Using the proportion , the 5% of 60 would be 3.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We are given that the number of 5% of 60.
5% of 60
= 0.05 x 60
= 3
Therefore, the 5% of 60 would be 3.
Using the proportion , the 5% of 60 would be 3.
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f(x) =
2/9x2+18x-216
Answer:
Domain: all real numbers
Step-by-step explanation:
The function is:
[tex] f(x) = \dfrac{2}{9}x^2 + 18x - 216 [/tex]
The domain of a function is the set of values of the x-coordinates of the points of the function.
In this function, there is no restriction on x, so the domain is all real numbers.
A credit card has an APR of 32.47%, and its billing cycle is 30 days long. What is the credit card's periodic interest rate?
If a credit card has an APR of 32.47%, and its billing cycle is 30 days long. The credit card's periodic interest rate is 2.67%.
What is credit card periodic interest rate?A credit card periodic rate can be defined as the interest amount that a person pays on the balance of their credit card.
Given data:
Billing cycle = 30 days long
APR = 32.47%
Using this formula to find the credit card periodic interest rate
Credit card periodic interest rate = APR / (Number of days in a year /Billing cycle)
Where:
Credit card periodic interest rate =?
Annual percentage rate (APR) = 32.47%
Number of days in a year =365 days
Billing cycle = 30 days
Now let find the credit card periodic interest rate
There is 365 days in a year.
Credit card periodic interest rate = 32.47% ÷ (365 days / 30 days)
Credit card periodic interest rate =32.47% / 12.17
Credit card periodic interest rate = 2.67%
Therefore the periodic interest rate is 2.67%
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A company that makes haircare products had 2,000 people try a new shampoo. Of the 2,000 people, 12 had a mild allergic reaction. What percent of the people had a mild
allergic reaction?
The percent of the people had a mild that has an allergic reaction is 0.6%.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
Given that the company that makes haircare products had 2,000 people try a new shampoo. Of the 2,000 people, 12 had a mild allergic reaction.
It should be noted the percentage will be:
= Allergic people / Total people × 100
= 12/2000 × 100
= 0.6%
The percentage is 0.6%.
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find the number of solutions to the equation 3x-1=1/3(9x-5)
Answer:
No Solution
Step-by-step explanation:
-1 is not equal to -5/3
the rectangular coordinates of a point are s2, 2, 21d. find the cylindrical and spherical coordinates of the point
The cylindrical and spherical coordinates of the point are ([tex]\sqrt{8}[/tex],0.78,-1),(3, 0.78rad, 1.91rad) respectively.
Rectangular coordinates of a point is written like (x, y, z)
Cylindrical coordinates of a point is written like (r, θ, z)
Spherical coordinates of a point is written like (p, θ, φ)
First talk about Rectangular vs Cylindrical.
x = rcosθ
y = rsinθ.
z = z
x^2 + y^2 = r^2
given rectangular coordinates as (2,2,-1)
x=2, y=2, z=-1.
r^2 = 4+4 = 8.
r = [tex]\sqrt{8}[/tex]
r = 2[tex]\sqrt{2}[/tex]
θ = [tex]tan \inv-1[/tex](y/x) = [tex]tan \inv-1[/tex](2/2) = [tex]tan -1[/tex](1) = 45° = 0.78rad .
z = -1.
So Cylindrical coordinates is (r,θ,z) = ([tex]\sqrt{8}[/tex],0.78,-1).
Now let's us talk about Rectangular vs Spherical Coordinates.
x = pcosθsinφ.
y= psinθsinφ.
z = pcosφ.
p^2 = x^2+y^2+z^2.
tanθ = y/x
cosφ = z/p = z/[tex]\sqrt{x^2+y^2+z^2}[/tex].
given rectangular coordinates as (2,2,-1)
x=2, y=2, z=-1.
p = [tex]\sqrt{x^2+y^2+z^2}[/tex] = [tex]\sqrt{2^2+2^2+(-1)^2}[/tex] = [tex]\sqrt{9}[/tex] = 3
θ = [tex]tan -1[/tex](y/x) = 0.78rad .
