A repeating decimal like 0.2222222.... is a rational number and can be written as the fraction 2/9.
A stopping decimal like 0.22 is a rational number and can be written as the fraction 22/100.
A non-stopping and non-repeating decimal like 0.1234567891011... or 0.121121112... is an irrational number that can be written as the fraction 1514013912/5000000
The square root of a perfect square is a rational number and also a whole number.
The square root of a prime number is an irrational number.
What are rational and irrational numbers?
The definition of a rational number is one that may be stated as a fraction or as a portion of a whole number. For example -7, 2/3, 3.75 Numbers that cannot be stated as a fraction or ratio of two integers are referred to be irrational numbers. There is no limit to how one might convey them. For example √2, √3, e
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4% as a fraction or mixed number in simplest form
Answer:
1 /25
Step-by-step explanation:
percent means
out of 100
⇒
4
%
=
4
100
as a fraction
To simplify the fraction we require to find a
common factor
to both 4 and 100 and reduce the fraction by dividing. The common factors are 2 and 4 . Choose the largest, that is 4
⇒
4
100
=
4
÷
4
100
÷
4
=
1
25
This calculation is usually set out using
cancelling
4
100
=
4
1
100
25
=
1
25
←
in simplest form
A fraction is in
simplest form
when no other factor but 1 will divide into the numerator/denominator.
Refer to the painting.
110°
7x
Write an equation that can be used to find the value of x.
An equation that can be used to find the value of x include the following: 110° + 7x = 180°.
What is a supplementary angle?In Mathematics and Geometry, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of the given angles are supplementary angles:
110 + 7x = 180°
7x = 180° - 110°
7x = 70°
x = 70°/7
x = 10°
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Given a slope and a point write a perpendicular equation in standard form.
slope: -2/5
point: (-5,3)
kira,boris,deshuan have a total of $119 in their wallets. Boris has 3 times waht deshuan has. Deshuan has $6 more than kira. How much do they have in their wallets.
Kira has $19, Boris has $75, and Deshuan has $25.
How much money does each person have in their wallets?We will denote as follows:
Kira has as K, Boris has as B, and Deshuan has as D.From information, we can set up equations:
B = 3D (Boris has 3 times what Deshuan has)
D = K + 6 (Deshuan has $6 more than Kira)
K + B + D = 119 (The total amount of money they have is $119)
Substituting equation 2 into equation 1, we have:
B = 3(K + 6)
Substituting equations 1 and 2 into equation 3:
K + 3(K + 6) + (K + 6) = 119
K + 3K + 18 + K + 6 = 119
5K + 24 = 119
5K = 119 - 24
5K = 95
K = 95 / 5
K = 19
Using equation 2, we can find D:
D = K + 6
D = 19 + 6
D = 25
Using equation 1, we can find B:
B = 3D
B = 3 * 25
B = 75.
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in a science experiment the intial temperature was 55 degrees faherheit
Answer:
Answer to your question ; f(t) = 55 = 4t
Is. She analyzes
st.
Martha graphs the data for the number of bracelets made, a, and the number of beads used,
y, and draws a line through the points.
Number of Beads Used
600
500
400
300
200
100
0
Bracelets Made
versus Beads Used
(31, 651)
(23, 483).
(10, 210)
5 10 15 20 25 30 35
Number of Bracelets Made
Write an equation that represents the relationship between the number of bracelets made
and the number of beads used. Show or explain how you found the slope and y-intercept.
Enter your equation and your work or explanation in the space provided.
You may use the drawing box to add a drawing to help explain your answer.
A
7
44
▶
Exhibits
P
The equation for the relationship between the number of bracelets made and the number of beads is y = 21x.
First, the rate of change
= (483 - 210) / (23 - 10)
= 273 / 13
= 21
So, the equation for the relationship between the number of bracelets made and the number of beads used.
(y - 210) = 21 (x- 10)
y - 210 = 21x - 210
y = 21x
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Astronomers believe that the radius of a variable star increases and decreases with the brightness of the star. Suppose a variable star has an average radius of 20 million miles and changes by a maximum of 1.6 million miles from this average during a single pulsation, and that the time between periods of maximum brightness is 5.2 days. Find an equation that describes the radius of this star as a function of time. (Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing.) R(t) =
Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing then R(t) = 20 + 1.6sin(2πt/5.2).
