Answer:
[tex](\frac{32}{243})^{-\frac{4}{5}}=39.0625[/tex]
Step-by-step explanation:
Given
[tex](\frac{32}{243})^{-\frac{4}{5}}[/tex]
Required
Solve
[tex](\frac{32}{243})^{-\frac{4}{5}}[/tex]
Express 32 as 2^5 and 243 as 3^5
[tex](\frac{2^5}{3^5})^{-\frac{4}{5}}[/tex]
The exponent can be expressed as 1\5 * -4
So we have:
[tex](\frac{2^5}{3^5})^{\frac{1}{5} * -4}[/tex]
Apply law of indices:
[tex](\frac{2^{5*1/5}}{5^{5*1/5}})^{-4}[/tex]
[tex](\frac{2}{5})^{-4}[/tex]
In indices:
[tex](\frac{a}{b})^{-c} = (\frac{b}{a})^{c}[/tex]
So, the expression becomes
[tex](\frac{5}{2})^{4}[/tex]
[tex](\frac{5^{4}}{2^{4}})[/tex]
[tex]\frac{625}{16}[/tex]
[tex]39.0625[/tex]
Hence:
[tex](\frac{32}{243})^{-\frac{4}{5}}=39.0625[/tex]
Verify sin4x-sin²x=cos4x-cos²x is an identity.
the 4 is supposed to be small like the 2
Answer:
It's an identityStep-by-step explanation:
[tex]\sin^4x-\sin^2x=\cos^4x-\cos^2x\\\\Ls=\sin^2x(\sin^2x-1)=-\sin^2x(1-\sin^2x)=-\sin^2x\cos^2x\\\\Rs=\cos^2x(\cos^2x-1)=-\cos^2x(1-\cos^2x)=-\cos^2x\sin^2x\\\\Ls=Rs\\\\\text{used}\\\\a^n\cdot a^m=a^{n+m}\\\\\text{distributive property}\ a(b+c)=ab+ac\\\\\sin^2x+\cos^2x=1\to \sin^2x=1-\cos^2x\\\\\sin^2x+\cos^2x=1\to \cos^2x=1-\sin^2x}[/tex]
Mary is 3 years older than twice her brother's age, a. Which expression
represents Mary's age?
A. 2a + 3
B. 2a - 3
C. 3a + 2
D. 3a - 2
Answer:
C. 3a + 2
Step-by-step explanation:
brainiest plz
What type of angle is shown?
Answer:
B. Obtuse angle
Step-by-step explanation:
Remember that a right angle is 90 degrees and would be like the edge of a square or rectangle going completely vertical. An obtuse angle is larger than 90 degrees so the vertex or point where both lines connect would have both lines farther apart. An acute angle is smaller than a 90-degree angle and is closer to touching the lines (a tip for remembering acute angles could be "a-cute angle" or a smaller cute angle). Hope this helps!
1- The Canada Urban Transit Association has reported that the average revenue per passenger trip during a given year was $1.55. If we assume a normal distribution and a standard deviation of 5 $0.20, what proportion of passenger trips produced a revenue of Source: American Public Transit Association, APTA 2009 Transit Fact Book, p. 35.
a. less than $1.55?
b. between $1.15 and $1.95? c. between $1.35 and $1.75? d. between $0.95 and $1.55?
Answer:
0.5
0.9545
0.68268
0.4986501
Step-by-step explanation:
The Canada Urban Transit Association has reported that the average revenue per passenger trip during a given year was $1.55. If we assume a normal distribution and a standard deviation of 5 $0.20, what proportion of passenger trips produced a revenue of Source: American Public Transit Association, APTA 2009 Transit Fact Book, p. 35.
a. less than $1.55?
b. between $1.15 and $1.95? c. between $1.35 and $1.75? d. between $0.95 and $1.55?
Given that :
Mean (m) = 1.55
Standard deviation (s) = 0.20
a. less than $1.55?
P(x < 1.55)
USing the relation to obtain the standardized score (Z) :
Z = (x - m) / s
Z = (1.55 - 1.55) / 0.20 = 0
p(Z < 0) = 0.5 ( Z probability calculator)
b. between $1.15 and $1.95?
