Answer:3329.95
Step-by-step explanation:
The value of the quantity after 0.7 decades, to the nearest hundredth is 1157.37.
Given that, a quantity with an initial value of 990 grows exponentially at a rate such that the quantity doubles every 4 years.
What is the exponential function?Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
We know that, S.I=(P×T×R)/100
Amount after 4 years is 1980
So, 990= (990×4×R)/100
⇒ 39.6R=990
⇒ R=990/39.6
⇒ R=25%
Amount = [tex]a(1+r)^t[/tex]
= [tex]990(1+0.25)^{0.7}[/tex]
= 1157.37
Therefore, the value of the quantity after 0.7 decades, to the nearest hundredth is 1157.37.
Learn more about the exponential function here:
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Write the quadratic equation and solve by using the general formula. "Find two consecutive numbers in which the double of the square of the smaller number plus the square of the greater number is 121"
Answer: 6 and 7
Step-by-step explanation:
Let the numbers be x and x + 1
We can form and equation as:
2(x²) + (x+1)² = 121
2x² + (x + 1)(x + 1) = 121
2x² + x² + x + x + 1 = 121
3x² + 2x = 121 - 1
3x² + 2x = 120
3x² + 2x - 120 = 0
3x² - 18x + 20x - 120 = 0
3x(x - 6) + 20(x - 6)
Therefore, x - 6 = 0
x = 0 + 6
x = 6
The numbers are 6 and 7
The two numbers given in the statement is required.
The two numbers can be [tex]6,7[/tex] or [tex]-\dfrac{20}{3},-\dfrac{17}{3}[/tex]
Quadratic equationLet [tex]x[/tex] be the first number
[tex]x+1[/tex] be the next consecutive number
From the statement we get
[tex]2x^2+(x+1)^2=121\\\Rightarrow 2x^2+x^2+2x+1=121\\\Rightarrow 3x^2+2x-120=0\\\Rightarrow x=\dfrac{-2\pm \sqrt{2^2-4\times3\left(-120\right)}}{2\times3}\\\Rightarrow x=6,-\dfrac{20}{3}[/tex]
If [tex]x=6[/tex]
the other number is [tex]x+1=6+1=7[/tex]
If [tex]x=-\dfrac{20}{3}[/tex]
the other number is [tex]x+1=-\dfrac{20}{3}+1=-\dfrac{17}{3}[/tex]
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Someone pleaseee help meeee
Ill tell you the answer if u mark me brainliest
Answer:
A. 9
Step-by-step explanation:
y2 - y = m(x2 - x) formula
7 - -2/ -6 - -7 = m
9/1 = m
9 = m
The equation would have a slope of 9.
Movie ticket sales are as follows: Adult: 20 tickets for $250 Child: 15 tickets for $71.25 Senior: 5 tickets for $37.50 How much does one (1) SENIOR ticket cost?
Answer:
$7.5
Step-by-step explanation:
you just divide 37.50 by 5 to get the price of an individual senior ticket price
What is 5+5x3+4x6x9x2x2+45
Answer:
929
Step-by-step explanation:
5 + 5x3 + 4x6x9x2x2 + 45 =5 + 15 + 864 + 45 =929find the two numbers having sum is 31 and product is 192
Answer:
24 and 8
Step-by-step explanation:
solve by trial and error
192/8 = 24
24+8 = 32
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Answer:
just crop it ok
Step-by-step explanation:
I'm not sure ok
A total of 762 people, consisting of parents, students, and teachers, attended the Community Fair. If 212 parents and 386 students were at the event, how many teachers attended?
Answer:
[tex]\boxed{\textsf{ The number of Teachers that attented is \textbf{ 164 } .}}[/tex]
Step-by-step explanation:
Here it's given that a total of 762 people consisting of parents, students, and teachers, attended the Community Fair. There were 212 parents and 386 students at the fair .That is ,
Number of students:-
[tex]\sf\implies n(students) = 386 [/tex]
Number of parents :-
[tex]\sf\implies n(parents) = 212 [/tex]
Number of teachers :-
[tex]\sf\implies n(teachers) = ? [/tex]
Here the Number of teachers could be simply find out by subtracting the number of students and teachers from the total number of attendees .
[tex]\sf\implies n_{(teachers)}= n_{(total)}- n_{(students)}- n_{(parents)} \\\\\sf\implies n_{(teachers)}= 762 - 386 - 212 \\\\\sf\implies n_{(teachers)}= 762 - 598 \\\\\sf\implies\boxed{\pink{\frak{ n_{(teachers)}= 164 }}}[/tex]
Tenley wants to exercise at least 15 hours per week. She walks at a speed of three miles per hour and bikes at a speed of 10 miles per hour. She wants to cover at least 90 miles total in her weekly workouts, biking no more than 10 hours and walking no more than 12 hours.
