The rate at which water is draining when the water is 8 feet deep is calculated to be 2.54 ft³/ h
The vertex angle of the conical-shaped reservoir can be given as follows;
tan θ = R/H
Here R represents the radius and H illustrates the depth
so here we can say that the vertex angle will remain constant; therefore;
r/y = R/H
r/8 = 10/20
r = (10/20) × 8
r = 4
now for the volume, we can say;
V=1/3πr^2h
also, we can say;
r = y/2
Therefore here we will have;
V = 1/3π(y/2)^2y = 1/12 πy³
now for volume flow rate, we can determine as follows;
Q = dV/dt = 3/12πy²(dy/dt)
Q = 1/4 πy²v
Substituting the values as follows;
Q = 1/4 π(8)²(1/2)ft³/h
Q = 2.54 ft³/ h
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Match each of the following planar vector fields with the corresponding plot. Note that the vectors are scaled to avoid overlap. A
nswer Bank F(x, y)=(8,8) F(x, y)=(8,0) F(x, y)=(0,8) F(x, y)=(-8,0)
The vector are quantity that has both magnitude and direction. they are normally visualized in graph.
A vector - values function F : R² ---> R² can be visualized as a vector field. At a point (x,y) , we plot a value of F(x,y) as a vector with the tail anchored as (x,y)
If we visualize the vector field it will look like an explosion emanating from the origin.
At each point (x,y) , the vector F(x,y) points precisely away from the origin.
If you drew the arrows to scale they would be as long as the distance to the origin but again the drawn arrows are shorter than the actual values of the vector field
The graph of a vector field is created by pointing arrows one at a time of substituting points into the plane to determine what error to draw at the point
The question is incomplete so, I have answered in general
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The article also reported that for a sample of 36 individuals who had taken quetiapine, the sample mean cholesterol level change and estimated standard error were 9.06 and 4.256, respectively. Make any necessary assumptions about the distribution of change in cholesterol level, test the hypothesis that the true average cholesterol level increases. Givens: State the appropriate hypotheses. (Use μD = μafter − μbefore.) H0: μD = 0 Ha: μD > 0 t value= 2.1 or 2.128759398 unrounded p value=? Identify the significance levels at which there is sufficient evidence to reject H0. (Choose all that apply.) ? = 0.1 ? = 0.05 ? = 0.01 ? = 0.001 For the sample of 45 individuals who had taken olanzapine, the article reported (7.520, 9.830) as a 95% CI for true average weight gain (kg). What is a 99% CI? (Round your answers to three decimal places.
P-value is equal to 0.0206 and the significance levels at which there is sufficient evidence to reject H0 are at = 0.05 and [tex]\alpha[/tex]=0.1 and value of 99% CI = 7.132, 10.218.
Here we have,
n= 36
e= 9.06
S.E. = 4.256
Hypothesis
H0: μD = 0
Ha: μD > 0
This a right-tailed test
Test statistics,
t = 2.12
P-value at t= 2.12 and degree of freedom(df) = n-1 =36-1 = 35
P-value = t-dist(t, df, tails)
= t-dist(2.12, 35, L)
= 0.020585
= 0.0206 Round to 4 decimals
If pvalue>[tex]\alpha[/tex], then we reject the null hypothesis.
So, [tex]\alpha[/tex]= 0.05 and [tex]\alpha[/tex]=0.1 we reject the H0.
For sample of n=45 df will be= 45 -1 =44
t0.025 = 2.015
Mean weight = (7.520 + 9.830)/2 = 8.675
Margin of error = 9.830 - 8.675 = 1.155
SE = 1.155/2.015 = 0.573
99%tc = 2.692
Margin of error = 2.692 x 0.573 = 1.543
99% CI = 8.675 ± 1.543
= 7.132, 10.218
99% CI = 7.132, 10.218.
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help meeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeee
{ax+3y=10
kx−3y=6
In the system of equations above, a and k are constants. If the solution to the system is (2,1) , what is the value of a+k ?
Answer:
a+k =7
Step-by-step explanation:
In the given system of equations, ax + 3y = 10 and kx - 3y = 6, we are told that the solution to the system is (2,1). This means that when we plug the values x = 2 and y = 1 into the equations, we get two true statements.
To find the value of a + k, we can start by plugging the values x = 2 and y = 1 into the first equation to get:
a(2) + 3(1) = 10
Next, we can solve for a by dividing both sides of the equation by 2:
a + 3/2 = 5
a = 5 - 3/2 = 5/2
Next, we can plug the values x = 2 and y = 1 into the second equation to get:
k(2) - 3(1) = 6
Next, we can solve for k by dividing both sides of the equation by 2:
k - 3/2 = 3
k = 3 + 3/2 = 9/2
Finally, we can add the values of a and k to find the value of a + k:
a + k = (5/2) + (9/2) = 14/2 = 7
Therefore, the value of a + k is 7.
Find the solution set 4x^2+9x-9=0
The solution sets for the given quadratic equation 4x²-9x-9=0 are -3/4, 3
What is a quadratic equation?Any equation in algebra that can be rearranged in standard form as follows is known as a quadratic equation (from Latin quadratus, which means "square").
[tex]{\displaystyle ax^{2}+bx+c=0\,,}[/tex]
While a, b, and c are known values, x is an unknown value, and vice versa. The assumption is that a > 0; equations with a = 0 are thought to be degenerate because they become linear or even simpler. The terms "quadratic coefficient," "linear coefficient," and "constant or free term" can be used to distinguish the three values that make up the equation's coefficients, respectively.
Given,
4x²-9x-9=0
4x²-12x+3x-9=0
4x(x-3)+3(x-3)=0
(4x+3)(x-3)=0
4x+3=0, x-3=0
4x-3=0
4x=3
x= -3/4
x-3=0
x=3
Therefore, the solution sets for 4x²-9x-9=0 are -3/4, 3
Hence, the solution sets for the given quadratic equation 4x²-9x-9=0 are -3/4, 3
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Kim wants to determine a 99 percent confidence interval for the true proportion pp of high school students in the area who attend their home basketball games. Out of nn randomly selected students she finds that that exactly half attend their home basketball games. About how large would nn have to be to get a margin of error less than 0.01 for pp?
[Use the values for z* from a z-table or t-table, and round to the smallest integer that works.]
n≈
Refer to the following scenario.
An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 339 people living in East Vancouver and finds that 39 have recently had the flu.
Suppose that the epidemiologist wants to re-estimate the population proportion and wishes for her 95% confidence interval to have a margin of error no larger than 0.04. How large a sample should she take to achieve this? Please carry answers to at least six decimal places in intermediate steps.
Sample size =
As per the margin of error, the value of n is 1068
Margin of error
In statistics, margin of error refers the statistic expressing the amount of random sampling error in the results of a survey.
Given
Kim wants to determine a 99 percent confidence interval for the true proportion pp of high school students in the area who attend their home basketball games. Out of n randomly selected students she finds that that exactly half attend their home basketball games.
Here we need to find how large would n have to be to get a margin of error less than 0.01 for p.
Let us assume the worst case of the point estimate of 99% and n refers size of sample
Here the margin of error is calculated as,
=> Margin of error = z1 - α * standard error of worst case point estimate
=> z x 99% x √(0.5(1-0.5)/n)
=> 1.96 * 0.5/√n
Now, we have to equate to given margin of error of 0.03, then
=> 0.03 = 1.96*0.5/√n
Then we have to solve for n
=> n = (1.96*0.5/0.03)²
=> n = 32.67²
=> n = 1067.11
When we round off it, then we get,
=> n = 1068
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Factor: 5x2 – 15x – 20.
Answer:
=5x2-(20-5)x-20
=5x2-20x+5x-20
=5x(x-4)+5(x-4)
=(x-4)(5x+5)
Answer:-5(2+3x)
Step-by-step explanation:
A group of campers and one group leader left a campsite in a canoe. They traveled at an average rate of 10 km/h. Two hours later, the other group leader left the campsite in a motorboat. He traveled at an average rate of 22 km/h.A. How long after the canoe left the campsite did the motorboat catch up with it?B. How long did the motorboat travel?
A .The canoe left the campsite did the motorboat catch up with it 3 hrs and 40 minutes
B . The motorboat travel at 1 hr 40 minutes
A group of campers and one group leader left a campsite in a canoe.
They traveled at an average rate of 10 km/h.
1st Group DATA:
rate = 10 km/h ; distance = x km ; time = d/r = x/10 hrs
Two hours later, the other group leader left the campsite in a motorboat.
He traveled at an average rate of 22 km/h.
Group Leader DATA:
rate = 22 km/h ; distance = x km ; time = d/r = x/22 hrs
A. How long after the canoe left the campsite did the motorboat catch up with it?
Group time - Leader time = 2 hr
x/10 - x/22 = 2
Multiply thru by 110 to get:
11x - 5x = 220
6x = 220
x = 110/3 = km
canoe total time = x/10 = (110/3)/(10) = 11/3 = 3 hrs and 40 minutes
B. How long did the motorboat travel?
motorboat time = x/22 = (110/3)/22 = 1 hr 40 minutes
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A mining company owns two mines. These mines produce an ore that can be graded into two classes: regular grade and low grade. The company must produce at least 350 tons of regular-grade and 610 tons of low-grade ore per week. The first mine produces 5 tons of regular-grade and 17 tons of low-grade ore per hour. The second mine produces 20 tons of regular-grade and 10 tons of low-grade ore per hour. The operating cost of the first mine is $7000 per hour, and the operating cost of the second mine is $29,000 per hour. The first mine can be operated no more than 54 hours a week, and the second mine can be operated no more than 27 hours a week. How many hours per week should each mine be operated to minimize the cost?
The number of hours to operate the mines to minimize cost are Mine 1 hour = 30 hours and Mine 2 hour = 10 hours
How to determine the number of hours?The given parameters can be represented using the following table of values
Mine 1 (x) Mine 2 (y) Available
Regular grade 5 20 350
Low grade 17 10 610
Operating cost 7000 29000
Time 54 27
From the table, we understand that we are to minimize cost
This means that:
Objective function: C = 7000x + 29000y
Subject to:
5x + 20y ≥ 350
17x + 10y ≥ 610
Next, we plot the constraints on a graph (see attachment)
From the graph, we have
(x, y) = (30, 10)
This means that
Mine 1 hour = 30 hours
Mine 2 hour = 10 hours
Hence, the number of hours are 30 and 10 hours
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what is square root of 727878
Answer:
853.15766421
Step-by-step explanation:
The square root of 727878 would be 853.15766421.
Answer:
= 853.157664
Step-by-step explanation:
√727878 = 853.157664
...
..
.
an independent random sample is selected from an approximately normal population with an unknown standard deviation. find the p-value for the given sample size and test statistic. (assume we're considering a two sided hypothesis tests in each question. round your answers to three decimal places.)
Also determine if the null hypothesis would be rejected at α = 0.05.
(a) HA : µ > µ0, n = 11, T = 1.91
(b) HA : µ < µ0, n = 17, T = −3.45
(c) HA : µ 6= µ0, n = 7, T = 0.83
(d) HA : µ > µ0, n = 28, T = 2.13
Using the t-distribution, it is found that the null hypothesis is rejected for a, b, c
Item a:
We have a right-tailed test, as it is being tested if the mean is more than a value.
The p-value is found using a t-distribution calculator, with 11 - 1 = 10 df and t = 1.91, hence it is of 0.0426.
The p-value is of 0.0426, which is less than 0.05, thus the null hypothesis is rejected.
Item b:
We have a left-tailed test, as it is being tested if the mean is less than a value.
The p-value is found using a t-distribution calculator, with 17 - 1 = 16 df and t = -3.45, hence it is of 0.0016.
The p-value is of 0.0016, which is less than 0.05, thus the null hypothesis is rejected.
Item c:
We have a two-tailed test, as it is being tested if the mean is different than a value.
The p-value is found using a t-distribution calculator, with 7 - 1 = 6 df and t = 0.83, hence it is of 0.4383.
The p-value is of 0.4383, which is more than 0.05, thus the null hypothesis is not rejected.
Item d:
We have a right-tailed test, as it is being tested if the mean is more than a value.
The p-value is found using a t-distribution calculator, with 28 - 1 = 27 df and t = 1.91, hence it is of 0.0195.
The p-value is of 0.0195, which is less than 0.05, thus the null hypothesis is rejected.
Therefore, in an independent random sample is selected from an approximately normal population with an unknown standard deviation. Using the t-distribution, it is found that the null hypothesis is rejected for a, b, c
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HELPPPPP IM ON MY QUIZ
Answer:
10mph
keeping it short so you can ace your quiz :D
if this helps you, it would help me a lot if you could mark this as brainliest :)
write log7t as a base 2 logarithm.
The logarithm of base 7 of t, as a logarithm of base 2 is given as follows:
log2(t)/log2(7).
How to change the base of the logarithm?A logarithm is defined as follows:
log_a(b).
In which:
a is the base.b is the term.To change the logarithm to a new base c, the logarithm is written by the fraction presented as follows:
log_c(b)/log_c(a).
In this problem, the logarithm is defined as follows:
log_7 t.
The new base is given as follows:
2.
(as stated in the problem, since we want the logarithm as a logarithm of base 2).
Hence, applying the change of base, the logarithm of base 2 will be given as follows:
log2(t)/log2(7).
As the term log2 represents the logarithm of base 2 of the term.
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A circle has an area of 49 pi in2. What is the circumference in the circle terms of pi?
Answer:
14π in.
Step-by-step explanation:
First, we use the area to find the radius.
A = πr²
πr² = 49π in.²
r² = 49 in.²
r = √(49 in.²)
r = 7 in.
Now, we use the radius to fins the circumference.
C = 2πr
C = 2 × π × 7 in.
C = 14π in.
Which of the following terms appear in the expansion of (x + y)10? The letter a in each term represents a real constant. ax3y7, ay5, ax5, ax5y
In the binomial expression (x + y)^10, the term that will appear in the expansion of expression is ax^3y^7.
Binomial expression refers to the algebraic expression which contains two terms. These expressions are expanded using binomial theorem. According to the theorem, it is possible to expand the binomial (x + y)^n into a sum involving terms of the form ax^by^c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b. Hence, for the given expression, the term which will appear in the expansion of binomial would have variables whose sum of power would be equal to the power of the expression i.e., the sum of the power would be 10. Hence, ax3y7 would appear in the expansion as the sum 3+7=10.
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Evaluate the integral ∫∫∫Dxyz dV, where D is the region bounded below by xy-plane and above by the hemisphere z=√9−x2−y2.
Refer to the photos taken.
Write the expressions in standard form 1/6(r-6)
Answer:
1/6 r-1
Step-by-Step Explanation:
1/6(r-6)
1/6 * (r-6) - distribute 1/6
1/6 r - 1/6 * 6 - simplify the expression
SOLUTION 1/6 r-1
The owner of a football team claims that the average attendance for games is 67,800, he therefore justified in moving the team to a city with a larger stadium.
express the null hypothesis in symbolic form- use the correct symbol for indicated parameter
The null hypothesis is H0: μ ≤ 68,800 for the given case of The owner of a football team claiming that the average attendance for games is 67,800.
Since we know that a null hypothesis (H0) shows that no significant variation exists between variables in other words it can be said that a single variable is much not different than its mean. since from the above case we were given the information that The owner of a football team claims that the average attendance for games is 67,800. So, the null hypothesis the that the average attendance at games is less than or equal to 68,800.
H0: μ ≤ 68,800
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Bruce says that if a number is a product of 6, then it is not a product of 3. What would you say to Bruce?
Bruce can be advised to correct his reasoning as the number divisible by six will also remain divisible to 3.
How to find the factors of a number?The factor of a number is any number that divides it completely.
In order to find the factors of a number keep dividing it with the known factors.
Given that,
A number is product of 6.
Then, 6 is the factor of that number.
But the factors of 6 are 2 and 3 which implies that 3 is also a factor of that number.
It implies that Bruce has not applied the correct reasoning to reach the conclusion.
Hence, a number which is a product of 6 can also be a product of 3.
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If 60% of the population supports massive federal budget cuts, what is the probability in that a survey of 250 people ,at most 155 people support such cuts
The probability that such cuts would be supported by at least 155 persons in a survey of 250 people is 0.62.
What exactly is probability?Probability is a branch of mathematics that deals with numerical descriptions of the likelihood of an event occurring or a statement being true. The probability of an occurrence is represented by a number between 0 and 1, where 0 signifies the event's impossibility and 1 denotes its certainty.
Assume 60% of the public favors huge government budget cutbacks.
We must determine the likelihood that, in a poll of 250 persons, at most 155 respondents approve such reduction.
As a result, the chance is 155/250 = 0.62.
Hence, probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.
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The median size of a new single-family house built in the United States between 1987 and 2001 can be modeled by the equation H(x) = 0.359x3 − 15.198x2 + 221.738x + 862.514 square feet where x is the number of years after 1980. † (a) Determine the time between 1987 and 2001 when the median house size was increasing least rapidly. (Round your answer to the nearest year.) Find the corresponding house size. (Round your answer to the nearest whole number.) square ft Find the corresponding rate of change in house size. (Round your answer to one decimal place.) square feet per year (c) Determine the time between 1987 and 2001 when the median house size was increasing most rapidly.
PLEASE SHOW WORK!
As per the given question the median size of a new house and the values of different parts of the question will be as follows:
(a) We must locate the period when the rate of change is the smallest in order to establish the period during which the median house size increased the least quickly. Finding the derivative of the following equation will provide us with the rate of change of the house size with respect to time, which we can utilize to do this.
derivative of the function H(x) = 0.359x3 - 15.198x2 + 221.738x + 862.514 given by the equation for the rate of change of the house size with respect to time as
H'(x) = 3 (0.359) x2 - 2 (15.198) x + 221.738
(b) By setting the derivative to 0 and figuring out x, we may determine the moment at which the rate of change is the least. We have x = 3.904 as a result. The time where the rate of change is the smallest is 3.904 years after 1980, or 1984.904, because x denotes the number of years after 1980. This roughly corresponds to 1984, making 1984 the year in which the median house size increased at the slowest rate.
We may enter the value of x into the previous equation to obtain H(1984) = 0.359 x [tex](1984)^{3}[/tex] - 15.198 x [tex](1984)^{2}[/tex] + 221.738 ( 984) + 862.514
= 2,532,358 sq ft. as the comparable house size at this time. In 1984, this was the size of the typical home.
We may enter the value of x into the derivative equation to obtain H'(1984) = 3 (0.359) x [tex](1984)^{2}[/tex] - 2 (15.198 x 1984 + 221.738) = 606.696 sq ft per year, which corresponds to the rate of growth in house size. This represents the median house size's rate of change during the slowest period of growth.
(c) The biggest rate of change must be found in order to pinpoint the period in which the median house size increased most quickly. Finding the derivative equation's greatest value will help us do this. To accomplish this, one can solve for x while setting the derivative equal to 0, then determine the values of x that are either more or less than the answers we obtained. The derivative equation can then be used to solve for the maximum value using these x values.
Using the quadratic formula to solve for x. The quadratic formula is given by x = [tex]\frac{(-b ± √(b^2 - 4ac))}{2a}[/tex], where a, b, and c are the coefficients of the quadratic equation. Here, a = 3 (0.359) = 1.077, b = -2 (15.198) = -30.396, and c = 221.738. Putting these values into the quadratic formula gives us x = [tex]\frac{(30.396 ± √(30.396^2 - 4 (1.077 X 221.738))}{2 (1.077)}[/tex]
= [tex]\frac{(30.396 ± √(928.822 - 948.512))}{2.154}[/tex]
= [tex]\frac{(30.396 ± √(-19.690))}{2.154}[/tex]
= [tex]\frac{15.198}{2.154}[/tex]
= 7.096.
The derivative equation will have a maximum or lowest value at the value of x that we just discovered because it is a quadratic. We can enter this value of x into the derivative equation to obtain H'(7.096) = 3 x 0 and use this result to determine the derivative equation's maximum value.
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A police officer claims that the proportion of accidents that occur in the daytime (versus nighttime) at a certain intersection
is not 35% To test this claim, a random sample of 500 accidents at this intersection was examined from police records it is
determined that 156 accidents occurred in the daytime.
The following is the setup for this hypothesis test:
HOD=0.35
Hkpl 0.35
।
Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.
The following table can be utilized which provides areas under the Standard Normal Curve
-1.6
1.S
0.036
0.045
0.055
0.01
9900
0.034
0.081 0.079 0.078
0.042
0.04
0.026 0.026
0.033
0.041
1500
0.063 0.062
0.075
1900
90'0
0.031
0.039
0.048
0.059
0.07
0.08
0.024
0.024
0.031
0.030
0.038 0.038
0.046
0.057
0.069
0.058
0.071
0.09
0.023
0.029
0.037
0.046
0.056
E
The p-value of the hypothesis test in this problem is given as follows:
0.075.
How to calculate the p-value of the test?The first step in calculating the p-value of the test is obtaining the test statistic, which is given by the equation presented as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which the parameters are defined as follows:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.The values of these parameters in this problem are given as follows:
[tex]p = 0.35, n = 500, \overline{p} = \frac{156}{500} = 0.312[/tex]
Hence the test statistic is of:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.312 - 0.35}{\sqrt{\frac{0.35(0.65)}{500}}}[/tex]
z = -1.78.
Now we have to consider that we have a two-tailed test, as we are testing if the mean is different of a value.
Using a z-distribution calculator, with a two-tailed test and z = -1.78, the p-value of the test is given as follows:
0.075.
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Raquel is playing a game where she throws a ball that paper called a trash ball into her trashcan the diameter of the top of the trashcan is 20 inches Raquel once the trash ball to have a diameter that is 1/4 the diameter of the top of the trashcan what should the timing of Raquel trash Be?
The diameter of the top of the trash ball is 5 inch.
What is a diameter?The diameter is the distance along the circle's center that must travel in order to touch two points on its periphery.
solution:
Given that the diameter of top of the trash can is 20 inch.
And the diameter of trash ball is 1/4th of the diameter of trash can.
The diameter of trash ball = 1/4 ( the diameter of trash can )
The diameter of trash ball = 1/4 (20 inch)
The diameter of trash ball = 20/4
The diameter of trash ball = 5 inch.
Therefore, the diameter of the top of the trash ball is 5 inch.
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Name the figure as precisely as possible and solve for x.
The polygon shown in the figure is trapezoid and the value if x is .
What is trapezoid?
A trapezoid may be a polygonal shape that has just one try of parallel sides. These parallel sides also are referred to as parallel bases of trapezoid. the opposite 2 sides of trapezoids area unit non-parallel and referred to as legs of trapezoids
Main body:
by using the property of trapezoid ,
1/2(sum of both bases) = mid-line passing through trapezoid
according to question:
x = 1/2(x-8+2x-12)
x = 1/2(3x -20)
2x = 3x - 20
x = 20
Hence value of x is 20.
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1. Select all expressions that are equivalent to 8 +16i.
(A.) 2(4 + 8)
(B.) 2i(8-4)
4(21-4)
4i(4-21)
(E.) -2i(-8-4i)
The equivalent expression for the given expression is -2i(-8+4i).
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is 8 +16i.
The given expression can be written as 8(1+2i)
-2i(-8+4i)
= -2i×(-8)-(-2i)×4i
= 16i-8i²
= 16i-8(-1)
= 8+16i
Therefore, the equivalent expression is -2i(-8+4i).
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a well known social media company is looking to expand their online presence by creating another platform. they know that they current average 2,500,000 users each day, with a standard deviation of 625,000 users. if they randomly sample 50 days to analyze the use of their existing technology, identify each of the following, rounding to the nearest whole number if necessary: Provide your answer below: read M users Guides o= users Gallery Webex = users deric Support - Users urveys FEEDBACKM ORE INSTRUCTION URIME . Provous O Type here to search
The value of standard deviation is 88,389.
The Normal distribution id the contionuouse distribution with unimodal and symmetric shaped, it is widely used to approximated discrete distribution and sample mean and a total sum of the random variable, the approximation depends on the concept og the Central limit theorem.
The Central limit theorem states that the sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough.
We have given that,
average = 2.500,000
standard deviation σ = 625,000
sample n = 50.
Therefore S = σ / √n
= 625000 / √50
= 625000 / 7.071
S = 88,389
Hence the standard deviation will be 88,389.
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which option describes a situation in which reduction occurs
The option which describes a situation in which reduction occurs Cl2 becoming Cl–. (Option B)
Reduction refers to the type of chemical reactions in which the number of electrons in an atom, or a group of atoms increases. The electrons taken up by the substance reduced are supplied by another substance, which is thereby oxidized. Hence, oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or a decrease in the oxidation state. In the given situation, Cl2 becoming Cl- represents reduction as the oxidation state is decreased from 0 to -1.
Note: The question is incomplete. The complete question probably is: Which option describes a situation in which reduction occurs? A) S2– becoming S. B) Cl2 becoming Cl–. C) Al becoming Al3+. D) Xe2+ becoming Xe6+.
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How do you figure out the slope of a line
Answer:
m = [tex]\frac{rise}{run}[/tex]
Step-by-step explanation:
1. take any two points on the line
2. figure out the vertical change between both points, known as the rise
3. figure out the horizontal change between both points, known as the run
4. slope is defined as the variable m and is the [tex]\frac{rise}{run}[/tex]
The product of two consecutive positive integers is greater than their sum by 209. Find these numbers.
The two consecutive positive integers as detailed in the question are;
15 and 16
How to solve quadratic equations?Let the two consecutive integers be;
x and (x + 1).
We are told that the product of two consecutive positive integers is greater than their sum by 209.
Thus, the expression for this is;
x(x + 1) - 209 = x + x + 1
x² - x - 210 = 0
Using quadratic equation formula, we get;
x = -(-1) ± √((-1)² - 4(1 * -210))]/2(1)
x = (3 ± √(9 + 840)]/2
x = 15
Thus, the second number is; x + 1 = 15 + 1 = 16
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the function relates the length of a skid mark measured in feet at an accident scene to the speed of the car in miles per hour. that means an accident reconstructionist can measure the length of a skid mark and find the speed the car was traveling. if a skid mark with a length of 82.5 ft was found, find the speed of the car. round your answer to the nearest tenth.
If a skid mark with a length of 82.5 feet was found, then the speed of the car is 13.59 miles per hour
The function is
l(s) = 0.46s^2 - 0.199s + 0.264
Where l is the length of a skid mark measured in feet at an accident scene
s is the speed of the car in miles per hour
Given that the skid mark length = 82.5 feet
Then the equation will be
0.46s^2 - 0.199s + 0.264 = 82.5
Rearrange the terms
0.46s^2 - 0.199s + 0.264 - 82.5 = 0
0.46s^2 - 0.199s - 82.236 = 0
Use the quadratic equation
= [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
Substitute the values in the equation
= [tex]\frac{0.199+/-\sqrt{(-0.199)^2-4(0.46)(-82.236)} }{2(0.46)}[/tex]
= (0.199 ± 12.30) / 0.92
Then
(0.199 + 12.30) / 0.92 = 13.59
(0.199 - 12.30) / 0.92 = -13.15
Therefore, the speed of the car is 13.59 miles per hour
The complete question is:
The function l(s) = 0.46s^2 - 0.199s + 0.264 relates the length of a skid mark measured in feet at an accident scene to the speed of the car in miles per hour. that means an accident reconstructionist can measure the length of a skid mark and find the speed the car was traveling. if a skid mark with a length of 82.5 ft was found, find the speed of the car. round your answer to the nearest tenth.
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