So, the insurance company should be concerned that they could potentially lose money.
To test whether the insurance company should be concerned about the true mean claim amount being higher than the original estimate of $1,800, we can perform a one-sample t-test.
The null hypothesis for this test is that the true mean claim amount is equal to the original estimate of $1,800, and the alternative hypothesis is that the true mean claim amount is greater than the original estimate.
The t-statistic for this test is calculated as follows:
t = (sample mean - null mean) / (standard deviation / sqrt(sample size))
Plugging in the values from the problem, we have:
t = ($1,950 - $1,800) / ($500 / sqrt(40)) = 2.5.
We can then use a t-table or a computer to find the critical value of t for a one-tailed t-test with 39 degrees of freedom and a significance level of 0.05. The critical value is 1.68.
Since the calculated t-value of 2.5 is greater than the critical value, we can reject the null hypothesis and conclude that the true mean claim amount is significantly greater than the original estimate of $1,800.
Therefore, the insurance company should be concerned that they could potentially lose money.
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To test whether the insurance company should be concerned about the true mean claim amount being higher than the original estimate of $1,800, we can perform a one-sample t-test.
t = (sample mean - null mean) / (standard deviation / sqrt(sample size))
Plugging in the values from the problem, we have:
t = ($1,950 - $1,800) / ($500 / sqrt(40)) = 2.5.
We can then use a t-table or a computer to find the critical value of t for a one-tailed t-test with 39 degrees of freedom and a significance level of 0.05. The critical value is 1.68.
Therefore, the insurance company should be concerned that they could potentially lose money.
DUE SOON! PLEASE SHOW HOW YOU KNOW! THIS IS A SSA SITUATION BUT NOT SURE HOW TO FIND OUT HOW MANY TRIANGLES ARE POSSIBLE!
This is a SAS situation, only one triangle is possible. Then the correct option is C.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
In triangle ΔABC, the angle ∠A is 22°. And the measure of the side BC is 18.9 cm and the measure of the side AC is 15.1 cm.
To fix a triangle, the known dimensions of the triangle should be three which one must be a side.
This is a SAS circumstance, just a single triangle is conceivable. Then the right choice is C.
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A researcher at the Centers for Disease Control and Prevention is studying the growth of a certain bacteria. He starts his experiment with 500 bacteria that grow at a rate of 18% per hour. He will check on the bacteria every 3 hours. How many bacteria will he find in 3 hours? Round your answer to the nearest whole number.
Answer:
The answer is approximately 770 bacteria after 3 hours.
NO LINKS!!
A cup of water at an initial temperature of 81°C is placed in a room at a constant temperature of 24°C. The temperature of the water is measured every 5 minutes during a half-hour period. The results are recorded as ordered pairs of the form (t, T), where t is the time (in minutes ) and T is the temperature (in degrees Celsius).
t T
0 81
5 69
10 60.5
15 54.2
20 49.3
25 45.4
30 42.6
a. Subtract the room temp. from each of the temp. in the ordered pairs. Use a graphing utility to plot the data points (t, T) and (t, T-24). An exponential model for the data (t, T-24) is T-24 = 54.4(0.964)^t. Solve for T.
T=
Graph the model. Compare the result with the plot of the original data.
b. Use a graphing utility to plot the points (t, ln(T-24)) and observe that the points appear to be linear. Use the regression feature of the graphing utility to fit a line to these data. This resulting line has the form ln(T-24) = at + b, which is equivalent to e^(ln(T-24)) = e^(at+b). Solve for T, and verify that the result is equivalent to the model in part (b). Round all numerical values to 3 decimal places).
T=
c. Fit a rational model to the data. Take the reciprocals of the y-coordinates of the revised data points to generate the points. (t, 1/(T-24))
Use a graphing utility to graph these points and observe that they appear to be linear. Use the regression feature of a graphing utility to fit a line to these data. The resulting line has the form 1/(T - 24) = at + b.
