Answer:
C
Step-by-step explanation:
Okay, here we have a reduction in the number of students by 20% from 2010 to 2011.
In 2011, we had k students, so we want to calculate the number of students we had in 2010.
Let the number of students present in 2010 be x
So mathematically;
x - 20% of x = k
x - 0.2(x) = k
0.8x = k
x = k/0.8
x = k * 1/0.8
x = k * 1.25
x = 1.25k
A.) pinky bought 1 1/2 kg of apples and 5 1/4 kg of mangoes and 1 1/2 Kg of oranges. Find the total weight of fruits B.) If her family eats 3/4 Kg of apples and 2 1/2 kg of mangoes and 1/2 Kg of oranges. Find the weight of the fruits left (Can any one say the answer please with explanation if who say the answer first I will mark them as the brainliest)
Answer:
a) The total weight of fruits is [tex]8\,\frac{1}{4}[/tex] kilograms, b) The weight of the fruits left is [tex]4\,\frac{1}{2}[/tex] kilograms.
Step-by-step explanation:
a) The total weight of fruits ([tex]m_{T}[/tex]) is calculated by the following formula:
[tex]m_{T} = m_{a} + m_{m}+m_{o}[/tex]
Where:
[tex]m_{a}[/tex] - Total weight of apples, measured in kilograms.
[tex]m_{m}[/tex] - Total weight of mangoes, measured in kilograms.
[tex]m_{o}[/tex] - Total weight of oranges, measured in kilograms.
If [tex]m_{a} = 1\,\frac{1}{2} \,kg[/tex], [tex]m_{m} = 5\,\frac{1}{4}\,kg[/tex] and [tex]m_{o} = 1\,\frac{1}{2}\,kg[/tex], then:
[tex]m_{T} = 1\,\frac{1}{2}\,kg + 5\,\frac{1}{4}\,kg + 1\,\frac{1}{2}\,kg[/tex]
[tex]m_{T} = \frac{6}{4}\,kg + \frac{21}{4}\,kg + \frac{6}{4}\,kg[/tex]
[tex]m_{T} = \frac{33}{4}\,kg[/tex]
[tex]m_{T} = 8\,\frac{1}{4}\,kg[/tex]
The total weight of fruits is [tex]8\,\frac{1}{4}[/tex] kilograms.
b) The weight eaten by her family is determined by the following expression:
[tex]m_{E} = m_{a,e} + m_{m,e} + m_{o,e}[/tex]
Where:
[tex]m_{a,e}[/tex] - Eaten weight of apples, measured in kilograms.
[tex]m_{m,e}[/tex] - Eaten weight of mangoes, measured in kilograms.
[tex]m_{o,e}[/tex] - Eaten weight of oranges, measured in kilograms.
Given that [tex]m_{a,e} = \frac{3}{4}\,kg[/tex], [tex]m_{m,e} = 2\,\frac{1}{2}\,kg[/tex] and [tex]m_{o,e} = \frac{1}{2}\,kg[/tex], the weight eaten by her family is:
[tex]m_{E} = \frac{3}{4}\,kg + 2\,\frac{1}{2}\,kg + \frac{1}{2}\,kg[/tex]
[tex]m_{E} = \frac{3}{4}\,kg + \frac{10}{4}\,kg + \frac{2}{4}\,kg[/tex]
[tex]m_{E} = \frac{15}{4}\,kg[/tex]
[tex]m_{E} = 3\,\frac{3}{4}\,kg[/tex]
The weight of the fruits left is found by subtraction:
[tex]m_{R} = m_{T}-m_{E}[/tex]
[tex]m_{R} = 8\,\frac{1}{4} \,kg -3\,\frac{3}{4}\,kg[/tex]
[tex]m_{R} = \frac{33}{4}\,kg-\frac{15}{4}\,kg[/tex]
[tex]m_{R} = \frac{18}{4}\,kg[/tex]
[tex]m_{R} = 4 \,\frac{1}{2}\,kg[/tex]
The weight of the fruits left is [tex]4\,\frac{1}{2}[/tex] kilograms.
