Answer:
(a): 10 civil servants who were absent.
(b): 15 civil servants are in field only.
Step-by-step explanation:
Let;
Civil servants in office be oCivil servants in field be f[tex]{ \rm{ \sum(n) = 90}} \\ \\ { \rm{n(o) = 65}} \\ \\ { \rm{n(f) = 50}} \\ \\ { \rm{(o \: { \huge{n}} \: f) = 35}}[/tex]
Question (a):
Let the absentees be x
[tex]{ \rm{x + (65 - 35) + (50 - 35) + 35 = 90}} \\ \\ { \rm{x + 80 = 90}} \\ \\ { \rm{x = 10}}[/tex]
There are 10 absentees.
Question (b):
Servants in field only;
[tex]{ \rm{n(f \: only) = 50 - 35}} \\ \\ { \rm{n(f \: only) = 15 \: servants}}[/tex]
Find the exact value of sin 29π/6
Group of answer choices
a 3/4
b 1/2
c -3/5
d 0
Answer:
b
Step-by-step explanation:
Remove full rotations of
2
π
until the angle is between
0
and
2
π
.
sin
(
5
π
6
)
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
sin
(
π
6
)
The exact value of
sin
(
π
6
)
is
1
2
.
1
2
The result can be shown in multiple forms.
Exact Form:
1
2
Decimal Form:
0.5
as a Given the function f(x) = - 3x + 2 then what is - 2f * (x) as a simplified polynomial ?
Answer: 6x - 4
Step-by-step explanation: -2*f(x) = -2 * (-3x+2) = (-2*-3x) + (-2*2) = 6x + (-4) = 6x - 4
f(x)=8x^3+125 find the zeros
Answer:
x = -5/2, (5+5i√3)/4, (5-5i√3)/4
A rectangular swimming pool is 8 ft deep. One side of the pool is 3.5 times longer than the other. The amount of water needed to fill the swimming pool is 2800 cubic feet. Find the dimensions of the pool. The smaller dimension of the pool is enter your response here ft and the larger dimension is enter your response here ft.
Answer:
smaller: 10 ftlarger: 35 ftStep-by-step explanation:
The volume of the pool is given by ...
V = LWH
Here, we have ...
V = 2800 ft³
H = 8 ft
L = 3.5W
Filling in these values, we have ...
2800 ft³ = (3.5W)(W)(8 ft)
100 ft² = W² . . . . . . . . . . . . divide by 28 ft
W = √(100 ft²) = 10 ft
L = 3.5W = 35 ft
The pool is 10 ft by 35 ft.
Yesterday, jack drove 28 1/2 miles. He used 1 1/4 gallons of gasoline. What is the unite rate for miles per gallon?
Answer
MPG= 30 4/5 or 30.8 is I think is the answer.
Please help it’s a test and it is past due!!! NO LINKS please!!!!
Use the substitution method to solve the system of equation!!! Choose the correct ordered pair!?!? Use the picture below to help you!!
Answer:
The answer is C. (-2, 7)
Good luck :)
AB with endpoints A(-2, -3) and B(4,4) is reflected in the line y = x to create its image A'B' Graph A' B' Then find the perimeter of the figure formed by the segments AB
BA' and AA to the nearest tenth
Answer:
Step-by-step explanation:
What is the square root of 12a^3b^5 times the square root of 6ab^2?
Step-by-step explanation:
sqrt(12×a³b⁵) × sqrt(6×ab²)
the content of multiplied square roots can be combined into one square root :
sqrt(12×6×a³×a×b⁵×b²) = sqrt( 72a⁴b⁷) =
= sqrt(4×9×2 × a⁴ ×b⁶×b) = 2×3×a²×b³×sqrt(2b) =
= 6a²b³×sqrt(2b)
Jarrod earns $12 an hour at his job. The table shows what Dale earns at his job. Which statement is true?
Answer:
Need the table, and the statements
Step-by-step explanation:
The marked price of a tablet is €800. During a sale its sold at €640. This means one saves €160 during the sale
a) Find the percentage discount
Answer:
c. $28.84
Step-by-step explanation:
C 28.84 just multiply 38.45 by .25 then you should get 9.6125 you subtract 38.45 by 9.6125 and get 28.84
Dr,Goode prescribes 0.2 grams of cold medicine for Donald. This medicine comes in tablets that are 0.5 grams or 0.05 grams. Should Donald dark 4 of the 0.5 gram tablets or 4 of the 0.05 gram tablets?
Using proportions, it is found that Donald should order 4 of the 0.05 gram tablets.
This question is solved by proportions, using a rule of three.4 tablets are needed, and they should combine for 0.2 grams. How many grams is there going to be on one tablet?The rule of three is:
1 tablet - x grams
4 tablets - 0.2 grams
Applying cross multiplication:
[tex]4x = 0.2[/tex]
[tex]x = \frac{0.2}{4}[/tex]
[tex]x = 0.05[/tex]
Donald should order 4 of the 0.05 gram tablets.
For more on proportions, you can check https://brainly.com/question/24372153
determining end behavior and intercepts to graph a polynomial function
Answer:
Step-by-step explanation:
(b). ( x , 0 )
Zero where the graph crosses the X-axis: 1
Zero where the graph touches, but does not cross the X-axis: ( - 1 )
(c). ( 0, y )
- ( 0 + 1 )²( 0 - 1 ) = 1
What is the range of y=3sin(x)?
