Answer:
37.5% are male
62.5% are female
Step-by-step explanation:
in total 120 teachers (45 male+75 female)
therefore:
for male
120 - 100%
45 - x% (we need to find x)
by using the butterfly method (or cross multiply) we get:
120x=100*45
x=4500/120=37.5% (male teachers)
we do the same for female but instead of using 45 we will use 75(the quantity of female theachers in school)
120x=100*75
x=7500/120=62.5%
Find the percentage of: 21% of 18 use a set of fraction operations method to find the percentage.
Answer:
4.8%
Step-by-step explanation:
21% of 18
following the BODMAS rule, OF means multiplication
and also this sign% always means 100
so,it will be 21/100 * 18/1
this a laptop so i cant put it in a fraction way.....okay
this is how it shows...21/100 * 18/1
lets divide....
21/100 * 18/1
we will use 2 to divide
2 in 100=50
2 in 18=9
so it will be 21/50 * 9/1
nothing can divide so we will multiply
21*9/50*1
189/50=3.78≈4.8%
HELP ME!!! Why is it possible to isolate the variable, x, in the equation 2x = 20 by using either the division property of equality or the multiplication property of equality?
Answer: Because division is the inverse of multiplication.
Step-by-step explanation:
By multiplying the equation 2x=20 by 1/2 you will be able to eliminate the x variable,
For example,
1/2 * 2x = 20*1/2
x= 10
The same way if you divide both sides of the equation 2x=20 by 2 you will be able to to eliminate the x variable.
For example
2x = 20 Divide both sides by 2
x= 10
As you can see 2 is the division inverse of 1/2.
A square window in Miranda's house has an area of 255 in2 (squared). What is the perimeter of the window?
Answer:
If you meant the area was 255 in²:
Perimeter is [tex]4\sqrt{255}[/tex], or around 63.89 in.
If you meant that the area was 225 in²:
Perimeter is 60 in
Step-by-step explanation:
If you meant the area was 255 in²:
If we have a square with an area of 255 in², then it's side length will be [tex]\sqrt{255}[/tex] inches long, since the area of a square is [tex]l^2[/tex], where l is the length.
Since [tex]\sqrt{255}[/tex] doesn't return a rational number, we'll leave it as [tex]\sqrt{255}[/tex].
Now that we know the side length, the perimeter of a square is represented as [tex]4l[/tex], where l is the length.
We know the length is [tex]\sqrt{255}[/tex], so we can multiply this by 4.
[tex]4\sqrt{255}[/tex]. This is the simplest it gets.
If you meant the area was 225 in²:
Following the same concept as again:
Length: [tex]\sqrt{225} = 15[/tex]
Perimeter: [tex]4\cdot15=60[/tex] in
Hope this helped!
Answer:
P = 63.87 in
Step-by-step explanation:
area of a square window = 255 in²
find perimeter of the window.
A = s²
255 = s²
s = 15.97 in.
perimeter = 4 * s
P = 4 (15.97)
P = 63.87 in
gage bought a new car for $29000 to use while he is away at college. The car decreases in value by 11% annually. What would the cars value after 4 years?
The value of the gauge car after 4 years will be $18195.25.
What is compound interest?Compound interest is applicable when there will be a change in principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
Given,
Principle amount (P) = $29000
Rate of decrement (R) = 11%
Time period(T) = 4 years
Percentage decrement over T time period is given by
Final amount = P[tex][1 - R/100]^{T}[/tex]
Final amount = 29000[tex][1 - 11/100]^{4}[/tex]
Final amount = 29000(0.89)⁴
Final amount = $18195.25.
Hence, The value of the gauge car after 4 years will be $18195.25.
For more information about compound interest,
brainly.com/question/26457073
#SPJ5
The value of the car after 4 years is $18195.24989.
Given,
Gage bought a new car for $29000 to use while he is away at college.
The car decreases in value by 11% annually.
We need to find what would the cars value after 4 years.
we have,
Cost of the car = $29000
The car decreases annually by = 11%
1st-year decrease.
$29000 x 11/100 = $3190
The cost of the car after 1st year = $29000 - $3190 = $25810
2nd-year decrease.
$25810 x 11/100 = $2839.1
The cost of the car after 2nd year = $25810 - $2839.1 = $22970.9
3rd-year decrease.
$22970.9 x 11/100 = $2526.799
The cost of the car after 3rd year = $22970.9 - $2526.799 = $20444.101
4th-year decrease.
$20444.101 x 11/100 = $2248.85111
The cost of the car after 4th year = $20444.101 - $2248.85111 = $18195.24
Thus the value of the car after 4 years is $18195.24989.
Learn more about the value of a product after an annual decrease here:
https://brainly.com/question/28231393
#SPJ2
Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = <10,0>, V = <0,-9>
Answer:
Orthogonal.
Step-by-step explanation:
Given:
u = <10, 0>
v = <0, -9>
In unit vector notation, the above vectors can be re-written as:
u = 10i + 0j
v = 0i - 9j
Now, note the following:
(i) two vectors, u and v, are parallel to each other if one is a scalar multiple of the other. i.e
u = kv
or
v = ku
for some nonzero value of a scalar k.
(ii) two vectors are orthogonal if their dot product gives zero. i.e
u . v = 0
Let's use the explanations above to determine whether the given vectors are parallel or orthogonal.
(a) If parallel
u = k v
10i + 0j = k (0i - 9j) ?
When k = 1, the above equation becomes
10i + 0j ≠ 0i - 9j
When k = 2,
10i + 0j ≠ 2(0i - 9j)
10i + 0j ≠ 0i - 18j
Since we cannot find any value of k for which u = kv or v = ku, then the two vectors are not parallel to each other.
(b) If Orthogonal
u.v = (10i + 0j) . (0i - 9j)
[multiply the i components together, and add the result to the multiplication of the j components]
u.v = (10i * 0i) + (0j * 9j)
u.v = (0) + (0)
u.v = 0
Since the dot product of the two vectors gave zero, then the two vectors are orthogonal.
At $15 per square foot, the cost of installing flooring in a room with these dimensions a.$121.50 b.$1215.00 c.$1290.00 d.$81
Answer:
b. $1215.00
Step-by-step explanation:
The area of the room can be figured any of several ways. One easy way is to figure the area of the enclosing 8 ft by 12 ft rectangle, then subtract area of the 3 ft by 5 ft cutout at upper left.
A = (8 ft)(12 ft) - (3 ft)(5 ft) = (96 -15) ft^2 = 81 ft^2
At a cost of $15 for each square foot, the installed flooring will cost ...
($15 /ft^2)(81 ft^2) = $(15·81) = $1215
Enter the mixed number as an improper fraction. 1 5/6 =
Answer:
11/6
Step-by-step explanation:
To find the improper fraction
Take the denominator times the whole number
6*1 = 6
Add the numerator
6+5 =11
Put this over the denominator
11/6
Answer:
[tex]\frac{11}{6}[/tex]
Step-by-step explanation:
What is 1 5/6 as an improper fraction?
If you wanna make 1 5/6 as a improper fraction, you must take the 5 from 1 5/6 and add it 6.
[tex]6+5=11[/tex]
[tex]\frac{11}{}[/tex]
Since the denominator is 6, you will put it down.
[tex]\frac{11}{6}[/tex]
So now you got your answer!
Hope this Helps!
Evaluate 9/g+2h+5
when g=3 and h=6
Answer:
20
Step-by-step explanation:
[tex] \frac{9}{g} + 2h + 5 \\ = \frac{9}{3} + 2 \times 6 + 5 \\ = 3 + 12 + 5 \\ = 20[/tex]
At present the sum of Geetha's age and her daughter's age is 44 years. After 2 years, Geetha's age will be three times that of her daughter's age. Find their present ages.
Answer:
Geetha is 32.5 years old
her daughter is 11.5 years old
Step-by-step explanation:
sum of their ages is 44 years
G + D = 44
in two years, Geetha's age is 3 times her daughters age. (to find present age, subtract 2)
G = 3D - 2
substitute
(3D - 2) + D = 44
combine like terms
4D - 2 = 46
4D = 46
D = 11.5
plug in D to either equation
G + (11.5) = 44
G = 32.5
G = 3(11.5) - 2
G = 32.5
help :/ ill give brainly :>
Answer:
A. Trapezoid
B. Isoclese triangle
c. Equilateral triangle
d. Kite
Answer:
A, Parallelogram (more specifically a trapezoid)
B. Isosceles Triangle
C. Equilateral Triangle
D. Kite
victor needs 30 feet of rope. the rope he want to buy is sold by the yard. he know that there are 3 feet in the 1 yard. how many yards should he buy?
Answer: 10 yards
Step-by-step explanation:
Covert 30 feet into yards to find how many yards he should buy.
[tex]\frac{30}{3} = \frac{x}{1}[/tex] Solve by cross product
3x = 30
x = 10
In the figure below, one side of the right triangle is a diameter of the semicircle.
10 units
6 units
8 units
What is the approximate total area of the shaded part of the figure?
Answer:
Option (A)
Step-by-step explanation:
One side of the given triangle is a diameter of the semicircle given.
Measure of the diameter = 10 units
Total area of the semicircle = [tex]\frac{1}{2}\pi (r^{2})[/tex]
= [tex]\frac{1}{2}\pi (5)^2[/tex]
= 39.27 square units
Area of the right triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(6)(8)[/tex]
= 24 square units
Area of the shaded region = Area of the semicircle - Area of the right triangle
= 39.27 - 24
= 15.27 square units
≈ 15 square units
Therefore, option (A) will be the answer.
is 0.987987 repeating rational or irrational
Answer:
is repeating rational
really need help solving this problem
Answer:
y = 8
Step-by-step explanation:
[tex] \frac{y}{4} = \frac{5 + 5}{5} \\ \\ \frac{y}{4} = \frac{10}{5} \\ \frac{y}{4} = 2 \\ y = 4 \times 2 \\ y = 8[/tex]
Integrated math ll I need help ASAP PLEASE
Greetings from Brasil...
We have 2 conditions:
1 - angles opposed by the vertex - the angles are equal
2 - supplementary angles - the sum of the two angles results in 180
2:
(4X + 15) and (5X + 30) are supplementary angles, so:
(4X + 15) + (5X + 30) = 180
9X = 180 - 15 - 30
9X = 135
X = 151:
(3Y + 15) and (5X + 30) are angles opposed by the vertex, so they are equal
3Y + 15 = 5X + 30
3Y = 5X + 30 - 15
3Y = 5X + 15 above we have already calculated the value of X
3Y = 5.(15) + 15
3Y = 75 + 15
3Y = 90
Y = 90/3
Y = 30Which expression is equivalent to (StartFraction 125 squared Over 125 Superscript four-thirds Baseline EndFraction? StartFraction 1 Over 25 EndFraction One-tenth 10 25
Answer:
[tex]\frac{125^2}{125^\frac{4}{3}} = 25[/tex]
Step-by-step explanation:
Given
[tex]\frac{125^2}{125^\frac{4}{3}}[/tex]
Required
Find an equivalent expression
[tex]\frac{125^2}{125^\frac{4}{3}}[/tex]
Apply the following law of indices;
[tex]\frac{a^m}{a^n} a^{m-n}[/tex]
The expression becomes
[tex]125^{2-\frac{4}{3}}[/tex]
Solve the exponents
[tex]125^{\frac{6-4}{3}}[/tex]
[tex]125^{\frac{2}{3}}[/tex]
Express 125 as 5³
[tex]5^{3^*\frac{2}{3}}[/tex]
Solve the exponents
[tex]5^2[/tex]
[tex]25[/tex]
Hence;
[tex]\frac{125^2}{125^\frac{4}{3}} = 25[/tex]
Answer:
d
Step-by-step explanation:
i just took it! edgen
Two friends went fishing on a lake. One friend’s lure went 23 feet below the lake’s surface, while the other friend’s lure sank to a depth of 81 feet below the surface. What was the difference in the depths of the lures?
Answer:
58 feet
Step-by-step explanation:
Find the difference by subtracting 23 from 81.
81 - 23
= 58 feet
Suppose the equation of line p is x = 2 and the equation of line q is x = –1. What translation is equivalent to (Rp ∘ Rq) (ΔABC)?
Answer:
T(6,0)
Step-by-step explanation:
Reflection across two parallel lines results in translation by double the distance between them. Assuming this means ...
Rp(Rq(∆ABC))
the translation is to the right by 6 units.
_____
The attached figure shows the reflections we understand to be indicated by the notation (Rp ∘ Rq) (ΔABC).
Answer:
above
Step-by-step explanation:
Christine is typing at a rate of 75 words per
minute. Paula is typing at twice Christine's
speed. If together they need to transcribe a 2000
word paper which of the following expressions
would illustrate the time in minutes, x, it would
take for them to do so.
A) 150
2000X
75
150
B)
+
= 2000
C) 150 + 75 =
2000
2000
D) x =
(150+75)
Answer:
X = 2000 / (75 + 150)
Step-by-step explanation:
Given the following :
Christine's typing rate = 75 words per minute
Paula's speed = 2 times Christine's speed
If 2000 words needs to be transcribed. The time taken in minute 'x' will be :
From the relation :
Time = distance / speed
Distance here is the number of words in the document
Christine's speed = 75 words per minute
Paula's speed = 150 words per minute
Combined speed per minute = 150 + 75 = 225 words per minute
Time taken (x) = 2000 / 225
X = 2000 / (75 + 150)
Two straight edges of a pizza slice meet at an angle of 30°. If the pizza has a radius of 12
inches, what is the area of the slice and how long is its crust? Show how you got your answer step-by-step.
Answer:
area of the slice: A = 12π in² ≈ 37.7 in² lenght of its crust: L = 24π in ≈ 6.28 inStep-by-step explanation:
R = 12 in
360°:30° = 12
so the area of the slice is ¹/₁₂ of whole pizza
A = ¹/₁₂•πR² = ¹/₁₂•π•12•12 = 12π in² ≈ 37.7 in²
Crust is the perimeter of pizza so crust of the slice is ¹/₁₂ of the perimeter:
L = ¹/₁₂•2πR = ¹/₁₂•2π•12 = 2π in ≈ 6.28 in
On her first quiz in social studies,Meg answered 92% of the questions correctly.On her second quiz,she answered 27 out of 30 questions correctly. On which quiz did Meg have the better score?
Answer:
on her first quiz
Step-by-step explanation:
27/30=
27÷30=
0.9=
09×100/100=
0.9×100%=
(0.9×100)% =
90%
Answer:
first quiz
Step-by-step explanation:
100 divided by 30 times 27<92%
Please someone help me...
Step-by-step explanation:
First factor out the negative sign from the expression and reorder the terms
That's
[tex] \frac{1}{ - (( \tan(2A) - \tan(6A) )} - \frac{1}{ \cot(6A) - \cot(2A) } [/tex]
Using trigonometric identities
That's
[tex] \cot(x) = \frac{1}{ \tan(x) } [/tex]Rewrite the expression
That's
[tex]\frac{1}{ - (( \tan(2A) - \tan(6A) )} - \frac{1}{ \frac{1}{ \tan(6A) } } - \frac{1}{ \frac{1}{ \tan(2A) } } [/tex]
We have
[tex] - \frac{1}{ \tan(2A) - \tan(6A) } - \frac{1}{ \frac{ \tan(2A) - \tan(6A) }{ \tan(6A) \tan(2A) } } [/tex]Rewrite the second fraction
That's
[tex] - \frac{1}{ \tan(2A) - \tan(6A) } - \frac{ \tan(6A) \tan(2A) }{ \tan(2A) - \tan(6A) } [/tex]Since they have the same denominator we can write the fraction as
[tex] - \frac{1 + \tan(6A) \tan(2A) }{ \tan(2A) - \tan(6A) } [/tex]
Using the identity
[tex] \frac{x}{y} = \frac{1}{ \frac{y}{x} } [/tex]Rewrite the expression
We have
[tex] - \frac{1}{ \frac{ \tan(2A) - \tan(6A) }{1 + \tan(6A) \tan(2A) } } [/tex]Using the trigonometric identity
[tex] \frac{ \tan(x) - \tan(y) }{1 + \tan(x) \tan(y) } = \tan(x - y) [/tex]Rewrite the expression
That's
[tex] - \frac{1}{ \tan(2A -6A) } [/tex]Which is
[tex] - \frac{1}{ \tan( - 4A) } [/tex]Using the trigonometric identity
[tex] \frac{1}{ \tan(x) } = \cot(x) [/tex]Rewrite the expression
That's
[tex] - \cot( - 4A) [/tex]Simplify the expression using symmetry of trigonometric functions
That's
[tex] - ( - \cot(4A) )[/tex]Remove the parenthesis
We have the final answer as
[tex] \cot(4A) [/tex]As proven
Hope this helps you
Answer: see proof below
Step-by-step explanation:
Use the following identities:
[tex]\cot\alpha=\dfrac{1}{\tan\alpha}\\\\\\\cot(\alpha-\beta)=\dfrac{1+\tan\alpha\cdot \tan\beta}{\tan\alpha-\tan\beta}[/tex]
Proof LHS → RHS
Given: [tex]\dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\cot 6A-\cot 2A}[/tex]
Cot Identity: [tex]\dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\dfrac{1}{\tan 6A}-\dfrac{1}{\tan 2A}}[/tex]
Simplify: [tex]\dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\dfrac{1}{\tan 6A}\bigg(\dfrac{\tan 2A}{\tan 2A}\bigg)-\dfrac{1}{\tan 2A}\bigg({\dfrac{\tan 6A}{\tan 6A}\bigg)}}[/tex]
[tex]= \dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\dfrac{\tan 2A-\tan 6A}{\tan 6A\cdot \tan 2A}}[/tex]
[tex]= \dfrac{1}{\tan 6A-\tan 2A}-\dfrac{\tan6A\cdot \tan 2A}{\tan 2A-\tan 6A}[/tex]
[tex]= \dfrac{1}{\tan 6A-\tan 2A}-\dfrac{\tan6A\cdot \tan 2A}{\tan 2A-\tan 6A}\bigg(\dfrac{-1}{-1}\bigg)[/tex]
[tex]= \dfrac{1}{\tan 6A-\tan 2A}+\dfrac{\tan6A\cdot \tan 2A}{\tan 6A-\tan 2A}[/tex]
[tex]= \dfrac{1+\tan6A\cdot \tan 2A}{\tan 6A-\tan 2A}[/tex]
Sum Difference Identity: cot(6A - 2A)
Simplify: cot 4A
cot 4A = cot 4A [tex]\checkmark[/tex]
help me plsssssssssssssssssssssssssssssssssssssss
Answer:
[tex] \frac{1}{5} ( - m - 4)[/tex]
Step-by-step explanation:
But method 1 best suits the question
Answer:
[tex] - \frac{1}{5} m - \frac{4}{5} [/tex]
Answer:
-1/5m -4/5
Step-by-step explanation:
2/5 m -4/5 - 3/5 m
Combine like terms
2/5m - 3/5m -4/5
-1/5m -4/5
What is the equation of the line that passes through the points (−2, 1) and (1, 10)?
Answer:
Slope-Intercept form: y=3x+7
Standard form: 3x-y=-7
Point-slope form: y-1=3(x+2)
Step-by-step explanation:
Slope-Intercept form:
First, find the slope, using the formula: [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Our x₁ and y₁ will be the point (-2,1) and our x₂ and y₂ wwill be the point (1,10).
So let's write those in our equation to find slope:
[tex]m=\frac{10-1}{1-(-2)}=\frac{9}{3}=3[/tex]
Therefore, our slope is 3.
Now let's write our linear equation with what we have already in slope-intercept form:
y=3x+b
Well, we still need to find the y-intercept, or "b".
Plug in one of your points for the x and y values of the equation. We'll use the point (-2,1)
[tex]y=3x+b\\1=3(-2)+b\\1=-6+b\\1+6=-6+6+b\\7=b[/tex]
This means our y-intercept is 7. Now we can write our equation in slope-intercept form completely:
y=3x+7
Standard form:
Now, let's find this equation is standard form.
Take your equation in slope-intercept form and write it out again:
[tex]y=3x+7[/tex]
Now, standard form of a linear equation is ax+by=c, so subtract 3x from both sides:
[tex]y-3x=3x-3x+7\\-3x+y=7[/tex]
The "a" coefficient in standard form cannot be negative, so divide the entire equation by -1:
[tex]\frac{-3x+y}{-1}=\frac{7}{-1}\\3x-y=-7[/tex]
Therefore, your equation in standad form is:
3x-y=-7
Point-Slope form:
The formula for point-slope form is y-y₁=m(x-x₁). We already know that our x₁ and y₁ is the point (-2,1) and we know that our slope, m, is 3, so we just have to plug then in where the fit in the equation.
x₁ is -2 and y₁ is 1 and m is 3, so:
y-1=3(x-(-2)) or y-1=3(x+2)
That means our equation in point-slope form is:
y-1=3(x+2)
What’s 5x-2=25x+14? (please explain)
Answer:
x = - [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Given
5x - 2 = 25x + 14 ( subtract 25x from both sides )
- 20x - 2 = 14 ( add 2 to both sides )
- 20x = 16 ( divide both sides by - 20 )
x = [tex]\frac{16}{-20}[/tex] = - [tex]\frac{4}{5}[/tex]
Intersecting lines are _____ coplanar. Sometimes Never Always
Answer:
Always
Step-by-step explanation:
Coplanar lines are lines that intersect making intersecting lines always coplanar.
What is the product?
Answer:
10x²+3xy+6x-y²+3y
Step-by-step explanation:
(2x+y)(5x-y+3) steps
2x(5x-y+3)=10x²-2xy+6x
y(5x-y+3)= 5xy-y²+3y
add: 10x²-2xy+6x+5xy-y²+3y
10x²+3xy+6x-y²+3y
Use the distributive property to evaluate the expression. Which statement is equal to 8(26)? Which expression shows the result after using the distributive property? Evaluate the expression.
Answer:
8(20 + 6)
8(20) +8(6)
208
Step-by-step explanation:
Got it right EDGE 2021
The value of 8(26) after using the distributive property will be 208.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
As per the given, 8(26)
8(26) = 8(20 + 6)
By using the distributive property of multiplication,
8(26) = 8 × 20 + 8 × 6
⇒ 160 + 48
⇒ 208
Hence "The value of 8(26) after using the distributive property will be 208".
For more about the number system,
https://brainly.com/question/22046046
#SPJ2
Two angles are supplementary one angle is 2/3 the measure of the other one find both angles
Answer:
The measures are 108 deg and 72 deg.
Step-by-step explanation:
The larger angle has measure x.
The smaller angle has measure (2/3)x.
They are supplementary, so the sum of their measures is 180 degrees.
x + (2/3)x = 180
(3/3)x + (2/3)x = 180
(5/3)x = 180
(3/5) * (5/3)x = (3/5) * 180
x = 108
(2/3)x = 2/3 * 108 = 72
Answer: The measures are 108 deg and 72 deg.
Please help as soon as possible Will mark BRAINLIEST!!!!!
Answer:
Width = 40ft
Step-by-step explanation:
Area of a rectangle = Length x Width
=> 1600 = 40 x W
=> 1600 = 40W
=> 1600/40 = 40W/40
=> 40 = W
So, the width is 40 ft
Answer:
40 ft is the correct answer