Answers
Answer:
inverse = ( log(x+4) + log(4) ) / (2log(4)), or
c. y = ( log_4(x+4) + 1 ) / 2
Step-by-step explanation:
Find inverse of
y = 4^(-6x+5) / 4^(-8x+6) - 4
Exchange x and y and solve for y.
1. exchange x, y
x = 4^(-6y+5) / 4^(-8y+6) - 4
2. solve for y
x = 4^(-6y+5) / 4^(-8y+6) - 4
transpose
x+4 = 4^(-6y+5) / 4^(-8y+6)
using the law of exponents
x+4 = 4^( (-6y+5) - (-8y+6) )
simplify
x+4 = 4^( 2y - 1 )
take log on both sides
log(x+4) = log(4^( 2y - 1 ))
apply power property of logarithm
log(x+4) = (2y-1) log(4)
Transpose
2y - 1 = log(x+4) / log(4)
transpose
2y = log(x+4) / log(4) + 1 = ( log(x+4) + log(4) ) / log(4)
y = ( log(x+4) + log(4) ) / (2log(4))
Note: if we take log to the base 4, then log_4(4) =1, which simplifies the answer to
y = ( log_4(x+4) + 1 ) / 2
which corresponds to the third answer.
Related Questions
help please and thank you
Answers
Explanation:
You could use any two points you want. For me, the easiest is when x = 0. Plug this into the equation to get
y = 2x-7
y = 2(0)-7
y = -7
So we have x = 0 and y = -7 pair up to get (0,-7) as our first point. This is the y intercept.
Repeat for x = 1
y = 2x-7
y = 2(1)-7
y = -5
So (1,-5) is another point on this line. You only need two points at minimum to graph a straight line.
What is the volume of the following
rectangular prism?
Answers
Answer: 13.5 units³
Step-by-step explanation:
[tex]\dfrac{5}{2}\times \dfrac{27}{5}\quad =\dfrac{27}{2}\quad =\large\boxed{13.5\ units^3}[/tex]
12. What is the distance from the directrix (the Crocodile River) to the po
River) to the point (x,y)? Write this equation.
Your answer will contain a y-term. (2 points)
Answers
Answer:
Distance= y - 4
Step-by-step explanation:
03.07A LC)Which of the following describes a situation in which a basketball player ends up 0 m from his starting point? The player runs 9 meters forward, and then runs 0 meters in the opposite direction. The player runs 5 meters forward, and then runs 6 meters in the opposite direction. The player runs 6 meters forward, and then runs 5 meters in the opposite direction. The player runs 4 meters forward, and then runs 4 meters in the opposite direction.
Answers
Answer:
The correct option is;
The player runs 4 meters forward, and then runs 4 meters in the opposite direction
Step-by-step explanation:
From the question relates to the displacement of a body, compared to the distance covered by the body
In the question instance, the situation in which the player displacement will be zero is one where both the players forward and backward displacement are equal such that they cancel each other
We have the instance where the forward and opposite displacement are equal is given by the situation where the player runs 4 meters forward, and then runs 4 meters in the opposite direction.
Answer:
d would be the answer if your so needy
Step-by-step explanation:
Sarah serves at a restaurant and makes 20% of what she sells as tips. Her base salary is $10.20an hour. Each hour she sells an average of $60 of food and drinks. She also makes time and a half when she works over 8 hours during a single shift. Her work week contains three 10-hour shifts, one 5-hour shift, and one 11-hour shift. Using the same income deductions as stated in the previous question, what is Sarah's annual gross income and annual net incom
Answers
Sara works 46 hours per week
9 hours are overtime and 37 hours are regular time
pay rate at time and a half: 10.20∗1.5=15.30
regular hours plus overtime pay
37∗10.20=377.40
9∗15.30=137.70
Income due to tips
Total hours worked∗60per hour∗20%
46∗60∗.20=552
Weekly Income=Hourly income + tips
Weekly Income=377.40+137.70+552.00
Weekly Income=1067.10
Annual income=Weekly income∗52
Annual income=55489.20
which of the following is the graph of
[tex] \sqrt{ \times } \geqslant 4[/tex]
Answers
Answer:
Hope this is correct and helpful
HAVE A GOOD DAY!
