Answer:
$65,000 , $50,000 and $35,000
Step-by-step explanation:
Lets us assume the CDs be C, stocks be S and Bonds be B
Given that
Total scholarship fund received = $150,000
i.e
C + S + B = $150,000 ......................... (1)
Now the each items invested percentage is given
And, the annual income from investment is $10,805
So, the next equation is
0.06C + 0.022B + 0.117S = $10,805 ....................... (2)
And, it is mentioned that
The $15,000 more in bonds than in CDs
B = C + $15,000 ........................ (3)
Now put the equation 3 in equation C is
2C + S = $135,000 ........................... (4)
0.082C + 0.117S = $10,475 ........................... (5)
Now multiply the 0.117S in equation 4
So
0.234C + 0.117S = $15,795
0.082C + 0.117S = $10,475
After solving this
0.152C = $5,320
C = CDS = $35,000
So
B = $35,000 + $15,000
B= Bonds = $50,000
And S = Stock = $65,000
Answer:
CDs = 35000, Bonds = 50000, Stock = 65000
Step-by-step explanation:
Let amount invested in : CDs be 'C' , stock be 'S' , bonds be 'B'
As per total funds : C + B + S = 150000 [E1]
As per interest rates : 0.06C + 0.022B + 0.117S = 10805 [E2]
Given (15000 more invested in bonds than CDs : B = C + 15000 [E3]
Putting equations : [E3] in [E2] & [E1]
C + (C+15000) + S = 150000 → 2C + 15000 + S = 150000
2C + S = 135000 [E4]0.06C+0.022(C+15000)+0.117S = 10805 → 0.06C+0.022C+330+0.117S = 10805
0.082C + 0.117S + 330 = 10805 → 0.082C + 0.117S = 10475 [E5]By putting value of S from [E4] in [E5] :
0.082C + 0.117 (135000 - 2C) = 10475 → 0.082C + 15795 - 0.234C = 10475
5320 = 0.152C → C = 5320 / 0.152 = 35000 [CDs]
B = C + 15000 = 35000 + 15000 = 50000 [Bonds]
By [E1]: 35000+50000+S = 150000 → S = 150000 - 85000 = 65000 [Stocks]
Indigo works as a salesperson at an electronics store and sells phones and
phone accessories. Indigo earns a $8 commission for every phone she sells
and a $4 commission for every accessory she sells. On a given day, Indigo
made a total of $160 in commission from all accessory and phone sales and
she sold 3 times as many accessories as phones. Determine the number of
phones sold and the number of accessories sold.
There were
phones sold and
accessories sold
The number of phones sold were 8 and the number of accessories sold were 24 .
In the question ,
it is given that
commission earned by Indigo for every phone sold = $8
and commission earned by Indigo for every accessory sold = $4
total commission earned = $160
let the number of phones sold be "p"
let the number of accessory sold be "a"
given that she sold 3 times as many accessories as phones
which means , a = 3p
and 8p + 4a = 160
substituting a=3p in 8p + 4a = 160 ,
we get
8p + 4(3p) = 160
8p + 12p = 160
20p = 160
p = 160/20
p = 8
and a = 3p = 3(8) = 24
Therefore , The number of phones sold were 8 and the number of accessories sold were 24 .
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Evaluate 3a - 4b for a = -1 and b =6
Answer:
-27
Step-by-step explanation:
3a - 4b
-3 - 4b
-3 - 24
-27
HURRY PLEASE!! I NEED TO TURN THIS IN SOON!!!
I WILL GIVE YOU BRAINLIEST!!
i need the equation you used to solve it with also!
Answer:
Step-by-step explanation:
3x-11+6x-10+x=180
10x-21=180
10x=201
x=20,1
The gasoline tax is a ______ tax
Answer:
Excise tax
Step-by-step explanation:
Correct me if I'm wrong <3
A car was bought for $18,000. It’s value depreciated by 15% each year for the first three years.
What was its value at the end of the first three years?
Answer: 11054.25
Step-by-step explanation:
The point is on the x acis and 12 units to the left of y axis
Answer:
(-12, 0)
Step-by-step explanation:
They are asking for the coordinates of the given point on the plane.
Therefore, since the point is on the x axis, we know that its y-coordinate must be zero. y = 0
Now, since it is 12 units to the left of the y axis, then its x coordinate is -12
x = -12
Therefore, the point in plane coordinates is written as: (-12, 0)
At Mason's factory, one part that the factory manufactures takes 824 seconds to make. Mason bought new technology that decreases that time by 25%. How long does it take to make the part now?
Answer asap ty
It takes 618 seconds to make the part now. This is solved using the concept of expression formation.
What is percentage?Percent is derived from the Latin word per centum, which means "by the hundred." In the 16th century, the Latin expression was adopted by English. Later, it was shortened to % with a period at the end. The present one-word form % was created after the period was eliminated and the two elements were combined.
