Answer:
A. 4 2/3 hours
B. (i) 9 4/5 hours
(ii) 1 19/30
Step-by-step explanation:
Firstly, to find the number of hours he used in visiting old folks, what we have to do is to multiply the fraction of hours he used by the total number of hours.
Mathematically, that would be;
4/7 * 8 1/6
8 1/6 is same as 49/6
So the number of hours he spent visiting old folks would be ;
49/6 * 4/7 = 14/3 = 4 2/3 hours
B. What we do here is simply multiply the fraction now by what he spent last year.
That would be 1 1/5 * 8 1/6 hours
= 6/5 * 49/6 = 49/5 = 9 4/5 hours
ii) Now we want to know how much more time will be spent this year than last year.
What to do here simply is to subtract the time taken last year from what we have this year
That would be;
49/5 - 49/6 = 49/30 = 1 19/30
A machine lifts up containers of coal from the mine and lowers empty containers down. The machine uses an electric motor connected to a 600 V d.c. supply.The maximum current in the motor is 4000 A. *Calculate the maximum power available from the motor. Give your answer in MW* power = voltage x current i believe
Answer:
The maximum power available to the motor is 2.4 MW
Step-by-step explanation:
The power of a circuit that has a current, I, and a voltage, V, is given by the relation
Electrical power, P = I²R = I× I×R = I × V
Therefore given that the parameters are;
Voltage in the d.c. power supply = 600 V d.c.
Maximum current in the motor = 4000 A
Therefore, we can find the power as follows;
Maximum motor power = Voltage × Current
The maximum motor power, P available = 600 V × 4000 A = 2400000 W which on converting to MW becomes;
The maximum power available to the motor , P = 2.4 MW.
Write 3x 1/2 in radical form
Answer:
3x^1/2 in radical form is
[tex] \sqrt{3x} [/tex]
Hope this helps you
There are eight marbles in a bag. Four marbles are blue (B), two marbles are red (R) and two marbles are green (G) Steve takes a marble at random from the bag. What is the probability that Steve will take a blue marble.
Answer:
1/2
Step-by-step explanation:
There are 8 marbles in total and 4 are blue, so 4/8 are blue. Then simplify 4/8 and you will get 1/2.
Answer:
1/2 or 50%
Step-by-step explanation:
Blue= 4, Red= 2, Green= 2
Total marbles= 8
P(B)= 4/8= 1/2 or 50%
Which of the following is the sum of the slopes of the line 3x+y=1 and a line perpendicular to this line? A 0 B 13 C −83 D −6
Answer:
-8/3
Step-by-step explanation:
First find the slope of the line
3x+y = 1
Solve for y
y = -3x+1
This is in slope intercept form
y = mx+b where m is the slope
The slope is -3
The slopes of perpendicular lines multiply to -1
m* -3 = -1
m = 1/3
The line perpendicular has a slope of 1 / (3) = 1/3
The sum is -3 + 1/3
-9/2 + 1/3 = -8/3
Simplify.
Rewrite the expression in the form b^n
(b^3)^2
Answer: b⁶
Step-by-step explanation:
The for bⁿ can be optained by multiplying 3 and 2. If there is an exponent on the outside of the parenthesis, you multiply it with the exponent on the inside.
(b³)²=b³ˣ²=b⁶
Mr. Hughes has contributed $4000.00 per year for the last ten years into a RRSP account earning 9.00% compounded annually. Suppose he leaves the accumulated contributions for another five years in the RRSP at the same rate of interest. A) How much will Mr. Hughes have in total in his RRSP account? B) How much did Mr. Hughes contribute? C) How much will be interest?
Answer:
A) $93,504.818
B) $40,000
C) $53,504.818
Step-by-step explanation:
Yearly contribution ( periodic payment) = $4000
Period (p) = 10years
Additional period(y) = 5years
Annual interest(r) = 9% = 0.09
Future value (FV) =
periodic payment [(1 + r)^y - 1] / r
4000 [(1 + 0.09)^10 - 1 / 0.09]
4000[1.09^10 - 1 / 0.09]
4000[1.3673636 / 0.09]
4000(15.192929)
= 60771.716
If left for five more years:
FV = 60771.716(1 + r)^n
FV = 60771.716(1 + 0.09)^5
FV = 60771.716(1.09)^5
FV = 60771.716(1.5386239549)
FV = $93,504.818
B) MR. HUGHES CONTRIBUTION :
Periodic payment × p ; $4000 was deposited annually for 10 years.