Solve for T. (Round all numerical values to 4 decimal places). Use a graphing utility the rational function and the original data points.
T=
Part (a)
Given data table.
[tex]\begin{array}{|c|c|} \cline{1-2}t & T\\\cline{1-2}0 & 81\\\cline{1-2}5 & 69\\\cline{1-2}10 & 60.5\\\cline{1-2}15 & 54.2\\\cline{1-2}20 & 49.3\\\cline{1-2}25 & 45.4\\\cline{1-2}30 & 42.6\\\cline{1-2}\end{array}[/tex]
where,
t = time in minutesT = temperature in CelsiusIt's unfortunate that T is used twice for these variables. It might cause some confusion.
This is what happens when we subtract 24 from each temperature.
[tex]\begin{array}{|c|c|} \cline{1-2}t & T-24\\\cline{1-2}0 & 57\\\cline{1-2}5 & 45\\\cline{1-2}10 & 36.5\\\cline{1-2}15 & 30.2\\\cline{1-2}20 & 25.3\\\cline{1-2}25 & 21.4\\\cline{1-2}30 & 18.6\\\cline{1-2}\end{array}[/tex]
The graph of each set of points is shown in figure A. I used GeoGebra to make the graph.
The first set of data points are in red. The second set in blue. Notice the set of blue points is the result of shifting the red points 24 units down.
The green exponential model is also shown as the curve through the set of red points.
The green regression exponential model doesn't go through each point perfectly. Rather it tries to get as close as possible.
To go from
T-24 = 54.4(0.964)^t
to
T = 54.4(0.964)^t + 24
we simply add 24 to both sides. This means there isn't much to show in terms of steps when solving for T.
=======================================================
Part (b)
Use spreadsheet technology or something like GeoGebra to generate this data table.
[tex]\begin{array}{|c|c|} \cline{1-2}t & ln(T-24)\\\cline{1-2}0 & 4.043051\\\cline{1-2}5 & 3.806662\\\cline{1-2}10 & 3.597312\\\cline{1-2}15 & 3.407842\\\cline{1-2}20 & 3.230804\\\cline{1-2}25 & 3.063391\\\cline{1-2}30 & 2.923162\\\cline{1-2}\end{array}[/tex]
The values in the 2nd column are approximate.
Then plot each of those points on the same xy grid. Use technology of your choice to determine the regression line is roughly
y = -0.03723x + 3.99739
So we can say
ln(T-24) = -0.03723t + 3.99739
the right hand side fits the format at + b where
a = -0.03723b = 3.99739both of which are approximate.
Then,
e^(ln(T-24)) = e^(at+b)
T-24 = e^(at+b)
T-24 = e^(-0.03723t + 3.99739)
T-24 = e^(-0.03723t)*e^(3.99739)
T-24 = e^(-0.03723t)*54.45583
T-24 = 54.45583*e^(-0.03723t)
T = 54.45583*e^(-0.03723t) + 24
T = 54.456*e^(-0.037t) + 24
Let's verify that this is equivalent to the model found in part (a).
T = 54.456*e^(-0.037t) + 24
T = 54.456*(e^(-0.037))^t + 24
T = 54.456*(0.963676)^t + 24
T = 54.5*(0.964)^t + 24
which is very close to the model mentioned in part (a). There's some slight rounding error. That's to be expected in problems like this.
-----------------------------
Answer: T = 54.456*e^(-0.037t) + 24
See figure B for the graph. Like with the other regression curve, this straight line doesn't go through all of the points. It tries to get as close as possible.
=======================================================
Part (c)
Refer to the 2nd table mentioned in part (a).
We'll apply the reciprocal to each item in the column labeled T-24.
For instance, the item 57 becomes 1/57 = 0.017544 approximately.
