The amount John saves off his minimums after 3 months is $450
Calculating amount savedFrom the question, we are to determine the amount John saves off his minimums after 3 months
The amount John saves off his minimums after 3 months =
($500 - $350) × 3
$150 × 3
= $450
Hence, the amount John saves off his minimums after 3 months is $450
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a card is drawn from a deck of cards. event A is that the card obtained is a 2 and B is that the card is a spade. these event do not overlap.
true
false
Event A and Event B are events that do not overlap. This statement is false.
Do events A and B overlap?Two events overlap if there is a chance that both events occur together. A spade has a number 2. Thus, it is possible to pick a spade that has the number 2 on it. Thus, these events are dependent events.
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Write as a single fraction
-8c-d/9c+9C+4d/3c-5
Thoughts: The best that I was able to do was simplify it in this form.
Answer: V
Find the x-intercepts of the parabola with vertex (5,-12) and y-interdept (0,63). Write your answer in this form: (x1,y1), (x2,V2). If necessary, round to the nearest hundredth.
The x-intercepts of the parabola are (3, 0) and (7,0)
How to determine the x-intercept?The given parameters are:
Vertex (h, k) = (5, -12)
Point (x, y) = (0, 63)
The equation of a parabola is:
y = a(x - h)^2 + k
Substitute (h, k) = (5, -12)
y = a(x - 5)^2 - 12
Substitute (x, y) = (0, 63)
63 = a(0 - 5)^2 - 12
Evaluate
63 = 25a - 12
Add 12 to both sides
25a = 75
Divide by 26
a = 3
Substitute a = 3 in y = a(x - 5)^2 - 12
y = 3(x - 5)^2 - 12
Set y to 0 to determine the x-intercepts
0 = 3(x - 5)^2 - 12
Add 12 to both sides
3(x - 5)^2 = 12
Divide by 3
(x - 5)^2 = 4
Take the square root of both sides
[tex]x - 5 = \pm 2[/tex]
Add 5 to both sides
[tex]x = 5 \pm 2[/tex]
Expand
x = (5 - 2, 5 + 2)
Evaluate
x = (3, 7)
Hence, the x-intercepts of the parabola are (3, 0) and (7,0)
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(sec x + tan x)((1-sin x/cos x)=1 Please show calculations why you did those calculations. I need help!!!
Step-by-step explanation:
[tex]( \sec(x) + \tan(x) )( \frac{1 - \sin(x) }{ \cos(x) } )[/tex]
[tex]( \frac{1}{ \cos(x) } + \frac{ \sin(x) }{ \cos(x) } )( \frac{1 - \sin(x) }{ \cos(x) } )[/tex]
[tex]( \frac{1 + \sin(x) }{ \cos(x) } )( \frac{1 - \sin(x) }{ \cos(x) } )[/tex]
[tex] \frac{1 - \sin {}^{2} (x) }{ \cos {}^{2} (x) } [/tex]
[tex] \frac{ \cos {}^{2} (x) }{ \cos {}^{2} (x) } [/tex]
[tex] = 1[/tex]
Sam earns $912 each week working his full time job. His employer has a 13.6% tax deduction on all monies earned each week. Calculate the tax deduction Sam paid for that week. Sam earns $ 912 each week working his full time job . His employer has a 13.6 % tax deduction on all monies earned each week . Calculate the tax deduction Sam paid for that week .
Sam paid $ 124.032 as tax deduction each week.
What is an Equation ?An equation is a mathematical statement formed when an algebraic expression is equated by an equal sign by a constant or algebraic expression.
It is given that
weekly earnings of Sam is $912
Tax deduction is 13.6 %
Let the amount of Tax deduction is represented by $x
Then the equation formed is
x = 13.6 % 912
x = 13.6 *912 /100
x = $ 124.032
Therefore Sam paid $ 124.032 as tax deduction each week.
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find the volume of the sphere
Answer:
The volume = 5 276.66928645188 cm³
Step-by-step explanation:
let V be the volume of the given sphere.
V = (4/3)×π×r³ ,where r is the radius of the sphere
r = 21.6÷2 = 10.8 cm
Then
V = (4÷3)×π×(10.8)³
= 5 276.66928645188 cm³
Write 3.3.3.3.3.3.3.3. With exponential notation
Answer:
the answer is 3power 7
3^7
Answer:
3^8
Step-by-step explanation:
On October 23, 2011, one U.S. dollar was worth 49.84 Indian rupees.
(a) On that date, how many rupees was 103.64 dollars worth?
Round your answer to the nearest hundredth of a rupee.
0
rupees
(b) On that date, how many dollars was 67.36 rupees worth?
