Step-by-step explanation:
We have,
[tex]\dfrac{20}{31}[/tex]
Show that [tex]\dfrac{20}{31}[/tex] is closer 66 % or 75 %.
∴ The percentage of [tex]\dfrac{20}{31}[/tex]
= [tex]\dfrac{20}{31}\times 100[/tex]
= [tex]\dfrac{2000}{31}[/tex]
= 64.516 %
≈ 66 %, shown.
Because the percentage of [tex]\dfrac{20}{31}[/tex] is 66 percent (%).
Thus, [tex]\dfrac{20}{31}[/tex] is closer 66 percent (%) , shown.
The fraction 20/31 is closer to 66%.
To determine which percentage 20/31 is closer to, we first need to convert the percentages into fractions and then compare them with 20/31.
66% can be written as a fraction as 66/100. Simplifying this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 2 in this case:
[tex]\[ \frac{66}{100} = \frac{66 \div 2}{100 \div 2} = \frac{33}{50} \][/tex]
Further simplifying by dividing both by 11, we get:
[tex]\[ \frac{33}{50} = \frac{33 \div 11}{50 \div 11} = \frac{3}{5} \][/tex]
75% as a fraction is 75/100. Simplifying this fraction by dividing both the numerator and the denominator by 25, we get:
[tex]\[ \frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4} \][/tex]
Now we compare the fraction 20/31 with 3/5 and 3/4. To compare these fractions, we can find a common denominator or convert them to decimal form.
Converting to decimal form:
[tex]\[ \frac{20}{31} \approx 0.645 \] \[ \frac{3}{5} = 0.6 \] \[ \frac{3}{4} = 0.75 \][/tex]
Now we can see that 0.645 is closer to 0.6 than it is to 0.75. Therefore, 20/31 is closer to 66% (or 3/5) than it is to 75% (or 3/4).
Alternatively, we could also cross-multiply to compare the fractions directly:
For 20/31 and 3/5:
[tex]\[ 20 \times 5 = 100 \] \[ 31 \times 3 = 93 \][/tex]
Since 100 is greater than 93, 20/31 is greater than 3/5, but not by much.
For 20/31 and 3/4:
[tex]\[ 20 \times 4 = 80 \] \[ 31 \times 3 = 93 \][/tex]
Since 93 is much greater than 80, 20/31 is less than 3/4 by a larger margin than its difference with 3/5.
Thus, by both methods, we conclude that 20/31 is closer to 66%.
An architect plans to buy 5 stone spheres and 3 stone cylinders. For the same amount, she can buy 2 stone spheres and 6 stone cylinders. If one stone cylinder costs $36.81, how much does each stone sphere cost?
The cost of each stone sphere is $ 36.81
Solution:
Given that,
An architect plans to buy 5 stone spheres and 3 stone cylinders
For the same amount, she can buy 2 stone spheres and 6 stone cylinders
Let "x" be that same amount
Let "a" be the cost of each stone sphere
Cost of each stone cylinder = $ 36.81
Therefore,
x = 5 stone spheres and 3 stone cylinders
x = 5a + 3(36.81)
Similarly,
x = 2 stone spheres and 6 stone cylinders
x = 2a + 6(36.81)
Equate both,
[tex]5a + 3(36.81) = 2a + 6(36.81)\\\\5a + 110.43 = 2a + 220.86\\\\5a - 2a = 220.86 - 110.43\\\\3a = 110.43\\\\a = 36.81[/tex]
Thus cost of each stone sphere is $ 36.81
By setting up and solving equations based on the given scenarios, we find that the cost of each stone sphere is also $36.81, the same as one stone cylinder.
Explanation:Let's denote the cost of one stone sphere as S and the cost of one stone cylinder as C. We know one stone cylinder costs $36.81. We are given two scenarios involving the purchase of stone spheres and cylinders with equal total cost. In the first scenario, 5 stone spheres and 3 stone cylinders are bought, and in the second, 2 stone spheres and 6 stone cylinders are purchased.
