Answer:
X= 6+y/7
Step-by-step explanation:
Sum and Product of Rational and Irrational Numbers
Step-by-step explanation:
4_/12=4_/3*4=4*2_/3=8_/3
5_/3+8_/3=13_/3
The result is irrational number because it cannot be written as the ratio of two integers. and its decimal extention is neither terminating nor repeting.
Find the volume of the shaded solid. Round your answer to 2 decimal places if necessary. Use 3.14 when necessary.
Answer:
Volume of a cuboid = length x width x height
8 x 8 x 32 = 2048
Volume of a cylinder = πr^2h
r = diameter/2 = 8/2 = 4
π(4)^2(32) = π(16)(32) = 1607.68
Volume of the shaded solid:
2048 - 1607.68 = 440.32
The correct answer would be C) 440.32 m^3
Combine the radicals
The combination of radical 5√27 - 17√3 is -2 √3, so option D is correct.
What are radicals?The opposite of an exponent, denoted by the symbol "√" and also known as the root, is a radical. The number before the symbol or radical is regarded as an index number or degree.
Given:
5√27 - 17√3
Simplify the value under roots,
5√(3 × 3 × 3) - 17√3
5 × 3 √3 - 17√3
√3 (15 - 17)
-2 √3
Therefore, the combination of radical 5√27 - 17√3 is -2 √3.
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John started his collection with 35 baseball cards and collects 4 new cards every week. Frank started the same collection with 50 baseball cards and collects 2 new cards every week. How long will it take John to collect more cards than Frank.
Answer: 8 weeks
Step-by-step explanation: It would take John 8 weeks to collect more basketball cards than Frank with 67 cards for John and 66 for Frank.
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The volume of this cylinder is 1,570 cubic inches. What is the radius?
Use ≈ 3.14 and round your answer to the nearest hundredth.
Therefore ,the radius of the given cylinder is 10 inches
What is volume ?A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected.
Here,
The volume of the cylinder is 1570 cubic inches
Volume of the cylinder = 1570 cubic inches
Volume of cylinder = π[tex]r^{2}[/tex]h
Where r is the radius of cylinder
h is the height of cylinder
So,
Volume of the cylinder = 1570 cubic inches
=> 1570 = π[tex]r^{2}[/tex]h
=> 1570 = 3.14*[tex]r^{2}[/tex]*5
=> 1570/3.14 = [tex]r^{2}[/tex]*5
=> 500=[tex]r^{2}[/tex] *5
=> 500/5 =[tex]r^{2}[/tex]
=>100 =[tex]r^{2}[/tex]
=>r=10 inches
Therefore the radius of the given cylinder is 10 inches.
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What is Q(1.5) if ()=cos() f(x)=cos(x) and Q(x) is centered atπ/2? Round your answer to 4 decimals, for example, 0.1234.
Step-by-step explanation:
This is a Taylor series because our center is non-zero.
The goal of Taylor series is to approximate non polynomial functions using Calculus.
So let's be intuitive.
In order to be accurate, we need to match the center value at some center a.
We know that cos(pi/2)=0, so our first constant should be 0.
[tex]q(x) = 0[/tex]
Next, we must be spot on with the linear approximation
at x=pi/2
we know that
[tex] \frac{d}{dx} \cos(x) = - \sin(x) = - \sin( \frac{\pi}{2} ) = - 1[/tex]
We also want to divide this by 1! , which is just one so our constant there is
-1, since we want to use this as an linear approximation and we want to be general, and we have a center to stay in respect to,
our next term is
[tex] 0 - 1(x - \frac{\pi}{2} ) {}^{1} [/tex]
Next, up, we must be similar in concavity.
So we take the second derivative of cosine which is just
[tex] - \cos(x) = - \cos( \frac{\pi}{2} ) = 0[/tex]
Since our constant is 0, we can skip this, even if we divide by 2!
