The curves r1(t) = (t, 4 - t, 63t^2) and r2(s) = (9 - s, s - 5, s^2) intersect at the point (x, y, z), which can be determined by solving the system of equations derived from the coordinates of the curves.
To find the intersection point of the curves r1(t) and r2(s), we need to solve the system of equations formed by equating the corresponding components of the two curves. Let's equate the x-components, y-components, and z-components separately.
From r1(t), we have x = t, y = 4 - t, and z = 63t^2.
From r2(s), we have x = 9 - s, y = s - 5, and z = s^2.
Equating the x-components: t = 9 - s
Equating the y-components: 4 - t = s - 5
Equating the z-components: 63t^2 = s^2
We can solve this system of equations to find the values of t and s that satisfy all three equations. Once we have t and s, we can substitute these values back into the expressions for x, y, and z to obtain the coordinates of the intersection point (x, y, z).
Solving the first equation, we get t = 9 - s. Substituting this into the second equation, we have 4 - (9 - s) = s - 5, which simplifies to -5s = -16. Solving for s, we find s = 16/5. Substituting this value back into t = 9 - s, we get t = 9 - (16/5) = 19/5.
Now, substituting t = 19/5 and s = 16/5 into the expressions for x, y, and z, we find:
x = 19/5, y = -1/5, z = (63(19/5)^2).
Therefore, the curves r1(t) and r2(s) intersect at the point (19/5, -1/5, 7257/25) or approximately (3.8, -0.2, 290.28).
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a cell phone plan costs $28.90 per month for 400 minutes of talk time. it costs an additional $0.07 per minute for each minute over 400 minutes. to get e-mail access, it costs 10% of the price for 400 minutes of talk time. your bill, which includes e-mail, is the same each month for 8 months. the total cost for all months is $298.56. write and solve an equation to find the number of minutes of talk time you use each month.
Answer:
Equation = 298.56=6(0.07m+23.90+0.10(23.90))
Minutes = 335
Step-by-step explanation:
Okay, so first simplify to get 298.56=0.52m+172.08
Next subtract to get 0.52m=126.48
Then divide 0.52 to get 335
I hope this helps ! :)
El largo total de una correa transportadora debe ser de 4,5 km para poder llevar el mineral hasta la planta- Si la correa mide 3200 m ¿Cuántos Km faltan para completar el largo requerido
Answer:
Distancia restante = 1,3 kilómetroslp
Step-by-step explanation:
Dados los siguientes datos;
Distancia total = 4,5 km
Distancia recorrida = 3200 metros a kilómetros = 3200/1000 = 3,2 km
Para encontrar la distancia restante para cubrir la longitud requerida;
Distancia total = distancia recorrida + distancia a la izquierda
4.5 = 3.2 + distancia a la izquierda
Distancia a la izquierda = 4.5 - 3.2 Distancia restante = 1,3 kilómetros
Find value(s) of k so that the linear system is consistent? (Enter your answers as a comma-separated list.) 8x1-7x2 = 2 12x1 + kx2 =-1
There are no values of k that make the linear system consistent.
To determine the values of k for which the linear system is consistent, we need to check if the system of equations has a unique solution, infinitely many solutions, or no solution.
The given system of equations is:
8x1 - 7x2 = 2
12x1 + kx2 = -1
We can solve this system using various methods, such as substitution or elimination. Let's use the elimination method to simplify the system.
To eliminate x2, we can multiply equation 1 by k:
8kx1 - 7kx2 = 2k
Now, we can subtract equation 2 from equation 3:
(8k - 12)x1 + (-7k - k)x2 = (2k + 1)
Simplifying equation 4, we have:
(8k - 12)x1 - 8kx2 = 2k + 1
Now, for the system to be consistent, the coefficient of x1 and the coefficient of x2 in the resulting equation should be the same.
Comparing the coefficients, we get:
8k - 12 = 0 (coefficient of x1)
-8k = -1 (coefficient of x2)
Solving the first equation:
8k - 12 = 0
8k = 12
k = 12/8
k = 3/2
Now, substitute the value of k in the second equation to check if it is satisfied:
-8k = -1
-8(3/2) = -1
-12 = -1
The equation -12 = -1 is false. Therefore, there are no values of k for which the linear system is consistent.