P(x < 1.15)
USing the relation to obtain the standardized score (Z) :
Z = (x - m) / s
Z = (1.15 - 1.55) / 0.20 = - 2
p(Z < - 2) = 0.02275 ( Z probability calculator)
P(x < 1.95)
USing the relation to obtain the standardized score (Z) :
Z = (x - m) / s
Z = (1.95 - 1.55) / 0.20 = 2
p(Z < - 2) = 0.97725 ( Z probability calculator)
0.97725 - 0.02275 = 0.9545
c. between $1.35 and $1.75?
P(x < 1.35)
USing the relation to obtain the standardized score (Z) :
Z = (x - m) / s
Z = (1.35 - 1.55) / 0.20 = - 1
p(Z < - 2) = 0.15866 ( Z probability calculator)
P(x < 1.75)
USing the relation to obtain the standardized score (Z) :
Z = (x - m) / s
Z = (1.75 - 1.55) / 0.20 = 1
p(Z < - 2) = 0.84134 ( Z probability calculator)
0.84134 - 0.15866 = 0.68268
d. between $0.95 and $1.55?
P(x < 0.95)
USing the relation to obtain the standardized score (Z) :
Z = (x - m) / s
Z = (0.95 - 1.55) / 0.20 = - 3
p(Z < - 3) = 0.0013499 ( Z probability calculator)
P(x < 1.55)
USing the relation to obtain the standardized score (Z) :
Z = (x - m) / s
Z = (1.55 - 1.55) / 0.20 = 0
p(Z < 0) = 0.5 ( Z probability calculator)
0.5 - 0.0013499 = 0.4986501
Picture attached - Two Column Proof - NEED HELP PLS PLS PLS WILL MARK BRAINLIEST
Answer:
hmm its would be o
Step-by-step explanation:
its O
A snail can crawl 2/5 of a meter in a minute.
How many minutes will it take the snail to crawl 6 meters?
Please give me an answer A S A P.
WILL MARK BRANLIEST TO THE CORRECT ANSWER!
You decide to invest $250 in an account that yields a return of approximately 4% each year. What is the value of you investment after 15 years if you make no further deposits or withdrawals?
Answer:
$450.24
Step-by-step explanation:
According to my quiz...
If f(x) = 4x + 5, what is the inverse of F(x)?
Answer:
f^-1(x) = 1/4 x - 5/4
Step-by-step explanation:
f(x) = 4x + 5
y = 4x + 5
x = 4y + 5
4y = x - 5
y = 1/4 x - 5/4
f^-1(x) = 1/4 x - 5/4
HELP DUE IN 2 MIN
The ratio of boys to girls in a classroom is 6 to 5. If
there are a total of 18 boys in the classroom, find
the number of girls in the classroom.
Answer:
15
Step-by-step explanation:
18/3=6
15/3=5
Answer:
15
Step-by-step explanation:
If the ratio is 6:5 and we know the boys are 18, we have 18:?
18/6=3, so we have to do 5*3. 5*3=15.
The ratio is 18:15, the number of girls in the classroom is 15
A U.S. government survey in 2007 said that the proportion of young Americans that earn a high school diploma is 0.87. a)Suppose you took a simple random sample of 100 young Americans. We know because of sampling variability that the sample proportion of those who earned a high school diploma would vary each time you took a sample. Assuming the value above can be taken as the population proportion (i.e. as a parameter), what model can be used to describe how these sample proportions would vary
Answer:
normal distribution can be used to model the sample proportions
Step-by-step explanation:
N ( sample size ) = 100
probability of earning high school diploma (p) = 0.87
probability of not earning high school diploma ( q ) = 0.13
hence ;
∈( P ) = p = 0.87
Var ( p ) = [tex]\frac{pq}{n}[/tex] = [tex]\frac{0.86 * 0.13 }{100}[/tex] = 0.001131
therefore ; p ~ N = ( 0.87 , 0.001131 )
One serving of yogurt is 95 calories. How many calories are in 2.5 servings of yogurt ?
