Answer:
Rs. 3923.08
Step-by-step explanation:
First principal invested = Rs. 10000
Interest rate = 5%
The interest is compounded yearly.
Time = 1 year
1 year compound interest is equal to simple interest.
Formula for simple interest:
[tex]SI = \dfrac{PRT}{100}[/tex]
Interest on first sum = [tex]\frac{10000\times 5\times 1}{100} = Rs\ 500[/tex]
Another sum is on fixed deposit 8% compounded half yearly.
Let the sum = Rs [tex]x[/tex]
Formula for compound interest is given as:
[tex]CI = P(1+\frac{R}{100})^T - P[/tex]
It is compounded half - yearly, therefore T = 2
[tex]CI = x (1+\frac{8}{100})^2 - x\\\Rightarrow CI = x(1.08)^2-x = 0.1664x[/tex]
As per question statement:
[tex]0.1664x - 500 = 152.80\\\Rightarrow x = \dfrac{652.80}{0.1664} = Rs\ 3823.08[/tex]
A spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute. (a) How fast is the radius of the balloon changing at the instant the radius is 40 centimeters
Answer:
[tex]\mathbf{ \dfrac{dr}{dt} = 0.03730 \ cm/min}[/tex]
Step-by-step explanation:
The rate of the inflation of the balloon with time can be denoted as:
[tex]\dfrac{dv}{dt} = 500 \ cm^3/m[/tex]
To determine; how fast does the radius change with time.
i.e.
[tex]\dfrac{dr}{dt}=???[/tex]
where r = 40 cm and the volume of sphere = [tex]\dfrac{4}{3} \pi r^2[/tex]
∴
[tex]\dfrac{dv}{dt}= \dfrac{4}{3} \pi 2(r^3) \dfrac{dr}{dt}[/tex]
[tex]500= \dfrac{4}{3} \pi \times 2(40^2) \dfrac{dr}{dt}[/tex]
[tex]500= 13404.13 \dfrac{dr}{dt}[/tex]
[tex]\dfrac{500}{13404.13} = \dfrac{dr}{dt}[/tex]
[tex]\mathbf{ \dfrac{dr}{dt} = 0.03730 \ cm/min}[/tex]
If X=sin130° + cos130° then 1)X <0 2)X=0 3)X>0 4) X> or equal to 0
Step-by-step explanation:
X = sin130° + cos130°
= sin50° - cos50°
= sin50° - sin40°.
sin50° is definitely greater than sin40°, therefore X > 0. (3)
write the equation of a line that is parallel to x=-5 and that passes through point (1,4)
Answer:
equation is then y= -5x + 9
Step-by-step explanation:
First the equation of a line is y=mx+b
if parallel the slope is the same
so m= -5
y= -5x +b
plug in point (1,4) into equation to find by
4= -5(1) + b
b=9
equation is then y= -5x + 9
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How many books does Brody read each month
Answer:
8
Step-by-step explanation:
y = 8x + 15
When x=0, y = 15
When y=0, x = -1.875
Prove that: (Sec A- cosec A)(1+ tan A+cot A) = tan A× sec A - cot A × cosec A
Answer:
Step-by-step explanation:
[tex](sec A-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA[/tex]
we take the LHS so here goes,
[tex](sec A-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA\\(\frac{1}{cosA} -\frac{1}{sinA})(1+\frac{sinA}{cosA}+\frac{cosA}{sinA})\\\\(\frac{sinA-cosA}{sinAcosA})(\frac{sinAcosA+sin^2A+cos^2A}{sinAcosA})\\[/tex]
since , [tex]sin^2A+cos^2A=1[/tex]
the identity becomes,
[tex](\frac{sinA-cosA}{sinAcosA})(\frac{1+sinAcosA}{sinAcosA})\\\\(\frac{sinA+sin^2AcosA-cosA-cos^2AsinA}{sin^2Acos^2A})\\\\[/tex]
now, we know,
[tex]sin^2A=1-cos^2A[/tex] and [tex]cos^2A=1-sin^2A[/tex]
the identity becomes,
[tex](\frac{sinA+(1-cos^2A)cosA-cosA-(1-sin^2A)sinA}{sin^2Acos^2A} )\\\\[/tex]
[tex](\frac{sinA+cosA-cos^3A-cosA-sinA+sin^3A}{sin^2Acos^2A})[/tex]
sin A and cos A cancel out it becomes zero
[tex]\frac{sin^3A-cos^3A}{sin^2Acos^2A} \\\\[/tex]
Splitting the denominator the identity becomes
[tex]\frac{sin^3A}{sin^2Acos^2A}-\frac{cos^3A}{sin^2Acos^2A} \\\\\frac{sinA}{cos^2A} - \frac{cosA}{sin^2A} \\\\\frac{sinA}{cosA}(\frac{1}{cosA})-\frac{cosA}{sinA}(\frac{1}{sinA})\\\\[/tex]
Hence,
[tex]tanAsecA-cotAcosecA[/tex]
Convert 0.008 to a percentage???