In conclusion, there are no values of k that make the given linear system consistent.
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The car consumes 6 liters per 100 km. How many kilometers can you drive with this car if the tank has 42 liters?
Answer:
If 100km enables consumption of 6lts
what about 42lts
42/6 multiply by 100km
42/6*100= 700km
The car will consume 42lts in 700 km.
Thank you.
Step-by-step explanation:
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
26 degrees
Step-by-step explanation:
180 - 48 = 132 - 106 = 26
this one should work
Answer: x = 106°
Step-by-step explanation:
106° + 48° + x° = 180°
154 + x = 180
x = 106°
A biologist has two brine solutions, one containing 7% salt and another containing 28% salt. How many milliliters of each solution should she mix to obtain 1 L of a solution that contains 19.6% salt?
Answer:
Each litters can be represented as; x and y respectively to the 7% and the 28%
x + y =1
7x + 28y =19.6
This a simultaneous equation and can either be solved by using elimination or substitution method
Using the substitution method
eqn1, x=1-y
putting into eqn2
7(1-y)+28y =19.6
7-7y+28y=19.6
21y=12.6
y=3/5
but x=1-y
so
x=1-3/5
x=2/5
HELP ASAP PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
Answer:
a. The price per ticket is 4 bucks, and b. you get 1/4 of a ticket for a dollar.
1. the penguin walks 75 feet in 45 seconds, and 2. it takes 27 seconds to walk 45 feet.
Step-by-step explanation:
Tickets:
16 dollars divided by 4 tickets is 4 dollars, so 4 dollars = 1 ticket. therefore, 1 dollar gives you 1/4 of a ticket.
Penguins
formula: X = feet, Y = seconds
X*0.6=Y
10 feet*0.6=6 seconds
(?) feet*0.6= 45 seconds
75 feet*0.6=45 seconds
same thing, but backwards this time
45 feet*0.6=(?) seconds
45 feet*0.6= 27 seconds
Hey can I have brainly please I am really close to leveling up
thx
Answer:
Step-by-step explanation:
I need help on this
Answer: 1/9
Step-by-step explanation: 9(1/3)^5-1, which is 9(1/3)^4.
Solve and you get 1/9.
Nationwide 13.7% of employed wage and salary workers are union members. At random sample of 200 local wage and salary workers showed that 30 belonged to a union. At 0.01 level of significance, is there sufficient evidence to conclude that the proportion of union members differs from 13.7%?
There is not sufficient evidence to conclude that the proportion of union members differs from 13.7% at the 0.01 level of significance.
To determine if there is sufficient evidence to conclude that the proportion of union members differs from 13.7%, we can perform a hypothesis test using the given sample data.
Let's define the hypotheses:
Null Hypothesis (H0): The proportion of union members is equal to 13.7%.
Alternative Hypothesis (H1): The proportion of union members differs from 13.7%.
We can set up the test using the z-test for proportions. The test statistic is calculated as:
z = (p(cap) - p) / √(p × (1 - p) / n)
where p(cap) is the sample proportion, p is the hypothesized proportion, and n is the sample size.
Given that the sample size is 200 and 30 workers belonged to a union, the sample proportion is p(cap) = 30/200 = 0.15.
The hypothesized proportion is p = 0.137.
Let's calculate the test statistic:
z = (0.15 - 0.137) / √(0.137 × (1 - 0.137) / 200)
z ≈ 1.073
To determine if there is sufficient evidence to conclude that the proportion differs from 13.7%, we compare the test statistic to the critical value.
At a significance level of 0.01, the critical value for a two-tailed test is approximately ±2.576 (obtained from a standard normal distribution table).
Since |1.073| < 2.576, the test statistic does not fall in the rejection region. Therefore, we fail to reject the null hypothesis.
Conclusion: Based on the given sample data, there is not sufficient evidence to conclude that the proportion of union members differs from 13.7% at the 0.01 level of significance.