A basket is filled with 8 white eggs and 10 brown eggs. Half of the white eggs are cracked.
An egg is randomly selected from the basket. What is the probability that it is a cracked, white egg?
Write your answer as a fraction in simplest form.
Answers
Answer:
4 by 9 should be the answer
Step-by-step explanation:
N/A
Answer:
I think it is 2/9. I'm not sure.
Step-by-step explanation:
10/18 are brown eggs.
8/18 are white eggs.
4/18 are cracked.
Simplified answer is 2/9 chance.
Select the correct answer.
Which relation is a function?
A. {(2,3), (1,5), (2,7)}
B. {(-1,5), (-2,6), (-3,7)}
C. {(11,9), (11,5), (9,3)}
D. {(3,8), (0,8), (3,-2)}
Answers
Answer:
The answer is option B.
Explanation:
A rule that uniquely associates elements of one set A with the elements of another set B and each element in set A maps to only one element in set B.
Each element from X is related to only one element in Y. But it is okay for two different elements in X to be related to the same element in Y. So its still a function. Let suppose
{ (1,a) , (2, b) , (2, c) , (3, d) }
This relation is not a function from X to Y because the element 2 in X is related to two different elements, b and c.
A film distribution manager calculates that 9% of the films released are flops.If the manager is right, what is the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%? Round your answer to four decimal places.
Answers
Answer:
the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4% is 0.0042
Step-by-step explanation:
Given that :
A film distribution manager calculates that 9% of the films released are flops
Let p be the probability for the movies that were released are flops;
[tex]\mu_p = P = 0.9[/tex]
If the manager is right, what is the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%
now; we know that our sample size = 442
the standard deviation of the variance is [tex]\sigma_p= \sqrt{\dfrac{p(1-p)}{n}}[/tex]
[tex]\sigma_p= \sqrt{\dfrac{0.9(1-0.9)}{442}}[/tex]
[tex]\sigma_p= \sqrt{\dfrac{0.9(0.1)}{442}}[/tex]
[tex]\sigma_p= \sqrt{\dfrac{0.09}{442}}[/tex]
[tex]\sigma_p= \sqrt{2.0361991 \times 10^{-4}}[/tex]
[tex]\sigma _p = 0.014[/tex]
So; if the manager is right; the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4% can be calculated as:
[tex]P(|p-P|>0.04)=1 -P(p-P|<0.04)[/tex]
[tex]P(|p-P|>0.04)=1 -P(-0.04 \leq p-P \leq 0.04)[/tex]
[tex]P(|p-P|>0.04)=1 -P( \dfrac{-0.04}{\sigma_p} \leq \dfrac{ p-P}{\sigma_p} \leq \dfrac{0.04}{\sigma_p})[/tex]
[tex]P(|p-P|>0.04)=1 -P( \dfrac{-0.04}{0.014} \leq Z\leq \dfrac{0.04}{0.014})[/tex]
[tex]P(|p-P|>0.04)=1 -P( -2.8571 \leq Z\leq 2.8571)[/tex]
[tex]P(|p-P|>0.04)=1 -[P(Z \leq 2.8571) -P (Z\leq -2.8571)[/tex]
[tex]P(|p-P|>0.04)=1 -(0.9979 -0.0021)[/tex]
[tex]P(|p-P|>0.04)=1 -0.9958[/tex]
[tex]\mathbf{P(|p-P|>0.04)=0.0042}[/tex]
∴
the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4% is 0.0042
The area of a rectangle can be expressed by 2x2 – 7x – 4. If the rectangle has an
area of 45, find the positive value for x.
