Answers
Answer:
[tex]b=-3[/tex]
Step-by-step explanation:
We have:
[tex]25^b\cdot 125^{b+2}=125^b[/tex]
Notice that 125 is the same as 5³. So:
[tex]25^b\cdot ((5)^3)^{b+2}=((5)^3)^b[/tex]
Also, 25 is the same as 5². So:
[tex]((5)^2)^b\cdot ((5)^3)^{b+2}=((5)^3)^b[/tex]
Power of a power property:
[tex]5^{2b}\cdot 5^{3(b+2)}=5^{3b}[/tex]
Power of a product property:
[tex]5^{2b+3(b+2)}=5^{3b}[/tex]
Since they have the same base, the exponents are equal. So:
[tex]2b+3(b+2)=3b[/tex]
Solve for b. Distribute on the left:
[tex]2b+3b+6=3b[/tex]
Combine like terms on the left:
[tex]5b+6=3b[/tex]
Subtract 5b from both sides:
[tex]6=-2b[/tex]
Divide both sides by -2. So, the value of b is:
[tex]b=-3[/tex]
And we're done!
Related Questions
Jose and Fernando are both working at the same company. Jose worked 42 hours last week while Fernando worked 38 hours during the same week. Jose makes $15/hour and Fernando makes $16/hour. Who made more money that week?
Answers
Answer:
Jose
Step-by-step explanation:
Jose:
Step 1:
42 × 15 Equation
Step 2:
$630 Multiply
Fernando:
Step 1:
38 × 16 Equation
Step 2:
$608 Multiply
Answer:
Jose earns more
Hope This Helps :)
Perform he operations in the correct order :
10 + 8 ÷ 1 -5
Answers
step 1: divide first (8 divided by 1 = 8)
step 2: add since it’s first (10 + 8 = 18)
step 3: subtract (18 - 5 = 13)
Andrew brings juice for lunch every 5 days and Hannah brings juice every 7 days they both brought juice today . How many day will it be before they both bring juice ?
Answers
Answer:
35 days
Step-by-step explanation:
Andrew brings juice for lunch every 5 days and Hannah brings juice every 7 days
Find the lowest common multiple of 5 and 7
Andrew (every 5 days) = 10, 15, 20, 25, 30, 35, 40, 45, 50
Hannah (every 7 days) = 14, 21, 28, 35, 42, 49, 56
The lowest common multiple of 5 and 7 is 35
Therefore, if Andrew and Hannah both brought juice today, it will take 35 days before they will both bring food again on the same day.
what percent of 50 is 18?
Answers
Answer:
36 %
Step-by-step explanation:
Convert the fraction to a decimal, then multiply by 100 .
Answer:
36%
Step-by-step explanation:
The same explanation as she said
Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.
Ps. I just need h(x)
Answers
Mariah owed her grandfather $2.25 but was recently able to pay him back $1.50 how much does Mariah currently owe her grandfather
Answers
Answer:
$0.75
Step-by-step explanation:
2.25-1.50=0.75
The sum of 6 consecutive odd numbers is 204. What is the fourth number in this sequence?
Answers
Answer:
35
Step-by-step explanation:
1. Set up a equation.
2. X is the first, so the ones after x are x+2, x+4, x+6, x+8, and x+10.
3. That means that x+x+2+x+4+x+6+x+8+x+10=204.
4. Simplify. You would get that 6x+30=204.
5. Solve for x. 6x=174, so x=29.
6. Get the fourth number in the sequence. 29+6=35.
Answer: The fourth number in this sequence is 35.
1 point
3. A bus driver stops at a gas station to put some gasoline in the bus. He
pays $2.48 per gallon for 15 gallons of gas. How much did he pay for the
gas?
Answers
solve for b
12=b/3-8
Answers
Answer:
b=60
Step-by-step explanation:
Add 8 to both sides to receive the equation of 20=b/3
Multiply all sides by 3 to get 60 as b
NEED HELP GIVING 15 POINTS
Choose the one problem that has NOT been done correctly. Start your response with the number you choose and explain the mistake that was made in the problem.
Answers
Answer:
1
Step-by-step explanation:
didn't mulitiply by -2
it says y=-4 (2 x -4)=-8
7-(-8) turns into 7+8 because two negatives make a positive
Write the function in standard form.
f(x) = - 3(x - 7)2 + 15
Answers
Answer:
The answer is f ( x ) = − 6 x + 57
Step-by-step explanation:
An investment of $6,530 earns interest at the rate of 4% and is compounded quarterly. What is the accumulated value of the investment at the end of 8 years?
