We apply the following property:
(x^n)^m = x^(n • m)
Let m = 2
(P^1/2)^2 = P^(1/2 • 2) = P
Follow below steps;
The property of exponents that you must apply to the expression p1/2 to derive p as the result is the power law for fractional exponents. This law states that when raising a number to a fractional exponent, it is equivalent to taking its root.
Example: p1/2 is the same as taking the square root of p, resulting in p.
When dealing with fractional exponents like 1/2, remember that they represent roots, such as square roots in this case.
Pick a number from the following list 1,2,3,4 write it down if each student in a class of 50 we’re also to pick a number how many would you guess had selected the same number as you did
Answer:
13 students
Step-by-step explanation:
We have a list of four numbers: 1, 2, 3, 4. If 50 persons were to pick a number randomly, it means that the probability of picking any of the numbers is 0.25.
Therefore, from 50 students, 0.25*50 = 12.5 ≈ 13 students aproximately would choose the same number as I did.
Write as an algebraic expression and then simplify if possible The distance traveled by a train in three hours with a constant speed of r miles per hour.
Answer:
Distance = 3r
Step-by-step explanation:
We are to write an algebraic expression and then simplify it for the given situation:
The distance traveled by a train in three hours with a constant speed of r miles per hour.
We know the formula of distance linking the speed and the time.
Distance = speed × time
Substituting the given values to get:
Distance = r × 3
Distance = 3r
Does anyone know this ? Please .
Answer:
5/4 hope this helps
Step-by-step explanation:
ANSWER
The correct answer is D.
EXPLANATION
The given exponentiial expression is
[tex] {5}^{ \frac{7}{3} } [/tex]
Recall that:
[tex] {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } [/tex]
We put a=5, n=3 and m=7
This implies that,
[tex]{5}^{ \frac{7}{3} } = \sqrt[3]{ {5}^{7} } [/tex]
The correct answer is D.
The last option is correct.
Which graph represents 2x-5y< 15
Answer:
Step-by-step explanation:
Rewrite 2x-5y< 15 as follows: Add 5y to both sides. Then 2x < 15 + 5y.
Next, subtract 15 from both sides: 2x - 15 < 5y.
Finally, divide all terms by 5: (2/5)x - 3 < y
Now find the y-intercept of this line. Let x = 0. Then y = -3. Plot (0, -3) on graph paper. Now, starting at (0, -3), move your pencil point 5 spaces to the right and 2 spaces up. Plot this new point, (5, -1). Now draw a dashed line through both (0, -3) and (5, -1). Shade the area ABOVE this dashed line.
Answer:
is op 4 (-3,7)
Step-by-step explanation:
Maria spent 1/5 of her savings on a storybook. She spent 3/8 of the remaining amount on a comic book. What fraction of her savings was spent on a comic book?
Which expression is not equivalent to the other three?
A: 2x + 2+ 2x + 3x – 8
B:4 + 7x – 2
C:–2 + 5x + 2x – 4
D:8x – x – 6
Answer:
b. 4+7x-2
Explanation:
when you add like terms for the first equation it becomes 7x-6
the second one becomes 7x+2
the third one becomes 7x-6
and the last one is also 7x-6
which means the second one is not equivalent
Answer:
B. 4 + 7x – 2
Step-by-step explanation:
PLEASE HELP!!! I'll give you the brainliest! a random sample of 3000 people was chosen for a survey. 47% of them had children under 18 living at home. find the 95% confidence interval - see picture
Answer: 0.4521 - 0.4879
Step-by-step explanation:
1) Find the standard deviation with the given information:
n=3000
p=47% ⇒ 0.47
1-p= 1 - 0.47 = 0.53
[tex]\sigma =\sqrt{\dfrac{p(1-p)}{n}}\\\\\\.\ =\sqrt{\dfrac{0.47(0.53)}{3000}}\\\\\\.\ =\sqrt{\dfrac{0.2491}{3000}}\\\\\\.\ =\sqrt{0.00008303}\\\\\\.\ =0.009112[/tex]
2) Find the margin of error (ME) with the given information:
C=95% ⇒ Z = 1.960
σ=0.009112
ME = Z × σ
= 1.96 (0.009112)
= 0.01786
3) Find the confidence interval with the given information:
p = 0.47
ME = 0.01786
CI = p ± ME
= 0.47 ± 0.01786
= (0.4521, 0.4879)
Raymond can paint 5/8 of a wall in 16minutes. How long would it take him to paint 1/3 of a wall?
Answer:
128/15 min or 8.5 min
Step-by-step explanation:
By using unitary method,
Time required to paint 5/8 of wall = 16 min.
Time required to paint 1/1 of wall = 16×8/5
Hence, Time required to paint 1/3 of wall = 16×8/5×1/3
Answer:
8 8/15
Step-by-step explanation:
simplify the two fractions you have to make them have the same denominater
enthen you can determine the answer.
Solve -37 + n = -56 for n. -93 -19 19 93
Answer:
n = -19Step-by-step explanation:
[tex]-37+n=-56\qquad\text{add 37 to both sides}\\\\-37+37+n=-56+37\\\\n=-19[/tex]
Answer:
n=-93
A. -93 *(first option)*
Step-by-step explanation:
First, you subtract by 37 from both sides of equation.
-37+n-37=-56-37
Then, simplify to find the answer.
-56-37=-93
n=-93 is the correct answer.
I hope this helps you, and have a wonderful day!
If a wheel has 64 spokes, how many spaces are there between the spokes?
Answer:
One
Step-by-step explanation:
It is one because each spoke has one space in the middle. However some people think it's 64 because they read the question wrong.
What is the equation of the line that passes through the points (-1, 7) and (2, 10) in Standard Form?
A) -3x + y = 4
B) -3x + y = 16
C) - x + y = 8
D) -x + y = 12
bearing in mind that standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{10}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{10-7}{2-(-1)}\implies \cfrac{3}{2+1}\implies \cfrac{3}{3}\implies 1[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-7=1[x-(-1)]\implies y-7=x+1 \\\\\\ y=x+8\implies \boxed{-x+y=8}\implies \stackrel{\textit{standard form}}{x-y=-8}[/tex]
just to point something out, is none of the options, however -x + y = 8, is one, though improper.
Wong’s Garage buys quarts of motor oil by the gross (144 units) for $0.75 per quart. When Wong’s changes the oil in customers’ cars, it marks up the oil 175% of the cost. What is the selling price of a quart of oil used in a standard oil change?
Answer:
Each quart is 1.31 to the customer.
Step-by-step explanation:
Cost of 1 quart to Wong = 0.75
Cost to you or I = 0.75 * 175/100 = 1.31
He sells each quart for 1.31 dollars.
What is true about the completely simplified sum of the polynomials 3x2y2 − 2xy5 and −3x2y2 + 3x4y?
The sum is a trinomial with a degree of 5.
The sum is a trinomial with a degree of 6.
The sum is a binomial with a degree of 5.
The sum is a binomial with a degree of 6.
Answer:
The sum is a binomial with a degree of 6
Step-by-step explanation:
we have
[tex](3x^{2}y^{2}-2xy^{5})+(-3x^{2}y^{2}+3x^{4}y)[/tex]
Group terms that contain the same variable
[tex](3x^{2}y^{2}-3x^{2}y^{2})-2xy^{5}+3x^{4}y[/tex]
[tex]0-2xy^{5}+3x^{4}y[/tex]
[tex]-2xy^{5}+3x^{4}y[/tex]
The sum is a binomial ( two terms) with a degree of 6
[tex]-2xy^{5}[/tex] has a degree of 6 (x has an exponent of 1, y has 5, and 1+5=6)
The sum of the polynomial is a binomial with a degree of 6. The correct option is D) and this can be determined by using arithmetic operations.
Given :
Polynomials -- [tex]3x^2y^2-2xy^5[/tex] and [tex]-3x^2y^2+3x^4y[/tex]
The following steps can be used to determine the sum of the given polynomials:
Step 1 - Write the sum of the given polynomials.
[tex]3x^2y^2-2xy^5-3x^2y^2+3x^4y[/tex]
Step 2 - Subtract [tex]3x^2y^2[/tex] from [tex]3x^2y^2[/tex] in the above expression.
[tex]-2xy^5+3x^4y[/tex]
The above expression cannot be further simplified. Therefore, this is the final expression of the sum of the given polynomials.
The sum of the polynomial is a binomial with a degree of 6. Therefore, the correct option is D).
For more information, refer to the link given below:
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Name the types of angles shown
Answer:
A
Step-by-step explanation:
Answer:
staight angle and supplementary angle
Step-by-step explanation:
Circle O has a circumference of 367 cm
What is the length of the radius, /?
6 cm
18 cm
36 cm
72 cm
To find the length of the radius, use the formula for the circumference of a circle. Divide the circumference by 2π to get the radius. In this case, the radius is approximately 59 cm.
Explanation:In order to find the length of the radius, we can use the formula for the circumference of a circle: C = 2πr, where C is the circumference and r is the radius. We are given that the circumference is 367 cm, so we can plug in the values to solve for r.
367 = 2πr
To isolate r, divide both sides of the equation by 2π: r = 367 / (2π)
Using a calculator to approximate π as 3.14, we can calculate the radius: r ≈ 367 / (2 * 3.14) ≈ 58.598
Therefore, the length of the radius, rounded to the nearest centimeter, is approximately 59 cm.
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Without graphing, identify the quadrant in which the point (x, y) lies if x < 0 and y < 0.
Answer:
B.
Step-by-step explanation:
Answer:
II
Step-by-step explanation:
The population of a city was 572,000 in 2010. In the 2000 census the population was 607,000. What was the rate of decrease of the population from one census to the next? Round to the nearest percent.
Answer:
6%
Step-by-step explanation:
To solve this you need to subtract 607000 by 572000 to see how many people in the population decreased.
607,000- 572,000= 35,000
Then you put 35,000 over 607,000
also you need x over 100
35000/607,000 x/100
Then do cross product property
35,000*100=3,500,000
607,000* x= 607,000x
3,500,000= 607,000x
Then do 3,500,000 divided by 607,000
You get 5.76%
Round to the nearest percent and get 6%
Final answer:
The rate of decrease of the population from the 2000 census to the 2010 census is 6% when rounded to the nearest percent.
Explanation:
To calculate the rate of decrease of the city's population, we use the population values from the 2000 and 2010 censuses. The population in 2000 was 607,000, and in 2010 it was 572,000. To find the population decrease, subtract the 2010 population from the 2000 population:
Population decrease = Population in 2000 - Population in 2010
Population decrease = 607,000 - 572,000
Population decrease = 35,000
Next, to find the rate of decrease as a percent, we divide the population decrease by the original population (in 2000) and then multiply by 100:
Rate of decrease (%) = (Population decrease / Population in 2000) × 100
Rate of decrease (%) = (35,000 / 607,000) × 100
Rate of decrease (%) = 0.0577 × 100
Rate of decrease (%) = 5.77%
Round this to the nearest percent, and you get a 6% decrease.
Which points represent an approximate solution to this system of equations? y=1/x-3 y=3-x³
A. (1.5, 1)
B. (1.5, -0.7)
C. (1.6, 1.6)
D. (2.9, -22.8)
Answer:
Options B and D
Step-by-step explanation:
we have
[tex]y=\frac{1}{x-3}[/tex] -----> equation A
[tex]y=3-x^{3}[/tex] -----> equation B
Solve the system of equations by graphing
The solution of the system of equations is the intersection point both graphs
The solutions are the points (1.545,-0.687) and (2.956,-22.835)
see the attached figure
The approximate solutions are
(1.5,-0.7) and (2.9,-22.8)
Answer:
Options B and D
Step-by-step explanation:
Which are the solutions to the inequality (x-3)(x+5)<_0
Answer:
[ - 5, 3 ]
Step-by-step explanation:
Solve (x - 3)(x + 5) = 0
The zeros are x = - 5 and x = 3
These divide the domain into 3 intervals
(- ∞, - 5 ], [- 5, 3 ], [ 3, + ∞ )
Choose a test point in each interval and consider the sign of the result.
x = - 10 : (- 10 - 3)(- 10 + 5) = (- 13)(- 5) = 65 > 0
x = 0 : (0 - 3)(0 + 5) = (- 3)(5) = - 15 < 0 ← required result
x = 5 : (5 - 3)(5 + 5) = (2)(10) = 20 > 0
The solution is [ - 5, 3 ] or - 5 ≤ x ≤ 3
Answer:
B
Step-by-step explanation:
Right on edge 2021
Solve for a.
a = 3
a = -3
a = 9
a = -9
Answer:
a=9
Step-by-step explanation:
1/a + 1/(2a) = 1/(a-3)
Get a common denominator for the left hand side
2/(2a) + 1/(2a) = 1/(a-3)
3/(2a) = 1/ (a-3)
Using cross products
3 * (a-3) = 1 * 2a
Distribute
3a -9 = 2a
Subtract 3a from each side
3a-3a-9 = 2a-3a
-9 = -a
Multiply by -1
-1*-9 = -1 *-a
9 = a
the ratio of chicken to pigs to horses in a farm is 10:2:3.if there is 120 chickens in the farm then the number of the horses in the farm is
Answer:
36
Step-by-step explanation:
The 10 part of the ratio represents 120 chickens. Divide 120 by 10 to find the value of one part of the ratio.
120 ÷ 10 = 12 ← value of 1 part of the ratio, hence
3 parts = 3 × 12 = 36 ← number of horses
The number of horses on the farm is 36.
Given that, the ratio of chicken to pigs to horses on a farm is 10:2:3 and the number of chickens on the farm is 120.
What is the ratio?Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another.
We can write the given ratio 10:2:3 as 10x: 2x: 3x.
So, 10x=120
⇒x=12
Then, the number of horses=3x=36
Therefore, the number of horses on the farm is 36.
To learn more about ratio visit:
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Find the perimeter of a triangle with side lengths of /80
20 and 45
Answer:
145
step by step explanation:
perimeter definition:
perimeter definition:the continuous line forming the boundary of a closed geometrical figure.
add up the length of the sides:
80+20+45=145
math help please its just one question
Use the law of sines:
Sin(angle) = Opposite Leg / Hypotenuse
Sin(30) = 14 / x
x = 14/sin(30)
x = 28
Your baseball team has won 6 games and lost 4 games. If the team
does not lose any more games, how many games must the team win
to have a win : loss ratio of 2:1? Explain your answer.
Answer:
2
Step-by-step explanation:
2:1 win / loss ratio
1 = 4 loses
4 x 2 = 8
the team has 6 wins it would need to win a total of 8 to have a 2:1 ratio
The baseball team must win 2 more games to achieve a win:loss ratio of 2:1, assuming they have no additional losses.
The student's baseball team currently has a record of 6 wins to 4 losses. The question asks how many more games the team must win to achieve a win:loss ratio of 2:1, assuming no more losses occur. To achieve a 2:1 win:loss ratio, the number of wins must be twice the number of losses. Since the losses are fixed at 4, the team needs 2 times 4 (which equals 8) wins to attain this ratio. The team has already won 6 games, so they need 8 - 6, which equals 2 more wins to reach a 2:1 ratio.
write each improper fraction as a mixed number. 9/4. 8/3. 23/6. 11/2. 17/5. 15/8. 33/10. 29/12.
Aloha~! My name is Zalgo and I am here to provide a bit more knowledge to you today. The following Improper Fractions have been changed into Mixed Numbers (and also into decimals because I like Math :3):
9/4 - 2.25 - 2 4/18/3 - 2.67 - 2 2/323/6 - 3.83 - 3 5/611/2 - 5.5 - 5 1/217/5 - 3.4 - 3 2/515/8 - 1.875 - 1 7/833/10 - 3.3 - 3 3/1029/12 - 2.416 - 2 5/12I hope that this info helps! :D
"Stay Brainly and stay proud!" - Zalgo
(By the way, can you mark me as Brainliest? I'd greatly appreciate it! Mahalo~! XP)
Answer:
In order; 2 1/4, 2 2/3, 3 5/6, 5 1/2, 3 2/5, 1 7/8, 3 3/10, 2 5/12
Step-by-step explanation:
The way mixed numbers work is how many times (improper fraction) the denominator can go into the numerator.
For example, in the improper fraction 9/4, 4 can go into 9 twice making the whole number a 2, then you get whatever is left and leave it as the fraction; there is 1/4 left making making the mixed number 2 1/4. Use this rule to apply to all the improper fractions.
Given a rectangular pyramid and a rectangular prism that have the same base and same height, how do their volumes compare? If the pyramid was full of water, how much of the prism would it fill up? Name another pair of three-dimensional objects that have a relationship similar to this.
