Answer:
Option B
Increases
Step-by-step explanation:
to solve this problem, let us plug in figures to replace the variables in the equation.
Let y be equals to the rational exponent which represents the cube root of x^m,
The equation is given as y =[tex]\sqrt[3]{x^{m}}[/tex]
let x= 3
and m =, 3, 4, and 5
when m = 3, we have [tex]y =\sqrt[3]{3^{3}} =3[/tex]
when m = 4, we have [tex]y =\sqrt[3]{3^{4}} =4.33[/tex]
when m = 5, we have [tex]y =\sqrt[3]{3^{5}} =6.24[/tex]
As we can see, the values of y are increasing. Hence, we can say that the value of the rational exponent increases as y increases
Final answer:
As the positive integer m increases in the rational exponent expression for the cube root of [tex]x^m[/tex], the rational exponent itself increases. This is because the base x is being raised to a higher power, exemplified by [tex]x^{2/3[/tex] compared to [tex]x^{3/3[/tex], showing an increase in expression value.
Explanation:
If a rational exponent represents the cube root of [tex]x^m[/tex], where m is a positive integer, the form used to represent this is [tex]x^{m/3[/tex]. As m increases, the value of the expression increases because the base (x) is being raised to a higher power. Therefore, the correct answer to how the rational exponent changes as m increases is it increases.
For example, consider x to equal 8, and compare [tex]x^{2/3[/tex] (the cube root of 8 squared) to [tex]x^{3/3[/tex] (the cube root of 8 cubed).
As m increases from 2 to 3, the exponent changes from 2/3 to 3/3 (or 1), and thus the result of the expression goes from 4 to 8, illustrating that the expression's value increases with m.
If (x-2/3)=6 find the value of (x^3-8/xcube)
Answer:
(x-2)(x^2+2x+4)/x^3
Step-by-step explanation:
if you were doing for x let me know
Find the inner product of (4,9,-3), (-6, 7,5)and state whether the vectors are perpendicular.
Answer:
24, not Perpendicular
Step-by-step explanation:
4×-6 + 9×7 + -3×5
-24 + 63 - 15
24
Perpendicular when inner product is 0
Find the simple interest on $8,000 at 4% interest for 2.5 years?
Answer:
800
Step-by-step explanation:
60
boys at a summer camp were asked to complete a survey about their favorite outdoor activity.
18
boys chose biking and
29
29
boys chose fishing.
The remaining boys did not complete the survey.
What expression gives the percent of survey participants who chose fishing?
Expression for percent of survey participants who chose fishing =
Explanation:
Total number of boys = 60
Number of boys who took part in survey = 18 + 29 =47
Number of boys who chose fishing = 29.
Percentage of an outcome = (Number of favorable outcome/ Total number of outcome) x 100
Percentage of boys who chose fishing = (29/47)x100
Expression for percent of survey participants who chose fishing =
Hope I helped! :)
Answer:
Expression for percent of survey participants who chose fishing =
Explanation:
Total number of boys = 60
Number of boys who took part in survey = 18 + 29 =47
Number of boys who chose fishing = 29.
Percentage of an outcome = (Number of favorable outcome/ Total number of outcome) x 100
Percentage of boys who chose fishing = (29/47)x100
Expression for percent of survey participants who chose fishing =
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Step-by-step explanation:
Which list is in order from least to greatest?
9.4 x 10 -8, 9.25 x 10 -6, 2.5 x 10 3, 7 x 10 3
2.5 x 10 3, 7 x 10 3, 9.25 x 10 -6, 9.4 x 10 -8
9.25 x 10 -6, 9.4 x 10 -8, 7 x 10 3, 2.5 x 10 3
9.4 x 10 -8, 9.25 x 10 -6, 7 x 10 3, 2.5 x 10 3
Answer:
Step-by-step explanation:
last list
Answer:
it's the one at the bottom
You acquired a 34.5 foot rope and are excited to string it between the ground and up a tree to create a delivery system. You need the rope to make a 25° angle with the ground. How high up the tree do you need to place the rope? Include a sketch that shows all known information and clearly shows what you need to find . Show all work and give the answer rounded to the nearest tenth of a foot.
The height of the tree is 14.5 ft.
Step-by-step explanation:
Let the height of the tree be 't'
The angle between the ground and the rope = 25°
Length of the rope = 34.5 ft.
