Answer:
139 boys
Step-by-step explanation:
Using the given information, we can set up a system of equations.
Let the number of girls in the class be x and let the number of boys in the class be y.
x + y = 351
x = y + 73
Solving this system of equations would tell you that there are 139 boys in this graduating class.
Leave a comment if you want me to be a bit more in-depth.
When faced with a problem or choice, humans can use two different strategies: "cognitive reflectivity," which results in slower responses and few mistakes, or "cognitive impulsivity," which results in quicker responses but also more mistakes. Depending on the individual, these two strategies are used differently.
A pilot experiment was conducted on 22 right-handed individuals who were administered a cognitive reflectivity-impulsivity questionnaire, while recording voxel-based morphometry (regional gray matter density) in the ventral medial prefrontal cortex.1. Based on the experimental design and the kind of data collected, which statistical test(s) should be used to determine whether there is an association between the cognitive strategy, cognitive reflectivity and the gray matter density of the ventral medial prefrontal cortex?
Select all that apply!O t-test of zero linear correlationO One-way ANOVAO z-testO correlation coefficient (r)O two sample t-test
Based on the experimental design and the data collected the statistical test that should be used is the correlation coefficient.
What are statistical tests?The statistical tests are tests that are used by researchers to determine the progress of a set process and make a quantitative decision during analysis of test results.
Example of statistical tests include the following:
t-test of zero linear correlation,One-way ANOVA,z-test,correlation coefficient, and two sample t-test.The correlation coefficient which is a type of statistical test is used to assess the strength and direction of the linear relationships between pairs of variables.
Therefore, the relationship between cognitive reflectivity and cognitive impulsivity in human data can be statistically analysed using correlation coefficient.
Learn more about statistical tests here:
https://brainly.com/question/15980493
Samuel bought 32 and 1/2 ft of window trim at a hardware store the trim cost $1.75 per foot including sales tax if Samuel paid with a $100 bill how much change should he have received
Answer:
The amount of change he should received is
$100 - $56.875
= $43.125
= $43.13
Step-by-step explanation:
Length of window trim = 32 and 1/2 ft
Cost per foot = $1.75
Amount paid = $100
Total cost of window trim = 32.5×1.75 = $56.875
The amount of change he should received is
$100 - $56.875
= $43.125
= $43.13
An old house in Pomona, CA is inhabited by a variety of ghosts. Ghost appearances occur in the house according to a Poisson process having a rate of 1.4 ghosts per hour. A professor from Cal Poly Pomona has developed a device that can be used to detect ghost appearances. Suppose it is now 1:00 p.m. and the last ghost appearance (the 6th overall) was at 12:35 p.m.
What is the probability that the 7th ghost will appear before 1:30 p.m., to the nearest three decimal places?
Answer:
The probability is 0.503
Step-by-step explanation:
If the ghost appearances occur in the house according to a Poisson process with mean m, the time between appearances follows a exponential distribution with mean 1/m. so, the probability that the next ghost appearance happens before x hours is equal to:
[tex]P(X\leq x)=1-e^{-xm}[/tex]
Then, replacing m by 1.4 ghosts per hour we get:
[tex]P(X\leq x)=1-e^{-1.4x}[/tex]
Additionally, The exponential distribution have a memoryless property, so if it is now 1:00 p.m. and we want the probability that ghost appear before 1:30 p.m., we need to find the difference in hours from 1:00 p.m and 1:30 p.m. no matter that the last ghost appearance was at 12:35 p.m.
Therefore, there are 0.5 hours between 1:00 p.m. and 1:30 p.m, so the probability that the 7th ghost will appear before 1:30 p.m is calculated as:
[tex]P(x\leq 0.5)=1-e^{-1.4*0.5} =0.503[/tex]
Final answer:
The probability that the 7th ghost will appear before 1:30 p.m. in an old house in Pomona, CA can be calculated as approximately 0.5034, or 50.34%. This calculation is based on the Poisson distribution, with a rate of 1.4 ghosts per hour and the last ghost appearance occurring at 12:35 p.m.
Explanation:
The probability of the 7th ghost appearing before 1:30 p.m. can be calculated using the Poisson distribution. We know that the rate of ghost appearances is 1.4 ghosts per hour, which means the average time between ghost appearances is 1/1.4 hours. From 12:35 p.m. to 1:00 p.m., there are 25 minutes, or 25/60 hours. So, the probability that the 7th ghost will appear before 1:30 p.m. is equal to the probability that there will be at least 1 ghost in the remaining time, i.e., the probability that at least one ghost appears in the next 30 minutes.
We can use the complementary probability method to calculate this. The complementary probability is the probability that none of the ghosts appears in the next 30 minutes. Since the time follows a Poisson process, we can use the Poisson probability formula. Let's calculate:
Calculate the average rate of ghost appearances in the next 30 minutes:Rate = (1.4 ghosts/hour) * (30/60 hours) = 0.7 ghostsCalculate the probability of no ghost appearing:P(X = 0) = (e^(-0.7) * 0.7^0) / 0! = e^(-0.7) ≈ 0.4966Calculate the complementary probability:P(at least 1 ghost) = 1 - P(no ghost) = 1 - 0.4966 ≈ 0.5034Therefore, the probability that the 7th ghost will appear before 1:30 p.m. is approximately 0.5034, or 50.34%.