Round your answer to the nearest hundredth of a dollar.
dollars
Answer:
(a) 5165.42 rupees
(b) $1.35
Step-by-step explanation:
Given information:
USD 1 = INR 49.84Part (a)
To find how many rupees $103.64 was worth, multiply the number of dollars by the number of rupees per dollar:
⇒ 103.64 × 49.84 = 5165.42 rupees (nearest hundredth)
Part (b)
To find how many dollars 67.36 rupees was worth, divide the number of rupees by the number of rupees per dollar:
⇒ 67.36 ÷ 49.84 = $1.35 (nearest hundredth)
Ethan sold some watches at $14 each and 20 bookmarks at $1.50 each. Roy sold the same number of watches at $13.50 each and 20 bookmarks at $1.80 each. They collected the same amount of money. How many watches did Ethan sell? Ethan Roy watches 17-114 watches come total Bookmarks 20 × $1.56-30 Bookmarly 20-11-80-36 Same total
[<Answer>] (1):
Heyy there, it's Avery. And I'm here to help! :)
----------------------------------------------------------------------------------------------------------[<The Explanation>]:
Let x= number of watches sold
Ethan= x(14) + (20)(1.50)
Roy = x(13.50) + (20)(1.80)
Since they collected the same amount of money:
14x + (20)(1.50) = 13.50x + (20)(1.80)
Combine like terms:
14x - 13.50x = (20)(1.80) - (20)(1.50)
0.50x = 36 - 30
0.50x = 6
x = 6/0.50
x= 12
Ethan sold 12 watches. And also Roy.
Andddd...We're done! :D
----------------------------------------------------------------------------------------------------------
[<Ending>] <3
Hope this helps and if it's wrong, you can't sue me! :D
Bye! Hope this works for you :)
Have a nice day! - Avery <3
complete the steps to add the equations from part CNE this will make one side of the Pythagorean theorem.
The equation that can be used for finding the lengths in the Pythagoras theorem include:
b² = c² - a²
a² = c² - b²
c² = a² + b²
What is Pythagoras theorem?It should be noted that a Pythagoras theorem is simply the theorem that's used in finding the missing length of a right angled triangle.
In this case, the equation that can be used to find the sides in a Pythagoras theorem has been given.
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8. The sum of a number and 11 less than twice the number is 13. Translate into a variable expression and find the number.
The algebraic expression is:
x + (2x - 11) = 13
And the solution is x = 8.
How to translate it into an expression?
Let's say that the number is defined by the variable x, then we can write the algebraic expression:
x + (2x - 11) = 13
Now we can solve this expression for x:
x + 2x - 11 = 13
3x = 13 + 11 = 24
x = 24/3 = 8
x = 8
The solution is x equal to 8.
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Drew conducted a survey of a simple random sample of high school seniors about
their plans after graduation. 65% responded: "Attend a four-year university." A week
later, Jane also conducted a survey of a simple random sample of high school
seniors about their plans after graduation. 68% responded: "Attend a four-year
university.
What could explain the difference in their results?
A. Samples vary from one another even if each sample is selected in a proper and random manner.
B. The surveys were conducted at different times of day.
C. The researchers were of different genders.
D. High school seniors change their minds often..
Answer:
b
Step-by-step explanation:
PLEASE HELP ME!!!!!!!!!
Answer:
(a) (5, -3)
Step-by-step explanation:
The "substitution method" for solving a system of equations requires that you write an expression that can be substituted for a variable in one or more of the other equations in the system.
Expression to substituteThe given equations are ...
y = x -82x +3y = 1We notice the first equation gives an expression for y. This is exactly what we want to substitute for y in the second equation.
SubstitutionWhen the expression (x-8) is substituted for y in the second equation, you get ...
2x +3(x -8) = 1
This simplifies to ...
5x -24 = 1
SolutionThis 2-step equation can now be solved in the usual way:
5x = 25 . . . . . . add 24 to isolate the variable term
x = 25/5 = 5 . . . . . divide by the coefficient of x
Note that we now know what the correct answer choice is.
Using the expression for y, we find ...
y = x -8 = 5 -8 = -3
The solution is (x, y) = (5, -3).
__
The attached graph confirms this solution.
