The advantages of using percentages are that they all are on the same scale (1/100) making it easier to work with compared to ratios.
We need to write the advantages of using percentages to represent the ratio.
What is the percentage?The percentage is a fraction or a ratio in which the value of the whole is always 100.
The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Ratio: The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.
The advantages of using percentages are that they all are to the same scale (1/100) making it easier to work with compared to ratios, they can be converted to decimals very quickly, and percentages can be used to show the change in a number (20% of 50: 50% of 10), telling you what the original number is (10:5 or 2:1 doesn’t give you the starting numbers).
Therefore, the advantages of using percentages are that they all are on the same scale (1/100) making it easier to work with compared to ratios.
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2. On rectangle ABCD below, if A is located at
(3, 4) and B is located at (7,6), is the slope
of BC ?
Answer: The slope of BC is -2.
Step-by-step explanation:
We know that a rectangle has all opposite sides equal and parallel.
Each interior angle is a right angle.
Therefore , if rectangle ABCD is a rectangle then , AB should perpendicular to BC. [ ∵ Angle between AB and BC is 90° .] (1)
Also , slope of line passing through (a,b) and (c,d) : [tex]\dfrac{d-b}{c-a}[/tex]
If A is located at (3, 4) and B is located at (7,6) .
Then , The slope of AB = [tex]\dfrac{6-4}{7-3}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]
Also, the product of slopes of two perpendicular lines is -1.
Then , (Slope of AB) x (Slope of BC) = -1 [From (1)]
[tex]\Rightarrow\ \dfrac{1}{2}\times (\text{Slope of BC})= -1\\\\\Rightarrow\ \text{Slope of BC}=-2[/tex]
Hence, the slope of BC is -2.
what is 54 percent of 489
Answer:
264.06
Step-by-step explanation:
Answer:
264.06
Step-by-step explanation:
54% of 489
0.54 x 489=264.06
6q-11=13
What does q equal to?
Answer:
q=4
Step-by-step explanation:
brainlest would be epic owo
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
6*q-11-(13)=0
Step by step solution :
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
6q - 24 = 6 • (q - 4)
Equation at the end of step 1 :
Step 2 :
Equations which are never true :
2.1 Solve : 6 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
2.2 Solve : q-4 = 0
Add 4 to both sides of the equation :
q = 4
Answer:
q=4
Step-by-step explanation:
6q-11=13 first you have to get all the like terms together so add 11 to both sides
6q=24 Now divide both sides by 6 so you just have q on one side
q=4
A basketball has a diameter of 9.5 in. When full, ABOUT how much air will the basketball hold? ( please do not guess)
A. 100 cubic inches
B. 380 Cubic inches
C. 450 Cubic inches
D. 3,600 Cubic inches
Answer:
I got 3591.36 cubic inches
Step-by-step explanation:
Its wrong its wrong
Ryan measures a rectangle that is 9 feet long and 5 feet wide. Teo measures a rectangle that has an area of 36 square feet. Which rectangle has the greater area/ explain
Answer:
Teo's rectangle has the greater area.
Step-by-step explanation:
Since a rectangle has the same opposite sides of parallel sides, you need to add or multiply 9 times 9 or 9 + 9 and 5 times 5 or 5 + 5. 9 x 9 or 9 + 9 equals 18, and 5 + 5 or 5 x 5 equals 10. Then, 18 and 10 is to be added. 18 + 10 is 28. So, that means Teo's rectangle has the greater area because, 28 is less than 36.
To compare the areas of the rectangles, calculate the area of each rectangle. Ryan's rectangle has a greater area of 45 square feet compared to Teo's rectangle which has an area of 36 square feet.
Explanation:To compare the areas of the two rectangles, we need to calculate the area of each rectangle. The area of a rectangle is found by multiplying its length by its width. For Ryan's rectangle, the length is 9 feet and the width is 5 feet, so the area is 9 feet × 5 feet = 45 square feet. For Teo's rectangle, we are given that the area is 36 square feet. Since 45 is greater than 36, Ryan's rectangle has the greater area.
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In the diagram, HK is tangent to Circle O. If HK is 24mm and the length from H to the
edge of the circle along OH is 18mm, what is the length of the radius of the circle?