Our fourth term is the third derivative of cosine
which is
[tex] \sin(x) = \sin( \frac{\pi}{2} ) = 1[/tex]
We then divide that by 3!, which becomes
[tex] \frac{1}{6} [/tex]
since we want to use this as an cubic approximation and we want to be general, and we have a center to stay in respect to,
our next term is
[tex] - (x - \frac{\pi}{2} ) {}^{} + \frac{1}{6} (x - \frac{\pi}{2} ) {}^{3} [/tex]
Let do one more term,
we know the 5th term is the fourth derivative of cosine evaluated at x=pi/2, which is just 0 so we can skip it.
The 6th term is the fifth derivative of cosine evaluated at x=pi/2, which is -1, then we divide by 5!, so we get
[tex]q(x) = - (x - \frac{\pi}{2} ) + \frac{1}{6} (x - \frac{\pi}{2} ) {}^{3} - \frac{1}{120} ( x - \frac{\pi}{2} ) {}^{5} [/tex]
Using the approximations, plug in 1.5 for x and we get approximately
0.0707
The half-life of Palladium-100 is 4 days. After 12 days a sample of Palladium-100 has been reduced to a mass of 6 mg. Round your answers to 5 decimal places as needed. What was the initial mass (in mg) of the sample? What is the mass 7 weeks after the start?
Rounded to 5 decimal places, the initial mass of the sample was 48.00000 mg, and the mass 7 weeks after the start was 0.00002 mg.
What is the half-life of a substance?
Half-life is the time required for the amount of something to fall to half its initial value. The converse of half-life is doubling time.
The half-life of a substance is the time it takes for half of the initial mass of the substance to decay.
Since the half-life of Palladium-100 is 4 days, after 4 days, the mass of the sample will be reduced to half of its initial value. After 8 days, it will be reduced to a quarter of its initial value, and after 12 days it will be reduced to an eighth of its initial value.
We are given that after 12 days, the mass of the sample is 6 mg. This means that the initial mass of the sample was 8 * 6 mg = 48 mg.
After 7 weeks (7 * 7 = 49 days), the mass of the sample will be reduced by a factor of
= [tex]8^{(49/4) }[/tex]
= [tex]8^{12.5}[/tex] =
approximately [tex]2.6 * 10^6[/tex]. The mass of the sample after 7 weeks will be approximately [tex]\frac{6 mg }{2.6 * 10^6}[/tex] = approximately [tex]2.3 * 10^{-6}[/tex] mg.
Rounded to 5 decimal places, the initial mass of the sample was 48.00000 mg, and the mass 7 weeks after the start was 0.00002 mg.
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a pizza has a diameter of 20 inches.one slice of the pizza is perfectly cut from the centre at a 360° angle.what is the area of sector of the pizza
Answer: The diameter of a pizza is 20 inches.
Statement 5.109. Letf:X→Ybe a function. Then the functionfis a bijection iff the relation{(y,x)∈Y×X∣(x,y)∈f}is a function.
Let f:X→Ybe a function. Then the function f is a bijection if the relation {(y ,x)∈Y×X∣ (x ,y)∈f} is a function.
Assume that X→Y is a bijective function.
i.e. f:X→Y is one-one and onto function.
so different elements in X have different images in Y
and b ∈ Y there exists a ∈ X such that f(a)=b.
R= {(y ,x)∈Y×X∣(x ,y)∈f} is a relation
we wish to prove R is a function.
R is a relation from Y to X
let Y∈Y by assumption f is bijection function from X to Y
for all y ∈ Y there exists X∈ X such that f(x)=y.
so for every element in Y there is mapping element in X.
if (x ,y) ∈ f then (y ,x) ∈ R
therefore R is a function.
let X1, X2, ∈ X then there exists some y1, y2,∈ y such that
take f ( x1 )= y1 and f( x2)=y2
by assumption R is a function from Y to X that is inverse of f is existing means f is bijection.
for bijective functions only inverse exists.
If f:X→Y is a function. Then the function f is a bijection if the relation
{(y ,x)∈Y×X∣(x, y)∈f} is a function.