This is what the data table looks like:
[tex]\begin{array}{|c|c|} \cline{1-2}t & 1/(T-24)\\\cline{1-2}0 & 0.017544\\\cline{1-2}5 & 0.022222\\\cline{1-2}10 & 0.027397\\\cline{1-2}15 & 0.033113\\\cline{1-2}20 & 0.039526\\\cline{1-2}25 & 0.046729\\\cline{1-2}30 & 0.053763\\\cline{1-2}\end{array}[/tex]
The values in the 2nd column are approximate.
The set of points and regression line are shown in figure C1. This line does not go through all of the points. Like with the others, it tries to get as close as possible to each point.
Use technology to determine the equation of the regression line is approximately:
y = 0.00121x + 0.01613
Which tells us that
1/(T-24) = 0.00121t + 0.01613
Let's solve for uppercase T.
1/(T-24) = 0.00121t + 0.01613
T-24 = 1/(0.00121t + 0.01613)
T = 1/(0.00121t + 0.01613) + 24
T = 1/(0.0012t + 0.0161) + 24
which is the approximate final answer.
Figure C2 shown below represents the original data points (t, T) in red. The blue curve is y = 1/(0.0012x+0.0161)+24, which is the rational regression curve we just found. This curve tries its best to get as close as possible to each red point.
Compare the regression curves of figure A and figure C2. We have a very close tie in terms of which curve does a better job of fitting the original data.
Ida wants to know if males and females prefer different brands of ready-made chocolate-chip cookie dough. She bakes eight dozen cookies from dough made by each of four manufacturers which she labels brands A, B, C, and D. She then selects a simple random sample of 96 students, records their gender, gives them one cookie of each brand and asks which brand they like best. Here are her results:
9. The conditional distribution for preferred cookie brand among males (in percents) is given by which of the following?
A. A: 27%; B: 19%; C: 25%; D: 29%
B. A: 4%; B: 6%; C: 13%; D: 15%
C. A: 11%; B: 16%; C: 34%; D: 39%
D. A: 23%; B: 13%; C: 11%; D: 14%
E. A: 38%; B: 21%; C: 19%; D: 22%
They like best brand C) A: 11%; B: 16%; C: 34%; D: 39%.
What is probability ?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Have given ,
Ida made four brands A , B , C and D
Mostly students like A brand 11% , B brand 16% , C brand 34% and D brand 39%
So this is best brand like by students male and female
They like best brand C) A: 11%; B: 16%; C: 34%; D: 39%.
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Solve for x using the quadratic formula: x² - 6x + 9 = 0
X=
-b± √b²-4ac
2a
Ox=6
Ox=3
Ox=1
Ox=0
Answer:
[tex] \huge{ \boxed{x = 3}}[/tex]
Step-by-step explanation:
[tex] {x}^{2} - 6x + 9 = 0[/tex]
Using the quadratic formula that's,
[tex] \bold{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}} \\ [/tex]
Comparing the equation to the general form of a quadratic equation ( ax² + bx + c), we have.
[tex]a = 1 \\ b = - 6 \\ c = 9[/tex]
Substituting the values into the formula we have.
[tex]x = \frac{- ( -6) \pm \sqrt{( - {6})^{2} - 4(1)(9) } }{2(1)} \\ x = \frac{6 \pm \sqrt{36 - 36} }{2} \\ x = \frac{ 6 \pm\sqrt{0} }{2} \\ x = \frac{6}{2} \: \: \: \: \: \\ \\ x = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
We have the final answer as
x = 3Lines PQ and BC are parallel.
What is the value of x ?
Answer:
x = 40
Step-by-step explanation:
since lines PQ and BC are parallel , then
∠ BCQ and ∠ AQP are corresponding angle and are congruent , that is
∠ BCQ = 80°
the sum of the 3 angles in Δ ABC = 180° , then
x + 80 + 60 = 180
x + 140 = 180 ( subtract 140 from both sides )
x = 40
pls help me with both of these questions
The number of times a large popcorn without butter is sold is, 49.
