Given:
percent of dividend = 6%
percent of interest = 9%
Total annual interest = $ 660
Let the amount invested in both stocks be x and y.
Annual interest on 6% dividend gives:
[tex]\begin{gathered} =\text{ }\frac{6}{100}\text{ }\times\text{ x} \\ =\text{ 0.06x} \end{gathered}[/tex]Annual interest on 9% interest rate:
[tex]\begin{gathered} =\text{ }\frac{9}{100\text{ }}\times\text{ y} \\ =\text{ 0.09y} \end{gathered}[/tex]The total annual interest is $ 660. We can write:
[tex]0.06x\text{ + 0.09y =660}[/tex]We are given that Nelson divided his investment in half. This implies:
[tex]x\text{ = y}[/tex]Substituting, we have:
[tex]\begin{gathered} 0.06x\text{ + 0.09x = 660} \\ 0.15x\text{ = 660} \end{gathered}[/tex]Divide both sides by 0.15:
[tex]\begin{gathered} \frac{0.15x}{0.15}\text{ = }\frac{660}{0.15} \\ x\text{ = 4400} \end{gathered}[/tex]Hence, the amount Nelson has invested:
[tex]\begin{gathered} x\text{ = y = 4400} \\ \text{Amount invested = 4400 + 4400} \\ =\text{ 8800} \end{gathered}[/tex]Answer:
Nelson has $4400 invested in each investment
Consider the line y =
9
7
x-9.
Find the equation of the line that is parallel to this line and passes through the point (-7, 4).
Find the equation of the line that is perpendicular to this line and passes through the point (-7, 4).
Answer:
Axis interception points [tex]97x-9[/tex] x intercepts: [tex](\frac{9}{97} ,0),[/tex]Y intercepts:[tex](0,-9)[/tex]
Step-by-step explanation:
Slope of 97x-9 : m=97
Domain: 97 x - 9
Range: 97 x - 9
What is the length of cd ?
Answer:
7
Step-by-step explanation:
since 3x-6 and x+8 are congruent x had to make both the equations equal eachother. 7 is the only number that does that
A boat traveled 240 miles downstream, then 240 miles back upstream. The trip downstream took 20 hours. The trip back upstream took 60 hours. Use this information to fill in the following blanks. Note: Express your answers as integers.
The speed of the boat in still water is 6miles/hour miles per hour.
The speed of the current is 3miles/hour miles per hour.
The distance travelled by the boat downstream(with the flow current of river) is 240 miles.
The distance travelled by the boat upstream(Against the flow current of river) is 240 miles.
Time taken to travel downstream = 20 hours.
Time taken to travel upstream = 60 hours.
Let us say the velocity of the boat is V and the velocity of the current flow of river is U.
The relative velocity of boat with respect to ground while going downstream is,
velocity of boat in downstream = V + U.
As we know,
Velocity = distance/time
Putting values of downstream motion,
V + U = 240/20
V + U = 10
Let us say this is our equation 1.
The relative velocity of boat with respect to ground while going upstream is,
velocity of boat in upstream = V - U
As we already know,
Velocity = distance/time
Putting the values of upstream motion,
V - U = 240/60
V - U = 3
Let us say this is our equation 2.
Now, on adding equation 1 and 2.
V+U+V-U = 10 + 3
2V = 13
V = 6.5 miles per hour.
Rounding off to the nearest integer,
V = 6 miles/hour.
Putting V = 6.5 miles/hour in equation 1,
6.5 + U = 10
U = 3.5 miles/hour.
Rounding off to the nearest integer,
U = 3 miles/hour
The velocity of river current is 3 miles/hour and velocity of boat is 6miles/hour.
To know more about Relative velocity, visit,
https://brainly.com/question/17228388
#SPJ1
A boat traveled 240 miles downstream, then 240 miles back up stream. The trip downstream took 20 hours. The trip back up stream took 60 hours. Use this information to fill in the following blanks.
The speed of the boat in still water is ______ miles per hour.
The speed of the current is ______ miles per hour.
(Can anyone answer this please? I need it ASAP!!) A2B3C4 (in hexadecimal) - 3F2E1D (in hexadecimal) = ______________
The hexadecimal value from the operation is 6385A7
Hexadecimal NumbersTo solve this problem, we have to subtract the hexadecimal numbers from one another.