The equation for a sine wave is y = A sin (Bx + C) where A is the amplitude, B is the frequency and C is the phase shift.
In this case, the amplitude is 1.6.
Since the radius changes by a maximum of 1.6 million miles.
The frequency is 2π/5.2 (one full cycle of the sine wave in 5.2 days)
The phase shift is 0, since when t = 0 the radius is increasing.
The equation then becomes R(t) = 20 + 1.6sin(2πt/5.2)
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Suppose the weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams. The weights of oranges are also normally distributed with a mean of 131 grams and a standard deviation of 20 grams. Amy has an apple that weighs 90 grams and an orange that weighs 155 grams.
Required:
a. Find the probability a randomly chosen apple exceeds 100 g in weight.
b. What weight do 80% of the apples exceed?
Answer:
a) 0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.
b) The weight that 80% of the apples exceed is of 78.28g.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams.
This means that \(\mu = 85, \sigma = 8\)
a. Find the probability a randomly chosen apple exceeds 100 g in weight.
This is 1 subtracted by the p-value of Z when X = 100. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{100 - 85}{8}\)
\(Z = 1.875\)
\(Z = 1.875\) has a p-value of 0.9697
1 - 0.9696 = 0.0304
0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.
b. What weight do 80% of the apples exceed?
This is the 100 - 80 = 20th percentile, which is X when Z has a p-value of 0.2, so X when Z = -0.84.
\(Z = \frac{X - \mu}{\sigma}\)
\(-0.84 = \frac{X- 85}{8}\)
\(X - 85 = -0.84*8\)
\(X = 78.28\)
The weight that 80% of the apples exceed is of 78.28g.
Use the Pythagorean Theorem to find the length of the missing side of the right triangle. Then find the value of each of the six trigonometric functions of .
θ
A
B
C
a = 16
b = 30
c
Question content area bottom
Part 1
The length of the missing side of the right triangle is
1) The length of the missing side of the right triangle is 34.
2) The values of the six trigonometric functions of θ are:
sin θ = sin A = 8/17
cos θ = cos A = 15/17
tan θ = tan A = 8/15
csc θ = csc A = 17/8
sec θ = sec A = 17/15
cot θ = cot A = 15/8
What is Pythagorean Theorem?
Pythagoras Theorem is a method for calculating the missing length of a right-angled triangle. The triangle has three sides: the hypotenuse (which is usually the longest), the opposite (which does not touch the hypotenuse), and the adjacent (which is always the shortest) (which is between the opposite and the hypotenuse).
Part 1
To find the length of the missing side (c) of the right triangle, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, we have:
a² + b² = c²
Substituting the given values, we get:
16² + 30² = c²
Simplifying, we get:
256 + 900 = c²
1156 = c²
Taking the square root of both sides, we get:
c = sqrt(1156) = 34
Therefore, the length of the missing side of the right triangle is 34.
Part 2
To find the values of the six trigonometric functions of θ, we need to know one of the acute angles of the triangle. Let's call the acute angle opposite side a as angle A. Using the given values, we can find the sine, cosine, tangent, cosecant, secant, and cotangent of angle A as follows:
sin A = a/c = 16/34 = 8/17
cos A = b/c = 30/34 = 15/17
tan A = a/b = 16/30 = 8/15
csc A = 1/sin A = 17/8
sec A = 1/cos A = 17/15
cot A = 1/tan A = 15/8
Therefore, the values of the six trigonometric functions of θ are:
sin θ = sin A = 8/17
cos θ = cos A = 15/17
tan θ = tan A = 8/15
csc θ = csc A = 17/8
sec θ = sec A = 17/15
cot θ = cot A = 15/8
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3 consecutive odd integers such that the sum of twice the first and three times the second is 55 more than twice the third
Answer:
Consecutive odd integers are 19 , 21 & 23
Step-by-step explanation:
Let the first 3 consecutive odd intergers be x , (x + 2) and (x + 4).