A rectangular piece of paper is 44 cm long and 20 cm wide. A cylinder is forms by rolling the paper along its length. Find its volume
ASAP ⠀⠀⠀⠀⠀⠀⠀
Answer:
3081.24 cm³ (nearest hundredth)
Step-by-step explanation:
Formulas
[tex]\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}[/tex]
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
If a rectangular piece of paper is rolled along its length to form a cylinder:
circumference = 44 cmheight = 20 cmTo calculate the volume of the formed cylinder, determine the radius by using the circumference formula:
[tex]\implies \sf 2 \pi r = 44[/tex]
[tex]\implies \sf r = \dfrac{44}{2 \pi}[/tex]
[tex]\implies \sf r =\dfrac{22}{\pi}[/tex]
Substitute the round radius into the formula for Volume and solve for V:
[tex]\implies \sf V=\pi \left(\dfrac{22}{\pi}\right)^2(20)[/tex]
[tex]\implies \sf V=\pi \left(\dfrac{484}{\pi^2}\right)(20)[/tex]
[tex]\implies \sf V=\left(\dfrac{484}{\pi}\right)(20)[/tex]
[tex]\implies \sf V=\dfrac{9680}{\pi}[/tex]
[tex]\implies \sf V=3081.239698...cm^3[/tex]
Therefore, the volume of the cylinder is 3081.24 cm³ (nearest hundredth).
What is the value of:
Step-by-step explanation:
[tex] \log(x) = - 1[/tex]
[tex] \log(y) = 6[/tex]
[tex] \log(z) = 2[/tex]
[tex] \: [/tex]
[tex] = \log( \frac{ {x}^{3}y }{ {z}^{2} } )[/tex]
[tex] = \log( {x}^{3} \times y \div {z}^{2} )[/tex]
[tex] = \log( {x}^{3} ) + \log(y) - \log( {z}^{2} )[/tex]
[tex] = 3 \log(x) + \log(y) - 2 \log(z)[/tex]
[tex] = 3.( - 1) + 6 - 2[/tex]
[tex] = - 3 + 6 - 2[/tex]
[tex] = 1[/tex]
Jessica has half of her investments in stock paying a 7% dividend and the other half in a stock paying 13% interest. If her total annual interest is $780, how much does she have invested?
Answer:
$7800
Step-by-step explanation:
The total interest earned can be found by summing the earnings from each of the investments.
SetupLet x represent the total amount invested. Then Jessica's earnings are ...
(x/2)(0.07) +(x/2)(0.13) = 780
SolutionSimplifying the equation gives ...
(x/2)(0.07 +0.13) = 780
0.10x = 780
x = 7800 . . . . . . . . divide by 0.10
Jessica has $7800 invested.
Kim is running in a marathon to raise money for a charity. She will run 26 kilometres. Her boss says she will double the total amount she collects from her colleagues. How much will her boss have to give Kim?
Her boss would give Kim a total of $2x
How to determine the total amount?The given parameters are:
Distance = 26 km
Assume that the amount raised during the marathon is
Amount = x
From the question, we have:
Boss = Double the amount
This means that:
Boss = 2 * Amount
Substitute Amount = x
Boss = 2x
Hence, her boss would give Kim a total of $2x
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Help solve please
H ( - 1) = 6 - x
Evaluating the function in x = -1, we get:
H(-1) = 7
How to evaluate a function?
When we have a function:
y = f(x)
Evaluating the function in a value, like x = a gives:
y = f(a).
This means that we need to replace all the "x" in the equation by the number "a".
In this case:
H(x) = 6 - x
And we want to get:
H(-1)
So we need to replace the x by -1.
H(-1) = 6 - (-1) = 7
H(-1) = 7
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I have data on lower class, middle class and upper class. What is a mathematical process that would provide a simple numerical summary value for the income levels in
each group.
Answer:
You can find the mean, by adding all the terms in each data set and dividing by the number of terms. For example, if there were four data points, you would add them all up and divide by four.
hope this helps!
Solve ABC. Round decimal answers to the nearest tenth.
The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The given triangle can be solved as shown below.
What is Sine rule?The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ B}{\beta} =\dfrac{Sin\ C}{\gamma}[/tex]
where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,
Sin B is the angle and β is the length of the side of the triangle opposite to angle B,
Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.
For the given triangle, using the sine rule the ratio of the angle and the sides of the triangle can be written as,
[tex]\dfrac{Sin\ A}{18} =\dfrac{Sin\ B}{11} =\dfrac{Sin\ C}{c}\\\\\dfrac{Sin\ 72^o}{18} =\dfrac{Sin\ y^o}{11} =\dfrac{Sin\ x^o}{c}[/tex]
Taking the first two ratios,
[tex]\dfrac{Sin\ 72^o}{18} =\dfrac{Sin\ y^o}{11}\\\\y = 35.54^o[/tex]
The sum of all the angles of a triangle is 180°.
72° + 35.54° + x° = 180°
x = 72.46°
Now, using the sine ratio,
[tex]\dfrac{Sin\ 72^o}{18} =\dfrac{Sin\ 72.46^o}{c}\\\\c = 18.046[/tex]
Hence, the given triangle is solved.