Formulating these scenarios into equations gives us:
5S + 3C = 2S + 6CConsidering C = $36.81Substituting the value of C into the equation simplifies it to:
5S + 3(36.81) = 2S + 6(36.81)
Simplifying further:
5S + 110.43 = 2S + 220.86
Subtracting 2S and 110.43 from both sides results in:
3S = 110.43
Dividing both sides by 3 gives:
S = $36.81
Therefore, each stone sphere also costs $36.81.
The farmer looks out in the barnyard and Cesar pigs and the chickens. He says to his daughter, “ I count 40 heads in 100 feet. How many pigs and how many chickens are out there?”
Answer:
There are 10 pigs and 30 chickens
Step-by-step explanation:
Let the number of pigs be x
let the number of chickens be y
Then there are 40 heads . So the total number of pigs and chickens is 40
x + y = 40-----------------------(1)
We know that pigs have 4 legs and chickens have 2 legs
4x + 2y = 100----------------------(2)
Solving (1) and (2)
multiply (1) by 2
2x + 2y = 80-------------------------(3)
subtract (3) from (2)
4x + 2y = 100
2x + 2y = 80
----------------------------
2x = 20
----------------------------
[tex]x = \frac{20}{2}[/tex]
x = 10
Now Substituting x in (1), we get
10 + y = 40
y = 40 - 10
y = 30
A bag contains colored marbles. The ratio of red marbles to blue marbles is 1 : 4. The ratio of blue marbles to yellow marbles is 2 : 5. What is the ratio of red marbles to yellow marbles?
Final answer:
To find the ratio of red to yellow marbles, given the ratios of red to blue and blue to yellow, we equalize the blue part of both ratios and combine them, resulting in a red to yellow ratio of 2:5.
Explanation:
The question concerns finding the ratio of red marbles to yellow marbles given the ratios of red to blue marbles and blue to yellow marbles. To solve this, we use the given ratios: the ratio of red marbles to blue marbles is 1 : 4, and the ratio of blue marbles to yellow marbles is 2 : 5. Firstly, we make the number of blue marbles consistent in both ratios by finding a common value. Multiplying the first ratio by 2 gives us red to blue as 2 : 8, and keeping the second ratio as is (blue to yellow as 2 : 5), we can now combine these to find the ratio of red marbles to yellow marbles. The red to yellow ratio, through the intermediary blue, becomes 2 : 5.
Elsa can type 75 words per minute on a Keyboard
Elsa's rate of typing = 1.25 words per sec
Time is taken for typing each word = 0.8 a
What is unitary method used?It is a method of solving by finding the value of one unit and the calculating the value of given unit by multiplying with the single value.
Step by step calculationNumbers of words Elsa can type in 1 minute(the 60s) = 75
Numbers of words Elsa can type in one second = 75/60
∴ Rate of typing = 1.25 words per sec
Time is taken to type one word = 60/75
= 0.8 sec
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How many square inches of wrapping paper will he need?
Graph the inequality x < 6
Please someone help now :(
Step-by-step explanation: To graph x < 6 on a number line, we start with an open dot at +6. The reason we use an open dot at +6 is that x is less than +6 but it is not equal to +6. Next we drawn an arrow going to the left to show that all numbers less than +6 are solutions to this inequality.
Image is attached below.
the base of parellogram is twice its height . if the area is 648msq find its base and height
Answer:
h=18m, b=2m
Step-by-step explanation:
Let the base be b and height be h
Condition 1:
b=2h ----(1)
Condition 2:
Area=b*h
b*h=648 -----(2)
Putting (1) into (2)
2h*h=648
2h^2=648
Dividing both sides by 2
h^2=324
Taking sq root on both sides
h=18 m
Now
Putting value of h in eq (1)
b=2(18)
b=36 m
prove the identity cos(x-y)-cos(x+y)=2sinx siny
Answer:
see explanation
Step-by-step explanation:
Using the Addition/ Subtraction formulae for cosine
Consider the left side
cos(x - y) - cos(x + y)
= cosxcosy + sinxsiny - (cosxcosy - sinxsiny) ← distribute
= cosxcosy + sinxsiny - cosxcosy + sinxsiny ← collect like terms
= 2sinxsiny = right side ⇒ proven
what is the twin prime conjecture?
