6. A large community college has professors
and lecturers. The total number of faculty
members is 228. The school reported that
they had 5 professors for every 14 lecturers.
How many of each type of faculty member™
does the community college employ?

The equation of the line that passes through point (-3,1) and perpendicular to y=-5x+2 is y = (1/5)x + 8/5.

Given the data in the question;

First we determine the slope of the initial line using the slope intercept-form. y = mx + b

y = -5x + 2

Compared with the slope intercept form,

Slope m = -5

Now, for the equation of line perpendicular to the initial line, its slope must be a negative reciprocal of the initial slope.

Hence, slope of the perpendicular line is;

Slope m = -1/(-5) = 1/5

To find the equation of the perpendicular line, we use the point slope formula.

y - y₁ = m( x - x₁ )

Plug in the slope m ( 1/5) and point (-3,1).

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

y - 1 = (1/5)( x + 3 )

Convert to slope-intercept form.

y - 1 = (1/5)( x + 3 )

y - 1 = x/5 + 3/5

y = x/5 + 3/5 + 1

y = x/5 + 3/5 + 1

y = x/5 + 8/5

y = (1/5)x + 8/5

Therefore, the equation of the perpendicular line is y = (1/5)x + 8/5.

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Answer:

sinTheta = 24/25

cotTheta = 7/24

cscTheta = 25/24

Step-by-step explanation:

Use pythagorean thm or pythagorean triples to find the missing side of the triangle.

7^2 + x^2 = 25^2

49 + x^2 = 625

x^2 = 576

x = 24

The third side of the triangle is 24. We'll need this in a sec.

The marked angle is called theta. That 0 with a belt is greek letter theta. They could just call it angleA or angleB or whatever. Its name is just theta no big deal.

25 is the hypotenuse (longest side). The side that's 7 units long is one of the pieces that makes up AngleTheta. So the 7 is "adjacent" to theta. The other leg, 24, is "opposite" from theta.

sinTheta is a ratio. It is OPPOSITE/HYPOTENUSE

sinTheta = 24/25

cotTheta is tanTheta flipped over.

tanTheta is OPP/ADJACENT

so...

cotTheta =

ADJ/OPP

=7/24

Last, cscTheta is sinTheta flipped over.

We already found sinTheta, so flip it over.

cscTheta = 25/24

SOH-CAH-TOA is supposed to help you memorize the ratios for sine (opp/hyp), cos (adj/hyp), and tan (opp/adj).

The math word for "flipped over" is reciprocal.

csc is the reciprocal of sin

sec is the reciprocal of cos.

cot is the reciprocal of tan.

Good luck! Hope this helps!

The required problems on probability application are detailed below.

Probability is the study of chance represented as a proper fraction between 0 and 1 .  

The manufacturing process of a particular rugby ball consists of two parts, a leather covering and a rubber bladder. The probabilities of defect in the leather covering is 5% and the probability of the rubber bladder is 15% respectively. What is the probability that the assembled Rugby ball will not have any defect.

Let A and B denote the event that  a rugby ball is defective due to defects in the leather covering and the rubber bladder respectively.

Then we can say that  P(A) = 5 / 100 = 1 / 20  and

P(B) = 15 / 100 = 3 / 20

Therefore  P(A') = 1 - 1/20 = 19/20 and P(B') = 1 - 3 / 20 = 17 / 20.

P(A') and  P(B') gives us the probabilities that the rugby ball will not have defective parts respectively.

Therefore the probability that the assembled product will not have any defect is:

P(A') ×  P(B')

[tex]=\frac{19}{20} \times \frac{17}{20}\\\\=\frac{323}{400} \\\\=0.8075[/tex]

Therefore the probability that the rugby ball will not have any defect is 80.75% .

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The size of the population of mosquito follows an exponential model.

the size of the population in 10 days is 1370

The size of the population in 10 days is 1370

The given parameters are:

p(0) = 574

p'(0)= 50

An exponential function is represented as:

p(t) =p(0) * e^ rt

So, we have:

p(t)=574*e^rt

Differentiate

p'(t)=574*r*e^rt

Substitute 0 for t

50=574 r

Divide both sides by 574

r=0.087

The function becomes

p(t)= 574*e^rt

   = 574*e^0.087 t

In 10 days, t = 10.