Answer:
The length of the radius of the circle is 7 mm
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
If HK is tangent to circle O at point K
then
The radius OK is perpendicular to segment HK and triangle OKH is a right triangle
Applying the Pythagorean Theorem
[tex]OH^2=OK^2+HK^2[/tex]
we have
[tex]OH=(r+18)\ mm\\OK=r\ mm\\HK=24\ mm[/tex]
substitute
[tex](r+18)^2=r^2+24^2[/tex]
solve for r
[tex]r^2+36r+324=r^2+576[/tex]
[tex]36r=576-324\\36r=252\\r=7\ mm[/tex]
therefore
The length of the radius of the circle is 7 mm
Angle x measures 42°. Find the measure of angle y.
42°
48°
138°
148°
The graph of a proportional relationship passes through (4, 32) and (1, y). Find y.
Answer:
[tex]y = \frac{32}{4} = 8[/tex]
What is the shape of the horizontal cross section of the given prism?
Answer:
pentagon
Step-by-step explanation:
In this problem we have a pentagonal prism
so
The solid has two pentagonal bases and five lateral rectangular faces
we know that
A plane parallel to the base of a pentagonal prism will intersect a cross section that is the same shape as its bases
so
The shape of the horizontal cross section of the given prism, is a pentagon
Answer: Pentagon
Step-by-step explanation:
the equation y=26.2x represents the number of miles y Conrad runs in x marathons. determine if there is a constant of variation. if so, explain what it represents:/
Final answer:
Yes, there is a constant of variation in the given equation y = 26.2x. The constant of variation represents the rate at which the number of miles y increases for every marathon x completed by Conrad.
Explanation:
Yes, there is a constant of variation in the given equation y = 26.2x. A constant of variation is represented by the coefficient or the number multiplied by x in the equation, which in this case is 26.2. It represents the rate at which the number of miles y increases for every marathon x completed by Conrad. So, for every marathon Conrad runs, the number of miles he runs increases by 26.2.
degree of inverse tangent of 0.83
Answer:
39.69 degrees
Step-by-step explanation:
Let
x ----> the measure of the angle
we have that
[tex]tan(X)=0.83[/tex]
using a calculator
[tex]m\angle X=tan^{-1}(0.83)=39.69^o[/tex]
How long is the minor axis for the ellipse shown below?
(x+3)^2/64 + (y-7)^2/4=1
A. 16
B. 4
C. 8
D. 64
Imagine is shown above.
The length of the minor axis is 4
Step-by-step explanation:
Step 1 :
The given equation is [tex]\frac{(x-3)^{2}}{64} + \frac{(y-7)^{2}}{4} = 1[/tex]
Here we see the denominator below the variable x is greater than below y. Hence the ellipse's major axis and the minor axis are parallel to x-axis and y-axis respectively
Step 2 :
The square of the semi minor axis will be the denominator of the y variable. So in the given ellipse ,
the square of the semi minor axis = 4
Hence the length of the semi minor axis = [tex]\sqrt{4}[/tex] = 2
Step 3 :
The length of the minor axis = 2 times the length of the semi minor axis
= 2 × 2 = 4
Answer :
The length of the minor axis is 4
Final answer:
The length of the minor axis of the given ellipse is 4 units, as the semi-minor axis length is derived from the square root of the denominator of the y-term in the ellipse equation. The correct option is B.
Explanation:
The minor axis of an ellipse is the shortest diameter of the ellipse, and it runs perpendicular to the major axis. In the given equation of the ellipse, (x+3)²/64 + (y-7)²/4=1, the denominators of the fractions correspond to the squares of the semi-axes lengths. Therefore, the length of the semi-minor axis 'b' is the square root of 4, which is 2. Since the minor axis is twice the length of the semi-minor axis, we must multiply 2 by 2 to get the length of the minor axis, which is 4.
So the correct answer for the length of the minor axis for the given ellipse is 4 units, which corresponds to option B.
you have 24 homework problems for math class. you finish 1/2 of them during some extra time in class. If you complete 4 more problems while waiting for the bus, what fracrion of the 24 problems will remain
Answer:
⅓ remaining
Step-by-step explanation:
½ of 24 = 12
12 + 4 = 16 done
24 - 16 = 8
8/24 = 1/3
Answer:
1/3
Step-by-step explanation:
1) we have 24 problems
2) we finish half of them
What is half of 24?
It’s 12
So far, we have 12 problems to do
Then we finished 4 more problems so we can subtract 4 from 12
12-4=8
8 more problems left out of the 24 we had
8/24=1/3
1/3 of the 24 problems remain
Hope this helps!
