18 patients per doctor = 6.7778 doctors.

Again, we can't have a fractional number of doctors, so we need to round this number up to the nearest whole number. Therefore, the clinic should hire at least 7 doctors to serve 122 patients per day.

In summary, the clinic should hire at least 7 doctors in order to serve 122 patients per day.

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1. To model the relationship between the parking hours and the cost, we can use the following equation:

\(\displaystyle\sf C(h) = \begin{cases} 5.00, & \text{if } h \leq 2 \\ 5.00 + 0.25(h - 2), & \text{if } h > 2 \end{cases}\)

Here, \(\displaystyle\sf C(h)\) represents the cost \(\displaystyle\sf C\) as a function of the parking hours \(\displaystyle\sf h\).

2. To calculate how much you have to pay for parking for 10 hours, we can substitute \(\displaystyle\sf h = 10\) into the equation:

\(\displaystyle\sf C(10) = 5.00 + 0.25(10 - 2) = 5.00 + 0.25(8) = 5.00 + 2.00 = 7.00\)

Therefore, you would have to pay $7.00 to park for 10 hours.

3. To find out how many hours $10 can buy, we need to solve the equation:

\(\displaystyle\sf 10 = 5.00 + 0.25(h - 2)\)

Simplifying the equation:

\(\displaystyle\sf 10 - 5.00 = 0.25(h - 2)\)

\(\displaystyle\sf 5.00 = 0.25(h - 2)\)

Dividing both sides of the equation by 0.25:

\(\displaystyle\sf \frac{5.00}{0.25} = h - 2\)

\(\displaystyle\sf 20 = h - 2\)

Adding 2 to both sides of the equation:

\(\displaystyle\sf h = 20 + 2 = 22\)

Therefore, $10 would buy you 22 hours of parking.

To clarify, the answer is 22 hours, not 20 hours.

Answer:

area =length × breadth

=7x × 5x

=35x