Your function is: [tex]f(x)=\frac{1}{2}\cos \Big( \frac{1}{4x}\Big) -1[/tex]
Domain: $(-\infty, +\infty)-\{ 0 \}$ or $R-\{ 0 \}$
Range: $[-\frac{3}{2}, -\frac{1}{2}]$
Midline: $y=-1$
Of a group of boys and girls at Central Middle School’s after-school party, 15 girls left early to play in a volleyball game. The ratio of boys to girls then remaining was 2 to 1. Later, 45 boys left for a football game. The ratio of girls to boys was then 5 to 1. How many students attended the party?
Answer:
90
Step-by-step explanation:
Let g and b represent the number of girls and boys attending, respectively.
After 15 girls left, the ratio of boys to girls was ...
b/(g -15) = 2/1
b = 2g -30 . . . . . multiply by (g-15)
__
After 45 boys left, the ratio of girls to boys was ...
(g -15)/(b -45) = 5/1
g -15 = 5b -225 . . . . . . multiply by (b-45)
g = 5b -210
Using the latter to substitute into the former, we have ...
b = 2(5b -210) -30
450 = 9b . . . . . add 450-b
50 = b . . . . . . 50 boys attended
g = 5(50) -210 = 40 . . . . . 40 girls attended
The number of students who attended the party was 50 +40 = 90.
_____
Check
After 15 girls left, the ratio of boys to girls was 50/25 = 2/1.
After 45 boys left, the ratio of girls to boys was 25/5 = 5/1.
Answer:
let b = original number of boys
let g = original number of girls
:
Of a group of boys and girls at Central Middle School's after-school party, 15 girls left early to play in a volleyball game.
The ratio of boys to girls then remaining was 2 to 1.
b%2F%28%28g-15%29%29 = 2%2F1
Cross multiply
b = 2(g-15)
b = 2g - 30
:
Later, 45 boys left for a football game. The ratio of girls to boys was then 5 to 1.
%28%28g-15%29%29%2F%28%28b-45%29%29 = 5%2F1
cross multiply
g - 15 = 5(b-45)
g - 15 = 5b - 225
g = 5b - 225 + 15
g = 5b - 210
Replace b with (2g-30)
g = 5(2g-30) - 210
g = 10g - 150 - 210
g = 10g - 360
360 = 10g - g
360 = 9g
g = 360/9
g = 40 girls originally
find b
b = 2(40) - 30
b = 50 boys originally
" How many students attended the party?"
40 + 50 = 90 students
Sally is swimming in a race that has 5 laps. Swimming 2 lengths of the pool
counts as one lap. If Sally is halfway through the fourth lap, what fractional
part of the total laps in the race is left for Sally to finish?
Answer:
3/10
Step-by-step explanation:
Sally has to run 5 laps(2000m)
One lap = 400m
So we multiply 3.5( 3 1/2) [this the the distance Sally ran] by 400
The answer we get is 1400( this the total distance in meters she ran)
Next we subtract 1400( total distance she ran in meters) from 2000(total distance in meters she needs to complete.
The answer we get is 600 meters( this is the distance she is left with)
As a fraction is 600/2000
THE ANSWER REDUCED TO ITS LOWEST TERM IS 3/10.
Answer:
3/10
Step-by-step explanation:
Find the term that must be added to the equation x2+4x=1 to make it into a perfect square
Answer:
add 4 to each side
Step-by-step explanation:
x^2+4x=1
Take the coefficient of the x term
4
Divide by 2
4/2 =2
Square it
2^2 =4
Add this to each side
x^2+4x +4=1+4
(x+2) ^2 = 5
What is the area of the polygon shown below? (in the image). A. 322 mm^2 B. 364 mm^2 C. 520 mm^2 D. 584 mm^2 Show all work please!
Answer:
A. 322 mm^2
Step-by-step explanation:
First split the shape into two (a rectangle and a triangle).
Then calculate the area of those shapes.