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The amount of money he earns is directly proportional to the number of hours he w The graph shows the amount of money, w dollars, he earns in t hours.
Find the constant of proportionality.
Answer: dollars per hour.
How much money does Jonathan earn after working 3 hours?
Answer:
55 I think if I'm wrong sorry
A copy machine makes 44 copies per minute. How long does it take to make 165 copies?
USING YOUR MATH
4. A semi-truck is being loaded with boxes of varying weights. The total weight of boxes loaded is shown below as a function of the number of boxes loaded into the truck.
(a) For each interval below, find the average rate of change. Do not round. Include units with your answers.
5 to 11 boxes:
11 to 20 boxes:
20 to 25 boxes:
(b) Over which interval was the average weight per box the greatest?
5. A hot liquid was placed in a freezer and its temperature was recorded. The data for the first 8 minutes is shown below.
At what average rate is the temperature changing from 2 to 8 minutes? Use proper units.
Average rate of change for interval 5 to 11 boxes is 4.5 , 11 to 20 boxes is 6 and 20 to 25 boxes is 3.2
What is average rate of change?Average rate of change can be defined as slope of function between two fixed values of x. It can also be defined as change in function per unit or we can say as an average.
Average rate of change (from x = a to x=b) = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Given table can we represented as No.of boxes = x
Total weight = y
So, for x = 5 , y = 18
x = 11 , y = 45
x = 20 , y = 99
x = 25 , y = 115
(a) Average rate of change for Intervals
5 to 11 boxes = [tex]\frac{45 - 18}{11-5}=\frac{27}{6} = \frac{9}{2}[/tex]
= 4.5
11 to 20 boxes = [tex]\frac{99-45}{20-11} = \frac{54}{9}[/tex]
= 6
20 to 25 boxes = [tex]\frac{115-99}{25-20}=\frac{16}{5}[/tex]
= 3.2
(b) for interval of 11 to 20 boxes we have greatest average weight per box.
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|v-8| +13=29
help me solve for v
Hello,
I hope you and your family are doing well!
To solve for V, we can start by subtracting 13 from both sides of the equation:
|v-8| = 16
Since the absolute value of a number is always nonnegative, we know that the value inside the absolute value must be either positive or zero. This means that we have two possible cases to consider:
Case 1: v-8 > 0
In this case, we can drop the absolute value symbols and solve the equation:
v-8 = 16
v = 24
Case 2: v-8 = 0
In this case, we can drop the absolute value symbols and solve the equation:
v-8 = 0
v = 8
So the possible values of V are 8 and 24.
-----
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Happy Holidays!
Step-by-step explanation:
|v-8| + 13 = 29
subtract 13 from both sides
|v-8| = 16
form two equations:
v-8 = 16 -(v-8) = 16
v-8 = 16
add 8 to both sides
v = 24
-(v-8) = 16
-v+8 = 16
subtract 8 from both sides
-v = 8
divide both sides by a -1
v = -8
check work:
|v-8| + 13 = 29
|24-8| + 13 = 29
|16| + 13 = 29
29 = 29
|v-8| + 13 = 29
|-8-8| + 13 = 29
|-16| + 13 = 29
|-29| = 29
29 = 29
10. A bag contains marbles: 5 purple, 6 blue, 8 yellow, 1 green. You will draw a
marble, keep it, and then draw another. What is the probability that you will
draw a purple and a green? SHOW YOUR WORK. Make sure to simplify your
answer if using a fraction. If using a percent, round to the nearest hundredth
after you change it to a percent.
Answer:
1st darw
[tex] p(purple)= \frac{5}{20} \\ = \frac{1}{4} [/tex]
[tex]p(green) = \frac{1}{20} [/tex]
2nd draw
[tex]p(purple) = \frac{4}{18} \\ = \frac{2}{9} [/tex]
[tex]p(green) = 0[/tex]
What is GM?
I need the answer pleaseee help me
Answer: 18
Step-by-step explanation:
[tex]\triangle HJK \cong \triangle HLK[/tex] by HL. Therefore, [tex]JK=2[/tex] by CPCTC.