To find :
The height of the tree.
We can use the sine to calculate the height of the tree.
sin 25° = t/34.5
sin 25° = 0.42
sin 25° = t/34.5
0.42 = t/34.5
t = 0.42 x 34.5
t = 14.5 ft.
The height of the tree is 14.5 ft.
A mug can hold 17.09 ounces of coffee without overflowing. The radius of the mug is 4 cm. Given that 1 cm³ equals 0.034 ounce, what is the height of the mug to the nearest centimeter
Answer:
10 centimeters
Step-by-step explanation:
Kindly refer to the attached image for explanations
Roberta jogs 3 laps the first day, 5 laps the second day, 7 laps the third, and so on. On which day will Roberta jog 13 laps if the pattern continues.
It seems that she runs two more laps each day, so:
day 1- 3
day 2- 5
day 3- 7
day 4- 9
day 5- 11
day 6- 13
simple patterns baby
Final answer:
Roberta will jog 13 laps on the sixth day of her jogging routine, following the arithmetic sequence of adding 2 laps each day, starting with 3 laps on the first day.
Explanation:
The student is asking about a pattern in which Roberta jogs an increasing number of laps each day, with the sequence starting at 3 laps and increasing by 2 laps each subsequent day. To determine on which day Roberta will jog 13 laps, we can identify this as an arithmetic sequence with a common difference of 2. The first day is 3 laps, the second day is 5 laps, and this pattern continues. Following this sequence, the number of laps jogged by Roberta each day is:
Day 1: 3 lapsDay 2: 5 lapsDay 3: 7 lapsDay 4: 9 lapsDay 5: 11 lapsDay 6: 13 lapsThus, Roberta will jog 13 laps on the sixth day, if the pattern continues.
Which equation could be used to find the length of the hypotenuse?
Answer:
aaaaaaaaaaaaaaaaa
Step-by-step explanation:
i dont if i made it clear but the answer is A
Which shows the following expression after the negative exponents have been eliminated?
A)StartFraction m Superscript 7 Baseline n cubed Over m n Superscript negative 1 Baseline EndFraction, m not-equals 0, n not-equals 0
B)StartFraction m Superscript 7 Baseline n cubed n Over m EndFraction
m Superscript 7 Baseline n cubed m n
C)StartFraction m Superscript 7 Baseline n cubed Over m (negative n) EndFraction
D)StartFraction m n Over m Superscript 7 baseline n EndFraction
Answer:
its A
Step-by-step explanation:
Hence, the correct answer is (C)[tex]\frac{m^7.n^7}{mn^{-1}}[/tex]
What is an expression?a mathematical phrase that can contain ordinary numbers, variables, and operators.
How to solve?Given the expression [tex]\frac{m^7.n^7}{mn^{-1}}[/tex]
on simplification, if can be found,
=[tex]m^{7-1}.n^{3-(-1)}\\m^6.n^4[/tex]
which is the required answer.
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Find the value of each numbered angle.
Answer:
See below.
Step-by-step explanation:
m < 1 = 180 - 125 = 55 degrees (adjacent angles),
m < 2 = 180 - 56 = 124 degrees (adjacent angles).
m < 3 = 124 - 55 = 69 degrees ( external angle of a triangle theorem).
An element with a mass of 120 grams decays by 27.5% per minute. To the nearest tenth of a minute, how long will it be until there are 2 grams of the element remaining?
Answer:
12.7
Step-by-step explanation:
its right
It will take approximately 9.9 minutes until there are 2 grams of the element remaining.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
We can use the exponential decay formula to solve the problem.
The formula for exponential decay is:
[tex]A = A_0e^{-kt}[/tex]
where:
A₀ = initial amount
A = amount remaining after time t
k = decay rate constant
t = time
We can find the decay rate constant k using the given percentage decay per minute.
If the element decays by 27.5% per minute, then the decay rate constant is:
k = ln(1 - 0.275) = -0.3185
where ln is the natural logarithm.
Let's substitute the given values into the formula and solve for t:
[tex]2 = 120 e^{-0.3185t}[/tex]
Divide both sides by 120:
[tex]0.0167 = e^{-0.3185t}[/tex]
Take the natural logarithm of both sides:
ln(0.0167) = -0.3185t
t = ln(0.0167) / (-0.3185)
t ≈ 9.9 minutes (to the nearest tenth of a minute)
Therefore,
It will take approximately 9.9 minutes until there are 2 grams of the element remaining.