Rectangle: 20 x 14 = 280 mm^2
Triangle: 6 x 14 / 2 = 42 mm^2
Add them together.
280 + 42 = 322 mm^2
Emanuel was charged \$32$32dollar sign, 32 for a 14\dfrac29 \text{ km}14 9 2 km14, start fraction, 2, divided by, 9, end fraction, space, k, m taxi ride. What was the cost per kilometer? \$Emanuel was charged \$32$32dollar sign, 32 for a 14\dfrac29 \text{ km}14
9
2
km14, start fraction, 2, divided by, 9, end fraction, space, k, m taxi ride.
What was the cost per kilometer?
Answer:
$2.25/km
Step-by-step explanation:
The cost charged for a total taxi ride of [tex]14\frac{2}{9}\ km[/tex] was $32. To get the cost per km, we divide the cost charged for the total taxi ride by the total distance that was traveled by the taxi. The cost per km is given by:
Cost per km = [tex]\frac{Cost \ of\ money\ charged}{Total\ distance}=\frac{\$ 32}{14\frac{2}{9} \ km}=\frac{32}{\frac{128}{9} }= \$2.25/km[/tex]
Therefore the cost per kilometer is $2.25 per kilometer. Each kilometer traveled by the taxi cost $2.25.
15 POINT!!!!!!!!!!!!!!!!!!!! Using the graph of f(x) and g(x), where g(x) = f(k⋅x), determine the value of k. Graph of two lines. f of x passes through 2, 0 and 3, 2, and g of x passes through two thirds, 0 and 1, 2. 3 one third negative one third −3
Answer:
k=(-1,5)=-5
Step-by-step explanation:
Answer:
ok i got the same question and i think it is and dont qoute me boy i aint said it but i think its B sorry if im wrong
Step-by-step explanation:
Sam's Lawn Service uses the equation, y = 15x + 25 to calculate the cost, y, to work on a
customer's lawn for x number of hours.
Ron's Lawn Service uses the table below to calculate the cost to work on a customer's
lawn.
Answer:
Rons costs less by 4 dollars
Step-by-step explanation:
Sams
y = 15x+25
x=3
y = 15*3+25
= 45+25
=70
Rons
Using averaging
for 3 hours Add 2 and 4 hours and divide by 2
(49+ 83) / 2 = 132/2= 66
Rons costs less by
70-66 =4
Factor 3x^2 – 12x – 36.
Answer:
The answer is 3( x - 2)(x + 6)Step-by-step explanation:
3x² - 12x - 36
To factorize the expression first factor 3 out of the expression
That's
3( x² - 4x - 12)
Factorize the terms in the bracket
To do so write - 4x as a difference
That's
3( x² + 6x - 2x - 12)
Factor out x from the expression
3[ x( x + 6) - 2 ( x + 6) ]
Next factor x + 2 out
We have the final answer as
3( x - 2)(x + 6)Hope this helps you
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Classwork for Alge.
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18
The curved parts of the figure are arcs centered at points A and C. What is the approximate length of boundary ABCD? Use the value = 3
and round the answer to one decimal place.
5
С
30°
А
120°
5
Answer:
The correct answer is
C. 23.1
Step-by-step explanation:
i think this is correct
The number of radians in a 720-degree angle can be
written as an, where a is a constant. What is the
value of a ?
Answer:
a=4
Step-by-step explanation:
When going from degrees to radians, 180 degrees is always going to equal π radians
That means 2π would be 360 degrees, and 4π would be 720
And since we're trying to find a in aπ when it's a 720 degree angle, we can conclude that a=4
Answer:
4
Step-by-step explanation:
We know that:
π rad= 180°Then:
720° = 4*180° = 4π radianThe value of a:
4π = aπ ⇒ a= 4A building casts a 33-m shadow when the sun is at an angle of 27° the vertical. How tall is the building to the
nearest meter? How far is it from the top of the building to the tip of the shadow?
Answer:
1. EF = 65m
2. DF = 73m
Step-by-step explanation:
1. EF = height of the building = h = 33 / tan 27 = 65m
2. DF = sqrt (65² + 33²) = 73m
The building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.