Answer:
Part 1) The volume of the prism is 3 times greater than the volume of the pyramid
Part 2) The prism would fill only one-third
Part 3) The cylinder and the cone
Step-by-step explanation:
Part 1) How do their volumes compare?
we know that
The volume of a rectangular prism is equal to
[tex]Vprism=BH[/tex]
where
B is the area of the base of rectangular prism
H is the height of the prism
The volume of a rectangular pyramid is equal to
[tex]Vpyramid=\frac{1}{3}BH[/tex]
where
B is the area of the base of rectangular pyramid
H is the height of the pyramid
Compare the volumes
[tex]Vprism=BH[/tex] -----> equation A
[tex]Vpyramid=\frac{1}{3}BH[/tex] -----> equation B
substitute equation A in equation B
[tex]Vpyramid=\frac{1}{3}Vprism[/tex]
[tex]Vprism=(3)Vpyramid[/tex]
The volume of the prism is 3 times greater than the volume of the pyramid
Part 2) If the pyramid was full of water, how much of the prism would it fill up?
Remember that
[tex]Vpyramid=\frac{1}{3}Vprism[/tex]
therefore
The prism would fill only one-third
Part 3) Name another pair of three-dimensional objects that have a relationship similar to this
we have the cylinder and the cone
The volume of the cylinder is equal to
[tex]Vcylinder=\pi r^{2}h[/tex]
The volume of the cone is equal to
[tex]Vcone=\frac{1}{3}\pi r^{2}h[/tex]
Compare the volumes
[tex]Vcylinder=(3)Vcone[/tex]
The volume of the cylinder is 3 times greater than the volume of the cone
The volume of the pyramid is one-third of the volume of the rectangular prism with the same base and height. Therefore, if the pyramid was full of water, it would fill one-third of the prism. Cones and cylinders with the same base and height have a similar volume relationship.
Explanation:When comparing the volumes of a rectangular pyramid and a rectangular prism that have the same base and the same height, the volume of the pyramid is exactly one-third the volume of the prism. This is because the volume of the prism is calculated by length × width × height, while the volume of the pyramid is ⅓ x (base area) x height, which is ⅓ x (length × width) x height.
If the pyramid was full of water, it would fill up exactly one-third of the prism. This corresponds to the geometric rule that says the volume of a pyramid is one-third the volume of a prism with the same base and height.
Another pair of three-dimensional objects with a similar relationship is a cone and a cylinder. Like the pyramid and prism, if the cone and cylinder have the same base and height, the cone's volume is one-third of the cylinder's volume.
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Given that lines b and c are parallel, select all that apply.
Answer:
C) angle 2 and angle 8
Step-by-step explanation:
HELP!! what is the value of x in this figure?
5
[tex]5 \sqrt{2} [/tex]
[tex]5 \sqrt{3} [/tex]
[tex] \frac{10 \sqrt{3} }{3} [/tex]
Check the picture below.
Also check your Unit Circle for the cosine of 30°, if you don't have a Unit Circle yet, this is a good time to get one, you'll need it, you can find many online.
What is the equation of the line in point-slope form?
Answer:
A
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 4, - 4) and (x₂, y₂ ) = (4, 0) ← 2 points on the line
m = [tex]\frac{0+4}{4+4}[/tex] = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]
Using (a, b) = (- 4, - 4), then
y - (- 4) = [tex]\frac{1}{2}[/tex] (x - (- 4)), that is
y + 4 = [tex]\frac{1}{2}[/tex] (x + 4) → A
how many 3/4 pound bags of peanuts can be from 5 pound bag
Final answer:
To determine how many 3/4 pound bags of peanuts can be made from a 5 pound bag, divide the weight of the 5 pound bag by the weight of each 3/4 pound bag.Therefore, 20/3 or 6 and 2/3 3/4 pound bags of peanuts can be made from a 5 pound bag.
Explanation:
To determine how many 3/4 pound bags of peanuts can be made from a 5 pound bag, we need to divide the weight of the 5 pound bag by the weight of each 3/4 pound bag. We can use the division operation to solve this.
5 pounds ÷ 3/4 pounds = 5 ÷ 3/4
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 3/4 is 4/3.
5 ÷ 3/4 = 5 × 4/3 = 20/3
Therefore, 20/3 or 6 and 2/3 3/4 pound bags of peanuts can be made from a 5 pound bag.