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The polynomial V(x)=x^3+9x^2-16x-144 represents volume of a shipping crate. Explain how to find the area of the base of the crate? if the polynomial H(x)=x+4 represents the height of the crate
Answer:
x = − 9 , − 4 , 4
Step-by-step explanation:
Each crate is in the shape of a rectangular solid. Its dimensions are length, width, and height. The rectangular solid shown in the image below has a length
4 units, width 2 units, and height 3
units. Can you tell how many cubic units there are altogether? Let’s look layer by layer.
Breaking a rectangular solid into layers makes it easier to visualize the number of cubic units it contains. This
4 by 2 by 3 rectangular solid has 24 cubic units.
A rectangular solid is shown. Each layer is composed of 8 cubes, measuring 2 by 4. The top layer is pink. The middle layer is orange. The bottom layer is green. Beside this is an image of the top layer that says
Altogether there are 24 cubic units. Notice that 24 is the length × width × height .
The top line says V equals L times W times H. Beneath the V is 24, beneath the equal sign is another equal sign, beneath the L is a 4, beneath the W is a 2, beneath the H is a 3.
The volume, V , of any rectangular solid is the product of the length, width, and height.
V = L W H
We could also write the formula for the volume of a rectangular solid in terms of the area of the base. The area of the base, B , is equal to length × width . B = L ⋅ W
We can substitute
B for L ⋅ W in the volume, formula to get another form of the volume formula.
The top line says V equals red L times red W times H. Below this is V equals red parentheses L times W times H. Below this is V equals red capital B times h.
We now have another version of the volume formula for rectangular solids. Let’s see how this works with the
4 × 2 × 3
rectangular solid we started with. See the image below.
Besides the solid is V equals Bh. Below this is V equals Base times height. Below Base is parentheses 4 times 2. The next line says V equals parentheses 4 times 2 times 3. Below that is V equals 8 times 3, then V equals 24 cubic units.
Let P(x, y) means x +1> y. Let 2 € Z and y € N, select all the formulas below that are true in the domain. A. Vay P(x,y) B. ByVx P(x,y) C. 3xVy P(x,y) D. Vyc P(x,y) E. 3xVy - P(x, y) F. ByVx - P(x, y) G. Vzy -P(,y) H. -3xVy P(x,y) I. None of the above.
The formulas below that are true in the domain.
The correct answer is (A, B, C, E, F). A. Vay P(x,y) B. ByVx P(x,y) C. 3xVy P(x,y) E. 3xVy - P(x, y) F. ByVx - P(x, y)
Let's evaluate each formula to determine which ones are true in the given domain:
A. Vay P(x, y): This formula states that for all y, there exists an x such that x + 1 > y. Since there is no restriction on x, this formula is true in the given domain.
B. ByVx P(x, y): This formula states that for all x, there exists a y such that x + 1 > y. Since there is no restriction on y, this formula is true in the given domain.
C. 3xVy P(x, y): This formula states that there exists an x such that for all y, x + 1 > y. Since there is no restriction on y, this formula is true in the given domain.
D. Vyc P(x, y): This formula states that for all y, there exists a constant c such that x + 1 > y. However, there is no mention of c in the given domain, so this formula is not true.
E. 3xVy -P(x, y): This formula states that there exists an x such that for all y, x + 1 ≤ y. This is the negation of the original condition x + 1 > y. Since there is no restriction on y, this formula is true in the given domain.
F. ByVx -P(x, y): This formula states that for all x, there exists a y such that x + 1 ≤ y. This is again the negation of the original condition x + 1 > y. Since there is no restriction on x, this formula is true in the given domain.
G. Vzy -P(x, y): This formula states that for all z, there exists a y such that x + 1 ≤ y. However, there is no mention of z in the given domain, so this formula is not true.
H. -3xVy P(x, y): This formula states that there does not exist an x such that for all y, x + 1 > y. Since the original condition x + 1 > y is true for any value of x and y in the given domain, this formula is not true.
Based on the evaluations above, the formulas that are true in the given domain are:
A. Vay P(x, y)
B. ByVx P(x, y)
C. 3xVy P(x, y)
E. 3xVy -P(x, y)
F. ByVx -P(x, y)
Therefore, the correct answer is (A, B, C, E, F).