So, we have:

p(10)=574*e^0.87

Solve

p(0)=1370

Hence, the size of the population in 10 days is 1370

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Step-by-step explanation:

Translate this sentence into an equation. The difference of Janelle's height and 9 is 65. Use the variable j to represent Janelle's height.

j - 9 = 65

to solve:

j - 9 = 65

add 9 to both sides:

j - 9 + 9 = 65 + 9

j = 74

Answer:

0.1037

Step-by-step explanation:

Answer:

a) (in order) {-1, 0, 1, 2, 3}
b) {-1, 0, 1, 2, 3}

Step-by-step explanation:

Answer:

w is 59

Step-by-step explanation:

63-4 =59 and this should be the answer your looking for

Answer:

w=12

Step-by-step explanation:

63+4w+15

collect like terms

63-15=4w

48=4w (divide all through by 4)

w=12

I will use the law of exponent below

⇒if you re multiplying powers of them same base, keep  one base and add the exponents mathematically we say:

[tex]x^{n} *x^{n} \\=x^{n+n}[/tex]

[tex]=m^{9+(-3)} \\=m^{9-3} \\=m^{6}[/tex]

OPTION D is the solution

Solution

The diagram below shows what is needed

As shown above

distance between points A and B is

distance between points C and D is

Answer: $3.20 is the sales tax

Step-by-step explanation:

[tex]\frac{8x40}{100} =3.2[/tex] (8 times 40 divided by 100)

please mark brainliest if this helped :)

Answer:

3.75 cups of flour

2.5 cups of sugar

1.25 cups of butter

Step-by-step explanation:

Hello!

Let the amount of sugar used be x:

The total sum of ingredients should be 7.5 cups, so we can add x, 1.5x, and 0.5x and set it to 7.5.

Clifford needs 2.5 cups of sugar.

The amount of flour can be found by multiplying 2.5 by 1.5: 3.75 cups

The amount of butter can be found by multiplying 2.5 by 0.5: 1.25

Clifford needs 3.75 cups of flour, 2.5 cups of sugar, and 1.25 cups of butter.

Any point satisfying the relation y = -[1 - (∛x²)]²(1/(∛x)) will be points on the graph where the tangent line has slope 1.

What is the slope of a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is the slope of a line is represented by the expression m = change in y/change in x =Δy/Δx.
Additionally, the slope of the line can be shown as tan θ = Δy/Δx
So, the slope of a line is tan θ.

The given equation is: (∛x²) + (∛y²) = 1
Therefore, (∛y²) = 1 - (∛x²) ⇒ y² = [1 - (∛x²)]³
Differentiating the equation formed with respect to x, we get
2y(dy/dx) = 3[1 - (∛x²)]²(-2/3)(1/(∛x)) ⇒ dy/dx = (-1/y)[1 - (∛x²)]²(1/(∛x)) -(i)
Given, the slope of the tangent line is = 1 -(ii)
Thus, equating (i) and (ii), we get,
(-1/y)[1 - (∛x²)]²(1/(∛x)) = 1 ⇒ y = -[1 - (∛x²)]²(1/(∛x))
Therefore any point satisfying the relation y = -[1 - (∛x²)]²(1/(∛x)) will be points on the graph where the tangent line has slope 1.

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Answer:

b

Step-by-step explanation:

Answer:

1 unit

Step-by-step explanation:

- 1 1/2 - (- 2 1/2)

= 1 unit

Answer:

f(-3)=10

Explanation:

Given the function:

When x = -3

Answer: 7921   123569 5410

Step-by-step explanation:

1. 7912

2. 123569

3. 5210

well, the difference is 39.14 - 38 = 1.14, so that's the tax.

if we take 38 to be the 100%, just the listed price alone, what is 1.14 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 38 & 100\\ 1.14& x \end{array} \implies \cfrac{38}{1.14}~~=~~\cfrac{100}{x} \implies 38x=114\implies x=\cfrac{114}{38}\implies x=3[/tex]

Answer:

To what please

Step-by-step explanation:

I am here to help you so please send your questions

The sequence of transformation that exhibits the similarity between the rectangles ABCD and rectangle A'B'C'D' is the option C.

C. Rectangle ABCD is reflected across the y-axis and then dilated by a scale factor of 2 with the center of dilation at the origin to obtain rectangle A'B'C'D'

A reflection transformation of an object gives or produces the mirror image of the object about a specified line.

The coordinates of the points of the rectangle ABCD obtained from the graph are; A(-4, -4), B(-4, 4), C(2, 4), and D(2, -4).