A percentage is essentially a component per one hundred. Both fractional and decimal forms of the expression are possible.
Finding a number or percentage in values of 100 has been done and use the percentage formula. Per hundred is what "percent" denotes in its most basic form. The percentage formula is used to represent a number between 0 and 1. A fractional representation of a number is what is meant by the definition.
Given that,
At Mason's factory, one part that the factory manufactures takes 824 seconds to make.
Mason bought new technology that decreases that time by 25%.
So, based on the given conditions: 824 × (1 - 25%)
= 824 × 0.75
= 618
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Right triangle LMN has vertices L(7, –3), M(7, –8), and
N(10, –8). The triangle is translated on the coordinate plane so the coordinates of L’ are (–1, 8).
In this case we have a translation of 8 units to the left and 11 units upwards.
How to find the translation?To find the translation, we just need to compare the two known vertices before and after the translation.
If we have a translation of a units in the x-axis and b units in the y-axis, we will get:
T(a, b)L ---> L'
We know that L = (7, -3) and L' = (-1, 8)
Then we can write:
(7 + a, -3 + b) = (-1, 8)
Then we have two equations:
7 + a = -1 ---> a = -1 - 7 = -8
-3 + b = 8 ---> b = 8 + 3 = 11
Then we have a translation of 8 units to the left and 11 units up-.
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Complete question:
"Right triangle LMN has vertices L(7, –3), M(7, –8), and
N(10, –8). The triangle is translated on the coordinate plane so the coordinates of L’ are (–1, 8).
Find the translation done"
ABC~A'B'C'. Their scale factor is 7:9. If the perimeter of smaller ABC is 42, then the
perimeter of A'B'C' is.
Pls hurry!!
Answer:
54
Step-by-step explanation:
ratio is 7:9
7=42
9=?
9×42÷7
What is the answer pleaseee
Answer: 803.84cm3
Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.
To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.
4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.
Now, we have the area of the circle. 50.24cm squared!
The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,
16cm x 50.24cm squared = 803.84cm cubed.
The volume of the can of soup is 803.84cm cubed.
A relay team of 4 people run 5 miles. How many miles does each person run?
Answer:
5 miles
Step-by-step explanation:
they all ran 5 miles
which is bigger 1 or
\( \frac{19}{9} \)
Answer:
19/9 because it equals to 2.111.. Which is greater than 1
Step-by-step explanation:
By the way if it's right can i get brainliest.
Answer:
1 < 19/9
Step-by-step explanation:
1 vs 19/9
Rewriting 19/9 as 9/9 + 9/9+ 1/9
1 vs 1+1 +1/9
1 vs 2 1/9
1 < 19/9
The diagram shows EFG. Which term describes point H?
A. Circumcenter
B. Incenter
C. Orthocenter
D. Centroid
Point H is the ortho-center of our given triangle and option c is the correct choice.
We have been given an image of a triangle. We are asked to find the term that describes point H.
We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.
We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option c is the correct choice.
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i needs help with it please
Answer:
(i) (0, -32)
(ii) (-4, 0) and (8, 0)
(iii) x = 2
(iv) (2, -36)
(v) (2, -36) minimum
Step-by-step explanation:
Given quadratic equation:
\(y=x^2-4x-32\)
Part (i)
The y-intercept is the point at which the curve crosses the y-axis.
To find the y-intercept, substitute x = 0 into the given equation:
\(\implies (0)^2-4(0)-32=-32\)
Therefore, the y-intercept is at (0, -32)
Part (ii)
The zeros are the points at which the curve crosses the x-axis.
To find the zeros, substitute y = 0 into the given equation and factor:
\(\implies x^2-4x-32=0\)
\(\implies x^2-8x+4x-32=0\)
\(\implies x(x-8)+4(x-8)=0\)
\(\implies (x+4)(x-8)=0\)
Therefore:
\((x+4)=0 \implies x=-4\)
\((x-8)=0 \implies x=8\)
So the zeros are (-4, 0) and (8, 0)
Part (iii)
The axis of symmetry is a vertical straight line that divides the curve into two symmetrical parts. The axis of symmetry is the x-value of the mid-point of the zeros.
\(\sf \implies midpoint=\dfrac{8+(-4)}{2}=2\)
Therefore, the axis of symmetry is: x = 2
Part (iv)
The vertex is the turning point of the parabola.
If the leading coefficient is positive, the parabola opens upwards and the vertex is the minimum point.
If the leading coefficient is negative, the parabola opens downwards and the vertex is the maximum point.
The axis of symmetry is the x-value of the vertex.
To find the y-value, substitute x = 2 into the equation:
\(\implies (2)^2-4(2)-32=-36\)
Therefore, the vertex is (2, -36)
Part (v)
The optimal value is also known as the vertex.
