Answer:
4(2)^(2/3) or 4∛(4)
Step-by-step explanation:
Rules of Exponents..
16^(2/3)
= (2^4)^(2/3)
= 2^(8/3)
= 2^(2 + 2/3)
= 2^2 · 2^(2/3)
= 4(2)^(2/3) or 4∛(4)
I need help with this someone please explain it to me
The length of the Antenna will be;
⇒ h = 18 meters
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
Tyler is 1.8 meters and his shadow is 6 meters.
And, Tyler is standing 54 meters from the antenna.
Now,
Since, Tyler is 1.8 meters and his shadow is 6 meters.
And, Tyler is standing 54 meters from the antenna.
Let the length of the Antenna = x
Hence, We get by definition of proportional, we get;
⇒ 1.8 / 6 = h / (54 + 6)
⇒ 0.3 = h / 60
⇒ h = 0.3 × 60
⇒ h = 18 meters
Thus, The length of the Antenna will be;
⇒ h = 18 meters
Learn more about the proportional visit:
https://brainly.com/question/24925348
#SPJ1
simplify (1+√3)(1-√3)
Answer:
- 2
Step-by-step explanation:
the factors of a difference of square are
a² - b² = (a + b)(a - b)
(1 + [tex]\sqrt{3}[/tex] )(1 - [tex]\sqrt{3}[/tex] ) ← are the factors of a difference of squares , then
(1 + [tex]\sqrt{3}[/tex] )(1 - [tex]\sqrt{3}[/tex] )
= 1² - ([tex]\sqrt{3}[/tex] )²
= 1 - 3
= - 2
Average movie prices in the United States are, in general, lower than in other countries. It would cost $78.93 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $75.82 How much does an average movie ticket cost in each of these countries?
In Japan, the average cost is $17.61 and in Switzerland, the average cost is $13.55.
What is the equation?An equation is a relationship between two or more variables expressed in equal to form. The equation of two variables look like ax + by=c. It is solved to find the value of variables.
According to the question, the equation are as under:
3x+2y=79.93----------------1
2x+3y=75.87 ----------------2
Multiply equation 1 by 2 and equation 2 by 3 and subtract the result from equation 2 from the result coming from equation 1.
6x+4y=159.86
6x+9y=227.61
Subtracting
6x+4y-6x-9y=159.86-227.61
-5y=-67.75
y=13.55
Put the value of y=13.55 in 3x+2y=79.93
3x+2(13.55)=79.93
3x+27.10=79.93
3x=79.93-27.10
3x=52.83
x=52.83/3
x=17.61
Hence the average cost in Japan is $17.61 and the average cost in Switzerland is $13.55.
Learn more about equations at,
brainly.com/question/2972832
#SPJ1
The value b is:
12.5
9.5
6.5
None of the choices are correct
D) none of these choices are correct
please help !
Find The Value Of X.
Answer:
x = 65 degrees
Step-by-step explanation:
Let's say z=the angle adjacent (next to) to the 145 degrees angle.
80 + x + z = 180 ==> 180 is the total number of degrees in a triangle
z + 145 = 180 ==> In addition, if you add up Angle z and 145
degrees, you get a straight line which totals to 180
degrees
z + 145 - 145 = 180 - 145 ==> solve for z
z = 35 degrees
80 + x + z = 180
80 + x + 35 = 180 ==> plug in 35 for z
80 + 35 + x = 180
115 + x = 180 ==> solve for x
115 - 115 + x = 180 - 115 ==> simplify
x = 65 degrees
What is the circumference of a circle with a radius of 11?
The circumference of a circle with a radius of 11 is 68.1
The route or boundary that encircles any shape in mathematics is defined by the shape's circumference. In other terms, the circumference is also known as the perimeter, which aids in determining how long a shape's outline is.
The formula to calculate the circumference of a circle is C=2[tex]\pi[/tex]r where r is the radius of the circle.
The problem tells us that r= 11, substituting that in the equation and solving:
C=2[tex]\pi[/tex]r =2[tex]\pi[/tex](11) = 22[tex]\pi[/tex]
The value of [tex]\pi[/tex] is approximately 3.14, putting the value of [tex]\pi[/tex] in the equation:
C= 22(3.14) = 68.08→ 68.1
To learn more about the circumference of a circle visit:brainly.com/question/29142813
#SPJ4
Madelyn has a large bush growing in her garden. When she planted it, the bush was 2 feet tall. Now it is 3 feet tall. What is the percent increase?
The percent increase of the trees is 50%
How to determine the percent increase?From the question, we have the following parameters that can be used in our computation:
Initial = 2 feet
Final = 3 feet
The percent increase can then be calculated using
Percentage increase = (Final length - Initial length)/Initial length * 100%
Substitute the known values in the above equation, so, we have the following representation
Percentage increase = (3 - 2)/2 * 100%
Evaluate
Percentage increase = 50%
Hence, the percentage increase is 50%
Read mroe about percentage increase at
https://brainly.com/question/11360390
#SPJ1
b) The perimeter of the shape is 25.71 cm
Calculate the value of the radius x.
Take – to be 3.142
Answer:
Questions and answers
Brainly.com
Question
The perimeter of a shape is 25.71 cm calculate the value of the radius X takes pie to be 3.142
Answer · 15 votes
Answer:5 cmStep-by-step explanation:Given a semicircle with perimeter 25.71 cm, we are required to find the radius of the circle.Circumference of a Semicircle=Length of the Circular part+Length of the diameter[tex]=\pi r+2r[/tex][tex]If \: \pi=3.142, C=25.71\Then:\25.71=3.142r+2r (3.142+2)=25.71\5.142r=25.71 =25.71 \div5.142 =5cm[/tex]
More
Brainly.com
Question
The perimeter of the semicircle is 25.71 cm. Calculate the value
PLEASE HELP EASY EASY EASY
Answer:
12
Step-by-step explanation:
2 is 40 percent of 5
12 is 40 percent of 30
Answer:
15 people would be running out of 30
Step-by-step explanation:
30/2
A box of 15 cookies costs $9 dollar sign, 9.
What is the cost for 1 cookie?
Answer: 0.6
Step-by-step explanation:
9/15 = 0.6
$9 / 15 cookies = $0.6 cents per cookie
Sales tax in NY is 8.875. How much tax would you pay on the sofa that costs $899?
Answer: $79.79
Step-by-step explanation:
First, take 899 divided by 100% = 8.99
Then take 8.99 times 8.875 = $79.79
Answer:
Below
Step-by-step explanation:
8.875 % is .08875 in decimal form:
899 * .08875 = 79.79 dollars
PLEASE HELP ME WITH THESE 2 QUESTIONS
A rectangle has sides of (4x + 13) and (5x – 2). What is the area of the rectangle?
Answer:
Below
Step-by-step explanation:
The area is just the two side lengths multiplied together
area = (4x+13)(5x-2) = 20x^2 +57x -26 units^2
Solve for X and y PLEASE GIVE FULL EXPLANATION HOW YOU GOT IT
Answer:
(1, -1)
Step-by-step explanation:
we isolate y in the first equation
2x+y=1
-2x. -2x
y=1-2x
and now we fill y into second equation
4x-2(1-2x)=6
4x-2+4x=6
8x-2=6
+2 +2
8x=8
/8 /8
x=1
and now to find y we insert x
2(1)+y=1
2+y=1
-2. -2
y= -1
hopes this helps
Which of the following statement is true ? a) X^2 + 5x -3 is a linear polynomial b) X^2+4x-1 is a binomial c) (x+1) is a monomial d) 5x^3 is a monomial
Answer:
d. [tex]5x^3[/tex] is a monomial
Step-by-step explanation:
⭐What is a monomial?
as "mono" means 1, monomial means an expression or equation that consists of 1 term onlyD is correct because the expression [tex]5x^3[/tex] consists of 1 term only.
⭐What is a linear polynomial?
a linear polynomial is an expression or equation that has a degree of 1⭐What is the degree of a polynomial?
the degree of a polynomial is the largest exponent found in the polynomialA is incorrect because the largest exponent in the expression [tex]x^2 + 5x -3[/tex] is 2, which makes expression A a quadratic polynomial.
⭐What is a binomial?
as "bi" means 2, a binomial is an expression or equation that consists of 2 terms onlyB is incorrect because the expression [tex]x^2 + 4x - 1[/tex] consists of 3 terms, not 2 terms. B is a trinomial.
C is incorrect because the expression [tex]x+1[/tex] consists of 2 terms, not 1 term. C is a binomial.
⭐if this response helped you, please mark it the "brainliest"!⭐
diseases tend to spread according to the exponential growth model. in the early days of aids, the growth factor (i.e. common ratio; growth multiplier) was around 1.9. in 1983, about 1700 people in the u.s. died of aids. if the trend had continued unchecked, how many people would have died from aids in 2005?
The number of people died from aids in U.S. in 2005 are 2,30,68,96,671
Given, diseases tend to spread according to the exponential growth model.
In the early days of aids, the growth factor (i.e. common ratio; growth multiplier) was around 1.9.
In 1983, about 1700 people in the U.S. died of aids.
we have to find the number of people died from aids in 2005.
Let the exponential function, be
P(x) = AB^x
where, A is the initial population of people died of aids in U.S.
B is the growth factor of aids in U.S.
as, B = 1.9
In 1983, x = 0
P(0) = AB^0
1700 = A
Now, P(x) = 1700(1.9)^x
and the number of years from 1983 to 2005 are, 22 years
The number of people died from aids in 2005 be,
P(22) = 1700(1.9)^22
P(22) = 2,30,68,96,671
So, 2,30,68,96,671 people died from aids in 2005.
Hence, 2,30,68,96,671 people died from aids in 2005.
Learn more about Exponential Functions here https://brainly.com/question/12472697
#SPJ4
jerry graded seven standardized tests with the following scores: 60, 74, 41, 87, 94, 79, 57 which standardized test score represents the 50th percentile? 41 57 74 79
Answer: 74
Step-by-step explanation:
Answer:
74
Step-by-step explanation:
Got it right on the test.
Evaluate the expression 5x^3 for x=2
PLS HELP!!!
Answer: 40
Step-by-step explanation:
Answer: 20
Step-by-step explanation:
5x^2
5 ( 2 )^2 (substituting the value of x)
5 ( 2 x 2) (working out the exponents of x)
5 (4) (solving the brackets)
20
christina, a restaurant manager, would like to make the claim that the average number of customers that her restaurant serves per hour is more than 57. christina samples 29 hours over the course of a week and records the number of customers served and obtains a sample mean of 62 customers per hour.at the 2.5% significance level, should christina reject or fail to reject the null hypothesis given the sample data below?
Reject the null hypothesis because [tex]$p$[/tex]-value [tex]$=0.0045$[/tex] is less than the Significance level x=0.025.
What is Null Hypothesis ?The null hypothesis is a widely used statistical theory that states that for any given single observable variable, there is no statistical relationship or significance between any two sets of observed data and measured events.
According to the given information
[tex]& H_0: \mu=57 \\[/tex]
[tex]& H_a ; \mu > 57 \\[/tex]
[tex]& \alpha=0.025 \\[/tex]
[tex]& \text { Test Statistic }=2.61[/tex]
So,
This is right tailed test
[tex]& \text { Using } z \text { table } \\[/tex]
[tex]& p(z > 2.61) \\[/tex]
[tex]&= 1-p(z < 2.61) \\[/tex]
[tex]&= 1-0.9955 \\[/tex]
[tex]& p \text {-value }= 0.0045[/tex]
Reject the null hypothesis because [tex]$p$[/tex]-value [tex]$=0.0045$[/tex] is less than the Significance level x=0.025.
To know more about Null hypothesis
https://brainly.com/question/28920252
#SPJ4
suppose a certain combination lock requires three selections of numbers, each from 1 through 25. (a) how many different combinations are possible? (b) suppose the locks are constructed in such a way that no number may be used twice. how many different combinations are possible?
The number of combination possible = 15625
When the numbers are repeating
The number of possible combinations = 13800
Given that a certain combination lock requires three selections of numbers
Total possible numbers = 25
Part a
Total number of combinations possible = 25 × 25 × 25
Multiply the numbers
= 15625 possible combinations
Part b
The given condition is no number may be used twice
Total number of combinations possible = 25 × 24 × 23
Multiply the numbers
= 13800 possible combinations
Therefore, when the number are repeating, the possible combinations are 15625 and when the numbers are not repeating the possible combinations are 13800
Learn more about combinations here
brainly.com/question/2295036
#SPJ4
How do you solve 2^(x) − 2^(−x) = 5 ?
The solution for the expression 2^(x) − 2^(−x) = 5 is x = log2(10)
Substitute 2^(−x) for 5 and solve for x, which is log2(10).
The given expression ,
2^(x) − 2^(−x) = 5
2^(x) = 5 + 2^(−x)
2^(2x) = (5 + 2^(−x))^2
2^(2x) = 25 + 10*2^(−x) + 2^(−2x)
25 + 10*2^(−x) + 2^(−2x) = 2^(2x)
25 − 2^(2x) = 10*2^(−x) − 2^(−2x)
25 − 2^(2x) = 10*2^(−x) − 2^(−2x) + 2^(2x)
25 = 10*2^(−x) + 2^(2x) − 2^(−2x)
25 = 10*2^(−x) + 2^(−2x) (2^(2x) - 2^(−2x))
25/(2^(−2x) (2^(2x) − 2^(−2x))) = 10*2^(−x)
25/(2^(2x) − 2^(−2x)) = 10*2^(−x)
2^(x) = 10
x = log2(10)
Substitute 2^(−x) for 5 and solve for x, which is log2(10).
Learn more about expression here
https://brainly.com/question/14083225
#SPJ4
we have discussed four tree-based methods: decision trees, bagging, random forests, and boosting. which approach relies on bootstrapped samples, i.e., taking repeated random samples with replacement from the training data? check all that apply.
The correct answer is boosting.
Given that,
The four tree-based techniques are boosting, bagging, random forests, and decision trees. Which method uses bootstrapped samples, or the process of repeatedly obtaining random samples from training data and replacing them?
Boosting is an emsemble machine learning approach, where we use bootstrapping sampling technique to get the required samples. It helps in the reduction of variance and thus bring in less bias in the sampling approach. Therefore boosting is the correct answer here.
In order to gather the necessary samples for boosting, we employ the bootstrapping sampling technique. It aids in lowering variance, which reduces bias in the sampling strategy. Thus, boosting is the appropriate response in this case.
To learn more about sampling click here:
brainly.com/question/13287171
#SPJ4
How many 1/3 cups do you need to make 1/2 cup?
With fraction calculation we know that 1 1/2 cups of 1/3 cup is needed in order to make a 1/2 cup.
In order to figure out the amount of 1/3 cup needed to fill a 1/2 cup, we will calculate the fraction with the following fraction division:
1/2 ÷ 1/3
To calculate a fraction division we will need to multiply the first fraction with the inverse of the second fraction and we will get the following calculation:
1/2 × 3/1 = 3/2 = 1 1/2
Therefore to fill a 1/2 cup we will then need 3/2 cups or 1 1/2 cups of a 1/3 cup.
To learn more about fraction division visit: https://brainly.com/question/1622425
#SPJ4
A person places $8620 in an investment account earning an annual rate of 6.1%, compounded continuously. Using the formula V = Pe^{rt}V=Pe
rt
, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 14 years.
thanks!!
The amount of money in the account after 14 years is $20248.59
How to determine the amount of money in the account after 14 years?From the question, we have the following parameters that can be used in our computation:
Principal Amount = $8620Rate of investment = 6.1%Number of years = 14 yearsAlso from the question, we have
V = Pe^{rt}
Where
V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithmr is the rate of interestSubstitute the known values in the above equation, so, we have the following representation
V = 8620 * e^(6.1% * 14)
Evaluate the products
So, we have the following representation
V = 8620 * e^(0.854)
Evaluate the exponent
So, we have the following representation
V = 8620 * 2.34902418149
Lastly, evaluate the products
So, we have the following representation
V = 20248.5884444
Approximate
V = 20248.59
This means that the value after 14 years is $20248.59
Read more about exponential functions at
https://brainly.com/question/29721834
#SPJ1
What is the smallest degree of rotation that will map a regular 16-agon (a 16 sided figure) onto itself?
The smallest degree of rotation that will map a regular 16-agon onto itself is 22.5 degrees.
What is a degree?
A degree is a unit of measurement used to express angles. It is defined as 1/360th of a full rotation, or 1/2π radians.
To see this, note that a regular 16-agon has 16 sides, and each angle between sides measures 180(16-2)/16 = 135 degrees. Therefore, to rotate the 16-agon so that it maps onto itself, we must rotate it an integer multiple of 135 degrees.
However, we want the smallest such angle, so we must find the smallest integer multiple of 135 degrees that is greater than or equal to 360 degrees (since a full rotation maps the figure onto itself). The smallest such multiple is 2, which is equal to 270 degrees.
The smallest degree of rotation that will map the 16-agon onto itself is 270 degrees / 2 = 135 degrees / 2 = 22.5 degrees.
Hence, The smallest degree of rotation that will map a regular 16-agon onto itself is 22.5 degrees.
To learn more about the degree in angles, visit:
https://brainly.com/question/5606439
#SPJ4
jerry is driving 35 mph as he approaches a park. A dog darts out into the street between two parked cars, and jerry reacts in about three-quarters of a second. what is his approximate reaction distance?
The distance of the reaction as Jerry drives at a rate of 35 mph is 11.73 m.
What is distance?Distance is the total movement of an object without any regard to direction.
To calculate the approximate reaction distance, we use the formula below.
Formula:
d = Vt............... Equation 1Where:
d = Reaction distanceV = Speed at which jerry was drivingt = TimeFrom the question,
Given:
V = 35 mph = 15.6464 m/st = 3/4 seconds 0.75 secondsSubstitiute these values into equation 1
d = (15.6464×0.75)d = 11.73 mHence, the distance of the reaction is 11.73 m.
Learn more about distance here: https://brainly.com/question/26046491
#SPJ1
the ratio of 6th and 7th graders are 11 to 9. if there was 108 7th graders how many 6th graders will there be
The number of the students in the sixth grade will be 132 students.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
The proportion of sixth and seventh graders is 11 to 9. In the event that there were 108 seventh graders.
The ratio of the number of students in the sixth and seventh will remain constant.
Let 'x' be the number of students in sixth grade. Then the equation is given as,
x / 108 = 11 / 9
Simplify the equation, then we have
x / 108 = 11 / 9
x = 108 × 11 / 9
x = 12 × 11
x = 132
The number of the students in the sixth grade will be 132 students.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ1
identify the surface whose equation is given. rho = sin(θ) sin(φ)
Step-by-step explanation:
Given;The equation of the surface is, ρ = sin(θ) sin(φ)The spherical and Cartesian coordinates are related by the equations,
x = ρ sin(φ) cos(θ)
y = ρ sin(φ) sin(θ)
z = ρ cos(φ)
Here, x, y and z represent the coordinates of the center of the sphere on x, y and z axes respectively.
Now, multiply the given surface equation by ρ.
ρ² = ρsin(θ) sin(φ)
We have, ρ² = x² + y² + z².
Substitute this value in above equation and also replace the RHS by y coordinate.
x² + y² + z² = y
Now, simplify the above equation.
x² + y² - y + z² = 0
x² + y² - 2y½ + (1/2)² + z² = (1/2)²
x² + (y - 1/2)² + z² = (1/2)² ...(1)
The general form of equation of sphere is,
(x - a)² + (y - b)² + (z - c)² = r²
Here, a, b, c are the coordinates of the center of the sphere on x, y, z axes respectively and r is the radius of the sphere.
Compare equation (1) with the general form of equation of sphere. Therefore we get,
a = 0b = 1/2c = 0r = 1/2Therefore, the radius of the sphere is 1/2 and center of sphere is at (0, 1/2, 0).
Thus, The given equation represents - a sphere of radius 1/2 centers at (0, 1/2, 0).
Which of the following is a root of the equation 2x^2 −5x−3=0?
Answer:
x = 3 or x = -1/2
Step-by-step explanation:
Solve for x:
2 x^2 - 5 x - 3 = 0
The left hand side factors into a product with two terms:
(x - 3) (2 x + 1) = 0
Split into two equations:
x - 3 = 0 or 2 x + 1 = 0
Add 3 to both sides:
x = 3 or 2 x + 1 = 0
Subtract 1 from both sides:
x = 3 or 2 x = -1
Divide both sides by 2:
Answer: x = 3 or x = -1/2
Which of the following is a solution to the equation
x² + 5x + 4 = 2x² - 10?
A) -7
B) -2
C) 0
D) 2
Answer:
x=−2
Step-by-step explanation:
x2+5x+4−(2x2−10)=2x2−10−(2x2−10)
−x2+5x+14=0
(−x−2)(x−7)=0
−x−2=0
Hence B is the correct option