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The weather reporter says that there is a 12% chance that it will be moderately windy tomorrow.
What is the probability that it will not be windy? & Will tomorrow be a good day to fly a kite? Explain.
(______Be specific ya numptys______)
The probability that it will not be windy is 88% or 0.88.
No, tomorrow be not a good day to fly a kite.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means
The weather reporter says that there is a 12% chance that it will be moderately windy tomorrow.
Now, the probability that it will not be windy
= 100 - 12
= 88%
= 0.88
No, the lite totally depends on the wind but the next day the probability of no wind is 88%.
This probability is high probability.
So, there is huge probability that the kite will not fly.
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What is the slope of the line containing points
A(4, -1) and B(0, 2)?
A.3/4
B. 4/3
C. -3/4
D. -4/3
What is the quotient of 58,110 and 65?
Answer:
894
Step-by-step explanation:
58,110 divided by 65 is 894
The quotient of the given numbers 58,110 and 65 would be equal to 894.
What are the Quotients?Quotients are the number that is obtained by dividing one number by another number.
Dividend ÷ Divisor = Quotients
The quotient of the given numbers is 58,110 and 65.
58,110 divided by 65
58,110 /65
= 894
Thus, the quotient of the given numbers is 894.
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identify the domain and range of the inverse of f(x) = 0.5x.
The domain and range of the inverse of the function f(x) = 0.5x need to be determined. The domain and range of the inverse function g(x) = 2x are both all real numbers.
To find the domain and range of the inverse of a function, we can swap the roles of x and y in the original function and then solve for y.
The original function is f(x) = 0.5x. Swapping x and y, we get x = 0.5y. Solving this equation for y, we multiply both sides by 2, giving us y = 2x.
The domain of the inverse function, denoted as g(x), is the set of all possible x-values. In this case, the domain of g(x) is the same as the range of the original function f(x). The range of f(x) is all real numbers, so the domain of g(x) is also all real numbers.
Similarly, the range of the inverse function is the set of all possible y-values. In this case, the range of g(x) is the same as the domain of the original function f(x). The domain of f(x) is all real numbers, so the range of g(x) is also all real numbers.
Therefore, the domain and range of the inverse function g(x) = 2x are both all real numbers.
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please help!
if a trail runner zig-zags 15m to the west and then 15m to the east:
what is the runner's total distance?
what is the runner's total displacement?
Answer:
Total distance = 30m
Total displacement = 0m
Step-by-step explanation:
a) Distance is a scalar quantity that does not specify direction
Hence if a trail runner zig-zags 15m to the west and then 15m to the east, the total distance will be the sum of the distance travelled both to the west and east.
total distance = distance through west + distance through east
total distance = 15m + 15m
total distance = 30m
Hence the runner's total distance is 30m
b) Displacement is a vector quantity and it specifies direction. Hence we will take into consideration the direction taken
Since East direction is positive, the displacement through east is +15m
Since West direction is negative, the displacement through west is -15m
Total displacement = +15 - 15
Total displacement = 0m
Hence the runner's total displacement is 0m
Quickly please I only have a few minutes
Answer:
1=4
5=8
2=5
Step-by-step explanation:
Answer:
1, 5, 2 is the x values.
Step-by-step explanation:
you just subtract 3 from the y's
Find the missing side of this right triangle 8 16
Answer:
[tex]\boxed {\boxed {\sf b= \sqrt{192}}}[/tex]
Step-by-step explanation:
Since this is a right triangle, we can use Pythagorean Theorem to find the sides.
[tex]a^2+b^2=c^2[/tex]
where a and b are the legs and c is the hypotenuse.
In this triangle, 8 and x are the legs because they form the right angle. 16 is the hypotenuse because it is opposite the right angle.
[tex]a=8 \\c=16[/tex]
Substitute the values into the formula.
[tex]8^2+b^2=16^2[/tex]
Solve the exponents.
8² = 8*8= 64 16²=16*16=256[tex]64+b^2=256[/tex]
Subtract 64 from both sides to isolate the variable.