Answers
Answer:
7
Step-by-step explanation:
2x^2 - 7x - 4 = 45
2x^2 - 7x - 49 = 0 : subtract 45 from both sides
Quadratic formula:
x = (7 ± sqrt(7^2 - 4*2*-49) ) / 4
x = (7 ± sqrt(49 - -392)) / 4
x = (7 ± sqrt(441)) / 4
x = (7 ± 21) / 4
x = (7 + 21) / 4 OR x = (7 - 21) / 4
x = 28 / 4 OR x = -14 / 4
x = 7 as it is the only positive answer
A game is played with a played pentagonal spinner with sides marked 1 to 5. The scorer is on the side which comes to rest on the table. In two spins what is the probability of getting two 5s, at least one 5, a total score of 5, a total score greater than 5.
Answers
Answer: probability of getting two 5s =0.04
probability of getting at least one 5 =0.36
probability of getting a total score greater than 5 =0.6
Step-by-step explanation:
Total outcomes on 1 spinner = 5
Then , total outcomes of spinning it 2 times= [tex]5\times5 = 25[/tex]
Number of outcomes for getting two 5's = 1
Then, the probability of getting two 5s [tex]=\dfrac{\text{Favorable outcomes of getting two 5's }}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{1}{25}=0.04[/tex]
Number of outcomes for getting at least one 5 [ {(1,5),(2,5),(3,5),(4,5),(5,5), (5,1), (5,2), (5,3), (5,4)} ] =9
Then, the probability of getting at least one 5[tex]=\dfrac{\text{Favorable outcomes of getting at least one 5 }}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{9}{25}=0.36[/tex]
Number of outcomes for getting a total score of 5, [ {(1,4),(4,1),(2,3),(3,2)} ] =4
Then, the probability of getting a total score of 5,[tex]=\dfrac{\text{Favorable outcomes of getting a total score of 5 }}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{4}{25}[/tex]
Number of outcomes for getting a total score greater than 5 [ {(1,5),(5,1),(2,4),(4,2),(2,5), (5,2), (3,4),(4,3), (3,5), (5,3), (3,3), (4,5), (5,4), (4,4), (5,5)} ] =15
Then, the probability of getting a total score greater than 5,[tex]=\dfrac{\text{Favorable outcomes of getting a total score greater than 5 }}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{15}{25}=\dfrac{3}{5}=0.6[/tex]
The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 24π cubic units. What is the height of the cylinder? 2 units 4 units 6 units 8 units
Answers
Answer:
6 unitsStep-by-step explanation:
Let, Radius = r units
Height ( h ) = 3r units
Volume ( V ) = 24π units³
Now,
Let's find the height of the cylinder:
[tex]\pi {r}^{2} h \: = 24\pi[/tex]
[tex] {r}^{2} (3r) = 24[/tex]
Calculate the product
[tex]3 {r}^{3} = 24[/tex]
Divide both sides of equation by 3
[tex] \frac{3 {r}^{ 3} }{3} = \frac{24}{3} [/tex]
Calculate
[tex] {r}^{3} = 8[/tex]
Write the number in the exponential form with an exponent of 3
[tex] {r}^{3} = {2}^{3} [/tex]
Take the root of both sides of the equation
[tex]r = 2[/tex]
Replacing value,
Height = 3r
[tex] = 3 \times 2[/tex]
Calculate
[tex] = 6 \: units[/tex]
Hope this helps..
Best regards!!
Answer:
[tex]\boxed{6 \: \mathrm{units}}[/tex]
Step-by-step explanation:
The formula for volume of cylinder is:
[tex]V=\pi r^2 h\\V:volume\\r:radius\\h:height[/tex]
[tex]V=24\pi\\h=3r[/tex]
Solve for r.
[tex]24\pi =\pi r^2 (3r)[/tex]
Cancel [tex]\pi[/tex] on both sides.