Which of the following are true about regression with one predictor variable (often called "simple regression")? Check all that apply.
A. The slope describes the amount of change in Y for a one-unit increase in X
B. The regression equation is the line that best fits a set of data as determined by having the least squared error
C. The slope, b, of the regression equation has the same value as r, the estimated correlation
Answer:
A. The slope describes the amount of change in Y for a one-unit increase in X .B. The regression equation is the line that best fits a set of data as determined by having the least squared error.Step-by-step explanation:
In statistics, linear regression is a analysis we do to describe the relationship between two variables. With this study, we pretend to know if there's a positive or negative correlation between those variables, if that correlation is strong or weak.
In a linear regression analysis, we modeled the data set using a regression equation, which is basically the line that best fits to the data set, this line is like the average where the majority of data falls. That means choice A is right.
When we use linear equations, we need to know its characteristics, and the most important one is the slope, which is the ratio between the dependent variable and the independent variable. Basically, the slope states the unit rate between Y and X, in other words, it states the amount of Y per unit of X. That means choice B is correct.
Therefore, the correct answers are A and B.
The options that are true about regression with one predictor variable include:
A. The slope describes the amount of change in Y for a one-unit increase in XB. The regression equation is the line that best fits a set of data as determined by having the least squared error.Regression simply refers to a statistical measurement which attempts to determine the strength that exists between a dependent variable and the independent variables.
It should be noted that in one predictor variable, the slope describes the amount of change in Y for a one-unit increase in X and the regression equation is the line that best fits a set of data as determined by having the least squared error.
Read related link on:
https://brainly.com/question/11503532
You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood. Let women and men be represented by populations 1 and 2, respectively. The relevant hypotheses are constructed as ____________.
H0: Mue1-Mue2 less than or equal 0.
Ha: Mue1-Mue2>0
H0: Mue1-Mue greater or equal 0.
Ha: Mue1-Mue<0
H0: P1-P2 less than or equal 0
Ha: P1-P2>0
H0: P1-P2 greater than or 0
Ha: P1-P2<0
Answer:
H₀: p₁ - p₂ < 0.
Hₐ: p₁ - p₂ > 0.
Step-by-step explanation:
In this case, we need to determine if there is a higher incidence of smoking among women than among men in a neighborhood.
An experiment can be performed involving collecting two samples of men and women and computing the proportion of men and women smokers in the neighborhood. Then these two sample proportions can be used to determine which proportion is higher.
We are computing proportions of men and women smokers instead of the mean number of men and women smokers because the we need to determine the incidence of smoking among men and women, i.e. the occurrence or frequency or rate of men and women smokers.
So, a two proportion test can be applied to determine whether the proportion of women smokers is higher than men.
The population proportion of women in the neighborhood is represented by p₁ and the population proportion of men in the neighborhood is represented by p₂.
The hypothesis can be defined as:
H₀: The proportion of women smokers is not higher than men, i.e. p₁ - p₂ < 0.
Hₐ: The proportion of women smokers is higher than men, i.e. p₁ - p₂ > 0.
Final answer:
The null hypothesis (H0) should be P1 - P2 ≥ 0, indicating no higher incidence of smoking among women, and the alternative hypothesis (Ha) should be P1 - P2 < 0, suggesting a higher incidence of smoking among women.
Explanation:
When conducting a hypothesis test to determine if there's a higher incidence of smoking among women than among men in a neighborhood, you would use two hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha). Since we are looking to find if the incidence is higher in women, the null hypothesis should reflect there is no difference or that the incidence in women is less than or equal to the incidence in men. Therefore, the correct setup using population proportions (P1 for men and P2 for women) would be:
H0: P1 - P2 ≥ 0 (there is no higher incidence of smoking among women compared to men)Ha: P1 - P2 < 0 (there is a higher incidence of smoking among women compared to men)The null hypothesis statement is that the proportion of women who smoke is less than or equal to the proportion of men who smoke. The alternative hypothesis is what you intend to prove, which is that more women smoke than men in the neighborhood, hence P1 - P2 < 0. This would be considered a left-tailed test.
Simplify the product using the distributive property. (5h - 5)(5h - 6)
A student has a monthly budget of $800. She can spend her budget on two items, X and Y. Each unit of X costs $20 and each unit of Y costs $10. If the student has a utility function of U = 348X + 100Y + 6X2 + 4Y2 + 2XY, what is the optimal amount of X and Y for her to consume to have the maximum utility? What is this total utility? What is the value of lambda and what does this mean?
Answer:
Check the explanation
Step-by-step explanation:
Total utility is the overall satisfaction that a particular consumer received from consuming a given overall quantity of a good or service, To calculate the value of total utility economists utilize the following basic total utility formula: TU = U1 + MU2 + MU3
Kindly check the attached image below to see the step by step explanation to the question above.
The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).
The center of the circle is at the point , and its radius is units. The equation of this circle in standard form is .
Answer:
Read the explanation for the answers
Step-by-step explanation:
To find the midpoint, you simply need to find the average of the two endpoints. The average of 10.5 and 5.5 is 8, and the average of 4 and 4 is 4. Therefore, the center of the circle is at (4,8). The radius is the distance from the center to either of these points, or 8-5.5=2.5 units. And finally, the formula for the circle in standard form is [tex](y-8)^2+(x-4)^2=6.25[/tex]. Hope this helps!
What is the product of (3y+4)2
Answer:
6y+8
Step-by-step explanation:
You should apply distributive property of the product, and multiply 2 by 3y and then add to that result the product of 2 times 4: [tex](3y+4)\times2= 2\times3y+2\times4=6y+8[/tex].
A cable runs along the wall from C to P at a cost of $4 per meter, and straight from P to M at a cost of $5 per meter. If M is 9 meters from the nearest point A on the wall where P lies, and A is 33 meters from C, find the distance from C to P such that the cost of installing the cable is minimized and find this cost.
Answer:
The minimum cost of installing the cable is $156.
Step-by-step explanation:
We have an optimization problem.
We have to minimize the cost of the cable.
We will use the variable x to express the the length of cable CP and PM, accordingly to the attache picture.
The length of the cable that goes from C to P (let's call it CP) is x.
[tex]\bar{CP}=x[/tex]
Then, the length of the cable that goes from P to M (PM) can be calcualted usign the Pithagorean theorem:
[tex]\bar{PM}=\sqrt{(33-x)^2+9^2}[/tex]
The cost function Y is:
[tex]Y=4*\bar{CP}+5*\bar{PM}=4x+5\sqrt{(33-x)^2+9^2}[/tex]
To optimize this cost funtion we have to derive and equal to 0:
[tex]\dfrac{dY}{dx}=0\\\\\\\dfrac{dY}{dx}=4+5(\dfrac{1}{2})((33-x)^2+9^2)^{-1/2} *(-2)(33-x)\\\\\\\dfrac{dY}{dx}=4+5\dfrac{x-33}{\sqrt{(33-x)^2+81}}=0\\\\\\\dfrac{x-33}{\sqrt{(33-x)^2+81}}=-\dfrac{4}{5}\\\\\\(x-33)=-\dfrac{4}{5}\sqrt{(33-x)^2+81}\\\\\\(x-33)^2=(-\dfrac{4}{5})^2[(x-33)^2+81]\\\\\\(x-33)^2=\dfrac{16}{25}(x-33)^2+\dfrac{1296}{25}\\\\\\\dfrac{25-16}{25} (x-33)^2=\dfrac{1296}{25}\\\\\\9(x-33)^2=1296\\\\\\x-33=\sqrt{\dfrac{1296}{9}}=\sqrt{144}=\pm12\\\\\\x=33\pm12\\\\\\x_1=33-12=21\\\\x_2=33+12=45[/tex]
The valid solution is x=21, as x can not phisically larger than 33.
The cost then becomes:
[tex]Y=4*\bar{CP}+5*\bar{PM}=4x+5\sqrt{(33-x)^2+9^2}\\\\\\Y=4*21+5\sqrt{(33-21)^2+81}\\\\Y=81+5\sqrt{144+81}\\\\Y=81+5\sqrt{225}\\\\Y=81+5*15\\\\Y=81+75\\\\Y=156[/tex]
This optimization problem in calculus can be solved by setting up a cost function for the total cable installation, taking its derivative, setting it equal to 0 to find the critical points, which will give you the distance from C to P that minimizes cost, check this point for being minimal and calculating the minimal cost by substituting the found distance into the originally defined cost function.
Explanation:The problem can be solved using the calculus principle of optimization. The situation described in your question makes a right triangle AMP. In this triangle, the vertical side (AP) measures 9 meters, and the hypotenuse (PM) represents cable installation that costs $5 per meter. The distance PC along the wall is $4 per meter. The cost of total cable installation from C -> P -> M is given as follows:
Cost = 4 * length CP + 5 * length PM
By the Pythagorean theorem, we know that [tex]PM = \sqrt{AP^2 + (33 - CP)^2}[/tex] Substituting PM into the equation, we get[tex]\text{Cost} = 4CP + 5 \cdot \sqrt{9^2 + (33-CP)^2}[/tex]
To minimize the cost, we take the derivative of the cost function and set it equal to 0 to find the critical points. Solving this equation will give you the value of CP that minimizes cost. Hence, by substituting found CP back to the original cost formula, we can find the minimal cost of installing the cable.
Learn more about Calculus Optimization here:https://brainly.com/question/35182200
#SPJ6
What is the first step in solving 2x=y X+y=30
Answer: x = 10 y=20
Step-by-step explanation:
You can answer this question by plugging in each equation:
2x=y, x+y=30. Let us plug y as 2x in the second equation x+y=30
x+2x= 30
3x= 30
x=10
After we found x we can then find y by plugging the 10 for x.
2(10) = y
y =20
or you could plug in the other equation
10+y=30
subtract 10 from 30 and we get 20
to double check we can plug in both numbers
2(10) = 20 which is correct
and 10 + 20 = 30 which is correct
The mean monthly food budget for 39 residents of the local apartment complex is $419. What is the best point estimate for the mean monthly food budget for all residents of the local apartment complex?
Answer:
The best point estimate for the mean monthly food budget for all residents of the local apartment complex is $419.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem:
The mean of the sample is $419.
What is the best point estimate for the mean monthly food budget for all residents of the local apartment complex?
By the Central Limit Theorem(inverse, that is, sample to the population), $419.
The best point estimate for the mean monthly food budget for all residents of the local apartment complex is $419.
jerome filled bags with trail mix. the weights of the bags are
draw a rectangle that is 28 units by 12 units
Answer:
Attached
Step-by-step explanation:
On a cartessian plane, we take four points as shown. Point A has coordinates as (4, 0) while point B is (32, 0). Since the y cordinates are zero, don't change, only x change. Change in x coordinates is 32-4=28 units.
Point C is (32, 12) where x has not changed when compared to point B but y changes by 12-0=12 units
Therefore, the diagram is triangle whose length is 28 units while width is 12 units.
Use Demoivres Theorem to find (1 + i) 20.
a. 1024i
b. -1024
C.-1024
D.1024
Answer:
-1024
Step-by-step explanation:
Moivre's theorem allows to easily obtain trigonometric formulas that express the sine and cosine of a multiple angle as a function of the sine and cosine of a simple angle.
De Moivre's theorem can be applied to any complex number [tex]z[/tex]
Where:
[tex]z\in Z[/tex]
Let:
[tex](1+i)=z\\n=20[/tex]
According to Demoivres Theorem, If:
[tex]z=||z||(cos(\theta)+isin(\theta))[/tex]
Then:
[tex]z^n=||z||^n(cos(n\theta)+isin(n\theta))[/tex]
For a complex number [tex]z[/tex]:
[tex]z=a+bi[/tex]
Its magnitude and angle are given by:
[tex]||z||=\sqrt{a^2+b^2} \\\\\theta=arctan(\frac{b}{a} )[/tex]
So:
[tex]||z||=\sqrt{1^2+1^2} =\sqrt{2}[/tex]
[tex]\theta=arctan(\frac{1}{1} )=45^{\circ}[/tex]
Therefore, using De Moivre's theorem:
[tex]z^n=(\sqrt{2} )^{20}(cos(20*45)+isin(20*45))\\\\z^n=(\sqrt{2} )^{20}(cos(900)+isin(900))\\\\z^n=1024(-1+i(0))\\\\z^n=1024(-1)\\\\z^n=(1+i)^{20}=-1024[/tex]
C on e2020
i did it *dab*
PLEASE HELP ASAP!! Major question points!! geometry
Answer:
A
Step-by-step explanation:
If you plug in the numbers to the formula, A is the correct answer.
A marketing consultant was hired to visit a random sample of five sporting goods stores across the state of California. Each store was part of a large franchise of sporting goods stores. The consultant taught the managers of each store better ways to advertise and display their goods.
The net sales for 1 month before and 1 month after the consultant's visit were recorded as follows for each store (in thousands of dollars):
Before visit: 57.1 94.6 49.2 77.4 43.2
After visit: 63.5 101.8 57.8 81.2 41.9
Do the data indicate that the average net sales improved? (Use a= 0.05)
Answer:
[tex]t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{4.94 -0}{\frac{3.901}{\sqrt{5}}}=2.832[/tex]
[tex]df=n-1=5-1=4[/tex]
[tex]p_v =P(t_{(4)}>2.832) =0.0236[/tex]
We see that the p value is lower than the significance level of 0.05 so then we have enough evidence to reject the null hypothesis and we can conclude that the average net sales improved
Step-by-step explanation:
Let put some notation
x=test value before , y = test value after
x: 57.1 94.6 49.2 77.4 43.2
y: 63.5 101.8 57.8 81.2 41.9
The system of hypothesis for this case are:
Null hypothesis: [tex]\mu_y- \mu_x \leq 0[/tex]
Alternative hypothesis: [tex]\mu_y -\mu_x >0[/tex]
The first step is calculate the difference [tex]d_i=y_i-x_i[/tex] and we obtain this:
d: 6.4, 7.2, 8.6, 3.8, -1.3
The second step is calculate the mean difference
[tex]\bar d= \frac{\sum_{i=1}^n d_i}{n}=4.94[/tex]
The third step would be calculate the standard deviation for the differences, and we got:
[tex]s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =3.901[/tex]
The next step is calculate the statistic given by :
[tex]t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{4.94 -0}{\frac{3.901}{\sqrt{5}}}=2.832[/tex]
The next step is calculate the degrees of freedom given by:
[tex]df=n-1=5-1=4[/tex]
Now we can calculate the p value, since we have a right tailed test the p value is given by:
[tex]p_v =P(t_{(4)}>2.832) =0.0236[/tex]
We see that the p value is lower than the significance level of 0.05 so then we have enough evidence to reject the null hypothesis and we can conclude that the average net sales improved
what is the slope intercept form of 2x-3y=9
Answer:
-3y=-2x+9
Step-by-step explanation:
flip the value
when flipping a value remember to invert its sign
Suppose that E and F are two events and that Upper P (Upper E and Upper F )equals0.3 and Upper P (Upper E )equals0.5. What is Upper P (F|E )? Upper P (F|E )equals nothing (Type an integer or a decimal.)
Answer:
[tex]P(\frac{F}{E}) =\frac{0.3}{0.5} =0.6[/tex]
Step-by-step explanation:
Step 1:-
Suppose that E and F are two events and that P(E n F) = 0.3
also given P(E) =0.5
Conditional probability:-
if E₁ and E₂ are two events in a Sample S and P(E₁)≠ 0, then the probability of E₂ , after the event E₁ has occurred, is called the Conditional probability
of the event E₂ given E₁ and is denoted by
[tex]P(\frac{F}{E}) = \frac{P(EnF)}{P(E)}[/tex]
[tex]P(\frac{F}{E}) =\frac{0.3}{0.5} =0.6[/tex]
Simplify the following equation as best as you can.
-6.4m + 4(0.5m - 0.8)
Answer:
-4.4m-3.2
Step-by-step explanation:
-6.4m+4(0.5m-0.8)
-6.4m+4*0.5+4*0.8
-6.4m+2m-3.2
-4.4m-3.2
Answer:
-4.4m-3.2
Step-by-step explanation:
multiply everything in the parentheses by 4 and then add.
Which equation represents the magnitude of an
earthquake that is 100 times more intense than a
standard earthquake?
Answer:
m=log 100s/S
Step-by-step explanation:
howdy!
answer is in the attachment below :)
A total of 1 232 students have taken a course in Spanish, 879 have taken a course in French, and 114 have taken a course in Russian. Further, 103 have taken courses in both Spanish and French, 23 have taken courses in both Spanish and Russian, and 14 have taken courses in both French and Russian. If 2 092 students have taken at least one of Spanish, French, and Russian, how many students have taken a course in all three languages
Answer:
[tex]n(S\cap F \cap R)=7[/tex]
Step-by-step explanation:
The Universal Set, n(U)=2092
[tex]n(S)=1232\\n(F)=879\\n(R)=114[/tex]
[tex]n(S\cap R)=23\\n(S\cap F)=103\\n(F\cap R)=14[/tex]
Let the number who take all three subjects, [tex]n(S\cap F \cap R)=x[/tex]
Note that in the Venn Diagram, we have subtracted [tex]n(S\cap F \cap R)=x[/tex] from each of the intersection of two sets.
The next step is to determine the number of students who study only each of the courses.
[tex]n(S\:only)=1232-[103-x+x+23-x]=1106+x\\n(F\: only)=879-[103-x+x+14-x]=762+x\\n(R\:only)=114-[23-x+x+14-x]=77+x[/tex]
These values are substituted in the second Venn diagram
Adding up all the values
2092=[1106+x]+[103-x]+x+[23-x]+[762+x]+[14-x]+[77+x]
2092=2085+x
x=2092-2085
x=7
The number of students who have taken courses in all three subjects, [tex]n(S\cap F \cap R)=7[/tex]
Using the principle of Inclusion-Exclusion, we find that 7 students have taken courses in all three languages: Spanish, French, and Russian.
Finding the Number of Students Taking All Three Language Courses
We can solve this problem using the principle of Inclusion-Exclusion. Let:
S = number of students taking Spanish
F = number of students taking French
R = number of students taking Russian
SF = number of students taking both Spanish and French
SR = number of students taking both Spanish and Russian
FR = number of students taking both French and Russian
SFR = number of students taking all three languages.
From the given data:
S = 1232F = 879R = 114SF = 103SR = 23FR = 14Total students taking at least one language = 2092The principle of Inclusion-Exclusion states:
Total = S + F + R - SF - SR - FR + SFR
2092 = 1232 + 879 + 114 - 103 - 23 - 14 + SFR
Solving for SFR:
2092 = 2085 + SFR
Thus, SFR = 2092 - 2085 = 7
Therefore, 7 students have taken courses in all three languages: Spanish, French, and Russian.
Rebekah wants to read a certain number of pages each day during summer vacation.
Today, she read 204 pages, which is 136% of her goal.
How many pages does Rebekah want to read each day?
A. 75 pages
B. 130 pages
C. 150 pages
D. 560 pages
Answer:
C. 150 pages
Step-by-step explanation:
204 divided by 136 = 1.5
1.5 * 100 = 150
Hope it helps! :)
Which point has coordinates of (2, 0)?
Answer:
J
Step-by-step explanation:
What is the constant proportionality
Answer:
The relationship between price and the number of empanadas is PROPORTIONAL.
1 Empanada = 50 cent = $0.5
Constant of PROPORTIONALITY = ½
Step-by-step explanation:
From the given table:
2 Empanadas = $1
6 Empanadas = $3
We see that, as the number of Empanadas increases, the amount in Dollars also increases. Such that:
Let E = Empanadas
$ = dollar
~ = sign of PROPORTIONALITY.
Therefore:
$ ~ E
$ = KE
Where K = constant of proportionality.
When E = 4; $ = 2
$2 = K4
K= 2/4
K = ½
$ = ½E (Binding formula)
This applies for all the number of Empanadas bought.
Answer:
.50
Step-by-step explanation:
I ready
Given the following information about a hypothesis test of the difference between two means based on independent random samples, which one of the following is the correct rejection region at a significance level of .05? Assume that the samples are obtained from normally distributed populations having equal variances.HA: μA > μB, = 12, = 9, s1 = 5, s2 = 3, n1 = 13, n2 = 10.A. Reject H0 if Z > 1.96B. Reject H0 if Z > 1.645C. Reject H0 if t > 2.08D. Reject H0 if t > 1.782E. Reject H0 if t > 1.721
Answer:
Null hypothesis:[tex]\mu_{A} \leq \mu_{B}[/tex]
Alternative hypothesis:[tex]\mu_{A} > \mu_{B}[/tex]
Since we dpn't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:
[tex]t=\frac{\bar X_{A}-\bar X_{B}}{\sqrt{\frac{\sigma^2_{A}}{n_{A}}+\frac{\sigma^2_{B}}{n_{B}}}}[/tex] (1)
Now we need to find the degrees of freedom given by:
[tex] df = n_A + n_B -2= 13+10-2=21[/tex]
And now since we are conducting a right tailed test we are looking ofr a value who accumulates 0.05 of the are on the right tail fo the t distribution with df =21 and we got:
[tex] t_{cric}= 1.721[/tex]
And for this case the rejection zone would be:
E. Reject H0 if t > 1.721
Step-by-step explanation:
Data given and notation
[tex]\bar X_{A}=12[/tex] represent the mean for 1
[tex]\bar X_{B}=9[/tex] represent the mean for 2
[tex]s_{A}=5[/tex] represent the sample standard deviation for 1
[tex]s_{2}=3[/tex] represent the sample standard deviation for 2
[tex]n_{1}=13[/tex] sample size for the group 1
[tex]n_{2}=10[/tex] sample size for the group 2
t would represent the statistic (variable of interest)
[tex]\alpha=0.05[/tex] significance level provided
Develop the null and alternative hypotheses for this study
We need to conduct a hypothesis in order to check if the mean for group A is higher than the mean for B:
Null hypothesis:[tex]\mu_{A} \leq \mu_{B}[/tex]
Alternative hypothesis:[tex]\mu_{A} > \mu_{B}[/tex]
Since we dpn't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:
[tex]t=\frac{\bar X_{A}-\bar X_{B}}{\sqrt{\frac{\sigma^2_{A}}{n_{A}}+\frac{\sigma^2_{B}}{n_{B}}}}[/tex] (1)
Now we need to find the degrees of freedom given by:
[tex] df = n_A + n_B -2= 13+10-2=21[/tex]
And now since we are conducting a right tailed test we are looking ofr a value who accumulates 0.05 of the are on the right tail fo the t distribution with df =21 and we got:
[tex] t_{cric}= 1.721[/tex]
And for this case the rejection zone would be:
E. Reject H0 if t > 1.721
a snack mix recipe calls for 1 1/4 cups of dip and 1/2 cups of veggies. Parkers want to make the same recipe using 1 cup of veggies. How many cups of dip will parker need?
Answer:
2 1/2 cups
Step-by-step explanation:
You are doubling your recipe. You would do 1 1/4 × 2. First, 1 × 2 = 2 and then 1/4 × 2 = 1/2. Put them together for your answer. I hope this helped.
Final answer:
Parker will need 2 1/2 cups of dip.
Explanation:
To find out how many cups of dip Parker will need, we can set up a proportion using the given information.
The snack mix recipe calls for 1 1/4 cups of dip and 1/2 cups of veggies.
Let's call the number of cups of dip Parker needs x.
The proportion will be: 1 1/4 cups / 1/2 cups = x cups / 1 cup.
To solve for x, we can cross multiply and then divide: (1 1/4) * 1 = (1/2) * x.
Simplifying both sides gives us 5/4 = 1/2 * x.
To isolate x, we can multiply both sides by the reciprocal of 1/2, which is 2/1: (5/4) * (2/1) = x.
Multiplying gives us x = 10/4, which simplifies to x = 2 1/2 cups.
Which polynomials are prime? Check all of the boxes that apply.
x² +9
x²_9
x2 + 3x + 9
-2x² +8
Answer: x^2+9 and x^2+3x+9
Step-by-step explanation:
A polynomial is prime if it cannot be factored into polynomials of lower degree. In this case, x² +9 and x² + 3x + 9 are prime polynomials while x² -9 and -2x² +8 are not.
Explanation:In mathematics, a polynomial is said to be prime if it cannot be factored into polynomials of lower degree, at least one of which must be non-constant. To determine if a polynomial is prime, we try to factor it. In our case:
x² +9 is a prime polynomial because it is a sum of squares and cannot be factored into real polynomials of lower degree. x² -9 is not a prime polynomial because it can be factored into (x-3)(x+3). x² + 3x + 9 is a prime polynomial because it cannot be factored into real polynomials of lower degree. -2x² +8 is not a prime polynomial as it can be factored into -2(x²-4). Learn more about Prime Polynomials here:
https://brainly.com/question/17489661
#SPJ3
Suppose parts (a) through (d) below provide results for a study on the role of calcium in reducing the symptoms of PMS. For each of the parts, compute an approximate 95% confidence interval for the difference in mean symptom scores between the placebo and calcium-treated conditions for the symptom listed. In each case, the results given are mean ± standard deviation. Suppose there were 228 participants in the placebo group and 212 in the calcium-treated group. (Round your answers to two decimal places.)
(a) mood swings: placebo = 0.70 ± 0.78; calcium = 0.50 ± 0.53
(b) crying spells: placebo = 0.39 + 0.57; calcium = 0.21 + 0.40
(c) aches and pains: placebo = 0.45 + 0.60; calcium = 0.37 + 0.45
(d) craving sweets or salts: placebo = 0.60 + 0.75; calcium = 0.44 + 0.61
Answer:
Step-by-step explanation:
Hello!
To test if calcium reduces the symptoms of PMS two independent groups of individuals are compared, the first group, control, is treated with the placebo, and the second group is treated with calcium.
The parameter to be estimated is the difference between the mean symptom scores of the placebo and calcium groups, symbolically: μ₁ - μ₂
There is no information about the distribution of both populations X₁~? and X₂~? but since both samples are big enough, n₁= 228 and n₂= 212, you can apply the central limit theorem and approximate the sampling distribution to normal X[bar]₁≈N(μ₁;δ₁²/n) and X[bar]₂≈N(μ₂;δ₂²/n)
The formula for the CI is:
[(X[bar]₁-X[bar]₂) ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S^2_1}{n_1} +\frac{S^2_2}{n_2} }[/tex]]
95% confidence level [tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]
(a) mood swings: placebo = 0.70 ± 0.78; calcium = 0.50 ± 0.53
X₁: Mood swings score of a participant of the placebo group.
X₂: Mood swings score of a participant of the calcium group.
[(0.70-0.50) ± 1.96 * [tex]\sqrt{\frac{0.78^2}{228} +\frac{0.53^2}{212} }[/tex]]
[0.076; 0.324]
(b) crying spells: placebo = 0.39 + 0.57; calcium = 0.21 + 0.40
X₁: Crying spells score of a participant of the placebo group.
X₂: Crying spells score of a participant of the calcium group.
[(0.39-0.21) ± 1.96 * [tex]\sqrt{\frac{0.57^2}{228} +\frac{0.40^2}{212} }[/tex]]
[0.088; 0.272]
(c) aches and pains: placebo = 0.45 + 0.60; calcium = 0.37 + 0.45
X₁: Aches and pains score of a participant of the placebo group.
X₂: Aches and pains score of a participant of the calcium group.
[(0.45-0.37) ± 1.96 * [tex]\sqrt{\frac{0.60^2}{228} +\frac{0.45^2}{212} }[/tex]]
[-0.019; 0.179]
(d) craving sweets or salts: placebo = 0.60 + 0.75; calcium = 0.44 + 0.61
X₁: Craving for sweets or salts score of a participant of the placebo group.
X₂: Craving for sweets or salts score of a participant of the calcium group.
[(0.60-0.44) ± 1.96 * [tex]\sqrt{\frac{0.75^2}{228} +\frac{0.61^2}{212} }[/tex]]
[0.032; 0.287]
I hope this helps!
Using the z-distribution, the 95% confidence intervals are:
a) (0.08, 0.32).
b) (0.09, 0.27).
c) (-0.02, 0.18).
d) (0.03, 0.29).
We have to find the critical value, which is z with a p-value of [tex]\frac{1 + \alpha}{2}[/tex], in which [tex]\alpha[/tex] is the confidence level.
In this problem, [tex]\alpha = 0.95[/tex], thus, z with a p-value of [tex]\frac{1 + 0.95}{2} = 0.975[/tex], which means that it is z = 1.96.
Item a:
The standard errors are:
[tex]s_P = \frac{0.78}{\sqrt{228}} = 0.0517[/tex]
[tex]s_C = \frac{0.53}{\sqrt{212}} = 0.0364[/tex]
For the distribution of the differences, we have that:
[tex]\overline{x} = \mu_P - \mu_C = 0.7 - 0.5 = 0.2[/tex]
[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.0517^2 + 0.0364^2} = 0.0632[/tex]
The interval is:
[tex]\overline{x} \pm zs[/tex]
Hence:
[tex]\overline{x} - zs = 0.2 - 1.96(0.0632) = 0.08[/tex]
[tex]\overline{x} + zs = 0.2 + 1.96(0.0632) = 0.32[/tex]
The interval is (0.08, 0.32).
Item b:
The standard errors are:
[tex]s_P = \frac{0.57}{\sqrt{228}} = 0.03775[/tex]
[tex]s_C = \frac{0.4}{\sqrt{212}} = 0.02747[/tex]
For the distribution of the differences, we have that:
[tex]\overline{x} = \mu_P - \mu_C = 0.39 - 0.21 = 0.18[/tex]
[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.03775^2 + 0.02747^2} = 0.0467[/tex]
Hence:
[tex]\overline{x} - zs = 0.18 - 1.96(0.0467) = 0.09[/tex]
[tex]\overline{x} + zs = 0.18 + 1.96(0.0467) = 0.27[/tex]
The interval is (0.09, 0.27).
Item c:
The standard errors are:
[tex]s_P = \frac{0.6}{\sqrt{228}} = 0.0397[/tex]
[tex]s_C = \frac{0.45}{\sqrt{212}} = 0.0309[/tex]
For the distribution of the differences, we have that:
[tex]\overline{x} = \mu_P - \mu_C = 0.45 - 0.37 = 0.08[/tex]
[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.0397^2 + 0.0309^2} = 0.0503[/tex]
Hence:
[tex]\overline{x} - zs = 0.08 - 1.96(0.0503) = -0.02[/tex]
[tex]\overline{x} + zs = 0.08 + 1.96(0.0503) = 0.18[/tex]
The interval is (-0.02, 0.18).
Item d:
The standard errors are:
[tex]s_P = \frac{0.75}{\sqrt{228}} = 0.0497[/tex]
[tex]s_C = \frac{0.61}{\sqrt{212}} = 0.0419[/tex]
For the distribution of the differences, we have that:
[tex]\overline{x} = \mu_P - \mu_C = 0.60 - 0.44 = 0.16[/tex]
[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.0497^2 + 0.0419^2} = 0.065[/tex]
Hence:
[tex]\overline{x} - zs = 0.16 - 1.96(0.065) = 0.03[/tex]
[tex]\overline{x} + zs = 0.16 + 1.96(0.065) = 0.29[/tex]
The interval is (0.03, 0.29).
A similar problem is given at https://brainly.com/question/15297663
ASK YOUR TEACHER An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.11 kgf/cm2 for the modified mortar (m = 42) and y = 16.83 kgf/cm2 for the unmodified mortar (n = 30). Let μ1 and μ2 be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that σ1 = 1.6 and σ2 = 1.3, test H0: μ1 − μ2 = 0 versus Ha: μ1 − μ2 > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
Answer:
Test statistics = 3.74
P-value = 0.0001
Step-by-step explanation:
We are given that an experiment to compare the tension bond strength of polymer latex modified mortar to that of unmodified mortar resulted in x = 18.11 kg f/[tex]cm^{2}[/tex] for the modified mortar (m = 42) and y = 16.83 kg f/[tex]cm^{2}[/tex] for the unmodified mortar (n = 30).
Assume that the bond strength distributions are both normal and assuming that σ1 = 1.6 and σ2 = 1.3.
Let [tex]\mu_1[/tex] = true average tension bond strengths for the modified mortars
[tex]\mu_2[/tex] = true average tension bond strengths for the unmodified mortars
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1-\mu_2=0[/tex] or [tex]\mu_1=\mu_2[/tex] {means that true average tension bond strengths for the modified and unmodified mortars are same}
Alternate Hypothesis, [tex]H_a[/tex] : [tex]\mu_1-\mu_2>0[/tex] or [tex]\mu_1>\mu_2[/tex] {means that the true average tension bond strengths for the modified mortars is greater than that for unmodified mortars}
The test statistics that will be used here is Two-sample z test statistics as we know about population standard deviations;
T.S. = [tex]\frac{(x-y)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{m}+\frac{\sigma_2^{2} }{n} } }[/tex] ~ N(0,1)
where, x = sample mean tension bond strengths for the modified mortars = 18.11 kg f/[tex]cm^{2}[/tex]
y = sample mean tension bond strengths for the unmodified mortars = 16.83 kg f/[tex]cm^{2}[/tex]
[tex]\sigma_1[/tex] = population standard deviation for modified mortars = 1.6
[tex]\sigma_2[/tex] = population standard deviation for unmodified mortars = 1.3
m = sample of modified mortars = 42
n = sample of unmodified mortars = 30
So, test statistics = [tex]\frac{(18.11-16.83)-(0)}{\sqrt{\frac{1.6^{2} }{42}+\frac{1.3^{2} }{30} } }[/tex]
= 3.74
Now, P-value is given by the following formula;
P-value = P(Z > 3.74) = 1 - P(Z [tex]\leq[/tex] 3.74)
= 1 - 0.9999 = 0.0001
Here, the above probability is calculated by looking at the value of x = 3.74 in the z table which gives an area of 0.9999.
To test the hypothesis H0: μ1 − μ2 = 0 versus Ha: μ1 − μ2 > 0 at level 0.01, calculate the test statistic and the P-value. The test statistic is Z = (x - y) / √((σ1² / m) + (σ2² / n)). Substituting the values gives Z = 1.278. The P-value is approximately 0.1019.
Explanation:To test the hypothesis H0: μ1 − μ2 = 0 versus Ha: μ1 − μ2 > 0 at level 0.01, we calculate the test statistic and the P-value. The test statistic is given by:
Z = (x - y) / √((σ1² / m) + (σ2² / n))
where x = 18.11, y = 16.83, σ1 = 1.6, σ2 = 1.3, m = 42, and n = 30.
Substituting the values, we get Z = (18.11 - 16.83) / √((1.6² / 42) + (1.3² / 30)).
Calculating Z gives Z = 1.278. To determine the P-value, we find the area to the right of Z in the standard normal distribution. The P-value is the probability that Z > 1.278. Consulting a Z-table or using a calculator, we find the P-value to be approximately 0.1019.
Learn more about Test statistic and P-value for hypothesis testing here:https://brainly.com/question/28957899
#SPJ3