$4000 × 10 = $40,000
C) Interest = Future value - contribution
$93,504.818 - $40,000
= $53,504.818
Which number is a perfect cube?
O9
O 18
0 27
O 36
Answer:
27
Step-by-step explanation:
9 is not a perfect cube.
18 is not a perfect cube.
27 is a perfect cube.
∛27 = 3
36 is not a perfect cube.
Answer:
27
Step-by-step explanation:
We want a number time itself times itself
27 = 3*3*3
27 = 3^3
Help im stuck on this question
Work out the area of the rectangle using a calculator and
giving your answer as a mixed number.
22 cm
5 cm
1
Note: To enter a mixed number in the answer boxes, please use the following method:
Type the fractional part of the mixed number first (e.g. for 6 first enter 5)
Then use the keyboard arrows to return to the front of the box and type the whole number (e.g. for 6
5 enter 6).
Answer:
11 17/21 cm²
Step-by-step explanation:
5 1/6 = (5*6 + 1)/6 = 31/6
2 2/7 = (2*7 + 2)/7 = 16/7
A = 31/6*16/7 = 496⁽²/42 = 248/21 = 11 17/21 cm²
Zaheer, a boy of height 1.5m was watching the entire programme. Initially he observed the top of theflagpoleat an angle of elevation 300 . When he moved 10 m towards the flag post the angle of elevation of the top of the flagpole increased to 450. What is the height of the flag pole?
Answer:
[tex]h = 15.163\ meters[/tex]
Step-by-step explanation:
(Assuming the correct angles are 30° and 45°)
We can use the tangent relation of the angle of elevation to find two equations, then we can use these equations to find the height of the pole.
Let's call the initial distance of the boy to the pole 'x'.
Then, with an angle of elevation of 30°, the opposite side to this angle is the height of the pole (let's call this 'h') minus the height of the boy, and the adjacent side to the angle is the distance x:
[tex]tan(30) = (h - 1.5) / x[/tex]
Then, with an angle of elevation of 45°, the opposite side to this angle is still the height of the pole minus the height of the boy, and the adjacent side to the angle is the distance x minus 10:
[tex]tan(45) = (h - 1.5) / (x - 10)[/tex]
So rewriting both equations using the tangents values, we have that:
[tex]0.5774 = (h - 1.5) / x[/tex]
[tex]1 = (h - 1.5) / (x - 10) \rightarrow (h - 1.5) = (x - 10)[/tex]
From the first equation, we have that:
[tex]x = (h - 1.5) / 0.5774[/tex]
Using this value of x in the second equation, we have that:
[tex]h - 1.5 = \frac{ (h - 1.5) }{0.5774} - 10[/tex]
[tex]h + 8.5 = \frac{ (h - 1.5) }{0.5774}[/tex]
[tex]0.5774h + 4.9079 = h - 1.5[/tex]
[tex]0.4226h = 6.4079[/tex]
[tex]h = 15.163\ meters[/tex]
NEED MATH HELP NOW. Please solve for the x-intercept. Please show work.
Answer:
x = 1 and x = 3.
Step-by-step explanation:
y = 2[tex]x^{2}[/tex] - 8x + 6
y = 2([tex]x^{2}[/tex] - 4x + 3)
y = 2(x - 3)(x - 1)
So, the x-intercepts would be at...
x-3 = 0
x = 3
and
x - 1 = 0
x = 1
Hope this helps!
PLEASE HELP ME WITH THESE QUESTIONS
Answer:
hope its wht u require....
x+x/7 + 1/11 (x + x/7) = 60
Answer:
X= 48.125
Step-by-step explanation:
pleaseee help! i need the answer for x (look at picture)
Answer:
180 - 133
Step-by-step explanation:
Answer:
x = 47 degrees
Step-by-step explanation:
Solve for X:
x + 133 = 180
180 - 133 = 47
x = 47
factor: (a+3)^2-a(a+3)
Answer:
Factor (a+3)2−a(a+3)
3a+9
=3(a+3)
Answer:
3(a+3)
I hope this help :)
Answer:
(a+3)(3)
Step-by-step explanation:
(a+3)^2-a(a+3)
(a+3)(a+3)-a(a+3)
Factor (a+3)
(a+3)(a+3-a)
(a+3)(3)
If the slope of the line joining the points (2k, -2) and (1, - k) be (-2), find k
Answer:
k=4/5
Step-by-step explanation:
(-k+2)/(1-2k) = -2 ( using the slope formula (y2-y1)/(x2-x1) )
-k+2 = -2 (1-2k)
-k+2 = -2 + 4k
2= -2 +5k
4 = 5k
k=4/5
Answer:
k = 4/5Step-by-step explanation:
To find k use the formula for finding the slope of a line and equate it to the slope which is - 2
So we have
(2k, -2) and (1, - k)
[tex] - 2 = \frac{ - k + 2}{1 - 2k} [/tex]
Cross multiply
That's
- 2( 1 - 2k ) = - k + 2
Expand and simplify
- 2 + 4k = - k + 2
Group like terms
4k + k = 2 + 2
5k = 4
Divide both sides by 5
k = 4/5
Hope this helps you
What the answer question
Answer:
Step-by-step explanation:
UV & UT are the sides
A piece of aluminum with a mass of 100.0 g has a temperature of 20.0°C. It absorbs 1100 J of heat energy. What is the final temperature of the metal?