Using the segment addition postulate, [tex]GK=9[/tex].
Furthermore, [tex]\triangle HGK \cong \triangle HMK[/tex] by HL. This means that [tex]MK=9[/tex] by CPCTC.
Using the segment addition postulate again, [tex]GM=9+9=18[/tex].
What is the probability that out of 125 babies born, at least 50 will be girls? Assume that boys and girls are equally probable, and round your answer to the nearest tenth of a percent.
When boys and girls are equally likely, the likelihood that at least 50 of 125 infants born will be females is 0.40.
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
total number of sample=125
number of girls=50
Probability that out of 125 babies born, at least 50 will be girls,
=50/125
=0.40
The probability that out of 125 babies born, at least 50 will be girls is 0.40 when boys and girls are equally probable.
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What is the domain of the graph? *
{-5,-4,-3,-1,0,2,4}
All real numbers
{-5,-4,-3,-1}
{-4,0,2,4}
The domain of the graph is {-5,-4,-3,-1}.
How can I determine a graph's domain?
Graphs can be used as another tool for determining the domain and range of functions. The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph represents the possible output values, or range.Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.To know more about domain check the below link:
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Complete the process of solving the equation.
Fill in all missing terms and select all missing descriptions. Simplify any fractions.
The missing terms are 34t and 0.
Solving Linear Equations:Finding the solution to linear equations in one, two, three, or more variables is referred to as solving a linear equation. In simple words, finding the values that satisfy a Linear equation.
Here we have
Equation 3(18t +1) = 20t +3
Let's solve the given expression to get the missing step
=> 3(18t +1) = 20t +3
Multiply (18t + 1) by 3
=> 54t + 3 = 20t + 3
Subtract 3 from both sides
=> 54t + 3 - 3 = 20t + 3 - 3
=> 54t = 20t
Subtract 20t from both sides
=> 54t - 20t = 20t - 20t
=> 34t = 0
Divide by 34 into both sides
=> 34t/34 = 0/34
=> t = 0
Therefore,
The missing terms are 34t and 0.
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The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 396 people entered the park, and the admission fees collected totaled 1,094.00 dollars. How many children and how many adults were admitted?
Therefore by solving the equations we get to know that 196 children and 200 adults were present on that day.
What is equation?
equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics. Equations range in complexity from straightforward addition-and-multiplication equations in mathematics through differential equations, exponential equations that use exponential expressions, and integral equations.
Let's initially configure our system by giving the letters x and y meanings. Assume x is the number of kids and y is the number of adults.
Children are priced at $1.50, while adults are priced at $4.00. We multiply the total number of children, x, by 1.5 to get how much each child will cost. 1.5x is used to indicate this. We will use 4y for adults, whose entry fee is $4. On the specified day, $1094 in total revenue was earned. This sum requires the addition of 1.5x and 4y.
1.5x + 4y = 1094 works for the money equation involved.
Second equation: The total number of individuals present on the day is 283. X and Y, or the number of children and adults, must be added together to arrive at this figure.
x + y = 396
System of equations:
1.5x + 4y = 1094
x + y = 396
Thus,
x + y = 396
y = 396- x
Substitute y = 396 - x into the first equation.
1.5x + 4 (396 - x) = 1094
1.5x + 1584 - 4x = 1094
1584 - 2.5x = 1094
-2.5x = -490
x = 196
Substitute x =196 back into y = 396 - x
y = 396 - 196 = 200
Therefore by solving the equations we get to know that 196 children and 200 adults were present on that day.
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Click on the measure of the angle.