Answers
Answer:
$8,978.36
Step-by-step explanation:
What is the quotient for 6 and 1/2 divided by 3/4
Answers
Answer:
I believe it is 4
Step-by-step explanation:
According to General Social Survey of 2016, the population distribution of number of years of education for self-employed individuals in the United States has a mean of 12.9 and a standard deviation of 4.0. The distribution is skewed slightly to the right. For each sample size below: Describe the mean, standard error, and shape of the sampling distribution of the means for a random sample of: (7 pts) a) 16 residents b) 49 residents c) 121 residents Describe the pattern as n increases
Answers
Answer:
a) Mean is 12.9
b) Standard Error
i) n = 16, Standard Error = 1
The shape of the sampling distribution means is not normal
ii) n = 49 , Standard Error = 0.5714285714
The shape of the sampling distribution means is normal
iii) n = 121, Standard Error = 0.3636363636
The shape of the sampling distribution means is normal
c)Describe the pattern as n increases
As the number of random samples(n) increases the value for the standard error decreases
Step-by-step explanation:
Central Limit Theorem states that
if the sample size is large (generally n ≥ 30), and the standard deviation of the population is finite, then the distribution of sample means will be approximately normal.
a) 16 residents
Mean = 12.9
Standard Error = Standard Deviation /√n
= 4/√16
= 4/4
= 1
n < 30, hence, The shape of the sampling distribution means is not normal
b) 49 residents
= Mean = 12.9
Standard Error = Standard Deviation /√n
= 4/√49
= 4/7
= 0.5714285714
n > 30, hence, The shape of the sampling distribution means is normal
c) 121 residents
Mean = 12.9
Standard Error = Standard Deviation /√n
= 4/√121
= 4/11
= 0.3636363636
n > 30, hence, The shape of the sampling distribution means is normal
Describe the pattern as n increases
As the number of random samples(n) increases the value for the standard error decreases
The graph shows f (x) and its transformation g(x) . Which equation correctly models g(x) ?
A) g(x) = 4x-2 + 4
B) g(x) = 4x+2 - 4
C) g(x) = 4x+4 + 2
D) g(x) = 4x-4 + 2
Answers
In 2008 the Better Business Bureau settled 75% of complaints they received (USA Today, March 2, 2009). Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is .75, the same as the overall proportion of complaints settled in 2008
a. Suppose you select a sample of 450 complaints involving new car dealers. Show the sampling distribution of .
b. Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion?
c. Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of .
d. Based upon the smaller sample of only 200 complaints, what is the probability that the sample proportion will be within .04 of the population proportion?
e. As measured by the increase in probability, how much do you gain in precision by taking the larger sample in part (b)?
Answers
Answer:
a) the sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.0204
b) the probability that the sample proportion will be within 0.04 of the population proportion is 0.95
c) sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.03061
d) the probability that the sample proportion will be within 0.04 of the population proportion is 0.8088
e) gain in precision is 0.1402.
Step-by-step explanation:
a) Let p represent the
Given that
population proportion of complaints settled for new car dealers p = 0.75.
and n = 450
mean of the sampling distribution of the sample proportion is the population proportion p
i.e up° = p
mean of the sampling distribution of the sample proportion p° = 0.75
so standard error of the proportion is;
αp° = √(p( 1-p ) / n)
we substitute
αp° = √(0.75 ( 1-0.75 ) / 450)
=√(0.1875 / 450
= √0.0004166
= 0.0204
therefore the sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.0204
b)
(p° - p) is within 0.04
so lets consider
p ( -0.04 ≤ p° - p ≤ 0.04) = p ( ( -0.04/√(0.75 ( 1-0.75 ) / 450)) ≤ z ≤ ( 0.04/√(0.75 ( 1-0.75 ) / 450))
= p( -0.04/0.0204 ≤ z ≤ 0.04/0.0204)
= p ( -1/96 ≤ z ≤ 1.96 )
= p( z < 1.96 ) - p( z < -1.96 )
now from the S-normal table,
area of the right of z = 1.96 = 0.9750
area of the left of z = - 1.96 = 0.0250
p( -0.04 ≤ p°- p ≤ 0.04) = p( z < 1.96 ) - p( z < -1.96 ) = 0.9750 - 0.0250
= 0.95
therefore the probability that the sample proportion will be within 0.04 of the population proportion is 0.95
c)
population proportion of complaints settled for new car dealers p = 0.75.
n = 200
mean of the sampling distribution of the sample proportion p°.
i.e up° = p
mean of the sampling distribution of the sample proportion p° = 0.75
Sampling distribution of the sample proportion p is determined as follows
αp° = √(p( 1-p ) / n)
we substitute
αp° = √(0.75 ( 1-0.75 ) / 200)
=√(0.1875 / 200
= √0.0009375
= 0.03061
therefore sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.03061
d)
(p° - p) is within 0.04
so lets consider
p ( -0.04 ≤ p° - p ≤ 0.04) = p ( ( -0.04/√(0.75 ( 1-0.75 ) / 200)) ≤ z ≤ ( 0.04/√(0.75 ( 1-0.75 ) / 200))
= p( -0.04/0.03061≤ z ≤ 0.04/0.03061)
= p ( -1.31 ≤ z ≤ 1.31 )
= p( z < 1.31 ) - p( z < -1.31 )
now from the S-normal table,
area of the right of z = 1.31 = 0.9049
area of the left of z = - 1.31 = 0.0951
p( -0.04 ≤ p°- p ≤ 0.04) = p( z < 1.31 ) - p( z < -1.31 ) = 0.9049 - 0.0951
= 0.8098
therefore the probability that the sample proportion will be within 0.04 of the population proportion is 0.8088
e)
From b), the sample proportion is within 0.04 of the population proportion; with the sample of 450 complaints involving new car dealers is 0.95.
sample proportion is within 0.04 of the population proportion; with the sample of 200 complaints involving new car dealers is 0.8098.
measured by the increase in probability, gain in precision occurs by taking the larger sample in part (b)
i.e
Gain in precision will be;
0.9500 − 0.8098
= 0.1402
therefore gain in precision is 0.1402.
While jumping rope, Juan jumped 24 times in 30 seconds. At this rate, how many times will he jump in 50 seconds?
Answers
Answer:
40
Step-by-step explanation:
In 50 times Juan will jump 40 times.
What is unitary method ?Unitary method is first finding the value of a single unit and then deriving the required units from the given data.
For example - : A can eat 2 bananas in 2 seconds.So he can eat one banana in 1 second.From this we can calculate how many bananas he can eat in any given time.
According to the given question Juan jumped 24 times in 30 seconds.
∴ In 1 sec Juan will jump 24/30 times which is
= 4/5 times.
So, in 50 secs Juan will jump ( 4/5 × 50 ) = 40 times.
learn more about unitary method here :
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Coach Brown made 50 pints of Gatorade for his team. How many gallons did he make?
Answers
Answer:
6.25 gallons
Step-by-step explanation:
Answer:
6.25
Step-by-step explanation:
A coordinate plane with 4 lines. The first line is labeled a(x) and passes through (2, negative 4) and (0, 2) and continues past (negative 1, 5). The second line is labeled f(x) and passes through (negative 6, negative 6), (negative 3, 0), and (0, 6). The third line is labeled g(x) and passes through (negative 2, negative 7), (0, negative 3), (1, negative 1) and (2, 1). The fourth line is labeled h(x) and passes through (negative 6, negative 6), (0, negative 3), and (6, 0).
When Janelle woke up, it was –3 degrees Fahrenheit outside. As the morning progressed, the temperature rose 2 degrees every hour.
Which line on the graph could represent this scenario?
a(x)
f(x)
g(x)
h(x)
Answers
Answer:
It is c which is g(x)
Step-by-step explanation:
Answer:
the answer is C : g(x)
Step-by-step explanation:
i just got the right answer on the assignment
Cindy and Victoria completed 8/9 of their job in a day. Cindy has done 1/9 of the work. How much of the work was done by Victoria?
Answers
Answer:
7/9 of the work was done by Victoria.
Step-by-step explanation:
8/9-1/9=7/9
Which expression is equivalent to Sine (StartFraction pi Over 12 EndFraction) cosine (StartFraction 7 pi Over 12 EndFraction) minus cosine (StartFraction pi Over 12 EndFraction) sine (StartFraction 7 pi Over 12 EndFraction)?
Answers
Answer:
EndRoot Over 2 EndFraction
StartFraction pi Over 6 EndFraction, StartFraction StartRoot 3 EndRoot Over 2 EndFraction
On using the trigonometric identity sin(x-y) = sin(x)cos(y) - cos(x)sin(y), we calculate that [tex]sin(\frac{\pi }{12})cos(\frac{7\pi }{12}) - cos(\frac{\pi }{12} )sin(\frac{7\pi }{12} ) =sin(\frac{-\pi }{2} )[/tex].
What are trigonometric identities?Trigonometric identities are equations that relate to different trigonometric functions and are true for any value of the variable that is there in the domain.
[tex]=sin(\frac{\pi }{12})cos(\frac{7\pi }{12}) - cos(\frac{\pi }{12} )sin(\frac{7\pi }{12} ) \\\\=sin(\frac{\pi }{12} -\frac{7\pi }{12})\\ \\ =sin(\frac{-\pi }{2} )[/tex]
Learn more about trigonometric identities here
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Given (64y^2)+(4x^2)+128y+16x+64=0, transform the equation into the appropriate form
Answers
Answer:
(8y+8)²+(4x²+16)=0
Step-by-step explanation:
Given:
(64y²)+(4x²)+128y+16x+64=0
Find:
Equation into the appropriate form
Computation:
(64y²)+(4x²)+128y+16x+64=0
(8y)²+(2x)²+128y+16x+64=0
(8y)²+(2x)²+2(8y)(8)+2(2x)(4) + 8²=0
(8y+8)²+(4x²+16)=0
Help ASAP
Find the sum (-3x + 7) + (2x - 5).
Answers
Answer:
-x + 2
Step-by-step explanation:
Find the median of the following data
2,8,7,8,6,15,6,8,3
Answers
Answer:
7
Step-by-step explanation:
Median is the middle value in a list of values arranged in increasing order.
The values given are :2,8,7,8,6,15,6,8,3
Arrange values in ascending order as: 2,3,6,6,7,8,8,8,15
The middle value is: 2,3,6,6,7,8,8,8,15
Median is 7
Which ratio is equivalent to 3:7?
A 6:7
B 3:21
C 24:56
D 15:30
Answers
Answer:
c
Step-by-step explanation:
Answer:
C. 24:56
Step-by-step explanation:
3/7 * 8/8
3*8 = 24
7*8 = 56
24/56
If the variance of the data values in a population is 225, what is the standard
deviation of the data values?
a.15
b.17
c.11
d.13
(apex)
Answers
Answer:15
Step-by-step explanation:
Apex
An elevator is 2/3 full. The people in the elevator weigh 1/3 ton altogether. How many tons can the elevator carry when it is completely full?
1/2 ton
2 ton
1 tons
1/6 ton
Answers
Answer:
Half of a ton
Step-by-step explanation:
2/3 of the elevator are already full and the elevator already weighs 1/3 of ton.The elevator needs 1/3 more of people to make the elevator full so that would be half of 1/3 of a ton which is a sixth.So add 1/6 and 1/3 together ams you get 1/2.
Could someone help me with number 17.
Answers
Answer:
y=-7
Step-by-step explanation:
if g(x) is g(-2) that means that x=-2 so we plug that in so 5*-2+3
5*-2+ -10
-10+3+ -7
so y=-7
Do you like a newspaper has letters to the editor for 60 people. If it’s number represents 5% of all the newspaper readers how many readers of the newspaper have
Answers
Answer:
5÷100
=0.05
0.05×60
=3
Answer:
1200 readers
Step-by-step explanation:
Let x = number of readers
x* 5% = 60
Change to decimal form
x* .05 = 60
Divide each side by .05
x * .05/.05 = 60/.05
x =1200
In Mrs. Bishop’s closet, there are 10 shirts and 15 skirts.
(a) Find the simplified ratio of shirts to skirts.
(b) If the ratio of shirts to skirts doesn’t change, but now the closet has 75 items in it. How many skirts will there be?
Answers
Answer:
(a) 2/3
(b) 45
Step-by-step explanation:
(a)
The "ratio of shirts to skirts" means "the number of shirts divided by number of skirts."
10 shirts
15 skirts
shirts : skirts = 10/15 = 2/3
Answer: 2/3
(b)
In the simplified ratio, there are 2 shirts for every 3 skirts.
Add 2 + 3 = 5.
The ratio of skirts to total number of items of clothing is 3:5.
There are 3 skirts to each 5 items of clothing.
Set up a proportion.
3/5 = x/75
5x = 3 * 75
x = 3 * 15
x = 45
Answer: 45