Answers
The first thing you should notice is that the exponent will be less than 1, as raising 27 to any power greater than 1 will make it larger, and you're trying to figure out what makes it equal to 3, a number less than 27.
Raising a number to a fractional power is taking its nth root: [tex] 21^{1/3} [/tex] is [tex] \sqrt[3]{21} [/tex], so you'll really need to take the nth root of 27 to get 3. To figure out which root, write the number in exponential form with a base of 3:
[tex] 27^{x} [/tex] = 3
[tex] 3^{3x} [/tex] = [tex] 3^{1} [/tex]
Now, the bases are the same (they are both 3), so you can set the exponents equal to each other:
3x = 1
Divide both sides by 3 and you've isolated x:
[tex]x = \frac{1}{3} [/tex]
Answer:
[tex] 27^{1/3} = 3[/tex]
Related Questions
Alexa's friends got her a skydiving lesson for her birthday. Her helicopter took off from the skydiving center, ascending in an angle of 20^\circ20
∘
20, degree, and traveled a distance of 3.43.43, point, 4 kilometers before she fell in a straight line perpendicular to the ground.
How far from the skydiving center did Alexa land?
Answers
Answer:
3.19495491 rounded to the nearest hundredth is 3.19
Step-by-step explanation:
The distance from the skydiving center did Alexa land will be 3.19 km. The formula of trigonometry is used in the given problem.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
From ΔABC it is obtained that;
[tex]\rm Cos A = \frac{AC}{AB} \\\\ COS 20^0 = \frac{AC}{3.4} \\\\ AC= 0.9694 \times 3.4 \\\\ AC = 3.19 \ km[/tex]
Hence the distance from the skydiving center did Alexa land will be 3.19 km.
To learn more about the trigonometry refer to the link;
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Which of the following best describes the algebraic expression 5(x+2)-3? A. Three less than five times a number plus two B. Three less than five times the quantity of a number plus two
Answers
b. three less again -3 than five times the quantity of a number plus two -3*5(x+2)
which means B best describes our situation
Answer:
Option B is correct.
Three less than five times of a quantity of a number plus two.
Step-by-step explanation:
Given the expression: [tex]5(x+2)-3[/tex]
To describe the given algebraic expression.
Here, x be the number.
x+ 2 means "a number plus 2"
5(x+2) means "five times the quantity of a number plus two".
and
5(x+2)-3 means "Three less than five times of a quantity of a number plus two".
Therefore, the following which best describe the algebraic expression [tex]5(x+2)-3[/tex] is, Three less than five times of a quantity of a number plus two.
Clark and his brother Kent played floor hockey in their living room. Each goal was worth 2 points. Clark scored 6 points. Kent scored 8 points. How many points did they score all together?
Answers
Find (19 x 10*5) -(5 x 10 *4)
Answers
(5 x 10*4) is 200
soo 950 - 200 = 750
Answer:d
Step-by-step explanation:
In the month of January, a certain restaurant claimed it sold 9,000 burgers and expects sales to grow at a rate of 4.8% per month over the next year. Which formula will determine the number of burgers the restaurant expects to sell this year?
Answers
Answer:
[tex]y=9000(1.048)^x[/tex]
Step-by-step explanation:
This will be an exponential growth problem. This is because the amount of burgers is expected to change at the same rate every month.
These equations are of the form
[tex]y=a(1+r)^x[/tex],
where a is the original amount, r is the growth rate and x is the amount of time.
In this problem, the original amount, a, is 9000.
The rate of growth is 4.8%; 4.8% = 4.8/1000 = 0.048
This gives us
[tex]y=9000(1+0.048)^x\\\\y=9000(1.048)^x[/tex]
Answer:
The answer is 9000(1.048)^t {limit from n = 1 to n = 12}.
Step-by-step explanation:
A pair of angles can be complementary and supplementary. The answers are sometimes? always? or never true? Justify the answer
Answers
Two angles are supplementary if their sum equals 180 °:
The supplementary angles are those that added are worth two right angles, that is, 180º.
answer:
A pair of angles can be never complementary and supplementary
what's the area of a square picture with 16 inch sides
Answers
To solve, we must plug in the given side length of 16 inches into the formula.
A = (16 inches)^2
A= 256 inches^2
Therefore, your answer is 256 inches^2.
Hope this helps!
Answer:
256
Step-by-step explanation:
9/20 as a percent
320% as a fraction
2 3/8 as a decimal and percent
.1% as a decimal and fraction
1.2 as a percent and fraction
5 1/3 as a percent and decimal
Answers
Answer:
1) 45%
2) [tex]\frac{16}{5}[/tex]
3) 2.335
237.5%
4) 0.0001
[tex]\frac{1}{1000}[/tex]
5) 120%
[tex]\frac{6}{5}[/tex]
6) 533.3%
5.333
Step-by-step explanation:
1) Divide the numerator by the denominator and multiply by 100, then:
[tex]\frac{9}{20}=0.45*100=45\%[/tex]
2) Write 320 has the numerator and 100 has the denominator, then reduce the fraction:
[tex]\frac{320}{100}=\frac{32}{10}=\frac{16}{5}[/tex]
3) As a decimal:
Divide the numerator by the denominator and add it to the integer part:
[tex]2+0.375=2.375[/tex]
As a percent:
Multiply the decimal number obtained above by 100:
[tex]2.375*100=237.5\%[/tex]
4) As a decimal:
Divide it by 100:
[tex]\frac{0.1}{100}=0.0001[/tex]
As a fraction:
As you can see, the decimal point were moved three spaces to the left. Therefore, the integer 1 is divided by 1000. Write 1 as the numerator and 1000 has the denominator:
[tex]\frac{1}{1000}[/tex]
5) As a percent:
Multiply 1.2 by 100, then:
[tex]1.2*100=120\%[/tex]
As a fraction:
To make 1.2 an integer you must multiply by 10, therefore, 12 will be the numerator and 10 the denominator:
[tex]\frac{12}{10}[/tex]
Reduce it:
[tex]\frac{6}{5}[/tex]
6) As a decimal:
Divide the numerator by the denominator and add it to the integer part:
[tex]5+0.33=5.333[/tex]
Multiply the decimal number obtained above by 100:
[tex]5.33*100=533.3\%[/tex]
Answer:
9/20 as a percent- 45%
320% as a fraction- 16/5
2 3/8 as a decimal- 2.38
2 3/8 as a percent- 237.5%
.1% as a decimal- 0.001
.1% as a fraction- 1/100
1.2 as a percent- 120%
1.2 as a fraction- 6/5
5 1/3 as a percent- 533.3%
5 1/3 as a decimal- 5.33
The dining room table in Logan’s dollhouse is a replica of the dining room table in the actual house . The replica is 4 7/8 in. Long how long is the table in the actual house
Answers
4 7/8 x 1/16 = ___ ↓
39/8 x 1/16 = 39/128.
Hope this helps,
♥A.W.E.S.W.A.N.♥
Answer:
6ft 6 in
Step-by-step explanation:
Write a proportion that uses the scale factor 1/16. The numerator corresponds to the dollhouse, and the denominator corresponds to the actual house. So 4 7/8 goes in the numerator, and the variable goes in the denominator.
1/16=478xx=16⋅478x=78
There are 12 in. in a foot, so 78 in. equals 6 ft 6 in.
What is simplified form of the expression -(4)^-2
Answers
-1/16
Explanation:
First, when we have a negative power in the numerator, the number with this power will be moved to the denominator and the power is converted to a positive one.
In other words: a^-x = 1 / a^x
In the question, we have:
-(4)^-2
This can be written as:
- 1 / 4^2 = -1 / (4*4) = -1/16
Hope this helps :)
By properties of exponents we have:
- (1 / (4) ^ 2)
Rewriting the expression:
- (1 / (4 * 4))
- (1 / (16))
Answer:
simplified form of the expression - (4) ^ - 2 is:
-1/16
The value of Maggie's car decreased by 10% since last year, when she bought it. If the car is now worth $11,000.00, how much was the car worth when she bought it?
Answers
90% $11000
100% $x
Now we cross multiply numbers and solve it for x:
90*x = 100 * 11000
90x = 1 100 000
x= 1 100 000 / 90
x= $12 222,22
When Maggie bought a car theprice was $12 222,22
A protractor is used to measure an angle. Which of the following could be the measure of the angle if we know it is an acute angle?
125°
75°
0°
it can't be determined
Answers
Final answer:
To find an acute angle using a protractor, choose the angle less than 90°. The acute angle could be 75°.
Explanation:
To determine an acute angle using a protractor, we look for an angle that is less than 90 degrees, as acute angles are those that measure less than 90 degrees.
75° could be the measure of the angle as it falls within the range of acute angles.
Hence, in this case, the angle that could be the measure of the acute angle is 75°.
ILL CHOOSE BRAINLIEST!!!Which region represents the solution to the given system of inequalities?
A
B
C
D
Answers
The solution of a set of inequalities is the place where the lines intersect.
Hope I helped!
Let me know if you need anything else!
~ Zoe
Answer :- D region represents the solution to the given system of inequalities.
Explanation:
In the graph we can see the two lines drawn from the given system are intersecting in the fourth quadrant.
⇒The solution of the system lie in the fourth quadrant.
∴region D represents the solution to the given system of inequalities.
The graph of the linear inequality is the graph of all solutions of the system where the solution of the system of inequalities is the intersection region of the solutions of the two inequalities.factor completely y^2-xy-56x^2
Answers
So [tex] y^{2} - xy - 56x^{2} [/tex] factored out is (y+7x)(y-8x)
We can check this using FOIL
F = (y)(y) = [tex] y^{2} [/tex]
O = (y)(-8x) = -8xy
I = (7x)(y) = 7xy
L = (7x)(-8x) = [tex] -56x^{2} [/tex]
[tex] y^{2} - 8xy + 7xy - 56x^{2} [/tex] Combine like terms
[tex] y^{2} - xy - 56x^{2} [/tex]
Answer: I got (y-8x)(y-7x) by factoring out the factors of 56, that have a sum of -1.
8 and 7 are factors of 56 when you multiply them and to get a sum of -1, 8 should change to negative. 7 + -8 = -1
What is the area of this figure?
Select from the drop-down menu to correctly complete the statement.
The area of the figure is ? cm2.
A. 102
B. 132
C. 168
D. 340
SOMEONE PLEASE HELP ASAP!!
Answers
[tex]A _{r} =(13cm)(6cm)[/tex]
[tex]A=78cm^{2} [/tex]
Similarly, the area of a triangle is one half times base times height, so [tex]At=( \frac{1}{2})bh [/tex]. Since we know that our base is 8cm and our height 6cm, lets replace those values in our equation to find the area of our triangle:
[tex]A_{t} =( \frac{1}{2})(8cm)(6cm) [/tex]
[tex]A_{t} =24cm^{2} [/tex]
Now the only thing left is add our areas:
[tex]A_{total} =78cm^{2}+24cm^{2} =102cm^{2} [/tex]
We can conclude that the correct answer is A. 102
Write three equations whose graphs are the same line as the equation 3x+2y=7.
Answers
1. rule: the equation will be the same if the both its parts are multiplied by one number ('0' is not included!).
2. using the rule, described upon:
-3x-2y=-7 (*(-1));
6x+4y=14 (*2);
-6x-4y=-14 (*(-2)).
Note, that not all the ways are described.
A graphic designer is planning the layout for a magazine advertisement of three pictures, shown below. The ratio of the sum of the widths of the three pictures to the total width of the advertisement is 4:5. If each picture is 4 inches wide, what is the length of each of the four empty spaces between the pictures (t)?
Answers
Let S be the sum of the width of the pictures and T be the total width of the advertisement. Our proportion would be
[tex]\frac{S}{T}=\frac{4}{5}[/tex]
Since there are 3 pictures and each is 4 inches long, S=3*4=12:
[tex]\frac{12}{T}=\frac{4}{5}[/tex]
Cross multiplying, we have:
12*5=4*T
60=4T
Divide both sides by 4:
60/4 = 4T/4
15=T
The total width of the advertisement is 15 inches. Subtract the known width of the pictures from this, 12, and we have 3 inches left over for the total of the 4 spaces. Thus our answer is 3/4.
Desiree made 100 cookies this week, she baked 4 more than three times the total she made last week. How many cookies did she bake last week?
Answers
3x + 4 = 100 x = 32 cookies
Desiree made 100 cookies this week. She baked 4 more than three times the total she made last week. How many cookies did she bake last week.
3x + 4 = 100 x = 32 cookies
If a stadium has 15,000 seats sold at $10.00, $12.50, and $15.00 equally distributed in three sections, how much can be made if the stadium sells out?
Answers
Answer:
$187,500
Step-by-step explanation:
There must be 15,000/3 = 5,000 seats in each section. Then the total revenue can be ...
5000·$10.00 + 5000·12.50 + 5000·15.00 = 5000·($10 + 12.50 +15.00)
= 5000·$37.50 = $187,500
Stadium revenue can be $187,500 if all seats are sold.
The total earnings from selling out the stadium with tickets priced at $10.00, $12.50, and $15.00, equally distributed, would amount to $637,500.
The total earnings from selling out the stadium would be $15 x 15,000 = $225,000 for tickets priced at $10.00.
For tickets priced at $12.50, the earnings would be $12.50 x 15,000 = $187,500.
Lastly, for tickets priced at $15.00, the earnings would be $15 x 15,000 = $225,000.
To find the total earnings, add the earnings from each section: $225,000 + $187,500 + $225,000 = $637,500.
Samatha has 24 cards. Chelsea saw 15 more cards than Samatha. How many cards does Chelsea have?
Answers
24 + 15 = 39
Chelsea has 39 cards
A large bottle of Dragon Breath mouthwash costs $5.00 before tax and $5.30 after tax. What is the percentage the tax?
Answers
the percentage tax is0. 30/500*100=6%
What is the order of 5x10^4 , 7x10^-5 , 3x10^-9 , 8x10^4 from least to greatest?
Answers
5x10^4=50000
7x10^-5=0.00007
3x10^-9=0.000000003
8x10^4=80000
Therefore, the order of 5x10^4, 7x10^-5, 3x10^-9, 8x10^4 from least to greatest is:
3x10^-9, 7x10^-5, 5x10^4, 8x10^4
The order from least to greatest of the given numbers 5x10^4, 7x10^-5, 3x10^-9, 8x10^4 is 3x10^-9, 7x10^-5, 5x10^4, and finally 8x10^4. This is determined by comparing the exponents and coefficients of the scientific notation.
To find the order of 5x10^4, 7x10^-5, 3x10^-9, and 8x10^4 from least to greatest, we have to compare their exponents as they determine the size of the numbers. The exponent indicates how many times the number 10 is used in a multiplication.
Here are these numbers in order from the smallest to the largest:
3x10^-97x10^-55x10^48x10^4The smaller the exponent (more negative), the smaller the number. The first is the smallest because it has the most negative exponent (-9), and the last is the largest with the exponent of 4. When exponents are the same, we then compare the coefficients (the numbers before the 'x10'), in this case, 5 is less than 8, so 5x10^4 is smaller than 8x10^4.
A zoo has two male lions 1/6 of the line on male lions how many lions are there at the zoo
Answers
6x2=12
12 lions in total
With two dice, each numbered 1-6, there are two possible ways to roll a 3: thus, for the outcome of 3 (a particular macrostate) there are 2 microstates. how many possible ways are there to roll a 4?
Answers
Microstates for a sum of 4: (1,3),(2,2),(3,1) so three possible microstates.
Can someone verify this for me please!
Answers
at the local baseball diamond,the distance from home base to second base is 100 feet. Determine the distance from home base to first base.
Answers
Answer:
70.7 ft
Step-by-step explanation:
The triangle formed by home plate, first base, and second base is an isosceles right triangle with hypotenuse 100 ft. Then the side length (base-line distance between bases) is (100 ft)/√2 ≈ 70.7 ft.
___
For an isosceles right triangle with side lengths 1, the hypotenuse can be found from the Pythagorean theorem to be ...
hypotenuse = √(side² + side²) = √(1²+1²) = √2
Then the diamond distances satisfy the proportion ...
hypotenuse/side = 100 ft/(base distance) = √2/1
or ...
base distance = (100 ft)/√2 ≈ 70.71068 ft
Recently in a large random sample of teens a proportion of 0.76 teens said they send text messages to friends. the margin of error for a 98% confidence interval was 0.030. (a) what is the sample statistic for the proportion of teens who send text messages to friends
Answers
p = 0.76
Margin of error at 98% confidence = E = 0.030
The point estimate for proportion of of teens who send the text message = p = 0.76
The interval estimate for the proportion of teens who send the text message will be in the range:
( p - E, p + E)
p - E = 0.76 - 0.030 = 0.730
p + E = 0.76 + 0.030 = 0.790
Thus with 98% confidence we can say, the population proportion of teens who send the text message is between 0.730 and 0.790.
The sample statistic for the proportion of teens who send text messages to friends is 0.76 or 76%. This result was obtained with a 98% confidence interval and a margin of error of 0.03.
Explanation:The sample statistic in this scenario is the proportion of teens who said they send text messages to friends. In statistics, a sample proportion (also known as a sample percentage) is a way to express the count of observations in a category as a ratio or a fraction of the total sample size.
In your case, the sample statistic is 0.76, meaning that 76% of the teens in your sample said they send text messages to friends. This result was accompanied by a margin of error of 0.030 for your 98% confidence interval.
A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.
The margin of error represents the range in which we are confident that the true population proportion lies given our sample statistic. With a confidence level of 98%, we are sure that if we repeated our sample many times, 98% of those samples would produce a proportion between 76%- 3% and 76% + 3%.
Learn more about Sample Proportion here:https://brainly.com/question/32638029
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The total weight of 15 boxes is 45 pounds .how much would 40 boxes weigh
Answers
You have two summer jobs. At the Burger Palace you earn $8 per hour. At the community center you teach soccer clinics for $10 per hour. You want to earn at least $200 a week. If x is the number of hours you work at Burger Palace and y is the number of hours you work at the community center, which graph shows all the ways you can earn at least $200 a week? A. 2003-09-04-00-00_files/i0160000.jpg B. 2003-09-04-00-00_files/i0160001.jpg C. 2003-09-04-00-00_files/i0160002.jpg D. 2003-09-04-00-00_files/i0160003.jpg Please select the best answer from the choices provided A B C D Mark this and return
Answers
we have that
x-------------> number of hours works at Burger Palace -----> $8
y-------------> number of hours works at community center -----> $10
8x+10y>=200
using a graph tool
see the attached figure
the answer is the option B
an appliance store sells lamps at $ 95.00 for two.a department store sells similar lamps at five for 250.00 which store sells at a better rate? how much is better?