[tex]64-64+b^2= 256-64 \\b^2=192[/tex]
Take the square root of both sides.
[tex]\sqrt {b^2}=\sqrt{192}\\ b=\sqrt{192}[/tex]
The missing side is equal to √192
g (b) find the amount of salt in the tank after 1.5 hours.a tank contains 90 kg of salt and 1000 l of water. a solution of a concentration 0.045 kg of salt per liter enters a tank at the rate 8 l/min. the solution is mixed and drains from the tank at the same rate what is the concentration of our solution in the tank initially?
The initial concentration of the solution in the tank is 0.036 kg of salt per liter.
Initially, the tank contains 90 kg of salt and 1000 liters of water, resulting in a total volume of 1000 liters. A solution with a concentration of 0.045 kg of salt per liter enters the tank at a rate of 8 liters per minute. Since the solution is mixed and drains from the tank at the same rate, the concentration remains constant throughout the process.
To find the initial concentration, we can calculate the amount of salt in the tank after a certain time period. After 1.5 hours, the solution has been entering and draining from the tank for 90 minutes (1.5 hours * 60 minutes/hour). During this time, the total volume of the solution that has entered and drained is 90 minutes * 8 liters/minute = 720 liters.
The amount of salt that has entered the tank is 720 liters * 0.045 kg/liter = 32.4 kg. Since the initial amount of salt in the tank was 90 kg, the amount of salt remaining after 1.5 hours is 90 kg - 32.4 kg = 57.6 kg.
To find the concentration, we divide the remaining amount of salt (57.6 kg) by the remaining volume of the solution (1000 liters - 720 liters = 280 liters). The concentration of the initial solution in the tank is 57.6 kg / 280 liters ≈ 0.206 kg of salt per liter.
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how do I write an equation for a quadratic function represented by a table ?
Answer:
Hello There!!
Step-by-step explanation:
Firstly,select three ordered pairs from the table. Secondly,substitute the first pair of values in to the form of the quadratic equation: f(x) = ax^2 + bx + c and then solve for a.
hope this helps,have a great day!!
~Pinky~
How am I supposed to do this?
Solve Systems of Equations Algebraically.
y=x-8
y=5x
Answer:
(- 2, - 10 )
Step-by-step explanation:
Given the 2 equations
y = x - 8 → (1)
y = 5x → (2)
Substitute y = 5x into (1)
5x = x - 8 ( subtract x from both sides )
4x = - 8 ( divide both sides by 4 )
x = - 2
Substitute x = - 2 into either of the 2 equations for y
Substituting into (1)
y = - 2 - 8 = - 10
solution is (- 2, - 10 )
The town of KnowWearSpatial, U.S.A. operates a rubbish waste disposal facility that is overloaded if its 4712 households discard waste with weights having a mean that exceeds 27.22 lb/wk. For many different weeks, it is found that the samples of 4712 households have weights that are normally distributed with a mean of 26.97 lb and a standard deviation of 12.29 lb. What is the proportion of weeks in which the waste disposal facility is overloaded? P(M> 27.22) = Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z- scores or Z-scores rounded to 3 decimal places are accepted. Is this an acceptable level, or should action be taken to correct a problem of an overloaded system? O No, this is not an acceptable level because it is not unusual for the system to be overloaded. O Yes, this is an acceptable level because it is unusual for the system to be overloaded.
The proportion of weeks in which the waste disposal facility is overloaded is approximately 0.4920. No, this is not an acceptable level because it is not unusual for the system to be overloaded.
To solve this problem, we need to find the proportion of weeks in which the waste disposal facility is overloaded, given that the weights of the samples of 4712 households are normally distributed with a mean of 26.97 lb and a standard deviation of 12.29 lb.
Let's denote X as the random variable representing the mean weight of the samples of 4712 households in a week. We want to find P(X > 27.22).
To calculate this probability, we can use the standard normal distribution. First, we need to standardize the random variable X using the z-score formula:
z = (X - μ) / σ
where μ is the mean and σ is the standard deviation.
