Therefore, 2 with an exponent of 0 is equal to 1.
When a number is raised to an exponent of 0, the result is 1. This applies to any non-zero number, including 2. Therefore, 2 with an exponent of 0 is equal to 1.
The reason is that any number raised to the power of 0 is 1. This is because any number multiplied by 1 is itself, and any number raised to the power of 1 is itself. Therefore, raising a number to the power of 0 is the same as multiplying it by 1, so the result is 1.
It is also important to note that a number raised to the power of 1 is the number itself, so 2^1=2, 2^2=4, 2^3=8 and so on.
Therefore, 2 with an exponent of 0 is equal to 1.
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A machine has 28 identical components which function independently. The probability that a component will fail is 0.19 . The machine will stop working if more than three components fail. Find the probability that the machine will be working. Round to the nearest thousandth.
By definition of a binomial random variable, the probability that the machine will be working is 0.82045.
Definition of probabilityFirst of all, you should know that the Probability is the greater or lesser possibility that a certain event will occur.
In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.
Definition of random variableOn the other hand, a random variable is a function that associates a real number, perfectly defined, to each sample point.
A random variable is discrete if the numbers it gives rise to are integers.
Definition of binomial distributionFinally, a binomial distribution is a discrete probability distribution that describes the number of successes in performing n independent experiments on a random variable.
The expression to calculate the binomial distribution is:
P(X=x)=([tex]n\\ x[/tex]) pˣ qⁿ⁻ˣ
Where:
n = Number of trials/experimentsx = Number of successesp = Probability of successq = Probability of failure (1-p)Remember that:
([tex]n\\ x[/tex])=[tex]\frac{n!}{x!(n-x)!}[/tex]
where the exclamation mark represents the factorial symbol, that is, the product of all positive integers from 1 to n.
Probability that the machine will be workingA machine has 28 identical components which function independently. The probability that a component will fail is 0.19.
The following random variable is defined:
x= the number of components will stop working.
Being n the total number of pieces (in this case, 12 pieces) and p the probability of success (the piece fails, in this case 0.19), the expression to be used is expressed as:
P(X=x)=([tex]12\\ x[/tex]) 0.19ˣ (1-0.19)¹²⁻ˣ
P(X=x)=[tex]\frac{12!}{x!(12-x)!}[/tex] 0.19ˣ (0.81)¹²⁻ˣ
Since the machine will stop working if more than three components fail, you need to know the probability that the machine will be working if 3 or less than 3 components fail. In other words, it may be that 0, 1, 2 or 3 pieces are broken and the machine continues to work:
P(X≤3)= P(X=0) + P(X=1) + P(X=2) + P(X=3)
Then:
P(X≤3)= [tex]\frac{12!}{0!(12-0)!}[/tex] 0.19⁰ (0.81)¹²⁻⁰ + [tex]\frac{12!}{1!(12-1)!}[/tex] 0.19¹ (0.81)¹²⁻¹ + [tex]\frac{12!}{2!(12-2)!}[/tex] 0.19² (0.81)¹²⁻² + [tex]\frac{12!}{3!(12-3)!}[/tex] 0.19³ (0.81)¹²⁻³
Solving:
P(X≤3)= [tex]\frac{12!}{0!12!}[/tex] ×1×(0.81)¹² + [tex]\frac{12!}{1!11!}[/tex] 0.19×(0.81)¹¹ + [tex]\frac{12!}{2!10!}[/tex] 0.19²×(0.81)¹⁰ + [tex]\frac{12!}{3!9!}[/tex] 0.19³×(0.81)⁹
P(X≤3)= 1×1×(0.81)¹² + 12×0.19×(0.81)¹¹ + 66×0.19²×(0.81)¹⁰ + 220×0.19³×(0.81)⁹
P(X≤3)= (0.81)¹² + 2.28×(0.81)¹¹ + 2.3826×(0.81)¹⁰ + 1.50898×(0.81)⁹
P(X≤3)= 0.82045
Finally, the probability that the machine will be working is 0.82045.
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What type of triange is this?
Answer: Right isosceles triangle
Step-by-step explanation: This is fairly easy to determine.
Side BC is roughly congruent to side CD. Both sides start from 0 to 7 and a little bit.
Side AC is also congruent by the reflexive property and is also congruent to both triangles' sides because it lines up perfectly. Since both sides BC and CD are congruent, the segment AC likely is perpendicular to segment BD and cuts it into 2 equal and congruent sides.
Sides AB and AD cannot be determined to be congruent.
Since the right angles are between two congruent sides of two triangles, the two triangles are congruent by the Side Angle Side congruence theorem.
Thus, we can say these are 2 right isosceles triangles conjoined together. Hope this helped!
(Proof is attached.)
The water park charges a $45 fee plus $5 per student for a field trip. The
bowling alley charges a $35 fee plus $7 per student. The lines in the graph
represent the cost of each field trip.
For what number of students will the total cost of each field trip be the same,
and what will that cost be?
Cost ($)
100
90
80
70
60
50
40
30
20
10
Field Trip Costs
y = 35+ 7x
y = 45 + 5x
1 2 3 4 5 6 7 8 9 10
Number of students
Using linear functions, the cost will be the same, of $70, when there are 5 students.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the functions are:
y = 45 + 5x.y = 35 + 7x.The costs are the same when:
45 + 5x = 35 + 7x
2x = 10
x = 5.
The cost is:
y = 45 + 5 x 5 = $70.
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visualize "4.298" on the number line
Answer:
Step-by-step explanation:
The visualization of "4.298" on the number line is attached below.
How does the dot plot work?Suppose we're measuring something whose values are numeric.
For each value of that thing we observe, we plot a dot above that value in the number line.
Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.
Thus, suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.
We know that 4.298 is greater than 4 but less than 5.
The visualization of "4.298" on the number line is attached below.
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what is the measure.. PLS HELP THIS IS URGENT
The angle of the given ray is of x = 150º.
What is the angle of the ray?The angle of the ray is given by the sum of the angles that compose the ray.
In this problem, the angles are of 65º, 40º and 45º, hence:
x = 65 + 40 + 45 = 150º
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For 2-3, Name a postulate or theorem that can be used to prove that the two triangles are similar. Then, write a similarity statement.
Postulate: AA
Similarity statement: [tex]\triangle CBA \sim \triangle FED[/tex]
Two poles of different heights are used for a climbing event and need to be secured to the ground using wires. The shorter pole is 6.0 m tall and the wire is secured 8.0 m from the base of the pole. If wire of the taller pole is 16.0 m long. Determine the height of the taller pole .
Using similar triangles, it is found that the height of the taller pole is of 9.6m.
What are similar triangles?Similar triangles are triangles that have the same angles, and whose side lengths are proportional.
The hypotenuse of the smaller triangle is given as follows:
h² = 6² + 8² -> h = 10.
Hence the proportional relationship is:
[tex]\frac{10}{16} = \frac{6}{h}[/tex]
Applying cross multiplication:
10h = 96
h = 9.6m.
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simplify 1/5 (-16-9) + 4^2 ÷ 8 A.-3 B.7 C. -7/5 D.3/5
The simplified form of the expression [1/5 (-16-9) + 4² ÷ 8] is -3.
Option A) is the correct answer.
What is the simplified form of the expression?
Given the expression; 1/5 (-16-9) + 4² ÷ 8
First we remove the parentheses and perform the operations using the guidelines of BODMAS
1/5 (-16-9) + 4² ÷ 8
1/5 × -25 + 4² ÷ 8
1/5 × -25 + 16 ÷ 8
-25/5 + 16/8
-5 + 2
-3
The simplified form of the expression [1/5 (-16-9) + 4² ÷ 8] is -3.
Option A) is the correct answer.
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What is 8 11/12 + 9 5/18
Step-by-step explanation:
The picture is the full explanation for this question answer.
18.19 is the solution for the given improper function.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
To add 8 11/12 and 9 5/18, we need to first find a common denominator. The smallest number that both 12 and 18 divide evenly is 36.
Converting 8 11/12 to an improper fraction:
8 11/12 = (8 × 12 + 11) / 12 = 107/12
Converting 9 5/18 to an improper fraction:
9 5/18 = (9 × 18 + 5) / 18 = 167/18
Now that we have a common denominator of 36, we can add the two fractions:
107/12 + 167/18 = (107 × 3) / (12 × 3) + (167 × 2) / (18 × 2)
= 321/36 + 334/36 = 655/36
So 8 11/12 + 9 5/18 = 655/36 or approximately 18.19.
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6.
Write
√18+10
√2
in the form a+b√√3 where a and b are integers.
Answer:
3+10 square root of 2
Step-by-step explanation:
[tex](3 + 10) \sqrt{2} [/tex]
Find three consecutive integers such as two times the first integer, plus three times the second integer, minus the third integer, is equal to 21.
The three consecutive integers are 5, 6, and 7.
What are consecutive integers?
Whole numbers that follow one another without a gap are known as consecutive integers. A few examples of consecutive integers are 15, 16, and 17, 1,2 and 3, and so on.
Finding the Consecutive Integers
Let the three consecutive integers be a, a + 1, and a + 2.
These three consecutive integers are to be such that two times the first integer when added to three times the second integer minus the third integer, it is equal to 21.
⇒ 2a + 3(a+1) - (a+2) = 21
2a + 3a + 3 - a -2 = 21
5a - a + 3 - 2 = 21
4a + 1 = 21
4a = 20
a = 20/4
a = 5
∴ a+1 = 5+1
a+1 = 6
And, a+2 = 5 + 2
a +2 =7
Hence, the three consecutive integers come out to be 5, 6, and 7
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2. Find the area of the circle. Round to the nearest tenth.
A.113.1
B.37.7
C.18.8
D.28.3
The answer is D.
The formula to find area of a circle is : πr²
Here, we are given the diameter, but we need the radius. Always remember that the radius is always half the diameter.
Let's find the area.
A = π × r²A = 3.14 × (3)²A = 3.14 × 9A = 28.26A ≈ 28.3Solve for x sim b (10, 0.75) for x = 5
The value of [tex]x \sim B (10, 0.75)[/tex] for x = 5 is 0.06
How to solve the probability?The expression is given as:
[tex]x \sim B (10, 0.75)[/tex]
This means that:
n = 10
p = 0.75
The probability is then calculated as
[tex]P(x)= ^nC_x * p^x *(1 - p)^{n-x[/tex]
This gives
[tex]P(5)= ^{10}C_5 * 0.75^5 *(1 - 0.75)^5[/tex]
Evaluate the combination expression
[tex]P(5)= 252 * 0.75^5 *0.25^5[/tex]
Evaluate
P(5)= 0.06
Hence, the value of [tex]x \sim B (10, 0.75)[/tex] for x = 5 is 0.06
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Michael rode on the train 168.45 miles the first week of work and 149.85
miles the second week. ABOUT how many miles did he ride on the train
during the two weeks?
a.) a little less than 320
b.) a little more than 320
c.) a little less than 330
d.) a little more than 330
Answer:
A little less than 320
Step-by-step explanation:
Round the miles to 168 and 150
Add together 168 + 150 = 318
Answer: a. a little less than 320
A designer created a kitchen floor tile in a triangular shape. two sides of the tile have lengths of 8 inches and 9 inches. what is the range of the possible lengths, x, of the third side of the tile?
Considering that it is a triangle, the range of the possible lengths, x, of the third side of the tile is: (1, 17).
What is the condition for 3 lengths to represent a triangle?In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.
Hence, if 9 is the greater side:
8 + x > 9
x > 1.
If 8 and 9 are the smaller sides:
x < 8 + 9
x < 17.
Hence the range of possible lengths is:
(1, 17).
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The tuition costs, c, for a local community college are modeled by c(h) = 250 200h, where h represents the number of credit hours taken. the local state university has tuition costs, s, modeled by the function s(h) = 300 180h. how many credit hours will a student have to take for the two tuition costs to be equal? round the answer to the nearest tenth of an hour. 250 200h = 300 180h 250 200h = 300 180h − 180h − 180h 250 20h = 300 h = credit hours
The number of credit hours a student have to take for the two tuition costs to be equal is 2.5 hours. Option A
Equationlocal community college;c(h) = 250 + 200h
local state University;s(h) = 300 + 180h
Where,
number of credit hours taken = hTo have equal tuition in both schools,
equate both function
250 + 200h = 300 + 180h
200h - 180h = 300 - 250
20h = 50
h = 50/20
h = 2.5 hours.
The number of credit hours a student have to take for the two tuition costs to be equal is 2.5 hours.
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Suppose a and b are independent events. if p(a) = .5 and p(b) = 0.45 what is p(a^b)
If P(a)=0.5 and P(b) =0.45, then P(a ∩ b) is 0.225.
What are independent events?Independent events are events such that the occurrence of one event won't affect the other.
Therefore,
P(a) × P(b) = P(a ∩ b)
Hence,
P(a) = 0.5
P(b) = 0.45
Therefore,
P(a ∩ b) = 0.5 × 0.45
P(a ∩ b) = 0.225
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What are two methods that can solve x^2+14x=-8
The two methods which can be used to solve the quadratic equation are; The completing the square method and the factor method.
Which two methods can be used to solve the quadratic equation?Although, not limited to the aforementioned methods of solving quadratic equations, the two methods are major methods of solving quadratic equations.
The completing the square method (also used in expressing quadratic equations in vertex form) and the factor method are very efficient method of solving quadratic equations.
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Find the volume of the pyramid. Round to the nearest tenth if necessary. PLEASE HELP!!
Answer:
27.183, 27.2
Step-by-step explanation:
First, do the formula for the triangle:
[tex]\frac{1}{2}[/tex] x 4.1 x 2.6 = 5.33
Next, multiply that by the base side:
5.33 x 5.1 = 27.183
Answer:
1/2 x 4.1 x 2.6 = 5.33
5.33 x 5.1 = 27.183
Rounding off to nearest tenth = 27.2 m^3
Use the explicit formula an= a₁ + (n-1) d to find the 500th term of the
sequence below.
24, 31, 38, 45, 52, ...
Therefore, the 500th term of the sequence exists 3517.
How to estimate the 500th term of the sequence?The given sequence is 24, 31, 38, 45, 52, ...
It exists an Arithmetic progression.
Here, the First term = 24
Common difference = 31 - 24 = 7
The given explicit formula for the nth term exists
an = a₁ + (n - 1)d
Where a₁ exists the first term, d exists a common difference.
Substitute a₁ = 24, d = 7 and n = 500
a(500) = 24 + (500 - 1)7
= 24 + (499)7
= 24 + 3493
a(500) = 3517
Therefore, the 500th term of the sequence exists 3517.
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Solve ΔABC with ABC=51°, c=8 and a=11. Draw a diagram.
To solve a triangle means to obtain al the missing parts of the triangle.
How do you solve a triangle?To solve a triangle means to obtain al the missing parts of the triangle. Now we have the following information;
<ABC = 51°
c = 8
a = 11
Then;
b^2 = a^2 + c^2 - 2acCos B
b^2 = (11)^2 + (8)^2 - [2 * 11 * 8 * cos 51]
b^2 = 121 + 64 - 55.38
b = 11.39
Now;
a/sinA = b/sinB
asinB = bsinA
sinA = asinB/b
sinA = 11 * sin 51/11.39
A = 48.6 or 49°
C = 180 - (49 + 51)
C = 80°
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How many ms in a second?
The probability of picking an ace at random out of a
deck of 52 cards is What would be the probabil-
13
ity of picking an ace at random if 2 aces were
removed from the deck?
Answer:
2/50=1/25
Step-by-step explanation:
2 aces are removed hence 2 aces are left out of 50 cards
how much would 500 invested at 4% interest compounded continuously be worth after 7 years? round your answer to the nearest cent
Answer: the answer is 661.55
Step-by-step explanation:
interest formula: F = Pe^(rt)
What is WX? Explain your reasoning.
I know all the angles but I’m not sure on how to find WX or what equation to use.
Answer:
180
Step-by-step explanation:
Solution 1: Any straight line is 180 degrees.
Solution 2: Angle WX=Angle YZW+ Angle YZX
Angle YZW=Angle YZX=90
Angle YZW+ Angle YZX=90+90=180
So Angle WX=180
Answer:
Step-by-step explanation:
You can find WX if you know some special properties of special triangles:
1. A 45-45-90 triangle (a triangle with angle measures of 45°, 45°, and 90°) will have a 1:1:√2 ratio (the legs of the triangle are the same length and the hypotenuse is the length of any leg times √2)
2. A 30-60-90 triangle (a triangle with angle measures of 30°, 60°, and 90°) will have a 1:√3:2 ratio (the hypotenuse is twice the measure of the shorter leg, and the longer leg is √3 times the length of the shorter leg)
For reference, a leg is a side on a right triangle that isn't the hypotenuse.
In this picture, the first type of triangle is on the right, and the second type is on the left.
WZThe shorter leg on the left triangle has a length of 10, and WZ is the longer leg. The longer leg is √3 times the shorter one, so WZ = 10√3
ZXBoth legs of a 45-45-90 triangle have the same measure, so ZX is 10.
Since WX is made up of WZ and ZX, it's length is the sum of both lengths.
[tex]{\rm WX} = 10\sqrt{3}+10[/tex]
[tex]{\rm WX} \approx 27.321[/tex]
The distance to your uncle's house is 444 miles, and the distance to Atlanta is 555 miles. If it took 12 hours to drive to your uncle's house, how long would you estimate the drive to Atlanta to take
It takes 15 hours to drive to Atlanta. Using the distance-time-speed formula the required time is calculated.
What is the distance-time-speed formula?The relation between distance 'd', time 't', and speed 's' is given by the formula,
s = d/t or
d = st or
t = d/s
Calculation:It is given that,
The distance to uncle's house = 444 miles
The time taken to drive to uncle's house = 12 hours
So,
speed = (444)/12 = 37 miles/hour
Then the time to drive 555 miles(to Atlanta) is calculated by,
time t = (555)/37 = 15 hours
Therefore, it takes 15 hours to drive to Atlanta at 555 miles of distance.
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To remain a member of the student council, a student must attend at least Three-fourths of the activities. Joey attends 15 of the activities and remains on the student council. Which inequality represents the total amount of student council activities, a?
Answer:
20
Step-by-step explanation:
so we need to see that
3/4 x ? = 15
so we say
3 x ? = 15x4
? =60/3
?= 20
Determine the unknown length or angle measurement. Round each answer to the nearest whole number.
The unknown sides and angles of the triangle are 18 cm and 39 degrees respectively.
How to find the side and angle of a triangle?The side and angle of a triangle can be found as follows:
using sine law,
Angle A = 180 - 68 - 59 = 53 degrees
19.5 / sin 59 = a / sin 53
19.5 sin 53 = a sin 59
a = 19.5 sin 53 / sin 59
a = 15.5733924459 / 0.8571673007
a = 18.1680280047
a = 18 cm
15 / sin ∅ = 20 / sin 57
15 sin 57 = 20 sin ∅
sin ∅ = 12.5800585192 / 20
sin ∅= 0.62900292595
∅ = sin ⁻¹ 0.62900292595
∅ = 38.9763828249
∅ = 39 degrees.
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John, and bill shared $900 in the ratio 7:3 respectively. how much money did each person get?
John get money $630 and bill get money $270.
Given that John and bill shared $900 in the ratio 7:3 respectively.
The ratio is defined as the comparison of two quantities of equal units, indicating the quantity of one quantity contained in the other quantity.
The total ratio is 7+3=10
For john:
John has money seven out of 10 for the $900, we get
J=900×(7/10)
J=90×7
J=630
For bill:
Bill is three out of ten for $900, we get
B=900×(3/10)
B=90×3
B=270
Hence, john get money $630 and bill get $270 when they both shared $900 in the ratio 7:3 respectively.
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A line passes through the points (p,a) and (p,−a) where p and a are real numbers and p ≠ 0. Describe each of the
following. Explain your reasoning.
.slope of the line
.equation of the line
.y-intercept
.slope of a line perpendicular to the given line
Answer:
slope: undefined
equation: x = p
y-intercept: there is none
slope of perpendicular: 0
Step-by-step explanation:
points: (p, a), (p, -a)
slope = (-a - a)/(p - p) = -2a/0
The slope is undefined since the line is vertical.
equation: x = p
Since p ≠ 0, the vertical crosses the x-axis at a point that is not x = 0 and never intersects the y-axis, so the is no y-intercept.
A line perpendicular to he given line is a horizontal line.
slope = 0