A power failure on the bridge of a Great Lakes freighter has resulted in the ship's navigator having to do her own calculations. She measures the angle between the ship's course and a lighthouse on shore as 32°. After the ship has travelled 1500 m, she measures the angle to be 72°. Determine if the ship was closer to or farther from the lighthouse at the second sighting, and by what distance. (4 marks)
It is impossible to measure the length of a particular swamp directly. Kendra put a stake in the ground and measured from the stake to opposite ends of the swamp, the results being 410 m and 805 m. She measured the angle between the distances to be 57°. What is the length of the swamp? (4 marks)
Answer:
1) The ship is closer
2) 675.73 m
Step-by-step explanation:
1) The given parameters are;
The initial angle between the ship's course and the lighthouse = 32°
The final angle between the ship's course and the lighthouse = 72°
The distance traveled by the sip between he two positions = 1500 m
Therefore we have a triangle formed between the distance covered by the ship and the two distances of the ship from the lighthouse, a and b
Where;
a = The initial distance fro the lighthouse
b = The final distance fro the lighthouse
The angles of the triangle are
32°, (180 - 72) = 108° and 180 - 32 - 108 = 40°
By sine rule we have;
1500/(sin(40)) = a/(sin(108)) = b/(sin(32)) =
Therefore, a = sin(108°) × 1500/(sin(40°)) = 2219.37 m
b = (sin(32°)) × 1500/(sin(40°)) = 1236.61 m
Therefore, a > b
The initial distance fro the lighthouse > The final distance fro the lighthouse, which shows that the ship is closer
2) By cosine rule we have
a² = b² + c² - 2× b×c×cos(A)
Where the given measurements by Kendra are;
410 m and 805 m with an included (in between) angle of 57°, we have;
Let b = 410 m, c = 805 m, and A = 57°, we have;
a² = 410^2 + 805^2 - 2× 410×805×cos(57 degrees) = 456608.77 m²
a = The length of the stream = 675.73 m.
Write and solve an equation to determine how many degrees the temperature T fell.
The temperature at 5 PM. is 20°F The temperature at 10 P.M. is -5°F
Equation?
Answer: First degree equation
Step-by-step explanation:
For each hour from 5pm , the temperature decreases 5F. So, let the variation of time t , the constant -5, and the final temperature, T:
T=5t-5 .: for 5pm , variation is 0,so T in F is -5.
Answer:
probably First degree equation
Step-by-step explanation:
A house was bought for $450 000 and 3 years later was valued at $540 000. Find: a. The new value as a percentage of the old value b. The increase in value over the three year period c. The increase in value as a percentage of the original value
Answer:
A) The percentage is given by (The new value)/(The old value)*100 = 120%
B) The increase in value is $90000
C) The increase as a percentage is (90000/450000)*100=20%
a. The new value is 120% of the old value.
b. The increase in value over the three-year period is $90 000.
c. The increase in value over the three-year period is 20% of the original value.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
a. To find the new value as a percentage of the old value, we can divide the new value by the old value and multiply by 100 to get a percentage:
New value as a percentage of old value = (New value / Old value) x 100%
= ($540 000 / $450 000) x 100%
= 120%
Therefore, the new value is 120% of the old value.
b. To find the increase in value over the three-year period, we can subtract the old value from the new value:
Increase in value = New value - Old value
= $540 000 - $450 000
= $90 000
Therefore, the increase in value over the three-year period is $90 000.
c. To find the increase in value as a percentage of the original value, we can divide the increase in value by the old value and multiply by 100 to get a percentage:
Increase in value as a percentage of original value = (Increase in value / Old value) x 100%
= ($90 000 / $450 000) x 100%
= 20%
Therefore, the increase in value over the three-year period is 20% of the original value.
Learn more about the percentages here:
brainly.com/question/24159063
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need help...!! plzzz
If the order of two matrices are different, then the addition of matrices does not exists true or false
Answer:
true
Step-by-step explanation:
A matrix can only be added/subtracted with another matrix if the two matrices have the same dimensions
Please help...25 points
Answer:
[tex]\huge\boxed{x = -\frac{5}{6}}[/tex]
Step-by-step explanation:
[tex]f(x) = -12x+7[/tex]
Given that f(x) = 17
[tex]17 = -12x+7[/tex]
Subtracting 7 to both sides
[tex]17-7 = -12x[/tex]
10 = -12 x
Dividing both sides by 12
[tex]x = - \frac{10}{12}[/tex]
[tex]x = -\frac{5}{6}[/tex]
Answer:
-5/6 =x
Step-by-step explanation:
f(x) = -12x+7
We want to find x when f(x) = 17
17 = -12x+7
Subtract 7 from each side
17-7 = -12x +7-7
10 = -12x
Divide each side by 12
10/-12 = -12x/-12
-5/6 =x
20 POINTS!!! Use the quadratic formula above to solve for h(t) = -4.9t^2 + 8t + 1 where h is the height of the ball in meters and t is time in seconds. Round to the nearest hundredth second!