Answer:
31.81°CStep-by-step explanation:
Using the formula for calculating heat energy H = mcΔT
m = mass of the aluminum (in g/kg)
c = specific heat capacity of aluminum
ΔT = change in temperature = T - Ti (in °C)
T is the final temperature
Ti is the initial temperature
Given m = 100.0g, c = 0.931096J/g °C, Ti = 20°C, H = 1100J T = ?
Substituting the given values into the formula;
1100 = 100*0.931096 (T - 20)
1100 = 93.1096T - 1862.192
93.1096 T = 1100+1862.192
93.1096 T = 2962.192
T = 2962.192/93.1096
T = 31.81°C
The final temperature of the metal is 31.81°C
Answer:
31.81c
Step-by-step explanation:
1100 = 100*0.931096 (T - 20)
1100 = 93.1096T - 1862.192
93.1096 T = 1100+1862.192
93.1096 T = 2962.192
T = 2962.192/93.1096
T = 31.81°C
Two cards are drawn in succession and without replacement from a standard deck of 52 cards. Find the probability that the second card is a face card if it’s known that the first card was a face card.
Answer:
The probability that the second card is a face card if it’s known that the first card was a face card is 0.0497
Step-by-step explanation:
Total number of face cards = 12
Total cards = 52
Probability of getting face card on first draw=[tex]\frac{12}{52}[/tex]
Remaining no. of face cards = 11
Remaining number of total cards = 51
Probability of getting face card on second draw=[tex]\frac{11}{51}[/tex]
The probability that the second card is a face card if it’s known that the first card was a face card =[tex]\frac{12}{52} \times \frac{11}{51}= \frac{12}{52} \times \frac{11}{51}=0.0497[/tex]
Hence The probability that the second card is a face card if it’s known that the first card was a face card is 0.0497
Write [tex]3x^{2} -x-3+x^{3}[/tex] in standard form. Identify the leading coefficient.
Answer:
Standard form: [tex]x^3+3x^2-x-3[/tex]
Leading coefficient: 1
Step-by-step explanation:
[tex]3x^2-x-3+x^3=\\x^3+3x^2-x-3[/tex]
The leading coefficient is 1 because the leading term is [tex]x^3[/tex].
Triangle DEF is an isosceles, so AngleDEF Is-congruent-toAngleDFE. A horizontal line has points C, F, E, G. 2 lines extend from the line at points F and E to form an isosceles triangle with point D. Angle DEF measures 75°. What is the measure of angle CFD? 105° 125° 150° 165°
Answer:
105 degrees
Step-by-step explanation:
Angle DEF measures 75°.Triangle DEF is an isosceles, so AngleDEF Is-congruent-toAngleDFE.
the angles all together is 180 degrees
so 180 - 75 = 105 degrees
The measure of angle CFD is 105 degrees.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
Angle DEF = 75°.
Triangle DEF is isosceles, so Angle DEF Is-congruent-to Angle DFE.
Angle DFE + Angle CFD = 180 (angle on a straight line)
so 180 - 75 = 105 degrees
Thus, Angle CFD = 105 degree
Learn more about the triangles;
https://brainly.com/question/2773823
#SPJ2
help can you also show how you do it too
Answer:
m the slope of function=-3
Step-by-step explanation:
to find the slope take two points from the graph:
(0,4), (1,1)
m= y2-y1/x2-x1
m=1-4/1-0
m=-3/1=-3
the equation : y=mx+b find b
when x=0, y=b=4
y=-3x+4
what is productivity?
a. quantity of input per unit of output
b. quantity of output per unit of input
c. quality of output per unit of input
d. quality of input per unit of output
Answer:
This is the quantity of output per unit of input.