In doing so, we would subtract 3F2E1D from A2B3C4.
This would give us,
[tex]A2B3C4 - 3F2E1D = 6385A7[/tex]
The value of the expression is 6385A7.
Learn more on hexadecimal number here;
https://brainly.com/question/28450899
#SPJ1
Which is larger, 52 or 33?
Answer:
52
Step-by-step explanation:
52 is a bigger number than 33?
A sea turtle is 3 feet below the surface of the sea. If its position can be recorded as −3 feet, what would the position 0 represent in this situation? (4 points)
Group of answer choices
A.) the height of the turtle
B.) the distance above the surface of the sea
C.) the distance below the surface of the sea
D.) the surface of the sea
Answer:
D
Step-by-step explanation:
-3 ft means that it is three feet below zero. That means 0 means the sea level.
Please help
Name the reciprocals of each equation
Equations in picture
1. (3/4)x = 9. Multiply both sides by the reciprocal of 3/4: (4/3)(3/4)x = (4/3)(9)
x = 12.
2 . -4=4/7*x
4x/7=-4
x=-7
3. -1/5*x=6
-x/5=6
Multiply all terms by the same value to eliminate fraction denominators
Cancel multiplied terms that are in the denominator
x=-30
With an example, what is a reciprocal equation?
An inverse of a number or value is referred to as reciprocal. If x is any real number, then 1/x will be the reciprocal of that number. For instance, 1/8 is the reciprocal of 8, which is 1 divided by 8. 1/8's reciprocal is equal to 8.
To learn more about reciprocal equation refer to:
https://brainly.com/question/8740734
#SPJ13
What is the answer to f(2)=
the answer is 2f
Re-order terms so constants are on the left
f×2=2f
Carmen is about to complete a jigsaw puzzle the puzzle and one remaining piece are shown below what transformation can shark Carmen apply to the final piece to fit into the puzzle
We can see that the holes of the piece are already oriented in a way the piece will fit in the missing hole of the puzzle, so it doesn't need a rotation or reflection.
Then, in order to fit the piece in the hole, we need to move the piece 3 positions to the left and 1 position down.
Therefore the transformation needed is: a translation of 3 units to the left and 1 unit down.
Please help!!!!
I’ll give you the Brainiest
A triangle has height 4ft and area 32 ft². What is the length of its base?
Step-by-step explanation:
1st
[tex]area = \frac{1}{2} base \times hight[/tex]
2nd
[tex]32 = \frac{1}{2} base \times 4[/tex]
3rd
[tex]32 \div 4 = \frac{1}{2} base[/tex]
4th
[tex]8 \times 2 = base[/tex]
answer
[tex]base = 16ft[/tex]
!!!Need Help ASAP
R=42−0.7t
Quinn returned home one summer's day to find it extremely hot. He turned the air conditioner on, and the room's temperature began decreasing at a constant rate. The equation shown above gives the room's temperature, R, in degrees Celsius, t minutes after Quinn turned on the air conditioner. What was the room's temperature, in degrees Celsius, when Quinn returned home?
The room's temperature when Quinn returned home is the y-intercept of the equation, which is: 40 degrees Celsius.
What is the Y-intercept or Initial Value of a Linear Equation?The equation of a linear relationship between two variables, x and y, can be expressed in slope-intercept form as y = mx + b, where we have the initial value or the y-intercept as "b", and the rate of change or unit rate as "m".
Alternatively, it can be rewritten as y = b + mx.
R = 42 - 0.7t represents the equation for the Quinn's room's temperature, R, in degrees Celsius, and t in minutes after Quinn turned on the air conditioner.
Interpreting the equation, we can deduce the following:
The initial value or the y-intercept (b) was the room's temperature when Quinn returned home.
The unit rate or rate of change (m) = -0.7 degrees per minute.
Thus, Quinn's room's temperature when she returned was 40 degrees Celsius.
Learn more about y-intercept of equation on:
https://brainly.com/question/15602982
#SPJ1
Can someone help me with this please?
Step-by-step explanation:
in general, a linear function is always of the structure
y = ax + b
"a" is the slope of the line and is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.