[tex]24=3r^3[/tex]
Divide 3 on both sides.
[tex]8=r^3[/tex]
Cube root on both sides.
[tex]2=r[/tex]
The radius of the base is 2 units.
Solve for h.
[tex]24\pi =\pi (2)^2 h[/tex]
Cancel [tex]\pi[/tex] on both sides.
[tex]24=4h[/tex]
Divide both sides by 4.
[tex]6=h[/tex]
Charlie creates and sells jewelry. He has designed a triangular pendant with two 2-inch sides and one 1.5-inch side.Charlie will use wire to form the triangle. He wants to make several of these pendants to sell at his store. How many pendants can Charlie make using 5 feet of wire?
Answers
Answer:
Number of pendant made = 10
Step-by-step explanation:
Given:
Sides of triangle = 2 in , 2 in , 1.5 in
Total wire = 5 ft = 5 × 12 = 60 in
Find:
Number of pendant made.
Computation:
Perimeter of 1 pendant = 2 in + 2 in + 1.5 in
Perimeter of 1 pendant = 5.5 in
Number of pendant made = Total wire / Perimeter of 1 pendant
Number of pendant made = 60 / 5.5
Number of pendant made = 10.90
Number of pendant made = 10 and 1 pendant incomplete
Mark says that the number square root two is irrational number because he can write it as a fraction square root two over one is more correct why or why not
Answers
Answer:
Step-by-step explanation:
A rational number are numbers that can be expressed as as fraction. They can be expressed as a ratio of two integers. An irrational is quite the opposite. An irrational number cannot be expressed as a ratio of two integers.
Taking square root of two as an example;
√2 cannot be expressed as a ratio of two integers because the result will always be a decimal. If expressed as √2/1, it is still not a rational number because of the square root of 2 at the numerator. Square root of 2 is not an integer even though 1 is an integer.
Mark is wrong because √2 is irrational and it is irrational because it cannot be expressed as a ratio of two integers not due to the fact that he can write it as a fraction.
Answer choice
C) All nonnegative real numbers
D) All positive integers
Answers
The number of boxes can't be negative or in fractions.
so the domain would be "All whole numbers from 0 to 10"
Answer:
A) All whole numbers from 0 to 10.
Step-by-step explanation:
The domain of a function is given by the available values of the independent variable.
In this case you have that the independent variable is the number of boxes, and the available values of this variable are integers in between 0 and 10, by including 0 and 10.
Then, the domain of the functions composed by all positive integers number from 0 to 10 including 0 and 10.
A) All whole numbers from 0 to 10.
1 (4/6 - 2√7) (4/6 +21)
Please tell the answer?
Answers
Answer:
-100.204779...
or tenth to rounding, -100.2
Hope this helps!
// Would you pick me Brainleist...?
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
All you have to do is simplify.
[tex]1 ( \frac{4}{6} - 2 \sqrt{7}) ( \frac{4}{6} + 21)\\\\= \frac{130}{9} + \frac{-130}{3} \sqrt{7}[/tex] (Decimal: -100.204779)
So the answer is : [tex]\frac{130}{9} + \frac{-130}{3} \sqrt{7}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
Which statement is true about the function f(x) = StartRoot negative x EndRoot? It has the same domain as the function f(x) = Negative StartRoot negative x EndRoot. It has the same range as the function f(x) = Negative StartRoot negative x EndRoot. It has the same domain as the function f(x) = Negative StartRoot x EndRoot. It has the same range as the function f(x) = .
Answers
Answer:
It has the same domain as the function [tex]f(x)=-\sqrt{-x}[/tex].
Step-by-step explanation:
The function ...
[tex]f(x)=\sqrt{-x}[/tex]
has a domain of all non-positive numbers and a range of all non-negative numbers. Anything with a -x under the radical will have the same domain. Any positive root will have the same range.
__
So, we can say it has the same domain as ...
[tex]f(x)=-\sqrt{-x}[/tex]
Answer:
A on edge
Step-by-step explanation:
hehe
The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 4 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will take between 2.5 and 5 minutes to find a parking spot in the library lot.
Answers
Answer:
the probability that a randomly selected college student will take between 2.5 and 5 minutes to find a parking spot in the library lot is 0.77454
Step-by-step explanation:
Given that:
mean = 4
standard deviation = 1
The objective is to find the probability that a randomly selected college student will take between 2.5 and 5 minutes to find a parking spot in the library lot.
i.e
[tex]P(2.5 \leq x \leq 5) = P(\dfrac{2.5 - \mu}{\sigma} \leq \dfrac{X-\mu}{\sigma}\leq \dfrac{5- \mu}{\sigma})[/tex]
[tex]P(2.5 \leq x \leq 5) = P(\dfrac{2.5 - 4}{1} \leq Z \leq \dfrac{5- 4}{1})[/tex]
[tex]P(2.5 \leq x \leq 5) = P(\dfrac{-1.5}{1} \leq Z \leq \dfrac{1}{1})[/tex]
[tex]P(2.5 \leq x \leq 5) = P({-1.5}\leq Z \leq 1)[/tex]
[tex]P(2.5 \leq x \leq 5) = P({Z < 1})- P(Z < -1.5)[/tex]
[tex]P(2.5 \leq x \leq 5) = 0.84134- 0.06680[/tex]
[tex]\mathbf{P(2.5 \leq x \leq 5) = 0.77454}[/tex]
Please answer this question now
Answers
Answer:
[tex]\boxed{u = 6.0}[/tex]
Step-by-step explanation:
Using the cosine rule
[tex]c^2= a^2+b^2-2abCosC[/tex]
Here c = u , a = 11 , b = 12 and C = 30
[tex]u^2 = 11^2+12^2-2(11)(12)\ Cos 30\\u^2 = 121+144-2(132)(0.866)\\u^2 = 265-228.6\\u^2 = 36.37[/tex]
Taking sqrt on both sides
u = 6.0 (To nearest tenth)
Find the value of x.
Answers
Answer:
8.8Option A is the correct option.
Step-by-step explanation:
As PW is the median.
PW = [tex] \frac{1}{2} [/tex] ( YZ + TM )
Plug the values
x = [tex] = \frac{1}{2} (5.5 + 12.1)[/tex]
Calculate the sum
x = [tex] = \frac{1}{2} \times 17.6[/tex]
Calculate the product
x = [tex] = 8.8[/tex]
Hope this helps...
Best regards!
(x+1)(x-2)=0
Solve the quadratic equation using factoring
Answers
Answer:
x= -1 or x= 2
Step-by-step explanation:
(x+1)(x-2) = 0x+1 = 0 or x-2=0 x = -1 or x = 2Which ordered pair is a solution of this equation?
Please and thank you
Answers
Answer:
Hey there!
-9x-y=-15
9x+y=15
A solution with integer values would be 9(1)+6=15
Thus, x=1 and y=6
(1, 6)
Hope this helps :)
Answer:
(6,1)
Step-by-step explanation:
5
Write 2 -% as a decimal (not
8
as a
percentage).
Answers
Answer: 0.4
Step-by-step explanation:
i think
Maddy and her cousin work during the summer for a landscaping company. Maddy's cousin has been working for the company longer, so her pay is 30% more than Maddy's. Last week, Maddy's cousin worked 27 hours, and Maddy worked 23 hours. Together, they earned $493.85. What is Maddy's hourly pay?
Answers
HELP MAJOR ASSIGNMENT PLEASE HELP pls?
Answers
Answer:
1: V:56.52 SA:94.2 Ratio: 3:5
2: V:113.04 SA:62.8 Ratio: 9:5
3: V:113.04 SA:138.16 Ratio: 9:11
4: V:113.04 SA:131.88 Ratio: 6:7
Step-by-step explanation:
Hey there!