Answer:
It is a prime number which is either 2 less or 2 more than another prime number
Step-by-step explanation:
Final answer:
The twin prime conjecture posits the existence of an infinite number of twin prime pairs, which are pairs of prime numbers that are two units apart.
Explanation:
The twin prime conjecture is an unsolved question in mathematics that relates to the distribution of prime numbers. It specifically addresses the existence of pairs of primes that are only two numbers apart, such as (11, 13), (17, 19), and (41, 43), which are known as twin primes. The conjecture proposes that there are an infinite number of these twin prime pairs, even though prime numbers themselves become less frequent as numbers increase. Despite many efforts, a definitive proof of this conjecture has not yet been found.
Miss Jacobs purchase 10.2 ounces of candy for her class. Each student gets 0.85 ounces. Right and solve an equation to determine how many students are in Miss Jacobs class.
Answer:
There are 12 students in Miss Jacobs class.
Step-by-step explanation:
Divided 10.2 and 0.85
If you check your answer. 0.85 multiplied by 12 is 10.2
A prism, bases of which are equilateral triangles, circumscribes a sphere of radius 6. What is the volume of the prism?
Answer:
1296√3 cubic units
Step-by-step explanation:
The volume of the prism will be the product of its base area and its height. Since it circumscribes a sphere with diameter 12, that is the height of the prism.
The central cross section of the sphere is a circle of radius 6, and that will be the size of the incircle of the base. That is, the base will have an altitude of 3 times that incircle radius, and an edge length of 2√3 times that incircle radius. Hence the area of the triangular base is ...
B = (1/2)(6×2√3)(6×3) = 108√3 . . . . . square units
The volume of the prism is then ...
V = Bh = (108√3)(12) = 1296√3 . . . cubic units
_____
Comment on the geometry
The centroid of an equilateral triangle is also the incenter and the circumcenter. The distance of that center from any edge of the triangle is 1/3 the height of the triangle. So, for an inradius of 6, the triangle height is 3×6 = 18. The side length of an equilateral triangle is 2/√3 times the altitude, so is 12√3 units for this triangle.
Choose the correct simplification of (xy2z)3.
xy2z3
x3y6z3
x3y8z3
x4y5z4
Answer:
[tex]x^3y^6z^3[/tex]
Step-by-step explanation:
we have
[tex](xy^2z)^3[/tex]
Applying the property of exponents
[tex](x^m)^n=x^{m*n}[/tex]
[tex](xy^2z)^3=(x^3)(y^2)^3(z^3)=x^3y^{2*3}z^3=x^3y^6z^3[/tex]
The correct simplification of [tex]\((xy^2z)^3\) is \(x^3y^6z^3\).[/tex]
To simplify the expression [tex]\((xy^2z)^3\),[/tex] you need to raise each component within the parentheses to the power of 3.
[tex]\(x^3\)[/tex] represents \(x\) raised to the power of 3, [tex]\(y^{2 \times 3}\)[/tex] represents [tex]\(y^6\)[/tex] (since you multiply the exponents when raising a power to a power), and [tex]\(z^3\)[/tex]represents \(z\) raised to the power of 3.
So, [tex]\((xy^2z)^3\) simplifies to \(x^3y^6z^3\).[/tex]
The given options are:
[tex]a) \(x^3y^3z^3\)\\b) \(x^3y^6z^3\)\\c) \(x^3y^8z^3\)\\d) \(x^4y^5z^4\)[/tex]
Comparing the simplified expression [tex]\(x^3y^6z^3\)[/tex] with the options, the correct answer is option (b) [tex]\(x^3y^6z^3\).[/tex]
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A rectangle has a perimeter of 25 meters. If the lengths of the sides of the rectangle are multiplied by 7 to make a new rectangle, what is the perimeter of the new rectangle?
Answer:
175 m
Step-by-step explanation:
We are given;
The perimeter of a rectangle as 25 mWe are required to determine the new perimeter if the sides of the rectangle are multiplied by 7.