The conditional relative frequency of no.of Item2 sold given that
50% off is 0.27.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
The number of times a large popcorn without butter is sold is,
= 49.
The total no. of items that is 50% off is (12 + 20 + 32) = 74.
The no. of Item2 which is 50% off is 20.
So, The conditional relative frequency of no.of Item2 sold given that 50% off is,
= 20/74.
= 0.27.
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Please can someone explain this question to me step-by step, i have a exam this Wednesday so pleasee help me!! Help is greatly greatly appreciated ^^
Thankyou!!
Answer:
AB = 45.688 metres
Step-by-step explanation:
* i used a scientific calculator for my working. i am not sure if calculators are permitted for your exam on Wednesday *
⭐AB = AD + DB
⭐AB = 16.5 + DB
Thus, we need to find DB in order to solve for AB.
First, I utilized the triangle sum theorem to find ∠BDC:
[tex]< BDC + < DCB + < B = 180\\ < BDC + 59 + 90 = 180\\ < BDC + 149 = 180\\ < BDC = 31[/tex]
Then, I utilized the linear pair sum to find ∠ADC:
[tex]< ADC + < BDC = 180\\ < ADC + 31 = 180\\ < ADC = 149[/tex]
Next, I utilized the triangle sum theorem to find ∠DAC:
[tex]< DAC + < ADC + < ACD = 180[/tex]
[tex]< DAC + 149 + 10 = 180[/tex]
[tex]< DAC + 159 = 180[/tex]
[tex]< DAC = 21[/tex]
After, I utilized the law of sines to find DC:
[tex]\frac{sin10}{16.5} = \frac{sin21}{DC}[/tex]
[tex]DCsin10 = 16.5sin21[/tex]
[tex]DC = \frac{16.5sin21}{sin10}[/tex]
[tex]DC = 34.052[/tex]
Then, I utilized the sine function to find DB for ΔBDC:
[tex]sin(59) = \frac{DB}{34.052}[/tex]
[tex]34.052sin(59) = DB[/tex]
[tex]29.188 = DB[/tex]
Finally, I substituted DB into our original equation for AB:
[tex]AB = AD + DB[/tex]
[tex]AB = 16.5 + 29.188[/tex]
[tex]AB = 45.688 metres[/tex]
Good luck on your exam on Wednesday! :-)
The height of the pole will be equal to 45 meters.
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.
Given that the angle BCD is 59 and the angle BCA is 69. The height will be calculated as,
tan(59) = BD / BC
BC = BD / tan(59)
BC = 0.6BD
tan(69) = AB / BC
tan(69) = ( 16.5 + BD ) / BC
BC = 0.38( 16.5 + BD )
Equate the values of BC,
0.6BD = 0.38 ( 16.5 + BD )
0.6BD = 6.27 + 0.38BD
0.22BD =6.27
BD = 28.5 meters
The height of the pole is,
AB = AD + DB
AB = 16.5 + 28.5
AB = 45 meters
The height is 45 meters.
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When constructing a confidence interval for a population mean μ from a sample of size 12, the number of degrees of freedom for the critical value tα/2 is ___________________________.
b. Find the critical value tα/2 needed to construct a confidence interval of the given confidence level 90% with sample size 23
When constructing a confidence interval for a population mean the Degrees of freedom is 11 and critical value is 1.717
Degrees of freedom = df = n - 1 =12 - 1 = 11
At 90% confidence level the t is ,
α = 1 - 90% = 1 - 0.90 = 0.1
α / 2 = 0.1 / 2 = 0.05
tα /2, df = t0.05,22 = 1.717 ( using student t table)
The level of confidence denotes the likelihood that the position of a statistical parameter (such as an arithmetic mean) in a sample survey is also true for the population.
A critical value is the test statistic's value that establishes a confidence interval's upper and lower boundaries or a test statistic's threshold for statistical significance.