Step-by-step explanation:
I'm very sure.
You have a wire that is 50 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum
Answer:
88.6647727273 cm²
Step-by-step explanation :
The perimeter of the square =(50/2)
= 25 cm
∴ Side of the square = (25/4)
= 6.25 cm
∴ Area of of the square = (6.25)²
= 39.0625 cm²
The circumference of the circle =(50/2)
= 25 cm
∴ 2πr = 25
⇒ r = 25/(22/7)(2)
Area of the circle = (22/7) { 25/(22/7)2} {25/(22/7)2}
= (25×25×7) / (2×2×22)
= 4365/88
= 49.6022727273 cm²
∴ Total area of the circle and the square =(49.6022727273+39.0625000000)
= 88.6647727273 cm²
Hope it helped
If yes mark BRAINLIEST!
Keith is the leading goal scorer for a team in an ice hockey league . Last season , he scored 42 goals in 82 games . Assuming he scores goals at at a constant rate , what is the slope of the line that represents this relashonships if the number of games is is along the x-axis and the number of goals is along the y-axis
Answer: The slope is 21/41.
Step-by-step explanation:
IF the goals he scores is at a constant rate the we know if you would have to graph it, it will go through the origin.
To find the slope of a constant relationship,you will divide the y value by the x value.Now it indicates to us that x is the number of games while y is the number of goals.
so 42/82 which reduces to 21/41 has to be the slope .
Answer:
it’s 21/41 or A (I got a 100% on the test)
HELP PLZZZZZZZZZZZ!!!!!!!
Answer:
A) 21/20
Step-by-step explanation:
Tangent = Opposite/Adjacent
Need help with #11 please
Answer: The graph is a linear graph or linear function in the form y= mx + b where m is the slope and b is the y-intercept. You could plot the points (0,5) (1,4) (2,3) (4,1) and draw a straight line through them.
Step-by-step explanation:
The equation y= 5-x can be rewrite as y = -1x + 5 and it can be identify as a linear equation in slope intercept form. Now you could plot in any value of x and solve for y.
x y (x,y)
0 5 (0,5) If you put in 0 for x y will be 5
1 4 (1,4) if you put in 1 for x, y will be 4
2 3 (2,3) if you put in 2 for x, y will be 3
4 1 (4,1) if you put in 4 for x, y will be 1
5 0 (5,0) if you put in 5 for x y will be 0.
To steam rice, Paul uses m cups of water for every p
cups of rice. In terms of m and p, how many cups of
water are needed to steam p + 2 cups of rice?
Answer:
[tex]\frac{(p + 2)m}{p}[/tex]
Step-by-step explanation:
Given
m cups of water = p cups of rice
Required
Cups of water required for p + 2 cups of rice
The question shows a direct proportion between cups of rice and cups of water.
So, the first step is to get the proportionality constant (k)
This is calculated using the following expression;
[tex]m = k * p[/tex]
Where k represents cups of water and p represents cups of rice
Make k the subject of formula
[tex]k = \frac{m}{p}[/tex]
Let x represents cups of water when cups of rice becomes p + 2;
k becomes:
[tex]k = \frac{x}{p + 2}[/tex]
Equate both expressions of k; to give
[tex]\frac{m}{p} = \frac{x}{p + 2}[/tex]
Multiply both sides by p + 2
[tex](p + 2) * \frac{m}{p} =(p + 2) * \frac{x}{p + 2}[/tex]
[tex](p + 2) * \frac{m}{p} =x[/tex]
[tex]x = (p + 2) * \frac{m}{p}[/tex]
[tex]x = \frac{(p + 2)m}{p}[/tex]
Hence, the expression that represents the cups of water needed is [tex]\frac{(p + 2)m}{p}[/tex]
What is 45% as a fraction in simplest form
⇒Answer:
[tex]\frac{9}{20}[/tex]
⇒Step-by-step explanation:
Well 45% is saying it is 45% out of 100,
So we can make the following fraction
45/100
Then we simplify by dividing 45 and 100 by 5
Hence, the answer is [tex]\frac{9}{20}[/tex]
Please answer this question fast in two minutes
Answer:
lines NP and OP are intersecting
Step-by-step explanation:
they touch at point P
Factored completely, the expression 2y^2 + 12y-54 is equivalent to
a. 2(y + 9)(y - 3)
b. 2(y - 3)(y-9)
c. (y+ 6)(2y - 9)
d. (2y + 6)(y-9)