Answer:
The answer is "[tex]\bold{i=0.05311 \ \ and \ \ x= \$ 2934.4670}[/tex]"
Step-by-step explanation:
2-year interest is:
[tex]\to (x)i + x(1 + i)i=320.......(i)[/tex]
The price of the discount is :
[tex]\to x(\frac{i}{1+i})=148......(ii)[/tex]
by mixing (ii) in (i), we get:
[tex]\to 148(1+i)+148(1+i)^2=320 \\\\\to (i+1)(i+2)= \frac{320}{148} \\\\\to i = 0.05311 \\[/tex]
[tex]\to[/tex] [tex]x= 148(\frac{i+1}{i}) \\\\[/tex]
[tex]= 148(0.054311)+ \frac{1}{(0.005311)}\\\\ =$2934.4670[/tex]
The Interest rate of annual impact:
i=0.05311
x=$ 2934.4670
N general, how do you find the theoretical and experimental probabilities of a favorable outcome if there are n equally likely outcomes and p of them are favorable?
Answer:
Binomial Distribution
Step-by-step explanation:
Unlike the normal or Gaussian probability distribution, the binomial distribution gives a curve representing the coefficient of the outcomes of every item in a sample or population.
the formula is ;
mean ( υ ) = n x p
where p is the probability and n is the population.
The probability density function which generates the probability curve;
Binomial Distribution function= f( k, n, p ) = [tex]\frac{n!}{k!(n-k)}[/tex] [tex]P^{k}[/tex][tex](1- P)^{(n -k)}[/tex]
find the image of (1,2) after a reflection about y=-1 followed by a reflection over y=1
Answer:
(1, 6).
Step-by-step explanation:
The reflection of the x coordinate of (1, 2) creates a point with y -coordinate
-1 - 3 = -4 while the x-coordinate remains 1.
The point (1, -4) is now reflected about y = 1, so -4 translates to 1 + 5 = 6. and x stays at 1.
Answer is (1, 6).
A coffee house blended 18 pounds of espresso flavored coffee beans with 17 pounds of vanilla flavored coffee beans. The 35 pound mixture cost $306.50. A second mixture included 19 pounds of espresso flavored coffee beans and 15 pounds of vanilla flavored coffee beans. The 34 pound mixture cost $298.50. Find the cost per pound of the espresso and vanilla flavored coffee beans.
Answer:
the price of the vanilla flavored coffee per pound is $8.50
the price of the espresso flavored coffee per pound is $9.00
Step-by-step explanation:
Let's give letters to the unknowns, so we can generate equations easily:
cost of espresso coffee beans per pound: "E"
cost of vanilla flavored coffee beans per pound : "V"
Now, the first statement:
18 pounds of E plus 17 pounds of V cost $306.50, can be written as:
18 E + 17 V = 306.5
The second statement:
19 pounds of E plus 15 pounds of V cost $298.50, can be written as:
19 E + 15 V = 298.5
Now, in order to solve this system of linear equations we can use substitution for example:
E = (306.5 -17 V)/18
and use this expression to substitute for E in the second equation:
19 (306.5 - 17 V)/ 18 + 15 V = 298.5
multiplying by 18 on both sides to eliminate denominators, we get:
19 (306.5 - 17 V) + 270 V = 5373
5823.5 - 323 V +270 V = 5373
5823.5 - 53 V = 5373
5823.5 - 5373 = 53 V
450.5 = 53 V
V = 8.5
Therefore the price of the vanilla flavored coffee per pound is $8.50
Now we use this found value in the substitution equation:
E = (306.5 -17 V)/18
E = (306.5 - 17 (8.5))/18
E = 9
Therefore the price of the espresso flavored coffee per pound is $9.00
Which square root represents 6.92?