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Can you explain it and help me out please
Answer:
c.
Step-by-step explanation:
2x² - 4x - 3 = 0
[tex]x= \frac{-b+/-\sqrt{b^{2}-4ac} }{2a} \\\\x= \frac{-(-4)+/-\sqrt{(-4)^{2}-4*2*(-3)} }{2*2} \\\\x= \frac{4+/-\sqrt{16+24} }{4} \\\\x= \frac{4+/-\sqrt{40} }{4} = \frac{4+/-2\sqrt{10} }{4}=\frac{2+/-\sqrt{10} }{2}[/tex]
The probability of rolling an even number with a six-sided number cube
is about 1/2 . Choose the likelihood that best describes the probability
of this event.
Answer:
Equally likely
Step-by-step explanation:
Equally likely means that it’s a 50% percent chance on both sides meaning that equally likely Is the answer.
Answer:
likely
Step-by-step explanation:
Solve the inequality.
5x - 7 < 8x + 8
The solution set is x |
Answer:
- 5 < x
Step-by-step explanation:
To solve, we need to isolate the variable: x
5x - 7 < 8x + 8
Subtract 5x from both sides
5x - 5x -7 < 8x -5x + 8
- 7 < 3x + 8
Subtract 8 from both sides
- 7 -8 < 3x + 8 -8
-15< 3x
Divide both sides by 3
- 15/3< 3x/3
- 5 < x
Answer:
-5 < x is correct, I double check her answer
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted:
Write an equation to determine the area, A, of the patio that will be painted.
A = (x + 18)(x + 35)
A = (x + 15)(x + 25) + 30
A = (x + 5)(x + 22)
A = (x + 25)(x + 15) − 30
Answer:
A = (x + 25)(x + 15) - 30
Step-by-step explanation:
This question is not complete without a figure; find the figure attached.
Marissa is painting a regular patio with dimensions as
Length = (x + 25) units
Width = (x + 15) units
Area of this rectangular patio = Length × Width
Area = (x + 25)(x + 15) unit²
She has to paint the patio except the bench that does not need to be painted.
Dimensions of the rectangular bench,
Length = 10 units
Width = 3 units
Area of the bench = 10×3 = 30 units²
Area of the patio to be painted = Area of patio - Area of bench
A = (x + 25)(x + 15) - 30
(r/s)(3) find the value.
A bag contains 3 blue
marbles and 2 yellow marbles.
One example of independent
events using this bag of marbles is randomly selecting a blue marble,__________,and then
randomly selecting another
blue marble.
Fill in the blank above with
one of these:
a) Not replacing it
b) Replacing it
Answer:
a) replacing it
if you dont replace the marble there will be 1 less marble than before it will effect the possiblity
translate the points two left and six up
W(4,8)
X(3,-2)
Y(6,5)
Answer:
W'(2, 14)X'(1, 4)Y'(4, 11)Step-by-step explanation:
To translate 2 left, subtract 2 from every x-value.
To translate 6 up, add 6 to every y-value.
__
W' = W +(-2, 6) = (4-2, 8+6)
W' = (2, 14)
__
X' = X +(-2, 6) = (3-2, -2+6)
X' = (1, 4)
__
Y' = Y +(-2, 6) = (6-2, 5+6)
Y' = (4, 11)
Solve the equation below.
k - 6.2 = 24.8
Answer:
k = 31
Step-by-step explanation:
k - 6.2 = 24.8
+6.2 +6.2 (Add 6.2 to both sides to isolate the variable: k)
__________
k = 31
Answer:
31
Step-by-step explanation:
To find the value of k, you have to add 6.2 and 24.8 . To check your work, you subtract 31 by 6.2 and you'll get 24.8.
A box contains ten cards labeled Q, R, S, T, U, V, W, X, Y, and Z. One card will be randomly chosen.
What is the probability of choosing a letter from Q to T?
Write your answer as a fraction in simplest form.
1
Olox
5
?
Answer: 2/5
Step-by-step explanation: The total number of letters available to choose from is 10. You want to know the probability of 4 of those 10. So you divide 4/10. When you simplify that fraction it becomes 2/5.
The solution is 2/5
The probability of choosing a letter from Q to T is given by the equation
A = 2/5
What is Probability?
