The mathematics department of a college has 15 male professors, 9 female professors, 6 male teaching assistants, and 12 female teaching assistants. if a person is selected of random from the group, find the probability that the selected person is a professor or a male. The probability is?
Answers
Given:
The number of male professors = 15.
The number of female professors = 9.
The number of male teaching assistants = 6.
The number of female teaching assistants = 12.
A person is selected randomly from the group.
Required:
We need to find the probability that the selected person is a professor or a male.
Explanation:
The total number of people in the group = 15+9+6+12 = 42
n(S) =The total number of people in the group
\(n(S)=42\)Let A be the event that the selected person is a professor or a male.
The number of people who are professors or male = 15+9+6 = 30
n(A)= The number of people who are professors or male.
\(n(A)=30\)Let P(A) be the probability that the selected person is a professor or a male.
\(P(A)=\frac{n(A)}{n(S)}\)\(P(A)=\frac{30}{42}\)\(P(A)=\frac{15}{21}=\frac{5}{7}\)Final answer:
The probability that the selected person is a professor or a male is 5/7.
Related Questions
In a simple linear regression model, if all of the data points fall on the sample regression line, then the standard error of the estimate is
Answers
In a simple linear regression model, the standard error of the estimate (also known as the standard deviation of the residuals) measures the variability or scatter of the observed data points around the sample regression line.
It is an important measure of the accuracy of the regression model and helps us to estimate the uncertainty in making predictions.
If all of the data points fall exactly on the sample regression line, then the residuals (i.e., the differences between the observed values and the predicted values) will be zero for each data point. This means that there is no variability or scatter in the data points around the regression line, and hence the standard error of the estimate will also be zero.
However, this scenario is highly unlikely in real-world situations, as there will always be some random error or measurement noise that affects the observed data points. Therefore, it is important to interpret the standard error of the estimate in the context of the data and the regression model. A smaller standard error of the estimate indicates a better fit of the regression line to the data, whereas a larger standard error of the estimate indicates more variability or scatter in the data points around the regression line.
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URGENT PlZ Help
which statement is an example of the transitive property of congruence
Answers
\(the \: answer \: is \: of \: option \: a \\ \\ for \: example \\ \\ if \: a = b \: and \: b = c \\ then \: we \: can \: say \: a = c \\ hope \: it \: helps\)
Answer:
A is the answer
Step-by-step explanation:
The transitive property is if ABC=DEF and DEF=GHI, then ABC=GHI. The concept is the same here, just with different letters.
A community recreational center has 500 ft of fencing with which to enclose a rectangular parking lot in the back of the property. The building itself will be used as one of the sides of the enclosed area.
What is the maximum area that can be enclosed by the fencing?
Answers
If the building itself will be used as one of the sides of the enclosed area. The maximum area that can be enclosed by the fencing is: 31,250ft².
How to find the maximum area?Let the area be x ft long
Let the width be (500 -x )/2
Hence,
x × (500 - x)/2 = -1/2x² + 250x
When,
x = 250
So,
Maximum area =-1/2 × 250² +250 ×250
Maximum area = -31,250ft + 62,500ft
Maximum area = 31,250ft²
Therefore 31,250ft² is the maximum area.
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Take the derivatives of the following functions. Do not simplify. a. f(x)=10x
4
f(x)= b. f(x)=20x+30x
3
f(x)= c. f(x)=(10+2x
2
)(5x−x
2
)f(x)=
d. f(x)=
20xx
2
f(x)=
Answers
a. f'(x) = 40x³
To find the derivative of f(x) = 10x⁴, we apply the power rule.
The power rule states that if f(x) = axⁿ, then f'(x) = naxⁿ⁻¹. Applying this rule, we get f'(x) = 4 * 10x³ = 40x³.
b. : f'(x) = 20 + 90x²
To find the derivative of f(x) = 20x + 30x³, we differentiate each term separately. The derivative of 20x is 20, and the derivative of 30x³ is 90x² (applying the power rule). Adding these derivatives, we get f'(x) = 20 + 90x².
r: f'(x) = (20x - 4x²)(5x - x²) + (10 + 2x²)(-2x + 5)
To find the derivative of f(x) = (10 + 2x²)(5x - x²), we apply the product rule. The product rule states that if f(x) = g(x) * h(x), then f'(x) = g'(x) * h(x) + g(x) * h'(x). Differentiating each term, we get f'(x) = (20x - 4x²)(5x - x²) + (10 + 2x²)(-2x + 5).
d.: f'(x) = 40x
To find the derivative of f(x) = 20x / (x²), we use the quotient rule. The quotient rule states that if f(x) = g(x) / h(x), then f'(x) = (g'(x) * h(x) - g(x) * h'(x)) / (h(x)²). In this case, g(x) = 20x and h(x) = x². After differentiating and simplifying, we obtain f'(x) = 40x.
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Dan runs for 15 minutes at an average speed of 8 miles per hour.
He then runs for 50 minutes at an average speed of 9 miles per hour.
It takes Carol 75 minutes to run the same total distance that Dan runs.
Work out Carol's average speed.
Give your answer in miles per hour.
Answers
Answer:
Carol's average speed is 7.6 mph
Step-by-step explanation:
yw;)
HELP ASAP YOU GET BRAIBLIEST FOR CORRECT ANSWER
Answers
Answer:
8x+9
if you are happy with my answer, please give brainliest :)
Step-by-step explanation:
Combine like terms:
2x+9+6x=8x+9
Step-by-step explanation:
Combine like terms:
2x+9+6x=8x+9
Answer:
8x+9
Plzzzz give me Brainliest!
Which one is linear or nonlinear?
Answers
Answer:
broo I have to download it just take a screenshot.....
If a mean weight of two groups of children were different with a p level of .03 is the difference statistically significant? What p level identifies statistical significance?
Answers
Yes, if the mean weight of two groups of children is different with a p-value of 0.03, the difference is statistically significant. Typically, a p-value of less than 0.05 is considered statistically significant, indicating that the observed difference is unlikely to be due to chance alone.
Yes, if the p level is .03, then the difference in mean weight between the two groups of children is statistically significant. The p level that identifies statistical significance is generally considered to be .05 or less, meaning that there is a 5% or less chance that the difference observed is due to random chance rather than a true difference between the two groups. Therefore, a p level of .03 is below the commonly accepted threshold for statistical significance and suggests that the difference in mean weight is not likely due to chance alone.
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Please help me with 24For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes.
Answers
Given the equation,
\(-9x^2+72x+16y^2+16y+4=0\)Complete squares as shown below,
\(\begin{gathered} -9x^2+72x-a^2=-(9x^2-72x+a^2)=-9(x^2-8x+b^2) \\ \end{gathered}\)Thus,
\(\begin{gathered} \Rightarrow-9x^2+72x-a^2=-9(x^{}-4)^2 \\ \Rightarrow a^2=16\cdot9=144\Rightarrow a=12 \\ \Rightarrow-9x^2+72x-144=-9(x^{}-4)^2 \end{gathered}\)Similarly,
\(\begin{gathered} 16y^2+16y=16(y^2+y) \\ \Rightarrow16(y+\frac{1}{2})^2=16(y^2+y+\frac{1}{4}) \end{gathered}\)Therefore,
\(\begin{gathered} -9x^2+72x+16y^2+16y+4=0 \\ \Rightarrow-9(x-4)^2+16(y+\frac{1}{2})^2+4=-144+4 \\ \Rightarrow-9(x-4)^2+16(y+\frac{1}{2})^2=-144 \end{gathered}\)Finally, the standard form is.
\(\begin{gathered} \Rightarrow-\frac{(x-4)^2}{16}+\frac{(y+\frac{1}{2})^2}{9}=-1 \\ \Rightarrow\frac{(x-4)^2}{16}-\frac{(y+\frac{1}{2})^2}{9}=1 \end{gathered}\)As for the vertices, foci, and asymptotes,
\(\begin{gathered} c=\pm\sqrt[]{16+9}=\pm5 \\ \text{center:}(4,-\frac{1}{2}) \\ \Rightarrow\text{foci:}(4-5,-\frac{1}{2})_{},(4+5,-\frac{1}{2})_{} \\ \Rightarrow\text{foci:}(-1,-\frac{1}{2}),(9,-\frac{1}{2}) \end{gathered}\)Foci: (-1,-1/2), (9,-1/2)
Vertices
\(\begin{gathered} \text{center:}(4,-\frac{1}{2}),\text{vertices:}(4\pm a,-\frac{1}{2}) \\ \text{vertices:}(4+4,-\frac{1}{2}),(4-4,-\frac{1}{2}) \\ \text{vertices:}(8,-\frac{1}{2}),(0,-\frac{1}{2}) \end{gathered}\)Vertices: (8,-1/2), (0,-1/2)
Asymptotes:
\(\begin{gathered} y=\pm\frac{3}{4}(x-4)-\frac{1}{2} \\ \Rightarrow y=\frac{3}{4}x-\frac{7}{2} \\ \text{and} \\ y=-\frac{3}{4}x+\frac{5}{2} \end{gathered}\)Asymptotes: y=3x/4-7/2 and y=-3x/4+5/2
good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
Answers
Answer:
C
Step-by-step explanation:
Causation is when one thing causes another.
Correlation means one thing is related to another but doesn't cause it.
A - we know more rain means more rainfall which means more water in a river.
B - We know hotter temperature means things melt or evaporate faster.
C - This does not work. How does vision loss cause people to have hearing aids? There might be a correlation but it can't cause it.
D - We know fewer mistakes mean higher grades.
Which situation best demonstrates the phrase "correlation is not causation"?
O As rainfall increases, so does the water level in the river.
O The hotter the temperature, the faster ice will melt
O As the number of people with vision loss increases, the sale of hearing aids increases. ✓
In this case ,the correlation isn't causation because the sale of hearing aids hasn't increased because of increasement in vission loss cases but hearing aids cases but perhaps there's a correction of the sales of hearing aids and vision lossO The fewer mistakes a student makes on a math test, the better their grade is on the math test.
Write down the possible values for n:
-15 < 3n ≤ 6
Answers
Step-by-step explanation:
Move all terms that do not contain nn from the middle section of the inequality.
−5 <n≤2 - 5 <n≤2
Answer:
- 4, - 3, - 2, - 1, 0, 1, 2
Step-by-step explanation:
Given
- 15 < 3n ≤ 6 ( divide the 3 intervals by 3
- 5 < n ≤ 2
Thus n can have values from - 4 to 2, that is
- 4, - 3, - 2, - 1, 0, 1, 2
Question 5. (14 Points)
A message g(t)=16x10³ sinc(16000zt) + 10×10³ sinc(10000zt) +20×10³ sinc(10000zt) cos(30000ft) is sampled at a sampling rate 25% above the Nyquist rate and quantized into L levels. The maximum acceptable error in sample amplitudes is not more than 0.1% of the peak signal amplitude.
1. Sketch the amplitude spectrum of g(t) with the horizontal axis as "f".
2. Sketch the amplitude spectrum of the sampled signal in the range - 50 kHz < f <30 kHz. Label all amplitudes and frequencies.
3. What is the minimum required bandwidth if binary transmission is used?
4. What is the minimum M if the available channel bandwidth is 50 kHz and M-ary multi-amplitude signaling is used to transmit this signal?
5. What is the pulse shape that satisfies M to be minimum?
6. If raised cosine pulse is used in part 4, what is the roll off factor? What is the required M?
7. If delta modulation is used with five times the Nyquist rate, find the number of levels L and the corresponding bit rate.
Answers
It is sampled at a rate 25% higher than the Nyquist rate and quantized into L levels. The maximum acceptable error in sample amplitudes is limited to 0.1% of the peak signal amplitude.
To sketch the amplitude spectrum of g(t), we observe that sinc functions centered at 16 kHz and 10 kHz contribute amplitudes of 16x10³ and 10x10³, respectively, while the cosine component centered at 30 kHz has an amplitude of 20x10³. The horizontal axis represents the frequency (f).
The amplitude spectrum of the sampled signal, within the range -50 kHz to 30 kHz, will exhibit replicas of the original spectrum centered at multiples of the sampling frequency. The amplitudes and frequencies should be labeled according to the replicated components.
The minimum required bandwidth for binary transmission can be determined by considering the highest frequency component in g(t), which is 30 kHz. Therefore, the minimum required bandwidth will be 30 kHz.
For M-ary multi-amplitude signaling within a channel bandwidth of 50 kHz, we need to find the minimum value of M. It can be determined by comparing the available bandwidth with the required bandwidth for each amplitude component of g(t). The minimum M will be the smallest number of levels needed to represent all the significant amplitude components without violating the bandwidth constraint.
To minimize M, we need to select a pulse shape that achieves the narrowest bandwidth while maintaining an acceptable level of distortion. Different pulse shapes can be considered, such as rectangular, triangular, or raised cosine pulses.
If a raised cosine pulse is used, the roll-off factor determines the pulse shape's bandwidth efficiency. The roll-off factor is defined as the excess bandwidth beyond the Nyquist bandwidth. The required M can be calculated based on the available channel bandwidth, the roll-off factor, and the distortion tolerance.
When using delta modulation with a sampling rate of five times the Nyquist rate, the number of levels (L) and corresponding bit rate can be determined by considering the quantization error and the maximum acceptable error in sample amplitudes. The bit rate will be determined based on the number of bits required to represent each level and the sampling rate.
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this was from yesterday and i need to finish it so help me plz
Answers
Answer:
3/4
Step-by-step explanation:
since they already have a common denominator you'd add the numerators and keep the denominator. you'd get 6/8. Then you'd divide both the numerator and denominator by 2. 3/4 is your final answer.
simplify
\(x {}^{a + b } \times x {}^{a + 2b} \times x {}^{2a - 3b} \)
\(x {}^{m} \times x {}^{n} = x {}^{m + n} \)
how to do this
![simplify[tex]x {}^{a + b } \times x {}^{a + 2b} \times x {}^{2a - 3b} [/tex][tex]x {}^{m} \times x {}^{n}](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/gmNibA8pXEThmKVzBa6JbrsF6Yy0i7E6.jpeg)
Answers
that is the answer of pictures ok
![simplify[tex]x {}^{a + b } \times x {}^{a + 2b} \times x {}^{2a - 3b} [/tex][tex]x {}^{m} \times x {}^{n}](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/NyJuGgW1fLxa18AKaftEyteP1qQDzKde.jpeg)
Which ordered pair is on the inverse of f(x)?
(-4,-2)
(-2,-2)
(-1,-2)
Function
X
-4
-2
0
2
4
f(x)
-2
-1
O
1
2
Answers
(-1,-2) is the correct-ordered pair for the inverse of f(x).
What is function?Function is a combination of different types of variable and constants.
A function is denoted by f(x).
The given function is f(x),
inverse function of f(x) is f⁻¹(x),
y=f⁻¹(x)
⇒x= f(y)
Implies that, values interchange in inverse function,
When x=-2, f(x) = -1
Then for inverse function f(x)=-2, and x=-1.
So (-1,-2) is the correct-ordered pair for the inverse of f(x).
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Suppose Q and R are independent events. Find P(Q and R). P(Q)=0.37,P(R)=0.24
Answers
To find P(Q and R), we can use the formula: P(Q and R) = P(Q) × P(R) Since the events Q and R are independent, we can multiply the probabilities of each event to find the probability of both events occurring together. P(Q) = 0.37P(R) = 0.24P(Q and R) = P(Q) × P(R) = 0.37 × 0.24 = 0.0888.
Therefore, the probability of both Q and R occurring together is 0.0888. Long Answer:Independent events:In probability theory, two events are independent if the occurrence of one does not affect the probability of the occurrence of the other. Two events A and B are independent if the probability of A and B occurring together is equal to the product of the probabilities of A and B occurring separately. Mathematically,P(A and B) = P(A) × P(B) Suppose Q and R are independent events. Find P(Q and R).
We can use the formula: P(Q and R) = P(Q) × P(R) Since the events Q and R are independent, we can multiply the probabilities of each event to find the probability of both events occurring together. P(Q) = 0.37P
(R) = 0.24
P(Q and R) = P(Q) × P(R)
= 0.37 × 0.24
= 0.0888
Therefore, the probability of both Q and R occurring together is 0.0888. Hence, P(Q and R) = 0.0888. In probability theory, independent events are the events that are not dependent on each other. It means the probability of one event occurring does not affect the probability of the other event occurring.
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As part of a grand opening, an arcade gave out free tokens to the first 100 customers. If you spent $5, you got 61 tokens. If you spent $6, you got 72 dollars, if you spent $7 you got 83. Construct an equation in y = mx + b
Answers
Answer:
your teacher is they are giving out FREEE tokens so why do you have to pay
Step-by-step explanation
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Use equation, find the maximum height reached by the rocket, to the nearest 10th of a foot . Y=-16x^2+261x+130
Answers
Answer:
Maximum height of the rocket = 1194.39 feet.
Step-by-step explanation:
The equation that shows the height of the rocket, y in feet, is related to the time after launch, x in seconds is as follows :
\(y=-16x^2+261x+130\) ...(1)
We need to find the maximum height reached by rocket. For maximum height,
\(\dfrac{dy}{dx}=0\\\\\dfrac{d(-16x^2+261x+130)}{dx}=0\\\\-32x+261=0\\\\x=\dfrac{261}{32}\\\\x=8.15\ s\)
Put x = 8.15 s in equation (1).
\(y=-16(8.15)^2+261(8.15)+130\\\\y=1194.39\ \text{feet}\)
So, the maximum height of the rocket is 1194.39 feet.
Calculate the slope of the line that passes through (12,15) and (10, 21). Reduce answer to lowest terms if
necessary
Answers
Answer:
-3
Step-by-step explanation:
Slope is rise divided by run. Y2-Y1 Divided by X2-X1
You get 6 divided by -2
-3
The equipment will cost $26,000. What lump sum should be invested today at 6%, compounded semiannually, to yield $26,000?a. $ 17,189.06 b. $ ...
Answers
To yield $26,000 in the future, compounded semiannually at an interest rate of 6%, a lump sum investment needs to be made today. The correct amount to invest can be calculated using the present value formula.
The present value formula can be used to calculate the amount that should be invested today to achieve a specific future value. The formula is given by:
PV = FV / (1 + r/n)^(n*t)
In this case, the future value (FV) is $26,000, the interest rate (r) is 6%, and the compounding is semiannually (n = 2). We need to solve for the present value (PV).
Using the formula and substituting the given values:
PV = 26,000 / \((1 + 0.06/2)^(2*1)\)
PV = 26,000 / \((1.03)^2\)
PV = 26,000 / 1.0609
PV ≈ $24,490.92
Therefore, the correct lump sum to invest today, at 6% compounded semiannually, to yield $26,000 in the future is approximately $24,490.92.
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Please help. I don't know the answer
Answers
Answer:
The answer is 3x+4y<-12
Step-by-step explanation:
(3x+10)(2x^2+1)(2-x)>0
Answers
After solving the given expression (3x+10)(2x²+1)(2-x)>0 the answer is
(- 6x⁴ - 3x³ + 37x² - 4x + 20) > 0.
What are expressions?A group of numbers or variables combined with the operations +, –, × or ÷ form an expression.Algebraic expressions with variables, numbers, and mathematical operators, as opposed to arithmetic expressions that only contain numbers and mathematical operators.So, (3x+10)(2x²+1)(2-x)>0:
Solve the expression as follows:
3x{(2x²+1)(2-x)} + 10{(2x²+1)(2-x)}3x{(2x²(2-x)+1(2-x)} + 10{(2x²(2-x)+1(2-x)}3x{4x² - 2x³ + 2 - x} + 10{4x² - 2x³ + 2 - x}12x³ - 6x⁴ + 6x - 3x² + 40x² - 20x³ + 20 - 10x- 6x⁴ + 12x³ - 20x³ + 40x² - 3x² + 6x - 10x + 20- 6x⁴ - 3x³ + 37x² - 4x + 20 > 0Therefore, after solving the given expression the answer is (- 6x⁴ - 3x³ + 37x² - 4x + 20) > 0.
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I WILL GIVE BRAINLIEST what comes next butter dog-
Answers
Answer:
the dog with the butter-butter dog
Step-by-step explanation:
:)
Answer:
DOG WITH THE BUTTER
Step-by-step explanation:
Mike has $84 less than three times as much as Dave. Together they have $132. How much money does Mike have?
I have to use either the system of equation strategy of elimination or substitution to solve this. I realize that the first equation is
m + d = 132. But I don’t get what the second equation should be!
Answers
Answer: $48
Step-by-step explanation:
132 - 84 = 48
If a = 6, then the value of b is...
Answers
Answer:
6/- 3
Step-by-step explanation:
Joseph has a bag filled with 3 red, 3 green, 9 yellow, and 10 purple marbles. Determine P(not purple) when choosing one marble from the bag. 60% 40% 24% 10%
Answers
The probability of not selecting a purple marble when choosing one marble from the bag is 60%.
To determine the probability of not selecting a purple marble when choosing one marble from the bag, we need to find the number of marbles that are not purple and divide it by the total number of marbles in the bag.
The number of marbles that are not purple is the sum of red, green, and yellow marbles. Therefore, the number of marbles that are not purple is 3 + 3 + 9 = 15.
The total number of marbles in the bag is the sum of all the marbles: 3 + 3 + 9 + 10 = 25.
So, the probability of not selecting a purple marble is 15/25 = 0.6, which is equivalent to 60%.
Therefore, the probability of not selecting a purple marble when choosing one marble from the bag is 60%.
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This meal costs $19.00 .A sales tax is applied, followed by an automatic tip of 18 %.What is the total with tax and tip?
Answers
The total cost of he meat with tax and tip is $ 22.42
How to find the totalTo calculate the total cost with tax and tip, we need to follow these steps:
multiply the meal cost by the tip rate. when the tip rate is 18%, we have:
Tip amount = $19.00 * 0.18 = $3.42
Add the meal cost, sales tax, and tip amount to get the total cost:
Total cost = Meal cost + Sales tax + Tip amount
= $19.00 + $3.42
= $ 22.42
Therefore, the total cost with tax and tip is $22.42
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If correct brainlist
Answers
Answer: Its D positive
Step-by-step explanation:
Answer: B pls vote branliest
Step-by-step explanation:
The AID Parcel Service wants to build a new distribution center in Charlotte. The center needs to be in the vicinity of Inerstate-77 and Intersatate-85 interchanges, and the Charlotte International Airport. The coordinates of these three sites and the number of weekly packages that flow to each are as follows:
I-77 I-85 Airport
X=16 X=35 X=40
Y=28 Y=10 Y=18
W=26,000 W=12,000 W=10,000
Determine the best site location using the center-of-gravity technique
Subject - Logistics management
Answers
Using the center-of-gravity technique, the best site location for the new distribution center in Charlotte is determined to be at coordinates (X, Y) = (27.92, 19.08).
The center-of-gravity technique is used to find the optimal location for a facility based on the distribution of demand. In this case, we will calculate the weighted average of the coordinates (X, Y) of the three sites, with the weights being the number of weekly packages flowing to each site.
To calculate the X-coordinate of the center of gravity, we use the formula:
Xc = (X1 * W1 + X2 * W2 + X3 * W3) / (W1 + W2 + W3)
Similarly, for the Y-coordinate:
Yc = (Y1 * W1 + Y2 * W2 + Y3 * W3) / (W1 + W2 + W3)
Substituting the given values:
Xc = (16 * 26000 + 35 * 12000 + 40 * 10000) / (26000 + 12000 + 10000) ≈ 27.92
Yc = (28 * 26000 + 10 * 12000 + 18 * 10000) / (26000 + 12000 + 10000) ≈ 19.08
Therefore, the best site location for the new distribution center in Charlotte is approximately at coordinates (X, Y) = (27.92, 19.08) based on the center-of-gravity technique.
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help me asap pleasee
Answers
The equivalent expression for \(\left(\frac{1.4^2}{1.2^4}\right)^{-6}\)is (D) \(\frac{1.2^{24}}{1.4^{12}}\).
The product of same base different exponent is given by the sum of exponents with same base.
Any power value of 1 is alsways 1.
Given that the expression is
\(\left(\frac{1.4^2}{1.2^4}\right)^{-6}=\frac{1^{-6}.4^{-12}}{1^{-6}.2^{-24}}=\frac{1.2^{24}}{1.4^{12}}\)
Hence the correct option is (D).
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