Answer:
The range is -3≤y≤3 - 3≤y≤3.
Step-by-step explanation:
I hope this helps! :)
what is the slope of a line with points (0,3) and (5,18)
Answer:
bye
Step-by-step explanation:
One week Roger earned $425.50 regular pay and $60.50 overtime pay. His net pay for the week was $275.30. How much did he have withheld for deductions?
Answer:
He had $210.7 withheld for deductions
Step-by-step explanation:
Add his regular pay to his overtime pay
$425.50 + $60.50 = $486
After adding both his overtime and regular pay, he'd have $486. Now, take that and subtract his net pay
$486 - $275.30 = $210.7 :)
5x+3y=17 x+y=4 substitution
Gracy was running errands around her neighborhood. First she went to the doctors but they were closed. She then drove to her house stopping to grab her library books. She went to the library to drop them off then headed to the grocery story passing her house on the way.
In total, how far would Gracy have traveled once she returned home from the grocery store?
9miles
3 miles
18 miles
6 miles
How would this question be solved?
Answer:
it would be solved by it mom
Simplify the complex number.
(8i) (5) (-4-6i)
Answer:
4th option
Step-by-step explanation:
noting that i² = - 1
(8i)(5i)(- 4 - 6i)
= 40i²(- 4 - 6i)
= 40(- 1)(- 4 - 6i)
= - 40(- 4 - 6i) ← distribute parenthesis by - 40
= 160 + 240i
[tex](8i)(5i)(-4-6i)\\\\=40i^2(-4-6i)\\\\=-40(-4-6i)~~~;[i^2=-1]\\\\=160+240i[/tex]
If you buy three of the ABC bonds with $10 commission for each, how much will it cost? a. $3142.50 b. $1047.50 c. $3172.50 d. $1077.50
The computation shows that the cost of each bond is A. $3142.50.
How to solve the cost?From the complete information given, the price of the bond is given as $2856.80 each.
Therefore, with the commission, the price will be:
= $2856.80 + (10% × $2856.80)
= $2856.80 + $285.68
= $3142.50
In conclusion, the cost of each bond is $3142.50.
Learn more about cost on:
https://brainly.com/question/25109150
Answer:
it's A
Step-by-step explanation:
maybe
A baseball traveled 330 feet in 5 seconds. Which rate is equivalent to the rate at which the baseball traveled?
Answer:
The ratio is equivalent to 65:1.Step-by-step explanation:
When we read the question carefully, we get the ratio 330:5
=> 330:5 = 330/5 = 65/1 = 65:1
Conclusion:
Therefore, the ratio is equivalent to 65:1.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Billy likes to go cycling.
His bike has wheels of diameter 80 cm.
He has a counter on his bike which
counts the number of revolutions
the wheels make.
One day the counter shows 350 revolutions.
How far has Billy cycled?
Give your answer to the nearest metre.
Answer:
560 metres
Step-by-step explanation:
80 cm in metres is 0.8 metres.
After 1 revolution any point on the wheel will be back to the original position before moving. 0.8 times 2, which gives us 1.6 metres. In 1 revolution the bike travels 1.6 metres.
Now 1.6 metres times 350 gives us 560.
So the answer is 560 metres.
need help in a math question
Answer:
- [tex]\frac{7}{6}[/tex]
Step-by-step explanation:
I hope this helps
Eugene is purchasing clothing to make different outfits. Each outfit consists of a top, a bottom and a pair of shoes. Eugene found 2 pairs of shoes and 4 bottoms he would like to purchase. What is the minimum number of tops Eugene needs to purchase to make at least 35 different outfits? Express your answer as a whole number.
Answer:
70
Step-by-step explanation:
The following angles are
Supplemnetary
Linear Pair
Adjacent
Vertical Angles
[tex]\huge \bf༆ Answer ༄[/tex]
The shown pair of Angles are known as Adjacent Angles, because they have one Arm in common.
H.C.F of 378 and 567 and 252
Answer:
Their highest common factor is the number 9
Does ANYONE Know How To Solve THIs…Brainliest Will be awarded!!!
Answer:
w = 8x = 8√2y = 8√2z = 16Step-by-step explanation:
A 45-45-90 right triangle is isosceles. That means both legs are the same length, and its hypotenuse is √2 times the leg length. You can figure these facts using trigonometry or the Pythagorean theorem, or you can rely on your memory of them.
w = 8 . . . . . . . . . . . same as the leg length shown
x = y = 8√2 . . . . . hypotenuse of smaller triangle; both legs are the same
z = (8√2)√2 = 16 . . . . hypotenuse of larger triangle
In Lucy’s coin collection, 15% of the coins are quarters.
If there are 12 quarters, find the total number of coins in Lucy’s coin collection
80 coins
.15x=12
divide both sides by .15
x= 80
in the expression 3² + 5 · 3 what needs to be done first? exponents addition multiplication
Answer:
If you use the PEMDAS method, you can see that exponents should be done first.
Step-by-step explanation:
Solve for x
16x^2 + 9 = 5
Answer:
X=-4
Step-by-step explanation:
16x^2+9=5
- 9 -9
16x^2= -4
16/-4 =
-4
