Given:
The rate of interest on three accounts are 7%, 8%, 9%.
She has twice as much money invested at 8% as she does in 7%.
She has three times as much at 9% as she has at 7%.
Total interest for the year is $150.
To find:
Amount invested on each rate.
Solution:
Let x be the amount invested at 7%. Then,
The amount invested at 8% = 2x
The amount invested at 9% = 3x
Total interest for the year is $150.
[tex]x\times \dfrac{7}{100}+2x\times \dfrac{8}{100}+3x\times \dfrac{9}{100}=150[/tex]
Multiply both sides by 100.
[tex]7x+16x+27x=15000[/tex]
[tex]50x=15000[/tex]
Divide both sides by 50.
[tex]x=\dfrac{15000}{50}[/tex]
[tex]x=300[/tex]
The amount invested at 7% is [tex]300[/tex].
The amount invested at 8% is
[tex]2(300)=600[/tex]
The amount invested at 9% is
[tex]3(300)=900[/tex]
Therefore, the stockbroker invested $300 at 7%, $600 at 8%, and $900 at 9%.
what is the area of this shape?
Answer:
D) 36 cm^2
Step-by-step explanation:
(9 x 3) + (2 x 4.5)(2)(0.5) = 36 cm^2
The population of a city has decreased by 33% since it was last measured. If the current population is 13,400, what was the previous population?
0
Х
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Continue
Answer:
8,978 People
Step-by-step explanation:
13,400 x 0.33 = 4,422
13,400 - 4,422 = 8,978
Find the number that belongs
in the green box.
322
7
125°
[?]
Round your answer to the nearest tenth.
Answer:
2.7
Step-by-step explanation:
322/7=46
46*125=2.71739
round off
2.7
100Pts fast plz
A triangular pen is modeled by △ABC. The vertices of △ABC are A(0, 8), B(12, 3), and C(7, –9). What is the area of the pen?
Answer:
The area of the triangle is 84.511 square units.
Step-by-step explanation:
First step, we need to calculate lengths of line segments AB, BC and AC by Pythagorean Theorem:
AB:
[tex]AB = \sqrt{(12-0)^{2}+(3-8)^{2}}[/tex]
[tex]AB = 13[/tex]
BC:
[tex]BC = \sqrt{(7-12)^{2}+(-9-3)^{2}}[/tex]
[tex]BC = 13[/tex]
AC:
[tex]AC = \sqrt{(7-0)^{2}+(-9-8)^{2}}[/tex]
[tex]AC \approx 18.385[/tex]
Now, we can determine the area of the triangle ([tex]A[/tex]) by Heron's formula:
[tex]A = \sqrt{s\cdot (s-AB)\cdot (s-BC)\cdot (s-AC)}[/tex] (1)
[tex]s = \frac{AB+BC+AC}{2}[/tex] (2)
Where [tex]s[/tex] is the semiperimeter of the triangle.
If we know that [tex]AB = 13[/tex], [tex]BC = 13[/tex] and [tex]AC \approx 18.385[/tex], then the area of the triangle is:
[tex]s = 22.193[/tex]
[tex]A = 84.511[/tex]
The area of the triangle is 84.511 square units.
Pleaseeee helpppp it’s due in 6 minutes helpp!! Explain
Answer:
I might be wrong but since ur in a rush: 173
Step-by-step explanation:
Answer:
287.25 miles in 5.75 hours
Step-by-step explanation:
so he was first driving at 48mph because 168/3.5=48
5 miles per hour faster than that is 53mph
53*2.25=119.25
then we add 119.25 and 168
I DONT WANT HOW TO DO IT JUST THE ANSWER
Answer:
87.5
Edited: Yea should be 56, misread it LOL.
Appoligise to that silly mistake
Step-by-step explanation:
What is 27^2/3 simplified
Answer:
3^3
Step-by-step explanation:
[27]^2/3 can also be written as,
[(3)^3]^2/3
Now we know that a^m * a^n = a^m+n, therfore,
[3]^ 3*2/3
Cut 3 and 3
Therefore, you get 3^3
Let me know if you understood. If you didnt I can try to explain it to you in another way.
Also, plz mark me as the brainliest!
HELP ME NOW
04 Fill in the blank Drag and Drop
Raven has driven 90 miles, which represents 30% of the total distance she diving
What is the total distance Raven is driving, and how many miles does she have left to drive
Drag a number into each box to complete the sentences
Raven is driving a total distance of
miles. She has
miles left to die
11 27
11 30
11 63
1 90
11 117
11 210
11 300
11990
Answer:
its blurry
Step-by-step explanation:
Find the coordinates of the point where the lines with equations y=x and y=-6 intersect
Answer:
(-6, -6)
Step-by-step explanation:
Find the coordinates of the point where the lines with equations y=x and y=-6 intersect.
