Answer:
[tex]\frac{7^2}{p^8 \cdot q^9}[/tex]
Step-by-step explanation:
[tex]\frac{p^{-8}}{7^{-2}} \cdot q^{-9} = \frac{\frac{1}{p^8}}{\frac{1}{7^2}} \cdot \frac{1}{q^9} = \frac{7^2}{p^8 \cdot q^9}[/tex] by the definition of negative exponents: [tex]a^{-b} = \frac{1}{a^b}[/tex] for all [tex]a,b[/tex] so long as [tex]a\ne 0[/tex].
The value of the exponential equation is A = 7²q⁹ / p⁸
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
A = p⁻⁸ / 7⁻² ( q ) ⁻⁹ be equation (1)
On simplifying the equation , we get
A = 7² ( q ) ⁹ / p⁸
Therefore , the value of A is 7²q⁹ / p⁸
Hence , the exponential equation is A = 7²q⁹ / p⁸
To learn more about exponents click :
https://brainly.com/question/28966438
#SPJ2
Which expression would produce the greatest product?
A.10x12/22. B.10x4/5. C.10x9/10. D.10x3/2.
Answer:
c.
Step-by-step explanation:
The table represents an exponential function.
What is the multiplicative rate of change of the function?
X
1
2.
у
2
2
5
3
2
25
2
2
5
125
Answer:
A. ⅕
Step-by-step explanation:
[tex] \frac{2}{5} [/tex] ÷ 2 = [tex] \frac{2}{5} * \frac{1}{2} = \frac{1}{5} [/tex]
[tex] \frac{2}{25} [/tex] ÷ 2/5 = [tex] \frac{2}{25} * \frac{5}{2} = \frac{1}{5} [/tex]
[tex] \frac{2}{125} [/tex] ÷ 2/25 = [tex] \frac{2}{125} * \frac{25}{2} = \frac{1}{5} [/tex]
Therefore, the multiplicative rate of change of the function would be ⅕
In 2010 there were 2000 American lions in a conservation park in Wisconsin. The lion population is decreasing
by 8% every year. Which of the following functions models the lion population after x years?
Step-by-step explanation:
After each year, the new population of the lions is 100% - 8% = 92% of the population of the lions the year before.
Hence our exponential base should be 0.92, indicating exponential decay. (A)
Answer:
after each year the new population of the lions
is 100% - 8% is equals to 92% of the population of the lion year before
Hence our exponential base should be 0.92 (A)
According to the National Institute for Occupational Safety and Health, job stress poses a major threat to the health of workers. A news report claims that 75% of restaurant employees feel that work stress has a negative impact on their personal lives. Managers of a large restaurant chain wonder whether this claim is valid for their employees. A random sample of 100 employees finds that 68 answer “Yes” when asked, “Does work stress have a negative impact on your personal life?”
1. Do these data provide convincing evidence at the α = 0.10 significance level that the proportion of all employees in this chain who would say “Yes” differs from 0.75? 2. A 90% confidence interval for the restaurant worker data was also created and found to be (0.603272, 0.756728). Explain how the confidence interval is consistent with, but gives more information than, the test.
Hypothesis test on the proportion of employees, gives an evidence
based conclusion which is consistent with the confidence interval.
Response:
There is insufficient or no convincing statistical evidence to conclude that the proportion differs from 0.75The confidence interval indicates that the proportion of workers that feel that work stress has a negative impact on their lives is between 0.603272 and 0.756728, a proportion that includes 0.75, which is consistent with the test, and also provides the minimum and maximum expected proportion at 95% confidence level.How can the test of the hypothesis be performed?1. The percentage of workers that the news report claims work stress have a negative impact on their personal lives, p = 75%
Number of employees in the sample, n = 100
Number that answered yes = 68
The null hypothesis is, H₀: p = 0.75The alternative hypothesis is, Hₐ: p ≠ 0.75The proportion of the employees that said yes, [tex]\hat p[/tex] = 68 ÷ 100 = 0.68
The z-test formula is; [tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p \cdot q}{n}}}[/tex]
q = 1 - p
Which gives;
[tex]z= \mathbf{\dfrac{0.68-0.75}{\sqrt{\dfrac{0.75 \times (1 - 0.75)}{100}}}} \approx -1.62[/tex]
The p-value ≈ 2 × p(Z < -1.62) = 2 × 0.0526 = 0.1052
The significance level, α = 0.10
Given that the p-value is larger than the significance level, we fail to
reject the null hypothesis, and conclude that as follows;
There is insufficient convincing statistical evidence that the proportion differs from 0.75.2. The 90% confidence interval is (0.603272, 0.756728)
The confidence interval indicates that at 90% confidence level, the true
proportion of employees that feel that work stress has a negative
impact on their personal lives is between 0.603272 and 0.756728.