According to the question,
\(2x + 3(x + 2) = 2(x + 4) + 55\)
\( = > 2x + 3x + 6 = 2x + 8 + 55\)
Eliminating 2x from both the sides,
\( = > 3x + 6 = 63\)
\( = > 3x = 63 - 6 = 57\)
\( = > x = \frac{57}{3} = 19\)
So, the consecutive odd integers are = 19 , 21 & 23.
at the community savings bank it takes a computer 18 minutes to process and print payroll checks when the second computer is used and the two computers work together the checks can be processed and printed in 14 minutes how long would it take the second computer by itself to process and print the payroll checks
Therefore, the second computer can process and print the payroll checks in 63 minutes.
Which values of a, b, and c represent the answer in simplest form?
7/9 * 4/9 = a b/c
Answer:
Option 2: A=1, B=3, C=4
Step-by-step explanation:
7/9÷4/9 = 7/9*9/4cancel 9 on each side=7/4= 1 3/4verify that the set of rational numbers together with the usual addition and multiplication operation is a field
To check whether the set of rational numbers together with the usual operation of addition and multiplication is a field, we must look into the properties for the set of rational numbers.
What are the properties?Closure under addition: For any two rational numbers a and b, a + b is also a rational number.Associativity of addition: For any three rational numbers a, b, and c, (a + b) + c = a + (b + c).Identity element of addition: There exists a rational number 0 such that a + 0 = a for any rational number a.Inverse element of addition: For any rational number a, there exists a rational number -a such that a + (-a) = 0.Commutativity of addition: For any two rational numbers a and b, a + b = b + a.Closure under multiplication: For any two rational numbers a and b, a x b is also a rational number.Associativity of multiplication: For any three rational numbers a, b, and c, (a x b) x c = a x (b x c).Identity element of multiplication: There exists a rational number 1 such that a x 1 = a for any rational number a.Inverse element of multiplication: For any non-zero rational number a, there exists a rational number 1/a such that a x (1/a) = 1.Distributivity of multiplication over addition: For any three rational numbers a, b, and c, a x (b + c) = (a x b) + (a x c).Commutativity of multiplication: For any two rational numbers a and b, a x b = b x a.So, All of these properties hold for the set of rational numbers with the usual addition and multiplication operation. Therefore, the set of rational numbers with these operations form a field.
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What is the answer to this combination lock
Answer: 375
Step-by-step explanation:
Ruling out each number:
6: In the first two rows, the 6's placement did not change but the clue did, meaning that it is talking about a different number. Otherwise, it would say it's in the right place twice or in the wrong place twice.
3 & 5: Since we know 6 is already ruled out, both 5 & 3 would have to be correct.
2 & 4 & 8: Is proven wrong in the 4th clue.
7: 7 would have to be in the middle since the second clue says it's in the wrong place. If it was 1, it would say it's in the right space.
1: Is proven wrong after 7 is proven true.
Figuring out placement:
5: For the first clue, it says that it's in the correct place meaning that 5 is the last digit.
3: For both of the times 3 appears, it is in the wrong spot, revealing that it's the first digit.
7: In the second clue, it could either be 1 or 7. However, since 3 took the first spot and 5 took the last spot, 7 would have to be in the middle since the clue says it's in the wrong place. If it was 1, it would say it's in the right space.
NO LINKS!! URGENT HELP PLEASE!!!
5. Find the domain and the range for each of the following graphs.
Answer:
Domain: x \(\geq\) -5
Range: y \(\geq\) -3
Step-by-step explanation:
The domain is all the possible inputs or x value. x will be greater than -5.
The range is all of the possible outputs or y value. y will be greater than -3
Answer:
Domain: [-5, ∞)
Range: [-3, ∞)
Step-by-step explanation:
The given graph shows a continuous curve with a closed circle at the left endpoint (-5, -3) and an arrow at the right endpoint.
A closed circle indicates the value is included in the interval.
An arrow shows that the function continues indefinitely in that direction.
DomainThe domain of a function is the set of all possible input values (x-values).
As the leftmost x-value of the curve is x = -5, and it continues indefinitely in the positive direction, the domain of the graphed function is:
Interval notation: [-5, ∞)Inequality notation: x ≥ -5Set builder notation: {x ∈ R | x ≥ -5 }RangeThe range of a function is the set of all possible output values (y-values).
From observation, it appears that the minimum y-value of the curve is y = -3. The curve continues indefinitely in the positive direction in quadrant I. Therefore, the range of the graphed function is:
Interval notation: [-3, ∞)Inequality notation: y ≥ -3Set builder notation: {y ∈ R | y ≥ -3 }Easy geometry please help!!