The lines intersect at y = y
Equating the right hand side of both expressions we have;
x = -6
Since y = x, hence y = -6
The required coordinate where they intersect is at (-6, -6)
What are the coordinates of B’ if Triangle ABC is reflected over the x-axis?
Answer:
the coordinates of b if it is reflected over the x-axis (-2,5)
an expression to represent ( w increased by 5 )
Answer:
W + 5
Step-by-step explanation:
Given a number, W
An increase in W by a constant 5 ; can be expressed as ;
W plus the constant value increase
Hence,
Increase in W by 5 equals ;
W + 5
Mr Mazibuko monthly salary before tax is R12 700 what will be his salary after paying 11% tax
Answer:
R11 303
Step :
Find 11% of R12 700
R12 700 × 11/100
=R1 397
then substract the 11% from R12 700
R12 700 - R1 397
=R11 303
Help pls also show work if needed!
Answer:
unknown value = 800
Step-by-step explanation:
f(x) = 1333/100·x + 1/5
so if x = 60 - > (1333/100)60+1/5 = 800
Answer: 800
Step-by-step explanation: 933.3-133.3=800-133.3=666.7-133.3=533.4
explain how 7/10 and 70/100 are equivalent decimals
Step-by-step explanation:
7/10 in percentage form is 70%
70/100 in percentage form is 70%
Simple as that
It is proved that the given decimals are equivalent decimals.
What are equivalent fractions? What is a mathematical function, equation and expression?equivalent fractions : Equivalent fractions can be defined as fractions that may have different numerators and denominators but they represent the same value.function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given are the fractions -
7/10 and 70/100
We have the following fractions -
A = (7/10) = 0.7
B = 70/100 = (7 x 10)/(10 x 10) = (7/10)
B = (7/10) = 0.7
It can be seen that fraction A equals to B.
Therefore, it is proved that the given decimals are equivalent decimals.
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Margie needs 7 ticket to the same soccer game.
Describe the best way to figure out Margies EXACT cost, if we know that 3 tickets cost $53.00.
Answer:
$123.66
Step-by-step explanation:
53 divided by 3 is 17.66, which is how much one ticket will cost. 17.66 multiplied by 7 is 123.66
How many years in a month
Answer: There are 12 months in one 1 year
Step-by-step explanation:
Find the maximum rate of change off at the given point and the direction in which it occurs.
f(x, y) = 4y √x, (4, 1)
Answer:
Maximum rate change |[tex]\nabla[/tex]f| = √65
Direction = ( 1, 8 ) / √65
i.e Maximum rate change is √65 and it occurs in a direction of ( 1, 8 )
Step-by-step explanation:
Given that;
f(x, y) = 4y √x, (4, 1)
{ x=4 and y=1 }
Maximum rate of change occurs with the gradient vector;
[tex]\nabla[/tex]f = [ df/dx, df/dy ] = [ 2y/√x, 4√x ]
we substitute in our value of x and y
[tex]\nabla[/tex]f = 2(1)/√4, 4√4
[tex]\nabla[/tex]f = 2/√4, 4√4
[tex]\nabla[/tex]f = ( 1, 8 )
Maximum rate change |[tex]\nabla[/tex]f| = | ( 1, 8 ) | = √( 1² + 8² ) = √(1 + 64)
Maximum rate change |[tex]\nabla[/tex]f| = √65
Direction = [tex]\nabla[/tex]f / |[tex]\nabla[/tex]f|
we substitute
Direction = ( 1, 8 ) / √65
i.e Maximum rate change is √65 and it occurs in a direction of ( 1, 8 )
Please help me with this I need to know
Answer:Just multiply Step-by-step explanation:do 12x10x20=2,400
If a price increases by 16%, what number can we multiply the old price by to get the new price?
Answer:
Multiply by 1.16
Step-by-step explanation:
Answer:
Multiply it by 0.16
A triangle has sides with lengths 8, 15, and 17.
1. Verify this is a Pythagorean Triple
2. Approximate the acute angles in this triangle
Yes, the given set of the sides of a triangle follows the Pythagorean Triple and the acute angles are 61.92° and 28.08°.
What is the Pythagorean Triple?Pythagorean triples are a²+b² = c² where a, b and c are the three positive integers. These triples are represented as (a, b, c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle.
Given that, A triangle has sides with lengths 8, 15, and 17.
1) Checking for Pythagorean triples;
17² = 289
8²+15² = 225+64 = 289 = 17²
∴ 17² = 8²+15²
Since, they are following the Pythagoras theorem so, they are Pythagorean triples.
