The Coordinates of the centroid of a triangle with the given vertices are (0, 4), (8, 10) and (6, 1) is (14/3, 5) and Centroid of triangle with vertices (1,5),(3,8),(0,2) is (4/3, 5).
What is Centroid of a triangle?The centroid of a triangle is one of the point where all three medians of the triangle intersect. The median is a line segment drawn from one vertex to the midpoint on the opposite side. Triangle centroid divides each median into individual words in a 2:1 ratio. The centroid is usually at 2/3 of the median.
If the three vertices of a triangle are A(x₁,y₁) B(x₂,y₂), C(x₃,y₃), the centroid of the triangle is given by the formula :
G(x₁+x₂+x₃/3, y₁+y₂+y₃/3 ).
We have , two triangles with vertices,
a) triangle whose vertices are A(0, 4), B(8, 10) and C(6, 0). So, the coordinates of the centroid of a triangle whose vertices are (0, 4), (8, 10) and (6 , 1) are ( (0+8+6)/3 , (4+10+1)/3 ) or (14/3, 5).
b) triangle whose vertices are P(1, 5), Q(3,8) and R(0, 2). So, the coordinates of the centroid of a ∆PQR are ( (1+3+0)/3 , (5+8+2)/3 ) or (4/3, 5).
Hence, the required coordinates of Centroid are (14/3, 5), (4/3, 5).
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Complete question:
Coordinate geometry find the coodinates of the centroid of each triangle with the given vertices are a) (0, 4), (8, 10) and (6, 1)
b) (1,5),(3,8),(0,2)
What percent of 75 is 36?
Answer:
48%
Step-by-step explanation:
Finding percents
P * 75 = 36
Divide each side by 75
P = 36/75
P =.48
Change to percent form
P = 48%
Answer:
48%%%%%
Step-by-step explanation:
3
Gerry and Claire have been out walking using a map with a scale of 2 cm: 1 km.
The distance they have walked on the map is 14 cm.
How far have they actually walked?
Answer:
7 km
Step-by-step explanation:
14/2 cm which equals 7km
based on the text, what is the meaning of collinear? responses a unconnected to any sort of lineunconnected to any sort of line b equally distant in every directionequally distant in every direction c lying on or passing through the same linelying on or passing through the same line d connected sections along a curved lineconnected sections along a curved line
On solving the provided question, we can that the answer - The distance between two points is the length of a line segment that connects them.
What is straight lines?A line is a shape that has no width, depth, or curve in its geometry. It is an item that can be used for a long time. A line can exist in a two-dimensional, three-dimensional, or more dimensional space, but is still a one-dimensional object. A line segment with two endpoints is commonly called a "line".
Main notations:
A plane is a flat, indefinitely long, 2D surface with no thickness. Option 1 is accurate. A point is a precise place. It just has position; it has no length, breadth, or depth. Option 2 is untrue. Collinear points are any two or more points that are situated differently yet are on the same line. Option 3 is untrue. A line has no thickness, is straight (has no bends), and goes in both directions without ending (infinitely). Option 4 is accurate. The length of a line segment that links two places represents their distance. Option 5 is accurate.
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How long does it take for an investment of $6,400 to increase to $14,000 if
it is invested at 5% per year compounded continuously? Round to the
nearest tenth of a year.
An investment of $6,400 to increase to $14,000 if it is invested at 5% per year compounded continuously is ≈15.6
Define compound interest?
Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods.Given that :
P = $ 6,400
Q = $ 14,000
r = 5%
Let P be the initial investment
r be the rate of interest
t be the time
Q be the increase amount
Q = P [tex]e^{rt} }[/tex]
14,000 = 6,400 ([tex]e^{0.05t}[/tex])
[tex]e^{0.05t}[/tex] = [tex]\frac{14000}{6400}[/tex]
[tex]e^{0.05t}[/tex] = 2.187
Taking log on both sides , we get
0.05t = ln (2.187)
0.05t = 0.78
t = [tex]\frac{0.78}{0.05}[/tex]
t ≈ 15.6
An investment of $6,400 to increase to $14,000 if it is invested at 5% per year compounded continuously is ≈ 15.6
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Suppose a certain state university's college of business obtained the following results on the salaries of a recent graduating class:Finance Majors Business Analytics Majorsn1 = 140 n2 = 30x1 = $48,237 x2 = $55,417s1 = $19,000 s2 = $10,000(a) Formulate hypotheses so that, if the null hypothesis is rejected, we can conclude that salaries for Finance majors are significantly lower than the salaries of Business Analytics majors. Use α = 0.05. (Let μ1 = the population mean salary for Finance majors, and let μ2 = the population mean salary for Business Analytics majors.
b) What is the value of the test statistic? (Use μ1 − μ2. Round your answer to three decimal places.)
(c)What is the p-value? (Round your answer to four decimal places.)
(d) What is your conclusion?
Reject H0. We can conclude that salaries for Finance majors are significantly lower than the salaries of Business Analytics majors.
Do not reject H0. We can conclude that salaries for Finance majors are significantly lower than the salaries of Business Analytics majors.
Reject H0. We cannot conclude that salaries for Finance majors are significantly lower than the salaries of Business Analytics majors.
Do not reject H0. We cannot conclude that salaries for Finance majors are significantly lower than the salaries of Business Analytics majors.
Using the confidence interval and null hypothesis we can conclude that the salaries for the finance majors are significantly lower than the salaries of the business analytics majors.
a) The null and alternative hypothesis is given by
H₀: μ1 − μ2 = 0
H₁: μ1 − μ2 < 0
b) Test statistic is given by [tex]\frac{\bar{x}_1-\bar{x}_2-0}{\sqrt{\frac{S_1^2}{n_1}+\frac{S_2^2}{n_2}}}[/tex]
here:
S₁ = 19000
S₂ = 10000
x₁ = 48237
x₂ = 55217
n₁ = 120
n₂ = 30
Putting the above values we get:
[tex]z=\frac{48237-55217}{\sqrt{\frac{19000^2}{120}+\frac{10000^2}{30}}}[/tex]
or, z = -2.7717744...
or, z ≈ -2.772
c) p-value
= P(Z<-2.772)
= 0.002786
= 0.0028
d) now we will use the p-value to essentially use or reject the the hypothesis.
So the confidence interval of 955 is used for the p-value.
p-value(0.0028) < ∝(0.05)
Hence we will reject the H₀ .
Hence we will conclude that the salaries for the finance majors are significantly lower than the salaries of the business analytics majors.
A confidence interval is a range of estimates for an unknown parameter (CI). The most common confidence level is 95%, but when calculating confidence intervals, other levels, such 90% or 99%, are also occasionally employed.
The confidence level is a measure of how many related CIs over the long run include the actual value of the parameter. For instance, the parameter's true value should be included in 95% of all intervals produced at the 95% confidence level.
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A researcher claims that the yearly consumption of soft drinks per person is 52 gallons. In a sample of 50 randomly selected people, the mean of the yearly consumption was 56.3 gallons. The standard deviation of the population is 3.5 gallons. Is the researcher's claim valid? alpha = .05 Find the P-Value, state what your final decision will be based on alpha = .05 and why?
The researcher claim is invalid and the p-value based on alpha = 0.05 is approx. = 0.
In the question ,
it is given that ,
a researches claims that per person yearly consumption (μ) is 52 gallons .
sample size (n) = 50 .
the mean of the consumption (x) = 56.3 .
the standard deviation (σ) is = 3.5 gallons .
the α = 0.05 .
let the null hypothesis ,
H₀ : μ = 52 and
H₁ : μ ≠ 52 .
the test statistics is : z = (x - μ)/(σ/√n)
the critical value ( rejection region ) : {z : |z| ≥ z₀.₀₂₅ = 1.96 }
So , z = (56.3 - 52)/(3.5/√50)
Simplifying further ,
we get ,
z = 8.69
We reject the null hypothesis H₀ , since the absolute value of the test statistics 8.69 is greater than the critical value 1.96 .
Since this is a two tailed test, p-value must be multiplied by two
2 × P(z > 8.69) ≈ 0
Since the p-value is less than α(0.05), So ,we reject the claim of the researcher that the mean yearly consumption of soft drinks per person is 52 gallons
Hence , the claim is not valid .
Therefore , The claim is invalid and p-value is ≈ 0 .
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This right circular cone has radius 2p and height
5p.
The dimensions are in centimetres.
The volume of the cone is 22500 cm³.
Work out the value of p
How do i work this out?
Answer:
p ≈ 10.24 cm
Step-by-step explanation:
r = 2p
h = 5p
Volume of a cone = (1/3)πr²h
22,500 = (1/3)π(2p)²(5p)
Now solve for p:
67500 = π4p²5p
67500 = π20p³
p³ = (67500)/π20 = 1074.3
p = ∛1074.3
p ≈ 10.24 cm
Use a generating function for modeling the number of different selections of r hot dogs when there are four types of hot dogs.
Using generating function number of different selections of r hot dogs when there are four types of hot dogs are g(x) = ( 1/(1-x) )⁴.
What is Generating function?For a sequence a₀,a₁,...,aₙ,... the corresponding generating function f(x) is the sequence
f(x)=a₀+a₁x+...+aₙxₙ+...= ∑aᵢxᵢ , 0 ≤ i ≤ ∞
Since here we have 4 types of hot dogs, from which we need to select "r" hot dogs, we would use a generating function as follows:
There can be any number of selections from any pile of hot dogs ( repitions is allowed). therefore, from each pile, you could pick up 1 or 2 or 3 or ... hot dogs. The same would go for all types of hot dogs. Therefore ,the generating function for the same would be,
g(x) = (1 + x + x² + x³ + x⁴ + ...)(1 + x + x² + x³ + x⁴ + ...)(1 + x + x² + x³+ x⁴ + ...)(1 + x + x² + x³+ x⁴+ ...)
Therefore, g(x) = (1 + x + x² + x³ + x⁴ + ...)⁴
This is an infinite geometric series, which can be solved to give the sum: g(x) = ( 1/(1-x) )⁴. Therefore, our required the coefficient of xʳ in (1/ (1-x) )⁴.
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11. Members of the student council are conducting a fundraiser by selling school calendars. After selling 80 calendars, they had a loss of $ 360. After selling 200 calendars, they had a profit of $600. Write an equation that describes the relation between y, the profit or loss, and x, the number of calendars sold. How much profit did they make from selling each calendar? How much would they have lost if they had sold no calendars?
a) The equation that describes the relation between x and y is y = 8x - 1000
b) They made 8% profit from selling the calendars
c) They will loss 1000 when they sold no calendars.
Given,
Members of student council had a loss of $360 after selling 80 calenders
They made a profit of $600 after selling 200 calenders.
y be the profit or loss
x be the calendars sold
We have to find the following;
a) The equation of the line in Slope-Intercept form is:
y = mx + b
Where "m" is the slope and "b" is the y-intercept.
We are aware that "y" here stands for the profit or loss and "x" for the quantity of calendars sold.
Then,
According to the exercise, the line passes through these two points:
(80, -360) and (200, 600)
Then,
We can find the slope of the line with the formula;
m = (y₂ - y₁) / (x₂ - x₁)
m = (-360 - 600) / (80 - 200)
m = -960/-120
m = 8
Now,
We can substitute the slope and one of those points into y = mx + b and solve for "b":
600 = 8 × 200 + b
-b = 1600 - 600
b = -1000
Then,
Substituting values, we get that the equation that describes the relation between the profit and loss and the number of calendars sold, is:
y = 8x - 1000
b) The slope of the line is the profit they made from selling each calendar
Profit = 8
c) The y-intercept is the amount they would have lost if they had sold no calendars:
b = -1000
They'd have lost $1000 if they had sold no calendars.
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use the student's t -distribution to find the t -value for each of the given scenarios. round t -values to four decimal places. find the value of t such that the area in the left tail of the t -distribution is 0.05, if the sample size is 48. t
the value of t such that the area in the left tail of the t -distribution is 0.05, if the sample size is 48. t is 0.76197086
Consider a t distribution with 7 degrees of freedom. Compute P(-1.29 < t < 1.29)
P(-1.29 < t < 1.29) would be the area under the t distribution curve with 7 degrees of freedom between -1.29 and 1.29, that is in the interval (-1.29, 1.29).
This can be done the old style by looking up in a table or by using the technology with a spreadsheet.
In Excel, the function TDIST(x,n,2) with x>0 gives the area outside the interval (-x, x) of the t distribution with n degrees of freedom.
So TDIST(1.29,7,2) gives the area outside (-1.29, 1.29).
If we subtract this value from 1 we get the desired result
Hence
P(-1.29 < t < 1.29) = 1 - TDIST(1.29,7,2) = 1 - 0.23802914 = 0.76197086
In OpenOffice Calc, the function is the same replacing “,” with “;”
That is
P(-1.29 < t < 1.29) = 1 - TDIST(1.29;7;2) = 0.76197086
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the random variable w can take on the values of 0, 1, 2, 3, or 4. the expected value of w is 2.8. which of the following is the best interpretation of the expected value of random variable w ?
The correct answer is Option E, For values of W repeatedly selected at random from the distribution the mean of the selected values will approach 2.8.
The expected value can be found by using the formula ∑x*p(x)
The random variable W can take on the values of 0, 1, 2, 3, or 4. The expected value of W is 2.8.
Expected value (EV) describes the long-term average level of a random variable based on its probability distribution.
The expected value can be found by using the formula ∑x*p(x)
A randomly selected value of W must be equal to 2.8.
This is not true as the expected value is like the average
B The values of W vary by about 2.8 units from the mean of the distribution.
This is not true, as it is not the difference between an observation to its mean.
с The mean of a random sample of values selected from the distribution will be 2.8 It is false
D A value of randomly selected from the distribution will be less than 2.8 units of the mean. This statement is also false
E For values of W repeatedly selected at random from the distribution the mean of the selected values will approach 2.8.
Thus the correct answer is Option E, For values of W repeatedly selected at random from the distribution the mean of the selected values will approach 2.8.
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What would be great resources
Answer:
depends for what?
Step-by-step explanation:
for shoes, stationary, clothes etc be a bit specific
How many different ID cards can be made if there are seven digits on a card and no digit can be used more than once? What if digits can be repeated?
The number of ID cards when no digit can be used more than once is 604,800 and when the digits can be repeated it will be 10,000,000 ID cards.
What is Permutations?Permutations are several ways to arrange things in a specific sequence. It can alternatively be stated as the linear reordering of items within an ordered set.
As per the given information in the question,
Let's first make a list of all the potential outcomes. As follows:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
a.
No numeral may be used multiple times in the first instance.
Therefore,
10 × 9 × 8 × 7 × 6 × 5 × 4
= 604,800 ID cards
b.
In the second scenario, assuming it is possible to repeat the digits, then,
10 × 10 × 10 × 10 × 10 × 10 × 10 = 10,000,000 ID cards.
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Two equalities that are equivalent
Answer:
there is 2/8 and 3/12 .they are both equivalent to each ,and equal 1/4.2 is 1/4 of because 2×4=8 is 1/4 of 12 because 3×4=12.
josh is 4 years older than 2 times kim's age. the sum of their ages is less than 25. what is the oldest kim could be? select the correct inequality for the situation, then determine the oldest age kim could be. select 2 correct answer(s) question 6 options: (4 2k) k > 25 (4 2k) k < 25 4 2k > 25 4 2k < 25 the oldest kim could be is 4. the oldest kim could be is 5. the oldest kim could be is 6. the oldest kim could be is 7.
The inequality for the situation is 2x + 4 < 25 and the oldest age of Kim is 10 years old
The inequality is the mathematical statement that shows the relationship between two expressions with inequality sign. The inequality signs are less than, less than or equal, greater than, greater than or equal.
Consider the Kim's age as x
Josh is 4 years older than 2 times Kim's age
Two times Kim's age = 2x
4 years older than 2 times Kim's age = 2x + 4
The age of Josh = 2x + 4
Sum of their ages is less than 25
The inequality is
2x + 4 < 25
2x < 21
x < 21/2
x < 10.5
Therefore, the oldest age of Kim is 10 years old and the inequality is 2x + 4 < 25
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Calculate the probability of being dealt the following poker hand. (Recall that a poker player is dealt 5 cards at random from a standard deck of 52.) Express your answer as a decimal rounded to four decimal places.HINT [See Example 3.] Two pairs: Two cards with one denomination, two with another, and one with a third. Example: 3, 3, Q , Q , J.
Answer:
Step-by-step explanation:
The odds of selecting 5 cards from a deck of 52 are 52c5. Probability = Maximum outcomes / Possible outcomes for the given circumstance = 52!/47!*5! = 2598960. Now, in poker, the chance of selecting any two numbers from a pool of 13 distinct numbers is 13c2.
Possible poker hands
C(n,r)= C(52,5)
=52!/(5!(52-5!)
=2598960
Hand with pattern
(X,X,Y,Y,Z)
Number of choices for x and y
C(n,r)= C(13,2)
=13!(2!(13-2)!)
=78
Ways to get 2 X's
C(n,r)= C(4,2)= 4!(2!(4-2)!) =6
Similarly, ways to get 2x's is 6
We have 44 choice of occurance for Z
Hands with two pairs =78*44*6*6= 123552
So, Probability of Two pairs is =123552/2598960=0.047539
P(Two pairs) = 0.0475
How many ways can we choose two pairs in a poker hand?
There are 13 ways to choose the denomination of the first pair, 12 ways to choose the denomination of the second pair, and 4 choices for the remaining card. Thus, there are 13\cdot 12\cdot 4 = 624 ways to choose two pairs in a poker hand.
In poker, a hand is made up of 5 cards from a deck of 52 cards. The different possible hands in poker include a royal flush, straight flush, four of a kind, full house, flush, straight, three of a kind, two pair, and one pair.
In this problem, we are asked to find the probability of getting a hand with two pairs.
To find the probability of two pairs, we first need to find the total number of possible poker hands. This is done using the combination formula C(n,r) where n is the total number of cards (52 in this case) and r is the number of cards needed to make a hand (5 in this case). This gives us a total of 2598960 possible poker hands.
Next, we need to find the number of possible hands with two pairs. A hand with two pairs has a pattern of X,X,Y,Y,Z where X and Y are the ranks of the pairs and Z is the remaining card. There are 13 ranks in a deck of cards (Ace, 2, 3, ..., 10, Jack, Queen, King) and we need to choose 2 of these ranks to be the ranks of the pairs. This can be done in C(13,2) ways, which is 78.
There are 4 cards of each rank in a deck, so there are 6 ways to choose the 2 cards of rank X and 6 ways to choose the 2 cards of rank Y.
Finally, we have 44 choices for the remaining card (Z) because there are 13 ranks and we have already used up 2 ranks for the pairs.
Therefore, the number of possible hands with two pairs is 78*6*6*44 = 123552. The probability of getting a hand with two pairs is then 123552/2598960 = 0.047539 or approximately 0.0475.
Therefore, the final answer is P(Two pairs) = 0.0475.
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Answer: The probability of receiving a hand with two pairs is 0.04322.
Step-by-step explanation:
How many ways are there in a poker hand to pick two pairs?
There are 13 ways to choose the denomination of the first pair, 12 ways to choose the denomination of the second pair, and 4 choices for the remaining card. Thus, there are 13*12*4 = 624 ways to choose two pairs in a poker hand.
In poker, a hand is made up of 5 cards from a deck of 52 cards. The different possible hands in poker include a royal flush, straight flush, four of a kind, full house, flush, straight, three of a kind, two pair, and one pair.
To choose the denominations of the two pairings, there are C(13,2)=78 possible options. There are C(4,2)=6 methods to select the two cards in each pair for each of these approaches. The remaining card's denomination can be determined in C(4,1)=4 different ways. As a result, there are 78*6*6*4=11232 different ways to deal a hand with two pairs.
A hand of five cards can be dealt in C(52,5)=2598960 different ways. Therefore, the probability of receiving a hand with two pairs is 11232/2598960=0.04322.
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If two loads are applied to a cantilever beam as shown in the drawing below, the bending moment at 0 due to the load is a1X1+a2X2.
Suppose that X1 and X2 are independent random variables with means of 2 and 4 kips respectively, and standard deviations pf .5 and 1 kip, respectively. If a1 = 5 ft and a2 = 10 ft, what is the expected bending moment and what is the standard deviation of the bending moment?
b) If X1 and X2 are normally distributed, what is the probability that the bending moment will exceed 75 kip-ft?
c) Suppose the positions of the two loads are random variables. Denoting them by A1 and A2, assume that these variables have means 05 5 and 10 ft, respectively, that each has a standard deviation of .5, and that all Ai's and Xi's are independent of one another. What is the expected moment now?
d) For the situation of part (c), what is the variance of the bending moment?
e) IF the situation is as described in part (a) except that Corr(X1, X2) = .5 (so that the two loads are not independent), what is the variance of the bending moment?
Answer: Step-by-step explanation:
Tan(300°)=z/7
What is z?
Answer:
x = -7 sqrt(3)
Step-by-step explanation:
Tan(300°)=z/7
Multiply each side by 7
7 Tan(300°)=z
Replacing tan 300 with tan 120 since they are equal
7 Tan(120°)=z
7 ( - sqrt(3)) = z
x = -7 sqrt(3)
What is the value of q?
O 4√5
O 2√14
O 20√5
O 64√5
Found the answer thought I would help
The measure of the length (q) of the right-angle triangle will be 2√14 units. Then the correct option is B.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The right-angle triangles are shown.
In similar triangles ΔQTS and ΔSTR, we have
ST / TR = QT / ST
ST / 4 = 10 / ST
s² = 40
Then the measure of the length (q) is given as.
q² = s² + 4²
q² = 40 + 16
q² = 56
q = 2√14
The measure of the length (q) of the right-angle triangle will be 2√14 units. Then the correct option is B.
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Given the following data sample, how confident can we be that the mean is greater than 40? 64 70 20 58 13 74 84 47 17 2. You are given the following sample of annual returns for portfolio manager: If you believe that the distribution of returns has been stable over time and will continue to be stable over time; how confident should you be that the portfolio manager will continue to produce positive returns? -7% 7% 19% 23 % -18 % -12% 49% 34% ~6% -20% 3 . You are presented with an investment strategy with a mean return of 20% and standard deviation of 10%_ What is the probability of a negative return if the returns are normally distributed? What if the distribution is symmetrical, but otherwise unknown?'
The probability of a negative return if the returns are normally distributed, we can use the mean and standard deviation of the returns and If the distribution is symmetrical but otherwise unknown, it may be more difficult to estimate the probability of a negative return without more information about the shape of the distribution.
To determine how confident we can be that the mean of the given data sample is greater than 40, we would need to perform a statistical test such as a t-test or a z-test to compare the sample mean to the value of 40.
We would need to know the sample size, standard deviation, and any other relevant information about the data to calculate the appropriate test statistic and determine the p-value, which would tell us the probability of observing a sample mean as extreme as the one we obtained if the true population mean was actually 40.
To determine how confident we should be that the portfolio manager will continue to produce positive returns, we would need to analyze the distribution of returns and determine whether it is skewed or symmetrical and whether it follows a normal distribution or a different distribution. If the distribution is skewed or non-normal, it may be more difficult to estimate the probability of positive returns. However, if the distribution is symmetrical and follows a normal distribution, we can use the mean and standard deviation of the returns to calculate the probability of a positive return using the normal distribution.
If the returns of the investment strategy are normally distributed, we can use the mean and standard deviation of the returns to calculate the probability of a negative return using the normal distribution. If the distribution is symmetrical but otherwise unknown, it may be more difficult to estimate the probability of a negative return without more information about the shape of the distribution.
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The question is -
Given the following data sample, how confident can we be that the mean is greater than 40? 64 70 20 58 13 74 84 47 17 2. You are given the following sample of annual returns for the portfolio manager: If you believe that the distribution of returns has been stable over time and will continue to be stable over time; how confident should you be that the portfolio manager will continue to produce positive returns? -7% 7% 19% 23 % -18 % -12% 49% 34% ~6% -20% 3. You are presented with an investment strategy with a mean return of 20% and a standard deviation of 10%_ What is the probability of a negative return if the returns are normally distributed? What if the distribution is symmetrical but otherwise unknown?'
A cart has 5 boxes on it. Each box weighs 70 pounds. The boxes will be removed from
the cart, one at a time. Which function models the relationship between x, the number of
boxes that have been removed from the cart, and y, the total weight, in pounds, of the
boxes remaining on the cart?
y=-70x+5
B) y = -5x + 350
y = 50x + 70
= 52 +350
D) y =
Y =
Pre calc
Solve e^2x +3e^x- 28=0
Answer:
x=ln(4)
Step-by-step explanation:
e^2x +3e^x- 28=0
u^2 + 3u - 28 = 0 ==> substitute u for e^x
u^2 - 4u + 7u - 28 = 0
u(u-4) + 7(u-4) = 0
(u-4)(u+7)=0 ==> simplify
u-4=0 u+7=0
u=4 u=-7
e^x=4 e^x=-7 ==> substitute e^x for u
ln(e^x)=ln(4) ln(e^x)=-7 ==> take natural log on each side
x=ln(4) x=ln(-7), which is not possible since natural log>0
x=ln(4)
Answer:
[tex]{e}^{x} = y \\ {y}^{2} + 3y - 28 = 0 \\ (y - 4)(y + 7) = 0 \\ y = 4 \\ y = - 7 \\ {e}^{x} = 4 \\ x = ln(4) \\ x = ln( - 7)[/tex]
c) Assume that the sample points in each interval are right endpoints. Find the following sample points:x 1 = 0∘x 2 =08x 3=0 8
Each interval's sample points are at the right ends. sample points :x 1 = 0∘x 2 =08x 3=0 8 is 0°, 8°, 16°
Since the sample points in each interval are right endpoints, we need to find the points that are 8° apart.
The first sample point x1 is 0°. To find the next two sample points, we need to add 8° to the first sample point.
Therefore, the second sample point x2 = 8°, and the third sample point x3 = 16°.
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Calculate the difference and enter below. -4 + (-4)
Answer: -8
Step-by-step explanation: When adding 2 negative numbers, you go farther back left on the number line. (Negative side) So, 4 + 4 = 8, and a negative + a negative = negative, so this results in -4 + (-4) = -8. I hoped this helped!
Alvin, Simon and Theodore do volunteer work at Adopt-a-Pet Animal Shelter. They worked a total of 284 hours at the shelter last summer. Alvin worked 15 hours more than Simon. Theodore worked 6 less than three times as many hours as Simon.
Write and solve an equation that expresses the relationship between the number of hours each person worked last summer and the total number of hours worked. Define the variable used in your equation. SHOW ALL WORK!!!!
How many hours did each person work?
Again, SHOW ALL WORK!!!!
Answer:
Therefore, Alvin worked 70 hours, Simon worked 55 hours, and Theodore worked 159 hours
Step-by-step explanation:
Let A be the number of hours Alvin worked, S be the number of hours Simon worked, and T be the number of hours Theodore worked.
We know that the total number of hours worked is the sum of the hours each person worked, so we can write the equation:A + S + T = 284
We also know that Alvin worked 15 more hours than Simon, so we can write the equation:A = S + 15
We also know that Theodore worked 6 less than three times as many hours as Simon, so we can write the equation:T = 3S - 6
Substituting the second equation into the first equation, we get:
S + S + 15 + 3S - 6 = 284
Combining like terms, we get:5S + 9 = 284
Subtracting 9 from both sides, we get:5S = 275
Dividing both sides by 5, we get:S = 55
Substituting this value into the equation A = S + 15, we get:
A = 55 + 15A = 70
Substituting this value into the equation T = 3S - 6, we get:T = 3 * 55 - 6T = 165 - 6T = 159
2/3x+5/6=1/2(x-1/3) simplify the algebraic expression
After solving the given expression, the value obtained for x will be equal to -6,
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. A mathematical operation like reduction, addition, multiplication, or division is used to include terms in an expression.
As per the given equation in the question,
2/3x + 5/6 = 1/2 (x - 1/3)
2/3x + 5/6 = 1/2x - 1/6
Substitute like terms together,
2/3x - 1/2x = -1/6 - 5/6
(4x - 3x)/6 = (-1 - 5)/6
x/6 = -6/6
x/6 = -1
x = -6
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The polygon circumscribes the circle. Which of the following is the perimeter of the polygon?
A. 39 cm
B. 56 cm
C. 61 cm
D. 78 cm
The perimeter of the polygon is 78 cm. (Option D)
The perimeter of a geometric shape refers to the length that encompasses the figure. Hence, the perimeter of any irregular pentagon can be determined by the adding up the lengths of all sides. As the given polygon circumscribes a circle, the sides of the polygon are tangent to the circle. The two tangent theorem states that if two lines are drawn from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same. Hence, if two lines that are tangent to a circle meet at a point, then the distance from that point to the points of intersection between the tangents and the circle are equal. Hence, the perimeter of the pentagon is:
P = 8 + 8 + 16 + 16 + 6 + 6 + 9 + 9 = 78 cm
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The equation y = 2x + 3 is graphedbelow. If this graph is shifted up 3 units, what will be the equation of the new graph
Answer:
y = 2x + 6
Step-by-step explanation:
The equation is in point slope form or y = mc + b
where m is the slope and b is the y intercept
Since the graph is simply shifted up 3 units, the y intercept will change by increasing by 3, but the slope will not
16.13- cerebral tumors and cell phone use. in a case-controlled study on cerebral tumors and cell phone use, tumors occurred more frequently on the same side of the head where cellular telephones had been used in 26 of 41 cases. test the hypothesis that there is an equal distribution of contralaterial and ipsilateral tumors in the population. use a two-sided alternative.
The two sided hypothesis of the given situation is H0 : p = 0.50 and Ha : p ≠ 0.50
in statistics, hypothesis is defined as a statement that explains the predictions and reasoning of your research.
Here we have given that cerebral tumors and cell phone use. in a case-controlled study on cerebral tumors and cell phone use, tumors occurred more frequently on the same side of the head where cellular telephones had been used in 26 of 41 cases.
And we need to find the test to the hypothesis that there is an equal distribution of contralateral and ipsilateral tumors in the population. use a two-sided alternative.
Here we have to find Hypothesis, for that we have to so the steps are shown below:
Let us considered the hypotheses for the study as shown below:
H0 : p =0.50
Versus,
Ha : p ≠ 0.50
Therefore, this is two tailed hypothesis test.
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roblem 9-15 (Algorithmic) Doug Casey is in charge of planning and coordinating next spring’s sales management training program for his company. Doug listed the following activity information for this project: Immediate Time (weeks) Activity Description Predecessor(s) Optimistic Most Probable Pesssimistic A Plan topic — 1 1.5 2 B Obtain speakers A 2 2.5 9 C List meeting locations — 1.5 2 2.5 D Select location C 2 2 2 E Finalize speaker travel plans B, D 0.5 1 1.5 F Make final check with speakers E 1.5 2 2.5 G Prepare and mail brochure B, D 4 4.5 8 H Take reservations G 2 4 6 I Handle last-minute details F, H 1.5 3 4.5 Prepare an activity schedule. If required, round your answers to two decimal places. If your answer is zero, enter "0". Activity Expected Time Variance A B C D E F G H I Earliest Latest Earliest Latest Critical Activity Start Start Finish Finish Slack Activity A B C D E F G H I What are the critical activities and what is the expected project completion time? If required, round your answer to one decimal place. Expected project completion time = weeks. If Doug wants a 0.99 probability of completing the project on time, how far ahead of the scheduled meeting date should he begin working on the project? Base your calculation solely on the critical path. Note: Use Appendix B to identify the standard score. If required, round your answer to one decimal place. T = weeks.
If the 0.99 probability of completing the project on time, then the scheduled meeting date should he begin working on the project is 2.39 weeks
How to calculate the probability?
In math, the probability can be determined by first knowing the sample space of outcomes of an experiment and then by dividing the number of outcomes of an event by the total number of possible outcomes or sample space.
Here we have given that Doug Casey is in charge of planning and coordinating next spring’s sales management training program for his company.
And we need to find the If Doug wants a 0.99 probability of completing the project on time, how far ahead of the scheduled meeting date should he begin working on the project.
Here we know that the duration of the critical path determines the completion of the whole project.
Therefore, the mean completion time of the project =μ=15
And the the variance of the critical path = sum of the variances of the activities A, B, G, H, and I =0.03+0.44+0.44+0.11+0.03=1.06
Therefore, the standard deviation of the critical path or that of the whole project =σ=√1.06=1.03
Here we know that, if a 0.99 probability of completion is required, then the corresponding Z-score =2.3263
Then the actual completion time corresponding to a Z-score of
=> 2.3263 = μ+(Z×σ) = 15+(2.3263×1.03) = 15+2.39 = 17.39 weeks
Which states that the extra time needed over and above the mean completion time of the project of 15 weeks to have a 0.99 probability of completion =17.39−15=2.39 weeks
Therefore, in order to have a 0.99 probability of completing the project on time, the project should be started 2.39 weeks ahead of the scheduled meeting date.
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