In the given parallelogram ABCD the values for variables are - g = 6, y = 5 and x = 4.
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
We know that in a parallelogram, opposite sides are congruent and parallel, and diagonals bisect each other.
Using this information, we can set up equations to solve for the variables.
From the given information, we have -
AE = CE = 2x - 5 = 5x - 17 (since diagonals bisect each other at point E)
BE = x + 2
DE = BE = (x + 2) = g (since diagonals bisect each other at point E)
We also know that opposite sides of a parallelogram are parallel.
Therefore, 10 is parallel to 2y, which means they have the same slope. We can write this as -
10/1 = 2y/1
10 = 2y
y = 5
Now we can use equation (1) to solve for x -
2x - 5 = 5x - 17
12 = 3x
x = 4
Finally, we can use x to solve for g -
(x + 2) = g
(4 + 2) = g
g = 6
Therefore, the values of x, y, and g are 4, 5, and 6, respectively.
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I need help quick 5 mins leftyttt
Answer:
I don't know sorry :((((((((((((((((
Step-by-step explanation:
5. Which of the given number sets contains all integer numbers?
{-5, √ō, π}
{0, 13, √/20}
{√4,-1,9.5}
{√49,-1,0}
Answer:
{√49,-1,0}
Step-by-step explanation:
√49 = 7, because 7*7 = 49
7, -1 and 0 are all integer numbers.
π isn't integer, √20 is not an integer (it's 2√5), 9.5 is not an integer.
College level
Attached photo.
The value of b form the logarithmic equation \(log_b}3=0.7925\) is 3.9998688.
What are logarithms?In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.
Given that, \(log_b}25=2.3219\) and \(log_b}3=0.7925\).
Solve the equation by rewriting in exponential form using the definition of a logarithm and simplifying.
We know that, logₐN=x is written exponential form as aˣ=N
Here, \(b^{2.3219}=25\)
b=4.00006709
\(b^{0.7925}=3\)
b=3.9998688
Therefore, the value of b is 3.9998688.
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OK for real this is a hard only verified experts can do this!!!!
The numeric value of the exponential expression in this problem is given by the following option:
A. 2^12.
How to obtain the numeric value of the exponential expression?The exponential expression for this problem is defined as follows:
8^x/2^y.
8 is the third power of 2, hence:
8 = 2^3.
When a term is elevated to two of it's powers, the powers are multiplied, hence:
(2^3)^x = 2^(3x).
Meaning that the exponential expression is then written as follows:
8^x/2^y = 2^(3x)/2^y.
When two terms of the same base and different exponents are divided, we keep the base and subtract the exponents, hence the expression is given as follows:
2^(3x)/2^y = 2^(3x - y).
As stated in the problem, the numeric value of the expression 3x - y is given as follows:
3x - y = 12.
Hence the entire expression is simplified as follows:
2^(3x - y) = 2^12.
Meaning that the correct option is given by option A.
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Answer:A. 2^12.
Step-by-step explanation:i did it and got it right
Variables y and x have a proportional relationship, and y = 21 when x = 14. What is the value of x when y = 12? Enter your answer in the box. x =
I NEED IT ASAP
The required value of the x in the proportional relationship is 8.
Given that,
Variables y and x have a proportional relationship and y = 21 when x = 14. What is the value of x when y = 12 is to be determined.
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
y = 21 when x = 14,
y = 12 when x = ?
So y is proportion to x,
21 / 12 = 14 / x
x = 14 (12 / 21)
x = 2 (12 / 3)
x = 2 (4)
x = 8
Thus, the required value of the x in the proportional relationship is 8.
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HELP PLEASE 16 points
Write and solve an equation for the problem described below.
The sum of 57 and a number x is 45.
Answer:
57+x = 45
The sum means your adding numbers. it says the sum of 57 and a number x. That means you are adding 57 and the number x. which is written as 57+x. It says after that "is 45" so the sum or answer is 45.
You can also solve for x.. if you want to, the answer would be x=-12.
because.. 57+-12 = 45
Step-by-step explanation:
Find the area of the triangle.
