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]f(x)=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]
What is the median of 6, 7, 3, 15, 4, 4.
Answer:
5
Step-by-step explanation:
The median is the middle when the numbers are lined up from smallest to largest
3,4,4,6,7,15
There are 6 number so the middle is the between the 3rd and 4th number
3,4,4, 6,7,15
Take the 3rd and 4th numbers and average
(4+6)/2 = 10/2 = 5
Answer:
median = 5
Step-by-step explanation:
Arrange the data in ascending order :
3 , 4 , 4 , 6 , 7 , 15
Choose the middle number.
Here there are even number of data. Take the average of the middle
numbers .
4 and 6 are the middle number. average of 4 and 6 = ( 4 + 6 ) /2 = 5
Therefore , median = 5
i need help. Also need the answer in step by step form
Answer: GIVEN : f(x)= -3x+1
f(x)= -5
REQUIRE: x=?
CALCULATION:
f(x)= -3x+1
As, given f(x)= -5.
Hence,
-5= -3x+1
OR
-3x+1= -5
-3x= -5-1
-3x=-6
x= -6/-3
x= 2
Which values are solutions to the inequality below? Check all that apply.
x < 64
O A. 9
11
B. 66
C. 64
D. 6
E. 8
F. no solutions
What is The sum of b and 11
What is the answer? The question is on the picture
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Answer:
D. 32 square units
Step-by-step explanation:
At 40% scale, the length is ...
(20 units)×40% = 8 units
and the width is ...
(10 units)×40% = 4 units
The area is the product of length and width, so is ...
A = (8 units)(4 units) = 32 square units
What is the value of
[tex] \frac{ - 2(7 - 15)}{4} [/tex]
○-4
○-2
○2
○4
Answer:
4
Step-by-step explanation:
Based on your math expression:
7-15 = -8
-2*(-8) = 16
16 / 4 = 4
Answer:
4
Step-by-step explanation:
-2(7-15)
=-14+30
=16÷4
=4
if gh¢400.00 is deposited at a bank at 10% per annum compounded quarterly, how long will it take the deposit to double it value.
Answer:
~ 7 years
Step-by-step explanation:
2 = (1 + .1/4)^(4t)
2 = (1.025)^(4t)
Take the log of both sides
log2 = 4t * log1.025
divide both sides by log1.025
log2/log1.025 = 4t
28.07103452593863 = 4t
Divide both sides by 4
7.017758631484657 = t
~ 7 years
simplify this fully x+x+y×y
Answer and Step-by-step explanation:
The answer would be 2x + 2y.
This is because we combine the x's together and the y's together. This is the simplest form of the expression.
#teamtrees #PAW (Plant And Water)
Answer:
2x+y^2
Step-by-step explanation:
Collect like terms and rewrite
2x+y*y
A rectangular garden covers 80 yd?. The length is 7 yd longer than the width. Find the length and width.
Round your answers to the nearest tenth of a yard.
Answer:
The width of the rectangle is 6,105 yards, and the length of the rectangle is 13,105 yards.
Step-by-step explanation:
Given that a rectangular garden covers 80 square yards, and the length is 7 yd longer than the width, to find the length and width of the rectangle the following calculation must be performed, knowing that the area of a rectangle arises from multiplying its width by its length:
X x (X + 7) = 80
5 x 12 = 60
6 x 13 = 78
8 x 14 = 112
6.1 x 13.1 = 79.91
6,105 x 13,105 = 80
Therefore, the width of the rectangle is 6,105 yards, and the length of the rectangle is 13,105 yards.
If a normal distribution has a mean of 104 and a standard deviation of 6, what is the z-score for a value of 110?
A. 1.5
B. 2
C. 1
D. 0.5
Answer: 1.5
mean: 104
S.D: 6
110-104/6=1.5
Evaluate the expression when a = 7 and c= -4.
-a+5c
pls help
Answer:
-27
Step-by-step explanation:
a = 7 and c = -4
- a + 5 c
- ( 7 ) + 5 ( - 4 )
- 7 - 20
- 27
Only answer if you're very good at Math.
What is the sum of 7x/x^2 - 4 and 2/x + 2?
A: 7x + 2/x^2 - 4
B: 9x - 4/x^2 - 4
C: 7x + 2/ x^2 + x - 2
D: 9/x
Answer:
Solution given:
B: 9x - 4/x^2 - 4
Step-by-step explanation:
.k
PLSSSSSSS HELP ASAP !!! PLSSS
Answer:wpeleoe
Step-by-step explanation:
{2x + y = -1}
{3x- 5y + -21}
Answer:
(-2, 3).
Step-by-step explanation:
2x + y = -1
3x- 5y = -21
Multiply the first equation by 5:
10x + 5y = -5 Adding this to the second equation:
13x = -26
x = -2.
Substituting this into equation 1:
2(-2) + y = -1
y = -1 + 4 = 3.
Checking this result in the second equation:
3(-2) - 5(3)
= -5 - 15 = -21
- Checks OK.
If i left Raleigh at 9:30 am and drove and drove 6 1/2 hours what time would it be
Answer: 4:00 pm
Step-by-step explanation:
The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increases by 10% in 10 years. What will be the population in 20 years? (Round your answer to the nearest person.)
510
Incorrect: Your answer is incorrect.
persons
How fast (in persons/yr) is the population growing at
t = 20?
(Round your answer to two decimal places.)
persons/yr
Answer:
The right answer is "605 persons".
Step-by-step explanation:
Given that,
⇒ [tex]\frac{dP}{dt} \alpha P[/tex]
or,
⇒ [tex]\frac{dP}{dt} =RP[/tex]
⇒ [tex]\frac{1}{R} \int\limits^{PT}_{500} {\frac{dP}{P} } = \int\limits^{t}_{0} dt[/tex]
⇒ [tex]\frac{1}{R} [log PT-log500]=t[/tex]
⇒ [tex]log[\frac{PT}{500} ]=Rt[/tex]
At t = 10 years,
⇒ [tex]PT=\frac{110}{100}\times 500[/tex]
[tex]=550[/tex]
∴ [tex]log[\frac{550}{500} ]=R\times 10[/tex]
[tex]R=\frac{log(1.1)}{10}[/tex]
At t = 20,
⇒ [tex]log{\frac{PT}{500} }=\frac{log \ 1.1}{10}\times 20[/tex]
[tex]PT=500\times (1.1)^2[/tex]
[tex]=605 \ persons[/tex]
Case Study 2
Based on the success of their new treatment for sickle cell disease,
Amitye-Baane-Fortaleza research team decided to start a new company and
open a research center dedicated to curing diseases that disproportionately
affect Black people in the United States and around the world. They hired
an engineering and architecture firm called Bishapham-Cummins, Rice,
and Holloway LLC. They assigned their lead architects Fatoumata Sylla
and Leudy Tejada, along with lead engineers Jerome Wade, Neveah
Rodrigues and Jarell Hunte to design and build the new research center
based on the following square pyramid scale outline:
Answer:
good for them i think
Step-by-step explanation:
this doesnt make any sense
- The area of a rectangle can be found by using A
24w + w2, where w represents the
width. What is the width of the rectangle when the area is 3456 in.2 ?
Answer:
26w
Step-by-step explanation:
An eagle flies towards south luzon at 90 meters for 5 seconds . What is the speed and velocity of the eagle
Answer:
the speed in 18mph
Step-by-step explanation:
x over 3 add 5 = 5
Pls help someone
Answer:
x=0
Step-by-step explanation:
0/3 = 0
0+5=5
Seventy-six percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 67% have an emergency locator, whereas 88% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. (Round your answers to three decimal places.)
Required:
a. If it has an emergency locator, what is the probability that it will not be discovered?
b. If it does not have an emergency locator, what is the probability that it will be discovered?
Answer:
a. 0.0535 = 5.35% probability that it will not be discovered
b. 0.9465 = 94.65% probability that it will be discovered
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
a. If it has an emergency locator, what is the probability that it will not be discovered?
Event A: Has an emergency locator.
Event B: Not discovered.
Probability of having an emergency locator:
67% of 76%(discovered).
100 - 88 = 12% of 100 - 76 = 24%(not discovered). So
[tex]P(A) = 0.67*0.76 + 0.12*0.24 = 0.538[/tex]
Probability of having an emergency locator and not being discovered:
12% of 24%. So
[tex]P(A \cap B) = 0.12*0.24[/tex]
Desired probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.12*0.24}{0.538} = 0.0535[/tex]
0.0535 = 5.35% probability that it will not be discovered.
b. If it does not have an emergency locator, what is the probability that it will be discovered?
