Answer:
20 New professors
Step-by-step explanation:The current ratio is 1200%2F80 = 15.
The new ratio/proportion should be %281500%29%2Fx = 15.
From here, find x = 1500%2F15 = 100 professors.
They must hire 100-80 = 20 new professors.
Answer: N=40
r=4
Step-by-step explanation:
We use the notation
�
P
�
nPrn, start text, P, end text, r to describe permutations. This notation represents the number of unique arrangements that exist when we select
�
rr objects without replacement from a set of
�
nn distinct objects.
In this scenario, how many students are we selecting to fill positions? How many students are we selecting from?
Hint #22 / 3
The student government is electing
4
44 of its
40
4040 members to fill the positions of president, vice president, secretary, and treasurer. So
�
nn should be
40
4040 and
�
rr should be
4
44.
Hint #33 / 3
These are the appropriate values of
�
nn and
�
rr:
�
=
40
�
=
4
n
r
=40
=4
(Multiple Choice) Solve In (2x + 3) = 7.
Round to the nearest thousandth.
A-
1095.133
B-
549.817
C-
1099.633
D-
546.817
Answer: it is D 546.817
what is the product of 2.31 and 0.21
Select the correct answer.
Which is the minimum or maximum value of the given function?
Answer:
C
Step-by-step explanation:
Line does not go over 1 on the y-axis
if 2⁴x ÷2x =64 find the value if x
with steps pls
Answer:
[tex]2 ^ { 4 } x \div 2x=64\\2^{4}x^{2}=128 \\16x^{2}=128 \\x^{2} = 128 \div 16\\x^{2}=8 \\x = \pm 2\sqrt{2}[/tex]
Answer: no solution or x ∈ Ø
Step-by-step explanation:
(2⁴ × x) ÷ 2x = 64
16x ÷ 2x = 64
[tex]\frac{16x}{2x} = 64[/tex]
8 = 64
8 = 64, x [tex]\neq[/tex] 0
8 = [tex]8^{2}[/tex]
2 = ㏒₈ 8
2 = 1
please help before 11 pm
B=?
Answer:
155.24
Step-by-step explanation:
[tex]\text{Apply sine rule,}\\\\~~~~~~~~\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}\\\\\\\implies \dfrac{b }{\sin B} = \dfrac{c}{ \sin C}\\\\\\\implies b = \dfrac{c \cdot \sin B}{\sin C}\\\\\\\implies b = \dfrac{197\sin 52^\circ}{\sin 51^{\circ}}~~~~~~~~~;\left[\angle C = 180^{\circ} - 77^{\circ} -52^{\circ} = 51^{\circ} \right]\\\\\\\implies b \approx 200[/tex]
Trains Two trains, Train A and Train B, weigh a total of 384 tons. Train A is heavier than Train B. The
difference of their weights is 288 tons. What is the weight of each train?
Train A weighs tons.
i think the answer is 336 bc 384+288=672 then divide
2 is 336,
(so sorry if im wrong)
Helppppp I really need this asap
Answer:
gago putangina mo bold
panget
need to paint an entire cylindrical tank (all sides) it is 29ft long and 9ft diameter find the total surface area.
Write the ratio 40.5 to 8.1 as a fraction
[tex]\cfrac{40.5}{8.1} ~~ \begin{cases} 40.5\implies \frac{405}{10}\\\\ 8.1\implies \frac{81}{10} \end{cases}\implies \cfrac{ ~~ \frac{405}{10} ~~ }{\frac{81}{10}}\implies \cfrac{405}{10}\cdot \cfrac{10}{81}\implies \cfrac{405}{81}\cdot \cfrac{10}{10} \\\\\\ \cfrac{5\cdot 81}{81}\cdot \cfrac{10}{10}\implies \cfrac{5}{1}\cdot \cfrac{81}{81}\cdot \cfrac{10}{10}\implies \cfrac{5}{1}\cdot 1\cdot 1\implies \cfrac{5}{1}[/tex]
PLEASE HELP WILL GIVE BRAINIEST HELPPP!!!!
Answer:
a. <B = 53°
b. BC = 14
c. x = 14
Step-by-step explanation:
Sine(theta) = Opp/HypCosine(theta) = Adj/HypTan(theta) = Opp/Adja. <B = ?
Use Sine.
Sine(<B) = 12 /15
<B = Sin^-1(12/15)
<B = 53.13
<B = 53°
b. BC = ?
Either use Sine(<A) = BC/16 or Cosine(<C) = BC/16
Will be using Cosine.
Cosine(<C) = BC/16
Cosine(30°) = BC/16
BC = 16 * Cos(30°)
BC = 13.856...
BC = 14
c. x = ?
Looking at the triangle. The triangle is isosceles which mean two side angle or side length are the same.
x = 14
Answer:
A: 53.13
B:13.86
C: 14
Step-by-step explanation:
A can be found by using the trigonometric ratio Sin.
Sin=
[tex] \frac{opp}{hyp} [/tex]
And we have our opposite side and hypotenuse. so insert it:
Sin=12/15
Therefore use sin inverse and input that fraction
[tex]sin { }^{ - 1} ( \frac{12}{15} )[/tex]
=53.13010235
Rounded off to two decimals
=53. 13
B can be found using sin again. Since we know that Sin is opp/hyp and we have the hyp, we are now looking for the opp.
So use Sin(60)=BC/16
Multiply 16 on both sides to get: 16Sin(30)=BC
13.85640646=BC
rounded off to two decimals:
13.86
C can be found using Tan. Tan is opp/adjacent
We have the adjacent and we are looking for the opposite.
So use:
tan(45)=X/14
Multiply 14 on both sides
14tan(45)=X
14=X
Hope that helps!
What percent of 6 is 9?
Answer:
150%
Step-by-step explanation:
half of 6 is three, and 9 has a value of 3 more than 6. meaning that 9/6 = 150%
Answer: [tex]150[/tex]% [tex]([/tex][tex]0.54[/tex][tex])[/tex]
Step-by-step explanation:
For fraction: divide 6 by 100 and remove the % sign.
{[tex]6[/tex]}% [tex]=\frac{6}{100}[/tex]
For decimal: move the decimal point 2 places to the left and remove the % sign.
{[tex]6[/tex]}% [tex]=0.06[/tex]
[tex]100[/tex]% [tex]=9[/tex]
[tex]\frac{6}{100}[/tex] × [tex]9=0.06[/tex] × [tex]9=0.54[/tex]
[tex]6[/tex]% [tex]of~9~is~0.54[/tex]
In the following function defined by an equation in the form y = a x squared + b x + c, identify the values of a, b, and c.
y = 5 x squared + 2 x minus 1
a.
a = negative 1, b = 2, c = 5
b.
a = negative 2, b = 5, c = 1
c.
a = 1, b = 5, c = 2
d.
a = 5, b = 2, c = negative 1
The correct answer is option D which is a = 5, b = 2, c = - 1.
What is a quadratic equation?It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given that:-
y = 5x² + 2x - 1The general form of the equation is given as:-
Y = ax² + bx + c
We have a quadratic equation:-
y = 5x² + 2x - 1
By comparing the equation with the general form the value of a, b and c is calculated:-
a = 5
b = 2
c = -1
Therefore the correct answer is option D which is a = 5, b = 2, c = - 1.
To know more about quadratic equations follow
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2x-17=51+61
Super easy!
[tex] \underline{ \boxed {\sf \color{cyan}{x = \frac{129}{2}}}}[/tex]
[tex]\pink{━━━━━━━━━━━━━━━━━━━━━━━━━━━━━}[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Solution :-[tex]\Longrightarrow\sf{2x- 17 =51 +61}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\sf{2x- 17= 112}[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\sf{2x- 17 + 17 = 112 + 17}[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\sf{2x = 129}[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\sf{\frac{ \cancel2x}{ \cancel2}=\frac{129}{2}}[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\sf{x = \frac{129}{2}}[/tex]
[tex]\pink{━━━━━━━━━━━━━━━━━━━━━━━━━━━━━}[/tex]
[tex]{\pink{\boxed{\blue{2x - 17 = 51 + 61}}}}[/tex]
SOLUTION =>2x - 17 = 51 + 61
[tex]{\blue{\boxed{{Take -17 \: \: to \: \: the \: \: other \: \: side \: \: and }}}}[/tex]
[tex]{\blue{\boxed{{its \: \: sign \: \: will \: \: change \: \: \: into \: \: + }}}}[/tex]
2x = 112 + 17
2x = 129
[tex]{\blue{x = {\pink{ \frac{129}{2} }}}}[/tex]
Stephen has 42 coins that are all dimes and nickels. The value of the coins is $3.65. How many dimes and how many nickels does Stephen have
answer is 31 dimes, 11 nickels
see picture attachment for the math
equation is .05N + .10D = 3.65
value of nickels and dimes
using D + N = 42
change to find value of N = 42 - D
plug value of N into the equation and solve
Which of the following are solutions to the equation cos^2 2x-1/4=0? Check all that apply.
A. 11pi/3
B. 12pi/6
C. 5pi/6
D. Pi/6
Answer:
D
Step-by-step explanation:
Cos^2 2x=1/4
Cos 2x =+-1/2
2x=z
Cos z=+-1/2
z1=pi/3
z2=11pi/3
z1 and z2 are possible.
x1=pi/6
x2=11pi/6
Is the answer b?????
Answer:
it should be A if not im sorry
Step-by-step explanation:
If you spin the spinner below, what is the
probability that you will land on a 2 ?
Calculate.
35 C12
Note: nCr=r(n=r)!
n!
[tex]\\ \rm\Rrightarrow {}^{35}C_{12}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{35!}{12!(35-12)!}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{35!}{12!23!}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1.0333148e+40}{12383157381152686026522624000000}[/tex]
[tex]\\ \rm\Rrightarrow 834451800[/tex]
Answer:
834,451,800
Step-by-step explanation:
Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.
Example: 4! = 4 × 3 × 2 × 1
Binomial Coefficient
[tex]\large \text{$ \rm ^{n}C_r=\dfrac{n!}{(n-r)!r!} $}[/tex]
[tex]\large \text{$ \rm \implies ^{35}C_{12}=\dfrac{35!}{(35-12)!12!} $}[/tex]
[tex]\large \text{$ \rm \implies ^{35}C_{12}=\dfrac{35!}23!12!} $}[/tex][tex]\large \text{$ \rm \implies ^{35}C_{12}=\dfrac{35!}{23!12!} $}[/tex]
[tex]\large \text{$ \rm \implies ^{35}C_{12}=\dfrac{35 \times 34 \times 33 \times ... \times 25 \times 24}{12!} $}[/tex]
[tex]\large \text{$ \rm \implies ^{35}C_{12}=834451800 $}[/tex]
Find the missing digit for the following bank identification numbers:
71100139█
321000█56
Answer:
711001392
321000759
Step-by-step explanation:
hope it helps ^o^
Type such digits that's are correlated to both numbers but they are not present in both rather than present in one.
They can be 2 and 7 or 5 and 9
711001392321000756You can write other one also
A 4-lb. force acting in the direction of (vector) 4,-2 moves an object just over 7ft from point (0,4) to (5,-1). Find the work done to move the object to the nearest foot-pound.
A) 35 ft*lbs
B) 27 ft*lbs
C) 18 ft*lbs
D) 7 ft*lbs
To solve this problem, we have to find the net displacement and the net force and the multiply the dot product together and get the work done.
The work done on moving the object is 27ft*lbs
Work done in moving the object from point A to point BTo find the work done on this object, let's find the net force on the object.
Data;
force = 4lbdirection = 4, -2displacement = 7ftdirection = (0, 4) to (5,1)The unit vector of the force is
[tex]\sqrt{4^2 +(-2)^2} =\sqrt{16 + 4} = \sqrt{20}[/tex]
[tex]\frac{4}{\sqrt{20} }, \frac{-2}{\sqrt{20} }[/tex]
The net force acting on the object is
[tex]F = 4(\frac{4}{\sqrt{20} }, \frac{-2}{\sqrt{20} })\\F= (\frac{16}{\sqrt{20} }, \frac{-8}{\sqrt{20} } )[/tex]
The displacement on the object is 7ft through (0,4) to (5, -1)
The unit vector on displacement is
[tex]\sqrt{5^2 + (-1-4)^2} = \sqrt{25+25} = \sqrt{50}[/tex]
[tex]\frac{5}{\sqrt{50} }, \frac{-5}{\sqrt{50} }[/tex]
The net displacement will be
[tex]7(\frac{5}{\sqrt{50} }, \frac{-5}{\sqrt{50} }) = \frac{35}{\sqrt{50} }, \frac{-35}{50}[/tex]
The work done will be F.d
[tex]w = f. d \\[/tex]
[tex]w = (\frac{16}{\sqrt{20} }, \frac{-8}{\sqrt{20} } ) * \frac{35}{\sqrt{50} }, \frac{-35}{50}\\w = 17.71+ 8.854\\w = 26.567 = 27ft*lbs[/tex]
The work done on moving the object is 27ft*lbs
Learn more on work done on an object here;
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Answer: the answer is B 27ft
Step-by-step explanation: its cam btw
after a 15% discount an item cost22.27 what was the origanl price
Answer:
26.2
X = 22.27/(1 - 0.15)
X = 22.27/0.85
X = 26.2
Step 1: 3x + 12 = 3 Step 2: ? Step 3: x = −9 ÷ 3 Step 4: x = −3 What is the missing Step 2? 3x = 9 3x = 15 3x = −9 3x = −15
The missing step is to subtract 12 from both sides of the equation.
The step would be:
3x = -9
A jar contains only dimes and nickels. The total number of coins in the jar is
15
. The total value of the coins is
$
1.00
. How many of each type of coin are in the jar?
Answer:
5 dimes and 10 nickels
Step-by-step explanation:
0.1d + 0.05n = 1
d + n = 15
d + 0.5n = 10
d + n = 15
0.5n = 5
n = 10
d + n = 15
d + 10 = 15
d = 5
Answer: 5 dimes and 10 nickels
Need help asap thanks
Answer:
x=1
Step-by-step explanation:
f(x)=-4x^2+8x-28 (Identify the cofficients)
a=-4, b=8 (Substitute the coefficients into the expression)
x=-8/2(-4) (solve the equation)
x=1
please tell me if i am wrong :)
Find the volume of a sphere with a surface area of 23041 in2.
Answer:V≈3.29×105in³
Step-by-step explanation:im smart
PLEASE ANSWER ASAP!
What is the slope of the line given by the equation? (Enter your answer as a decimal if necessary)
y= 2.25x+ 2.44
Answer:
slope = 2.25
Step-by-step explanation:
This equation is written in slope-intercept form, which has the general structure: y = mx + b.
In this form, "m" = slope and "b" = y-intercept.
Therefore, the slope is 2.25 since it is replacing the "m" variable.
How do you do this?
Answer:
you will have to get a protractor and angle side right
What is the measurement at plot a?
Answer:
An Acre is a propduct of any rectangular plot of land giving a total of 4,046sqm OR 43,560sq ft. An Acre consist of 6 plots each measuring 6 x 120ft. In Lagos State, the standard size of a plot is 60 x 120ft (18m x 36m ie 648sqm), while in some other cities of the country, plots are measured in 50 x100ft.
Step-by-step explanation:
Look at the corners of the shape below. Which of the following points is located at one of the corners?
(1,6)
(2,2)
(6,1)
(1,7)
Answer: (6,1)
Step-by-step explanation:
Coordinate points are written as (x, y).
Here is a tip for finding coordinate points on a graph:
[1] Start at the origin, point (0, 0) on the graph
[2] "Walk left/right to the elevator" - this is the x-coordinate value
[3] "Go up/down the elevator" - this is the y-coordinate value
Here is an example, using your problem:
-> See attached
[Points in Blue] Move one unit right, three units up to (1, 3)
[Points in Red] Move two units right, seven units up to (2, 7)
[Points in Green] Move 6 units right, one unit up to (6, 1)
-> This means the answer to your problem is the third option, (6, 1)
If you are color blind, let me know and I will rephrase it.
Please help! 100points! A sequence is defined recursively by the given formulas. Find the first five terms of the sequence.
an = 2(an − 1 + 4) and a1 = 5 (the n and n-1 is suppose to be a subscript, I just can't figure out how to make it like that)
Answer:
5, 18, 44, 96, 200
Step-by-step explanation:
Given
aₙ = 2(aₙ₋₁ + 4)a₁ = 5First term : 5
Second term : a₂ = 2(a₁ + 4)
a₂ = 2(5 + 4) = 2(9) = 18Third term : a₃ = 2(a₂ + 4) = 2(18 + 4) = 2(22) = 44
Fourth term : a₄ = 2(a₃ + 4) = 2(44 + 4) = 2(48) = 96
Fifth term : a₅ = 2(a₄ + 4) = 2(96 + 4) = 2(100) = 200
Hence, the first 5 terms of the sequence are :
5, 18, 44, 96, 200Answer:
5, 18, 44, 96, 200
Step-by-step explanation:
[tex]\textsf{Given sequence}: \quad a_n=2(a_{n-1}+4)[/tex]
[tex]\textsf{Given first term}: \quad a_1=5[/tex]
[tex]\implies a_1=5[/tex]
[tex]\implies a_2=2(a_{1}+4)=2(5+4)=2(9)=18[/tex]
[tex]\implies a_3=2(a_{2}+4)=2(18+4)=2(22)=44[/tex]
[tex]\implies a_4=2(a_{3}+4)=2(44+4)=2(48)=96[/tex]
[tex]\implies a_5=2(a_{4}+4)=2(96+4)=2(100)=200[/tex]