Answer:
Check Explanation
Step-by-step explanation:
In finding the public's view on pollution, the researchers waited outside a car dealership they had randomly selected from a list of such establishments. They stopped every 10th person who came out of the dealership and asked whether he or she thought pollution was a serious problem.
A) The population
The population is the sum total of every member of the public whose opinions on pollution, the researchers are interested in.
B) The population parameter of interest
Since the researchers stopped every member of the sample to ask them whether they thought pollution was a serious problem or not, it follows that the population parameter of interest is the proportion of the population who think that pollution is a serious problem.
C) The sampling frame
The sampling frame is defined as the source material where the sample is drawn from. And for this question, the sampling frame is the population of people leaving car dealership establishments.
D) The sample
The sample is the set of people that were asked the question of whether population was a serious problem or not. The sample includes every 10th person that came out of the chosen car dealership establishments.
E) The sampling method
Note that
- In random sampling, each population member would have an equal chance of being surveyed.
- Stratified sampling divides the population into groups called strata. A sample is taken from some or all of these strata using either random, systematic, or convenience sampling.
- In systematic sampling, a particular number, n, is counted repeatedly and each of the nth member is picked to be sampled.
Hence, this stratified sampling method uses random sampling technique to pick the strata where the samples will be obtained from and systematic sampling is now used for the picking of the members of the sample.
F) Any potential sources of bias you can detect and any problems you see in generalizing to the population of interest.
This survey only limits the members of the sample to those who visit a car dealership, and this cuts out a large percentage of the total population of humans.
Mostly men visit car dealership establishments, Hence, women, children, old people are at a disadvantage as they do not all have an equal chance of being surveyed.
Infact, only a financial class of the population visits car dealership establishments, so, it would be very wrong with all of this bias to use the results of this surveyor generalize for the whole population of people.
Hope this Helps!!!
A local coffee house surveyed 317 customers regarding their preference of chocolate chip or cranberry walnut scones . 150 customers prefer the Cranberry Walnut Scones . 81 customers who responded were males and prefer the Chocolate Chip Scones . 172 female customers responded . Find the probability that a customer chosen at random will be a male or prefer the Chocolate Chip Scones .
1. 25.6%
2. 24.1%
3. 72.9%
4. 98.4%
Answer:
3. 72.9%
Step-by-step explanation:
Let's call M the event that the customer is male and C the event that the customer prefer chocolate chips Scones.
So, the probability P(M∪C) that a customer chosen at random will be a male or prefer the Chocolate Chip Scones is calculated as:
P(M∪C) = P(M) + P(C) - P(M∩C)
Then, there are 145 males (317 customer - 172 females = 145 males), so the probability that the customer is a males is:
P(M) = 145/317 = 0.4574
There are 167 customers that prefer chocolate chips Scones ( 317 customers - 150 customers that prefer the Cranberry Walnut Scones = 167), so the probability that a customer prefer chocolate chips Scones is:
P(C) = 167/317 = 0.5268
Finally, 81 customers were males and prefer the Chocolate Chip Scones, so the probability that a customer will be a male and prefer chocolate chip scones is:
P(M∩C) = 81/317 = 0.2555
Therefore, P(M∪C) is equal to:
P(M∪C) = 0.4574 + 0.5268 - 0.2555
P(M∪C) = 0.7287
P(M∪C) = 72.9%
Answer:
3. 72.9%
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Desired outcomes:
Male or prefers the Chocolate Chip Scones. That is, males and females who prefer the Chocolate Chip Scones.
There are 172 female customers and 317-172 = 145 male customers.
150 customers prefer the Cranberry Walnut Scones. So 317 - 150 = 167 customers prefer the Chocolate Chip Scones.
81 of those are male, so 167 - 81 = 86 are female.
So the total of desired outcomes is 86 + 145 = 231
Total outcomes:
317 total customers.
Probability:
231/317 = 0.729
So the correct answer is:
3. 72.9%
COMPUTE:
A) 40−5÷ 1/5 =
B) (4.8−1.8÷6)÷5=
Answer:
A) 15
B) 0.9
Step-by-step explanation:
Use the correct order of operations.
A) 40 − 5 ÷ 1/5 =
= 40 − 5 * 5
= 40 - 25
= 15
B) (4.8 − 1.8 ÷ 6) ÷ 5 =
= (4.8 − 0.3) ÷ 5
= 4.5 ÷ 5
= 0.9
Suppose that a random sample of size 36 is to be selected from a population with mean 50 and standard deviation 7. What is the approximate probability that X will be within .5 of the population mean
Answer:
Step-by-step explanation:
Let us assume that x is normally distributed. The sample size is greater than 30. Since the the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = standard deviation
n = number of samples
From the information given,
µ = 50
σ = 7
n = 36
If x is within 0.5 of the population mean, it means that x is between (50 - 0.5) and (50 + 0.5)
the probability is expressed as
P(49.5 ≤ x ≤ 50.5)
For x = 49.5
z = (49.5 - 50)/(7/√36) = - 0.43
Looking at the normal distribution table, the probability corresponding to the z score is 0.334
For x = 49.5
z = (50.5 - 50)/(7/√36) = 0.43
Looking at the normal distribution table, the probability corresponding to the z score is 0.666
Therefore,
P(49.5 ≤ x ≤ 50.5) = 0.666 - 0.334 = 0.332
Find the percent of area under a normal curve between the mean and the given number of standard deviations from the mean. (Note that positive indicates above the mean, while negative indicates below the mean.)0.20
Answer:
15.86%
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Percent of area between the mean and 0.20 standard deviations from the mean:
pvalue of Z = 0.2 subtracted by the pvalue of Z = -0.2
Z = 0.2 has a pvalue of 0.5793
Z = -0.2 has a pvalue of 0.4207
0.5793 - 0.4207 = 0.1586
So this percentage is 15.86%
What’s the correct answer for this question?
Answer:
A and B
Step-by-step explanation:
1) Distance to the focus
From (x,y) to the focus(2,-4) {using distance formula}
=√(x-2)²+(y+4)²
2) Distance to the directrix
Is, y+p where P here is (-6)
So
d2 = y+p
= y+(-6)
= y-6
Given that f(x) = x² + 4x, evaluate f(-2).
Answer:
-4
Step-by-step explanation:
A tank contains 5,000 L of brine with 13 kg of dissolved salt. Pure water enters the tank at a rate of 50 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate.
Required:
a. How much salt is in the tank after t minutes?
b. How much salt is in the tank after 20 minutes?
Answer:
a) [tex]x(t) = 13*e^(^-^\frac{t}{100}^)[/tex]
b) 10.643 kg
Step-by-step explanation:
Solution:-
- We will first denote the amount of salt in the solution as x ( t ) at any time t.
- We are given that the Pure water enters the tank ( contains zero salt ).
- The volumetric rate of flow in and out of tank is V(flow) = 50 L / min
- The rate of change of salt in the tank at time ( t ) can be expressed as a ODE considering the ( inflow ) and ( outflow ) of salt from the tank.
- The ODE is mathematically expressed as:
[tex]\frac{dx}{dt} =[/tex] ( salt flow in ) - ( salt flow out )
- Since the fresh water ( with zero salt ) flows in then ( salt flow in ) = 0
- The concentration of salt within the tank changes with time ( t ). The amount of salt in the tank at time ( t ) is denoted by x ( t ).
- The volume of water in the tank remains constant ( steady state conditions ). I.e 10 L volume leaves and 10 L is added at every second; hence, the total volume of solution in tank remains 5,000 L.
- So any time ( t ) the concentration of salt in the 5,000 L is:
[tex]conc = \frac{x(t)}{1000}\frac{kg}{L}[/tex]
- The amount of salt leaving the tank per unit time can be determined from:
salt flow-out = conc * V( flow-out )
salt flow-out = [tex]\frac{x(t)}{5000}\frac{kg}{L}*\frac{50 L}{min}\\[/tex]
salt flow-out = [tex]\frac{x(t)}{100}\frac{kg}{min}[/tex]
- The ODE becomes:
[tex]\frac{dx}{dt} = 0 - \frac{x}{100}[/tex]
- Separate the variables and integrate both sides:
[tex]\int {\frac{1}{x} } \, dx = -\int\limits^t_0 {\frac{1}{100} } \, dt + c\\\\Ln( x ) = -\frac{t}{100} + c\\\\x = C*e^(^-^\frac{t}{100}^)[/tex]
- We were given the initial conditions for the amount of salt in tank at time t = 0 as x ( 0 ) = 13 kg. Use the initial conditions to evaluate the constant of integration:
[tex]13 = C*e^0 = C[/tex]
- The solution to the ODE becomes:
[tex]x(t) = 13*e^(^-^\frac{t}{100}^)[/tex]
- We will use the derived solution of the ODE to determine the amount amount of salt in the tank after t = 20 mins:
[tex]x(20) = 13*e^(^-^\frac{20}{100}^)\\\\x(20) = 13*e^(^-^\frac{1}{5}^)\\\\x(20) = 10.643 kg[/tex]
- The amount of salt left in the tank after t = 20 mins is x = 10.643 kg
A city has just added 100 new female recruits to its police force. The city will provide a pension to each new hire who remains with the force until retirement. In addition, if the new hire is married at the time of her retirement, a second pension will be provided for her husband. A consulting actuary makes the following assumptions: (i) Each new recruit has a 0.4 probability of remaining with the police force until retirement. (ii) Given that a new recruit reaches retirement with the police force, the probability that she is not married at the time of retirement is 0.25. (iii) The events of different new hires reaching retirement and the events of different new hires being married at retirement are all mutually independent events. Calculate the probability that the city will provide at most 90 pensions to the 100 new hires and their husbands. (A) 0.60 (B) 0.67 (C) 0.75 (D) 0.93 (E) 0.99
Answer:
E) 0.99
Step-by-step explanation:
100 recruits x 0.4 chance of retiring as police officer = 40 officers
probability of being married at time of retirement = (1 - 0.25) x 40 = 30 officers
each new recruit will result in either 0, 1 or 2 new pensions
0 pensions when the recruit leaves the police force (0.6 prob.)1 pension when the recruit stays until retirement but doesn't marry (0.1 prob.)2 pensions when the recruit stays until retirement and marries (0.3 prob.)mean = µ = E(Xi) = (0 x 0.6) + (1 x 0.1) + (2 x 0.3) = 0.7
σ² = (0² x 0.6) + (1² x 0.1) + (2² x 0.3) - µ² = 0 + 0.1 + 1.2 - 0.49 = 0.81
in order for the total number of pensions (X) that the city has to provide:
the normal distribution of the pension funds = 100 new recruits x 0.7 = 70 pension funds
the standard deviation = σ = √100 x √σ² = √100 x √0.81 = 10 x 0.9 = 9
P(X ≤ 90) = P [(X - 70)/9] ≤ [(90 - 70)/9] = P [(X - 70)/9] ≤ 2.22
z value for 2.22 = 0.9868 ≈ 0.99
Please answer this correctly
Answer:
452
Step-by-step explanation:
plz mark brainliest!
Answer:
i'll say you have to multiple 9 by 9 than 5 by 5 BUT 23 25 13 and 7 IDK sorry hope i helped :)
Step-by-step explanation:
A person needs to fill 20 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes. How long to finish filling the remaining jugs
Answer:
Step-by-step explanation:
=20
This take 30 minutes to finish filling the remaining jugs.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A person needs to fill 20 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes.
Now,
Let the time to finish filling the remaining jugs = x
Since, A person needs to fill 20 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes.
Hence, By definition of proportion we get;
⇒ 20 / x = 2 / 3
⇒ 20 × 3 / 2 = x
⇒ x = 30
Thus, The time to finish filling the remaining jugs = 30 minutes
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Graph the line with slope -1/3 and y -intercept 6 .
Answer:
plot a point at 6 up from (0,0) and then go down one and over three places then plot another point- and so on - and so on
Step-by-step explanation:
To graph the line using the slope and intercept, first understand what the slope and intercept mean:
Slope is how steep or flat the line appears on the graph.
A very high or low slope (100 or -100) will be very steep on the graph.A slope very close to zero (0.0001 or -0.0001) will be very flat on the graph.A positive slope will travel northeast and southwest (for linear equations).A negative slope will travel northwest and southeast (for linear equations).The y-intercept is the point at which the line hits the y-axis. In this equation, the line hits the y-axis at positive 6, which means that the point is (0, 6).
You can use a method called "rise over run" to graph. The slope is negative one over three, so the line will "rise" negative one units after "running" three units.
So, for every one unit down, the line will travel three units to the right.
Graph this from the point (0, 6), your y-intercept, and plot the points according to the slope:
Score: 4 of 8 pts
TA
23.1.59
A ball is thrown upward and outward from a height of 5 feet. The height of the ball, f(x), in feet, can be mo
f(x) = -0.2x² +2.1x+5
where x is the ball's horizontal distance, in feet from where it was thrown. Use this model to solve parts (
a. What is the maximum height of the ball and how far from where it was thrown does this occur?
The maximum height is feet, which occurs feet from the point of release
(Round to the nearest tenth as needed.)
Answer:
10.5 ft high
5.3 ft horizontally
Step-by-step explanation:
The equation can be written in vertex form to answer these questions.
f(x) = -0.2(x² -10.5x) +5
f(x) = -0.2(x² -10.5x +5.25²) +5 +0.2(5.25²)
f(x) = -0.2(x -5.25)² +10.5125
The vertex of the travel path is (5.25, 10.5125).
The maximum height is 10.5 feet, which occurs 5.3 feet (horizontally) from the point of release.
Please hurry
On each bounce, a ball dropped from 100 feet rises to the height
from which it has fallen. How high does the ball rise, in feet, on the 10th bounce?
Answer:
D
Step-by-step explanation:
divide 10 times starting with 100.
The answer is 25/256 or 0.09765625
The height of the ball dropped from 100 feet on the 10th bounce is 0.09766 feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the height of the ball after x bounce. Given that the ball rises to the height from which it has fallen, hence:
y = 100(1/2)ˣ
After the 10th bounce:
y = 100(1/2)¹⁰ = 0.09766
The height of the ball dropped from 100 feet on the 10th bounce is 0.09766 feet.
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One side of a rectangle is 14 meters. The perimeter of the rectangle is 44 meters. What is the area of this rectangle?
A multiple-choice standard test contains total of 25 questions, each with four answers. Assume that a student just guesses on each question and all questions are answered independently. (a) What is the probability that the student answers more than 20 questions correctly
Answer:
[tex]P(x>20)=9.67*10^{-10}[/tex]
Step-by-step explanation:
If we call x the number of correct answers, we can said that P(x) follows a Binomial distribution, because we have 25 questions that are identical and independent events with a probability of 1/4 to success and a probability of 3/4 to fail.
So, the probability can be calculated as:
[tex]P(x)=nCx*p^{x}*q^{n-x}=25Cx*0.25^{x}*0.75^{25-x}[/tex]
Where n is 25 questions, p is the probability to success or 0.25 and q is the probability to fail or 0.75.
Additionally, [tex]25Cx=\frac{25!}{x!(25-x)!}[/tex]
So, the probability that the student answers more than 20 questions correctly is equal to:
[tex]P(x>20)=P(21)+P(22)+P(23)+P(24)+P(25)[/tex]
Where, for example, P(21) is equal to:
[tex]P(21)=25C21*0.25^{21}*0.75^{25-21}=9.1*10^{-10}[/tex]
Finally, P(x>20) is equal to:
[tex]P(x>20)=9.67*10^{-10}[/tex]
Ares is making 14 jars of honey peanut butter. He wants to use 45 milliliter (ML) of honey in each jar. How much honey (in ML) will ares use in all?
Answer:
630 milliliters.
Step-by-step explanation:
The statement tells us that the final product is 14 jars of honey peanut butter and that in each jar use 45 mliliters of honey. This means that to know the total honey to be used, the required quantity for each jar must be multiplied by the total number of jars, that is:
14 * 45 = 630
Which means that he would spend a total of 630 milliliters.
Step-by-step explanation:
Ares uses 630 ml of honey, because 14×45=630
Please answer this correctly
Answer:
676
Step-by-step explanation:
lxw
14x35
4x24
6x15
676
∠BAD is bisected by . If m∠BAC = 2x - 5 and m∠CAD = 145, the value of x is:
Answer:
x = 75
Step-by-step explanation:
Assuming the angles are equal ( bisected means divided in half)
2x-5 = 145
Add 5 to each side
2x-5+5 = 145+5
2x = 150
Divide by 2
2x/150/2
x = 75
Answer:
x=75
Step-by-step explanation:
∠BAD is bisected by AC and measurement of BAC is equal to 2x - 5 and measurement of CAD is equal to 145. Since they are bisected, they are equal and the solution is shown below:
m ∠ BAC = m ∠ CAD
2x - 5 = 145 , transpose -5 to the opposite side such as:
2x = 145 + 5 , perform addition of 145 and 5
2x = 150
2x / 2 = 150 / 2 , divide both sides by 2
x = 75
The answer is 75 for the x value.
A triangle has sides of lengths 8, 15, and 17. Is it a right triangle? Explain.
Answer:
yes it does
17 is the longest side.
Iff Iff 17%5E2+=+8%5E2+%2B+15%5E2 it's a right triangle. it's a right triangle.
Ps "iff" means if and only if
hope it helps
if so please mark me as brainliest
Find the produce 2 1/3 times 3 1/2
Answer:
49/6 or 8 16/99
Step-by-step explanation:
2 1/3 *3 1/2 = (7/3*7/2)= 49/6
First convert to fraction form
then multiply across numerator to numerator and denominator to deominator
Simplify if needed
Turn to mixed fraction if needed
The probability of drawing a pearl bead out of a bag of mixed beads is 2/3. What is the probability of drawing a bead which is not a pearl?
Answer:
[tex]\frac{1}{3}[/tex] probability of drawing a bead which is not a pearl
Step-by-step explanation:
For each bead that you draw, there are only two possible outcomes. Either it is a pearl bead, or it is not. The sum of these probabilities = 100% = 1.
So
2/3 probability of drawing a pearl bead.
p probability of drawing a non pearl bead.
What is the probability of drawing a bead which is not a pearl?
[tex]p + \frac{2}{3} = 1[/tex]
[tex]p = 1 - \frac{2}{3}[/tex]
[tex]p = \frac{3*1 - 2}{3}[/tex]
[tex]p = \frac{1}{3}[/tex]
[tex]\frac{1}{3}[/tex] probability of drawing a bead which is not a pearl
The mean of the data set(9,5,y,2,x)is twice the data set (8,x, 4,1,3).What is (y-x)
Answer:
y - x = 16
Step-by-step explanation:
Explanation:-
Step(i):-
Given data set A is 9,5,y,2,x
Mean of the Data set A
= [tex]\frac{9 + 5 + y + 2 +x}{5}[/tex]
= [tex]\frac{16 +x+y}{5}[/tex]
Given data set B is 8, x, 4, 1, 3
Mean of the Data set B
= [tex]\frac{8+ x+4+1+3}{5}[/tex]
Step(ii):-
Mean of the Data set A = 2 X Mean of the Data set B
[tex]\frac{16 +x+y}{5} = 2 X \frac{16+x}{5}[/tex]
On simplification , we get
16 +x + y = 2( 16 +x)
16 + x + y = 32 + 2 x
16 + x + y - 32 - 2 x = 0
y - x -16 =0
y - x = 16
Anyone know the answer ?
Answer:
A. SASD. LLStep-by-step explanation:
Two sides and the angle between are marked as congruent. That immediately tells you that the Side-Angle-Side (SAS) theorem of congruence applies.
The angle is a right angle, which makes the adjacent sides be "legs" of the right triangle. Then the Leg-Leg (LL) theorem of congruence for a right triangle also applies.
Appropriate choices are ...
SAS, LL
Graph y < x2 + 4x. Click on the graph until the correct graph appears.
Answer: The correct answer is:
_________________________
The given "graph" in the bottom right, lowest corner
Step-by-step explanation:
_________________________
Note: When there is only one (1) equation give for a graph;
and/or: only one (1) "inequality given";
we look for the symbol.
If the symbol is "not" an "equals" symbol (i.e. not an: = symbol) ;
we check for the type of "inequality" symbol.
If there is a: "less than" (<) ; or a "greater than" (>) symbol; the graph of the "inequality" will have "dashed lines" (since there will be a "boundary").
If there is an "inequality" that is a: "less than or equal to" (≤) ;
or a: "greater than or equal to" (≥) ;
→ then there will be not be a dashed line when graphed;
but rather—a "solid line" ; since "less than or equal to" ;
or "greater than or equal to" —is similar to:
"up to AND including"; or: "lesser/fewer than AND including".).
_________________________
Note: We are given the "inequality" :
→ " y < x² + 4x " .
_________________________________
Note that we have a "less than" symbol (< ) ; so the graph will have a:
"solid line" [and not a "dotted line".].
_________________________________
Note that all of the graphs among our 4 answer choices have "dotted lines".
Not that all values (all x and y coordinated) within the "shaded portion" of the corresponding graph are considered part of the graph.
As such, given any point within the shaded part, the x and y coordinates must match the inequality (i.e. the given inequality must be true when one puts in the "x-coordinate" and "y-coordinate" into the "given inequality" :
→ " y < x² + 4x " .
_________________________
Likewise, we can take any point within the "white, unshaded" portion of any of the graph, and take the "x-coordinate" and "y-coordinate" of that point, and the inequality: → " y < x² + 4x " ; will not hold true when the "x-coordinate" and "y-coordinate" values of that point— are substituted into the "inequality".
_________________________
{Note: Answer is continued on images attached.}.
Wishing you the best!
Consider the homogeneous second-order linear differential equation y′′+4y′−12y=0. Which of the following pairs gives two solutions to this equation? A. y1=e2x,y2=e−6x B. y1=e3x,y2=e1x C. y1=e2x,y2=e−2x D. y1=e−12x,y2=xe−12x E. y1=cos(−12x),y2=sin(−12x) F. y1=e−4x,y2=e−12x Then for these solutions find a particular solution of the form y=c1y1+c2y2 that satisfies the initial conditions y(0)=−5,y′(0)=0. y = y1 + y2.
A farmer was interest in determining how many grasshoppers were in his field. He knows that the distribution of grasshoppers may not be normally distributed in his field due to growing conditions. As he drives his tractor down each row he counts how many grasshoppers he sees flying away. After several rows he figures the mean number of flights to be 57 with a standard deviation of 12. What is the probability of the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor
Answer:
= 0.0041
Step-by-step explanation:
Given that:
A farmer was interest in determining how many grasshoppers were in his field. He knows that the distribution of grasshoppers may not be normally distributed in his field due to growing conditions. As he drives his tractor down each row he counts how many grasshoppers he sees flying away
mean number of flights to be 57
a standard deviation of 12
fewer flights on average in the next 40 rows
[tex]\mu = 57\\\\\sigma=12\\\\n=40[/tex]
so,
[tex]P(x<52)[/tex]
[tex]=P(\frac{x-\mu}{\sigma/\sqrt{n} } <\frac{52-57}{12/\sqrt{40} } )\\\\=P(z<\frac{-5\times6.325}{12} )\\\\=P(z<\frac{-31.625}{12})\\\\=P(z<-2.64)[/tex]
using z table
= 0.0041
The probability of the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor is 0.0041 and this can be determined by using the properties of probability.
Given :
The distribution of grasshoppers may not be normally distributed in his field due to growing conditions.The mean number of flights to be 57 with a standard deviation of 12.The probability of the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor, can be determined by using the following calculations:
[tex]\rm P(x<52)=P\left (\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n} }}<\dfrac{52-57}{\dfrac{12}{\sqrt{40} }}\right)[/tex]
[tex]\rm P(x<52)=P\left (z<\dfrac{-5\times 6.325}{12 }}\right)[/tex]
[tex]\rm P(x<52)=P\left (z<\dfrac{-31.625}{12 }}\right)[/tex]
[tex]\rm P(x<52)=P\left (z<-2.64\right)[/tex]
Now, using z-table:
P(x < 52) = 0.0041
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if F (x) equals 4x + 7 which of the following is the inverse of F(x)
Answer:
[tex]F^{-1}(x)=\dfrac{x-7}{4}[/tex]
Step-by-step explanation:
To find the inverse function, solve for y the relation ...
F(y) = x
4y +7 = x
4y = x - 7
y = (x -7)/4 . . . . the inverse function
[tex]\boxed{F^{-1}(x)=\dfrac{x-7}{4}}[/tex]
Classify the triangle by its sides, and then by its angles.
128 degrees
26 degrees
26 degrees
16 cm
16 cm
28 cm
Classified by its sides, the triangle is a(n)
▼
isosceles
scalene
equilateral
triangle.
Classified by its angles, the triangle is a(n)
▼
obtuse
acute
right
triangle.
How would you use a completely randomized experiment in each of the following settings?
Is a placebo being used or not? Be specific and give details.
a. A charitable nonprofit organization wants to test two methods of fund-raising. From a list of 1000 past donors, half will be sent literature about the successful activities of the charity and asked to make another donation. The other 500 donors will be contacted by phone and asked to make another donation. The percentage of people from each group who make a new donation will be compared.
b. A tooth-whitening gel is to be tested for effectiveness. A group of 85 adults have volunteered to participate in the study. Of these. 43 are to be given a gel that contains the tooth-whitening chemicals. The remaining 42 are to be given a similar-looking package of gel that does not contain the tooth-whitening chemicals. A standard method will be used to evaluate the whiteness of teeth for all participants. Then the results for the two groups will be compared. How could this experiment he designed to be double-blind?
c. Consider the experiment described in part (a). Describe how you would use a randomized block experiment with blocks based on age. Use three blocks: donors younger than 30 years old. donors 30 to 59 years old. donors 60 and older.
Answer:
Step-by-step explanation:
a. Two methods of fund raising is being tested here in the first case study. To make a completely randomized experiment. I would use and randomly assign half the population of the 1000 donor sample that will be sent literature about the successful activities of the charity and asked to make another donation to one of the two treatment conditions: which is a sent literature about the successful activities of the charity. While the placebo group would be the other 500 donors contacted by phone and asked to make another donation with no influence whatever from the charity.
b. For the second case study, To make a completely randomized experiment. I would use and randomly assign 43 particupants which are to be given a gel that contains the tooth-whitening chemicals to the treatment condition containing the tooth-whitening chemicals while the placebo group would be the remaining 42 which are to be given a similar-looking package of gel that does not contain the tooth-whitening chemicals.
c. Using three blocks: the completely randomized design experiment would be:
Donors younger than 30 years old:
Sent literature: Yes No
Contact by phone: Yes No
Donors 30 to 59 years old:
Sent literature: Yes No
Contact by phone: Yes No
Donors 60 and older:
Sent literature: Yes No
Contact by phone: Yes No
(Yes means yes to another donation and No means no to another donation)
Answer:
Step-by-step explanation:
a. Two methods of fund raising is being tested here in the first case study. To make a completely randomized experiment. I would use and randomly assign half the population of the 1000 donor sample that will be sent literature about the successful activities of the charity and asked to make another donation to one of the two treatment conditions: which is a sent literature about the successful activities of the charity. While the placebo group would be the other 500 donors contacted by phone and asked to make another donation with no influence whatever from the charity.
b. For the second case study, To make a completely randomized experiment. I would use and randomly assign 43 particupants which are to be given a gel that contains the tooth-whitening chemicals to the treatment condition containing the tooth-whitening chemicals while the placebo group would be the remaining 42 which are to be given a similar-looking package of gel that does not contain the tooth-whitening chemicals.
c. Using three blocks: the completely randomized design experiment would be:
Donors younger than 30 years old:
Sent literature: Yes No
Contact by phone: Yes No
Donors 30 to 59 years old:
Sent literature: Yes No
Contact by phone: Yes No
Donors 60 and older:
Sent literature: Yes No
Contact by phone: Yes No
(Yes means yes to another donation and No means no to another donation)
Which expession is equivalent to -3(6c + 2) + 5c
Answer:
-13c-6
Step-by-step explanation:
-3(6c + 2) + 5c
Distribute
-18c -6 +5c
Combine like terms
-13c-6
Answer:
-13c -6
Step-by-step explanation:
-3 (6c) -3x2+5c
multiply 6 by -3
-18c-3x2+5c
multiply -3 by 2
-18c -6+ 5c
add 18c and 5c
-13c -6