what is the value of A when we rewrite (32/5)^-2x as A^x
Answers
Answer:
\((\dfrac{25}{1024})^x\)
Step-by-step explanation:
The given expression is :
\((\dfrac{32}{5})^{-2x}\)
We need to rewrite it in the form of \(A^x\).
We know that, \((\dfrac{1}{x})^{-a}=x^a\)
So,
\((\dfrac{32}{5})^{-2x}=(\dfrac{5}{32})^{2x}\\\\=(\dfrac{5^2}{32^2})^x\\\\=(\dfrac{25}{1024})^x\)
So, \(A=\dfrac{25}{1024}\). Hence, this is the required solution.
Answer: A = (32/5)^-2
Step-by-step explanation:
Related Questions
if i had 1000 apples and gave 39 away
how many wouldd i have left
Answers
Answer:
1000-39=961
so 961 apples are left.
A fighter jet F and a helicopter H leave the airport A at the same time. The jet flies 25 km on a bearing of 040° and the helicopter flies 30 km on a bearing of 320°. How far apart are the aircraft? (Use a scale of 1 cm to represent 5 km.)
Answers
Answer:
FH = 35.64
Step-by-step explanation:
(∠A = 360 so the other angle is 40)
By law of cosines,
FH² = AH² + FA² - 2(AH)(FA) * cos(A)
= 30² + 25² - 2(30)(25) * cos(80)
= 900 + 625 - 1500 * 0.17
= 1525 - 255
FH² = 1270
FH = √1270
FH = 35.64
HELP PLSZZZZSZZZZZZZZZZ need asap
Answers
Answer:
thursday
Step-by-step explanation:
there are 7 days in a week, and the multiple of 7 closest to 100 is 14, so after 98 days, it will be a monday. 3 days after monday is thursday, which is your answer. I hope this helps!
please help.. all my points are gone and I need this asap
NO LINKS
Answers
Answer:
Step-by-step explanation:
Can someone give me the answer please 4(2x-3)=5x+7
Answers
Step-by-step explanation:
x=6.33333
the three just continue so u can keep it x=6.3
A movie theater can seat a maximum of 25 people. Let p represent the total number of people. Which inequality represents p, the number of people the theater can seat?
Answers
The inequality that represents p, the number of people the theater can seat is p ≤ 25
Which inequality represents p, the number of people the theater can seat?From the question, we have the following parameters that can be used in our computation:
A movie theater can seat a maximum of 25 people
This means that
Maximum = 25 people
In other words, the movie theatre can allow 25 or less people to attend a movie
In inequality, 25 or less means less than or equal to 25
When represented as an inequality expression, we have
≤ 25
Using the variable p, we have
p ≤ 25
Hence, the inequality is p ≤ 25
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Joe told Mickey he got an hourly raise at work and his new rate will be $10.25 per hour. Mickey wants to know what Joe’s hourly rate was before his raise. If r represents the amount of the raise, which expression represents Joe’s hourly rate before his raise?
Answers
Answer:10.25-r= hourly rate
Step-by-step explanation:
guess what property is used:
\( \frac{-4}{7} + \frac{5}{8} = \frac{5}{8} + ( \frac{ - 4}{7} )\)
\(( \frac{1}{2} \times \frac{4}{7} ) \times ( \frac{ - 2}{3} )= \frac{1}{2} \times ( \frac{4}{7} \times ( \frac{ - 2}{3} ))\)
7/-8 x (-8/7)=1
i will mark u brainliest if u answer this correctly
Answers
Answer:
Step-by-step explanation:
1 no is commutative property.
2 no is associative property
3 no is multiplicative inverse property.
Solve the following algebraic equation. Show each step of the process.6(x -8) = 96
Answers
start by distributing the 6 on the parentheses
\(\begin{gathered} 6(x-8)=96 \\ 6x-48=96 \end{gathered}\)Continue by moving the numbers that are not multiplied by x on the right side, and leaving all numbers with the x on the left side
\(\begin{gathered} 6x-48=96 \\ 6x=96+48 \\ 6x=144 \\ \end{gathered}\)since that is the value for '6x' divide by 6 on both sides
\(\begin{gathered} \frac{6x}{6}=\frac{144}{6} \\ x=\frac{144}{6} \end{gathered}\)simplify
\(\begin{gathered} x=\frac{144}{6} \\ x=24 \end{gathered}\)Which term listed below is missing from the sequence 26 23 17 11
Answers
The missing term in the sequence 5, 11, 17, ?, 31, 41 is B. 23.
How to calculate the missing termWe have been given the series 5, 11, 17, ?, 31, 41. We need to find the missing number out of the given sequence.
Let us write the prime numbers upto 50.
2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47.
By looking into the above prime numbers we can make out our sequence. The series is formed by the alternate prime numbers. Thus we can complete the given sequence as,
5, 11, 17, 23, 31, 41.
Thus we got the missing number as 23 in the sequence 5, 11, 17, 23, 31, 41.
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Find the missing term in the sequence 5, 11, 17, ?, 31, 41.
by substituting the given values for x calculate the y value for the following equation y=x+2
Answers
Solve −6s−5+2s=−13 help
Answers
Answer:
s=2
Step-by-step explanation:
-4s-5=-13
+5. +5
-4s = -8 ÷ -4
Find the indicated margin of error. In a clinical test with 2161 subjects, 1214 showed improvement from the treatment. Find the margin of error for the 95% confidence interval used to estimate the population proportion.
Answers
Answer:
The margin of error is \(E = 0.021\)
Step-by-step explanation:
From the question we are told that
The population size is \(n = 2161\)
The number that showed improvement is \(k = 1214\)
Generally the sample proportion is mathematically represented as
\(\r p = \frac{ 1214}{2161}\)
=> \(\r p = 0.56\)
Given that the confidence level is 95% then the level of significance is mathematically represented as
\(\alpha =(100-95) \%\)
=> \(\alpha =0.05\)
The critical value of \(\frac{\alpha }{2}\) from the normal distribution table is
\(Z_{\frac{\alpha }{2} } = 1.96\)
Generally the margin of error is mathematically represented as
\(E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1 - \r p )}{n} }\)
=> \(E = 1.96 * \sqrt{\frac{ 0.56(1 - 0.56 )}{2161} }\)
=> \(E = 0.021\)
Find the annual rate of interest.Principal = 4600 rupeesPeriod5 yearsTotal amount =6440 rupeesAnnual rate of interest =%Stuck? Review related articles/videos or use a hint.
Answers
The compound interest is given, in general, by the next formula:
\(A=P(1+\frac{r}{n})^{nt}\)Where A is the amount, P is the initial amount, r is the rate of interest, n is the number of times the interest rate is applied in a period, and t is the numbers of periods.
Then, in our problem:
\(A=6440,P=4600,t=5,n=1\)Solving the formula for r:
\(\begin{gathered} n=1 \\ \Rightarrow A=P(1+r)^t \\ \Rightarrow(1+r)^t=\frac{A}{P} \\ \Rightarrow r=-1+\sqrt[t]{\frac{A}{P}} \end{gathered}\)Then, using the numerical values above:
\(r=-1+\sqrt[5]{\frac{6440}{4600}}=-1+\sqrt[5]{\frac{7}{5}}\approx-1+1.0696\approx0.07\)Then, the rate of interest is approximately equal to 7%
how do it prove this without approximately calculating the logarithm ?
Answers
Answer:
\(10 < {e}^{8} \)
\( ln(10) < 8\)
\( ln(10) - 8 < 0\)
Since ln(10) > 0, it follows that ln(10) + 1 > 0, and so:
\(( ln(10) + 1)( ln(10) - 8) < 0\)
\( {( ln(10)) }^{2} - 7 ln(10) - 8 < 0\)
\(( { ln(10) })^{2} - 7 ln(10) + 1 < - 9\)
\( {( ln(10)) }^{2} + 2 ln(10) + 1 < 9 ln(10) - 9\)
\( {( ln(10) )}^{2} + 2 ln(10) + 1 < 9( ln(10) - 1)\)
(ln(10) + 1)^2 < 9(ln(10 - 1)
ln(10) + 1 < 3√(ln(10) - 1)
(1 + ln(10))/3 < √(ln(10) - 1)
√(ln(10) - 1) > (1+ ln(10))/3
Write the standard form of the complex number
sqrt 108[cos(−30°) + i sin(−30°)]
Answers
Answer:
\(9-3\sqrt{3} i.\)
Step-by-step explanation:
\(1. \ cos(-30)=\frac{ \sqrt{3}}{2}; \ sin(-30)=-0.5;\)
\(2. \sqrt{108} (cos(-30)+isin(-30))=\frac{\sqrt{108} \sqrt{3}}{2}-i*\sqrt{108}*0.5=9-3\sqrt{3} i.\)
A cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches. What is the surface area of the vase? Use the formula SA = B + Ph, since the vase has a bottom but no top. Use 3.14 for π
and round to the nearest tenth of a square inch.
Answers
The surface area of the cylindrical pottery vase is 177.55 in².
Given that a cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches, we need to find the surface area of the vase,
SA of a cylinder = 2π×radius(h+r)
= 2×3.14×2.15(2.15+11)
= 177.55 in²
Hence, the surface area of the cylindrical pottery vase is 177.55 in².
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A board that measures 3/4 feet long is cut into 6 equal pieces . What is the length of each price
Answers
Step-by-step explanation:
8 cm² is the correct answer for that question
Given:
Board Length = 3/4
6 equal pieces = 3/4 ÷6
= 3/4 × 1/6
= 1/4 × 1/2
= 1/8
Therefore each equal piece will be 1/8 feet long
Answered by GauthMath if you like please click thanks and comment thanks too.
Pls help !!!!!!!!!!!!!!!!
Answers
Answer:
median: 6
Range: 9
Mode: 7
Step-by-step explanation:
Answer:
a) 6
b) 0
c) 7
Step-by-step explanation:
a) the middle number in a sorted ascending or descending order.
b) the difference between the highest number and the lowest
c) The most frequent number
Terri buys five and seven-eighths ounces of chocolate chips. She uses four and four-sixths ounces in a recipe. How many ounces of chocolate chips does she have left?
Answers
Answer:
1 5/24 ounces--------------------------
Find the difference of the initial and used amounts:
5 7/8 - 4 4/6 = 5 - 4 + 7/8 - 4/6 = Combine whole and fraction parts1 + 7/8 - 2/3 = Simplify1 + 21/24 - 16/24 = Common denominator is 241 + 5/24 = Convert to mixed fraction1 5/24dentify an equation in standard form for an ellipse with its center at the origin, a vertex at (0, 6), and a co-vertex at (2, 0).
Answers
Answer:x2/b2 + y2/a2 = 1 or y2/a2+x2/b2=1
Step-by-step explanation:First of all, only A) and B) are ellipse equations. The other two are hyperbola equations, since they are subtractions.
The vertexes are (x,y) --> (0,6) and (2,0). So a = 6 and b = 2. The major axis is on the y-axis, since 6>2
x2/b2 + y2/a2 = 1 or y2/a2+x2/b2=1
What is the image of (2, 10) after a dilation by a scale factor of 1/2 centered at the origin?
Answers
Answer: (1,5)
Analysis = \(\frac{1}{2}(2,10)\)
\(=(\frac{1}{2}\times2,\frac{1}{2}\times10)\)
\(=(1,5)\)
I hope this helps you :D
Given: Line a and line b intersect Prove: <1 = <3Which statement and reason best completes the proof?
Answers
When lines a and b overlap, angle 1 equals angle 3.
What is intersecting lines?The intersection of two lines in Euclidean geometry might be the empty set, a point, or another line. Distinguishing these circumstances and locating the intersection have applications in computer graphics, motion planning, and collision detection, among others. When two or more lines intersect on a plane, they are referred to as intersecting lines. The crossing lines have a common point, which exists on all of them and is known as the point of intersection. The intersecting lines are two lines that have precisely one common point. The crossing lines have a point in common. The point of intersection is the common point that exists on all intersecting lines.
Here,
To prove ∠1 ≅ ∠ 3, we can use the congruent supplements theorem. According to the congruent supplements theorem, If two angles are supplements of the same angle then two angles are congruent.
Line a and line b intersect (given)
∠3 is supplementary to ∠2 because of linear pair theorem (given)
So, if we take ∠2 as the common angle
And ∠1 is supplementary to ∠2 by linear pair theorem ( option D)
Then, ∠1 is supplementary to ∠2 which is supplementary to ∠3
Therefore, ∠1 ≅ ∠3 (according to the congruent supplements theorem)
This is proved when line a and line b intersect, angle 1=angle 3.
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Martin wants to buy a new bedroom set that cost $1590 including tax. Unfortunately he doesn’t have $1590 so he secures a 2 year loan from the furniture store at 9% interest to be repaid in 254 equal monthly installments. Find the monthly payment
Answers
The monthly Payment of a 2-year loan of $1590 with 9% interest that needs to be repaid in 254 equal monthly installments is approximately $11.92.
The monthly payment of a 2-year loan of $1590 with 9% interest which needs to be repaid in 254 equal monthly installments, we need to use the loan repayment formula. The formula is given as:
Monthly Payment = (Loan Amount x Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))
Here,
Loan Amount = $1590
Interest Rate = 9% per annum
Time = 2 years = 24 months
number of Months = 254 (as there are 254 monthly installments)
First, we need to calculate the Monthly Interest Rate using the following formula:
Monthly Interest Rate = Annual Interest Rate / 12
The Annual Interest Rate is 9%,
so the Monthly Interest Rate is: Monthly Interest Rate = 9 / 12 = 0.75%Putting the given values into the loan repayment formula,
we get: Monthly Payment = (1590 x 0.0075) / (1 - (1 + 0.0075)^(-254))= 11.92 (approx)
Therefore, the monthly payment of a 2-year loan of $1590 with 9% interest that needs to be repaid in 254 equal monthly installments is approximately $11.92.
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the sum of four number is 20500.three of the numbers are 2341.578 and 10690.What is the fourth number?
Answers
Answer:
5216.844
Step-by-step explanation:
Let x be the fourth number.
We know that the sum of the four numbers is 20500:
2341.578 + 10690 + x + 2341.578 = 20500
Simplifying and solving for x:
x = 20500 - 2341.578 - 10690 - 2341.578
x = 5216.844
grand pa gave $35 to linda and diane. linda received $19. find the ratio of the amount of money linda received to the amount of money diane received
Answers
N over 7 = 20
Solve for N
Answers
Answer: 140
Step-by-step explanation: N/7=20, so we have to isolate N. Hence, we multiply 7x7 because we are dividing by 7. We must multiply the other side too, so it is 140.
Answer:
N/7 = 20.
Cross multiply.
N x 1 = 20 x 7
N = 140.
Help me solve the following 5(2x+7)=
Answers
Answer:
= 10x+35
Step-by-step explanation:
(5)(2x+7)
(5)(2x)+(5)(7)
=10x+35
Paul has a pocket full of 150 coins containing pennies, nickels and dimes. If 24% of his coins are pennies, and 51 of his coins are nickels, how many dimes does he have?
Answers
Answer:He has 63 dimes
Step-by-step explanation:
Hope this helps!
24% of 150=36
51+36=87
150-87=63
Select the correct answer.
What is the solution to this equation?
91 – 1 = 2
OA 1 / 1
OB. 2
oc. 1 / 1
OD.
1
1
Answers
Answer:
x = 1/2
Step-by-step explanation:
9^x -1 = 2
Add 1 to each side
9^x = 2+1
9^x = 3
Rewriting 9 as 3^2
3^2x = 3
3^2x = 3^1
The bases are the same so the exponents must be the same
2x =1
2x/2 =1/2
x = 1/2
Answer:
\(9 {}^{x} - 1 = 2 \\ 9 {}^{x} = 2 + 1 \\ 9 {}^{x} = 3 \\ 3 {}^{2(x)} = 3 \\ 3 {}^{2x} = 3 {}^{1} \\ since \: the \: \: bases \: are \: the \: same \\ 2x = 1 \\ x = \frac{1}{2} \)