The difference between the largest and the smallest fraction is 0.24.
What are fractions?A fraction is a component of a whole.
Mathematically, the number is expressed as a quotient, where the numerator and denominator are divided.
In a simple fraction, both are integers.
In a complex fraction, a fraction can be found in either the numerator or the denominator.
A suitable fraction has a numerator that is less than its denominator.
So, first, we will figure out the smallest and the greatest fraction:
We have: 3/5, 5/6, 2/3, 9/8, 7/9 and 3/4
LCM of denominators: 2*2*2*3*3*5 = 360
216/360, 300/360, 240/360, 405/360 (Improper), 280/360, 270/360
Smallest: 216/360
Largest: 300/360
Subtract smallest from largest:
300/360 - 216/360
84/360
7/30
0.2333
Round off: 0.24
Therefore, the difference between the largest and the smallest fraction is 0.24.
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(quickly!) What is the value of x
The value of x for the given triangle is x = 86°.
What is triangle?
Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C. In Euclidean geometry, any three points that are not collinear determine a singular triangle and a singular plane at the same time.
From the given triangle we have to find the value of x.
By triangle's property.
(x - 45)° + (x + 3)° = (x + 44)°
2x - 42 = x + 44
2x -x = 44 + 42
x = 86°
Hence, the value of x for the given triangle is x = 86°.
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-7/12=1 5/6+d what is d?
Answer:
-3/2
Step-by-step explanation:
[tex]-\frac{7}{12}=1 \frac{5}{6}+d \\ \\ -\frac{7}{12}=\frac{11}{12}+d \\ \\ -7=11+12d \\ \\ -18=12d \\ \\ d=-3/2[/tex]
-14 – x = -21 pls help
Answer:
x = 7
Step-by-step explanation:
Given equation,
→ -14 - x = -21
Now the value of x will be,
→ -14 - x = -21
→ -x = -21 + 14
→ -x = -7
→ [ x = 7 ]
Hence, the value of x is 7.
Answer:
x=7
Step-by-step explanation:
Isolate the variable by dividing each side by factors that dont contain the variable
Determine the degree measure of one angle of a 45-sided regular polygon.
8,100°
7,740°
172°
180°
The measure of one interior angle of the 45-sided polygon is (c) 172 degrees
How to determine the measure of one interior angle?From the question, we have the following parameters that can be used in our computation:
Shape = 45-sided polygon
Parameter to calculate = the measure of one interior angle
The sum of the interior angles is calculated using the following angle formula
The sum of the interior angles = ( n − 2 ) × 180 ∘ where is the number of sides
In this case
n = 45
Substitute the known values in the above equation, so, we have the following representation
The sum of the interior angles = (45 − 2) × 180∘
Evaluate
The sum of the interior angles = 7740∘
So, the internal angle is
Angle = 7740/45
Evaluate
Angle = 172
Hence, the angle is (c) 172 degrees
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Use four of the eight image tiles below to graph the solution to this inequality on the number line. Be sure to cover the entire number line.
To represent an inequality on a number line, such as x>3, first draw a circle around the number. Fill in the circle if the sign also says equal to (or ).
How do you graph an inequality's solution on a number line?To represent an inequality on a number line, such as x>3, first draw a circle around the number.Fill in the circle if the sign also says equal to (or ).Leave the circle blank if the sign doesn't include equal to (> or ).Equation notation, set notation, interval notation, and solution graph are the four ways to display an inequality.Always begin by separating the variable y from the inequality's left side.Step 2: Replace the inequality symbol with the equality symbol.Step 3: In the X, Y, XY, XY plane, graph the boundary line from step 2.The final step is to shade a portion or one side of the boundary line.To learn more about Graphing Linear Inequalities refer to:
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Bruno recorded 2/12 of his new album in
August, 1/3 of his new album in July, and the
rest in June.
What fraction of the album did he record in June?
The fraction of the album he recorded in June is 1/2
How to determine this?When all the fractions of the album will be = 1
Bruno recorded 2/12 was recorded in August
2/12 to the lowest term = 1/6
And 1/3 was recorded in July
So,
The fraction of the rest of the album in June is unknown
Let fraction recorded in June will be = x
x = 1 - 1/6 - 1/3
x = 1/1 - 1/6 - 1/3
x = [tex]\frac{18 - 3 - 6}{18}[/tex]
x = [tex]\frac{9}{18}[/tex]
x = [tex]\frac{1}{2}[/tex] to lowest term
Therefore, he recorded 1/2 of his Album in June
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The probability of rain on Monday is .1. The probability of rain on Tuesday is .8. What is the probability of rain on both Monday and Tuesday?
Answer:
The probability of rain on both Monday and Tuesday is .08, or approximately 8%.