Answer:
Two solutions: -0.12 and 1.75.
Step-by-step explanation:
The quadratic formula is:
[tex]\begin{array}{*{20}c} {\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \end{array}[/tex]. Assuming that the x² term is a, the x term is b, and the constant is c, we can plug the values into the equation.
[tex]\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {8^2 - 4\cdot-4.9\cdot1} }}{{2\cdot-4.9}}} \end{array}[/tex]
[tex]\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {64 + 19.6} }}{{-9.8}}} \end{array}[/tex]
[tex]\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {83.6} }}{{-9.8}}} \end{array}[/tex]
[tex]\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {9.14} }}{{-9.8}}} \end{array}[/tex]
[tex]\frac{-8 + 9.14}{-9.8} = -0.12[/tex]
[tex]\frac{-8-9.14}{-9.8} =1.75[/tex]
Hope this helped!
Does anyone know how to find these measures. Pls it’s due in a few hrs
Answer:
17) 120°
18) 85°
Step-by-step explanation:
→ Find the sum of angles in each shape
Quadrilateral = 360°
Triangle = 180°
→ Add the angles together and subtract it from the sum
360 - ( 80 + 80 + 80 ) = 120° for number 17
180 - ( 35 + 60 ) = 85° for number 18
Explain why they substituted cos(60) with 1/2 ?
(Look at image)
9514 1404 393
Answer:
equals can be substituted anytime anywhere
Step-by-step explanation:
cos(60°) = 1/2, so wherever one appears, the other can be substituted. This is allowed by the substitution property of equality.
__
If you don't substitute at some point, you find the answer to be ...
x = 10/cos(60°)
Most of us are interested in a numerical value for x, so we prefer that cos(60°) be replaced by a numerical value.
Find the measure of the missing angle. A
Answer:
a = 38
Step-by-step explanation:
The two angles add to 90 degrees
a+52 = 90
a = 90-52
a = 38
Answer:
Below
Step-by-step explanation:
The little box on the angle indicates that it is 90 degrees
All you need to do now to find angle a is to subtract 52 from 90...
90 - 52 = 38 degrees
Hope this helped!
An isosceles triangle has two sides of equal length. The third side is five less than twice the length of one of the other sides. If the perimeter of the triangle is 23 cm what is the length of the third side?
Answer:
9
Step-by-step explanation:
We can set up a systems of equations to find the value of the third side.
Let's assume that [tex]x[/tex] is the length of both sides 1 and 2. Let's also assume that [tex]y[/tex] is the length of the third side.
We know that [tex]x + x + y = 23[/tex], and looking at the first clue we can make the equation [tex]y = 2x-5[/tex].
We can substitute y into the equation [tex]x + x + y = 23[/tex].
[tex]x + x + (2x-5) = 23\\\\2x + 2x-5 = 23\\4x-5 = 23\\4x = 28\\x = 7[/tex]
So the length of the side that is the same as the second is 7.
Now we can plug this into the equation [tex]y = 2x-5[/tex] to find [tex]y[/tex].
[tex]y = 2(7) - 5\\\\y = 14-5\\\\y = 9[/tex]
Hope this helped!
Answer:
9 cm
Step-by-step explanation:
Let's say that the length of the 2 equal sides is x.
That means:
Side 1 = x
Side 2 = x
We know that the third side is 5 less than twice the length of the 2 equal sides, or 2x-5
Side 3 = 2x-5
The perimeter is all sides together.
Side 1 + Side 2 + Side 3
We know the length of each side, so let's put that in instead.
x + x + 2x-5
Let's simplify this expression:
x + x + 2x - 5
2x + 2x - 5
4x - 5
We know the perimeter, 4x-5, is 23 cm.
4x - 5 = 23
4x = 28
x = 7
The third side is 2x-5. If x is 7...
2*7 - 5 = 14-5 = 9
Answer: 9 cm
Please Help! Three times the quantity of a number increased by 7 is equal to the same number decreased by 15
The equation is written as 3x + 7 = x - 15. And the solution of the equation will be negative 11.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Multiple times the amount of a number expanded by 7 is equivalent to a similar number diminished by 15.
Let the number be 'x'.
The three times the number plus 7. Then the expression is given as,
⇒ 3x + 7
The number 'x' is decreased by 15. Then the expression is given as,
⇒ x - 15
Both expressions are equal to each other. Then we have
3x + 7 = x - 15
3x - x = - 15 - 7
2x = - 22
x = - 11
The equation is written as 3x + 7 = x - 15. And the solution of the equation will be negative 11.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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Simplify the following expression -10x + 10x
Answer:
0
Step-by-step explanation:
the x after the 10 is literally just 1
so 10 x 1 =10
-10 + 10 = 0
23. The measure of an angle is 46º. The measure of
the complement is
The measure of the
supplement is.
help if you can
Answer:
Complement = 44 degrees, supplement = 136 degrees
Step-by-step explanation:
Complement of an angle is the difference of the angle from 90 degrees.
Complement of 46 = 90-46 = 44 degrees.
Supplement of an angle is the difference of the angle from 180 degrees.
Supplement of 46 = 180-46 = 134 degrees.
Answer:
Complement = 44 degrees, supplement = 136 degrees
Step-by-step explanation:
31. Solve for w:
[tex] \frac{3w + 6}{28} = \frac{3}{4} [/tex]
HELP! answer if you can
Answer:
w = 5
Step-by-step explanation:
Hey there!
Cross multiply,
84 = 12w + 24
-24 to both sides
60 = 12w
Divide both sides by 12
w = 5
Hope this helps :)
Solve for x.
X + 10
2x - 50
x = [?]
Answer:
x +10 = 2x-50
x-2x = -50-10
-x. = -60
-x/-1 = -60/-1
x = 60°
When you roll two number cubes, what are the odds, in simplest form, in favor of getting two numbers less than 3? A. 1:8 B. 8:1 C. 1:9 D. 9:1
Answer:
1:9 is my best guess because 9 is a factor of 3 and 1 would be the lowest ratio for a number less than 3 :)
Step-by-step explanation:
Hope this helps, have a good day :)
If p-1 is a factor of p^4+p^2+p-k,the value of k is ?
[tex]1^4+1^2+1-k=0\\3-k=0\\k=3[/tex]
Answer:
k=3
Step-by-step explanation:
Hello, if p-1 is a factor of
[tex]f(p)=p^4+p^2+p-k[/tex]
it means that f(1)=0, so
1+1+1-k=0
3-k=0
k=3
thank you
Find a49 of the sequence 70,63,56,49,…. A. -63 B. -266 C. -273 D. -243
Answer:
(B) -266
Step-by-step explanation:
The formula to find the nth term in a sequence is:
[tex]x_{n} = a + d(n-1)[/tex], where a is the first term and n is the "difference."
Looking at this equation, we can see that the number decreases by 7 each time and the first term is 70.
So:
[tex]x_n = 70 + -7(n-1)[/tex]
Solve for the equation:
[tex]x_n = 70 + -7n+7\\x_n = -7n+77[/tex]
Since we want to find the 49th term:
[tex]x_9 = -7(49) + 77\\x_9 = -343+77\\x_9 = -266[/tex]
Hope this helped!
3. Which word phrase can be used to represent the algebraic expression 4(21+ n)? (2 point) 4 plus the sumn of 21 and a number » O4 times the product of 21 and a number » ne the sum of 21 and a number x 4 less than the sum of 21 and a number : O4 timeſ the
Answer:
4 times the sum of 21 and a number
Step-by-step explanation:
4(21+ n)
The four is being multiplied by the sum of 21 and n
2x.tg60= 10+csc30 plis
Answer:
[tex]2\sqrt{3}[/tex]
Step-by-step explanation:
I'm assuming the angles are in degrees.
[tex]2x \tan(60\º)=10+\csc(30\º)[/tex]
[tex]$2x\cdot \sqrt{3}=10+\frac{1}{\sin(30\º)} $[/tex]
[tex]$2x\cdot \sqrt{3}=10+\frac{1}{\frac{1}{2} } $[/tex]
[tex]$2x\cdot \sqrt{3}=10+2} $[/tex]
[tex]$x=\frac{12}{2\sqrt{3}} $[/tex]
[tex]$x=\frac{6}{\sqrt{3}} =\frac{6\sqrt{3}} {3} }=2\sqrt{3} $[/tex]
When solving (x + 35) = −7, what is the correct sequence of operations?
Answer:
x= -42
Step-by-step explanation:
put the liketerms together
x+35= -7
x=-35-7
note*the operation sign changes after crossing the equal sign
x= -42
HELP! WIll MARK BRAINLIEST! ACME Hardware is introducing a new product called Greener Cleaner. Complete the table by finding the cost per milliliter for each size based on the sales price. One liter is 1,000 milliliters. (Answer the questions too, please!)
