Answer: 0.06x
Step-by-step explanation:
An algebraic expression is an expression consist of integer constants, variables, and algebraic operations.The given statement: A number is 30% of 20% of the number x.
The required algebraic expression would be:
30% of 20% of x
[tex]=\dfrac{30}{100}\times \dfrac{20}{100}\times x[/tex] [we divide a percentage by 100 to convert it into decimal]
[tex]=\dfrac{6}{100}\times x\\\\=0.06x[/tex]
Hence, the required algebraic expression would be :
0.06x
Base: z(x)=cosx Period:180 Maximum:5 Minimum: -4 What are the transformation? Domain and Range? Graph?
Answer:
The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is [tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex].
The domain of the function is all real numbers and its range is between -4 and 5.
The graph is enclosed below as attachment.
Step-by-step explanation:
Let be [tex]z (x) = \cos x[/tex] the base formula, where [tex]x[/tex] is measured in sexagesimal degrees. This expression must be transformed by using the following data:
[tex]T = 180^{\circ}[/tex] (Period)
[tex]z_{min} = -4[/tex] (Minimum)
[tex]z_{max} = 5[/tex] (Maximum)
The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of [tex]2\pi[/tex] radians. In addition, the following considerations must be taken into account for transformations:
1) [tex]x[/tex] must be replaced by [tex]\frac{2\pi\cdot x}{180^{\circ}}[/tex]. (Horizontal scaling)
2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:
[tex]\Delta z = \frac{z_{max}-z_{min}}{2}[/tex]
[tex]\Delta z = \frac{5+4}{2}[/tex]
[tex]\Delta z = \frac{9}{2}[/tex]
3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)
[tex]z_{m} = \frac{z_{min}+z_{max}}{2}[/tex]
[tex]z_{m} = \frac{1}{2}[/tex]
The new function is:
[tex]z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)[/tex]
Given that [tex]z_{m} = \frac{1}{2}[/tex], [tex]\Delta z = \frac{9}{2}[/tex] and [tex]T = 180^{\circ}[/tex], the outcome is:
[tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex]
The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.
Need answers please !!!!
inital height is 2 meters
Step-by-step explanation:
For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate Lim Sn to obtain the value of the series or state that the series diverges.
n→[infinity]
[infinity]
Σ (4/√k+5 ) - 4/ √ k+6)
k=1
Looks like the series is
[tex]\displaystyle\sum_{k=1}^\infty\left(\frac4{\sqrt{k+5}}-\frac4{\sqrt{k+6}}\right)[/tex]
This series has n-th partial sum
[tex]S_n=\displaystyle\sum_{k=1}^n\bullet[/tex]
(where [tex]\bullet[/tex] is used as a placeholder for the summand)
[tex]S_n=\displaystyle\left(\frac4{\sqrt6}-\frac4{\sqrt7}\right)+\left(\frac4{\sqrt7}-\frac4{\sqrt8}\right)+\cdots+\left(\frac4{\sqrt{n+4}}-\frac4{\sqrt{n+5}}\right)+\left(\frac4{\sqrt{n+5}}-\frac4{\sqrt{n+6}}\right)[/tex]
In each grouped term, the last term is annihilated by the first term of the next group; that is, for instance,
[tex]\displaystyle\left(\frac4{\sqrt6}-\frac4{\sqrt7}\right)+\left(\frac4{\sqrt7}-\frac4{\sqrt8}\right)=\frac4{\sqrt6}-\frac4{\sqrt8}[/tex]
Ultimately, all the middle terms will vanish and we're left with
[tex]S_n=\dfrac4{\sqrt6}-\dfrac4{\sqrt{n+6}}[/tex]
As [tex]n\to\infty[/tex], the last term converges to 0 and we're left with
[tex]\displaystyle\sum_{k=1}^\infty\bullet=\lim_{n\to\infty}S_n=\frac4{\sqrt6}=\boxed{2\sqrt{\dfrac23}}[/tex]
2. The table below shows the activity on the credit card statement of Miss Pepper Mills for the month of April. She started the month with a balance of $342.57.
