Adam invested $350 at 6% and $450 at 10%
Amount invested by Adam = $800
Interest paid by one account = 6%
Interest paid by another account = 10%
Let the amount invested in one account be x and the other be y
The formula for simple interest is given by:
Simple interest = (P*R*T)/100
where P = Principal
R = rate of interest
T = number of years amount is invested
Substituting the value in the formula we get:
Simple interest in one account = (x*6*1)/100-------(1)
Simple interest in another account = (y*10*1)/100--------(2)
The question states that interest earned would be the same when $800 is invested at 8.25%, therefore
Simple interest = (800*8.25*1)/100
= 66----(3)
Equating (1), (2) and (3) we get:
x + y = 800-----(4)
6x/100 + 10y/100 = 66
6x + 10y = 6600-----(5)
Multiplying (4) with 6 and equating it with (5)
6x + 6y = 4800
6x + 10y = 6600
4y= 1800
y = 450
x = 350
So, Adam invested $350 at 6% and $450 at 10%
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Find the sticker price
River City Autos has a pickup truck for sale. Its base price is $22,225. Prices for available options are 6-speed transmission, $2,908; cruise control, $240; trailer towing package, $230; and power windows, $738. Its destination charge is $900.
The total price of the pick up truck is $27,241.
What is mathematic expression?
A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Base price = $22,225.
Additional options pricing,
6-speed transmission = $2,908
cruise control = $240
trailer towing package = $230
power windows = $738
destination charge = $900
All the other charges will be added to the base price if a person chooses all the options available, therefore,
= 22,225 + 2,908 + 240 + 230 + 738 + 900
= $27241
Therefore, The total price of the pick up truck is $27,241.
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(27/8)-^2/3??????????/
Answer: 4/9
Step-by-step explanation:
[tex]\displaystyle\\(\frac{27}{8} )^{-\frac{2}{3}} =\\\\(\frac{3*3*3}{2*2*2})^{-\frac{2}{3}}=\\\\ (\frac{3^3}{2^3} )^{-\frac{2}{3}} =\\\\((\frac{3}{2})^3)^{-\frac{2}{3} } =\\\\(\frac{3}{2})^{-\frac{3*2}{3}} =\\\\(\frac{3}{2})^{-2}=\\\\(\frac{2}{3})^2 \\\\\frac{2^2}{3^2} =\\\\\frac{4}{9}[/tex]
(01.01 MC)
Which value of x would make the expression (75)* equal to 5?
a
b
3
12
C 4
5
d 5
4
Answer: (sidenote, I'm sorry if I answered incorrectly ;-;)
C: 4/5 or D 5/4
Step-by-step explanation:
if you solve the numbers inside the radical symbol you'll get 16807. it's hard for it to be separated into 4 groups since it can only be separated in 5, that being 7*7*7*7*7.
so, by process of elimination i suggest you answer either c or d
Select all the roots of 49?
Answer:
{2401, {-2401
Step-by-step explanation:
Sorry couldnt type the root symbol on my ipad.
These questions are about calculus, I would greatly appreciate your help on both questions! .
asap , please !
The 107th derivative of f(x) =cos(x) is sin(x).
What is derivative of a function?The derivative of y = f(x) function is the rate of change of y with respect to the independent variable x.
Derivative is represented by [tex]\frac{d}{dx}[/tex] and
First derivative to y is given by [tex]\frac{d}{dx}f(x) = \lim_{h\to \00} \frac{f(x+h)-f(x)}{h}[/tex]
Second derivative [tex]\frac{d^{2}y }{dx^{2} } = \frac{d}{dx} (\frac{dy}{dx} )[/tex] and so on higher derivatives can be defined.
[tex]\frac{d(sinx)}{dx} = cosx\\\frac{d(cosx)}{dx} = -sinx[/tex]
Given f(x) = cos(x)
Then the first derivative of cos(x) is [tex]\frac{d(cosx)}{dx} = -sinx[/tex]
The second derivative of cos(x) is [tex]\frac{d^{2}(cosx) }{dx^{2} } = \frac{d}{dx} (\frac{dcosx}{dx} ) = \frac{d(-sinx)}{dx} =-cosx[/tex]
Third derivative [tex]\frac{d^{3}(cosx) }{dx^{3} } = \frac{d }{dx } (\frac{d^{2} cosx}{dx^{2} } ) = \frac{d(-cosx }{dx } = sinx[/tex]
[tex]\frac{d^{4}(cosx) }{dx^{4} } = \frac{d(sinx) }{dx } = cosx\\\frac{d^{5}(cosx) }{dx^{5} } = \frac{d(cosx) }{dx } = -sinx\\\\\frac{d^{6}(cosx) }{dx^{6} } = \frac{d(-sinx) }{dx } = -cosx\\\\\frac{d^{7}(cosx) }{dx^{7} } = \frac{d(-cosx) }{dx } = sinx\\[/tex]
Eighth derivative if cos(x) is cos(x)
and so on
Therefore , the first , fifth , ninth ,... derivative of f(x) =cos(x) is -sin(x)
The second, sixth, tenth.... derivative of f(x) =cos(x) is -cos(x)
The fourth , eighth , 12th,... derivative of f(x) =cos(x) is cos(x)
We can say that very multiple of fourth derivative of f(x) =cos(x) is cos(x)
We can write 107 as 104 + 3
As 104 is multiple of 4 therefore 104th derivative of cos(x) is cos(x)
[tex]\frac{d^{107}(cosx) }{dx^{107} } = \frac{d^{3} }{dx^{3} } (\frac{d^{104} cosx}{dx^{104} } ) \\\frac{d^{107}(cosx) }{dx^{107} } = \frac{d^{3}(cosx) }{dx^{3} } = sinx[/tex]
Therefore, the 107th derivative of f(x) =cos(x) is sin(x).
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true or false 18:5= 5/18
FALSE because they are two different ratios
Evaluate 11,000,000,000 ÷ 100, write your answer in exponent form.
Answer this fraction based Question. I will make you brainliest and provide you 50 points.
6/7 of people are not having a disease, the whole is 1 so the difference is:
1 - 6/7 = 7/7 - 6/7 = 1/7 of the totalPart ii2/3 of those having a disease is:
1/7*2/3 = 2/21 of the totalPart iii15 people are the 1/7 fraction of total people referred to quarantine.
The total number is:
15 : 1/7 = 15 * 7 = 105 peoplePart iv3/5 of 105 people are male, that is:
3/5*105 = 63 peopleNumber of female is:
105 - 63 = 42 peopleAnswer:
[tex]\sf (i) \quad \dfrac{1}{7}[/tex]
[tex]\sf (ii) \quad \dfrac{2}{21}[/tex]
[tex]\sf (iii) \quad 315\:people[/tex]
[tex]\sf (iv) \quad 126\: females[/tex]
Step-by-step explanation:
Part (i)If 6/7 of people who are quarantined do not have the disease then the fraction of people that do have the disease is:
[tex]\begin{aligned} \implies 1-\dfrac{6}{7} & =\dfrac{7}{7}-\dfrac{6}{7}\\\\ & =\dfrac{7-6}{7}\\\\ & =\dfrac{1}{7}\end{aligned}[/tex]
Therefore, 1/7 of people in quarantine have the disease.
Part (ii)We are told that 2/3 of the people who have the disease come from abroad. Therefore, the fraction of diseased people coming from abroad is 2/3rds of the diseased people:
[tex]\begin{aligned} \implies \dfrac{2}{3} \textsf{ of }\dfrac{1}{7} & = \dfrac{2}{3} \times \dfrac{1}{7}\\\\ & = \dfrac{2 \times 1}{3 \times 7}\\\\ & = \dfrac{2}{21}\end{aligned}[/tex]
Therefore, the fraction of diseased people who have come from abroad is 2/21.
Part (iii)We are told that 15 people who have the disease do not come from abroad. So if 2/3 of the people who have the disease come from abroad, then 1/3 of the people who have the disease do not come from abroad. Remember that 1/7 of the total people have the disease.
[tex]\begin{aligned} \implies \dfrac{1}{3} \textsf{ of }\dfrac{1}{7} & = \dfrac{1}{3} \times \dfrac{1}{7}\\\\ & = \dfrac{1 \times 1}{3 \times 7}\\\\ & = \dfrac{1}{21}\end{aligned}[/tex]
Therefore, 1/21 of the total number of people have the disease and do not come from abroad.
Therefore, 15 people are equal to 1/21 of the total number of people:
[tex]\implies \sf Total\:number\:of\:people=15 \times 21 = 315[/tex]
Therefore, the total number of people in quarantine is 315.
Part (iv)If 3/5 of the total are male, then 2/5 must be female.
[tex]\begin{aligned} \implies \dfrac{2}{5} \textsf{ of }315 & = \dfrac{2}{5} \times 315\\\\ & = \dfrac{2 \times 315}{5}\\\\ & = \dfrac{630}{5}\\\\& = 126 \end{aligned}[/tex]
Therefore, 126 females are in quarantine.
Given m n, find the value of x.
Answer:
x = 21°
Step-by-step explanation:
180 - 159 = 21
Alternate angles (see image below) are equal, so x = 21
Using corresponding angles and adjacent angles concept, the value of x from the given parallel lines is 21°.
Given that, straight line m parallel to straight line n and t is the transversal.
The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.
Here, y°=159°
Now, y°+x°=180° (Adjacent angles on straight line)
159°+x°=180°
x°=21°
Therefore, the value of x from the given parallel lines is 21°.
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I’m in need of help with this math problem!!!
Answer:
Flowers: $19.98Jewelry: $18.92Gift Certificates: $14.52Step-by-step explanation:
You want the values of three expenditures, given three relations between them.
(The first thing to realize is that the question isn't about averages at all. It is about values that are described as averages.)
SetupLet f, j, c represent the (average) amounts spent on flowers, jewelry, and gift certificates, respectively. The three given relations are ...
f + j + c = 53.42
j = 4.40 + c
f + c = 15.58 + j
SolutionUsing the second equation to substitute for j in the third, we have ...
f +c = 15.58 +(4.40 +c)
f = 19.98 . . . . . . . . . . . . . . simplify
Using this and the second equation to substitute into the first, we have ...
19.98 +(4.40 +c) +c = 53.42
24.38 +2c = 53.42
2c = 29.04
c = 14.52
Then ...
j = 4.40 +c = 4.40 +14.52 = 18.92
The average expenditures are ...
Flowers: $19.98Jewelry: $18.92Gift Certificates: $14.52__
Additional comment
This solution is one of many ad hoc methods that could be used. There are also graphing and matrix methods available for solving a set of equations like this. The attachment shows a calculator matrix solution.
The quadrilaterals ABCD and JKLM are similar.
Find the length x of MJ.
Answer:
x = 4.8
Step-by-step explanation:
since the quadrilaterals are similar then the ratios of corresponding sides are in proportion , that is
[tex]\frac{MJ}{DA}[/tex] = [tex]\frac{LM}{CD}[/tex] ( substitute values )
[tex]\frac{x}{6}[/tex] = [tex]\frac{2.4}{3}[/tex] ( cross- multiply )
3x = 6 × 2.4 = 14.4 ( divide both sides by 3 )
x = 4.8
Select the 2 values of X that are root of this equation X² + 2X (-6) = 0
The two values that serves as the root of the equation are -1-√7 and -1+√7
Root of quadratic equationGiven the quadratic equation below;
X² + 2X (-6) = 0
x^2 + 2x - 6 = 0
Using the general formula
x = -2±√2²-4(1)(-6)/2(1)
x = -2±√4+24/2
x = -2±√28/2
x = -2±2√7/2
x = -1±√7
Hence the two values that serves as the root of the equation are -1-√7 and -1+√7
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Find the coordinates of the point
7/10 of the way from A to B.
The coordinates of the point
7/10 of the way from A to B are
Answer:
(4,-4)
is the way from AtoB
Write 12 ⋅ 12 ⋅ 12 ⋅ 12 ⋅ 12 ⋅ 12 ⋅ 12 ⋅ 12 ⋅ 12 in exponential form. Write your answer as: base^exponent
Answer: I could be wrong but I'm pretty sure it's 12^9 but again I could be wrong
Step-by-step explanation:
The total area of Wisconsin
is 65,498 square miles. Of that, about
80% is land area. About how many
square miles of Wisconsin is not land
area?
Answer:
the other 20%
Step-by-step explanation:
calculate 20% of 65498
Answer:
13,099.6 square miles
Step-by-step explanation:
80%*65,498=
80/100 * 65,498=
4/5 * 65,498=52,398.4 square miles of land area
65,498-52,398.4= ==> subtract the total area of Wisconsin by the total land area to get the total area that isn't land.
65,498.0-52,398.4=13,099.6 square miles of area that isn't land
In the diagram below, ΔABC ≅ ΔDEF. Complete the statement BC⎯⎯⎯⎯⎯⎯⎯⎯≅ B C ¯ ≅ ___
Answer:
[tex]\overline{BC} \cong \overline{EF}[/tex]
Step-by-step explanation:
Corresponding parts of congruent triangles are congruent.
Simplify the expression below:
-3/7 ( y-28) - 1/21 y
please show your work and i'll give brainliest :,)
What is the place value of 5 in 62,506,300,782?
A. Hundred thousands
B. Ten thousands
C. Millions
D. Hundred millions
Simplify the radical √20
I think of a number. I add 1090 to the number.
I subtract 450 from the result. The answer is 760.
What is the number I first thought of?
Answer:
120
Step-by-step explanation:
call the number x,
then x+1090-450
so x+640=760
x=760-640
x=120
hope this works :)
Answer:
120 is the number u thought of first
Step-by-step explanation:
1090-450=640
if we add 120 into 1090
then it will be 1210
so 1210-450=760
Solve the inequality.
6 (x/2+4)>9
Answer is x > -5
fid comon demoninator
Answer: x>−5
Step-by-step explanation:
[tex]6(\frac{x}{2} +4) > 9[/tex]
Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.
[tex]\frac{x}{2} +4 > \frac{9}{6}[/tex]
Reduce the fraction
[tex]\frac{9}{6}[/tex]
to lowest terms by extracting and canceling out 3.
[tex]\frac{x}{2} +4 > \frac{3}{2}[/tex]
Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.
x+8>3
Subtract 8 from both sides.
x>3−8
Subtract 8 from 3 to get −5.
x>−5
On Flight #447 if 130 people are on the flight how many can get both headphones and a blanket
Answer: 106
Step-by-step explanation:
because there is 106 headphones 106 people can get and there is 16 blankets 156 people can get so 106 people can get headphones and blankets
How do u write Nineteen million three hundred thousand twenty five and twenty two hundredths
i need this in a hour O_o
Answer:
x= 5/12,y=− 5/4
Step-by-step explanation:
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
6x−12y=24,4x+2y=8
Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
6x−12y=24
Add 12y to both sides of the equation.
6x=12y+24
Divide both sides by 6.
x= 6/1 (12y+24)
Multiply 6
1 times 24+12y.
x=2y+4
Substitute 4+2y for x in the other equation, 4x+2y=8.
4(2y+4)+2y=8
Multiply 4 times 4+2y.
8y+16+2y=8
Add 8y to 2y.
10y+16=8
Subtract 16 from both sides of the equation.
10y=−8
Divide both sides by 10.
y=− 5/4
Substitute − 5/4 for y in x=2y+4. Because the resulting equation contains only one variable, you can solve for x directly.
x=2(− 5/4 )+4
Multiply 2 times − 5/4 .
x=− 5/8 +4
Add 4 to − 5/8 .
x= 5/12
what is a - b + 8 = 42
Answer:
a-b+8=42
a-b=42-8
a-b=36
espero t sirva
Answer:
b=34
Step-by-step explanation:
The line y=kx+4 goes through the point (2,-2)
Find the value of k.
Answer:
k= -3
Step-by-step explanation:
Since we know the line will go through the point (2,-2), we can plug these values into our x,y variables to solve for k. Our 2 is the x-value and our -2 is the y-value.
y = kx+4
-2 = k(2)+4
To get k by itself, we first have to subtract the 4 from both sides.
-2-4 = k(2)+4-4
-6 = k(2)
Then, we can divide each side by the 2 to get our answer.
-6/2 = k(2)/2
k = -3
Answer:
k=-3
Step-by-step explanation:
12.4%of what number is 7.13?
Answer:57.7
Step-by-step explanation:
Given P(A) = 0.74, P(B) = 0.85 and P(A|B) = 0.84, find the vi P(A and B), rounding to the nearest thousandth, if necessary.
The value of the given statement rounding to the nearest thousandth = 0.714.
What exactly are dependent events?Dependent occurrences are ones that are dependent on previous events. The outcomes of prior events have an impact on these occurrences. Dependent events are two or more occurrences that are dependent on one another. If one event is altered by chance, another is most likely to differ.
What exactly is the distinction between dependent and independent?The independent and dependent factors are the two most crucial variables in a research experiment. The experimental has authority over the independent variable. The variable that varies in reaction toward the independent variable is known as the dependent variable.
According to the information provided:P(A) = 0.74
P(B) = 0.85
P(A|B) = 0.84
Using dependent events formula:
P(A∩B) = P(A/B) × P(B)
= 0.84 X 0.85
= 0.714
The value of the given statement rounding to the nearest thousandth = 0.714.
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what is the value of the sum 1/3 and 2/5
Answer:11/15
Step-by-step explanation:
you have to change them to common denominators.
i chose 15.
to make the denominator for 1/3 into 15 you have to multiply it by 5 which means you have to multiply the numerator (1) by the same thing which gives you 5/15
to make the denominator for 2/5 into 15 you have to multiply the denominator by 3 so you have to multiply the numerator (2) by the same thing which gives you 6/15
you now have the equation 5/15 + 6/15
to add them together you leave the bottom numbers the same and add the top ones which gives you 11/15
Answer:
0.7333333333333333 = 11/15
Step-by-step explanation:
1/3 = 5/15
2/5 = 6/15
add them, and now you get
(5+6)/15 = 11/15
Graph = 2/3x
Please graph the graph right and answer the ones that apply
1. Yes, the equation represent the proportionality relationship.
2. Yes, the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].
3.Yes, The slope of the line is [tex]\frac{2}{3}[/tex]
Given a picture in that we can see a graph and 3 option.
We have to check weather that 3 option satisfy the equation and what are they.
Given equation [tex]y=\frac{2}{3}x[/tex]
1st option: Is the equation represent the proportionality relationship.
Yes, the equation represent the proportionality relationship.
If we see the proportionality rule that is
The equation y = kx represents a proportionate relationship between two quantities y and x that have the same proportionality constant, k.
A proportionate relationship exists if an equation in a different form can be rewritten as shown above.
Here, the equation is in the form of y=kx.
Therefore, Yes, the equation represent the proportionality relationship.
2nd option: the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].
Yes, the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].
The amount of change in y for a change of one unit in x is the unit rate of change of y with respect to x.
The slope is [tex]\frac{2}{3}[/tex].
Therefore, Yes, the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].
3rd option: The slope of the line is [tex]\frac{2}{3}[/tex]
Yes, The slope of the line is [tex]\frac{2}{3}[/tex]
It is possible to simplify the equation of the slope to the form
y=mx+b, where m is the slope of the line and b is constant.
y is the dependent variable and x is the independent variable.
By the equation [tex]y=\frac{2}{3}x[/tex]
Therefore, Yes, The slope of the line is [tex]\frac{2}{3}[/tex]
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