We know that;
Perimeter of a rectangle = 2(L+W)
Therefore, initially;
2(L+W) = 25 m
Hence;
L + W = 12.5 m
if the sides are multiplied by 7, then;
New length = 7L
New Width = 7W
Thus;
New perimeter = 2(7L+7W)
= 14 (L + W)
but, L + W = 12.5
Thus;
New perimeter = 14 (12.5)
= 175 m
Therefore, the new perimeter will be 175 m
Answer:
The answer to the problem is 175
Step-by-step explanation:
(6x10^-6) (5.2x10^4 scientific notation
Step-by-step explanation:
[tex](6 \times {10}^{ - 6} )(5.2 \times {10}^{4} ) \\ = 6 \times 5.2 \times {10}^{ - 6} \times {10}^{4} \\ = 31.2 \times {10}^{4 - 6} \\ = 31.2 \times {10}^{ - 2} \\ = 0.312 \\ = 3.12 \times {10}^{ - 1} [/tex]
What is
2x-3y=-19
4x+3y=7
URGENT
Solve by elimination.
2x-3y=-19
+(4x+3y=7)
-----------------
6x=-12
x=-2
2(-2)-3y=-19
-3y=-15
y=5
Intersection Point: (-2,5)
please answer this, and HURRY I am giving away 20points.
Question: What is the measure of angle DBA?
____Degrees
Answer:
132
Step-by-step explanation:
65+67=132 || 180-132=48 || 180-48=132
Answer:
132 Degrees.
Step-by-step explanation:
The interior of any triangle is 180 degrees.
Solve for angle DBC
65 + 67 = 132
180 - 132 = 48 degrees
Since the sum of DBA and DBC is 180, and we already know what 180 - 48 is, there you have it.
0.230769231 as a fraction
Final answer:
To express 0.230769231 as a fraction, the numerator is 230769231 and the denominator is 10^9.
Explanation:
To express the decimal 0.230769231 as a fraction, we need to determine the numerator and denominator. The numerator is the decimal without the decimal point, which is 230769231. The denominator is based on the number of decimal places, which is 9 because there are 9 digits in the decimal part. Therefore, the fraction is 230769231/10^9.
Question 3
Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR) of
4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment?
$104.54
$378.21
$450.71
$1225.56
Answer:
The monthly payment, PMT = $450.71
Therefore the correct option is C.) $450.71
Step-by-step explanation:
i) Value of Loan, or Present value, PV = 24000
ii) Annual percentage rate , APR = 0.048
iii) number of periods, n = 12
iv) periodic interest, R = APR / n = 0.048 / 12 = 0.004
v) number of years, t = 5
v) Monthly Payment, PMT = [tex]\frac{PV\times R}{1 - (1 + R)^{(-1\times n \times t})} = \frac{24000 \times 0.004}{1 - ( 1 + 0.004)^{-60}}[/tex] = $450.71
Henry’s disability insurance pays 70% of his salary for up to 26 weeks if his salary is $450 and he is disabled for 20 weeks how much disability will he get?
Answer:
$1575
Step-by-step explanation:
70 % of his salary is 0.7 X 450 = 315
He gets it for 20 weeks
presuming the salary is monthly.
You do 315 X 5 = 1575 20 /4 = 5 months
The population of a species of fish in a river increased by a factor of 1.05 every day for the amount of days shown in the graph. The function shows the number of fish in the river f(x) after x days:
f(x) = 100(1.05)x
Answer: C: 0 < x < 31
Step-by-step explanation: Because the < sign shows the line is going up towards the top. It starts from 0 and travels to the top-right to 31
A reasonable domain for this function to have would be 0 ≤ x ≤ 31.
How to solve for the domain of the functionWe have f(x) as the number of fishes that are present in this water. The month is October and October has 31 days.
The x values is the maximum of the number of days in October. The minimum value is given as 0 because it is the population in the beginning of the month.
Hence we have 0 ≤ x ≤ 31
Complete questionWhich of the following is a reasonable domain for the function?