Event A: Has an emergency locator.
Event B: Discovered.
Probability of having an emergency locator:
67% of 76%(discovered).
100 - 88 = 12% of 100 - 76 = 24%(not discovered). So
[tex]P(A) = 0.67*0.76 + 0.12*0.24 = 0.538[/tex]
Probability of having an emergency locator not being discovered:
67% of 76%. So
[tex]P(A \cap B) = 0.67*0.76[/tex]
Desired probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.67*0.76}{0.538} = 0.9465[/tex]
0.9465 = 94.65% probability that it will be discovered
Carrie walked 6 miles per day. Which table represents y, the number of miles Carrie walked in x days.
D. Says 1. 18
2. 36
3. 54
4. 72
Answer:
C
Step-by-step explanation:
Since Carrie walked 6 miles her day, the function that best suits this relationship is given by [tex]y=6x[/tex] where [tex]x[/tex] is the number of days she walked and [tex]y[/tex] is the number of miles.
Table C represents this function [tex]y=6x[/tex] because all y values are exactly 6 times the x value.
Answer:
The answer is C.
Step-by-step explanation:
18 ÷ 3 = 6 miles a day
36÷6 = 6 miles a day
54÷9 = 6 miles a day
72÷12 = 6 miles a day
What is the measure of n?
Answer:
n = √108 or 6√3
Step-by-step explanation:
n is the altitude of the right triangle
Based on the right triangle altitude theorem, we would have:
h = √(xy)
Where,
h = n
x = 18
y = 6
Substitute
n = √(18*6)
n = √108
Or
n = 6√3
Please help!!!! Anyone!!
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Answer:
g(x) = |x -7|
Step-by-step explanation:
The form given for your answer has parameters 'a', 'h', and 'k'. The parameter 'a' is the vertical scale factor. Since g(x) is a translation only, that factor is 1. The parameters (h, k) identify the translation (right, up). The translation is 7 units right and 0 units up, so (h, k) = (7, 0).
Filling in these values of the parameters, your g(x) is ...
g(x) = |x -7|
Answer this as soon as possible please!!!!!
what would be the integer for this problem
???+-8=-2
Answer:10
Step-by-step explanation:
10 because 10 minus 8 would be 2
please help
no links please
Answer:
3rd choice
Step-by-step explanation:
multiply by 9/5: F=9/5 C
then add 32: F = 9/5C +32
maya raised 286.00
lian raised 192.84 less than maya
rei earned 113.25 more than lian
what is the total amount of money raised by all three?
Answer:
585.57
Step-by-step explanation:
Maya got 286.00
if lian got 192.84 less than we do 286-192.84 which is 93.16
if lian got 93.16, we add 113.25 to 93.16 to get rei's amount.
113.25 + 93.16 = 206.41
Now we add all their amounts, 286+93.16+206.41
585.57
20 5 4 2 X 2.5 12 1.5 3
Answer:
x = 10
Step-by-step explanation:
if two prisms are similar then the side lengths are proportional
2/4 = x/20 cross multiply expressions
40 = 4x divide both sides by 4
10 = x
a fuel mixture consists of 3 parts oil and 11 parts gasoline. the oil costs $0.75 per liter, and the gasoline costs $1.60 per liter. a mechanic makes 392 liters of the mixture. how much should he charge for 15% profit
Answer:
Total selling price= $663.82
Selling price per liter= $1.69
Step-by-step explanation:
Giving the following information:
Proportion of oil and gasoline:
Oil= 3/14= 0.21
Gasoline= 11/14= 0.79
The oil costs $0.75 per liter.
The gasoline costs $1.60 per liter.
First, we need to calculate the number of liters of oil and gasoline required:
Oil= 0.21*392= 82.32 liters
Gasoline= 0.79*392= 309.68
Now, the total cost to produce 392 liters:
Total cost= 82.32*0.75 + 309.68*1.6
Total cost= $577.23
Finally, the total and unitary selling price:
Total selling price= 577.23*1.15= $663.82
Selling price per liter= 663.82 / 392= $1.69