working out pleaseeee brainlest
Answer:
0.8%
Step-by-step explanation:
8/1000 x 100%
8/10 = 0.8% or 4/5%
Answer:
0.8%
Step-by-step explanation:
it is the answer answer
Can somebody plz help answer these questions for the word problem. They have to be correct!!! Thanks
WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DD
two agent angles of a parallelogram are in the ratio 1 by 3 find the measures of all the angles
Answer:
The measure of all the angles are;
45°, 135°, 45°, and 135°
Step-by-step explanation:
The given parameters are;
The ratio of two adjacent angles of the parallelogram = 1:3
Let x represent one of the adjacent angles, and let y represent the other adjacent angle
Given that two adjacent angles of a parallelogram are supplementary, we have;
x + y = 180°
x:y = 1:3
Therefore, y = 3 × x = 3·x, which gives;
x + 3·x = 180°
4·x = 180°
x = 180°/4 = 45°
y = 3 × x = 3 × 45° = 135°
Given that opposite interior angles of a parallelogram are equal, we have, the measure of all the angles are;
45°, 135°, 45°, and 135°.
find the selling price: original price of a radio: 53.50 discount: 30
Answer:
48.69
Step-by-step explanation:
Step-by-step explanation:
30% off $53.50
= 70% of $53.50
= $53.50 * (70/100) = $37.45.
Help me please!!!!!!
Answer:
c
Step-by-step explanation:
Since the perimeters are equal, then equate the perimeter expressions, that is
4(x - 2) = 6([tex]\frac{1}{2}[/tex] x + 5) ← distribute parenthesis on both sides
4x - 8 = 3x + 30 ( subtract 3x from both sides )
x - 8 = 30 ( add 8 to both sides )
x = 38
Substitute x = 38 into either of the 2 perimeter expressions
perimeter = 4(x - 2) = 4(38 - 2) = 4 × 36 = 144 in → c
Priya family exchangers 125 dollers for 4,250 pesos. Priya bought a sweater for 340 pesos how many dollers did the sweater cost
Answer:
The sweater costs 10 dollars.
Step-by-step explanation:
We can use proportion to solve this:
[tex] \frac{125 \: dollars}{4250 \: pesos} = \frac{x}{340 \: pesos} \\ \\ \frac{4250x}{4250} = \frac{42500}{4250} \\ \\ x = 10 \\ x = 10 \: dollars[/tex]
Kate cycle the first 350 km of a 470-km journey at a certain avearge speed and the remaining distanceat an average that is 15km/h less than that for the first part of the journe. If the time taken for her to travel each part for her to travel each part of her journey is the same, find the average speed for the second part of her journey
Answer:
7.83 km/h
Step-by-step explanation:
Let v = average speed for first part, v' = average speed for second part.
Given that v' = v - 15, the distance covered by the first part d = 350 km. The distance covered in the second part d' = 470 km - 350 km = 120 km.
Since both parts are covered in the same time,
d = vt and d' = v't = (v - 15)t
So, 350 = vt (1) and 120 = vt - 15t (2)
substituting vt = 350 into (2), we have
120 = 350 - 15t
collecting like terms, we have
15t = 350 - 120
simplifying, we have
15t = 230
dividing through by 15, we have
t = 230/15
t = 15.33 h
Since d' = v't, then
v' = d'/t
= 120 km/15.33 h
= 7.83 km/h
So, the average speed for the second part of the journey is 7.83 km/h
*BRAINIEST & 25 POINTS*
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
*irrelevant answers will be reported*
Answer:
63 degrees
Step-by-step explanation:
All angles add up to 180
(5x+6) + (4x-6) + (5x-2) = 180
put like terms together
5x+4x+5x + 6-6-2 = 180
14x -2 = 180
add 2 to both sides
14x = 182
divide both sides by 14
x=13
angle G is 5x-2, so if x=13, angle G is 5(13) -2
= 65 -2 = 63 degrees
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if two lines are perpendicular , what do we know about their slopes ?
Answer:
If two lines are perpendicular and neither one is vertical, then one of the lines has a positive slope, and the other has a negative slope. Hope this helps.
Step-by-step explanation:
A shirt originally cost $46.25, but it is on sale for $37.00. What is the percentage decrease of the price of the shirt? If necessary, round to the nearest percent.
Answer:
20%
Step-by-step explanation:
Original cost = $46.25
Decreased cost = $37.00
Decrease in cost = 46.25 - 37.00 = $9.25
Percentage decrease
[tex] = \frac{9.25}{46.25} \times 100 \\ \\ = \frac{92500}{4625} \\ \\ = 20\% [/tex]
A drama club made $3,200 from a school play. Seventy-five percent of that amount came from ticket sales. Identify the values of the variables in the model. Then use the model to find the amount of ticket sales.
a =
b =
The amount of ticket sales is $
.
Answer: $2400
Step-by-step explanation:
Based on the question above, a will be the percentage of tickets that were sold while b will be tickwt sales. Therefore,
a = 75%
b = 75% × $3,200
= 0.75 × $3200.
= $2400
Based on the information above, the amount of tickets sales is $2400
Help me with this please
Answer:
15 cans or D
Step-by-step explanation:
so it’s a pattern every 5 days add 3 cans
so Now do a table
5 = 3
10 = 6
15 = 9
20 = 12
25 = 15
Answer:
15 cans
D
Step-by-step explanation:
Set up a proportion.
3 cans / 5 days = x cans / 25 days
Note: both sides contain the same units on top and the same units on the bottom of each fraction.
3/5 = x / 25 Cross multiply
5x = 3*25
5x = 75
x = 75 / 5
x = 15
(x+2)² (x-100)²
Do it
Answer:
x⁴-196x³+9204x²+32200x+40000
Step-by-step explanation:
(x+2)(x+2)×(x-100)(x-100)=
(x²+4x+4)×(x²-200x+10000)=
(x⁴-200x³+10000x²+4x³-800x²+40000x+4x²-800x+40000)
=x⁴-196x³+9204x²+32200x+40000
x⁴-196x³+9204x²+32200x+40000
What is the image of the point (-1,-2)after a rotation of 180∘
counterclockwise about the origin?
Answer:
The image of the point is (1, 2)
Step-by-step explanation:
If the point (x, y) rotated about the origin by angle 90° counterclockwise, then its image is (-y, x)If the point (x, y) rotated about the origin by angle 180° counterclockwise, then its image is (-x, -y)If the point (x, y) rotated about the origin by angle 270° counterclockwise, then its image is (y, -x)Let us use the rules above to solve the question
∵ The point (-1, -2) is rotated 180° counterclockwise about the origin
→ By using the 2nd rule above change the signs of x and y coordinates
∴ Its image is (1, 2)
∴ The image of the point is (1, 2)
Answer:
(1,2)
Step-by-step explanation:
Estimate 40% of 128
Please help :c
Answer:
51.2 is 40% of 128
Step-by-step explanation:
Answer:
76.8
Step-by-step explanation:
128 x .40 = 51.2
128 - 51.2 =76.8
The Mexican Hot Chocolate Recipe makes 2 cups of hot chocolate per batch. 1 serving is equal to 1 cup.
How many batches of the recipe will you need to make to have enough hot chocolate for 6 people
Answer:
3
Step-by-step explanation:
For one batch there is 2 cups so for one person it's one serving so you will need 3 batches for 6 people.