Step-by-step explanation:
The probability of an event occurring on two separate days (such as rain on Monday and Tuesday) is calculated by multiplying the probabilities of the two events occurring separately. In this case, the probability of rain on both Monday and Tuesday is given by:
Probability of rain on Monday * Probability of rain on Tuesday = .1 * .8 = .08
Therefore, the probability of rain on both Monday and Tuesday is .08, or approximately 8%.
It's important to note that this probability assumes that the likelihood of rain on each day is independent of the other day. In other words, the probability of rain on Tuesday does not depend on whether or not it rained on Monday. If this is not the case, the probability of rain on both days may be different.
Eloise practiced piano for 25 of an hour. Sarah practiced piano for 34 of an hour.
Answer:im assuming you need to know the difference and its nine
Step-by-step explanation: 34-25=9
...............................................................
Answer:
a) 53.33 miles per hour
b) 1.7 pages per minute
c)2.25 $ per avocado
Step-by-step explanation:
a) 320/6 = 53.33333
b) 68/40 = 1.7
c) 27 /12 = 2.25
Multiply. Write the answer in simplest form.
4 2/3 x 9/10
Answer:
[tex] 4\frac{1}{5} [/tex]
Step-by-step explanation:
[tex] 4\frac{2}{3} \times \frac{9}{10} [/tex]
[tex] \frac{14}{3} \times \frac{9}{10} [/tex]
[tex] \frac{126}{30} [/tex]
[tex] \frac{21}{5} [/tex]
How do I rewrite “y = -9x² + 18x +0” into vertex form?
Question #8
Cameron read that his favorite NBA team won their game last night by a score of 142 to 124.
Which is true about the digit 2 in each number?
The true statement is that 2 in 142 represents a greater value than 2 in 124 because 142 > 124.
How to identify the place value of a digit in a number?The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol. The place values on the left ofthe decimal point start as ones, tens, hundreds, and so on.
The place value on the right of the decimal point starts from a point and goes to right as tenths, hundredths, and so on.
We are given that encore or points for an NBA Team are usually as whole numbers.
For example, 1, 2, 3, 4, e.t.c. points of an NBA Team are not in decimals or fractions.
The withiner of points awarded for an NBA match is called Discrete because that can be counted with a given amount of time.
Hence, 2 in 142 represents a greater value than 2 in 124 because 142 > 124.
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For 8 Bonus Points, find all the missing angles! You just get them all correct to receive credit. Good Luck!
All angles are:
a = 37
b = 143
c = 37
d = 58
e = 37
f = 53
g = 48
h = 94
k = 96
m = 26
p = 69
r = 111
s = 69
What is sum of angles of a triangle?
A triangle's total angles equal the straight angle (180 degrees, radians, two right angles, or a half-turn) in a Euclidean space. Three angles, one at each vertex and bounded by two neighbouring sides, make up a triangle.
For a very long period, it was unknown if there were any alternative geometries for which the total is different. During the 19th century, this issue had a particularly significant impact on mathematics. Ultimately, it was determined that the response was correct: in other geometries, this total can be higher or smaller, but it must then depend on the triangle. Its deviation from 180° represents an instance of an angular defect and is a crucial distinction for geometric systems.
From the fig.
we know,
e=37
b= 143 (vertically opposite angle)
143 + a = 180 (Linear pair)
a = 180 - 143
a = 37
e = 37
So, c = 37 (Vertically opposite angle)
c + d + 85 = 180 (Sum of angles on straight line)
37 + d + 85 = 180
d = 180 - 122
d = 58
e + 90 + f = 180 (Sum of all angles of a triangle)
37 + 90 + f = 180
f = 180 - 127
f = 53
g = 48 (if two sides are equal , then the two angles opposite to the equal
sides will also be equal.)
48 + 48 + h = 180 (Sum of angles of a triangle)
h = 180 - 96
h = 94
h+ k = 180 (Linear pair)
94 + k = 180
k = 180 - 94
k = 96
d + k + m = 180 (Sum of angles of a triangle)
58 + 96 + m = 180
m = 180 - 154
m = 26
26 + 85 + p = 180 (Sum of angles of a triangle)
p = 180 - 111
p = 69
p + r = 180 (Linear pair)
r = 180 - 69
r = 111
p = s (corresponding angles)
s = 69
Hence all angles are:
a = 37
b = 143
c = 37
d = 58
e = 37
f = 53
g = 48
h = 94
k = 96
m = 26
p = 69
r = 111
s = 69
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$2, 900 is invested in an account earning 6.1% interest (APR), compounded quarterly. Write a function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
Answer: The value of the account after t years can be found using the formula:
Value = 2900 * (1 + 0.0061/4)^(4t)
The annual growth rate, or APR, is 6.1%. When this rate is compounded quarterly, the effective annual growth rate, or APY, is 6.17%, which is the nearest hundredth of a percent.