φ = [tex]cos -1[/tex](z/p) = [tex]cos -1[/tex](-1/3) = 1.91rad
So Spherical coordinates is (3, 0.78rad, 1.91rad).
The cylindrical and spherical coordinates of the point are ([tex]\sqrt{8}[/tex],0.78,-1),(3, 0.78rad, 1.91rad) respectively.
Given Question is incomplete, Complete Question here
The Rectangular Coordinates Of A Point Are (2,2,-1) Find The Cylindrical And Spherical Coordinates Of the Point,
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what is 10 to the 10th power rounded to the nearest 10th?
Answer:
10,000,000,000
Step-by-step explanation:
[tex]10^{10}[/tex]= 10,000,000,000
rounded to the nearest 10th = 10,000,000,000
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
b.) 8/7≈ 1.1
Final.) and then using the exponential decay formula, 18.1 will be left after
4. Here is a diagram of the track King'sis thinking of adding around the new field. It
consists of two parallel lines and a semicircle at each end. The track is 10 meters wide. -
100-
СР
64m
a) If someone runs one lap on the inside of the track, how far will they have run?
b) If someone runs one lap on the outside of the track, how far will they have run?
c) Find the difference between the distances of running on the inside or outside of the
track.
Answer:
Step-by-step explanation:
what is the future value of $800 one year from today if the interest rate is 7 percent?
Answer:
800(1+7/100)
800(1.7)
1360
Step-by-step explanation:
formula isp(1+r/100)power t
The exponential or the future value with interest is A = $ 856
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 future value be represented as A
To calculate the future value of $800 after one year with an interest rate of 7%, we can use the formula for simple interest:
The future value = present value x (1 + (interest rate x time))
So , the exponential equation is
x ( t ) = x₀ × ( 1 + r )ⁿ
Plugging in the values we have:
The future value = $800 * (1 + (0.07 * 1))
The future value = $800 * 1.07
The future value = $856
Hence , the future value of $800 one year from today with a 7% interest rate would be $ 856
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If 50% of a number is 120 and 80% of the same number is 192, find 30% of that
number.
Answer: the answer is 72
Step-by-step explanation:
if 50% of a number is 120 then that means its only half of that number so to find out the whole number multiply 120 by 2 which gives you the answer of 240
Now we need to determine 30% of 240 and the procedure explaining it as such
Step 1: In the given case Output Value is 240.
Step 2: Let us consider the unknown value as x.
Step 3: Consider the output value of 240 = 100%.
Step 4: In the Same way, x = 30%.
Step 5: On dividing the pair of simple equations we got the equation as under
240 = 100% (1).
x = 30% (2).
(240%)/(x%) = 100/30
Step 6: Reciprocal of both the sides results in the following equation
x%/240% = 30/100
Step 7: Simplifying the above obtained equation further will tell what is 30% of 240
x = 72%
Therefore, 30% of 240 is 72
I hope this helps
Answer:
72
Step-by-step explanation:
You want 30% of a number, given that 50% of it is 120, and 80% of it is 192.
SolutionThe 30% you want will be the difference between 80% and 50%:
80% -50% = 30%
192 -120 = 72
30% of the same number is 72.
Suppose K⊆Rn is compact, f:K→R is continuous, and ϵ>0. Show that there is a number A>0 such that
|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.
By using the concept of compact set, it can be proved that
|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.
What is compact set?
A set K is said to be compact if every open cover of K has a finite subcover.
Let K⊆Rn is compact f:K→R is continuous, and ϵ>0
Let there exist [tex]x_n, y_n[/tex] ∈ K such that |f([tex]x_n[/tex])−f([tex]y_n[/tex])| > n∥[tex]x_n[/tex]−[tex]y_n[/tex]∥+ϵ,
Since K is compact there is a subsequence [tex]x_{nk}[/tex] and [tex]y_{nk}[/tex] of [tex]x_n, y_n[/tex] respectively such that [tex]x_{nk}[/tex] converges to x and [tex]y_{nk}[/tex] converges to y.