Date Activity Location Amount
04/05 Payment Payment $200.00
04/15 Charge Gas $26.37
04/22 Charge Macy's $105.42
04/25 Charge Starbuck's $4.24
a. Find the average daily balance.
b. If her card charges an 18.5% annual interest rate on her average daily balance, calculate Miss Pepper Mill’s finance charge for the month of April.
Answer:
Miss Pepper Mills
Credit Card Statement for the month of April:
a. Average Daily Balance:
Average balance = $618.66/5 = $123.73
b. Calculation of Miss Pepper Mill's Finance Charge for the month of April:
Finance charge
= 18.5% of $20.55 x 1/12
= $0.32
Step-by-step explanation:
a) Data and Calculations:
Activity on the credit card statement for April
Beginning balance = $342.57
Date Activity Location Amount Daily Balance
04/01 Balance $342.57
04/05 Payment Payment $200.00 $142.57
04/15 Charge Gas $26.37 $116.20
04/22 Charge Macy's $105.42 $10.78
04/25 Charge Starbuck's $4.24 $6.54
30 days Total = $618.66
Average balance = Total of the daily balances divided by 30 days
= $618.66/30 = $20.55
The value of the average daily balance and the finance charge for Miss pepper mills are $123.732 and $0.32 respectively.
The average daily balance :
(Sum of balances) ÷ number of purchasesSum of balances = (342.57+ (342.57-200) +(342.57 - 200 - 26.37) +(342.57-200-26.37-105.42) + (342.57-200-26.37-105.42-4.24)) = $618.66
Average daily balance :
(618.66) ÷ 5 = 123.732Finance charge for April :
Monthly rate = 18.5% ÷ 12 = 1.541666%Average balance × daily rate
Average balance = (618.66) ÷ 30 = 20.62220.622 * 1.5416666% = 0.32Therefore, the average daily balance and finance charge are $123.732 and $0.32 respectively
Learn more : 149.9448066146972668163077278862934016
solve for the variable x^2 - 8 = -1 Show all work please
Answer:
x = ±sqrt(7)
Step-by-step explanation:
x^2 - 8 = -1
Add 8 to each side
x^2 - 8+8 = -1+8
x^2 = 7
Take the square root of each side
sqrt(x^2) = ±sqrt(7)
x = ±sqrt(7)
Need help finding the length
Answer:
27
Step-by-step explanation:
First, we need to find x. We are given the perimeter, which is 2l + 2w, so from there, we have an equation of 2(4x-1) + 2(3x+2) = 100. By working through it, we get that x = 7. We're asked to find WX, so plug 7 into 4x - 1 and get 27.
Answer:
27 unitsStep-by-step explanation:
Perimeter of rectangle is 2(l) + 2(w).
The perimeter is given 100 units.
2(4x-1) + 2(3x+2) = 100
Solve for x.
8x-2+6x+4=100
14x+2=100
14x=98
x=7
Plug x as 7 for the side WX.
4(7) - 1
28-1
= 27
Solve the equation: 1/3(y - 2) - 5/6(y + 1) = 3/4(y - 3) - 2
Answer:
y=2.2
Step-by-step explanation:
1: Distribute all numbers to get rid of all parenthesis
2: Solve
Hope this helped :) LET ME KNOW IF YOU NEED THE ANSWER IN A DIFFERENT FORM I CAN GET IT FOR YOU
Choose the correct answer.
1/1,000 liter
A: 1 milliliter
B: 1 deciliter
C: 1 centiliter
Answer:
A. 1 milliliter
Step-by-step explanation:
1000 milliliters = 1 liter
0.001 liters = 1 milliliter
Identify which equations have one solution, infinitely many solutions, or no solution. No
Answer: all of them have one solutions
Step-by-step explanation:
In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $112 with a standard deviation of $16. Use a 0.05 level of significance and determine whether or not the average room price is significantly different from $108.50.
Which form of the hypotheses should be used to test whether or not the average room price is significantly different from $108.50?
H0:
a. mu is greater than or equal to $108.50
b. mu is greater than $108.50
c. mu is less than $108.50mu is less than or equal to $108.50
d. mu is equal to $108.50mu is not equal to $108.50
Ha:
a. mu is greater than or equal to $108.50
b. mu is greater than $108.50mu is less than $108.50
c. mu is less than or equal to $108.50
d. mu is equal to $108.50mu is not equal to $108.50
Answer:
H0 :
a. mu is greater than or equal to $108.50
Ha:
c. mu is less than or equal to $108.50
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the z - score for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence
In the given scenario the test is to identify whether the average room price significantly different from $108.50. We take null hypothesis as mu is greater or equal to $108.50.
What is the angle between the given vector and the positive direction of the x-axis? (Round your answer to the nearest degree.) i + 3 j
Answer:
72°
Step-by-step explanation:
Given two vectors a and b, The vector i+3j will form a right angled triangle with the x-axis (i.e the horizontal axis).
The opposite side of the triangle on the Cartesian plane will be 3units along the y axis while the adjacent will be 1 unit along the x axis.
The angle between thus two vectors is expressed as tan (theta) = opp/adj
tantheta = 3/1
theta = tan^-1(3)
Theta = 71.57° ≈ 72° to nearest degree
Use the given categorical data to construct the relative frequency distribution. Natural births randomly selected from four hospitals in a highly populated region occurred on the days of the week (in the order of Monday through Sunday) with the frequencies 53, 63, 68, 58, 61, 43, 54. Does it appear that such births occur on the days of the week with equal frequency?
Answer: Yes
Step-by-step explanation:
See explanations in the attached document
12. What is m∠GEA?
Answer:
90°
Step-by-step explanation:
Circumcenter of a triangle is obtained by drawing perpendicular bisectors of the sides of a triangle. Hence GE is perpendicular to AC.
Therefore, m∠GEA = 90°
Find two numbers in a given ratio such that the difference of their squares is to the sum of the numbers in a given ratio.Ratios, respectively, are 3 to 1 and 6 to 1.
According to the given situation, the computation of two number in a given ratio is shown below:-
We assume the numbers is x and y
Given that
[tex]\frac{x}{y} = \frac{3}{1}[/tex]
x = 3y
and
[tex]\frac{x^2-y^2}{x + y} = \frac{6}{1} \\\\\frac{(x + y) (x - y)}{(x + y)} = 6[/tex]
With the help of above formula we will put the value and be able to find the values of x and y
x - y = 6
3y - y = 6
2y = 6
y = 3
x = 3y = 9
x = 9, y = 3
Therefore the correct answer is x = 9 where as y = 3
Holly wants to save money for an emergency. Holly invests $500 in an account that pays an interest rate of 6.75% How many years will it take for the account to
reach $14,300? Round your answer to the
nearest hundredth.
Answer:
51.339
Step-by-step explanation:
Hello,
At the beginning Holly has $500
After one year
he will get 500*(1+6.75%)=500*1.0675
After n year (n being real)
he will get
[tex]500\cdot1.0675^n[/tex]
and we are looking for n so that
[tex]500\cdot1.0675^n=14,300\\<=> ln (500\cdot1.0675^n)=ln(14,300)\\<=>ln(500)+n\cdot ln(1.0675)=ln(14,300)\\<=> n= \dfrac{ln(14,300)-ln(500)}{ln(1.0675)}=51.338550...\\[/tex]
so we need 51.339 years
Hope this helps
please Help will mark brainliest !!1!Use the linear combination method to solve the system of equations. Explain each step of your solution. 2x -3y = 13 x+2=- 4
Answer:
work is shown and pictured
The height of a cylinder is 9.5 cm. The diameter is 1.5 cm longer than the height. Which is closest to the volume of the cylinder?
Answer:
853.8cm^3
Step-by-step explanation:
[tex]h = 9.5cm\\d = 1.5cm + 9.5 = 10.7\\r =d/2=10.7/2=5.35\\\\V = \pi r^2 h\\V = 3.14 \times (5.35)^2 \times 9.5\\\\V =853.8 cm^3[/tex]
Identify the initial amount a and the growth factor b in the exponential function. f(x) = 620 • 7.8x
Answer:
Initial amount (a)= 620
Growth factor (b)= 7.8
Step-by-step explanation:
620 is the initial amount and is multiplied by 7.8 x which is the growth factor.
A hypothesis test is to be performed for a population proportion. For the given sample data and null hypothesis, compute the value of the test statistic, Z.
415 people were asked if they were satisfied with their jobs. 49% said they were. H0: p= 0.3
a. 8.446
b. 2.612
c. 0.415
d. 4.125
Answer:
The correct option is a
Step-by-step explanation:
From the question we are told that
The sample size is n = 415
The sample proportion is [tex]\r p = 0.49[/tex]
Now
The null hypothesis is [tex]H_o : p = 0.3[/tex]
The alternative hypothesis is [tex]H_a : p \ne 0.3[/tex]
The test statistics is mathematically evaluated as
[tex]t = \frac{\r p - p }{ \frac{\sqrt{ p (1- p )} }{n} }[/tex]
substituting values
[tex]t = \frac{0.49 - 0.3 }{ \sqrt{ \frac{0.3 (1- 0.3 ) }{415} }}[/tex]
[tex]t = 8.446[/tex]
amanda teaches the art of quilling to 4 students. These students each teach art of quilling to 4 other students. If this process continues for 5 generation after amanda, BLANK people other than amanda will know the art of qiulling
Answer:
1024
Step-by-step explanation:
4 * 4 * 4 * 4 * 4
I really need help! Please help, i don't understandddd
Answer:
x is 2
Step-by-step explanation:
To solve this you have to use the Pythagoram theorem A^2+B^2=C^2. So 9+16=C^2.
25=C^2
c=5
Than since u know the radius of the circle is 3, its 5-3 so x is 2.
Starting from an airport, an airplane flies 210 miles southeast and then 210 miles south. How far, in miles, from the airport is the plane? (Round your answer to the nearest mile.)
Answer:
The plane is 388 miles far from the airport.
Step-by-step explanation:
We know that, the angle between southeast and south directions is [tex]135^\circ[/tex].
The plane travels as per the triangle as shown in the attached image.
A is the location of airport.
First it travels for 210 miles southeast from A to B and then 210 miles south from B to C.
[tex]\angle ABC = 135^\circ[/tex]
To find:
Side AC = ?
Solution:
As we can see, the [tex]\triangle ABC[/tex] is an isosceles triangle with sides AB = BC = 210 miles.
So, we can say that the angles opposite to the equal angles in a triangle are also equal. [tex]\angle A = \angle C[/tex]
And sum of all three angles of a triangle is equal to [tex]180^\circ[/tex].
[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow \angle A+135^\circ+\angle A = 180^\circ\\\Rightarrow \angle A = \dfrac{1}{2} \times 45^\circ\\\Rightarrow \angle A =22.5^\circ[/tex]
Now, we can use Sine Rule:
[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB}[/tex]
a, b are the sides opposite to the angles [tex]\angle A and \angle B[/tex] respectively.
[tex]\dfrac{210}{sin22.5^\circ} = \dfrac{b}{sin135^\circ}\\\Rightarrow \dfrac{210}{sin22.5^\circ} = \dfrac{b}{cos45^\circ}\\\Rightarrow b = 210\times \dfrac{1}{\sqrt2 \times 0.3826}\\\Rightarrow b = 210\times \dfrac{1}{0.54}\\\Rightarrow b \approx 388\ miles[/tex]
So, the answer is:
The plane is 388 miles far from the airport.
1/2 of a right angle is a? answers: A. reflex angle B. obtuse angle C. acute angle D. straight angle
Answer:
C. acute angle
Step-by-step explanation:
As you know ,right angle is equal to 90 degrees so half of 90 degrees is 45 degree which is an acute angle (acute angles are the angles which are less than 90 degrees)
Hope this helps and pls mark as brainliest :)
Answer: acute
Step-by-step explanation:
An angle that is less than 90 degrees
Consider a normal distribution with mean 21 and standard deviation 4. What is the probability a value selected at random from this distribution is greater than 21
Answer:
P [ Z > 21 ] = 0,5 or P [ Z > 21 ] = 50 %
Step-by-step explanation:
Normal Distribution N(21;4)
The question here is what is the area of the bell shape curve. As 21 is a mean for this distribution is in the middle of the bell, so values bigger than 21 will have a probability of 0,5, and values smaller than 21 will have the same probability 0,5. We must remember that the whole area under the curve has an area of 1 ( or 100% )
Which steps can be used in order to determine the solution to Negative 1.3 + 4.6 x = 0.3 + 4 x?
Answer:
x=8/3 OR 2.7
Step-by-step explanation:
-1.3+4.6x=0.3+4x
4.6x-4x=0.3+1.3
0.6x=1.6
x=1.6/0.6=8/3
x=8/3 OR 2.7
Hope this helps!
Answer:
[tex]\boxed{x = 2\frac{2}{3} }[/tex]
Step-by-step explanation:
[tex]-1.3+4.6x = 0.3 +4x[/tex]
Collecting like terms
[tex]4.6 x -4x = 0.3+1.3[/tex]
[tex]0.6x = 1.6[/tex]
Dividing both sides by 0.6
x = 1.6 / 0.6
x = 2 2/3
If Juan drives 50 mph for 1/2 hour then 60 mph for 1 1/2 an hour, how far does he drive?
Answer:
115 miles
Step-by-step explanation:
First find the distance at 50 mph
d = 50 mph * .5 hours
= 25 miles
Then find the distance at 60 mph
d = 60 mph * 1.5 hours
= 90 miles
Add the distances together
25+90
115 miles
Answer:
he drives a 115 miles
Step-by-step explanation:
if he drives 50 mph for half an hour he drove 25 miles then if he drives 60 mph for 1 hour and 30 minutes he would of drove 90 miles. 60 + 30=90
90+25=115 so he drove 115 miles.
A basketball team plays half of its games during the day and half at night. Ten scores from day games and ten scores from night
games were randomly selected by the team's statistician. The following statistical information was calculated from the final game
scores.
Day Night
Mean 58 72
Median 46 63
Mode 50. 70
Range 21 33
Based on these samples, what generalization can be made?
A. The basketball team scored the same number of points in day games as night games.
OB. The basketball team scored more points in night games than in day games.
OC. The basketball team scored more points in day games than in night games.
OD. Not enough information is provided to draw any of these conclusions,
Option B
Because the average points scored in the night is more than that of the day
If 4 bushels of oats weigh 58 kg, how much do 6.5 bushels of oats weigh?
Answer:
94.25 kg I think
Step-by-step explanation:
58/4 =14.5 kg per bushel
6.5 x 14.5=94.25 kg
Answer:
94.25
Step-by-step explanation:
First you need to find the unit rate which is 58/4 which equals to 14.5 then you multiply by 6.5 to find 94.25
Which is the graph of x – y = 1?
Answer:
Step-by-step explanation:
Hope you can see it.
The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.4 in/s. At what rate is the volume of the cone changing when the radius is 109 in. and the height is 198 in.
Answer:
[tex]79591.8872 in^3/s[/tex]
Step-by-step explanation:
we know that the volume of a right circular cone is give as
[tex]V(r,h)= \frac{1}{3} \pi r^2h\\\\[/tex]
Therefore differentiating partially with respect to r and h we have
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [2rh\frac{dr}{dt} +r^2\frac{dh}{dt}][/tex]
[tex]\frac{dV}{dt} = \frac{\pi}{3} [218*198*1.1+109^2*2.4][/tex]
[tex]\frac{dV}{dt} = \frac{\pi}{3} [47480.4+28514.4]\\\\\frac{dV}{dt} = \frac{\pi}{3} [75994.8]\\\\ \frac{dV}{dt} = 3.142 [25331.6]\\\\ \frac{dV}{dt} =79591.8872 in^3/s[/tex]