Substituting the given values:
z = (27.22 - 26.97) / 12.29
z ≈ 0.0203
Next, we can use a standard normal distribution table or a calculator to find the proportion of weeks in which the waste disposal facility is overloaded:
P(X > 27.22) = P(Z > 0.0203)
Looking up the z-score 0.0203 in the standard normal distribution table, we find that the corresponding proportion is approximately 0.4920.
Therefore, the proportion of weeks in which the waste disposal facility is overloaded is approximately 0.4920. This means that it is not unusual for the system to be overloaded.
So the correct answer is:
No, this is not an acceptable level because it is not unusual for the system to be overloaded.
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Find the confidence interval specified. Assume that the population is normally distributed. The principal randomly selected six students to take an aptitude test. Their scores were: 84.1 79.8 79.6 81.3 88.1 81.0 Determine a 90% confidence interval for the mean score for all students.
The 90% confidence interval for the mean score for all students is [79.35, 86.75].
What is the range within which the mean score for all students lies with 90% confidence?A 90% confidence interval was calculated to estimate the mean score for all students based on a sample of six students' scores. The sample mean was found to be 82.83, and the standard deviation was 3.67.
Using a t-distribution with five degrees of freedom (n-1), the critical value for a 90% confidence level was determined to be 2.571. By applying the formula for confidence intervals, the lower bound of the interval was calculated as 82.83 - (2.571 * (3.67/√6)) = 79.35, and the upper bound was calculated as 82.83 + (2.571 * (3.67/√6)) = 86.75.
This means that we can be 90% confident that the mean score for all students falls within the range of 79.35 to 86.75.
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You take out a loan for $478 at an interest rate of 8% compounded annually. What is the
total amount that you will have paid at the end of 4 years?
Answer:
650.3
Step-by-step explanation:
Answer:
the total payment will be 91.43 and the total interest pay will be 13.43.
Step-by-step explanation:
Tbh I dont get what you mean that much, but I think you mean 48 months of payment times the monthly payment, soooo.
13.43x 48= 644.64
644.64 after four years. I really really hope this helps you. Have a good day
If a linear function has the points (3,-1) and (-3,0) on its graph, what is the rate of change of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The rate of change is (Type an integer or a simplified fraction.) B. There is no solution.
The rate of change of the function is -1/6
How to determine the rate of change of the functionFrom the question, we have the following parameters that can be used in our computation:
(3,-1) and (-3,0)
The rate of change of the function is calculated as
Rate = Change in y/Change in x
Using the above as a guide, we have the following:
Rate = (0 + 1)/(-3 - 3)
Evaluate
Rate = -1/6
Hence, the rate of change of the function is -1/6
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A salt shaker company produces salt shakers of varying heights. They create
a table showing how many salt granules each size salt shaker holds. Does this
data represent a proportional relationship? Click on the correct response, then
answer the question below.
Height of Salt Shaker
Number of Salt Granules
Answer:
Proportional and h.200=g
Step-by-step explanation:
Simplify the expression e3 x e9
Answer:
e^12
Step-by-step explanation:
Write the problem as a mathematical expression.
e^3 ⋅ e^9
Use the power rule and combine the exponents.
e^3 + 9^e
Add 3 and 9.
e^12
The result can be shown in multiple forms.
Exact Form:
e^12
If not the answer
The Decimal Form:
162754.79141900…
evaluate the exponent expression for a = –2 and b = 3. question 15 options: a) –9∕8 b) –2∕5 c) –6 d) 3
The correct option is A) 9∕8, evaluating the exponent expression with a = -2 and b = 3, we find that the value is -8.
We are given the expression a^b, where a = -2 and b = 3. Substituting these values into the expression, we have (-2)^3.
To evaluate this expression, we raise -2 to the power of 3. When we raise a negative number to an odd power, the result will be a negative number.
So, (-2)^3 will yield a negative value.
Calculating (-2)^3, we multiply -2 by itself three times: (-2) × (-2) × (-2). This equals -8.
Therefore, the correct option is A) 9∕8 and the value of the exponent expression (-2)^3 is -8.
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I need help on this question it's confusing
Answer:
Well what's the question lol
Answer:
show the question
Step-by-step explanation: