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PLEASE HELP QUICK!!
Javier will evaluate the expression 2a(to the power of 3) - 1 for a = 2. Once he submitted 2 for a in the expression, what is the next step Javier needs to take in order to evaluate the expression?
The next step Javier needs to take in order to evaluate the expression is to simplify it to it's lowest term. Details below
Data obtained from the questionExpression = 2a³ - 1Evaluation =?How to evaluate the expressionFrom the question given, we were told that Javier submitted 2 for a
Thus, the new expression becomes
2 × 2³ - 1
Recall
Aⁿ × Aᵐ = Aⁿ⁺ᵐ
Thus,
2 × 2³ = 2¹⁺³ = 2⁴
Therefore,
2 × 2³ - 1 = 2⁴ - 1
But
2⁴ = 16
Thus,
2⁴ - 1 = 16 - 1
2⁴ - 1 = 15
Therefore,
2 × 2³ - 1 = 15
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What popular Song-era art idea does this image represent?
Answer:
the 3 pefections
Step-by-step explanation:
took the test
Answer:
the three perfections
Step-by-step explanation:
Solve each system of equations by graphing.
y = 2x
y = x + 1
Step-by-step explanation:
The system of linear equations are , (i) y = 2x and (ii) y = x + 1 . We will find some coordinates and then we will plot its graph. The point where both Graphs will meet will be the solution of the graph .
• Finding coordinates of Equⁿ (i) :-
Step 1 : Put x = 0 :-
\(\tt y = 2x = 2(0) = \red{0}\)
Step 2: Put x = 1 :-
\(\tt y = 2x = 2(1) = \red{2}\)
\(\boxed{\begin{array}{c|c|c} \bf x & \tt 0 &\tt 1 \\ \bf y &\tt 0 & \tt 2 \end{array}}\)
_________________________________
• Finding coordinates of equⁿ (ii) :-
Step 1 : Put x = 0 :-
\(\tt y = x + 1 = 1 + 0 = \red{1}\)
Step 2: Put x = 1 :-
\(\tt y = x + 1 = 1 + 1 = \red{2}\)
\(\boxed{\begin{array}{c|c|c} \bf x & \tt 0 &\tt 1 \\ \bf y &\tt 1 & \tt 2\end{array}}\)
Now plot these points on the graph Taking appropriate scale . Refer to the attachment in graph . From graph the Solution is (1,2) .
The hexagonal prism has a base area of 38.8 units^2 and a volume of 504.4 units^3. Find it’s height.
Answer:
13 units
Step-by-step explanation:
V = B • h
504.4 = 38.8 h
504.4 / 38.8 ( divide to isolate the variable)
Height = 13 units
PLEASE HELP due in a few hours!!
Answer:
75 meters²
Step-by-step explanation:
4 cm= 5 m
12 cm= 15 m
15×5=75
Area of Patio=75 m²
Describe the sampling distribution of p. Assume the size of the population is 30,000. n=900, p=0.532 Describe the shape of the sampling distribution of p. Choose the correct answer below. OA The shape
The normal approximation to the binomial distribution also implies that the sampling distribution of p is roughly bell-shaped, as the normal distribution is. Therefore, the answer is A) The shape.
The sampling distribution of the proportion is the distribution of all possible values of the sample proportion that can be calculated from all possible samples of a certain size taken from a particular population in statistical theory. The state of the examining dispersion of p is generally chime molded, as it is an illustration of a binomial conveyance with enormous n and moderate p.
The example size (n=900) is sufficiently enormous to legitimize utilizing an ordinary guess to the binomial dissemination, as indicated by as far as possible hypothesis. In order for the binomial distribution to be roughly normal, a sample size of at least 30 must be present, which is achieved.
Subsequently, the examining dispersion of p can be thought to be around ordinary with a mean of 0.532 and a standard deviation of roughly 0.0185 (involving the equation for the standard deviation of a binomial distribution).The typical estimate to the binomial dissemination likewise infers that the inspecting conveyance of p is generally chime molded, as the ordinary circulation is. As a result, A) The shape is the response.
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Describe and correct the error in finding the solution
(look at picture for problem)
Answer:
divide both sides by 2
Step-by-step explanation:
Aaron bought a pair of shorts online for $22. He used a coupon code to get a 20% discount. The website also applied a 10% processing fee to the price after the discount. How much did Aaron pay, in the end? Round to the nearest cent.
Answer:
19.36
Step-by-step explanation:
First you figure out what 20% of 22 is, which is 4.4
Then you subtract 4.4 from 22, which gets you 17.6
Then you add 10% of 17.6, that 10% being 1.76
So you lastly add 1.76 to 17.6 which gets you 19.36.
Round to the nearest ten thousand.
923,079
The slope of this line is 8 and it goes through the point (-4, 4)
What is the Equation of the Line?
pls i really need help
Answer:
y = 8x + 36
Step-by-step explanation:
(y-4) / (x - -4) = 8
y - 4 = 8x + 32
y = 8x + 36
2. Use a proof by mathematical induction to show that your equation from question 1 applies to the minimum number of moves required to defeat the Tower of Hanoi game, based on the number of disks you must move. Think about the process of the game; and describe how your equation applies to it.
By mathematical induction, the formula holds for all positive integers n, and the Tower of Hanoi game with n discs can be solved with a minimum of 2n - 1 steps.
Explain:
I will use mathematical induction to show that the equation I derived in answer 1 holds for the bare minimum of movements needed to solve the Tower of Hanoi game for any specific number of discs.
Let's first review the formula:
Code's minimal motion count is 2n - 1, where n is the total number of discs.
Base case: The least number of moves needed is 21 - 1 = 1, which corresponds with the formula when there is only one disc and we can move it from the beginning peg to the ending peg with just one move.
Step one of induction: Assume that the formula is valid for n=k, where k is a positive integer. If so, then 2k - 1 moves are the absolute least needed to solve the Tower of Hanoi game using k discs. We must demonstrate that the formula also applies to n=k+1, i.e., that 2(k+1) - 1 movements are all that are needed to solve the Tower of Hanoi game with k+1 discs.
We can divide the issue into three steps to move k+1 discs from the starting peg to the ending peg:
Step 1: Using the ending peg as a spare, move k discs from the beginning peg to the spare peg.
Step 2: Transfer the final disc from the beginning to the finish peg.
Step 3: Using the beginning peg as a spare, move the k discs from the spare peg to the ending peg.
According to the inductive hypothesis, Step 1 and Step 3 both necessitate a minimum of 2k - 1 moves. The least amount of moves necessary to complete the procedure is one for Step 2, making a total of:
scss
Duplicate the formula-conforming code 2k - 1 + 1 + 2k - 1 = 2(k+1) - 1.
As a result, by mathematical induction, the formula is true for all positive integers n, and 2n - 1 movements are all that are needed to solve the Tower of Hanoi game with n discs.
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Number 5 please help need answers thanks!!!!Have a great day!
Answer:
3 = 275, 5 = 305, 8= 350, 12 = 410
Step-by-step explanation:
3x15+230, (305-230)/15, im bored plz just take the answer
9x-y= 29 and 9x + y = -29
Answer:
(0,-29) x = 0, y = -29
Step-by-step explanation:
Answer:
x= - 29 over 9 - 1 over 9y, y
Step-by-step explanation:
Simplify the expression. 2y−5(y−3)=
Answer:
-3y -15
Step-by-step explanation:
2y - 5(y-3) = 2y -5y - 15
= -3y -15
Your welcome, and feel free to comment if you need have any questions!
The simplified value of the expression, 2y−5(y−3) using the Distributive property is 15- 3y.
Given Expression:
2y−5(y−3)
Using Distributive property
\({\text} a *(b+c) = (a *b) + (a*c)\)
So, applying the Distributive property in the expression 5(y - 3) gives
5(y - 3) = 5y - 15
Substituting the value 5y - 15 in 2y−5(y−3) as
2y−5(y−3) = 2y - (5y-15)
= 2y - 5y + 15
Now, operating the simplified value is
2y−5(y−3) = 15 - 3y
Thus, the simplified expression is -3y + 15.
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real estate ads suggest that 60% of homes for sale have garages, 30% have swimming pools, and 18% have both features. what is the probability that a home for sale has garage but no pool?
The probability of a home for sale having a garage but no pool is 0.42.
To do this, we need to use some probability rules. One useful rule is the formula for calculating the probability of an event not occurring. This is given by:
P(not A) = 1 - P(A)
where A is the event we are interested in, and not A is the event of A not occurring.
In this case, we are interested in the probability of a home having a garage but no pool. Let's call this event GNP (short for garage no pool). Using the information given, we know that 60% of homes have garages and 18% have both garages and pools. We can use this information to calculate the probability of a home having a garage but no pool as follows:
P(GNP) = P(G) - P(G and P)
where G is the event of a home having a garage and P is the event of a home having a pool.
Substituting the values we have:
P(GNP) = 0.6 - 0.18
P(GNP) = 0.42
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Determine whether each ordered pair is a solution or not a solution to this system of inequalities.
y< −x
2x+y>2
The ordered pair that is the solution of the given system of inequalities is (2, -2)
What is inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given is a system of inequalities, y < -x and 2x+y > 2, we need to determine solution set of the given system of inequalities,
The inequalities are,
y < -x....(i)
2x+y > 2
y < 2-2x...(ii)
To find the ordered pair, put y = -x in equation Eq(ii) and replace < by =
-x = 2 - 2x
x = 2
y = -2
Therefore, the ordered pair, is (2, -2) {look at the graph attached}
Hence, the ordered pair that is the solution of the given system of inequalities is (2, -2)
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PLS PLS ANSWER ASAP
Patch traveled from his office to the seashore at a speed of 62 mph. He traveled the same route back to his office but on the return trip his speed was 66 mph. If altogether, patch spent a total of 4 hours on the road, how many hours did the trip to the seashore take? Round your answer to the nearest hundred (two decimal places)
The trip to the seashore takes about 2.1 hours (rounded to the nearest hundredth).Thus, the correct option is 2.1 hours.
In this question, Patch traveled from his office to the seashore at a speed of 62 mph. He traveled the same route back to his office but on the return trip his speed was 66 mph.
If altogether, Patch spent a total of 4 hours on the road, we have to calculate how many hours did the trip to the seashore take.To solve this problem,
we will use the formula of speed, distance and time:Speed = Distance / Timeor Distance = Speed x TimeWe have given that the distance between Patch’s office and seashore is the same for both the trip to and from the seashore.
Let's suppose that the distance between the Patch’s office and seashore is “d”.Given speed when he travels from office to seashore = 62 mph
Time taken to travel from office to seashore = Distance / Speed= d / 62Given speed when he travels from seashore to office = 66 mph
Time taken to travel from seashore to office = Distance / Speed= d / 66Total time taken = Time taken from office to seashore + Time taken from seashore to office= d / 62 + d / 66= (33d + 31d) / (62 x 66) = 64d / 2046= 32d / 1023We have given that Total time taken by Patch is 4 hours.
Therefore,32d / 1023 = 4d = 1023/8 ≈ 127.88 milesNow, we know the distance is 127.88 miles and speed is 62 mph. Therefore,Time taken to travel from office to seashore = Distance / Speed= 127.88 / 62= 2.06 ≈ 2.1 hours
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Use synthetic division to find the result when x³ + 7x² - 12x + 14 is divided by a 1. If there is a remainder, express the result in the form q(x) + b(x)*
Using synthetic division, we can divide the polynomial x³ + 7x² - 12x + 14 by the divisor 1. Performing the synthetic division, we obtain a quotient of x² + 6x - 6 and a remainder of 8.
To divide the polynomial x³ + 7x² - 12x + 14 by the divisor 1 using synthetic division, we set up the synthetic division table as follows:
1 | 1 7 -12 14
We begin by bringing down the coefficient of the first term, which is 1, and place it on the line below the division bar. Then we multiply the divisor, 1, by the value we brought down and write the result under the next coefficient. Adding the values in the second row, we obtain the new value. We continue this process for each term until we reach the last term.
1 | 1 7 -12 14
1 8 -4 10
The values in the last row represent the coefficients of the quotient polynomial. Therefore, the quotient is x² + 6x - 6. The remainder, which is the last value in the last row, is 10. Since the divisor is 1, the remainder does not affect the quotient. Hence, the result of the division is x² + 6x - 6 with a remainder of 10.
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If
CE
and
FH
are parallel lines and mCDB= 65°, what is mEDB?
Answer:
65° or 115°
Step-by-step explanation:
there is no picture but if
mEDB looks like mCDB then its 65°
but if they dont look alike then
180-65=115
straight line is 180°
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Exercises 9–10: State each function described by the graph. The function is of the form f(x)=|x-h|+k
Answer:
9) |x-2| + 0
10) |x+2|-3
Step-by-step explanation:
9) f(x) = |x-2| + 0
h = 2
k = 0
This is because the equation of the line is -x+2 (when x is less than 2) and x-2 (when x is greater than 2). Once you plot this, you can get the graph shown.
10) f(x) = |x+2|-3
h = -2
k = -3
This is because the equation is -x-2, however, it has been translated by -3 units down the y-axis. Hence, k = -3 and h = -2
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The correlation coefficient, r, is defined as measuring the direction and __________ of a linear relationship.
The correlation coefficient, r, is defined as measuring the direction and Strength of a linear relationship.
What is the Correlation Coefficient?The Correlation coefficient (r) is defined as a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables.
A correlation coefficient is a number between -1 and 1 that indicates the strength and direction of the relationship between variables. In other words, it reflects how similar the measurements of two or more variables in the dataset are.
Now, looking at the given statement in the question and comparing with the definitions above, we can say that the missing word is "Strength"
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A large office dek ha an area of 42ft2. If the width i 3. 5 feet, write an equation to repreent the area
The equation to represent the area of the desk is A=3.5 x 12. The length of the large office desk is 12.
The area a rectangle occupies on a two-dimensional plane is known as the area of the rectangle. A quadrilateral, a type of two-dimensional shape with four sides and four vertices, is what a rectangle is.
A large office desk is given, with area 42 ft^2. The shape of the desk is rectangle. The area of the rectangle is given by A=l*w.
Given, the area is 42 ft^2.
w=3.5 feet.
A= 42
42=3.5*l
l=42/3.5
l=12 feet.
The length of the rectangular desk is 12 feet. The equation to represent the area of the large office desk is A=12*3.5.
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Ms.Lawrence buys 8 ounces of smoked salmon at 17.98 per pound how much money did ms.Lawrence spend on smoked salmon
Answer:
$8.99
Step-by-step explanation:
1 pound = 16 ounces
y pound = 8 ounces
\(\frac{1}{16} :\frac{y}{8}\)
y · 16 = 1 · 8
16y = 8
16y ÷ 16 = 8 ÷ 16
y = 0.5
0.5 pound = 8 ounces
----------------------------------
1 pound = $17.98
0.5 pound = y
\(\frac{1}{17.98} :\frac{0.5}{y}\)
y · 1 = 17.98 · 0.5
y = $8.99
Estimate σA and σB using the loan allocation deviation formula.
A. σ(A) = 12.25% ; σ(B) = 14.14%
B. σ(A) = 17.32% ; σ(B) = 20.0%
C. σ(A) = 16.33% ; σ(B) = 14.14%
D. σ(A) = 14.14% ; σ(B) = 16.33%
The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)
Here,
σ1 = 15%
σ2 = 10%
w1 = 50%,
w2 = 50%
Substituting the values in the above formula:
σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)
= (0.0225 + 0.0100)^(1/2)
= 0.0158 = 1.58%σB
= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)
= (0.0225 + 0.0100)^(1/2)
= 0.0158
= 1.58%
Hence, the correct option is
D. σ(A) = 14.14%;
σ(B) = 16.33%.
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Cuánto es -a +28 =14
a = -14
-14+28= 14
14 x 2 = 28
1/2 of -28 --> -14
This means a equals -14.
Esto significa A=-14
(sorry my spanish is not good, hope this helps)
In the past, the output of a process had a mean of 2.050 and a standard deviation of 0.020 liters. If a current sample of output had these values {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, would that indicate that the process is still "in order" (as opposed to being "out of order")? What if the sample was {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}?
For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."
To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.
For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:
Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):
Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.
Compare the sample mean to the known process mean (2.050):
The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."
Calculate the sample standard deviation using the formula:
Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))
Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.
Compare the sample standard deviation to the known process standard deviation (0.020):
The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."
For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:
Calculate the sample mean:
Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034
Compare the sample mean to the process mean (2.050):
The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."
Calculate the sample standard deviation:
The sample standard deviation is approximately 0.019 liters.
Compare the sample standard deviation to the process standard deviation (0.020):
The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.
In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.
However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.