Therefore, the function showing the value of the account after t years is:
Value = 2900 * (1 + 0.0061/4)^(4t)
And the annual growth rate, or APY, is 6.17%.
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The correct answer is option is a) x^4 – 6x^2 – 27 = 0 , d) 6(2x + 4)2 = (2x + 4) + 2 , e) 6x^4 = -x^2 + 5.
How do you write a quadratic form?
A quadratic equation can be expressed using the formula au^2+bu+c=0. where u is a mathematical expression. In each case, the leading term's exponent is equal to the middle term's exponent multiplied by two.
What is quadratic standard form?
Standard form refers to the quadratic function f(x) = a(x - h)2 + k, where an is not equal to zero. The graph opens either upward or downward depending on the value of a. The vertex is the point, while the line of symmetry is the vertical line x = h.
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The radius of a circle is 8 meters. What is the circle's area?
r=8 m
Use 3.14 for .
Answer:
200.96
Step-by-step explanation:
3.14*r²
so 3.14*8²=200.96
John entered a cross-country ski race. The first part of the race was 14 km long, and he completed it in 1 hour. The second part was 18 km long, and he completed this part in an hour and a half. What was John's average speed for the whole race?
A.
12.8 kilometers per hour
B.
26 kilometers per hour
C.
27.3 kilometers per hour
John's average speed for the whole race would be; 12.8 kilometers per hour
How to calculate the average speed?The first part of the race was 14 km long, and he completed it in 1 hour.
Now, formula for speed is;
Speed = distance/time
Thus, John's speed in the first part of the race would be;
14/1 = 14km/hr
The second part was 18 km long, and he completed this part in an hour and a half. This means that his speed in the second part of the race is;
18/1.5 = 12km/hr
Average speed = Total distance/total time
Total distance for both parts of the race is;
14 + 18 = 32km
Total time for the race is;
1 + 1.5 = 2.5 hours
John's average speed for the whole race would be;
32/2.5 = 12.8 kilometers per hour
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Parking Spaces múltipl
on graphs of linear relationships slope describes the what of a line
Answer: it describe the steepness of the line
Step-by-step explanation:
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Ann is 11 more than two times older than Stacy. If Ann is 59 years old,
solve an equation to determine Stacy's age
The age of Stacy is 24 years old provided the age of Ann is 59 years old.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, Ann is 11 more than two times older than Stacy.
Let the age of Stacy and Ann be s and a respectively, then:
a = 11 + 2s
Substitute a = 59 into the above equation:
59 = 11 + 2s
2s = 59 -11
s = 24
Hence, the age of Stacy is 24 years old provided the age of Ann is 59 years old.
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p+ 1.4 ≤ 0.5; p = 0.1
The inequality expression p + 1.4 ≤ 0.5 is false for p = 0.1
How to determine if the expression is trueFrom the question, we have the following parameters that can be used in our computation:
p + 1.4 ≤ 0.5;
p = 0.1
Substitute p = 0.1 in p+ 1.4 ≤ 0.5;
So, we have the following representation
0.1 + 1.4 ≤ 0.5;
Evaluate the like terms
This gives
1.5 ≤ 0.5;
The above inequality is false
This is because 1.5 is greater than 0.5
Hence, p + 1.4 ≤ 0.5; p = 0.1 is false
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f(x) = -9x+14 g (x) = -3x^2
Answer: Graphed: f(x)=-9x+14gx Answer: =-3x2
Use the given functions to set up and simplify .
Exact Form: x=0,-1/3
Decimal Form: x=0,-0.3
Step-by-step explanation:
A tree is currently 8 feet tall and grows 3 feet per year
a. Model this scenario with an arithmetic sequence in explicit form
b. Rewrite the explicit form of the sequence using function notation
c. How tall will the tree be in 12 years?
Answer:
You have to multiple to get you answer
Step-by-step explanation:
3. Un barco de exploración de aguas profundas está sacando a un buzo a
razón de 25 pies por
minuto. El buzo está a 200 pies bajo el nivel del mar. ¿Qué tan profundo
estaba el buzo
hace 10 minutos?
The diver was 450 feet deep in the water 10 minutes ago.
How deep was the diver 10 minutes ago?Let our D be the depth of the diver 10 minutes ago.
Since diver is pulled out at 25 ft/minute, the depth formula can be written as:
[tex]D - 25t = 200[/tex] where t is the time in minutes.
Substituting t = 10, we have:
[tex]D - 25(10) = 200\\D - 250 = 200\\D = 200 + 250\\D = 450 feet.[/tex]
Translated question "A deep-sea exploration vessel is pulling a diver out to rate of 25 feet per minute. The diver is 200 feet below sea level. How deep was the diver 10 minutes ago?"