The report claim of 75% or 0.75 is within the confidence interval, which consistent with the hypothesis testThe information in the confidence interval also indicates that at 90% confidence level, the proportion of the employee that say yes is between (0.603272, 0.756728), thereby giving more informationLearn more about hypothesis testing here:
https://brainly.com/question/23082833
please help!!! if you can thank you so much and have a bless day!!!!
Answer:
6
Step-by-step explanation:
Compare the two sets of data. Who gets more sleep? Why?
Jason, because he gets higher median hours of sleep
Jason, because he has less variability in sleep hours
Mitch, because he gets higher median hours of sleep
Mitch, because his maximum hours of sleep were greater than Jason’s maximum
Answer:
C. Mitch, because he gets higher median hours of sleep
Step-by-step explanation:
50 PTS
Please Make sure its easy to understand
Answer:
1) -95.
2) 15.
3) The conference center is on floor 5.
Step-by-step explanation:
1) Evaluating gives [tex]-52-30-13=-(52+30+13)=-(95)=-95.[/tex]
2) Substituting gives [tex]x+27=(-12)+27=15.[/tex]
3) After going 4 floors down, we are on level -4. After going 9 floors up to the desired room, we are on level -4+9=5. So the conference center is on floor 5.
Answer:
1. -95
2. 15
3. 5th Floor (-4 + 9)
Step-by-step explanation:
Determine whether the ratios 5:7 and 10:21 are equivalent
Answer:
Step-by-step explanation:
No, thoose two ratios are not equivalent, but I can show you the ones that are equivalent, {You can write 5/7 or 10/14 or 20/28 or 40/56. There! 3 equivalent ratios.}
The product of two numbers is 42.63. If one number is 21. What is the other number
Answer:
21.63 is the other number
Step-by-step explanation:
21 + 21.63 equals 42.63
Answer:
Hi dear. I'm helping you to solve the question and in return you help me with my question.
Step-by-step explanation:
Question : The product of two numbers is 42.63. If one number is 21. What is the other number?
Solution :-
Product of two numbers = 42.63
One of the number = 21
Therefore , the other number = 42.63 ÷ 21 = 2.03
Hope my solution helps you and don't forget to help me with maths questions in return...
which is greatest and which is the least 7/12 5/8 3/4
Answer:
The most is 3/4 and the least is 7/12
Step-by-step explanation:
Becasue the demonitaor have a facotr of 24 so if we convert them to ?/24 we can get our answer by doing this 7/12 -> 14/24, 5/8 --> 15/24, 3/4 --> 18/24
A bottling company produces bottles that hold 10 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 64 bottles and finds the average amount of liquid held by the bottles is 9.9145 ounces with a standard deviation of 0.40 ounce. Suppose the p-value of this test is 0.0436. State the proper conclusion. choose from below and explain why.
A) At α = 0.05, reject the null hypothesis.
B) At α = 0.10, fail to reject the null hypothesis.
C) At α = 0.025, reject the null hypothesis.
D) At α = 0.05, accept the null hypothesis.
Answer:
A) At α = 0.05, reject the null hypothesis.
Step-by-step explanation:
Given a p-test value of 0.0436 ;
P-value = 0.0436
Recall :
Decision region :
Reject Null if p value < α
Testing the options :
A) At α = 0.05,
0.0436 < 0.05 (true)
Since p value < α ; Reject the null hypothesis.
B) At α = 0.10,
0.0436 < 0.1
True conclusion is to reject the Null Hypothesis
Hence, option B is incorrect.
C) At α = 0.025, reject the null hypothesis.
0.0436 > 0.025
True conclusion is ; Fail to reject the Null ;
Hence, option C is incorrect
D) At α = 0.05, accept the null hypothesis.
0.0436 < 0.05
True conclusion is ; reject the Null
Hence, option D is incorrect
How do I turn 42-5=37 into 42=37+5?
Answer:
You move the -5 to the other side.
Answer:
you move the -5 to the other side equation
Jerry’s teacher wants him to draw a triangle. He starts by drawing a line 15 cm long and two angles 35º and 65º. What will the third angle measure?
Answer:
the total must be 180
40 + 70 + X = 180
the third one is = D.70
Step-by-step explanation:
Answer:
80 degrees
Step-by-step explanation:
angles in a triangle add up to 180 degrees
35+65=100
180-100=80 degrees
f(x) = X/x-1 and g(x) = 1+1/x find (g. f) (x) and (f. G) (x)
Answer:
Given f(x)=(1−x)21 and g(x)=ln(x)
gof(x)
=g(f(x))
=ln(1−x)1/2
=21ln(1−x)
∴ For the composite function to be defined 1−x>0
x<1
∴ Domain is (−∞,1)
what is the symbol of an inverse function
Answer:
f(-1
Step-by-step explanation:
The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced "f inverse".