Answer:
Step-by-step explanation:
Answer:
2.6305
Step-by-step explanation:
A ball is dropped from a building at the same time a balloon rises from the ground. The heights, in feet, of the ball and balloon above the ground after x seconds are modeled by the functions below. Ball: f(x)=24−16x2Balloon: g(x)=4x After how many seconds are the ball and the balloon at the same height? Use a graphing calculator and round to the nearest hundredth. A. 1.36 B. 4.42 C. 1.11 D. 5.42
Answer:
C. 1.11
Step-by-step explanation:
Ball: f(x) = 24 − 16x^2
Balloon: g(x) = 4x
4x = 24 - 16x^2
16x^2 + 4x - 24 = 0
4x^2 + x - 6 = 0
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-1 \pm \sqrt{1^2 - 4(4)(-6)}}{2(4)} [/tex]
[tex] x = \dfrac{-1 \pm \sqrt{1 + 96}}{8} [/tex]
[tex] x = \dfrac{-1 \pm \sqrt{97}}{8} [/tex]
[tex] x = \dfrac{-1 + \sqrt{97}}{8} [/tex] or [tex] x = \dfrac{-1 - \sqrt{97}}{8} [/tex]
We discard the negative solution.
[tex] x = 1.11 [/tex]
Answer: C. 1.11
if a motercycle is moving at a constant speed down the highway of 40 km/hr, how long would it the motorcycle to travel 10 km
Answer:
15 minutes
Step-by-step explanation:
First, the motorcycle goes at a speed of 40 km/hr.
The question asks for how long it would take to travel 10 km.
Well, there are 60 minutes in an hour, since we will be translating into minutes.
Also, 10 km is 1/4 of 40 km, so it would make sense that the time length would be 1/4 of an hour as well.
1/4 of 60 minutes is 15 minutes. So it takes 15 minutes for the motorcycle to travel 10 km.
Now, if all this wordy stuff is too much to comprehend, you can also solve using proportional relationships.
[tex]\frac{40km}{60min}=\frac{10km}{xmin}[/tex]
Now cross multiply:
[tex]40km*xmin=10km*60min\\40x=600[/tex]
Divide both sides by 40:
[tex]\frac{40x}{40}=\frac{600}{40}\\x=15[/tex]
Again, this shows that it wouls take 15 minutes for the motorcycle to travel 10 km.
Convert 12 km/hr into m/min
Answer:
200 meters per minute
Step-by-step explanation:
12/60 since hr into minutes
0.2 x 1000 since km and meters
Explain why the sum or product of rational numbers is rational; why the sum of a rational number and an irrational number is irrational; and why the product of a nonzero rational number and an irrational number is irrational. You can do this by providing examples of each
Answer:
Rational numbers are fractional numbers, whose numerator and denominator are integers and the denominator is ever zero.
Step-by-step explanation:
The sum of rational numbers gives a rational number;
[tex]\frac{1}{3}[/tex] + [tex]\frac{1}{3}[/tex] = [tex]\frac{2}{3}[/tex] , because the evaluation of the denominator always results to a non-zero integer.
The product of [tex]\frac{1}{3}[/tex] x [tex]\frac{1}{3}[/tex] = [tex]\frac{1}{9}[/tex], which multiply both numerator and denominator to give integer numbers.
The sum and product of rational and irrational numbers are always irrational numbers, for instance,
[tex]\frac{1}{3}[/tex] x 7 = 2.3 , which is a number which decimal points that can only be represented by the product irrational number and rational number , where 7 is an irrational number.
[tex]\frac{1}{3}[/tex] + 7 = 7[tex]\frac{1}{3}[/tex] , which is a whole number and fractional number combined.
Simplify the equation step by step listing the property or operations used -5/6*(-5/8)*6/5
Answer:
5/8
Decimal Form: 0.625
Step-by-step explanation:
Cancel 6.
−5×-5/8*1/5
cancel 5
- -5/8
Move the negative sign to the left.
- (-5/8)
remove parentheses
answer is 5/8
hope i helped
-lvr
I'm taking a homeschooling course and my parents put me in a couple grades before my level, so its a little difficult for me sometimes. So if someone could explain this it would be super helpful. ^_^ Select the correct scientific notation form of this numeral using only 2 significant figures. 8,421,032.9266
Answer: 8.4 * 10^6
Step-by-step explanation:
Hope this helps^^
PLEASE HELP The domain is {x∈R| x≠1}, and the range is {y∈R| y≠0}. The domain is all real numbers, and the range is {y∈R| y≠0}. The domain is {y∈R| y≠1}, and the range is {x∈R| x≠0}. The domain is {x∈R| x≠1}, and the range is all real numbers.
Answer:
The domain is x cannot equal 1 and range cannot equal 0. The first option you have is correct
Step-by-step explanation:
108/40 in its simplest form
Answer:
27/10
Step-by-step explanation:
A calculator can tell you the fraction value is 2.7. As the ratio of integers, this is ...
108/40 = 27/10
An open-top box is to be made from a 42-inch by 48-inch piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side. What should be the length of the side x of the square cut out of each corner to get a box with the maximum volume
Answer:
x = 7.45 inch for the maximum volume.
The area of the square = x² = 7.45² = 55.5025 inch²
Step-by-step explanation:
From the given information:
An open-top box is to be made from a 42-inch by 48-inch piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side.
The objective is to determine the length of the side x of the square cut out of each corner to get a box with the maximum volume
The volume of the box = l×b×h
The volume of the box = [tex](42 - 2x) \times (48-2x) \times (x)[/tex]
The volume of the box = [tex](2016 - 84x - 96x +4x^2)x[/tex]
The volume of the box = [tex](2016 -180x+4x^2)x[/tex]
The volume of the box = [tex](2016x -180x^2+4x^3)[/tex]
The volume of the box = [tex]4x^3 - 180x^2 +2016x[/tex]
For the maximum volume V' = 0
V' = [tex]12x^2 - 360x + 2016[/tex]
Using the quadratic formula; we have:
[tex]= \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
where;
a = 12 , b = -360 c = 2016
[tex]= \dfrac{-(-360) \pm \sqrt{(-360)^2 -4(12)(2016)}}{2(12)}[/tex]
[tex]= \dfrac{360 \pm \sqrt{129600 -96768}}{24}[/tex]
[tex]= \dfrac{360 \pm \sqrt{32832}}{24}[/tex]
[tex]= \dfrac{360 \pm 181.196}{24}[/tex]
[tex]= \dfrac{360 + 181.196}{24} \ \ \ OR \ \ \ \dfrac{360 - 181.196}{24}[/tex]
[tex]= \dfrac{541.196}{24} \ \ \ OR \ \ \ \dfrac{178.804}{24}[/tex]
[tex]= 22.55 \ \ \ OR \ \ \ 7.45[/tex]
For the maximum value , we check the points in the second derivative term
V'' = 24x - 360
V'' ( 22.55) = 24(22.55) - 360
V'' ( 22.55) = 541.2 - 360
V'' ( 22.55) = 181.2 (minimum)
V'' ( 7.45) = 24(7.45) - 360
V'' ( 7.45) = 178.8 - 360
V'' ( 7.45) = -181.2 < 0 (maximum)
Therefore, x = 7.45 inch for the maximum volume.
The area of the square = x² = 7.45² = 55.5025 inch²
The maximum volume of a box is the highest volume the box can take.
The side length that ensures maximum volume is 22.55 inches or 7.45 inches.
The dimension of the plastic is:
[tex]\mathbf{Length = 42}[/tex]
[tex]\mathbf{Width = 48}[/tex]
Assume the side length cut-out is x
So, the dimension of the box is:
[tex]\mathbf{Length = 42 - 2x}[/tex]
[tex]\mathbf{Width = 48 - 2x}[/tex]
[tex]\mathbf{Height = x}[/tex]
So, the volume of the box is:
[tex]\mathbf{Volume = Length \times Width \times Height}[/tex]
This gives;
[tex]\mathbf{Volume = (42 - 2x) \times (48 - 2x) \times x}[/tex]
Expand
[tex]\mathbf{Volume = (42 - 2x) \times (48x - 2x^2)}[/tex]
Expand
[tex]\mathbf{Volume = 2016x - 96x^2 - 84x^2 + 4x^3}[/tex]
Differentiate
[tex]\mathbf{V' = 2016 - 192x - 168x + 12x^2}[/tex]
[tex]\mathbf{V' = 2016 -360x + 12x^2}[/tex]
Rewrite as:
[tex]\mathbf{V' = 12x^2 -360x + 2016}[/tex]
Set to 0
[tex]\mathbf{12x^2 -360x + 2016 = 0}[/tex]
Divide through by 12
[tex]\mathbf{x^2 -30x + 168 = 0}[/tex]
Using a calculator, the values of x are:
[tex]\mathbf{x = 22.55\ or\ x = 7.45}[/tex] ------ approximated to 2 decimal places
Hence, the side length that ensures maximum volume is 22.55 inches or 7.45 inches.
Read more about maximizing volumes at:
https://brainly.com/question/11599887
Given: AE ≅ CE ; DE ≅ BE Prove: ABCD is a parallelogram. Parallelogram A B C D is shown. Diagonals are drawn from point A to point C and from point D to point B and intersect at point E. Line segments A E and E C are congruent. Line segments D E and E B are congruent. We have that AB || DC. By a similar argument used to prove that △AEB ≅ △CED, we can show that △ ≅ △CEB by. So, ∠CAD ≅ ∠ by CPCTC. Therefore, AD || BC by the converse of the theorem. Since both pair of opposite sides are parallel, quadrilateral ABCD is a parallelogram.
Answer:
1.AED
2.SAS
3.ACB
4.Aternate interior angles
Step-by-step explanation:
Answer:
edg just did it
Step-by-step explanation:
find the perimeter of the square of the length 8cm
Answer:
[tex] \boxed{ \boxed{ \bold{32 \: cm}}}[/tex]Step-by-step explanation:
Length ( L ) = 8 cm
Perimeter of square = 4 L
( where L is the side of the square )
Plug the value of length
⇒[tex] \sf{4 \times 8}[/tex]
Multiply the numbers
⇒[tex] \sf{32 }[/tex] cm
Hope I helped!
Best regards!
Answer:
[tex]\huge \boxed{\mathrm{32 \ cm}}[/tex]
Step-by-step explanation:
The formula to calculate the perimeter of a square is given as:
[tex]\sf Perimeter = 4 \times side \ length[/tex]
The side length of the square is 8 centimeters.
[tex]P=4 \times 8[/tex]
Solve for the perimeter.
[tex]P=32[/tex]
The perimeter of the square is 32 centimeters.
what property is this 3[5(4)] + 3 = [3(5)]4 + 3
Answer:
Associative Property of Mulitplication
Step-by-step explanation:
The associative property of multiplication states that if all the operations are multiplication, then one can group and add them in whatever order they prefer.
Hope this helps! Tell me if I'm wrong!
determine how many solutions each equation has. If one solution, state the value of x. +6+8=2−+14
help me and ill give you brainliest answer ;))) deal? (/ω＼*)……… (/ω•＼*)
Step-by-step explanation:
....
.........
.
graph 7/4 on the number line
Answer:
Step-by-step explanation:
First you have to change your fraction:
Change 7/4 into a mixed number
7/4 = 1 3/4
Then you 'guestamate' about 3/4 of the distance between 1 and 2 and mark your point. Like this:
Hope this helps
The number is expressed as the equation A = 7/4 or A = 1.75
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 7/4 be equation (1)
On simplifying the equation , we get
A = 1.75
Now , the number 1.75 lies on the positive side of the number line and is between 1 and 2
So , the number 1.75 lies between 1 < 1.75 < 2
Hence , the number is A = 1.75
To learn more about equations click :
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help me please? :( (;´༎ຶД༎ຶ`)(;´༎ຶД༎ຶ`)(;´༎ຶД༎ຶ`)
Answer:
a) 22:53
b)213 min
Step-by-step explanation:
c) 10 17 + 4 = 14 17
she has 2 minutes to spare
Answer:
she has 2 minutes to spare
Step-by-step explanation:
nancy was saving to buy a brand new iphone. she had already saved $78.00. the cost of the phone that she wanted was $899 plus 8.50% plus tax. every day that she works at the car wash she makes. $42. approximately how many more days does she need to work at the car wash to have enough money for her iphone?
Answer:
21.37 days.
Step-by-step explanation:
Step 1
Find the total amount Nancy is paying for her iPhone
Cost of the phone = $899
Tax = 8.50%
Amount paid for tax = 8.5% × 899
= 8.5/100 × 899
= $76.415
Total amount Nancy is paying = Tax + Cost of the phone
= $76.415 + $899
= $975.415
Step 2
We are told in the question that Nancy had already saved $78
Hence, Totally amount left for Nancy to buy her iPhone = $975.415 - $78
= $897.415
Step 3
Nancy works at a car wash and earns $42 every day.
The number of days left for her to work in the car wash in order to buy her phone is calculated as:
$42 = 1 day
$897.415 = x days
Cross Multiply
= $42 × x = $897.415 × 1 day
x = $897.415/$42
x = 21.36702381 days.
Approximately, x = 21.37 days
Therefore, Nancy has to work for 21.37 days at the car wash to have enough money for her iphone
There are 8 tennis balls in a bag. Five of
the balls are yellow and the other 3 are
green What's the probability of pulling out
a green ball without looking? Write your
answer as a decimal.
Answer:
3/8 or a a decimal 0.375
simplify 1/3 - 1/2 + 2/5
Answer:
[tex] \frac{1}{3} - \frac{1}{2} + \frac{2}{5} [/tex]
[tex] = \frac{10 - 15 + 2 \times 6}{30} [/tex]
[tex] = \frac{10 - 15 + 12}{30} [/tex]
[tex] = \frac{ - 5 + 12}{30} [/tex]
[tex] = \frac{7}{30} [/tex]
Answer:
[tex] \frac{1}{3} - \frac{1}{2} + \frac{2}{5} [/tex]
[tex] = \frac{10 - 15 + 2×6}{30} [/tex]
[tex] = \frac{10 - 15 + 12}{30} [/tex]
[tex] \frac{-5 +12}{30} [/tex]
= 7 /30
The solutions to the equation 2x^2+x-1=2 are x=-3/2 or x= blank
Answer:
Step-by-step explanation:
hello :
2x²+x-1=2 means : 2x²+x-3=0
a=2 b= 1 c= -3
the solutios are : x1 and x2 when the product is : x1×x2 = c/a
let x1 = -3/2 you have : (-3/2)×x2 = -3/2 so x2 = (-3/2)/(-3/2) = 1
The solutions to the equation 2x²+x-1=2 are x=-3/2 or x= 1
A park is a rectangle a fence runs along all four sides the area of the park is 5,400 yards squared the length is 1.5 times longer then the width what is the perimeter of the park
Answer:
Perimeter of the park = 300 yards
Step-by-step explanation:
Area of a rectangle= length * width
Area of the rectangular park = 5,400 yards squared
Let
Width= x
Length= 1.5 * x = 1.5 x
Area of a rectangle= length * width
5,400= 1.5x * x
5400= 1.5x^2
x^2= 5400 / 1.5
x^2 = 3600
Take the Square root of both sides
√x^2 = √3600
x=60
Therefore,
Width = x = 60 yards
Length = 1.5x
=1.5(60)
=90 yards
Perimeter of the rectangular park = 2(length + width)
=2(90+60)
=2(150)
= 300 yards
PLEASE HELP ME WITH THE QUESTION BELOW
Answer:
C: (-5, 1)
Step-by-step explanation:
If you put the equation in a graphing calculator and examine all the points, C is the only one not on the line.