Therefore, the optimal value is (2, -36).
As the leading coefficient of the given quadratic equation is positive, the parabola opens upwards and so the optimal value is a minimum.
a)
b)
1. Convert the following Mayan numbers to
decimal (base 10).
: :|| :||
The given Mayan number which is : :|| :|| in decimal (base 10) is 42.
The Mayan number system is a base-20 system that uses three symbols: a dot (.), a horizontal bar (|), and a shell-like symbol (:). The symbol for zero is a shell-like symbol (:).
To convert the given Mayan number to decimal (base 10), we need to understand the positional value of each symbol. Each position in the number represents a power of 20, with the rightmost position being 20⁰, the next position to the left being 20¹, and so on.
The Mayan number given, : :|| :||, can be broken down as follows:
The leftmost position has no symbol, which represents a value of 0.
The second position from the left has two shell-like symbols (:), which represents a value of 2x20¹ = 40.
The third position from the left has two horizontal bars (||), which represents a value of 2x20⁰ = 2.
The given Mayan number in decimal (base 10) is 40 + 2 = 42.
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Complete question is:
Convert the following Mayan number to decimal (base 10).
: :|| :||
Use the drop-down menus to complete the statements
What is 4 divided by 1/3 ?
This problem asks how many groups of ? are in ?
The quotient of 4 divided by 1/3 is ?
Answer:
This problem asks how many groups of
1/3 are in 4
The quotient is 12
Step-by-step explanation:
This is the right answer on edge
Answer:
B, C, C
Step-by-step explanation:
Its right in edge
Write the equation in standard form for the circle with center (0,5) and radius 7.
Answer:
\(x^2+(y-5)^2=49\)
Step-by-step explanation:
Recall the formula for the graph of a circle:
\((x-h)^2+(y-k)^2=r^2\\\)
Where h is the x-coordinate of the vertex, k is the y-coordinate of the vertex, and r is the radius.
We are given the vertex and the length of the radius.
Substitute the values:
\((x-0)^2+(y-5)^2=7^2=\\x^2+(y-5)^2=49\)
Thus, the standard form is:
\(x^2+(y-5)^2=49\)
Given the function R(x)=x+3x−4, find the values of x that make the function less than or equal to zero. Write the solution in interval notation.
The values of x that make the function less than or equal to zero are x ≤ -3 or x ≥ 4. This can be written in interval notation as (-∞, -3] ∪ [4, ∞).
The given function is R(x) = (x + 3)/(x - 4)
We have to find the values of x that make the function less than or equal to zero
We need to set the expression equal to zero and solve for x.
Let the function (x + 3)/(x - 4) = 0.
We can solve this equation by rearranging it to get x + 3 = 0, or x = -3.
We also get x - 4 = 0, or x = 4.
Therefore, the values of x that make the function less than or equal to zero are x ≤ -3 or x ≥ 4. This can be written in interval notation as (-∞, -3] ∪ [4, ∞).
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Find the inverse function in slope-intercept form (mx+b):
F(x)= 5/4 x-10
10 points help me in the last question i will give 30
Answer:
f^-1(x)=4x/5+8
Step-by-step explanation:
f^-1(x)=4x/5+8
$155 $267 $284 $194 $299 $284 $287 $179 What is the mean, median, and mode of this data set?
Answer:
Mean = 243.625
Median = 275.5
Mode = 284
Each value is exact without any rounding.
=================================================
Original data set:
$155 $267 $284 $194 $299 $284 $287 $179
Let's remove the dollar signs, and separate each item with a comma:
155,267,284,194,299,284,287,179
Then sort the values from lowest to highest.
155,179,194,267,284,284,287,299
---------------------
To find the mean, we add up the values and divide by n = 8 since there are 8 items in the list.
(155+179+194+267+284+284+287+299)/8 = 243.625 is the mean
----------------------
Refer to the sorted data set.
The median is the middle-most value. Because the sample size n = 8 is even, we'll have two values tied for the middle.
n/2 = 8/2 = 4
The items in slot 4 and 5 are tied for the middle.
The values in slot 4 and 5 are 267 and 284 in that exact order.
Compute the midpoint: (267+284)/2 = 275.5 is the median
----------------------
The mode is the most frequent value. Look through the sorted data set to see that 284 shows up twice. This is the most frequent compared to the other values (that show up only once).
Therefore, the mode is 284
Side note: It's possible to have multiple modes. It's also possible to not have any modes at all.
PLEASE HELP ASAP For each expression below, select the letter that corresponds to the equivalent expression from the given list.
(4x^3 – 4 + 7x) – (2x^3- 8)
is equivalent to expression___
(-3x^2 + x^4 + x) + (2x^4 - 7 + 4x) is equivalent to expression ____
(12 – 2x)(2x + 3) is equivalent to expression___
The blanks are for the letters in the picture
BAnswer:
B-D-A
Step-by-step explanation:
-
3/4 = 12/y Find the missing value
3/4 = 12/y
3/4 * y = 12
.25 * y = 12
y = 3
Hope this helps! :)
A triangle has two sides that measure 5 cm and 7 cm which of the following cannot be the measure of the third side
Answer
what are the answer choices
Step-by-step explanation:
I says which of the following so I need the choices.
Answer:
i pretty sure its 10cm
Step-by-step explanation:
Use a proof by contraposition to prove that if m and n are integers and mn is even, then m is even or n is even.
In order for mn to be even, m must be even or n must be an even number.
What is Contraposition ?The relationship between two propositions when the subject and predicate of one are respectively the negation of the predicate and the negation of the subject of the other.
Suppose that the statement “m is even or n is even” is not true. Then both m and n are supposed to be odd. Let’s see if the product of two odd numbers is an even or an odd number:
Let n and m be equal to 2a +1 and 2b + 1 respectively, then their product is:
(2a +1) (2b + 1) = 4ab + 2a + 2b + 1
= 2(2ab +a + b) + 1
This shows that the expression 2(2ab +a + b) + 1 is of the form 2n +1, thus the product is odd. If the product of odd numbers is odd, then mn is not true to be even. Therefore, in order for mn to be even, m must be even or n must be an even number.
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A tank contains 5832 litres of water. Each day one-third of the water in the tank is removed and not replaced. How much water remains in the tank at the end of 6 days? [Hint: answer 512 litres] Show me the steps
Here is your answer.
A tank contains 5832 litres of water.
Total amount of water in tank = 5832 litres.
Each day one-third of the water in the tank is removed and not replaced.
Since one third of the water is removed for six days.
1st day = 1/3rd of 5832 litres is removed
\( = \dfrac{5832}{3} = 1944\)
Amount of water left = 5832 - 1944 = 3888 litres
2nd day = 1/3rd of 3888 litres is removed
\( = \dfrac{3888}{3} = 1296 \)
Amount of water left = 3888 - 1296 = 2592 litres
3rd day = 1/3rd of 2592 litres is removed
\( = \dfrac{2592}{3} = 864 \)
Amount of water left = 2592 - 864 = 1728 litres
4th day = 1/3rd of 1728 litres is removed
\( = \dfrac{1728}{3} = 576 \)
Amount of water left = 1728 - 576 = 1152 litres
5th day = 1/3rrd of 1152 litres is removed
\( = \dfrac{1152}{3} =384 \)
Amount of water left = 1152 - 384 = 768 litres
6th day = 1/3rrd of 768 litres is removed
\( = \dfrac{768}{3} = 256 \)
Amount of water left = 1768 - 256 = 512 litres
So, 512 litres water remains in the tank at the end of 6 days
Simplify (use only positive exponents) : (3y^10)(2y^2)/8y^5
please explain how you did it so that I can understand what I'm doing <3
A Sumer job pays $5 per hour
b. After working 24 hours, do you have enough money to buy an MP3
player that costs $100? Explain your reasoning.
Answer:
Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.
Step-by-step explanation:
hourly pay: $5/hour
number of hours: 24 hours
total pay = hourly pay × number of hours
total pay = $5/hour × 24 hours
total pay = $120
MP3 player costs $100.
Total pay is $120.
Answer: Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.
which grows at the fastest rate for increasing values of x
\(f(x)=4*2^x\\h(x)=9x^2+25\\\\g(x)=15x+6\)
The function that grows at the fastest rate for increasing values of x is f(x) = 4×2ˣ.
We can see this by comparing the growth rates of the three functions for larger and larger values of x.
As x gets larger, the exponential function f(x) grows much faster than the other two functions, which are both polynomial functions.
if we plug in x = 10, we get:
f(10) = 4×2¹⁰ = 4×1024 = 4096
h(10) = 9×10² + 25 = 925
g(10) = 15×10 + 6 = 156
As we can see, f(10) is much larger than h(10) and g(10), indicating that f(x) grows at a much faster rate than the other two functions.
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what is the value of the expression 2c(c+3)^2 if c=2 5 20 25 40 100
Answer:
100
Step-by-step explanation:
To find the value of the expression with the given value of c, substitute that given value for every c in the expression. So, since c = 2, substitute 2 in place for each c and simplify like below. Remember to follow PEMDAS.
\(2c(c+3)^2\\2(2)(2+3)^2\\= 2(2)(5)^2\\= 2(2)(25)\\= 4(25)\\= 100\)
Thus, the answer is 100.
what are the measurements of 1 and 2?
Answer:
8 tablespoons1/2 cup4 ounces10 tablespoons plus 2 teaspoons2/3 cup5.2 ounces12 tablespoons3/4 cup6 ounces16 tablespoons1 cup8 ounces