So, |f([tex]x_{nk}[/tex])−f([tex]y_{nk}[/tex])| > [tex]n_k[/tex]∥[tex]x_{nk}[/tex]−[tex]y_{nk}[/tex]∥+ϵ,
Since f is continuous,
We can write
|f(x)−f(y)| > [tex]n_k[/tex]∥x - y∥+ϵ,
This is true for infinite many [tex]n_k[/tex]
So ||x - y|| = 0
|f(x) - f(y)| > ϵ, a contradiction since f is continuous
So, there is a number A>0 such that
|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.
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A line has a slope of 1/2 and includes the points (-4,-7) and (w,-3) What is the value of w?
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{w}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{w}-\underset{x_1}{(-4)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{\cfrac{1}{2}} \\\\\\ \cfrac{-3+7}{w+4}=\cfrac{1}{2}\implies \cfrac{4}{w+4}=\cfrac{1}{2}\implies 8=w+4\implies 4=w[/tex]
estimate using compatibl numbers.
241 divided by 34
Magic number puzzle. Help asap
Answer:
Step-by-step explanation:
1. 0
2. 3
3. 18
4. 33
5. 48
6. 198
Identify the solution set of the following quadratic inequality:
-a^2+4a+7>2
options
(-1,5)
(-∞,-1)∪(5,∞)
(-∞,-1]∪[5,∞)
(-∞,-3]∪[0,∞)
The solution set of the quadratic inequality is (-1,5)
What is Quadratic inequality?
Inequalities can take many various forms, just like equations, one of which is the quadratic inequality.
A second-degree equation with a quadratic inequality substitutes an inequality sign for an equal sign.
The two roots are always provided in the answers to quadratic inequality. Different types of roots may exist, and discriminating between them is possible (b2 – 4ac).
The following are the quadratic inequalities' generic forms:
ax2 + bx + c < 0
ax2 + bx + c ≤ 0
ax2 + bx + c > 0
ax2 + bx + c >= 0
According to the given question
-a^2 + 4a + 7 > 2
-a^2 + 4a + 5 >0
multiplying with - 1
a^2 -4a -5 < 0
a^2 - 5a + a - 5 < 0
a(a-5) + 1(a-5) < 0
(a+1)(a-5) < 0
a<-1 & a< 5
a is in between -1 and 5
(-1,5)
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Which polygon appears to be regular?
Answer:
Figure b
Step-by-step explanation:
the sides are equal
a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 402402 gram setting. is there sufficient evidence at the 0.020.02 level that the bags are overfilled? assume the population is normally distributed. state the null and alternative hypotheses for the above scenario.
Yes there is sufficient evidence that the alternative hypothesis is;
bag filling machine works incorrectly at the 402 gram setting which is;
H_o ; μ ≠ 402
Null hypothesis; H_o ; μ = 402
Alternative hypothesis; H_o ; μ ≠ 402
The null hypothesis states that there is no difference in the test which is denoted by H_o. However, the sign of null hypothesis is denoted by the signs of = or ≥ or ≤.
Meanwhile, the alternative hypothesis is one that defers from the null hypothesis. This therefore implies a significant difference in the test. Thus, the signs of alternative hypothesis is denoted by; < or > or ≠.
Now, the question we have is a two tailed test. Thus;
The null hypothesis is;
bag filling machine works correctly at the 402 gram setting which is;
H_o ; μ = 402
The alternative hypothesis is;
bag filling machine works incorrectly at the 402 gram setting which is;
H_o ; μ ≠ 402
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A planet rotates through one complete revolution every 17 hours. Since the axis of rotation is perpendicular to the equator, you can think of a person standing on the equator as standing on the edge of a disc that is rotating through one complete revolution every 17 hours. Find the angular velocity of a person standing on the equator.
The angular velocity of a person standing on the equator is ω = 1.026 × 10⁻⁴ rad/s
What is angular velocity?Angular velocity is the number of revolution per second of an object.