Question 1:
Price per milliliter
Small $4.50 / 250ml
Medium $9.95 / 500 ml
Large $16.95 / 1000 ml
Question 2:
$9.95 / 500 ml > $4.50 / 250ml > $16.95 / 1000 ml
Question 3 - 4:
$4.50 / 250ml = ($4.50 * 6) / (250ml * 6 ) = $27 / 1500ml = 0.018
$9.95 / 500 ml = ($9.95 * 3) / (500 ml * 3) = $29.85 / 1500ml = 0.019
$16.95 / 1000 ml = ($16.95 * 3) / (1000 ml * 3) = $50.85 / 1500ml = 0.0339
( Use the first one for question 3 and the second for question 4)
$4.50 / 250ml would be the cheapest way to get 1500ml.
$9.95 / 500ml would be the most expensive way to get 1500ml.
I hope this helps you! Tell me if I'm wrong!
Solve.
-7(2z + 4) = 21
Answer:
-7/2
Step-by-step explanation:
cuz thats right
a rectangular garden is 52m long and 34m broad a path 2m wide is running inside the garden calculate the cost of travelling the path at rs 40 per sq metre snd calculate the cost of covering the empty space with tires at rs 20 per sq metre
Answer:
Answer From Gauth Math
Step-by-step explanation:
The product of 2 rational numbers is -16/9 . If one of the numbers is -4/3 find the other plz fast
Answer:
4/3
Step-by-step explanation:
let the other number be x.
-4/3 x=-16/9
x=-16/9×-3/4=4/3
Please help me with this question. Thank you so much everyone.
Answer:
1159
Step-by-step explanation:
She wants to read 1000 pages per week for five weeks.
So in total she wants to read 1000 * 5 = 5000 pages.
The first three weeks she read 894 pages per week.
So during the first three weeks she read a total of 894 * 3 = 2682 pages.
We want to find how many pages she must read per week for the last two weeks to reach her goal.
Goal: 5000 pages
Pages read so far: 2682
Weeks remaining: 2
To find how many pages she must read for the last two weeks we simply subtract the number of pages she read during the first 3 weeks (2682 ) by her goal ( 5000 )
5000 - 2682 = 2318
So she must read 2318 pages during the last 2 weeks.
If we want to find the amount of pages she must read per week during the last 2 weeks to reach her goal, we simply divide the amount of pages she must read during the last few weeks to reach her goal ( 2318 ) by the number of remaining weeks ( 2 )
2318 / 2 = 1159
So for the last two weeks she must average 1159 pages per week.
Answer:
1159 pages
Step-by-step explanation:
According to Briana's goal,
Pages to be read per week = 1000 pages
Number of weeks = 5
So, pages to be read in 5 weeks
= 5×1000 pages
= 5000 pages
But in reality,
Pages read in each first 3 weeks = 894 pages
So, total pages read in all first 3 weeks
= 3×894 pages
= 2682
Pages remained to be read to complete the goal
= Pages to be read in 5 weeks according to her goal - Pages actually read in all first 3 weeks
= 5000 pages - 2682 pages
= 2318 pages
So, pages to be read in each last 2 weeks
= 2318 pages/2
= 1159 pages
So, Briana will have to need to average 1159 pages over the last two weeks to complete her goal.
Please help me I promise I will mark brainliest, I need an answer asap!!!!!!!! please hurry!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! f(x) = 3x + 9, g(x) = 5x^2 Find (f + g)(x). A). -5x^2 + 3x + 9 B). Quantity three x plus 9 divided by five x squared. C). 15x^3 + 45x D). 5x^2 + 3x + 9
Answer:
D
Step-by-step explanation:
(f+g)(x) = f(x) + g(x)
=3x + 9 + 5x²
=5x² + 3x + 9
PLS HELP!!
what is the value of x?
log2(x+7) = 2
Answer: Choice A) -3
Work Shown:
[tex]\log_{2}(x+7) = 2\\\\x+7 = 2^2\\\\x+7 = 4\\\\x = 4-7\\\\x = -3\\\\[/tex]
Which leads us to choice A. In the second step, I used the rule that [tex]\log_b(y) = x[/tex] is equivalent to [tex]y = b^x[/tex]. For each equation, the b is the base. Note how logs undo exponents and vice versa.
Answer:
-3
Step-by-step explanation:
log2(x+7) = 2
Raise each side by base 2
2^log2(x+7) = 2^2
x+7 = 4
Subtract 7 from each side
x+7-7 = 4-7
x=-3