Answer:
The answer is below
Step-by-step explanation:
Let x represent the number of hours spent on walking and let y represent the number of hours spent on biking.
Tenley wants to exercise at least 15 hours per week, therefore:
x + y ≥ 15 (1)
Tenley cover at least 90 miles total in her weekly workout, therefore:
3x + 10y ≥ 90 (2)
x ≤ 12, y ≤ 10 (3)
Plotting the above constraints using geogebra online graphing tool. The solution to the problem is:
(5, 10) , (12, 10), (12, 5.4), (8.57, 6.43)
The triangles are similar. Find the missing side.*
- 36
- 25
- 29
Step-by-step explanation:
[tex] \frac{30}{6} = \frac{x}{5} \\ x = 25[/tex]
3 A garage is to be built with a skillion roof (a roof with a single
slope). The measurements are given in the diagram. Calculate
the pitch line length, to the nearest millimetre. Allow 500 mm
for each of the eaves.
Answer:
1e1e
Step-by-step explanation:
The pitch line length of the garage with the skillion roof, with the given dimensions and eave overhangs, is approximately 7.5 meters.
To calculate the pitch line length for the garage with a skillion roof, we need to consider the dimensions provided in the diagram and add the eave overhangs.
Let's assume the length of the garage is L meters, and the height from the top of the walls to the peak of the roof is H meters.
Calculate the pitch line length of the roof:
The pitch line length is the diagonal length of the triangular roof face. We can use the Pythagorean theorem to find it.
Pitch Line Length (PL) = √(L² + H²)
Add the eave overhangs:
The eave overhang is 500 mm on each side, so we need to add 1 meter (1000 mm) to the pitch line length.
Total Pitch Line Length (TPL) = PL + 1000
Now, let's calculate the pitch line length to the nearest millimeter.
For example, let's assume L = 6 meters and H = 2.5 meters.
Calculate the pitch line length (PL):
PL = √(6² + 2.5²)
PL = √(36 + 6.25)
PL = √42.25
PL = 6.5 meters
Add the eave overhangs:
TPL = 6.5 + 1
TPL = 7.5 meters
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What is 6q+4-q+5 equals tooo PLEASE I REALLY NEED HELP THIS IS DUE TODAYY
Answer:
5q+9
Step-by-step explanation:
1. combine like terms
6q-q=5q and 4+5=9
2. combine those two
5q+9
I need help with the last three
2(4x+5)=9(3x+2)? I need help
Answer:
[tex]x=-\frac{8}{19}[/tex]
Step-by-step explanation:
2(4x + 5) = 9(3x + 2)
Solve for x
___________________
We have an alrebaric expressio and are asked to solve for x, which to do this, we need to isolate x.
2(4x + 5) = 9(3x + 2)
Distribute :
(2(4x) + 2(5)) = (9(3x) + 9(2))
8x + 10 = 27x + 18
Subtract 10 from both sides :
8x = 27x + 8
Subtract 27x from both sides :
-19x = 8
8 = -19x
Divide both sides by -19 :
[tex]x=-\frac{8}{19}[/tex]
Katrina has $210 in her savings account. She plans to buy books for her friends for Christmas. The books cost $7 per book. Which equation best represents this situation? Let y represent the amount of money in Katrina's account and x represents the number of books she purchases.
what is the correct answer
y=210-7x
y=7x+210
y=210x+7
y=-7+210x
Answer:
Option 1 y = 210 - 7x
Step-by-step explanation:
Since she will be buying "x" amount of books she will lose money because she has to pay for them. Each book costs $7 so if she buys "x" books she will lose 7x dollars. Therefore the right equation would be...
y = 210 - 7x (which is the first option)
Help needed ASAP!!!
Answer:
Angle b = 30 degrees
Step-by-step explanation:
3x = 90.
X= 30
Angle b = 30 degrees
Answer:
45
Step-by-step explanation:
because in total it's a 90-degree agle half of 90 is 45.
Find the total number of outcomes if Johnny can choose between 6 pair of pants, 5 shirts, and 4 belts
Question 10 options:
A. 120
B. 40
C. 360
D. 15
Answer:
I believe it would be A 120 sorry if I'm wrong
A construction crew is lengthening a road. The crew is adding 6 miles to the road each week. The road originally measured 52 miles long. The crew's goal is given by 6x+52>130, where x is the number of weeks the crew works.
6x + 52 > 130
Subtract 52 from both sides:
6x > 78
Divide both sides by 6:
X > 78/6
X > 13
I need this answer ASAP
Answer:
EE
Step-by-step explanation:
E
PLEASE HELP THIS IS DUE SOON
Answer
interior angles 370
exterior angles 350
I hope this helps!