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Solve the system using elimination. ''x-3y=9 and -x+3y=-9
Answer:
Infinitely many solutions.
Step-by-step explanation:
Let's solve your system by elimination.
x−3y=9;−x+3y=−9
x−3y=9
−x+3y=−9
Add these equations to eliminate x:
0=0
Answer:
Infinitely many solutions.
x=y^2 is x a function of y
It is false that x is a function of y
How to determine the true statement?The equation is given as:
x = y^2
Set y = 2
x = (2)^2
x = 4
Set y = -2
x = (-2)^2
x = 4
Different values of y give the same x value.
This means that x is not a function of y
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Perform the indicated operation. Be sure the answer is reduced
. a+b/a^(2) b + a-b/ab^2
Answer:
Step-by-step explanation:
[tex]\frac{a+b}{a^2b} +\frac{a-b}{ab^2} \\=\frac{b(a+b)+a(a-b)}{a^2b^2} \\=\frac{ab+b^2+a^2-ab}{a^2b^2} \\=\frac{b^2+a^2}{a^2b^2} \\or\\=\frac{1}{a^2} +\frac{1}{b^2}[/tex]
Sonia works at a bakery. The function f(x) represents the amount of money Sonia earns per loaf, where x is the number of loaves she makes. The function g(x) represents the number of bread loaves Sonia bakes per hour, where x is the number of hours she works. Show all work to find f(g(x)), and explain what f(g(x)) represents.
f(x) = 9x2 + 1
g of x equals the square root of the quantity 2 x cubed
A function assigns the value. The function f(g(x)) represents the amount that Sonia will earn per hour by baking bread.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given f(x)=9x²+1 and g(x)=√(2x³). Therefore, the value of f(g(x)) will be,
[tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex]
= 9(2x³) + 1
= 18x³ + 1
The function f(g(x)) represents the amount that Sonia will earn per hour by baking bread.
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what is x(3x+2) expanded
Answer:
[tex]3x^{2} +2x[/tex]
Step-by-step explanation:
Using the rainbow expansion method:
[tex]x(3x+2)=3x*x+x*2\\ = 3x^{2} +2x[/tex]
Answer:
3x² + 2x
Step-by-step explanation:
x (3x + 2)
= x*3x + x*2
= 3x² + 2x
Problem
Let [tex]\alpha[/tex] and [tex]\beta[/tex] be the solutions of the quadratic equation [tex]2x^2-6x-7=0[/tex]. Find the value of [tex]\frac{\alpha^3}{\beta}+\frac{\beta^3}{\alpha}[/tex].
Answer:
[tex]-\dfrac{463}{7}[/tex]
Explanation:
Given equation: 2x² - 6x - 7 = 0
In quadratic equation: ax² + bx + c
[tex]Sum \ of \ roots : \alpha + \beta = \dfrac{-b}{a}[/tex]
[tex]product \ of \ roots : \alpha \beta = \dfrac{c}{a}[/tex]
So, here given:
[tex]Sum : \alpha + \beta = \dfrac{-(-6)}{2} = 3[/tex]
[tex]Product : \alpha \beta = \dfrac{-7}{2} = - 3.5[/tex]
For finding value:
[tex]\dfrac{\alpha^3}{\beta } + \dfrac{\beta^3 }{\alpha }[/tex]
join fractions
[tex]\dfrac{\alpha^4+ \beta^4}{\alpha \beta }[/tex]
factor out
[tex]\dfrac{(\alpha^2 + \beta ^2)^2 -2\alpha ^2 \beta ^2 }{\alpha \beta }[/tex]
when factored more
[tex]\dfrac{((\alpha + \beta)^2 -2\alpha \beta )^2 -2(\alpha \beta)^2 }{\alpha \beta }[/tex]
insert values inside
[tex]\dfrac{((3)^2 -2(-3.5) )^2 -2(-3.5)^2 }{-3.5 }[/tex]
calculate for value
[tex]-\dfrac{463}{7}[/tex]
What amount of money must Kurt Blixen invest at 4.75% to have it earn $10,000 in 90 days?
Answer:
He have to invest $527.777778 .
Step-by-step explanation:
X : 4.75% = $10,000 : 90
fill the blank
7,504,12_ is divisible by 4
Answer:
4
Step-by-step explanation:
When we substitute the blank for 4 and divide by 4, 7,504,124/4 is 1,876,031 :)
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Which expression is equivalent to –2(5x – 0.75)? 10x – 0.75 10x 0.75 –10x – 1.5 –10x 1.5
Answer: -10x+1.5
Step-by-step explanation:
[tex]-2(5x-0.75)=-10x+1.5[/tex]
what is = x
help please
Answer:
about x=38.1
Step-by-step explanation:
9x38.1=342.9