"b" is the y-intercept (the y-value when x = 0).
so, if we don't see the solution right away with experience, we have to use the data points (usually starting with the first 2) to solve them 2 equations with 2 variables a, b :
2 = a×1 + b = a + b
1 = a×2 + b = 2a + b
now we can simply subtract the first equation from the second and get
1 = 2a + b
- 2 = a + b
------------------
-1 = a + 0
a = -1
1 = 2×-1 + b = -2 + b
b = 3
and the equation is
y = -x + 3
therefore, when the input is n (that means f(n))
y = output = -n + 3
find the area. please explain how to get it
Answer:
Step-by-step explanation:
(the small double lines like = means that the length of those sides are all same)
So, if one length is considered as x
the other two will also be x
we see that the length of one side is given which is 27
to find x
x + x + x = 27
3x = 27
so, x = 27/3
x = 9m
(the small vertical single line means that those sides are equal)
so if one side is y, the other two are also y
so , y + y+ y = 30
3y = 30
y = 10m
If we imagine the stairs to be made of small rectangles of length 10m and base 9m , finding area will be easier.
we will see that there are 9 rectangles in total
area of rectangle = length x base
so, area of 1 rectangle = 9x10
= 90[tex]m^{2}[/tex]
so area of 9 identical rectangles = 9 x 90
= 810 [tex]m^{2}[/tex]
the cost to rent a moving van is $51 plus an additional $7 per hour. If a moving van is rented for 2 hours, what is the cost?
We know that
The cost to rent a moving van is $51 plus an additional $7 per hour.Based on the given information, we define the following
[tex]51+7(2)=51+14=65[/tex]Therefore, the cost is $65.The cost to rent a moving van is $51 plus an additional $7 per hour.
Based on the given information,
You invested $101 and received $106.05 after one year. What was the interest rate?
The rate of interest was 5%.
The rate of interest and simple interest can be related through the formula -
S.I. = PRT/100, where S.I. stands for simple interest, P stands for principal, R stands for rate of interest and T stands for time.
Amount = Principal + Interest
Interest = 106.05 - 101
Performing subtraction on Right Hand Side of the equation
Interest = $5.05
Rate of interest = (5.05×100)/(101×1)
Performing multiplication in numerator and denominator
Rate of interest = 505/101
Performing division
Rate of interest = 5
Therefore, to earn $106.05 from $101 in one year, the rate of interest should be 5%.
Learn more about rate of interest -
https://brainly.com/question/25793394
#SPJ9
Give a polynomial of degree 3 that has zeros of 18, 10i, and −10i, and has a value of −3434 when x=1. Write the polynomial in standard form axn+bxn−1+….
The polynomial in standard form is 2x³+200x-36x²-3600
A polynomial is a mathematical formula that involves only the operations subtraction, addition, multiplication, and powers of positive integers of the variables and is composed of coefficients and indeterminates.
It is common to refer to the x of a polynomial as a variable or an indeterminate. The symbol x is fixed and has no significance when the polynomial is viewed as an expression (its value is "indeterminate"). The argument of the function is represented by x, which is referred to as a "variable" when considering the function that the polynomial defines.We know the roots of the polynomial as 18, 10i, and −10i.
therefore the polynomial is of the form.
a(x-18)(x-10i)(x+10i)
= a (x-18)(x²-100i²)
= a (x-18)(x²+100)
= a (x³+100x-18x²-1800)
Now at x =1 The value of the polynomial is -3434
Therefore
-3434 = a(1+100-18-1800)
or, a = 2
Therefore the polynomial is of the form: (2x³+200x-36x²-3600)
to learn more about polynomials visit:
https://brainly.com/question/20121808
#SPJ1
A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 48.5 (ft) with superscript (3). What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary.
The dimensions that yield the minimum surface area of the open-top square-based, rectangular metal tank that will have a volume of 48.5 ft³ are:
Length = 3.65 ftWidth = 3.65 ft.What are the dimensions of an area?The dimensions of an area, which is a two-dimensional object, refer to the length and the width.
On the other hand, the dimensions of the volume refer to the length, width, and height.
The volume of the square-based rectangular tank = 48.5ft³.
The length of each side of the surface area = 3.6468 ft (∛48.5ft)
Check:
Volume = height x length x width
= 3.6468 x 3.6468 x 3.6468
= 48.499 ft³
= 48.5 ft³
Thus, the dimensions of the surface area include the length and the width without the height.