Batteries are sold in boxes and packets
Each packet contains 8 batteries
Each box contains 25 batteries
Jonathon buys p packets of batteries and b boxes of batteries
write down an expression of the terms p and b for the total number of batteries bought
Answer:
8p + 25b
Step-by-step explanation:
The expression of the word problem above can be written thus:
[tex]8p + 25b[/tex]
Betty is planning to give this box as a gift, so she plans to wrap it. The box is shaped like a rectangular prism, where the length is 14 inches, the width is 5 inches, and the height is 4 inches. How many square inches of paper will she need to cover the entire box?
Answer:
292 in^2
Step-by-step explanation:
Area of the top and bottom combined is 2(14 inches)(5 inches)), or 140 in^2.
Area of the two ends, combined, is 2(4 inches)(5 inches)) = 40 in^2.
Are of the two sides, combined, is 2(14 inches)(4 inches)) = 112 in^2.
Summing up these three subtotals, we get the total area 292 in^2.
Which best explains why a hot air balloon rises into the air?
A. As the air is cooled, it becomes more dense and the balloon rises.
B. As the air is cooled, it becomes less dense and the balloon rises.
C. As the air is heated, it becomes less dense and the balloon rises.
Answer:
C. As the air is heated, it becomes less dense and the balloon rises.
Step-by-step explanation:
A is wrong. The denser cold air would cause the balloon to drop.
B is wrong. As the air is cooled, it becomes less dense.
please help I NEED HELP PLS SKDJLAK
Answer: -√6 + 1
Step-by-step explanation:
[tex]\dfrac{\tan\bigg(-\dfrac{2\pi}{3}\bigg)}{\sin\bigg(\dfrac{7\pi}{4}\bigg)}-\sec(-\pi)\\\\\\=\dfrac{\tan(240^o)}{\sin(315^o)}-\sec(180^o)\\\\\\=\dfrac{\sqrt3}{-\dfrac{\sqrt2}{2}}-(-1)\\\\\\=\dfrac{-2\sqrt3}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)+1\\\\\\=\large\boxed{-\sqrt6+1}[/tex]
What is the solution set for this inequality?
−8x + 40 > −16
A) x > 7
B) x < 7
C) x > -3
D) x < -3
Answer:
B) x < 7
Step-by-step explanation:
−8x + 40 > −16
Subtract 40 from each side
−8x + 40-40 > −16-40
-8x > -56
Divide each side by -8, remembering to flip the inequality
-8x/-8 < -56/-8
x <7
Is 36/6 a rational number
Answer:
yes
Step-by-step explanation:
Any ratio of two integers is a rational number, as long as the denominator is not zero.
Which lines best approximate the directrices of the ellipse? Round to the nearest tenth. x = −4.6 and x = 4.6 x = −3.5 and x = 3.5 y = −4.6 and y = 4.6 y = −3.5 and y = 3.5
Answer: c
Step-by-step explanation:
Answer:
C y = −4.6 and y = 4.6
Step-by-step explanation:
Edge 2023
Select the correct answer
Psychologists have identified four stages of personality growth. In which stage does a person develop life skills and learn to take initiative?
A
infancy
childhood
B.
c. adolescence
D. adulthood
Reset
Next
Answer:
adolescence
Step-by-step explanation:
credit card customer owes $523.85. They
re only able to make a payment of $184.50. How
much money does the customer still owe?
Answer:
$339.25
Step-by-step explanation:
Since the credit card customer owes $523.85 and is only able to make a payment of $184.50
Amount still owed
= $523.85 - $184.60
= $339.25
The customer still owes $339.25
Isolate the identity
cos 2x - cos 8x
cos 2x + cos 8x
HELP PLS
Answer:
Cos 2x = Cos (5x-3x)
Cos(5x)Cos(3x) + Sin(5x)Sin(3x)
Cos 8x = Cos (5x + 3x)
Cos(5x)Cos(3x) - Sin(5x)Sin(3x)
Cos 2x - Cos 8x
= Cos(5x)Cos(3x) + Sin(5x)Sin(3x) -
[Cos(5x)Cos(3x) - Sin(5x)Sin(3x)]
= 2Sin(5x)Sin(3x)
Cos 2x + Cos 8x
= Cos(5x)Cos(3x) + Sin(5x)Sin(3x) +
[Cos(5x)Cos(3x) - Sin(5x)Sin(3x)]
= 2Cos(5x)Cos(3x)
= 2Sin(5x)Sin(3x) ÷ 2Cos(5x)Cos(3x)
2 gets cancelled out
Sin(5x)/Cos(5x) is Tan(5x)
Sin(3x)/Cos(3x) is Tan(3x)
Hence the fraction is identical to
Tan(5x)Tan(3x)
A napkin is 37 centimeters long.How many millimeters is this?