2) Calculating the acute angles:- [please refer to attached figure]
Let 15 be the perpendicular, 8 be the base and 17 is the hypotenuse,
sinC = 15/17 (sine of an angle is ratio of perpendicular to hypotenuse)
∠ C = sin⁻¹(15/17)
∠ C = 61.92°
∠ A = 90°-61.92°
∠ A = 28.08°
Hence, the given set of the sides of a triangle follows the Pythagorean Triple and the acute angles are 61.92° and 28.08°.
For more references on Pythagorean Triple, click;
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I need help to do this dont know how to do!
Answer:
Step-by-step explanation:
Even I need help with that
What is the sum of the measures of the interior angles of a 20-sided figure?
Enter your answer in the box.
__°
The sum of the measures of the interior angles of a 20-sided figure is 3240.
What are Interior angles ?
An interior angle of a polygon is an angle that is created between two of the polygon's adjacent sides. The interior angle of a polygon is also known as the angle measured at the interior of a polygon.
the number of sides of given polygon is 20.
we know that, sum of the measures of the interior angles can be found by using formula : (n-2) × 180
where n= no. of sides of given polygon
So, sum of the measures of the interior angles of 20 sided figure :
= (n-2) × 180
= (20-2) × 180
= 18 × 180
= 3240 .
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HelllpFind an equation of a line that contains the points (-3,-1) and (2,-2). Write the equation in slope-intercept form.
Answer:
y = -1/5x -8/5
Step-by-step explanation:
(-3,-1) and (2,-2)
m=(y2-y1)/(x2-x1)
m = ( -2 + 1)/(2 + 3)
m = (-1)/(5)
m = -1/5
y - y1 = m(x - x1)
y + 1 = -1/5(x + 3)
y + 1 = -1/5x -3/5
y = -1/5x -8/5
What is the value of x? Please help asap
Answer:
x=27
Step-by-step explanation:
It’s a ratio:
9.9/11=x/30
cross multiply
11x=297
x=27
Find the surface area of the right triangular prism (above) using its net (below).
units
Answer:
120 units^2
Step-by-step explanation:
(12)(5)(0.5)(2) + (12)(2) + (13)(2) + (5)(2) = 120 units^2
Mr Kinney biology class completed a lab to determine blood type. The results are reported in the frequency table. What is the relative frequency of a student having o type blood? 0.1 0.2 0.3 0.4
Answer:
o . ooo 2 and dr 45009.7 ok byy
A single die is rolled once. Find the probability of rolling a number less than 7.
Answer:
1/6
Step-by-step explanation:
The die is rolled once, so it is 1 out of the total number on the die ie 6, as a die has only faces or sides so its obvious out of these 6 faces only one will show.
Does anyone know the answer?
Answer:
15°
Step-by-step explanation:
2x+5=3x
5=3x-2x
5=x
Now we can solve the angle.
<BAD=2x+5 = 2(5)+5 = 10+5 = 15°
One month Maya rented 2 movies and 3 video games for a total of $20. The next month she rented 6 movies and 5 video games for a total of $38. Find the
rental cost for each movie and each video game.
Rental cost for each movie:
Rental cost for each video game:
Answer:
[tex]M = 1.75[/tex] --- Movies
[tex]V = 5.5[/tex] --- Video games
Step-by-step explanation:
Represent the movies with M and the video games with V.
The first month, the expression is:
[tex]2M + 3V = 20[/tex]
The next month, the expression is:
[tex]6M + 5V = 38[/tex]
Required
Find M and V
We have:
[tex]2M + 3V = 20[/tex] --- (1)
[tex]6M + 5V = 38[/tex] --- (2)
Multiply (1) by 3.
3 * [tex]2M + 3V = 20[/tex]
[tex]6M + 9V = 60[/tex] --- (3)
Subtract (1) from (3)
[tex]6M + 9V = 60[/tex]
- [tex]6M + 5V = 38[/tex]
-------------------------
[tex]6M - 6M + 9V - 5V = 60 -38[/tex]
[tex]4V = 22[/tex]
Divide by 4
[tex]V = 5.5[/tex]
Substitute 5.5 for V in (1)
[tex]2M + 3V = 20[/tex]
[tex]2M + 3 * 5,5 = 20[/tex]
[tex]2M + 16.5= 20[/tex]
Subtract 16.5 from both sides
[tex]2M = 3.5[/tex]
Divide by 2
[tex]M = 1.75[/tex]
Choose the linear Inequality that describes the graph. The gray area represents the shaded region.
Answer:
3
Step-by-step explanation:
the y axis