1. Circle the figure you would use to make the Escher‐like tessellation given.
Answer:
b ? i have never seen anything like this though so please dont take my word
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
What is the slope and y-intercept of the line y - 2x = 8
Answer:
Slope is 2x and y-intercept is 8
Step-by-step explanation:
First you have to get y all by itself on the left side of the equal sign. To do that, you must add 2x on both sides. You will get: y=2x+8.
Answer:
Slope= 2
Y-intercept= (0,8)
Explain your answer !!
Have a great day
Will give brainlst
Answer:
Dang this looks hard
Step-by-step explanation:
Wish could help
can someone help asap!
ANSWERS:
1) ∛216²=36
2) √81= 9
3) √4∧5=32
4)1.55
5)25
6)X
Is 24a+16b+8 equivalent to 4(6a+2) +8b+ 2
Answer:
No
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer/how I got this answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
On a number line, the directed line segment from Q to S has endpoints Q at -14 and S at 2. Point R partitions the
directed line segment from Q to Sin a 3:5 ratio.
Which expression correctly uses the formula [m/m+n](x2-x1)+x1 to find the location of point R?
9514 1404 393
Answer:
A
Step-by-step explanation:
Using m=3, n=5, x2=2, x1=-14, the only match is the first one.
The correct expression for the point on the line is [tex]M=\frac{3}{3+5} (2-(-14))+(-14)[/tex]
Midpoint of a lineThe formula for expressing the midpoint of a line is expressed as:
[tex]M=\frac{m}{m+n} (x_2-x_1)+x_1[/tex]
Given the following parameters
m=3,
n=5,
x2=2,
x1=-14,
Substitute
[tex]M=\frac{3}{3+5} (2-(-14))+(-14)[/tex]
This given the correct expression for the point on the line
Learn more on midpoint here: https://brainly.com/question/18315903
#SPJ6
Guys I’m struggling help please ! I need by tomorrow!
Answer:
if you are not finding the function but the range:
(i cant see the full graph so the first part may not be accurate)
[tex]-8\leq y\leq 4[/tex]
[tex]y=3[/tex]
[tex]2<y\leq -4[/tex]
Find the midpoint M of the line segment joining the points P=(4,-7) and Q=(-6,-3)
Answer:
midpoints (-1, -5)
Step-by-step explanation:
midpoints
[tex] ( \frac{4 + ( - 6)}{2} \: \frac{ - 7 + ( - 3)}{2} )[/tex]
[tex]( \frac{4 - 6}{2} \: \frac{ - 7 - 3}{2} )[/tex]
[tex]( \frac{ - 2}{2} \: \frac{ - 10}{2} )[/tex]
[tex]( - 1 \: - 5)[/tex]
Does the equation represent a function? * (WILL GIVE BRAINLIEST IF RIGHT)
y = x^2 + 36
Yes this is a function because for any input value (x) you will get a unique output value (y).
ASAP PLS MARKING BRAINLIEST PLSSSSS
The sales tax in Whittle City is 7%, how much tax is charged on a purchase of $53?
Answer:
3.71$
Step-by-step explanation:
Answer:
$3.71 hope this helps
Step-by-step explanation:
Round 342.296269789 to 2 decimal places.
Answer:
342.29
Step-by-step explanation:
You take away the other decimal places.
The round-up to 2 decimal places of 342.296269789 will be 342.30.
How do round any digit?To round up or down of tens place then we need to look at the unit place if it is less than 5 then we need to round down and if it is greater than 5 then we need to round up of tens digit.
In order to round to a hundred, we need to look at the tens digit if it is less than 5 then we round down and if it is 5 or greater than 5 then we will round up.
For example round of 346 will, be350 and round of 344 will be 340
Given the digit,
342.296269789
Now,
The 3rd decimal digit is 6 which is greater than 5
So,
2nd digit will round up since it is 9 so it will round as 10 and gives 1 to the first decimal place.
So,
342.296269789 ⇒ 342.30.
Hence "The round-up to 2 decimal places of 342.296269789 will be 342.30".
To learn more about rounding a digit,
https://brainly.com/question/116595
#SPJ2
The sum of two numbers is 54. The smaller number is 14 less than the larger number. What are the numbers?
Larger number:
Smaller number:
Answer:
larger number: 34
smaller number: 20
Step-by-step explanation:
54= y+y-14
54= 2y - 14
54+14 = 2y
68 = 2y
68/2 = 2y/2
34 = y, the larger number
y - 14 = 34-14 = 20 the smaller number
HELP!!!!!
Find the value of x.
Answer:
70
Step-by-step explanation:
formula we will be using: [tex]\sqrt{y} (y+z)[/tex]
7 (7+3)
7 · 10 = 70
On a roulette wheel, half of the slots numbered 1 through 36 are red and half are black. Two slots numbered 0 and 00, are green. What are the odds against a ball landing in a red slot on any spin of the wheel? I'm also having a hard time on this please help me!!!! :(
Answer:
Two slots, numbered 0 and 00, are green.
What are the odds against a red slot's coming up on any spin of the wheel?
Step-by-step explanation:
