Answer:
[tex]\frac{214}{99}[/tex]
Step-by-step explanation:
We require to create 2 equations with the repeating digits after the decimal point. Then by subtracting them we eliminate the repeating part.
let x = 2.1616.... → (1)) ← multiply both sides by 100
100x = 216.1616..... → (2)
Subtract (1) from (2)
99x = 214 ( divide both sides by 99 )
x = [tex]\frac{214}{99}[/tex]
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
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:
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.
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 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:
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
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Which square root represents 6.92?
Answer:
Step-by-step explanation:
Answer:
2.6305
Step-by-step explanation:
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]
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.
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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
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
If you are on a ship at sea navigating to a point that is 300 miles north and 400 miles west, find the distance from tour ship to that point. Show your work.
Answer:
[tex]\huge \boxed{\mathrm{500 \ miles}}[/tex]
Step-by-step explanation:
A right triangle is formed.
300 miles and 400 miles are the legs of the triangle.
We can apply Pythagorean theorem.
[tex]c=\sqrt{300^2 +400^2 }[/tex]
[tex]c=\sqrt{90000 +160000}[/tex]
[tex]c=\sqrt{250000}[/tex]
[tex]c=500[/tex]
Write the following solution in interval notation:
Z < 20
Answer:
(-infinity, 20)
Step-by-step explanation:
the lower bound is negative infinity because no lower bound was given. The higher bound is 20, and it has a parentathesis because it is less than.
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
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
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
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^^
I need help... this is from a textbook Jamal and Moshe began a business with a capital of S7500. If Jamal furnished half as much capital as Moshe, how much did each furnish?
Answer:
Moshe made $1875 and Jamal made $5625
Step-by-step explanation:
divide it in half, then divde Moshe's half in half because he only made half as much,
hope this helps and remember to mark brainliest
Moshe furnishes $5000 and Jamal furnishes $2500 of the capital. Computed by solving the linear equation x + x/2 = 7500, where x is the capital furnished by Moshe.
What are linear equations?Linear equations are an equation involving constants and variables, where variables are raised to a power of not greater than 1.
How do we solve the given question?We are informed that Jamal and Moshe starts a business with a capital of $7500. Also, we are informed that Jamal furnishes half as much capital as Moshe does.
We will try to make a linear equation and solve for it to find the capital furnished by each of them.
Let the capital furnished by Moshe be $x.
Jamal furnishes half as much capital as Moshe does.
∴ Capital furnished by Jamal = 1/2 of Moshe's capital = 1/2 of $x.
∴ Jamal's capital + Moshe's capital = Total capital furnished
We know the total capital is $7500.
∴ Our linear equation is: 1/2 of $x + $x = $7500.
Now we solve this equation in the following ways:
or, (1/2)*x + x = 7500
or, x/2 + x = 7500
or, (x + 2x)/2 = 7500
or, 3x/2 = 7500
or, x = (7500*2)/3 = 15000/3 = 5000.
∴ x = 5000.
∴ Moshe's share = $x = $5000
Jamal's share = 1/2 of $x = 1/2 of $5000 = $2500.
∴ Moshe furnishes $5000 and Jamal furnishes $2500 of the capital. Computed by solving the linear equation x + x/2 = 7500, where x is the capital furnished by Moshe.
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On a 40‐point test, Steve received an 80%. How many points did he receive on the test?
Answer:
Steve got 32 points
Step-by-step explanation:
Take the total score and multiply by the percentage received
40 * 80%
Change to decimal form
40 * .80
32
Steve got 32 points
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
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.
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
Use the spider tool located on page 1 of this activity to draw a 12-pointed star for the new logo. (Hint:If the spider rotates 360 degrees -- or 720 degrees or 1080 degrees -- she will be facing in the same direction in which she started. When the spider is done drawing, you want her to be facing in the same direction in which she started. She'll be making 12 rotations, all the same size, so each rotation must be some multiple of 360/12 = 30 degrees.)
Please help urgently. Been stuck on this problem for around 45 minutes now. Thanks.
PLEASE HELPPPPP! IT SHOULD BE EASY IF YOU'RE SMART ENOUGH
Answer:
each of the 12 turns is 150°
Step-by-step explanation:
If we number the points of the star 1–12, in order for the star to be symmetrical, each point must connect to two points symmetrically located around the centerline.
That is, point 1 may connect to points {2, 12} or {3, 11} or {4, 10}, or {5, 9} or {6, 8} or {7, 7}. For each of these connections, the angle made at the point of the "star" is, respectively, 150°, 120°, 90°, 60°, 30° or 0°. For these angles, the figure obtained will be ...
150° - dodecagon, a 12-sided figure
120° - hexagon
90° - square
60° - equilateral triangle
30° - 12-pointed star
0° - straight line
The two 12-pointed figures are shown in the attachment.
__
We suspect the star you're interested in is the one with points that are 30°. In order to have that point angle, the spider must make a turn of 180° -30° = 150°.
The spider will make 12 turns of 150°, for a total of 1800°, for a total of 5 full turns of 360°.
Answer:
Move the spide by 100 units and then turn the spider by 150 degrees. Repeat until you complete the star.
Step-by-step explanation:
people above are correct! I'm just making the steps as clear as possible for those who need it :)
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).
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
h²=p²+b² make b the subject of formula
Answer:
done same as before put value and do process like simplify
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.
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.
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