Answer:
370 millimeters
Step-by-step explanation:
Have a nice day :)
Step-by-step explanation:
1 cm = 1 millimeters
[tex] \therefore \: 37 \: cm \: = 37 \times 10 = 370 \: mm[/tex]
Kyle is renting a jetski for the day. If he can rent the jetski in 1-hour increments, what is the minimum number of hours must he rent the jetski for option 2 to be a better deal than option 1? A) 2 hours B) 3 hours C) 4 hours D) 5 hours
Complete Question:
Option 1: $30 an hour plus a non-refundable deposit of $50.
Option 2: $20 an hour plus a non-refundable deposit of $75.
Kyle is renting a jetski for the day. If he can rent the jetski in 1-hour increments, what is the minimum number of hours must he rent the jetski for option 2 to be a better deal than option 1?
Answer:
Kyle must rent the jetski for three hours for option 2 to be a better deal than option 1
Solution:
Let "x" be the number of hours
Option 1: $30 an hour plus a non-refundable deposit of $50.Therefore,
Charge for option 1: 50 + 30x
For 1 hour,
Charge = 50 + 30(1) = 80
For 2 hours,
Charge = 30(2) + 50 = 110
For 3 hours,
Charge = 30(3) + 50 = 140
For 4 hours,
Charge = 30(4) + 50 = 160
Option 2: $20 an hour plus a non-refundable deposit of $75Charge for option 2 : 75 + 20x
For 1 hour,
Charge = 20(1) + 75 = 95
For 2 hours ,
Charge = 20(2) + 75 = 115
For 3 hours,
Charge = 20(3) + 75 = 135
For 4 hours,
Charge = 20(4) + 75 = 155
For the first two hours , the charge of option 2 is more than the rent of option 1
From 3 hours, option 2 will be better deal than option 1
The difference of a number and six is seven. Find the number.
Answer 13-6=7
Step-by-step explanation:
The given expression indicates a difference of six and an unknown number equals to seven. To solve, we isolate the unknown number by adding six to both sides of the equation. Thus, the unknown number is 13.
Explanation:The question states that 'The difference of a number and six is seven.' To find out the number, we can set up the following equation where x represents our unknown number:
x - 6 = 7
To solve for x, we can add 6 to both sides of the equation, which balances it rendering the final result:
x = 7 + 6
Finally, adding 7 and 6, we find that x = 13. The number we are seeking is 13.
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what is (5a+2)(a+4) in polynomial standard form
Answer:
5a²+22a+8
Step-by-step explanation:
(5a+2)(a+4)
5a² + 20a + 2a + 8
5a² + 22a + 8
Select the most SPECIFIC name for this shape
O Trapezoid
O Rectangle
O kite
O Quadrilateral
Answer:
Option A, Trapezoid
Step-by-step explanation:
Since there is two parallel sides and two nonparallel, that means it is a trapezoid.
Answer: Option A, Trapezoid
if you qre travelling @90 km/h how far will you travel in 42 mins? Can someone show me step by step solution pls on how to work it out.
Answer:
Distance = 63 km
Step-by-step explanation:
Speed = 90 km/h
Time = 42 mins
Time = 42 / 60 = 0.7 hrs
Distance = Speed × time
Distance = 90 km/h × 0.7 hr
Distance = 63 km
find the difference in length between a walking stick and a bumblebee PLS HELP HURRY
Difference between the lengths of walking stick and lengths of bumble bee is [tex]3\frac{4}{8}[/tex] inch.
Solution:
Given data represents the length of the insects.
Length of the walking stick = 4 in
Length of the bumble bee = [tex]\frac{5}{8}[/tex] in
Difference between their length
[tex]$=4-\frac{5}{8}[/tex]
[tex]$=\frac{4}{1} -\frac{5}{8}[/tex]
To make the denominator same, multiply and divide the first term by 8.
[tex]$=\frac{32}{8} -\frac{5}{8}[/tex]
[tex]$=\frac{32-5}{8}[/tex]
[tex]$=\frac{27}{8}[/tex]
Now, change improper fraction into mixed fraction, we get
[tex]$=3\frac{4}{8}[/tex]
Difference between the lengths of walking stick and lengths of bumble bee is [tex]3\frac{4}{8}[/tex] inch.