Which of the following is a solution of the function graphed below?
Answer:
Option A
Step-by-step explanation:
It's a point on the function's graph
b - 9 = 21
linear equations
Answer: b=30
Step-by-step explanation: add 9 to both sides
b−9+9=21+9
b=30
add 9 from 9 this will cancel out the nine then add 9 to 21 and what ever u get is ur answer b=30
Step-by-step explanation:
b-9=21
+9
Steph makes scones in three flavours: cheese, fruit and plain. She makes: • 4 times as many fruit scones as cheese scones, • 3 times as many plain scones as cheese scones. She sells each scone for the same price. She makes a total of £96 from the sale of all the scones. How much does she make from the sale of the plain scones?
Upon drafting an equation based on the information provided and solving it, it is concluded that Steph earns £36 by selling the plain scones.
An equation is a combination of numbers, variables, functions, or often symbols according to a peculiar rule. It consists of expressions and equality sign(=).
Let's assume that Steph earns x from selling cheese scones then she earns 4x from selling fruit scones and 3x from selling plain scones.
The total amount she earns by selling all the scones is 96.
So,
x + 4x + 3x = 96
8x = 96
x = [tex]\frac{96}{8}[/tex]
x = 12
The amount she earns by selling plain scones = 3 × 12 = 36.
So, she makes £36 by selling the plain scones.
Learn more about Equation here:
https://brainly.com/question/28953876
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What is the cube root of 864
Answer:
Cube root of 864 can be represented as 3√864.
Answer:
9.52441
Step-by-step explanation:
[tex] \sqrt[3]{864} [/tex]
[tex] = \sqrt[3]{(9.524 \times 9.524 \times 9.524)} [/tex]
[tex] = 9.52441[/tex]
The original price of an iPad is $429. The sale price is 30% off the original price. What is the sale price of the iPad? Show your work.
Answer:
297.3
Step-by-step explanation:
30% of 429 is 128.7
429 which is the original price - 128.7 which is the price off = 297.3
Answer:
$300.30
Step-by-step explanation:
100% - 30% = 70%
429 * 0.70 = 300.30
Therefore the sale price of the ipad is $300.30!
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Erica sells magazine subscriptions and makes a flat rate of $5.35 for each subscription she sells. If Erica made $42.80 on Monday, $64.20 on Tuesday and $74.90 on Wednesday, how many subscriptions did she sell in the three days
to find the number of subscribtion sold we divide the money she made by the price of subscription
monday:
42.80/5.35=8 subscriptions sold
tuesday:
64.20/5.35=12 subscriptions sold
wednesday:
74.90/5.35=14 subscriptions sold
8+12+14=34 subscriptions sold in 3 days
Answer:
34 subscriptions she sold
Justin and Elena each launched a toy rocket into the air. The height of Justin's rocket is modeled by the equation h = –16t2 + 60t + 2. Elena launched his rocket from the same position, but with an initial velocity double that of Justin's. Which equation best models the height of Elena's rocket? h(t) = at2 + vt + h0
Answer:
b
Step-by-step explanation:
In a unit circle, ø = 2pi radians What is the terminal point?
A. (0,1).
B. (0, -1)
C. (-1,0)
D. (1,0)
Answer:
The terminal point is (1, 0) ⇒ D
Step-by-step explanation:
In the unit circle, Ф is the angle between the terminal side and the positive part of the x-xis.
The terminal point on the positive part of the x-axis is (1, 0),which means Ф = 0° or 360° and cosФ = 1, sinФ = 0The terminal point on the positive part of the y-axis is (0, 1),which means Ф = 90° and cosФ = 0, sinФ = 1The terminal point on the negative part of the x-axis is (-1, 0),which means Ф = 180° and cosФ = -1, sinФ = 0The terminal point on the negative part of the y-axis is (0, -1),which means Ф = 270° and cosФ = 0, sinФ = -1In a unit circle
∵ Ф = 2π radians
∵ 2π radians = 360°
→ By using the 1st rule above
∴ The terminal point is (1, 0)
PLEASE HELP ME I NEED HELP

Step-by-step explanation:
the question is not clear