0 ≤ x ≤ 100
0 ≤ x ≤ 31
All positive integers greater than 100
All positive integers less than 100
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Find two nontrivial functions f(x) and g(x) so that f(g(x)) = (-6-3x)^6
Two nontrivial functions f(x) and g(x) that satisfy the equation f(g(x)) = (-6-3x)^6 are f(x) = x^6 and g(x) = -6 - 3x. These functions were found by assigning the inner function to g(x) and the outer function to f(x).
Explanation:Looking at the expression [tex]f(g(x)) = (-6-3x)^6[/tex], we can see that it is a composition of two functions. A possible way to choose the functions f(x) and g(x) is to let g(x) be the inner function and f(x) be the outer function.
Let's choose g(x) = -6 - 3x. This function linearly transforms the input x. Now, let's choose the function [tex]f(x) = x^6[/tex]. This function takes any input (including results from the g(x) function) and raises it to the power of 6.
So, when we apply g to x (g(x)) and then f to the result (f(g(x))), we get the original equation[tex]f(g(x)) = (-6-3x)^6[/tex]. Therefore, the two nontrivial functions f(x) and g(x) that satisfy the equation are f(x) = x^6 and g(x) = -6 - 3x.
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A store offers a discount of 30 % on all refrence of books. If a dictionary cost $12 before the discount what is the dollar amount of the discount.
Answer:
3.6
Step-by-step explanation:
30%×12= 3.6
30%=0.3
find the rule solve for n please help me
Answer:
Your answer is 9
Step-by-step explanation:
the answer is nine because if you look at the pattern, every number to the left is times 3 to the right. For example, 4 to 12 is times 3. this would work for n because 9x3 equals 27. the rule is times three.
Does 27/8 equal 2 7/8
No if you simplify 27/8 it equals 3 3/8.
Fill in the missing angle measures
Yo sup??
by angle sum property we know that the sum of all angles in a triangle is 180
let the unknown angle be x
then,
x+60+90=180
x=180-150
x=30
Hope this helps
The sum of the angles of a triangle is 180°.
The angle measures you know are 60° and 90° (because the box in the top right corner of the triangle means that it is a right angle, which equals 90°). So you can do this to find the missing angle:
60° + 90° + ? = 180° Add 60 and 90
150° + ? = 180° Subtract 150 on both sides
? = 30° The missing angle is 30°
Graph f(x)=3sin(12x)−5 . Use 3.14 for π .
Answer:
see attached
Step-by-step explanation:
The given function is a vertical expansion of the sine function by a factor of 3 and a translation downward by 5 units.
It will oscillate between -8 and -2, with a midline at y = -5. The multiplier 12 indicates the period of the function will be 2π/12 = π/6 ≈ 0.5233... for the given value of π.
A graphing calculator is a useful tool for creating the graph.
Answer:
Step-by-step explanation:
took the test
Find the volume of each figure
solve x+3y=-28
y=-5x using substitution
Answer:
Step-by-step explanation:
x + 3y = - 28
y = -5x
x + 3(-5x) = -28
x -15x = -28
-14x=-28
x=2
y = -5(2)
y=-10
Kelly read 40% of a novel, and she now has 108 pages left. How many pages does the novel have?
Answer:
The novel has 180 pages.
Step-by-step explanation:
108 pages is 60% of the novel.
108 / 3 = 36.
20% of the novel is 36 pages.
36 * 5 = 180 pages
Mark is in training for a marathon race. He has been training by running 10 miles each day. He will
be increasing his running by this weekly formula: y = 10 (1.1), where y is the number of miles he
will run each day, x weeks from now.
What is the value of y if x = 0?
Round to the nearest mile.
Answer:
For x = 0, the value of y will be 10 miles.
Step-by-step explanation:
Mark is in training for a marathon race. Each day he runs 10 miles for this training purpose. He will be increasing his running by this weekly formula: [tex]y = 10(1.1)^{x}[/tex], where y is the number of miles he will run each day, x represents the number of weeks from now.
Now, for x = 0, the value of y will be [tex]y = 10(1.1)^{0} = 10[/tex] miles. (Answer)
Answer:
The Value of y is 10
Step-by-step explanation: