Answer:
The base is: [tex]3 \sqrt[3]{4}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \frac{1}{4}(\sqrt[3]{108})^x[/tex]
Required
The base
Expand 108
[tex]f(x) = \frac{1}{4}(\sqrt[3]{3^3 * 4})^x[/tex]
Rewrite the exponent as:
[tex]f(x) = \frac{1}{4}(3^3 * 4)^\frac{1}{3}^x[/tex]
Expand
[tex]f(x) = \frac{1}{4}(3^3^\frac{1}{3} * 4^\frac{1}{3})^x[/tex]
[tex]f(x) = \frac{1}{4}(3 * 4^\frac{1}{3})^x[/tex]
Rewrite as:
[tex]f(x) = \frac{1}{4}(3 \sqrt[3]{4})^x[/tex]
An exponential function has the following form:
[tex]y=ab^x[/tex]
Where
[tex]b \to base[/tex]
By comparison:
[tex]b =3 \sqrt[3]{4}[/tex]
So, the base is: [tex]3 \sqrt[3]{4}[/tex]
Answer:
B
Step-by-step explanation:
good luck
What is the y-intercept of the graph of the line whose equation is y = -2/5x + 4?
1) - 5/2
2) - 2/5
3) 0
4) 4
I’ve been stuck on this question for so long I need help with it.
Answer:
4
Step-by-step explanation:
in y=mx+b, the "b" is the y-intercept
Answer:
4
it's in y = mx + b form, where b is the y-intercept
which statement is true?
Answer:
The y-intercept of function a is greater than the y intercept of function b
Step-by-step explanation:
function a:
y = 4x + 2
function b:
y = 2x + 1
I am one of Jehovah's Witnesses reply if you are to
Answer:
I am
Step-by-step explanation:
Use the given values to complete each table.
PLEASE HELP.
The length of a rectangle is 4 meters more than the width of the rectangle. The perimeter of the rectangle is 40 meters. What are the length and the width of the rectangle? *
Answer:
Length = 12 m, Width = 8 m
Step-by-step explanation:
Let the width of the rectangle is b.
Length, l = 4+b
The perimeter of the rectangle = 40 m
We know that,
Perimeter of rectangle = 2(l+b)
2(4+b+b) = 40
4+2b = 20
Subtract 2 from boths sides,
2b = 16
b = 8
Width = 8 m
Length = 4+8 = 12 m
Hence, the length and the width of the rectangle is 12 m and 8 m respectively.
Find the value of x to the nearest tenth. 2 4 x 8
192 because if you put 24 into 8 groups there are 192
11
Akhtar gets a bonus of 20% of £70
Karl gets a bonus of £26
Work out the difference between the bonus Akhtar gets and the bonus Karl gets.
help
Answer:
8.8
Step-by-step explanation:
Akhtar's bonus = 20% × £70 = £14
karl's bonus = 20% × £26 = £5.2
Difference = £14 - £5.2 = 8.8
**I'm not sure about the answer sorry, please get it checked.
Paul signs up for a new cell phone plan. He is offered a discount for the first five months. After this period, his rate increases by $8.50 per month. His total cost at the end of the year is $245.50. Paul wrote the following equation to represent his plan. 5x + 7(x + 8.50) = 245.50
Answer:
The first 5 months Paul paid $ 15.50, and in the next 7 months he paid $ 24.
Step-by-step explanation:
Since Paul signs up for a new cell phone plan, and he is offered a discount for the first five months, and after this period, his rate increases by $ 8.50 per month, and his total cost at the end of the year is $ 245.50, and Paul wrote the following equation to represent his plan: 5x + 7 (x + 8.50) = 245.50; To determine the value of X, the following calculation must be performed:
5X + 7 x (X + 8.50) = 245.50
5X + 7X + 59.50 = 245.50
12X + 59.50 = 245.50
12X = 245.50 - 59.50
12X = 186
X = 186/12
X = 15.50
Therefore, the first 5 months Paul paid $ 15.50, and in the next 7 months he paid $ 24.
factorise fully 16c^4p^2+20cp^3
Answer:
4cp^2 ( 4c^3+5p
Step-by-step explanation:
See image below:)
The factored form of the expression will be [tex]4cp^2 (4c^3+5p)[/tex]
Factorization:Given the expression 16c^4p^2+20cp^3
Get the factor for each term
[tex]16c^4p^2 = 4 * 4 * c^3 * c * p^2 \\20cp^3= 4 * 5 * c * p^2 * p[/tex]From the factors, you can see that 4cp^2 is common to both terms. Hence the factored form of the expression will be:
[tex]4cp^2 (4c^3+5p)[/tex]
Learn more on factored form here: https://brainly.com/question/25948667
ou want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 99% confident that you esimate is within 0.1% of the true population proportion. How large of a sample size is required
Answer: the required sample size =1658944
Step-by-step explanation:
When the prior population proportion for the study is unknown , then the formula for sample size is [tex]Sample \ size = 0.25(\dfrac{z^*}{Margin\ of \ error})^2[/tex]
z-value for 99% confidence = 2.576
[tex]Sample \ size = 0.25(\dfrac{2.576}{0.001})^2\\\\=0.25(2576)^2\\\\=1658944[/tex]
Hence, the required sample size =1658944
Which of the following figures has reflectional symmetry?
Help !!
Answer:
Figure D. (A)
When you flip the figure across like a mirror, it remains the same shape as the other side. An easy way to determine this is by cutting a line down the middle.
Reflectional symmetry states that if there exists at least one line that divides a figure into two halves such that one-half is the mirror image of the other half.
Edit: Typo!
1 ÷ 7
pls help me
hi)
Answer:
7 lol
Step-by-step explanation:
self explanatory-
but you divide 1 by 7 you get 7
14. Anna, Bella, Claire, Dora and Erika meet at a party. Each pair who know each other shake hands exactly once.
Anna shakes hands only once, Bella twice, Claire three times and Dora four times. How many people does Erika
shake hands with?
(A) 1
(B)2
(C) 3
(D) 4
(E) 5
Answer:
(B) part is the answer which means he shook hands with 2.
Step-by-step explanation:
Since Dora shook hands four time with: Alan, Bella, Claire, Erik. Then Erik shook hands only with Dora. Claire shook hands three times with Bella, Claire and Dora. Then Bella shook hands with two people Claire and Dora. Now Erik would shook hands only with those who shook hands with him. 2 people Claire and Dora
The required handshake Erika had is given as 2. Option B is correct.
What are permutation and combination?In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
Here,
According to the question,
Dora shake hands 4 times,
So Dora shakes hands with Anna, Bella, Claire, and Erika.
Anna shake hands 1 time,
From the above combination.
Dora shakes hands with Anna,
Implies Anna does not shake hands with Erika,
Clair shakes hands 3 times,
So Clair shakes hands with Bella, Claire, and Erika.
Bella shake hands 2 times,
So Bella shakes hands with Bella and Claire.
From the above reasoning, Erika shakes hands with Dora and Clair.
Learn more about permutations and combinations here: https://brainly.com/question/2295036
#SPJ2
HELP QUICK I NEED ANSWER
Answer:
The answer is 23
Step-by-step explanation:
Answer:
the answer of the question is 23
The height ofthe saddle ofa horse above the base ofa carousel can be modeled 4t by the equation f-rr) : 12 sin ^ r 42, where I represents seconds after the ride started. I How much time does to take for the horse to complete one cycle of motion and return to its starting height. What is the maximum height and the minimum height ofthe horse's saddle above the base ofthe carousel
Answer:
(a) The time to complete 1 cycle and return is 16/3
(b) The minimum height is 30 inches and the maximum is 54 inches
Step-by-step explanation:
Given
[tex]f(t)=12\sin(\frac{3\pi}{8}t) + 42[/tex]
Solving (a): Time to complete 1 cycle and return
This implies that we calculate the period.
This is calculated using:
[tex]T = \frac{2\pi}{w}[/tex]
Where:
[tex]w = \frac{3\pi}{8}[/tex]
So, we have:
[tex]T = \frac{2\pi}{3\pi/8}[/tex]
Rewrite as:
[tex]T = \frac{8*2\pi}{3\pi}[/tex]
[tex]T = \frac{16}{3}[/tex]
Solving (b): The maximum and the minimum height
To do this, we have:
[tex]-1 \le \sin(\theta) \le 1[/tex]
Which means:
[tex]-1 \le \sin(\frac{3\pi}{8}) \le 1[/tex]
So, the maximum and the minimum of [tex]\sin(\frac{3\pi}{8})[/tex] are:
[tex]\sin(\frac{3\pi}{8}) = -1[/tex] --- minimum
[tex]\sin(\frac{3\pi}{8}) = 1[/tex] --- maximum
Given that:
[tex]f(t)=12\sin(\frac{3\pi}{8}t) + 42[/tex]
So, the minimum height is:
[tex]h_{min} = 12 * -1 + 42 = 30[/tex]
The maximum is:
[tex]h_{max} = 12 * 1 + 42 = 54[/tex]
Two angles are complementary ( the sum of the two angles is 90°). The sum of the first angle plus twice the second angle is 150°. Find the measures of the angles.
Answer:
30 and 60
Step-by-step explanation:
Let x represent the first angle
(x) the sum of the first angle plus twice of the second angle 2(90 - x)
x + 180 - 2x = 150
180 - 150 = 2x - x (we export like terms to the same side of the equation)
30 = x is the measure of the first angle and since the second angle is complementary to this the measure of the second angle is 90 - 30 = 60
what is the ratio of 20cm to 1m
9514 1404 393
Answer:
1 to 5
Step-by-step explanation:
20 cm to 1 m = 20 cm to 100 cm = 20 to 100 = 1 to 5
PLEASE HELP !!! WILL MARK WHOEVER GETS IT RIGHT AS BRAINLIEST !!
Answer:
Last one (x + 4, y - 1).
Step-by-step explanation:
From the point, you go right 4 (going right on a graph is positive).
From there, you go down 1 (going down on a graph is negative).
What is the equation of the line that is perpendicular to the line y= 3/5x+10 and passes through the point (15,5)?
Answer:
Step-by-step explanation:
This is really super super simple as long as you know the rules for finding a perpedicular slope from a given line. The perpendicular slope of a line is the opposite reciprocal of the given slope. Our given slope is 3/5, therefore, the perpendicular slope is -5/3. There's only one line with that exact slope, so the choice is the last one. (BTW, check the coordinate you gave. It should be
(15, -5), not (15, 5)!)
Why are unit fractions important?
Answer:
Unit fractions play an important role in modular arithmetic, as they may be used to reduce modular division to the calculation of greatest common divisors. Specifically, suppose that we wish to perform divisions by a value x, modulo y. In order for division by x to be well defined modulo y, x and y must be relatively prime.
Step-by-step explanation:
If 50% of the students in your class are men and 20% of the men have blond hair, which of the following describes the percentage of students in your class who are men with blond hair?
Answer:
10%
Step-by-step explanation:
10% of the Male students have blonde hair
What is the slope of the line described by the equation below?
y-5=-3(x - 17)
O A. -3
O B. 3
O c. 5
O D. -5
PLEASE HELP ME
Answer:
A
Step-by-step explanation:
Hi there!
The given equation of the line is in slope-point form, which is y-y1=m(x-x1), where (x1,y1) is a point and m is the slope
the given equation is y-5=-3(x - 17)
-3 is in the place of where m is, so -3 is the slope. Remember that the sign is part of the slope, so it can't be B (3). Therefore, the answer is A
Hope this helps!
If each 2 cm on the scale drawing below equals 9 feet, what is the actual area of the shape in square units?
Answer: 18 cm
Step-by-step explanation: 9 feet x 2
A website posts evaluations on airlines. It posts the most positive and the most negative comments for each airline. Discuss the usefulness of this feedback for a reader wanting to know about the airline.
choose the correct statement below. SELECT ALL THAT APPLY:
A. The reader can accurately assess the airline based on the posted evaluations.
B. the reader cannot accurately assess the airline because the evaluations are not necessarily representative of all evaluations.
C. the reader cannot accurately assess the airline because the method of choosing the sample is unclear.
D. the reader cannot accurately assess the airline without reading all the evaluations.
Answer:
B. the reader cannot accurately assess the airline because the evaluations are not necessarily representative of all evaluations.D. the reader cannot accurately assess the airline without reading all the evaluations.Step-by-step explanation:
Using the most positive and the most negative comments to evaluate the airlines will not be an accurate measure of the airline because these are not a good enough sample. The opinions of those who fall in-between the most positive and negative should also be included as they could have some vital details as well.
Also, in order to be completely accurate, all the comments of the airline should have been posted because this would represent the entire population of comments and so would give the best assessment.
Match each system of equations to the inverse of its coefficient matrix, A^-1and the matrix of its solution, X.
Answer: Hello the system of equations and other data required are missing attached below are the missing data
answer :
attached below
Step-by-step explanation:
1st system of equations ( top left ) = Image number 8
system of equation ( Image 10 ) = Image 4
system of equation ( Image 9 ) = Image 6
system of equations ( Image 7 ) = Image 2
attached below is a pictorial representation of the solution
(120+2x)+(70+2x)=15,000
not angles, area. also foiling
Answer:
x =3702.5
Step-by-step explanation:
Given data
(120+2x)+(70+2x)=15,000
Let us open the bracket
120+2x+70+2x=15,000
Collect like terms
120+70+2x+2x=15,000
190+4x=15000
4x=15000-190
4x= 14810
Divide both sides by 4
x=14810/4
x= 3702.5
Hence the value of x =3702.5
A cone-shaped paper drinking cup is to be made to hold 24 cm3 of water. Find the height and radius of the cup that will use the smallest amount of paper. (Round your answers to two decimal places.)
Answer:
I. Radius, r = 2.90 cm
II. Height, h = 4.10 cm
Step-by-step explanation:
Given the following data;
Volume of cone = 24 cm³
To find the height and radius of the cup that will use the smallest amount of paper;
Mathematically, the volume of a cone is given by the formula;
[tex] V = \frac{1}{3} \pi r^{2}h[/tex] ......equation 1
Where;
V is the volume of the cone.
r is the radius of the base of the cone.
h is the height of the cone.
Substituting into the formula, we have;
[tex] 36 = \frac{1}{3} \pi r^{2}h[/tex]
Multiplying both sides by 3, we have;
[tex] 108 = \pi r^{2}h[/tex]
Making radius, r the subject of formula, we have;
[tex] r^{2} = \frac {108}{ \pi h} [/tex]
Taking the square root of both sides, we have;
[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]
Mathematically, the lateral surface area of a cone is given by the formula;
[tex] LSA = \pi rl [/tex] ......equation 2
Where;
r is the radius of a cone
l is the slant height of a cone.
To find the slant height, we would apply the Pythagorean' theorem;
[tex] l = \sqrt {r^{2} + h^{2}} [/tex]
Substituting r into the above equation, we have;
[tex] l = \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]
Substituting the values of r and l into eqn 2, we have;
[tex] LSA = \pi * \sqrt { \frac {108}{ \pi h}} * \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]
Simplifying further, we have;
[tex] LSA = \sqrt {108} * \sqrt { \frac {\pi h^{3} + 108}{\pi h}} [/tex]
[tex] LSA = \sqrt {108} * \sqrt { \frac {108}{ h^{2}} + \pi h}} [/tex]
Next, to find the value of h, we differentiate the above mathematical equation with respect to h;
[tex] \frac {dS}{dh} = \sqrt {108} * (\pi - \frac {216}{h^{3}}) * (\pi h + \frac {108}{h^{2}}) [/tex]
Limiting [tex] \frac {dS}{dh} [/tex] w.r.t 0;
[tex] \frac {dS}{dh} = 0 [/tex]
[tex] (\pi - \frac {216}{h^{3}}) = 0 [/tex]
Rearranging the equation, we have;
[tex] \pi = \frac {216}{h^{3}} [/tex]
We know that π = 3.142
[tex] 3.142 = \frac {216}{h^{3}} [/tex]
Cross-multiplying, we have;
[tex] 3.142h^{3} = 216 [/tex]
[tex] h^{3} = \frac {216}{3.142} [/tex]
[tex] h^{3} = 68.75 [/tex]
Taking the cube root of both sides, we have;
Height, h = 4.10 cm
Lastly, we find the value of r;
[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]
[tex] r = \sqrt { \frac {108}{3.142 * 4.10}} [/tex]
[tex] r = \sqrt { \frac {108}{12.88}} [/tex]
[tex] r = \sqrt {8.39} [/tex]
Radius, r = 2.90 cm
The height and radius of the cup that will use the smallest amount of paper is;
Radius = 2.52 cm
Radius = 2.52 cmHeight = 3.58 cm
Let us first state some relevant formulas;
Volume of a cone is;
V = ⅓πr²h
Surface area of a cone is;
S = πrL
Where L is Slant height and has a formula;
L = √(h² + r²)
We are told that the cone is to hold 24 cm³. Thus; V = 24 cm³
24 = ⅓πr²h
πr²h = 72
r = √(72/πh)
Putting √(72/πh) for r in the Slant height equation gives;
L = √(h² + (72/πh))
Thus;
S = π × √(72/πh) × √(h² + (72/πh))
Differentiating with respect to h gives;
dS/dh = √72 × (π - 144/h³) × 1/√(πh + 72/h²)
At dS/dh = 0,we will have;
(π - 144/h³) = 0
Thus;
h³ = 144/π
h = 3.58 cm
Thus, from r = √(72/πh);
r = √(72/(π × 3.58))
r = 2.52 cm
Read more at; https://brainly.com/question/4405937
What is the slope of the line through (-5, -10) and (-1, 5)
Answer:
Slope = 15/4
Step-by-step explanation:
Use the slope formula and you'll get the same answer.
Hope this helps:)
Use the net to find the surface area of the regular pyramid.
Answer:
D
Step-by-step explanation:
Base perimeter = side x 5 = 8 x 5 = 40 cm
LA = (base perimeter x slant height)/2 = (40 x 9)/2 = 180 cm^2
SA = base area + lateral area = 110.1 + 180 = 290.1 cm^2
To evaluate whether or not the intake of a vitamin or mineral is adequate, comparisons are made between the intake distribution and the requirement distribution. Here is some information about the distribution of vitamin C intake, in milligrams per day, for women aged 19 to 30 years:
Percentile (mg/d)
Mean 1st 5th 19th 25th 50th 75th 90th 95th 99th
84.2 31 43 47 60 79 103 126 141 180
Use the 5th, the 50th, and the 95th percentiles of this distribution to estimate the mean (±0.01) and standard deviation (±0.01) of this distribution assuming that the distribution is Normal.
μ = _________
σ = _________
Answer:
[tex]Mean=79[/tex]
[tex]\sigma=30.3951.[/tex]
Step-by-step explanation:
From the question we are told that:
[tex]Age Bracket :19-20[/tex]
[tex]5th\ percentile = 42[/tex]
[tex]50th\ percentile = 79[/tex]
[tex]95th\ percentile = 142.[/tex]
Generally the mean Median and mode of the 50th percentile is are all equal
[tex]Mean=Median=Mode[/tex]
Therefore
[tex]Mean=79[/tex]
Generally for Normal distribution
[tex]5th\ percentile\ = mean - 1.645*\sigma[/tex]
[tex]95th\ percentile\ = mean + 1.645*\sigma[/tex]
Therefore
[tex](95th\ percentile\ - 5th\ percentile) = 2*(1.645*SD).[/tex]
[tex]\sigma=(95th\ percentile\ - 5th\ percentile)/3.29[/tex]
[tex]\sigma=\frac{142-42}{3.29}[/tex]
[tex]\sigma=30.3951.[/tex]