From the triangle DEF, we find the value of EF by using tan function.
tan function is a ratio of opposite side and adjacent side.
tan(27)= 33/FE
0.5095 = 33/FE
Apply cross multiplication:
FE=33/0.5095
FE=64.76
Now DF is the hypotenuse, we find it by using pythagoras theorem.
DF²=DE²+EF²
DF²=33²+64.76²
DF²=1089+4193.85
DF²=5282.85
Take square root on both sides:
DF=72.68
In a triangle the the sum of three angles is 180 degrees.
∠D + 27 +90 =180
∠D + 117 =180
Subtract 117 from both sides:
∠D =63 degrees.
Hence, the building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.
To learn more on trigonometry click:
https://brainly.com/question/25122835
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A percent is the numerator of a ratio whose denominator is A. 25 B. 50 C. 75 D. 100
I am sure the answer is D
Answer:
D 100
Step-by-step explanation:
60% = 60/100
70% =70/100
What is the volume of the square pyramid shown to the nearest tenth? The figure is not drawn to scale. width of 16 and a length of 17 A. 1,280.0 ft^3 B. 85.3 ft^3 C. 1,920.0 ft^3 D. 3,840.0 ft^3
The volume of the pyramid is 1,280 cubic feet. Thus, the correct option is A.
What is the volume of the pyramid?Let h be the height of the pyramid, l be the slant height, and A be the base area of the pyramid. Then the volume of the pyramid will be given as,
Volume = (1/3) × A × h
The slant height is given as,
l² = (half of the side)² + h²
Given that:
Slant height, l = 17 ft
Side length, a = 16 ft
The height of the pyramid is calculated as,
17² = (16/2)² + h²
h = 15
The volume of the pyramid is calculated as,
V = 1/3 x 16 x 16 x 15
V = 256 x 5
V = 1,280 cubic feet
Thus, the correct option is A.
More about the volume of the pyramid link is given below.
https://brainly.com/question/17615619
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The quotient of 32 and 4 divided by the sum of 1 and 3
Answer:
2
Step-by-step explanation:
32 divided by 4 = 8 (quotient)
1 + 3 = 4 (sum)
8 divided by 4 = 2
Answer:
88
Step-by-step explanation:
What is the determinant of H = 2 4 9
3 3 1
4 5 3
Answer:5,3,7
2,4,9
3,6,4
Step-by-step explanation:he determinant of a 2 x 2 matrix A,
EVALUATING A 2 X 2 DETERMINANT,
DETERMINANT OF A 3 X 3 MATRIXFINDING THE DETERMINANT OF' A MATRIX,
FINDING THE COFACTOR OF AN ELEMENT, ,EVALUATING A 3 X 3 DETERMINAN,
EVALUATING A 4 X 4 DETERMINANT
voila
Answer: The answer is 15. You can use the calculator in Edge2020
Step-by-step explanation:
Edg2020
Graph the function. h ( x ) = 8 ⋅ ( 3 4 ) x h(x)=8⋅( 4 3 )
answer....
Step-by-step explanation:
h
(
x
)
=
3
x
+
8
Name four fractions between 5/11 and 5/6
Answer:
6/11, 20/33, 2/3, 25/33 (answers vary)
Step-by-step explanation:
First, we need to convert both of these fractions to the same denominator. To do that, we need to find the least common denominator for both fractions.
6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72
11: 11, 22, 33, 44, 55, 66, 77
The LCM of 6 and 11 is 66. (6 * 11 = 66)
Now, we multiply 5/6 by 11/11 and 5/11 by 6/6.
[tex]\frac{5}{6} *\frac{11}{11}=\frac{55}{66}\\\\\\\frac{5}{11} *\frac{6}{6} =\frac{30}{66}[/tex]
Now, we can just choose four numbers between 30 and 55 and get our answer (remember to simplify!).
[tex]\frac{36}{66} =\frac{6}{11}[/tex]
[tex]\frac{40}{66}=\frac{20}{33}[/tex]
[tex]\frac{44}{66} =\frac{2}{3}[/tex]
[tex]\frac{50}{66} =\frac{25}{33}[/tex]
can somewon help me i am bad at math
Answer:
480 in3
Step-by-step explanation:
10 * 8 * 5 + ( 4 * 4 * 5 ) = 480in3
Answer:
480 in^3
Step-by-step explanation:
The first, smaller container where I split it has an equation of V= 4*4*6=80 in^3 and the second, larger container has an equation of V= 5*10*8= 400 in^3
80+400= 480 in^3
help me plz i dont get this
Answer:
56 [tex]in^2[/tex]
Step-by-step explanation:
We can first break this down into 2 smaller rectangles.
1x2x4 rectangle
4x3x4 rectangle.
Then we can find out the area of each, and we get 8+48 = 56.
You also could find this out by subtracting the area that is missing.
Answer:
The volume of the container is 56 in^3
Step-by-step explanation:
To solve, I split this figure vertically at the corner between the two steps. We know that the formula for volume of a container is V= l*w*h. The first, smaller portion of the container has a length of 4, a width of 1, and a height of 2. 4*1*2= 8 in^3
The second, larger portion of this container has a length of 4, (look at the side of the first portion), a width of 3, (4-1=3), and a height of 4. 4*3*4= 48 in^3.
Finally, add together the volumes of the two portions and that is the volume of the whole figure. V= 56 in^3
You weigh six packages and find the weights to be 34, 24, 74, 29, 69, and 64 ounces. If you include a package that weighs 154 ounces, which will increase more, the median or the mean? A. The median and the mean will stay the same. B. The median and mean are affected the same amount. C. The mean increases more. D. The median increases more.
Answer:
C. the mean increases more
Step-by-step explanation:
the mean is more affected by outliers because it is an average of all the numbers.
Answer:
C. the mean increases more
Step-by-step explanation:
18 silly bands are equally shared by 6 children. 2 children put their silly bands in the same drawer. How many silly bands are in the drawer?
Answer:
6
Step-by-step explanation:
18 silly bands / 6 children = 3 silly bands per child.
2 children * 3 bands each = 6 bands total
Answer:
6 silly bands
Step-by-step explanation:
18 divided by 6 = 3 , so each child gets 3 so 3 + 3 is 6 which means 6 silly bands are in the drawer
What are the coordinates of the vertices of the polygon in the graph that are in Quadrant II? A) (4,–2) B) (4,3), (0,5), (0,1) C) (–5,2), (–3,2), (–3,4) D) (–1,0), (–5,2), (–3,2), (–3,4), (0,5), (0,1)
Answer:
C) (–5,2), (–3,2), (–3,4)
Step-by-step explanation:
A) (4,–2)
B) (4,3), (0,5), (0,1)
C) (–5,2), (–3,2), (–3,4)
D) (–1,0), (–5,2), (–3,2), (–3,4), (0,5), (0,1)
For quadrant two the points are always (-x,y) and x is always negative.
Image shows quadrant places.
What is the equation that is perpendicular to the line y=2x-3 and passes through the point (-6,5)? Show all of your work.
Answer: y=(-1/2)x+5.5
Step-by-step explanation:
y=2x+3
This equation is in the slope-intercept form y=mx+b
m is the slope.
b is the y-intercept, the value of y when x=0.
m=2
The slope of the perpendicular line is -1/2.
(y-y1)=m(x-x1)
(y-4)=(-1/2)(x-3)
y-4=(-1/2)x+1.5
add 4 to both sides
4+y-4=(-1/2)x+1.5+4
y=(-1/2)x+5.5
Answer:
y = -1/2x + 2
Step-by-step explanation:
The slope of a perpendicular line will be the opposite reciprocal (opposite sign, and reciprocal)
The line's slope is 2, so the perpendicular line's slope will be -1/2.
Now, we know part of the equation: y = -1/2x + b
Plug in the point given:
5 = -1/2(-6) + b
5 = 3 + b
2 = b
Now, we can plug in b into the equation:
y = -1/2x + 2
*PLEASE ANSWER TY* What is the density of a 50-gram pyramid with rectangular base 4 cm x 8 cm and height 10 cm?
Answer:
[tex]\frac{0.47 g}{cm^{3} }[/tex]
Step-by-step explanation:
→ First work out volume of pyramid using the formula [tex]\frac{lwh}{3}[/tex] where 'l' is the length, 'w' is the width and 'h' is the height
[tex]\frac{lwh}{3}[/tex] ⇔ [tex]\frac{4*8*10}{3}[/tex] ⇔ [tex]\frac{320}{3}[/tex] ⇔ 320 ÷ 3 = 106.666666667
→ Volume of pyramid = 106.666666667. Substitute this value into the density formula
Density = Mass ÷ Volume
Density = 50 ÷ 106.666666667
Density = 0.46875 to 1 decimal place is 0.47
Graph the line 2x + 3y = 12
Answer:
your answer y=4 x=6
Step-by-step explanation:
helpyffhvjvjnvhdfuguig
Answer:
x = 0, x = 4
Step-by-step explanation:
12x - 21 = 5x + 7(x - 3)
First, foil out the right side --> 5x² - 15x + 7x - 21, which simplifies down to 5x² - 8x - 21.
Move the 12x - 21 to the right side by subtracting --> 0 = 5x² - 20x.
Factor out a 5x --> 0 = 5x(x - 4)
If you want to solve for x, set 5x = 0 and x - 4 = 0.
For 5x = 0, divide both sides by 5 to isolate the x --> x = 0/5, which simplifies down to x = 0.
For x - 4 = 0, add 4 to both sides to isolate the x --> x = 0 + 4, which simplifies down to x = 4.
Plug the values back into the original equation to check if it works
12(0) -21 = 5(0) + 7((0) - 3) --> -21 = -21
12(4) - 21 = 5(4) + 7((4) -3) --> 27 = 27
Hope this helps!
4/3 to the third power as a simplified fraction
Answer:
64/27
Step-by-step explanation:
(4/3)^3=(4/3)*(4/3)*(4/3)=64/27
Answer:
[tex]2 \frac{10}{27}[/tex]
Step-by-step explanation:
4/3 × 4/3 × 4/3 = 64/27
You can turn it into a mixed number ([tex]2 \frac{10}{27}[/tex]).
Hope that helps and maybe earns a brainliest!
Have a great day! :)
Round the number 53.18474629
a) To the nearest tenth
b) To the nearest thousandth
c) To the nearest whole number
Answer:
Step-by-step explanation:
To the nearest tenth: 53.2
To the nearest thousandth: 53.185
To the nearest whole number: 53
Enrique has to pay 80% of a $200 phone bill. Explain how to use equivalent ratios to find 80% of $200. please help
Answer:
Heres a simple way:
Step-by-step explanation:
80% in to dec. 0.8
0.8 x 200 = 160
So,
80% of $200 is
$160
Find the median of the data in the dot plot below.
Answer:
40
Step-by-step explanation:
The median is the middle value of the data arranged in ascending order. If there is no exact value in the middle then it is the average of the values either side of the middle.
The data is arranged in ascending order within the dot plot
There are 10 values in the data set
Thus the median is between the fifth and sixth values.
Counting from the left (35)
The fifth value = 39 and the sixth value = 41, thus
median = [tex]\frac{39+41}{2}[/tex] = [tex]\frac{80}{2}[/tex] = 40
Answer:
Step-by-step explanation:
Data:
35 , 38, 38 , 39 , 39, 41, 42 , 43, 43, 44
Total number of data = 10
Number of data is even. so, median is the average of (n/2)th term & ([tex]\frac{n}{2}+1[/tex] ) middle term,
Median = average of 5th and 6th term
= (39 + 41)/2 = 80/2 = 40
