There are 50 ways for Marvin to reach his destination without passing through the forbidden point.
To solve this problem, we can use the unitary method. This method involves breaking the problem down into smaller, simpler units to solve it more easily.
In this case, we can break the path from Marvin's starting point to his destination into two smaller paths. The first path is from (0,0) to (1,4), and the second path is from (1,4) to (4,6).
There are five paths from the bottom left corner to the point (1,4) that do not go through the forbidden point.
Once Marvin reaches the point (1,4), he can only go up or to the right to reach his destination. So, we need to count the number of ways to get from (1,4) to (4,6)
We can visualize this by drawing another grid and counting the paths:
In total, there are
=> 5 x 10 = 50
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Psychology and Human Behavior The mattress company Amerisleep recently conducted a survey and concluded that more than half of all Americans sleep on the job, but the type of work and salary affect how often people grab some shut eye. 41 Suppose that the mean number of naps per month on the job by a randomly selected American worker is four. A. What is the probability that a randomly selected American worker does not take a single nap during a month? One nap? Two naps? B. Suppose two American workers are selected at random. What is the probability that the total number of naps for the two Americans during a month is zero? One? Two? C. Suppose the mean number of times per month an American worker naps on the job is eight. What is the probability that a randomly selected American worker does not take a single nap during a month? One nap? Two naps? D. How do your answers in parts (b) and (c) compare? What property does this suggest about a Poisson random variable?
A. The probability of no nap is 0.390625, one nap is 0.234375 and two naps is 0.156250. B. The probability of zero naps is 0.152587890625, one nap is 0.3076171875, and two naps is 0.146484375. C. The probability of no nap is 0.02734375, one nap is 0.14453125, and two naps is 0.271484375. D. The probability of no naps decreases as the mean number of naps increases.
A. We can calculate the probability of no nap, one nap, and two naps by using the Poisson Distribution formula. The mean number of naps (λ) is four, so the probability of no nap (x=0) is 0.390625, one nap (x=1) is 0.234375, and two naps (x=2) is 0.156250.
B. We can calculate the probability of zero naps, one nap, and two naps by using the Poisson Distribution formula. The mean number of naps (λ) is four, so the probability of zero naps (x=0) is 0.152587890625, one nap (x=1) is 0.3076171875, and two naps (x=2) is 0.146484375.
C. We can calculate the probability of no nap, one nap, and two naps by using the Poisson Distribution formula. The mean number of naps (λ) is eight, so the probability of no nap (x=0) is 0.02734375, one nap (x=1) is 0.14453125, and two naps (x=2) is 0.271484375.
D. We can see from the answers in (b) and (c) that the probability of no naps decreases as the mean number of naps increases, suggesting that a Poisson random variable follows a decreasing probability distribution.
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Dont really understand. Algebra 1 class
The equation of line r is x = -3/2y + 5/2.
What is the equation of the line?A line's equation is typically expressed in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. A line's equation expresses the y coordinate of any point on the line in terms of its x coordinate. In other terms, a line equation is a formula that can be used to compute the y coordinate of any point on a line given its x coordinate.
In the given question,
The equation of line r is y = -1/3x + 7.
Line r is perpendicular to line q, so the slopes of the two lines must be opposite reciprocals of one another. The slope of line q is 3, so the slope of line r must be -1/3.
To find the equation of line r, we can use the point-slope formula. The point-slope formula is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
In line r, (x1, y1) is (1, 3). The slope, m, is -1/3.
Substituting values into the point-slope formula, we have y - 3 = -1/3(x - 1).
Solving for y, we have y = -1/3x + 7.
This equation is written in slope-intercept form, which is the form y = mx + b, where m is the slope and b is the y-intercept.
In line r, the slope is -1/3 and the y-intercept is 7.
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new flowers are being planted in a circular flwoer bed with a 14-foot diameter. if each flower requires 2 square feet of space, about how many flowers can be planted? (1 point) 308 flowers, 154 flowers, 77 flowers, 66 flowers
A total of 77 new flowers can be planted on the flower bed.
New flowers has to be planted in a circular flower bed that has a diameter of 14 ft.
Each one of the flower requires to square feet of the space.
The radius of the flower bed will be 7 feet.
The area of the flower bed can be calculated by using the formula,
A = πr²
Where r is the radius.
Put in the value of radius to find the area of the flower bed,
A = 3.14 x 7 x 7
A = 153.86 ft²
Now, let us say that N number of floors can be planted,
So,
N)(2) = 153.82
N = 76.93
So we can say that about 77 flowers can be planted on the flower bed.
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Solve for k:
k-
-
k =
I
96
Answer: look it up frfr
Step-by-step explanation:
4x-(6x+1)≤ 8x + 2(x-3)
Answer:
-1/6
Step-by-step explanation:
To solve the inequality 4x-(6x+1)≤ 8x + 2(x-3), we can simplify both sides of the inequality and isolate x on one side:
4x - (6x + 1) ≤ 8x + 2(x-3)
4x - 6x - 1 ≤ 8x + 2x - 6
-2x - 1 ≤ 10x - 6
Subtract 10x from both sides:
-12x - 1 ≤ -6
Add 12x to both sides:
-1 ≤ 6x
Divide both sides by 6:
-1/6 ≤ x
The solution to the inequality is x ≥ -1/6. This means that x is greater than or equal to -1/6, so any value of x that is greater than or equal to -1/6 will satisfy the inequality.
the ogive shown is based on u.s. census data and shows the average annual personal income per capita for each of the 50 states. the data are rounded to the nearest thousand dollars. ogive showing cumulative percentage of data webassign plot what percentage of the states have average per capita income more than 32.5 thousand dollars?
The estimated percentage of states with an average per capita income greater than 32.5 k is:we need to use the ogive (cumulative frequency curve) to determine the percentage of states with an average per capita income greater than 32.5k.
Assuming that the ogive is a continuous curve, we can estimate the percentage by finding the value on the horizontal axis corresponding to the 50% mark on the vertical axis, and then subtracting it from 100%. From the graph, we can see that the 50% mark corresponds to a value of around 30 k, which is between the values for Oklahoma and Pennsylvania. To get a more accurate estimate, we can use linear interpolation between these two data points.
Let's assume that the values for Oklahoma and Pennsylvania are
(x₁,y₁) = (25k,40%) and (x₂,y₂) = (35k,60%)
respectively. Then the equation of the straight line connecting these two points is:
(y-y₁) =(y₂-y₁) / (x₂-x₁) * (x-x₁)
Substituting in the values gives:
y - 40 = (0.6 - 0.4)/(35 - 25) * (x - 25)
y - 40 = 0.02(x - 25)
y = 0.02x - 0.5
To find the value of x that corresponds to the 50% mark, we can set y = 50% and solve for x:
50 = 0.02x - 0.5
0.02x = 50.5
x = 2525
So the estimated value for x is 25.25k. Therefore, the estimated percentage of states with an average per capita income greater than 32.5k is:
scss
Copy code
100% - 40% - (10% * (32.5 - 25.25)/(30 - 25))
= 50.5%
Therefore, we estimate that about 50.5% of the states have an average per capita income greater than 32.5k.
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which of the following statements best explains the steps to solve the pair of equations graphically
y= -x+1
y=2x+4
The following statements best explains the steps to solve the pair of equations graphically is Option D.
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
The first equation is:
y = -x +1
so the slope is -1, and the y-intercept is +1.
The second equation is:
y = 2x +4
so the slope is 2, and the y-intercept is 4.
The slopes and intercepts are properly described in the last selection.
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The complete question:
A pair of linear equations is shown below:
y = -x + 1
y = 2x + 4
Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points)
On a graph, plot the line y = -x + 1, which has y-intercept = -1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of
Intersection of the two lines as the solution.
On a graph, plot the line y = -x + 1, which has y-intercept - 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of
intersection of the two lines as the solution.
On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = -2 and slope = 2, and write the coordinates of the point
of intersection of the two lines as the solution.
On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of
intersection of the two lines as the solution.
Ideas Math FL B.E.S.T. - Geometry > Checkpoint: Similarity transformations G6J
The side lengths of AGHI are 8, 12, and 16 units. Two of the side lengths of ALMN are 10 and
15 units. If AGHI and ALMN are similar, what is the length of the third side of ALMN?
units
The length of the third side of ALMN is 20 units.
What is the length of the third side of ALMN?
If AGHI and ALMN are similar, then their corresponding sides are proportional.
Let's call the length of the third side of ALMN "x". We can set up the proportion using the two sides of AGHI and ALMN that we know:
10/8 = 15/12 = x/16
To find x, we can cross-multiply and simplify:
15 × 16 = 12x
240 = 12x
x = 240/12
x = 20
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2. Choose one of the pair of starting angles in the table below:: each table has () over them
(a = 50 degrees
y = 110 degrees )
(a= 30 degrees
b=70 degrees)
(c =30 degrees
y=120 degrees)
Please note you are only using 1 of the the selections above, and they will give different results
(a) What is the angle measurement of first unknown angle? Explain the angle relationship you used.
(b) What is the angle measurement of second unknown angle? Explain the angle relationship you used.
Hint: Remember to start with a relationship where you have one unknown.
Answer:
If A=30 and B= 70 the first unknown angle Y would be 100. When using the E.A.T (exterior angle theorem) you add the 2 remote interior angles to get the exterior angle. (Y)
Unknown angle 2 is a interior angle, so we know all 3 of the interior angles must equal 180.
30+70=100
180-100=80
C=80
Step-by-step explanation:
Can someone help a stoned brotha out
how many 3-digit numbers have exactly one zero?
Answer:
162
Step-by-step explanation:
Whether the zero is in the ones position or the tens position, there are only 9 possibilities for each of the other two digits and they can occur (with possible repetition) in either order. That’s 81 for each zero position for a total of 162.
There are 171 three-digit numbers that have exactly one zero. The zero can be in either the tens or units places, yielding 90 and 81 possibilities respectively.
Explanation:To determine how many 3-digit numbers have exactly one zero, we need to consider the possible placements of the zero. A 3-digit number has three positions: the hundreds place, tens place, and units place. The zero cannot be in the hundreds place, as that would make it a 2-digit number. So, the zero can only have two possible positions: the tens or units place.
For each case:
The zero in the tens place: In this case, we have 9 options (1-9) for the hundreds place, 1 option for the tens place (0), and 10 options (0-9) for the units place. This gives 9 * 1 * 10 = 90 numbers.The zero in the units place: Similarly, we have 9 options for the hundreds place, 9 options (1-9) for the tens place, and 1 option for the units place (0). This gives 9 * 9 * 1 = 81 numbers.So, in total, we have 90 + 81 = 171 3-digit numbers with exactly one zero.
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Which equation correctly represents the statement shown?
The value of t is 41 more than 24.
A.
t = 41 + 24
B.
t = 41 × 24
C.
24 = t ÷ 24
D.
41 = t − 24
Answer:
option A is the correct answer.
(-8x²y²-27xy³ + 12x³y²)÷(−3x²y4)
Answer:
(- 12x ^ 2 + 8x + 27y)/(3x * y ^ 2)
Step-by-step explanation:
a sample of 64 account balances from a credit company showed an average daily balance of $1,040. the standard deviation of the population is known to be $200. we are interested in determining if the mean of all account balances (i.e., population mean) is significantly higher than $1,000. n determining if the mean of all account balances (i.e., population mean) is significantly higher than $1,000. a. develop the appropriate hypotheses for this problem. b. determine the test statistic (t statistic or z statistic?), and then compute the test statistic. c. compute the p-value. d. using the p-value approach at 95% confidence, test the above h
The test static is 1.60 and the p-value is 0.1096, null hypothesis is not rejected and the population mean is not significantly different from $1000.
Assuming normal distribution
N( μ₀ , σ )
In this case N ( 1000, 200)
From a random sample of 64 accounts we get:
n = 64
x = sample mean x = 1040
σ = standard deviation of the population σ = 200
a) Test Hypothesis
Null Hypothesis H₀ x = μ₀ = 1000
Alternative Hypothesis Hₐ x ≠ μ₀
The alternative hypothesis implies a two tail-test. Given that n > 30 and σ is known we will use z-table
b) z(s) = ( x - μ₀ ) / σ/√n
z(s) = ( 1040 - 1000 ) / 200/ √64
z(s) = 40*8/200
z(s) = 1.60
c) P-value for z (score 1.6) p-value = 0.1096
d) If significance level is 0.05 then α = 0.05 and α/2 = 0.025
p-value > α/2
Then the z(s) < z(c) 1.6 < 1.96 where z(c) is z score for α/2
Hence, null hypothesis is not rejected
e) We can claim that at 95 % (of Confidence Interval) the population mean is not significantly different from $1000.
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Question is not complete. The complete question is :
A sample of 64 account balances from a credit company showed an average daily balance of $1,040. The standard deviation of the population is known to be $200. We are interested in determining if the mean of all account balances (i.e., population mean) is significantly different from $1,000. 1. State the null and alternative hypothesis. 2. Compute the test statistic. 3. Compute the p-value. 4. Based on the p-value and the significance level of 0.05% make a decision regarding the hypotheses. 5. Interpret your results in the context of the problem.
round 0.1347 to the nearest tenth
The rounding off the value 0.1347 to the nearest tenth is 0.1
What is rounding off?
When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.
The act of rounding off is merely an estimation. Rounding off is the process of estimating an actual number to a close number.
Given, 0.1347 round to the nearest tenth
While rounding to the nearest tenth, the value after the digit has been noticed.
In the number 0.1347, rounding to the nearest tenth, digit 3 should play a role to round the digit 1 which is in the tenth position. 3 is not equal to 5 and less than 5.
So, 0.1347 becomes 0.1
Hence, the required answer is 0.1
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Find the output, y, when the input, a, is 7
Answer: Y would be 4
If you look at the graph and find 7 on the x axis where the inputs are, you can see that if you go up, the only output for 7 is 4.
identify the zeros and asymptotes of
f(x)=
X²-9
x²-16
The zeros of f(x)= x²-9 is +3 and -3
The zeros of f(x) = x²-16 is +4 and -4
What are zeros and asymptotes?An asymptote is a line that the graph of a function approaches as either x or y go to positive or negative infinity. There are three types of asymptotes: vertical, horizontal and oblique. Vertical Asymptotes.
The zeros of a function are defined as the values of the variable of the function such that the function equals 0.
Therefore when f(x) =0
x²-9 = 0
x² = 9
x =√9
x = ±3
therefore the zeros of x²-9 is ±3
The vertical asymptote is 0 and horizontal asymptote is infinity.
x²-16 = 0
x² = 16
x = √16
x = ±4
the vertical asymptote is 0 and horizontal asymptote is infinity.
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Select the correct answer.
Given: PR bisects ZQPS, PQ = 12 units, and PS = 12 units
Prove: QR ~ SR
PI
How could you show QR ~ SR?
O A. Use SAS to show triangle PRQ is congruent to triangle SRP
O B. Use SAS to show triangle PRQ is congruent to triangle PRS
O c. Use AAS to show triangle PRQ is congruent to triangle PRS
O D.
Use ASA to show triangle
PRQ is congruent to triangle PRS
To prove QR ~ SR, Use SAS to show triangle PRQ is congruent to
triangle PRS.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
Given, PR bisects ZQPS, PQ = 12 units, and PS = 12 units
Now, The two triangles formed PQR and PSR share the same side PR.
Also m∠SPR = m∠QPR, Therefore these two triangles are congruent, and hence QR ~ SR
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How many envelopes can be made from a sheet of paper measuring 324 cm by 172 cm, if
each envelope requires a piece of paper of size 18 cm by 12 cm?
Answer: 258 envelopes
Step-by-step explanation:
The following table shows the length (in days) of each of the
9
99 Tucker family vacations.
Based on this data, what is a reasonable estimate of the probability that the next Tucker family vacation lasts less than
3
33 days?
Answer:because
Step-by-step explanation:a
Answer: 0.56
Step-by-step explanation:
which expression is equal to 45 4 5 responses 4 x 15 1 5 4 x 1 fifth 4 x 51 5 1 4 x 5 over 1 5 x 14 1 4 5 x 1 fourth 5 x 41 4 1 5 x 4 over 1
Option A, which is 4 x 15 + 1 - 5 x 4 x 1, is the correct expression that is equal to 45 x 4 + 5.
To show this, we can simplify the expression as follows:
4 x 51 + 1 - 5 x 4 x 1
= 204 + 1 - 20
= 205 - 20
= 184
Then, we can check if 185 is equal to 45 x 4 + 5:
45 x 4 + 5
= 180 + 5
= 185
Since 185 is equal to 185, it is concluded that an expression that is "equal to" 45 x 4 + 5, is held by option A.
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for safety reasons, 5 different alarm systems were installed in the vault containing the safety deposit boxes at a beverly hills bank. each of the 5 systems detects theft with a probability of 0.82 independently of the others. the bank, obviously, is interested in the probability that when a theft occurs, at least one of the 5 systems will detect it. what is the probability that when a theft occurs, at least one of the 5 systems will detect it?
The probability that when a theft occurs, at least one of the 5 systems will detect it is approximately 0.9997.
How likely something is to occur is known as its probability. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
We can solve this problem using the complement rule. The probability that none of the 5 systems detect the theft is given by:
(1 - 0.82)^5 = 0.00033124
So the probability that at least one system detects the theft is:
1 - 0.00033124 = 0.99966876
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If g(x) = x² + 2, find g(3).
Answer:
[tex]g(3) = 11[/tex]
Step-by-step explanation:
Greetings!!!
The given function
[tex] g(x) = x {}^{2} + 2[/tex]
What we are looking now is what will be the value when 3 is substituted in the variable x.
[tex]g(3) = (3) {}^{2} + 2[/tex]
Solve the expression
[tex]g(3) = 9 + 2[/tex]
Add the numbers
[tex]g(3) = 11[/tex]
Thus, the value of g(3)= 11
Hope it helps!!!
Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x
The constant of proportionality (r) in the equation y = rx represents the rate of change of y with respect to x, indicating the factor by which x and y are related.
The constant of proportionality (r) in the equation y = rx is simply the coefficient in front of the x term. In this case, r is the constant of proportionality, and it represents the rate at which y changes as x changes. In other words, it gives the relationship between x and y, such that y is directly proportional to x with a constant of proportionality of r.
So, in the equation y = rx, the value of r is the constant of proportionality.
In a direct proportion, if x increases, then y also increases, and if x decreases, then y decreases as well. The constant of proportionality (r) gives us the factor by which x and y are related.
For example, if y is equal to twice x (y = 2x), then the constant of proportionality (r) is 2. If x increases by 1 unit, y increases by 2 units, and if x decreases by 1 unit, y decreases by 2 units. The constant of proportionality in this case is 2.
In the equation y = rx, the variable x represents the input and y represents the output. The constant of proportionality (r) tells us how much y changes for a unit change in x. It can be thought of as the ratio of the change in y to the change in x. The constant of proportionality can also be expressed as the slope of a line that represents the relationship between x and y.
In summary, the constant of proportionality (r) in the equation y = rx gives us the factor by which x and y are related and represents the rate of change of y with respect to x.
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What is the area of the figure?
(NEED THE ANSWER ASAP. PLEASE DONT PUT ANYTHING NONSENSE OR I'LL REPORT U. THANK U FOR UR HELP)
The area of the given figure is 12 square meters
The given figure is a parallelogram
Parallelogram is a geometric figure that has both pair of opposites parallel sides and opposite sides are equal . Number of vertices and edges are four
The height of the parallelogram = 2 meters
The base length of the parallelogram = 6 meters
The area of the parallelogram = The height of the parallelogram × The base length of the parallelogram
Substitute the values in the equation
The area of the parallelogram = 2 × 6
Multiply the numbers
= 12 square meters
Therefore, the area is 12 square meters
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I have solved the question in general , as the given question is incomplete
The complete question is :
What is the area of the figure ?
Please fjnd the measure of angle x!
The value of the angle 'x' in the right-angle triangle will be 42.99°.
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.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The value of the variable 'x' is given by the sine of the angle 'x'. Then we have
sin x = 15 / 22
sin x = 0.6818
sin x = sin 42.99°
x = 42.99°
The value of the angle 'x' in the right-angle triangle will be 42.99°.
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a dye is injected into the pancreas during a certain medical procedure. a physician injects 0.3 grams of the dye, and a healthy pancreas will secrete 4% of the dye each minute. predict the amount of dye remaining, to the nearest hundredth of a gram, in a healthy pancreas 30 minutes after the injection.
The estimated quantity of dye left in a healthy pancreas 30 minutes after the injection, rounded to the closest hundredth of a grams, is 0.07 grams.
As per the question given,
After the dye is injected, a healthy pancreas will secrete 4% of the remaining amount of dye each minute. Let's use exponential decay to model the amount of dye remaining in the pancreas over time.
The amount of dye remaining after t minutes can be expressed as:
R(t) = 0.3 * (1 - 0.04)^t
We want to find the amount of dye remaining after 30 minutes, so we can substitute t=30 into the equation and calculate:
R(30) = 0.3 * (1 - 0.04)^30
R(30) = 0.3 * (0.96)^30
R(30) = 0.3 * 0.2312
R(30) = 0.0694
Rounding to the nearest hundredth of a gram, the predicted amount of dye remaining in a healthy pancreas 30 minutes after the injection is 0.07 grams.
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Answer:
0.09 g
Step-by-step explanation:
You want to know the amount remaining of 0.3 g of dye after 30 minutes if the amount decreases by 4% per minute.
Exponential functionThe amount can be modeled by the exponential function ...
q = a·b^t
where q is the quantity remaining, 'a' is the initial quantity, b is the growth factor per minute, and t is the number of minutes.
The growth factor is related to the growth rate by ...
b = 1 + growth rate
ApplicationHere, the growth rate is -4% per minute, so the growth factor is ...
b = 1 +(-0.04) = 0.96
The initial quantity is 0.3 grams, so the remaining quantity after 30 minutes is ...
q = 0.30·0.96^30 ≈ 0.08816 ≈ 0.09 . . . . grams
The amount of dye remaining after 30 minutes is predicted to be 0.09 g.
<95141404393>
4 ×(1 × – 10–3) Evaluate the expression.
i need help
schoology
question1
The measure <h = 45 degree, <g= 135 degree, <h = 55 degree and
<k = 125 degree.
What is Vertical Angles?When two lines converge, vertical angles are created. Because the angles are opposite one another, vertical angles are also known as vertically opposite angles. They are constantly on par.
Given:
As, from the Figure
<h + 135 = 180 (Linear Pair)
<h = 180 - 135
<h = 45
and, <g = 135 (Vertical Opposite Angle)
Now, <m + 125 = 180 (Linear Pair)
<m = 180 - 125
<h = 55
and, <k = 125 (Vertical Opposite Angle)
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because the median is not affected by the size of an outlier and does not change even if a particular outlier is replaced by an even more extreme value, we say the median is _____ to outliers.
Answer:
resistant
because the median is not affected by the size of an outlier and does not change even if a particular outlier is replaced by an even more extreme value, we say the median is resistant to outliers.