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If u=(1,2,−3), w=(3,0,−1),k=−3, then find: a) k⋅u b) u+w c) u−w d) 2w−u e) k⋅(u+w) f) k⋅u+k⋅w Q4. If u=(1,−3,2),v=(1,1,2), w=(3,1,1) and k=−2, then find a) ∥u∥ b) ∥k,u∥ c) ∣k∣∥u∥ d) w/∥w∥ e) −w/∥w∥ f) v⋅w g) v⋅v g) k(u⋅v) h) (kv)⋅w
a) To find k⋅u, multiply each component of u by k:
k⋅u = -3(1, 2, -3) = (-3, -6, 9)
b) To find u+w, add the corresponding components of u and w:
u+w = (1, 2, -3) + (3, 0, -1) = (4, 2, -4)
c) To find u-w, subtract the corresponding components of w from u:
u-w = (1, 2, -3) - (3, 0, -1) = (-2, 2, -2)
d) To find 2w-u, multiply each component of w by 2 and subtract the corresponding components of u:
2w-u = 2(3, 0, -1) - (1, 2, -3) = (6, 0, -2) - (1, 2, -3) = (5, -2, 1)
e) To find k⋅(u+w), first find u+w and then multiply each component by k:
k⋅(u+w) = k(4, 2, -4) = (-12, -6, 12)
f) To find k⋅u+k⋅w, multiply each component of u by k and add the corresponding components of k⋅w:
k⋅u+k⋅w = k(1, 2, -3) + k(3, 0, -1) = (-3, -6, 9) + (-9, 0, -3) = (-12, -6, 6)
a) ∥u∥ = √(1^2 + (-3)^2 + 2^2) = √(1 + 9 + 4) = √14
b) ∥k,u∥ = √((-2)^2 + 1^2 + (-3)^2 + 2^2) = √(4 + 1 + 9 + 4) = √18
c) ∣k∣∥u∥ = |-2| * √14 = 2√14
d) w/∥w∥ = (3, 1, 1)/√(3^2 + 1^2 + 1^2) = (3, 1, 1)/√11
e) −w/∥w∥ = -(3, 1, 1)/√11
f) v⋅w = 1*3 + 1*1 + 2*1 = 3 + 1 + 2 = 6
g) v⋅v = 1*1 + 1*1 + 2*2 = 1 + 1 + 4 = 6
g) k(u⋅v) = -2 * (1*-3 + (-3)*1 + 2*2) = -2 * (-3 - 3 + 4) = -2 * (-2) = 4
h) (kv)⋅w = (-2)(1, 1, 2)⋅(3, 1, 1) = (-2)(3 + 1 + 2) = (-2)(6) = -12
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Graph the given function.
f(x) = 7^x
Which key features apply to the graph?
A. The graph has an asymptote at y = 7 and is increasing as x approaches positive infinity.
B. The graph has an asymptote at y = 0 and is increasing as x approaches positive infinity.
C. The graph has an asymptote at y = 0 and is decreasing as x approaches positive infinity.
D. The graph has an asymptote at y = 7 and is decreasing as x approaches positive infinity.
QuestionSolve the inequality 37v < -18 and write the solution in interval notation, using improper fractions if necessary.
Determine if the lines through each pair of points are parallel, perpendicular, or neither.(5, 10) and (1, 6), (2,-6) and (-1, -3)-parallel-perpendicular -neither
Perpendicular
Explanation:Find the slope for the points (5, 10) and (1, 6)
\(x_1=5,\text{ y}_1=10,\text{ x}_2=1,\text{ y}_2=6\)The slope is calculated below
\(\begin{gathered} m_1=\frac{y_2-y_1}{x_2-x_1} \\ \\ m_1=\frac{6-10}{1-5} \\ \\ m_1=\frac{-4}{-4} \\ \\ m_1=1 \end{gathered}\)For the points (2,-6) and (-1, -3)
\(\begin{gathered} m_2=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ m_2=\frac{-3-(-6)}{-1-2} \\ \\ m_2=\frac{-3+6}{-3} \\ \\ m_2=\frac{3}{-3} \\ \\ m_2=-1 \end{gathered}\)Note that:
\(\begin{gathered} m_1m_2=1(-1) \\ \\ m_1m_2=-1 \end{gathered}\)Since the product of the two slopes is -1, the lines through the pairs of points are perpendicular