How to find the angular velocity of a person standing on the equator?Since a planet rotates through one complete revolution every 17 hours and since the axis of rotation is perpendicular to the equator, you can think of a person standing on the equator as standing on the edge of a disc that is rotating through one complete revolution every 17 hours. We thus require its angular velocity.
The angular velocity is given by ω = 2π/T where T = period of revolution
Since the planet rotates through one complete revolution every 17 hours, its period, T = 17 hours = 17 h × 60 min/h × 60 s/min = 61200 s
So, substituting the period into the equation for the angular velocity, we have
ω = 2π/T
ω = 2π/61200 s
ω = π/30600 s
ω = 0.0001026 rad/s
ω = 1.026 × 10⁻⁴ rad/s
So, the angular velocity is ω = 1.026 × 10⁻⁴ rad/s
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alexis likes to go for boat rides along a river with her family. in still water, the boat travels about 7 kilometers per hour. in the river, it takes them the same amount of time t to go upstream 4 kilometers as it does to travel downstream 8 kilometers. if the speed of the river is r, which of the following expressions represents the time it takes to travel 4 kilometers upstream?
It takes 51.33 min or 6/7 hrs to travel upstream 4 km.
What is relative velocity?
it is the speed measured with respect to an observer whether he is moving or stationary and it might differ for different observers.
speed of boat = 7 km/hr
speed of river = r km/hr
speed upstream = 7-r km/hr
speed downstream = 7+r km/hr
time taken to go upstream 4 km = 4/(7-r)
time taken to go downstream 8 km = 8/(7+r)
as time taken is equal in both scenario:
4/(7-r) = 8/(7+r)
on solving we get:
r = 7/3 km/hr
put this value in time taken for upstream
4/(7-(7/3)) = 6/7 km/hr or 51.33 min
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Using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.
What is relative velocity?Think about two trains that are traveling in the same direction and at the same pace.
Even though the tracks, buildings, and trees on either side of the track indicate that both trains are moving, to the observer of one train, the other train appears to be stationary.
The other train seems to be moving at a constant speed.
So, we know that:
Speed of boat = 7 km/hr
Speed of river = r km/hr
Now,
Speed upstream = 7-r km/hr
Speed downstream = 7+r km/hr
Time taken to go upstream 4 km = 4/(7-r)
Time taken to go downstream 8 km = 8/(7+r)
As the time taken is equal in both scenarios:
4/(7-r) = 8/(7+r)
On solving we get:
r = 7/3 km/hr
Put this value in time taken for upstream as follows:
4/(7-(7/3)) = 6/7 km/hr or 51.33 min
Therefore, using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.
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H(d) models the basketball's height (in meters) at a horizontal distance of dd meters from Kaori. What does the statement H(R)=4H(R)=4 mean
The statement H(R)=4H means the height of ball is 4H meter at a horizontal distance of R meters from Kaori.
It is given that Kaori is taking a free-throw. H(d) models the basketball's height (in meters) at a horizontal distance of d meters from Kaori.
The given statement is H(R) = 4H.
Here we have H(R) instead of H(d) and it shows the height of basketball. So it clear that the height of basketball's is 4H because H(R)=4H at d = R
Since d represents the horizontal distance from Kaori, therefore the horizontal distance from Kaori is R.
Thus, Answer: The statement H(R)=4H means the height of ball is 4H meter at a horizontal distance of R meters from Kaori.
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Type the integer that makes the following subtraction sentence true:
–7 − ? = 10
Answer:
-17
Step-by-step explanation:
-7-x=10
+7. +7
-x=17
/-1 /-1
x= -17
hopes this helps please mark brainliest
Marco has 2 peices of rope that are each 8 yards long.how many feet of rope does m arco have
Answer:
48 feet
Step-by-step explanation:
Marco has 2 pieces of rope that are each 8 yards long.
2 x 8 = 16 yards.
Marco has a total of 16 yards of rope.
Note that for converting yard to feet, that: 1 yard = 3 feet.
Marco, in this case, has 16 yards. Multiply 16 yards with 3 feet to obtain your answer:
16 yards x (3 feet/1 yard) = 48 feet/16 yards.
Marco has 48 feet worth of rope.
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if i have a b and then i get a 72% on a test that is 30% of my grade, what will my grade be?
Answer:
if you have about an 85 now than you shouldn’t go below a b
Step-by-step explanation:
I need help with this question, I don't understand how we get the x value in the equation.
I'm not trying to cheat, I just need steps to see how we get to the end of it.
y=x-1
y=-x+3
Step-by-step explanation:
the x value comes from the slope when graphing. for example, the slope on this problem is just x which means its only one. so you move up one and to the right one. for the second equation, its negative so you move back one or down one. the x value coms from when they are both intercepted when graphed.
Find the equation of a line that passes through the point (0,-1) and has a gradient of 2.
Leave your answer in the form
y=mx+c
Answer:
Step-by-step explanation:
y = 2x - 1
when you sub in 0 in x and -1 in y, the y-intercept is -1.
Simplify -1(15+4-27) over 16
Answer:
1/2
Step-by-step explanation:
-1(15+4-27)/16
Add 15 and 4 to get 19.
Now you have -1(19-27)/16
Subtract 27 from 19 to get −8.
-1(-8)/16
Reduce the fraction 16/−8 to lowest terms by extracting and canceling out 8.
-(-1/2)
Simplify
1/2
Answer:
1/2
Step-by-step explanation:
⁻¹⁽¹⁵⁺⁴⁻²⁷⁾⁄₁₆
Calculate:
-(15 + 4 - 27) / 16
-(19-27)/16
-(-8) / 16
= 8/16
Simplify:
= 1/2
What is the solution to the inequality 2n-5 > 1
Answer:
n > 3
Step-by-step explanation:
2n - 5 > 1
Add 5 on both sides
2n > 6
Divide by two on both sides to isolate n
n > 3
if the points below represent a direct variatin find the missing value (2, -6) and (5, y)
The missing value if the point is a direct variation is -15
How to determine the missing value?From the question, we have the following ordered pairs
(2, -6) and (5, y)
These ordered pairs are direct variation
A direct variation is represented as
k = y/x
This means that
y/5 = -6/2
Evaluate the quotient
y/5 = -3
Multiply both sides by 5
y = -15
Hence, the value of y is -15
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simplify (8^(5))/(8^(-9))
1.8^-45
2.8^-4
3.8^14
4.8^45
The expression (8^(5))/(8^(-9)) is simplified to 8^14. Option 3
What are index forms?Index form of a number can simply be described as that number written in the form of an exponential expression.
The number can also be written as a single number which is raised to another number.
Some rules of indices to note;
Multiplying index form results in addition of their powersDivision results in subtraction of their powersGiven that;
(8^(5))/(8^(-9))
Then, we have;
8^5-(-9)
8^5+9
Add the powers
8^14
Hence, the value is 8^14
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The heights, in feet, of the trees for sale at two nurseries are shown below.
Yard Works: 7, 9, 7, 12, 5
The Grow Station: 9, 11, 6, 12, 7
Which statements are true regarding the measures of center and variability of these data sets? Select three choices.
The mean of the tree heights at Yard Works is less than the mean of the tree heights at The Grow Station.
The median of the tree heights at Yard Works is greater than the median of the tree heights at The Grow Station.
The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station.
The mean absolute deviation of the tree heights at Yard Works is greater than the mean absolute deviation of the tree heights at The Grow Station.
The mean absolute deviation of the tree heights at Yard Works is equal to the mean absolute deviation of the tree heights at The Grow Station.
THIS IS URGENT NEED NOW
The correct option regarding the heights of the trees include:
The mean of the tree heights at Yard Works is less than the mean of the tree heights at The Grow Station.The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station.The mean absolute deviation of the tree heights at Yard Works is equal to the mean absolute deviation of the tree heights at The Grow StationHow to calculate the value?The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station. This was illustrated as:
(12 - 5) > (12 - 7)
7 > 5
The mean of tree heights at Yard Works is 8 feet.
The mean of tree height at The Grow Station is 9 feet.
The mean absolute deviation of the tree heights at both yards is 2.
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