The coordinates of the image of the rectangle ABCD (rectangle (A'B'C'D') are; A'(8, -8), B'(8, 8), C'(-4, 8) and D'(-4, -8)

The coordinates of the reflection of the point (x, y), following a reflection across the y-axis is the point (-x, y)

The vertices of the image of rectangle ABCD formed following a reflection across the x-axis are therefore;

A(-4, -4)  [tex]\underrightarrow{R_{x-axis}}[/tex] A''(4, -4)

B(-4, 4)  [tex]\underrightarrow{R_{x-axis}}[/tex] B''(4, 4)

C(2, 4)  [tex]\underrightarrow{R_{x-axis}}[/tex] C''(-2, 4)

D(2, -4) [tex]\underrightarrow{R_{x-axis}}[/tex] D''(-2, -4)

The coordinates of the point (x, y) following a dilation by a scale factor of k, with the center of dilation at the origin is (k·x, k·y)

The dilation of the image of the rectangle ABCD by a scale factor of 2 gives;

A''(4, -4)  [tex]\underrightarrow{D_{2}}[/tex] (2×4, 2×(-4)) = A'(8, -8)

B''(4, 4)  [tex]\underrightarrow{D_{2}}[/tex] (2×4, 2×(4)) = B'(8, 8)

C''(-2, 4)  [tex]\underrightarrow{D_{2}}[/tex] (2×(-2), 2×(4)) = C'(-4, 8)

D''(-2, -4)  [tex]\underrightarrow{D_{2}}[/tex] (2×(-2), 2×(-4)) = D'(-4, -8)

The points of the image of rectangle ABCD following a a reflection and a dilation are A'(8, -8), B'(8, 8), C'(-4, 8) and D'(-4, -8), which are the same as the coordinates of the points of the given rectangle A'B'C'D'

The correct option is therefore option C;

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The expression for [tex]\sqrt{-27}[/tex] is 3i[tex]\sqrt{3}[/tex]

What is an expression?

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

given [tex]\sqrt{-27}[/tex] we know that

3 multiplied by 9 gives 27 and the square root of 9 is 3

we can write

[tex]\sqrt{-3(3)(3)}[/tex]

or [tex]3\sqrt{-3}[/tex]

square root of minus gives iota

we get,

[tex]3i\sqrt{3}[/tex]

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All the points are P1=(0, 2), P2= (1,3), P3(2,4), P4(3,5 ), and P5(4,6).

y=x+2 is obtained function through the equation y-x=2.

Consider the value of X=0 for P1.

Y= 0+2

Y=2

If X=0, then Y=2.

∴ (0, 2)

Consider the value of X=1 for P2.

Y=1+2

Y=3

If X=1, then Y=3

∴ (1,3)

Consider the value of X=2for P3.

Y=2+2

Y=4

If X=2, then Y=4

∴ (2,4)

Consider the value of X=3for P4.

Y=3+2

Y=5

If X=3, then Y=5.

∴ (3,5 )

Consider the value of X=4 for P5.

Y=4+2

Y=6

If X=4, then Y=6.

∴ (4,6)

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Answer: 56.25 = u

Step-by-step explanation:

1) Multiply 3 on both sides to leave u by itself

18.75 = u/3

18.75*3 = u

56.25 = u

Using mathematical operations, Maury bought 6 tickets at the Ticket Outlet if he paid $77 at $12 each.

The basic mathematical operations are addition, subtraction, multiplication, and division.

These basic operations are used to manipulate numbers and variables in mathematical expressions to produce mathematical results.

The first mathematical operation used here is the subtraction operation.  

After subtracting the fixed cost from the total cost, the difference is the total variable cost.

This difference is then divided by the unit variable cost to get the number of tickets.

The unit cost of the ticket = $12

The service charge (fixed cost) = $5

The total cost = $77

The number of tickets bought = 6 ($77 - $5)/$12

Thus, using mathematical operations, Maury did buy 6 tickets for $77.

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Answer: the answer is ..

Step-by-step explanation: fec r/sm mkdnjervc

Answer:

121

Step-by-step explanation:

11^6/11^4

= 11^(6-4)

= 11^2

= 121

[tex]=2t+5x+3-9t-4x+7\\=2t-9t+5x-4x+3+7\\=-7t+x+10[/tex]

Be aware I used the plus sign for 3 since you DID NOT insert the sign. For Future purposes Be careful.

Answer: -7t+x+10 (if the 3 in your equation is positive)

Step-by-step explanation: Add all like variables and integers.

The ordered pair which is a solution to the system of linear equations is: A. (3, 0).

In order to determine a solution to the system of linear equations, we would have to test the given ordered pairs by substituting their values into the linear equations as follows;

For ordered pair (3, 0), we have:

y = −x + 3

0 = -3 + 3

0 = 0 (True).

2x − y = 6

2(3) - 0 = 6

6 - 0 = 6

6 = 6 (True).

For ordered pair (3, -1), we have:

y = −x + 3

-1 = -3 + 3

-1 = 0 (False).

For ordered pair (0, 3), we have:

y = −x + 3

3 = 0 + 3

3 = 3 (True).

2x − y = 6

2(0) - 3 = 6

0 - 3 = 6

-3 = 6 (False).

For ordered pair (-1, 3), we have:

y = −x + 3

3 = -1 + 3

3 = 2 (False).

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