Un grupo de amigos quiere realizar una actividad de recaudación de fondos, para ello han decidido vender pizzas. La primera pizzería vende pizzas de 40 cm de diámetro a S/ 40 y otra vende pizzas de 25 cm de diámetro a S/ 25. ¿Qué pizza será recomendable que los amigos adquieran para lograr mejores ganancias?
Answer:
Los Amigos deberían comprar pizzas vendidas por la primera pizzería que cuestan S / 0.032 por cm² para obtener más ganancias.
Step-by-step explanation:
Los parámetros dados son;
El diámetro de las pizzas vendidas por la primera pizzería = 40 cm
El precio de las pizzas vendidas por la primera pizzería = S / 40
El diámetro de las pizzas vendidas por la segunda pizzería = 25 cm
El precio de las pizzas vendidas por la segunda pizzería = S / 25
El área de las pizzas vendidas por la pizzería = π × D² / 4
El área de las pizzas vendidas por la primera pizzería = π × 40² / 4≈1256.64 cm²
El costo por unidad de superficie de las pizzas vendidas por la primera pizzería = S / 40 / (1256.64 cm²) ≈ S /0.032/cm²
El área de las pizzas vendidas por la segunda pizzería = π × 25² / 4≈490.87 cm²
El costo por unidad de superficie de las pizzas vendidas por la primera pizzería = S / 25 / (490.87 cm²) ≈ S /0.051/cm²
Las pizzas vendidas por la primera pizzería que cuestan S /0.032/cm² s más baratas y producirán mejores ganancias que las pizzas vendidas por la segunda pizzería que cuestan S /0.051/cm²
Por lo tanto, los amigos deben comprar pizzas vendidas por la primera pizzería que cuestan S /0.032 / cm² para obtener más ganancias.
Solve for x.
Enter the solutions from least to greatest.
3x^2 +4= 436
lesser x =
greater x =
Answer:
lesser x = -12
greater x = 12
Step-by-step explanation:
3x^2 +4= 436
3x^2 = 432
x^2 = 144
lesser x = -12
greater x = 12
root 3 + root 2 /root 3- root 2 = a+b root 6
Answer:
5 + 2[tex]\sqrt{6}[/tex]
Step-by-step explanation:
Given
[tex]\frac{\sqrt{3}+\sqrt{2} }{\sqrt{3}-\sqrt{2} }[/tex]
Multiply numerator/ denominator by the conjugate of the denominator
The conjugate of [tex]\sqrt{3}[/tex] - [tex]\sqrt{2}[/tex] is [tex]\sqrt{3}[/tex] + [tex]\sqrt{2}[/tex]
= [tex]\frac{(\sqrt{3}+\sqrt{2})(\sqrt{3}+\sqrt{2}) }{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2}) }[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{3+\sqrt{6} +\sqrt{6}+2 }{3-2}[/tex]
= [tex]\frac{5+2\sqrt{6} }{1}[/tex]
= 5 + 2[tex]\sqrt{6}[/tex] → with a = 5 and b = 2
please help me on this
Answer:
A: (x-3, y+4)
Step-by-step explanation:
A coordinate plane is basically just a number line with two axes.
If we move a numbet right 3, to return it back we’d need to bring it left 3.
If we move a number down 4, we need to bring it up 4 to bring it back to it’s original position.
So to get it back, we need to add the opposite.
(x + 3), 3’s opposite is -3
(y - 4), -4’s opposite is 4.
Hope this helped!