A. 34
B. 144
C. 36
D. 146
Answer:
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A can of campbell's chicken Noodles Soup has a diameter of 30 millimeters and a height of 5 inches Find the volume of the can in cubic millimeters
The volume of the can of campbell's chicken Noodles Soup in cubic millimeters is 89,725.5 cubic millimeters
What is the volume of the can?Volume of a cylinder = πr²h
Convert inch to millimeters:
1 inch = 25.4 millimeters5 inch = 127 millimetersHeight of the cylinder = 5 inches = 127 millimeters
Radius = diameter / 2
= 30 millimeters / 2
= 15 millimeters
Volume of a cylinder = πr²h
= 3.14 × 15² × 127
= 3.14 × 225 × 127
= 89,725.5 cubic millimeters
Consequently, the can of campbell's chicken Noodles Soup has a volume of 89,725.5 cubic millimeters
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Work out the size of an exterior angle of a regular polygon with 8 sides.
In how many ways can a committee of five Democrats and four
Republicans be formed from a group of twelve Democrats and twelve
Republicans?
Answer:
392040 ways------------------------------
Find the combination of 4 of 12 and 5 of 12:
C(12, 4) × C(12, 5) = 12!/(4!8!) × 12!/(5!7!) = 495 × 792 = 392040For what value of X is the parallelogram a rhombus?
Answer:
x = 8
Step-by-step explanation:
a rhombus has all equal sides so this means that you must set them equal to each other
8x - 5 = 5x + 19
now subtract 5x to both sides
3x = 24
x = 8
that is your answer
what is the value of p?
The value of p, using the exterior angle property is 53°.
What is the exterior angle property of a triangle?
The exterior angle property of a triangle states that the sum of the measures of the two non-adjacent angles of a triangle is equal to the measure of the exterior angle of the triangle. This means that if a triangle has three interior angles, the measure of any non-adjacent angle of the triangle must be equal to the measure of the exterior angle of the triangle. This property is useful in solving for unknown angles when the measures of two angles are known. For example, if two angles of a triangle measure 30° and 45°, then the measure of the third angle must be 105°, which is the same measure of the exterior angle.
The Exterior angle is = Sum of the Interior opposite angles.
By using the exterior angle property, we can get the following:
p+p-13°=p+40°
=>p=40°+13°
=>p=53°
The value of p is 53°
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Please answer the question that is stated in the image below. Thank you. It really means a lot to me.
Answer:
Below
Step-by-step explanation:
a) they won 120 games out of 369 played = 40/23=.325
b) they lost 248 out of 369 played = 248/369 = .672
c) Home games are 185 out of 369 = .501
d ) at home they won 72 out of (72+112+1) = 72/ 185 = .389
what is 122222×2222221÷12
Answer:
The result of the calculation is approximately 22535940185.17
Step-by-step explanation:
To solve this problem, we can use the order of operations. First, we perform the multiplication:
122222 * 2222221 = 2704312822242
Then, we perform the division:
2704312822242 / 12 = 22535940185.17
4) Which ordered pair is a solution to the linear
inequality below?
y ≥ -2x + 7
A. (-1, 5)
B. (3, 2)
C. (2, -8)
D. (-4, 0)
Answer: B
Step-by-step explanation:
Answer:
B. (3, 2)
Step-by-step explanation:
When looking for a solution to an inequality you have to look for a point that is located in the shaded part of the inequality when graphed. B.) (3,2) is the only point that is located in the shaded part meaning that, that is a solution to the inequality
The ratio of men to women working for a company is 5 to 6. If there are 308 employees total, how many women work for the company?
Answer:
Step-by-step explanation:
115 woman
Julie wanted to match Lisa's obstacle course record of 73.4 seconds. She has already spent twenty and one-fourth seconds on wall climbing and 11.78 seconds on the ropes. How much time did she have left to match the record? 61.62 seconds 53.15 seconds 41.37 seconds 8.47 seconds
The time required to match the record is 41.37 seconds. The correct option is (c).
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
The given problem can be solved as follows,
The remaining time for matching the record is given by,
73.4 - (20(¹/₄) + 11.78)
= 73.4 - (81/4 + 11.78)
= 73.4 - (20.25 + 11.78)
= 73.4 - 32.03
= 41.37
Hence, the time Julie have left to match the record is 41.37.
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