Answer:
237.5 calories
Step-by-step explanation:
One serving has 95
so 2.5 serving has
2.5×95= 237.5
Plz mark brainliest
thanks
Mrs. Jones places 3 orders for school T-shirts. Each order has 16 boxes of shirts and each box holds 17 shirts. How many T-shirt does Mrs.Jones order?
Answer:
816 T-shirts
Step-by-step explanation:
16 boxes * 17 shirts = 272 shirts total in 16 boxes
272 shirts * 3 orders = 816 shirts
1, 4, 16, 64, ______what follows
Answer:
[tex]256[/tex]
Step-by-step explanation:
[tex]We\ observe\ that,\\For\ every\ number\ n\ in\ the\ sequence, the\ number\ next\ to\ it\ is\ 4n.\\Hence,\\In\ order\ to\ continue\ the\ sequence:\\1,4,16,64,256[/tex]
Answer:
1, 4, 16, 64, 256
Step-by-step explanation:
The sequence follows the rule: n * 4
1 * 4 = 4
4 * 4 = 16
16 * 4 = 64
Multiply 64 by 4.
64 * 4 = 256
Hope this helps.
what is the relationship of the angles
Answer:
Alternate Interior Angles
Answer:
a
Step-by-step explanation:
What is the equation relating x and
y together?
y
1
2
3
4
5
25
23
21
19
17
y=-2x + [?]
Answer:
ommmm I have no idea Butt 1 of my fav numb is 17 so pick that
I NEED HELP ASAP PLZ
first one
Step-by-step explanation:
Answer:
1/2 is the answer
Step-by-step explanation:
Solve the equation.
k/-9 =7
Answer:
k=-63
Step-by-step explanation:
multiply both sides by -9
k=7*-9
k=-63
Answer:
-63
Step-by-step explanation:
by simplifying both sides of the equation, then isolating the variable. k= -63
-9 x 7 = -63
The graph of y=-3x+4 is:
A. a point that shows one solution to the equation.
B. a line that shows only one solution to the equation.
c. a line that shows the set of all solutions to the equation.
D. a point that shows the y-intercept.
Find the distance represented by x
the distance of X is 180ft
if you can buy 3 loaves of bread for $5 how many loaves can you buy for $12
Answer:
You can buy 6 because it cost 2.50 for 1 loaf
Step-by-step explanation:
can someone help me with this
Answer:
30
Step-by-step explanation:
3 + (6 * 4) + 3 = 30
hope this helps
Daryl has 7 hats. David has h times more hats than Daryl. How many hats does David
have?
for 10 points!!
Answer:
David has 7h hats
Step-by-step explanation:
Daryl: 7
David: 7h
Slope for (5,-5) (3,5)
Answer:
-5
Step-by-step explanation:
5-(-5)/3-5=10/-2=-5
(can I get brainliest please)
Order the side lengths HI, IK, HJ, IJ, and K J from least to greatest.
Answer:
I think it's IH, IJ, JK, HJ, IK.
help meeeeeeeeeeeeeeeeeee
Answer:
18
Step-by-step explanation:
the other right triangle is 3-4-5. so, 3*4/2=6
4*6/2=12
6+12=18
give brainliest pls
Which equation should you solve to find x?
Answer:
B
Step-by-step explanation:
[tex]sin ~26^\circ=\frac{x}{10}[/tex]
Answer:
sin 26 = x/10
Step-by-step explanation:
5.6 x 10 __= 5,600
hurry
Answer:
its 10^3 power or 1000
Step-by-step explanation:
57.351 rounded to the ones place
How do you round to the ones place?
Look to the next smallest place value, the digit to the right of the place value you're rounding to. For example, if you want to round to the nearest ten you'd look at the ones place. If the digit in the next smallest place value is less than five (0, 1, 2, 3, or 4), you leave the digit you want to round to as-is.
Answer:
Step-by-step explanation:
do u mean round to the nearest 10th as in one decimal place or to the nearest one not decimal place?
Help me on this questionnnn
Answer: 2,3,5
Step-by-step explanation:
20 pts and brainlyest to correct-
Answer: c
Step-by-step explanation:
First find 2 points like say
(0,3) and (1,-2)
now find the slope
3-(-2)/0-1 = -5
the y intercept is already known so the equation is y=-5x+3