Learn more about dimensions and areas at https://brainly.com/question/27404871
#SPJ1
Quadrilateral ABCD is translated 6 units right and 5 units down to create quadrilateral EFGH. Determine the correct orientation and location of quadrilateral EFGH.
The translation of Quadrilateral ABCD with coordinates A(-3, 4), B(1, 3), C(3, 6), and D(1, 6) using the given transformation rule is; E(3, -1), F(7, -2), G(9, 1), H(7, 1)
What is the translation?
We are given the vertices of Quadrilateral ABCD as;
A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)
Now, we are told that it is first translated right by 6 units. This means that we would add 6 units to each x-value to get;
A'(-3 + 6, 4) = A'(3, 4)
B'(1 + 6, 3) = (7, 3)
C'(3 + 6, 6) = C'(9, 6)
D'(1 + 6, 6) = D'(7, 6)
It is now translated by 5 units downwards and we subtract 5 from each y-value and this gives us;
E(3, -1), F(7, -2), G(9, 1), H(7, 1)
Read more about Translation of Objects at; https://brainly.com/question/12861087
#SPJ1
Complete question is;
Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6) is translated 6 units right and 5 units down to create quadrilateral EFGH. Determine the correct orientation and location of quadrilateral EFGH.
a box has 12 red cards and 12 black cards. another box has 24 red cards and 24 black cards. you want to draw two cards randomly from one of the two boxes, one card at a time. which box has a higher probability of getting cards of the same color and why?
Select red from A and B then the probability of getting cards of same color is 12/24 * 24/48 = 1
Box A: 12 Red
12 Black
Box B: 24 Red
24 Black
One card is selected from Box A and placing the selected card into Box B.
One card is selected from Box B.
What is the probability that a red card is selected from Box B?
Two things can occur:
1) Select red from A and B:
12/24 * 24/48 = 1
2) Select black from A and red from B:
12/24 * 24/48 = 1
learn more about of probability here
https://brainly.com/question/13403296
#SPJ4
Given a normal distribution with mean M = 8 and σ = 3,
What is the x value corresponding to z = 0.4?
123
[tex]123 > x = 10 > 6[/tex]
please someone help me there are only 3 questions
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
Definition of the proportionality constant?
The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.
K = y/x is the equation for the proportionality constant. The equation for the slope of a line through the origin, m = y/x, is the same as this. One can determine the value by using the equation for the line's slope.
To learn more about Constant proportional refer to:
https://brainly.com/question/28413384
#SPJ13
A farmer has 25 goats with a mean mass of 74 kg.
The farmer acquires a new goat and the mean mass becomes 72 kg.
What is the mass of the new goat?
Answer: 72
Step by step explanation:
sum of the masses of the 25 goats take as x then x/25=74 so 74×25=x x=1850 after buying a new goat number of goats =26
hope i helped <3
x²y6/xy²
What is the value of the expression above
if x = -2 and y = 2?
answer
11
Step-by-step explanation:
4x+1/3y^24(2)+1/3(3)^28+1/3(9)8+3
Which numbers I have to put in the boxes
Express each phrase as a rate and unit rate.
(Round your answer to the nearest hundredth.)
1) 7 calculators cost $120.00
Answer:
$100.00
Step-by-step explanation:
5 and above ex: 150 =200 140=100 under 5 keep the first letter then turn the other numbers into 0's 5 and above make the first number go up one then turn the rest of the numbers in to 0's
Simplify the expression. 1-31
1. 5/6(-2y+3)=
2. 6(3s-2.5-5s)=
3. 3/10(4m-8)+9m=
4. 2.25-2(7.5-4h)=
5. 3(a-7)=
6.-6(2+x)=
7. -5(3m-4)=
8. -9(-5-4c)=
9. 4.5(3s+6)=
10. -1.4(-5+7g)=
11. 2/5(6-5p)=
12. -4/3(3q-10)=
13. 2(3+4y+5)=
Factor the expression using the GCF.=
14. The expression 8x + 2 factored using the GCF is=
15. The expression 3y-24 factored using the GCF is =
16. The expression 14p-28 factored using the GCF is=
17. The expression 6+16k factored using the GCF is=
Factor out the coefficient of the variable term.=
18. The expression 1/7a + 1/7 factored is=
19. The expression 1/3b - 1/3 factored is=
20. The expression 3/8d + 3/4 factored is=
21. The expression 2.2x+ 4.4factored is=
22. The expression 0.15c - 0.072 factored is=
23. The expression 3/8z + 1 factored is=
24. The expression 6s - 3/4 factored is=
25. The expression 5/2k - 2 factored is=
26. Factor -4 out of 8d + 20 The factored expression is=
27. Factor -6 out of 18z - 15 The factored expression is=
28. Factor -0.25 out of 7g + 3.5 The factored expression is=
29. Factor -1/2 out of -1/2x+ 6 The factored expression is=
30. Factor -1.75 out of -14m - 5.25n The factored expression is=
31. Factor -1/4 out of -1/2x - 5/4y The factored expression is=
The answers are given below.
First of all, we will know about GCF and expressions.
GCF (GREATEST COMMON FACTOR) - The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both.
Expression are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
1). 5/6(-2y+3) (simply multiply 5/6 with both terms using expansion)
=-2(5/6)+3(5/6)
=-5/3+5/2
2). 6(3s-2.5-5s)= 18s-15-30s = -12s-15
3). 3/10(4m-8)+9m = 12/10m-24/10+9m
= 6/5m-12/5+9m
=6/5m+9m-12/5
=51/m-12/5
4). 2.25-2(7.5-4h)= 2.25-15+8h
= 8h-12.75
5). 3(a-7)= 3a-21
6). -6(2+x)= -12-6x
7). -5(3m-4)= -15m+20
8). -9(-5-4c)= 45+36c
9). 4.5(3s+6)= 13.5s+27
10). -1.4(-5+7g)= 7-9.8g
11). 2/5(6-5p)= 12/5-2p
12). -4/3(3q-10)= -4q+40/3
13). 2(3+4y+5)= 6+8y+10 = 8y+10
14. The expression 8x + 2 factored using the GCF is= 2(4x+1)
15. The expression 3y-24 factored using the GCF is = 3(y-8)
16. The expression 14p-28 factored using the GCF is= 14(p-2)
17. The expression 6+16k factored using the GCF is= 2(3+8k)
The coefficient of the variable terms of following are given below
18. The expression 1/7a + 1/7 factored is= 1/7
19. The expression 1/3b - 1/3 factored is= 1/3
20. The expression 3/8d + 3/4 factored is= 3/8
21. The expression 2.2x+ 4.4factored is= 2.2
22. The expression 0.15c - 0.072 factored is= 0.15
23. The expression 3/8z + 1 factored is=3/8
24. The expression 6s - 3/4 factored is=6
25. The expression 5/2k - 2 factored is=5/2
26. Factor -4 out of 8d + 20 The factored expression is= -4(-2d-5)
27. Factor -6 out of 18z - 15 The factored expression is=-6(-3z+5/2)
28. Factor -0.25 out of 7g + 3.5 The factored expression is=-0.25(-28g-14)
29. Factor -1/2 out of -1/2x+ 6 The factored expression is=-1/2(x-12)
30. Factor -1.75 out of -14m - 5.25n The factored expression is=-1.75(8m+3n)
31. Factor -1/4 out of -1/2x - 5/4y The factored expression is=-1/4(2x+5y)
To know more about GCF and expression, visit:
https://brainly.com/question/2654704
https://brainly.com/question/17155901
#SPJ9
A 100ml tub of ice cream costs £1.50. Work out how much 500ml tub of ice cream would cost.
Answer:
Answer: 7.5 or 7 1/2.
please answer these question
What age would a dog be in human years if he is 3 in dog years?
what is glow in the dark things made out of?
Answer:
Dog be 28
Phosphors apparently
Step-by-step explanation:
Find the equation of a line perpendicular to y=x-1 and passes through the point (-1,-5)
A. y+5= -(x+1)
B. y-5=x-1
C. y+5=x+1
D. y-5= -(x-1)
Step-by-step explanation:
d
since you add them up you will have a certain answer that will match up
A. Solve each absolute value equation. /2.5pts
1)| 3x| = 9
Answer:
x = 3
or
x = -3
(explanation in the picture above)
Answer: x = 3 or x = -3
Step-by-step explanation:
Absolute values make the answer always positive, as they cancel out the negative sign. So to solve an absolute value equation, we must solve for both the positive and negative of the answer.
3x = 9
3x = -9
x = 3 or x = -3