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Anne Richards purchased two slippers at one price and three pajamas at another price. Let s = the price of each slipper and p = the price of each pajama. Each slipper
cost $12. How much did each pajama cost if the total purchase price was $120?
Each pajama cost $. (Simplify your answer.)
Answer:
[tex]E[/tex]ach pajama costs $32
Step-by-step explanation:
So, the said person bought:
2 slippers at a price, 3 pajamas at another price. (The prices are unknowns, s, and p)
Each slippers cost $12
We are to find the cost of each pajama, where the total purchase price is $120
With the given conditions, we formulate an equation: 2s + 3p = 120
Since s = 12, we replace for the value of s in the equation. s becomes 2 × 12 = 24.
The new equation is then: 24 + 3p = 120, where we are to find the value of p.
Collect like terms: 3p = 120 - 24 → 3p = 96
Divide both sides of the equation by 3 to find the value of p: 3p/3 = 96/3 → p = 32
Therefore, the price of each pajama is $32
I hope this helpscalculating Nominal GDP, Real GDP, and other economic indicators and can successfully use these indicators to draw conclusions because…
You can successfully use nominal GDP, real GDP, and other economic indicators to draw conclusions because they health of the country's economy.
What is GDP?GDP stands for Gross Domestic Product. This is a very common economic indicator that shows the value of the services and products produced by a country usually in a one year period.
What is the difference between real and nominal GDP?In general real GDP is considered to be more accurate as nominal GDP is influenced by factors such as inflation that can distort the general idea you can get about a country's economy and the total output of it.
What do economic indicators reveal?Both real, nominal GDP and other indicators show the health of the economy in a country, which makes it useful to draw conclusions about the economy.
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What is the exponential form of the expanded form below?
3.3.3.3.3.3.3
3•7
3^7
7^3
3^6
Answer:
Step-by-step explanation:
okay so its 3•7
that's all u need put that
Answer:
[tex]3^{7}[/tex]
Step-by-step explanation:
3×3×3×3×3×3×3= [tex]3^{1+1+1+1+1+1+1+1} =3^{7}[/tex]
3+3+3+3+3+3+3= 3×7
Image below to be answered
a.The formula that describe the sequence or progression is a+(7-7n)
b. 2nd term = -10 , 3rd term = 10, 4th term = -10 and 5th term = 10
What is arithmetic and geometric progression?Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio.
Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.
The nth term of an arithmetic progression is given as a(n)= a + (n − 1) × d
In geometric progression the nth term is given as a(n)= ar^(n-1)
where a is the first term
therefore if a = 12 and d is - 7
the formula for the arithmetic progression =
a(n) = 12+(n-1) -7 = 12+( 7-7n)
If the first term of a GP is 10 with common ratio of -1
then the second term = 10×-1 = -10
third term = -10×-1 = 10
fourth term = 10×-1 = -10
fifth term = -10× -1 = 10
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How is 25 to 5 and 10 to 2 equivalent ratios
Answer:
They are equivalent ratios because if you multiply 10 to 2 by 2.5 you get 25 to five
Answer:
equals 25
Step-by-step explanation:
30-(-2)*(-10)+(-5)-(-2)=
Answer:
Step-by-step explanation:
-2 * -10 = 20
Answer:
30×2×(-10)-5+2
=60×(-10)-3
=-60-3
=-63
is it correct? i will brinlist to who answer first
I don't see the full picture but your answer should look like this:
4ab+(-12ab)+9ab+(-5ab)
= 4ab-12ab+9ab-5ab
= (4-12+9-5)ab
= -4ab
I need help with the statement and the reasons
Explanation:
You can make use of the properties of parallel lines to prove ∠ACB≅∠DAC.
Statement . . . . Reason
2. ∠DAB +∠ABC = 180° . . . . definition of a right angle
3. AD║BC . . . . consecutive interior angles are supplementary
4. ∠ACB≅∠DAC . . . . alternate interior angles are congruent
(Factoring Algebraic Expressions MC)
x3y2 is the result of the expression employing the common factor (x - 6y).