Answer:
119 ft ^2
Step-by-step explanation:
area of a triangle = 1/2 x base x height
=1/2 x 17 x 14
=119
The factored form of 5 x squared minus 18 x minus 8 is __________
The factored form is (5x+2)(x-4).
What is factorization?
A number, matrix, or polynomial may be broken up or decomposed into factors that, when multiplied together, produce the original number, matrix, etc. This process is known as factorization or factoring.
Here, we have
Given: 5 x squared minus 18 x minus 8
we have to find the factored form.
= 5x² - 18x - 8
= 5x² - 20x + 2x - 8
= 5x(x-4) + 2(x-4)
= (5x+2)(x-4)
Hence, the factored form is (5x+2)(x-4).
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help please!!!! need it asap
If triangles ABC and DEF are similar, what is y? Show your work.
The value of y is 18
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.
Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.
Therefore;
14/21 = 12/y
14y = 21 × 12
14y = 252
divide both sides by 14
y = 252/14
y = 18
Therefore the value of y is 18.
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This list shows the lengths in feet of the 25 longest bridges in the United States.
1010
1470
1600
2000
2800
1053
1495
1632
2150
3500
1200
1596
1750
2150
3800
1207
1600
1800
2300
4200
1380
1600
1850
2310
4260
Jamie made a frequency table of the bridge data.
U.S. Bridges
Length (ft)
Tally
Frequency
(first interval)
|||| ||
7
(last interval)
||
2
Based on the tallies and frequencies for the first and last intervals, how many intervals of what length did Jamie use?
a.
4 intervals of 1000 feet
c.
6 intervals of 500 feet
b.
5 intervals of 1000 feet
d.
7 intervals of 500 feet
Answer:
D. 7 intervals of 500 feet
Step-by-step explanation:
Got it right
Jamie used 5 intervals of 1000 feet as per the given data. The correct option is b.
What are tallies and frequencies?A tally chart is a straightforward method of recording and counting frequencies. Each occurrence is represented by a tally mark, and every fifth tally is drawn diagonally to form a five-pointed star.
The first interval has a frequency of 7, which corresponds to the first 7 data points in the list:
1010
1470
1600
2000
2800
1053
1495
The last interval has a frequency of 2, which corresponds to the last 2 data points in the list:
2310
4260
Since there are 25 data points in total, and the first 7 and last 2 have been accounted for, that leaves 16 data points for the remaining intervals.
If Jamie used 1000-foot intervals, each interval would cover a 1000-foot range. The remaining data points range from 1200 to 4200 feet, so they are divided into 1000-2000, 2000-3000, and 3000-4000 foot intervals.
If Jamie used 500-foot intervals, each interval would cover a 500-foot range.
Thus, because the remaining data points range from 1200 to 4200 feet, they are divided into 1000-1499, 1500-1999, 2000-2499, 2500-2999, 3000-3499, 3500-3999, and 4000-4499 foot intervals.
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how do you find volume of sphere, cylinder, cone ? ... explaining please
Answer:
hmmmm
Step-by-step explanation:
Cone
The volume of a cone is linked to the volume of a cylinder. A cone is one third of the volume of a cylinder. The volume of a cone is ¹/₃ × π × r² × l. To calculate the volume we multiply these values together. The answer will be written in units³.
Sphere
The volume of a sphere is ⁴/₃ × π × r³. To calculate the volume we multiply these values together. The answer will be written in units³.
Cylinder
The volume of a cylinder is π × r² × l (r is the radius of the circle and l is the length of the cylinder). To calculate the volume we multiply these values together. The answer will be written in units³. It is more accurate to use π = 3.142 or the π button on a calculator.
A cone is a 3D shape with 2 faces and one edge
A sphere is a 3D shape. It has one continuous face and no edges
A cylinder is a type of prism. It has 3 faces and 2 edges
website I used: https://www.bbc.co.uk/bitesize/topics/zrf3cdm/articles/ztqsdxs
I hope this helped!
Which graph represents the function fx) =|x–4?
The image below shows the graph f(x) = |x| – 4
Hope this helps! :)
Give the equation of the line
with a slope of 3 that goes
through the point (2,-1)
Answer:
y=3x-7
Step-by-step explanation:
y-y1=m(x-x1)
y-(-1)=3(x-2)
y+1=3(x-2)
y+1=3x-6
y=3x-6-1
y=3x-7
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