The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability of choosing a letter from Q to T be represented as A
Now , the equation will be
Let the letters be represented as set 1 = { Q , R , S , T , U , V , W , X , Y , Z }
The total number of letters = 10 letters
The number of letters from Q to T = 4 letters
So , the probability of choosing a letter from Q to T is A = number of letters from Q to T / total number of letters
Substituting the values in the equation , we get
Probability of choosing a letter from Q to T is A = 4/10
On simplifying the equation , we get
Probability of choosing a letter from Q to T is A = 2/5
Therefore , the value of A is 2/5
Hence , the probability is 2/5
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This is for algebra 2 and I got stuck on this anyone know this?
The temperature drops 10 degrees and then rises 10 degrees.
Write an addition expression that represents this situation.
Please answer ASAP
Answer:
10-10+10=10 degrees
what is the volume of the following rectangular prism?
Answer:
I dont really know how to multiply fractions but i do know the step.
Step-by-step explanation:
Since 23/4 units square's formula is L × B. and the H is 4/3 units.All you needed to do to find the recrangular prism was to multiply 23/4 and 4/3 to get it.Then simplify it.Sorry i dont really know whether this helps but its what i know:'D
Answer:
volume= 23/4 x 4/3
volume= 7 2/3 units3
What is the gradient of the line 12x=15-3y
Answer:
-4
Step-by-step explanation:
12x=15-3y
+3y
12x+3y=15
-12x
3y=-12x+15
/3
y=-4x+15
Gradient= -4 as in the equation y=mx+c
, m=the gradient therefore the gradient is -4
Answer:
-4
Step-by-step explanation:
12x=15-3y +3y
12x+3y=15 -12x
3y=-12x+15 /3
y=-4x+15
20 points
About 50% of the students at a high school opted for Spanish classes and of these,
about 32% opted for both Spanish and German classes. What percentage of the
students opted for German classes given that they have also opted for Spanish?
Answer:
32%
Step-by-step explanation:
P(G/S) = P(G&S)/P(S)
= (0.32×0.5)/0.5
= 0.32
32%
The percentage of students who have opted for German classes among those who also chose Spanish classes is 32%. This is because 50% of the students chose Spanish, and of these, 32% also selected German classes.
The question revolves around the percentage of students at a high school who have opted for German classes among those who have opted for Spanish classes. To solve this, we consider that 50% of the students chose Spanish classes, and of those, 32% also chose German classes. This means that among the students who took Spanish, 32% is the percentage of students who elected to take German classes as well.
The angle of depression between a bird and its prey is 70 degrees. If the bird is 18 ft off the ground, what is the distance between the bird and its prey? Round to the nearest foot
Answer:
19 ft
Step-by-step explanation:
We are given that
[tex]\theta=70^{\circ}[/tex]
Height of bird from the ground=h=18 ft
We have to find the distance between the bird and its prey.
We know that
[tex]sin\theta=\frac{perpendicular\;side}{hypotenuse}[/tex]
Using the formula
[tex]sin70=\frac{18}{hypotenuse}[/tex]
[tex]hypotenuse=\frac{18}{sin70}=19.1 ft\approx 19ft[/tex]
Hence, the distance between the bird and its prey=19 ft
9x^2-25
How do you solve this?
Answer:(3x+5) (3x-5)
Step-by-step explanation: a2-b2 =(a+b) (a-b) where a= 3x and b=5
Which is closest to the circumference of the CD?
1. 18.84
2. 28.26
3. 37.68
4. 113.04
Answer:
,
Step-by-step explanation:
Given the equation 5 + x - 12 = x - 7.
Part A. Solve the equation 5 + x - 12 = x - 7. In your final answer, be sure to state the solution and include all of your work.
Part B. Use the values x = -4, 0, 5 to prove your solution to the equation 5 + x - 12 = x - 7. In your final answer, include all of your calculations.
Answer:
part A= x=1
part B= -13=-11 and -7=-7 and -2=-2
Step-by-step explanation:
part A
5+x-12=x-7
-7+x=x-7
x=1
part B
5+(-4)-12=-4-7
-1-12=-4-7
-13=-4-7
-13=-11
5+x-12=x-7
5+(-12)=-7
-7=-7
5+x-12=x-7
5+5-12=5-7
10-12=-2
-2=-2