What is Mathematical expression?Here,
The sentence is,
x⁴y² - 6x³y³
We must use the common factor to solve.
Mathematical expression refers to the combining of numbers and variables utilizing the operations addition, subtraction, multiplication, and division.
Now,
The sentence is,
x⁴y² - 6x³y³
The common factor is used to solve as,
6x3y3 - x4y2 equals x*x*x*y*y - 6*x*x*x*y*y.
= x³y² (x - 6y) (x - 6y)
Consequently, x3y2 is the value of the expression employing the common factor (x - 6y).
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What is the value of sin0 given that (-3,4) is a point on the terminal side of 0?
Martha has a $200 deductible and 20% co-payment on her health
insurance. Last year she had $6,500 in medical bills. What was
Martha's out-of-pocket expense?
Answer:
Step-by-step explanation:
To solve this problem, we need to calculate Martha's out-of-pocket expenses, and the total amount of money she had to pay for her medical bills.
First, we need to calculate the amount of money Martha had to pay toward her deductible. Since her deductible is $200, this is the amount she had to pay out of pocket.
Next, we need to calculate the amount of money Martha had to pay toward her co-payment. Since her co-payment is 20%, we can calculate this by multiplying her medical bills by the co-payment rate: $6,500 x 0.2 = $1,300.
To find Martha's total out-of-pocket expense, we can add the amount she paid towards her deductible ($200) and the amount she paid towards her co-payment ($1,300):
$200 + $1,300 = $1,500
Therefore, Martha's out-of-pocket expense was $1,500.
Martha's insurance required her to pay a $200 deductible and a 20% co-payment on the remaining balance of her medical bills. After paying the deductible, she pays 20% of the remaining $6,300 which is $1,260. So, Martha's total out-of-pocket expense was $1,460.
Explanation:Martha's health insurance plan includes a $200 deductible and a 20% co-payment. The deductible is the amount Martha has to pay before the insurance company starts to pay. In this case, Martha first pays a $200 deductible from her $6,500 medical bills, which leaves her with $6,300 to be covered by insurance and her co-payment. The 20% co-payment means Martha is responsible for paying 20% of the remaining $6,300. To calculate this, we multiply $6,300 by 0.20 (20%), which equals $1,260. Therefore, Martha's total out-of-pocket expense for her medical bills last year was the $200 deductible plus the $1,260 co-payment, equalling $1,460.
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need help with all these
Answer:
|
|
|
∆∆∆∆∆∆∆∆∆∆∆∆∆∆
Step-by-step explanation:
get better
Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year.
What is the 95% confidence interval for this population proportion? Answer choices are rounded to the hundredths place.
The 95% confidence interval for this population proportion is (0.10, 0.23).
What is a confidence interval?A confidence interval is a range of values that are constrained by the statistic's mean and that are likely to include an unidentified population parameter. The proportion of likelihood, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn several times is referred to as the confidence level.
Sample size n = 125
number of people who planned to take an extended vacation = 21
sample proportion p = 21/125 = 0.168
Confidence level = 0.95
significance level α = 1-0.95 = 0.05
Z score =[tex]Z_{\alpha 2}[/tex] = Z(0.05) = 1.96, from Z table.
The confidence interval for population proportion is-
p±[tex]Z_{\alpha 2}[/tex] x √{p(1-p)}/n =0.168±1.96 x 0.168 x √{(1-0.168)}/125
=0.168±1.96 x 0.0334
=0.168±0.0655
=(0.1025, 0.2335)
=(0.10, 0.23)
Therefore, the confidence interval is (0.10, 0.23).
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In 1950, a U.S. population
model
was y = 151. (1.013)^t-1950 million
people, where t is the year. What did
the model predict the U.S. population
would be in the year 2000?
In a case whereby In 1950, a U.S. population model was y = 151. (1.013)^t-1950 million people, where t is the year, the model predict the U.S. population would be 288 million in the year 2000.
What is population model ?Population models are mechanical theories that link alterations in population structure and density to responses at the individual level (life history features in eco-evolutionary theory or vital rates in demographic theory).
The model was given as y=151x(1.013)^t-1950
where the future time t = 2000
Then we can substitute the given year 2000 as the value of 't'
then we will have y=[151x(1.013)^(2000-1950)] = 288 million
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I need help asap i don’t get it
∠SWV is congruent to ∠TWU because vertically opposite angle.
Define congruent.If one of the geometric figures can be superimposed on the other so that their entire surface coincides, then the two are said to be congruent, or to be in the relation of congruence. Two triangles are said to be congruent if their two sides and their included angle are the same in both of them. Congruence appears to be based on the concept of a "rigid body," which may be transported from one location to another without affecting the internal relationships between its components.
Given
∠SWV ≅ ∠TWU
Vertically opposite angle
∠SWV is congruent to ∠TWU because vertically opposite angle.
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PLS HELP ASAP pic attached
The slope and y-intercept, or the points, should be used to graph the line. Slope: 3 y-intercept: (0, 1 )
How to find the Calculation?g ( x ) = − 3 x − 1
Create an equation using the function.
y = − 3 x − 1
Calculate the slope and y-intercept using the slope-intercept form.
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In the slope-intercept form, y = m x + b denotes the slope and the y-intercept, respectively.
y = m x + b
With the use of the formula y = m x + b, determine the values of m and b.
m = − 3 b = − 1
m is the line's slope, and is the value of the y-intercept.
B. Slope: 3 Y-intercept: (0, 1 )
Two points are all that are required to graph any line. To determine the associated y values, enter two x values into the equation.
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Assign the x and y values to a table.
x y
0 − 1
1 − 4
The slope and y-intercept, or the points, should be used to graph the line.
Slope: 3 y-intercept: (0, 1 )
x y
0 1
1 4.
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find the indefinite integral and check the result by differentiation. (use c for the constant of integration.) $$ \int \sqrt[3]{{\color{red}3} - {\color{red}4} x^2} ({\color{red}-8} x) \text{ }dx $$
The indefinite integral is - 1 / [5(6 + [tex]x^{5}[/tex])] + C.
An integral is considered to be indefinite if it has no upper or lower bounds. In mathematics, the most generic antiderivative of f(x) is known as an indefinite integral and expressed by the expression f(x) dx = F(x) + C. Without upper and lower bounds on the integrand, indefinite integrals are stated using the notation f(x), which represents the function as an antiderivative of F. Consequently, "f(x) dx=F" (x). As we observed in the same example with antiderivatives, the integral, x3 dx=14x4+C, is one example.
The area under the f(x) curve from x=a to x=b is represented by the definite integral of f(x), which is a NUMBER. Integral indefinite. An indefinite integral of a function f(x), also known as an antiderivative, is denoted by and its derivative is denoted by f. (x). The indefinite integral is not the only solution because the derivative of a constant is zero. Integration is the action of locating an indefinite integral.
Use a u-substitution with u = (6 + [tex]x^{5}[/tex])
du = 5[tex]x^{4}[/tex]dx
1/5 ∫ [tex]u^{-2}[/tex]du
= -1/5 [tex]u^{-1}[/tex] + C
= - 1 / [5(6 + [tex]x^{5}[/tex])] + C
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Correct Question:
Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.)
[tex]\int\limits^ {} \frac{x^{4} }{(6+x^{5})^{2} } dx[/tex]
Suppose that the function h is defined, for all real numbers, as follows.
=hx +−12x24 ≠if x2
−2 =if x2
Find h−3, h2, and h4.
The function h is defined, for all real numbers h(-3) = -1/2 , h(2) = -2 and h(4) = -4.
What is a function ?
When it comes to arithmetic, a function is represented as a rule that produces a different result for each input x. Mathematicians refer to functions as mapping or transformations.
The given function,
h(x) = -1/2 x^2 + 4 if x≠ 2
-2 if x=2
So, h(-3) = -1/2 (-3)^2 + 4
= - 9/2 + 4
= -1/2
h(2) = -2 ( given )
h(4) = -1/2 (4)^2 + 4
= -8 + 4
= -4 .
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If the opposite corners of the rectangle ABCD are A (5, 3) and C (10, 1) and the equation of side BC is x-2y=8, find the equations of the other three sides. You must show your work and explain why you are doing it. (Note: opposite side of a rectangle are parallel and consecutive sides are
perpendicular)
Answer:
Equation of side AB:
We know the coordinates of A and B, so we can use the point-slope form to create the equation of the line:
y - 3 = (3/5)(x - 5)
y - 3 = 3/5x - 15/5
5/3y - 15/3 = x - 5
5/3y - x = -15/3 + 5
5/3y - x + 15/3 = 5
5/3y - x + 15/3 = 0
Equation of side AB: 5/3y - x + 15/3 = 0
Equation of side DC:
We know the coordinates of C and D, so we can use the point-slope form to create the equation of the line:
y - 1 = (2/5)(x - 10)
y - 1 = 2/5x - 20/5
5/2y - 10 = x - 10
5/2y - x = -10
5/2y - x - 10 = 0
Equation of side DC: 5/2y - x - 10 = 0
Equation of side BD:
We know the equation of side BC (x - 2y = 8) and that consecutive sides are perpendicular, so we can use the slope-intercept form to find the equation of line BD:
Slope of BC = -2/1
Slope of BD = -1/-2 = 1/2
y = (1/2)x + b
We can use the coordinates of B to find b:
1 = (1/2)(8) + b
2 = 4 + b
b = -2
Equation of side BD: y = (1/2)x - 2
Step-by-step explanation:
Of all the fish in a certain river, 20 percent are salmon. Once a year, people can purchase a fishing license that allows them to catch up to 8 fish. Assume each catch is independent. Which of the following represents the probability of needing to catch 8 fish to get the first salmon? A. 0.2 B 1/0.2 C. 0.2^8 D 0.2 (0.8)^7
E. 0.8 (0.2)^7
The probability of needing to catch 8 fish to get the first salmon is D) 0.2 (0.8)^7.
How to calculate probability of needing to catch 8 fish to get the first salmon?
Given that he probability of fishing a salmon in a certain river is 20% i.e. 0.2. Now, the probability of not getting a salmon will be
1 - probability of not getting salmon = 1 - 0.2 = 0.8.
So, the first fish should be salmon and the others should not be salmon. So, the required probability of independent events can be calculated as,
P =0.2×0.8×0.8×0.8×0.8×0.8×0.8×0.8×0.8
P = 0.2× (0.8)^7
Hence,the probability of needing to catch 8 fish to get the first salmon is 0.2 (0.8)^7.
The probability of needing to catch 8 fish to get the first salmon is D) 0.2 (0.8)^7.
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the purpose of a check sheet is to quickly understand the primary sources of a problem using the 80/20 rule, wherein 80 percent of defects often come from only about 20 percent of all the sources.
Based on the following question the primary sources of a problem using the 80/20 rule, wherein 80 percent of defects often come from only about 20 percent of all the sources is false
What is 80/20 rule?
Only 20% of causes result in 80% of all consequences, according to the 80/20 rule. It is used to pinpoint the crucial elements of success (often in a corporate context) and concentrate efforts therein to enhance outcomes.
What is the 80-20 rule in life?According to the 80-20 rule, 20% of activities produce 80% of the consequences. Or, to put it another way, just 20% of the input results in 80% of the outcome. An old proverb that promotes focus is the 80-20 rule, often known as the Pareto Principle.
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