By using the following formula for volume of a cylinder I got,
[tex](3.14) r^2h[/tex]
1: 56.52
2: 113.04
3: 113.04
4: 113.04
Now to find SA we'll use the following formula,
1: 94.2
2: 62.8
3: 138.16
4: 131.88
Now for the ratio,
56.52:94.2 - 3:5
113.04:62.8 - 9:5
113.04:138.16 - 9:11
113.04:131.88 - 6:7
Hope this helps :)
There are 6 different colored pens in a box. Each pen has a unique color. In how many orders can 4 pens be chosen? In other words, what is the number of permutations of picking 4 pens from the box?
Answers
Answer:
360 different permutations.
Step-by-step explanation:
It goes 6*5*4*3 because as you pick the pens the amount of pens in the jar would obviously decrease. Picking one leaves you with 5 new options. If you repeat that 4 times then you are left with 360 options.
The number of permutations of picking 4 pens from the box is 6P4, or 6!/(6-4)! = 654×3 = 360.
We have 6 pens and we are picking 4 of them. The order in which we pick the pens matters, so we are dealing with permutations.
The number of permutations of n objects is given by n!, or n factorial. So, the number of permutations of 6 objects is 6!.
However, we need to divide by the number of permutations of the 2 pens that we are not picking. There are 2 pens that we are not picking, so the number of permutations of those pens is 2!.
Therefore, the number of permutations of picking 4 pens from the box is 6!/(6-4)! = 654×3 = 360.
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Explain why a drop in temperature would lead to adding a negative integer.
Answers
Step-by-step explanation:
a drop in temperature means the temperature will decrease.
That decrease is represented with a negative integer which should be added to the previous temperature.
Mr. SMITH had 4 daughters, each daughter had a brother ... How many sons does Mr. Smith have?
Answers
He tells us that the 4 daughters have a brother, so, since they belong to the same family, the sisters are the same because they have only one brother.
Answering our question:
or Mr. Smith has 4 daughters and also 1 son.
Answer:
one son
Step-by-step explanation:
each daughter had a brother, means there is only one son
Mr. smith has 1 son
What is the value of a for the exponential function in the
graph represented in the form of f(x) = a(b)?
O -4
O -3
O 3
O 4
Answers
Answer:
Option (4)
Step-by-step explanation:
If the given exponential function is in the form of f(x) = [tex]a(b)^x[/tex]
From the graph we find that two points (0, 3) and (0.5, 6) lie on the graph.
For (0, 3),
f(0) = [tex]a(b)^0[/tex]
3 = a
For (0.5, 6),
f(0.5) = [tex]3(b)^{0.5}[/tex]
6 = [tex]3\sqrt{b}[/tex]
[tex]\sqrt{b}=2[/tex]
b = 4
Therefore, value of b in the given function 'f' is 4.
Option (4) will be the answer.
Answer:
(D) 4
Step-by-step explanation:
♥☺
which of the following rational functions are graphed below
Answers
Answer:
1st one
Step-by-step explanation:
The rational function which is graphed below is F(x)=-1/x, the correct option is B.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output;
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships;
Linear function is a function whose graph is a straight line;
We are given that;
The graph of the function
Now,
Points on 1/(x + 4);
The function y = 1/(x + 4) is a hyperbola. It has two branches that extend infinitely in opposite directions. The x-axis and y-axis are both asymptotes of the hyperbola.
Points on y= 1/x-4;
The function y = 1/(x - 4) is also a hyperbola. Its asymptotes are the vertical line x = 4 and the horizontal line y = 0;
Points on y = 1/(x-1);
The function y = 1/(x-1) is also a hyperbola. Its asymptotes are the vertical line x = -4 and the horizontal line y = 0.
Therefore, by the given graph function will be F(x)=-1/x;
Learn more about function here;
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