Someone please saveee meee on this :(
Answer:
the answer is 5
Answer:
yea the answer is 5
1) Pat mixes 5 quarts yellow, 2 quarts
orange and 1 quart whte paint .If she
wants to make 24 quarts
of this mixture , how many quarts of
each color does she need?
Answer:
5 quarts yellow + 2 quarts orange + 1 quart white = 8 total quarts.
To make 24 quarts you need 3 times as much, because 8 * 3 = 24.
Multiply each measurement by 3:
5 quarts yellow --> 15 quarts yellow
2 quarts orange --> 6 quarts orange
1 quart white --> 3 quarts white
A coffee mug has a diameter of 8 centimeters. What is the mug's
circumference?
Use 3.14 for n.
centimeters
Submit
Answer:
25.12 cm
Step-by-step explanation
circumfernce=3.14n
c=3.14·8
c=25.12
Someone please help me state all the possible names for the figure
Please help this is geometry I would really appreciate it <3
Answer:B
Step-by-step explanation:
What is the area of and the perimeter of this triangle?
A= 33 square yards; P= 40 yards
A= 40 square yards; P= 33 yards
A= 80 square yards; P= 33 yards
A= 25 square yards; P= 28 yards
Answer:
A = 40 square yards; P = 33 yards.
Step-by-step explanation:
Perimeter of the triangle
= ( 8 + 15 + 10)
= 36 yards.
Area of the right angled triangle
= 1 /2 * 10 * 8
= 40 square yards.
Hope it will help :)
The slope of the line that passes through the points (3,14) and (7,9) is?
A:-5/4
B:-3/4
C:5/4
D:-4/5
-2x -4y = -10
-7x -4y = -15
What is this in a ordered pair? (x,y)
Answer:
x=1,y=2
-2x-4y= -10 maltiple by -1 then 2x +4y
-7x-4y= -15
therfore 2x+4y=10
-7x-4y=-15 to find x or y you must zero one of them
ther fore 4y-4y=0
then 2x+(-7x)= -5x
-5x=10 +(-15) =-5
-5x = -5
divide by -5 both side,
x =1
to get the value of y the value of x supersed in to equation
-2(1) -4y = -10
-4y =-10 +2
-4y = -8 both dived by -4
y=2
3x + 16
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Answer:
3x+16=0
x=-16/3
is your answer
Answer:
3x+16= 125 answer is 109/3
Step-by-step explanation:
D is the 4th letter of the alphabet and u have 5 d which means 4×5=20(repeat the same step for the other letters
J is 10thh so 7×10=70
Next letter is F, you have 2 f's
F is the 6th letter of the alphabet
6×2=12
W which is the the last letter we have to do here is the 23rd letter of the alphabet and u have 1 so 23×1 is 23
(1+tan^2 A)cot A/cosec^2 A= tanA
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
1 + tan²A = sec²A , secA = [tex]\frac{1}{cosA}[/tex], cosecA = [tex]\frac{1}{sinA}[/tex] , cotA = [tex]\frac{cosA}{sinA}[/tex] , tanA = [tex]\frac{sinA}{cosA}[/tex]
Consider the left side
[tex]\frac{(1+tan^2A)cotA}{cosec^2A}[/tex]
= [tex]\frac{sec^2AcotA}{cosec^2A}[/tex]
= [tex]\frac{\frac{1}{cos^2A}(\frac{cosA}{sinA}) }{cosec^2A}[/tex]
= [tex]\frac{\frac{1}{cosAsinA} }{\frac{1}{sin^2A} }[/tex]
= [tex]\frac{1}{cosAsinA}[/tex] × sin²A
= [tex]\frac{sinA}{cosA}[/tex]
= tanA = right side , thus proven
8.5×7/2 ____
please
Antonia currently has $4,500 in her
savings account. She saves $150 per
month. Cal currently has $3,400 in his
account. He saves $250 per month. How
much more money than Antonia will Cal
have after 12 months?
Answer:
The amount of more money than Antonia that Cal will have in his account after 12 months is $100
Step-by-step explanation:
The given parameters are;
The amount Antonia currently has in her savings account, P₁ = $4,500
The amount Antonia saves per month, S₁ = $150
The amount Cal currently has in his savings account, P₂ = $3,400
The amount Cal saves per month, S₂ = $250
Let the
The amount, 'A₁', Antonia has in 12 months is given as follows;
A₁ = P₁ + 12 × S₁
∴ A₁ = $4,500 + 12 × $150 = $6,300
Similarly, the amount, 'A₂', Cal has in 12 months is found as follows;
A₂ = P₂ + 12 × S₂
∴ A₂ = $3,400 + 12 × $250 = $6,400
The amount of money than Antonia that Cal will have after 12 months, 'A₂₋₁', is given as follows;
A₂₋₁ = A₂ - A₁ = $6,400 - $6,300 = $100.
The amount of money than Antonia that Cal will have after 12 months, A₂₋₁ = $100.