The College employee in total count will be 60 professors and 168 lecturers in the college community.
As given total number of faculty member in the school is 228.
Also we have information that for every 14 lecturers the college community has 5 professors counting ratio.
∴ Let's Combine the number of professor and number of lecturers and make one group as a set.
∴ Total of one set will be 5 + 14 = 19.
Now as we have total 228 members and we have the set value as 19 so we can find the total number of set that can be possible with the given members as follows [tex] \frac{228}{19} = 12 [/tex]
Hence total number of set will be 12.
As one set contains 5 number of professors so 12 sets will contain in total ( 12 * 5 ) = 60 number of professors.
As one set contains 14 number of lecturers so 12 sets will contain in total ( 12 * 14 ) = 168 number of lecturers .
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Which sequence exhibits the similarity between rectangles ABCD which A’B’C’D’ shown in the coordinates plane below
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'
What is a reflection transformation in geometry?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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Bricklayers use the formula n = 7th to estimate the number n
of bricks needed to build a wall of length and height h, where and hare in
feet. Solve the formula for h. Estimate the height of a wall 28 ft long that requires
1568 bricks.
(Round to the nearest tenth if necessary)
Answer: the answer is ..
Step-by-step explanation: fec r/sm mkdnjervc
Find sin 8, cot0, and csc0, where 8 is the angle shown in the figure.
Give exact values, not decimal approximations.
Continue
25
0
sin 0
11
▬
cot 8 = 0
CSC8 = 0
믐
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!
Pot the points (4, 4), (8, 4), (3, 1), and (7, 1) on the coordinate plane.Use the points to draw two parallel, horizontal segments. Label theendpoints of one segment A and B. Label the endpoints of the othersegment C and D What is the distance between points A and B?What is the distance between points C and D
Solution
The diagram below shows what is needed
As shown above
distance between points A and B is
[tex]4[/tex]distance between points C and D is
[tex]4[/tex]If f(x) = –2x+4 Evaluate the function when x= -3. f(-3) = ?
Answer:
f(-3)=10
Explanation:
Given the function:
[tex]f\mleft(x\mright)=-2x+4[/tex]When x = -3
[tex]\begin{gathered} f(-3)=-2(-3)+4 \\ =6+4 \\ =10 \end{gathered}[/tex]trucks in a delivery fleet travel a mean of 80 miles per day with a standard deviation of 26 miles per day. the mileage per day is distributed normally. find the probability that a truck drives at least 113 miles in a day. round your answer to four decimal places.
Answer:
0.1037
Step-by-step explanation:
Write an equation that passes through the given points and is perpendicular to the line , (-3,1); y=-5x+2, write it in slope-intercept form pls.
The equation of the line that passes through point (-3,1) and perpendicular to y=-5x+2 is y = (1/5)x + 8/5.
What is the equation of line that passes through the given points and is perpendicular to the given line?Given the data in the question;
Equation of line: y = -5x + 2Point: (-3,1)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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Write the relation as a set of ordered pairs. a. ordered pairs: {(–1, 1), (2, 0), (3, 1)} b. ordered pairs: {(–1, 1), (0, 2), (1, 3)} c. ordered pairs: {(1, –1), (0, 2), (1, 3)} d. ordered pairs: {(1, –1), (2, 0), (3, 1)} Please select the best answer from the choices provided A B C D
Answer:
a) (in order) {-1, 0, 1, 2, 3}
b) {-1, 0, 1, 2, 3}
Step-by-step explanation:
Which point is a solution to the system of linear equations?
y = −x + 3
2x − y = 6
(3, 0)
(3, −1)
(0, 3)
(−1, 3)
The ordered pair which is a solution to the system of linear equations is: A. (3, 0).
How to determine the solution?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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It took Elsa 18 minutes to make 3 bookmarks.
Which of the following pairs of equivalent fractions could be used to determine how many bookmarks she can make in 90 minutes?
y=x+2 find the coordinates of the x and y intercept
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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Evaluate. Write your answer as a whole number or as a simplified fraction.
Answer:
121
Step-by-step explanation:
11^6/11^4
= 11^(6-4)
= 11^2
= 121
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.
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
Find the points on the graph of[tex]x^{2/3}[/tex] + [tex]y^{2/3}[/tex] = 1 where the tangent line has slope 1
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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A $40 phone case is taxed with
an 8% sales tax. How much tax will be
paid?
Answer: $3.20 is the sales tax
Step-by-step explanation:
[tex]\frac{8x40}{100} =3.2[/tex] (8 times 40 divided by 100)
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63= 4w + 15 solve for w and simplify your anwser as much as possible.
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
uppose p ( t ) p(t) represents the population of a certain mosquito colony, where t t is measured in days. the current population of the colony is known to be 578 578 mosquitos; that is, p ( 0 )
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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Which expressions are equivalent to ✓-27?
3i√3
91√√/3
O √27i
O i√27
3√/91²
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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18.75 = u/3 solve for u please
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
Answer the question in the photo for EASY points ( 20 points )
Answer: 7921 123569 5410
Step-by-step explanation:
1. 7912
2. 123569
3. 5210
(2t + 5x 3) + (-9t - 4x + 7)
[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.
DOES ANYONE KNOW THE ANSWERSSSS
65 pt
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:
Flour = 1.5xButter = 0.5xThe 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.
Solve for xx + 0.5x + 1.5x = 7.53x = 7.5x = 2.5Clifford 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.
I need help please. Find the distance between Points U and Q.
Answer:
1 unit
Step-by-step explanation:
- 1 1/2 - (- 2 1/2)
= 1 unit
9th grade math helppp
Answer:
b
Step-by-step explanation:
Simplify m^9 m^−3.
A. -m^12
B. 1 / m^27
C. 1 / m^6
D. m^6
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
The listed price of the pair of pants was $38, but the price with tax came to $39.14. Find the percent sales tax.
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]
i need the right answers please help
Answer:
To what please
Step-by-step explanation:
I am here to help you so please send your questions
HELP PLEASE!!A(5,1), B(7,1), C(7,6), D(5,6) What is the perimeter of rectangle ABCD?
45. Maury bought concert tickets at the Ticket Outlet. He paid $12 for each
ticket, plus a $5 service charge for the whole set of tickets. The total cost
was $77. How many tickets did he buy? 3-11
Using mathematical operations, Maury bought 6 tickets at the Ticket Outlet if he paid $77 at $12 each.
What are the mathematical operations?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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Create three probability application problems of your own. Solve your problems. Explain your answers.
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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