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Note that given the speed at which he is being pulled out, the diver was 50 feet about 10 minutes ago.
How is this so?The diver is being pulled out at the rate of 25 feet per minute.
This means that after 10 minutes, he would have been pulled by a total of
25 x 10 = 250 feet.
Since the diver was 200 feet below sea level,
200-250 = -50ft.
hence 10 minutes ago, he was 50 feet below sea level.
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Translation:
A deep-sea exploration vessel is pulling a diver out to rate of 25 feet per minute. The diver is 200 feet below sea level. how deep there was the diver 10 minutes ago?
how to we convince other people that geometric claim is true?
you might want to write an essay on, but it's your choice.
Please help asap!!!!!!
By SAS congruence triangle MLN and triangle OLN are congruent.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Given that, LM≅LO, ∠MLN≅∠OLN.
LM≅LO (Given)
∠MLN≅∠OLN (Given)
LN≅LN (Reflexive property of congruence)
ΔMLN≅ΔOLN (SAS congruence)
∠M≅∠O (CPTC)
MN≅ON (CPTC)
Therefore, by SAS congruence triangle MLN and triangle OLN are congruent.
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The mean amount of time it takes a kidney stone to pass is 14 days and the standard
deviation is 6 days. Suppose that one individual is randomly chosen. Let X=time to pass
the kidney stone. Round all answers to two decimal places.
The probability that an individual will take far longer than 21 days to complete it is 0.12.
What is standard deviation?In the descriptive analysis, the standard deviation is the amount of scatter or dispersal of the pieces of data in relation to their mean. It provides information on the distribution of values within the sample data and serves as a gauge for how widely apart the measured values are from the mean.
As per the information available in the question,
Meantime, μ = 14 days
Standard deviation, ρ = 6 days
Assume the time to pass the kidney stone be x.
The probability that it will take someone more time than 21 days to complete it.
Let's find out the Z-score first,
Z-score = (x - μ)/ρ
Substitute values in above equation,
= (21 - 14)/6
Z-score = 1.166.
The probability that it will take someone more time than 21 days to complete it :
P(x > Z) = P(x > 1.16) = 0.12
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A woman has 8 skirts, 5 blouses, and 5 pairs of shoes. How many different skirt-blouse-shoe outfits can she wear? Any combination
Answer: A woman has 8 skirts, 5 blouses, and 5 pairs of shoes. This means that she has a total of 8 * 5 * 5 = <<855=200>>200 different skirt-blouse-shoe outfits that she can wear.
Step-by-step explanation: To find the number of different skirt-blouse-shoe outfits that a woman can wear, we need to find the total number of combinations of skirts, blouses, and shoes that she has. To do this, we simply multiply the number of skirts that she has by the number of blouses that she has by the number of pairs of shoes that she has. In this case, the woman has 8 skirts, 5 blouses, and 5 pairs of shoes, so the total number of combinations is 8 * 5 * 5 = 200. This means that she can wear 200 different skirt-blouse-shoe outfits.
What is the slope-intercept equation for the linear function represented by the
table?
X
y
O Ay=-¹2-2
OB. y = 2x --2
OC. y =
-2
OD. y = 2x+4
0
-2
2
-1
4
0
6 8
1
2
The linear equation represented in the table is:
y = (1/2)*x - 2
What is the equation of the line in the table?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Remember that if a line goes through two points (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Here we can use the first two points on the table (0, -2) and (2, -1), so we will get:
a = (-1 + 2)/(2 - 0) = 1/2
And because of the point (0, -2) we know that the y-intercept is -2, so we can write:
y = (1/2)*x - 2
The correct option is C.
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Country X had a population of 12 million in 2010. With a population of 15 million in 2022, calculate the country's growth rate.
Round your answer to four decimal places
Use A = Pert
[tex]A=Pe^{rt} \\ \\ 15000000=10000000e^{12r} \\ \\ 1.5=e^{12r} \\ \\ \ln(1.5)=12r \\ \\ r=\frac{\ln(1.5)}{12} \\ \\ r \approx \boxed{0.0338}[/tex]
The exponential growth rate of the population of the country is given by the relation r = 1.8595 %
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the initial population of the country in 2010 be = 12 million
Let the final population of the country in 2022 = 15 million
Now , let the growth rate be represented as r
And , growth rate r = [ ln( final population - ln (initial population ) / no of years ] x 100
Growth Rate = (ln(15 ) - ln(12 )) / (2022 - 2010)
r = (2.70805 - 2.48491) / 12
r = 0.018595
r = 1.8595 %
Hence , the growth rate r = 1.8595 %
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