Answer:
y = 12 + 6x
y = 12x
Step-by-step explanation:
From the information provided, the following equations are derived:
y = 12 + 6x ------- Eqn 1
y = 12x ------- Eqn 2
Since Eqns 1 and 2 have the same subject, we equate them to solve for x. We have:
12x = 12 + 6x
Putting like terms together, we have:
12x - 6x = 12 ⇒ (12 - 6)x = 12
6x = 12 ⇒ x = 2
x = 2
Substitute x into Eqn 1 or 2
Eqn 1
y = 12 + 6x
y = 12 + 6(2) = 12 + 12
y = 24
Eqn 2
y = 12x
y = 12(2)
y = 24
It means that it will take Ms. Ironperson and Mr. Thoro 2 days apiece to produce the same number of posters at the current rate (which is 24 posters). Both Ms. Ironperson and Mr. Thoro will individually take 2 days to produce 24 Avenger posters apiece.
Which ordered pair is the solution of the system of equations? 3x+2y=4, -2+2y=24, I need help Im very confused on how to solve this...
Answer:
x = -7.33 OR x = [tex]\frac{-22}{3}[/tex]
y = 13
Step-by-step explanation:
→You can use the substitution method. First, make y by itself in (-2 + 2y = 24):
-2 + 2y = 24
2y = 26
y = 13
→Then, plug in 13 for y into the other equation:
3x + 2y = 4
3x + 2(13) = 4
3x + 26 = 4
3x = -22
x = -7.33 OR x = [tex]\frac{-22}{3}[/tex]
What is the measure of XYZ?
please help me out
Answer:
The answer is C.
Step-by-step explanation:
You have to divide it by 2 :
∠XYZ = 148° ÷ 2
= 74°
A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq. Ft. How much were the dimensions increased?
Answer:
4 ft
Step-by-step explanation:
288=16 * 18
12+4=16
14+4=18
The dimensions increased by 4 feet.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Given;
Dimensions of rectangle = 12 + x and 14 + x
The area of the rectangle= (12 + x) (14 + x) = 288
x² + 26x + 168 = 288
x² + 26x - 120 = 0
(x + 30) (x - 4) = 0
x=-30, x =4
Hence, The dimensions increased by 4 feet.
Learn more about the area;
https://brainly.com/question/1658516
#SPJ2
subtract 2 16/21 - (-8 5/21). reduce if possible
Answer:
11
Step-by-step explanation:
A coffe storage bin contains 1500 grams of coffe beans. To make a cup of coffee, n grams of coffe beans are removed
Answer:
The amount remaining in coffee storage bin after making 10cups if coffee = (1500-10n) grams
Step-by-step explanation:
This question is incomplete as we are not told what to determine.
Let's consider the following question:
A coffee storage bin contains 1500 grams of coffee beans. To make a cup of coffee, n grams of coffee beans are removed. How many grams of coffee would be left after making 10 cups of coffee?
Solution:
Total amount of coffee in storage bin = 1500grams
To make one cup of coffee, we need n grams of coffee
The amount remaining for one cup = 1500grams - n grams
To make 10 cups of coffee, we would need = 10× n grams of coffee= 10n grams
The amount remaining in coffee storage bin after making 10cups of coffee = total amount in storage - amount for making 10cups
(1500-10n) grams
Please answer this correctly
Answer:
432
Step-by-step explanation:
l x w
4x3
4x19
8x24
8x19
432
A voter receives a call in which the caller claims to be conducting a national opinion research poll. The voter is asked if his or her opinion about a congressional candidate would change if he or she knew that the candidate once had a car crash while driving under the influence of alcohol. Identify and explain at least one source of bias in the study described. Then suggest how the bias might have been avoided?
a. The data do not seem to support the claims being made by the study. The researcher should consult an expert to make sure that he or she is correctly interpreting the data.
b. The study does not appear to have a well-defined goal. The researcher should determine his or her goal and precisely define the variables of interest.
c. Since the sample is self-selected, there is a definite participation bias in this study. The researcher should randomly select the subjects of the study.
d. The wording of the question is biased to strengthen opposition against a particular candidate. The question wording should be changed to be more neutral.
Answer:
The correct answer is D. The wording of the question is biased to strengthen opposition against a particular candidate. The question wording should be changed to be more neutral.
Step-by-step explanation:
The phrasing and setup of the poll will produce responses that are biased against the candidate. The setup of the poll should be changed to avoid influencing the opinions of the respondents.
Angelina read 30% of her book containing 360 pages. How many pages has she read so far
Answer:
108 pages
Step-by-step explanation:
Angelina read 30% of the book that contains 360 pages.
30% of 360 pages
"of" also means multiply, so we must multiply 30% and 360.
30% * 360
Convert 30% to a decimal. Divide 30 by 100, or move the decimal place 2 spots to the left.
30/100=0.30
or
30.0---> 3.0---> 0.30
Plug the decimal in for the percent.
0.30*360
Multiply the 2 numbers together
108
Angelina has read 108 pages so far.
A gas company president for a particular city is interested in the proportion of homes heated by gas. Historically, the proportion of homes heated by gas has been 0.72. A sample of 75 homes was selected and it was found that 45 of them heat with gas. Perform the appropriate test of hypothesis, at level .05, to determine whether the proportion of home heated by gas has changed. Group of answer choices
Answer:
p-value (0.0208) is less than alpha = 0.05 reject H0.
Step-by-step explanation:
we have the following data:
sample size = n = 75
x, the number to evaluate is 45
the sample proportion would be: x / n = 45/75
p * = 0.6
Now, the null and alternative hypotheses are:
H0: P = 0.72
Ha: P no 72
two tailed test
statistic tes = z = (p * - p) / [(p * (1-p) / n)] ^ (1/2)
replacing we have:
z = (0.6 - 0.72) / [(0.72 * (1-0.72) / 75)] ^ (1/2)
z = -2.31
p-vaule = 2 * p (z <-2.31)
using z table, we get:
p-vaule = 2 * (0.0104)
p-vaule = 0.0208
Therefore, p-value (0.0208) is less than alpha = 0.05 reject H0.
The manufacturer of a smart watch claims that individuals who pay attention to how many steps they take per day will inadvertently take more steps per day than individuals who pay no attention to how many steps they take per day. To investigate this claim, the manufacturer conducts a study to estimate the difference in the mean number of steps taken by those that pay attention to how many steps they take per day and those that do not. To do so, 40 volunteers are recruited. Half of the volunteers are randomly assigned to receive a smart watch and are taught how to use it to track their steps. The other half of the volunteers are given a wristband to wear, but are not informed that the wristband is tracking their steps. The volunteers are monitored for 30 days. The mean and standard deviation of the number of steps taken per day are computed for each group. Here are the data:
Payti
Do not pay itin 01 0 10 20 87 64 82 350
Which of the following is a 99% confidence interval for the difference in the mean number of steps taken by all people like these that do and do not pay attention to the number of steps they take per day using df - 192
(A) 1596 + 2.861/15802 + 23502
(B) 1596 +2.861, 15.302 – 23502
(C) 1596 +2.576,15802 + 23502
(D) 1596 + 2.576 ( 15802 + 23502) °
(E) 1596 + 2.576 ( 15892 – 23502)
Here is the correct question.
The manufacturer of a smart watch claims that individuals who pay attention to how many steps they take per day will inadvertently take more steps per day than individuals who pay no attention to how many steps they take per day. To investigate this claim, the manufacturer conducts a study to estimate the difference in the mean number of steps taken by those that pay attention to how many steps they take per day and those that do not. To do so, 40 volunteers are recruited. Half of the volunteers are randomly assigned to receive a smart watch and are taught how to use it to track their steps. The other half of the volunteers are given a wristband to wear, but are not informed that the wristband is tracking their steps. The volunteers are monitored for 30 days. The mean and standard deviation of the number of steps taken per day are computed for each group. Here are the data:
[tex]n[/tex] [tex]\bar x[/tex] [tex]S_x[/tex]
Pay attention 20 10,244 1,580
Do not pay attention 20 8.,648 2,350
Which of the following is a 99% confidence interval for the difference in the mean number of steps taken by all people like these that do and do not pay attention to the number of steps they take per day using df - 19 ?
[tex](A) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}} \\ \\ \\ (B) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} - \dfrac{2350^2}{20}} \\ \\ \\ (C) \ 1596 \pm 2.576 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}} \\ \\ \\ (D) 1596 \pm 2.576 ( \dfrac{1580^2}{\sqrt{20}} + \dfrac{2350^2}{\sqrt{20}}) \\ \\ \\ (E) 1596 \pm 2.576 ( \dfrac{1580^2}{\sqrt{20}} - \dfrac{2350^2}{\sqrt{20}})[/tex]
Answer:
[tex]\mathbf{(A) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}}}[/tex]
Step-by-step explanation:
Given that :
significance level [tex]\alpha = \mathbf{0.01}[/tex]
From the Given data;
Using Excel with the function : TINV(0.01,19);
Critical value t* = 2.861
The margin of error can now be represented by the illustration:
Margin of error = [tex]t^* \sqrt{ \dfrac {s_1 ^2}{n_1} + \dfrac {s_2 ^2}{n_2}[/tex]
Lower Limit = [tex](\bar x_1 - \bar x_2)- (Margin \ of \ error)[/tex]
Upper Limit = [tex](\bar x_1 - \bar x_2)+ (Margin \ of \ error)[/tex]
Thus; the confidence interval for the difference in the mean number of steps taken by all people like these that do and do not pay attention to the number of steps they take per day using df - 19 is:
[tex]\mathbf{(A) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}}}[/tex]
Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an average of grams of fat per pound, with a standard deviation of grams of fat per pound. A random sample of farm-raised trout is selected. The mean fat content for the sample is grams per pound. Find the probability of observing a sample mean of grams of fat per pound or less in a random sample of farm-raised trout.
Complete question is:
Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an average of 32 grams of fat per pound, with a standard deviation of 7 grams of fat per pound. A random sample of 34 farm-raised trout is selected. The mean fat content for the sample is 29.7 grams per pound. Find the probability of observing a sample mean of 29.7 grams of fat per pound or less in a random sample of 34 farm-raised trout. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
Answer:
Probability = 0.0277
Step-by-step explanation:
We are given;
Mean: μ = 32
Standard deviation;σ = 7
Random sample number; n = 34
To solve this question, we would use the equation z = (x - μ)/(σ/√n) to find the z value that corresponds to 29.7 grams of fat.
Thus;
z = (29.7 - 32)/(7/√34)
Thus, z = -2.3/1.200490096
z = -1.9159
From the standard z table and confirming with z-calculator, the probability is 0.0277
Thus, the probability to select 34 fish whose average grams of fat per pound is less than 29.7 = 0.0277
A team of researchers published an article on the study of how vehicles are dispatched based on an airport-based taxi service. The researchers modeled this system with an underlying assumption that travel times of successive trips to and from the terminal are independent exponentially distributed random variables with β = 15 minutes. (a) Find the mean and standard deviation of trip time distribution (b) How likely is it for a particular trip to take more than 25 minutes? (c) If two taxis are dispatched together, what is the probability that both of them will be gone for more than 25 minutes? (d) what is the likelihood of at least of one of the taxis returning within 25?
Answer:
a. The mean would be 0.067
The standard deviation would be 0.285
b. Would be of 1-e∧-375
c. The probability that both of them will be gone for more than 25 minutes is 1-e∧-187.5
d. The likelihood of at least of one of the taxis returning within 25 is 1-e∧-375
Step-by-step explanation:
a. According to the given data the mean and the standard deviation would be as follows:
mean=1/β=1/15=0.0666=0.067
standard deviation=√1/15=√0.067=0.285
b. To calculate How likely is it for a particular trip to take more than 25 minutes we would calculate the following:
p(x>25)=1-p(x≤25)
since f(x)=p(x≤x)=1-e∧-βx
p(x>25)=1-p(x≤25)=1-e∧-15x25=1-e∧-375
c. p(x>25/2)=1-p(x≤25/2)=1-e∧-15x25/2=1-e∧-187.5
d. p(x≥25)=1-e∧-15x25=1-e∧-375
A credit card company monitors cardholder transaction habits to detect any unusual activity. Suppose that the dollar value of unusual activity for a customer in a month follows a normal distribution with mean $250 and variance $2400.
(a) What is the probability of $250 to $294 in unusual activity in a month? Round your answer to four decimal places (e.g. 98.7654) P-0.4861
(b) What is the probability of more than $294 in unusual activity in a month? Round your answer to four decimal places (e.g. 98.7654) P 0.0139
(c) Suppose that 10 customer accounts independently follow the same normal distribution. What is the probability that at least one of these customers exceeds $294 in unusual activity in a month? Round your answer to four decimal places (e.g. 98.7654)
Answer:
Step-by-step explanation:
Let x be the random variable representing the dollar value of unusual activity for a customer in a month. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 250
σ = √variance = √2400 = 48.99
a) the probability of $250 to $294 in unusual activity in a month is expressed as
P(250 ≤ x ≤ 294)
For x = 250,
z = (250 - 250)/48.99 = 0
Looking at the normal distribution table, the probability corresponding to the z score is 0.5
For x = 294
z = (294 - 250)/48.99 = 0.9
Looking at the normal distribution table, the probability corresponding to the z score is 0.8159
Therefore,
P(250 ≤ x ≤ 294) = 0.8159 - 0.5 = 0.3159
b) the probability of more than $294 in unusual activity in a month is expressed as
P(x > 294) = 1 - P(x < 294)
P(x > 294) = 1 - 0.8159 = 0.1841
c) since n = 10, the formula becomes
z = (x - µ)/(σ/n)
z = (294 - 250)/(48.99/√10) = 2.84
Looking at the normal distribution table, the probability is 0.9977
Therefore, the probability that at least one of these customers exceeds $294 in unusual activity in a month is
1 - 0.9977 = 0.0023
Peter has invented a game with paper cups. He lines up 121 cups face down in a straight line from left to right and consecutively labels them from 1 to 121. He then walks from left to right down the line of cups, flipping all of the cups over. He returns to the left end of the line, then makes a second pass from left to right, this time flipping cups 2,4,6,8... On the third pass, he flips cups 3,6,9,12.... He continues like this: On the ith pass, he flips over cups i, 2i, 3i, 4i,.... (By "flip," we mean changing the cup from face down to face up or vice versa.) After 121 passes, how many cups are face up?
Answer:
After 121 passes, there will be 11 cups facing up
Step-by-step explanation:
Given that:
Peter initially lines up 121 cups facing down in a straight line from left to right and consecutively labels them from 1 to 121.
We can have an inequality ; i.e 1 ≤ n ≤ 121; if n represents the divisor including n itself for which n = odd number. Thus at the end of this claim, the cup will be facing up.
On the ith pass, he flips over cups i, 2i, 3i, 4i,.... (By "flip," we mean changing the cup from face down to face up or vice versa.)
For each divisor on the ith pass of n;
[tex]i \ th \ pass \ = \ n \ \to \ p |n[/tex] since we are dealing with possibility of having an odds number:
Thus; [tex]p =i[/tex] and [tex]i^2 = n[/tex] where ; n = perfect square.
Thus ; we will realize that between 1 to 121 ; there exist 11 perfect squares. Therefore; as a result of that ; 11 cups will definitely be facing up after 121 passes
A rectangular box is 4 cm wide, 4 cm tall, and 10 cm long. What is the diameter of the smallest circular opening through which the box will fit? Round to the nearest tenth of a centimeter.
Answer:
The diameter of the smallest circular opening through which the box will fit is 5.7 cm to the nearest tenth
Step-by-step explanation:
The dimensions of the rectangle are :
height: 4 cm
length: 10 cm
breadth: 4 cm
The diameter of the smallest circular opening through which the box will fit will be equals to the diagonal of a face of the rectangular box.
The face we will try to fit in first will determine the diagonal that we will calculate.
Let us try to fit in the right side of the rectangular box. The face we will have at that side is a square of 4 cm by 4 cm which is formed by the height and the width of the box.
We can calculate the diagonal using Pythagoras Theorem:
diagonal = [tex]\sqrt{height^{2}+ breadth^{2}}= \sqrt{4^{2}+4^{2}}=5.657 \approx 5.7cm[/tex] to the nearest tenth
The radius of inscribed circle is 10 what is the perimeter of square cabd
Answer:
P=80
Step-by-step explanation:
R= 10
P = R*2 *4
P of a square = 10*2 *4 = 80
Just divide by any fraction of the squares ratio.
ie) if square = 2/3 of the length of the circle then 80 x 2/3 = 53.333...
ie) if square = 3/4 of the length of the diameter of the circle then 80 x 3/4 = 60
As 3/4 pf 10 = 7.5
7.5 * 2 = 15
15* 4 = 60
Howver the square is outside of the circle as described circle inscribed exactly how much if it fits exactly then the length will be same as circles diameter = 10*2 = D;20.
20 *4 = 80. P;80
Etc.
An accident Investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid
marks, d, was 117ft. Use the formula s = 24d to find s, the speed of the vehicle before the brakes were applied. Fund
Answer:
2,808
Step-by-step explanation:
since 117 = d then we would just plug that into the equation of s = 24d and get s = 24(117), after that you would just solve.
Answer:
53
Step-by-step explanation:
4x and 16y are like terms.
O A. True
O B. False
Solve 23 - Q >-3(2-6)
Answer:
q < 11
Step-by-step explanation:
Distribute the -3
23 - q > 12
Add q and subtract 12
q < 11
Step-by-step explanation:
the answer is
q<11
23-q>12
please help !!!
Find the probability that x = -10
Answer:
20%
Step-by-step explanation:
Use the table provided... it says -10 is .2 which is the same as 20%
Answer:
0.20
Step-by-step explanation:
requires decimal not percentage
A hospital needs 0.100 gg of 133 54Xe 54133Xe for a lung-imaging test. If it takes 10 daysdays to receive the shipment, what is the minimal amount mXemXem_Xe of xenon that the hospital should order? Express your answer numerically in grams
Answer:
The correct answer will be "0.400 gm".
Step-by-step explanation:
The give values are:
Needs of hospital, N = 0.100 gm
Time, t = 10 days
Minimum amount of Xenon, N₀ = ?
As we know,
⇒ [tex]N(t)=N_{0} \ e^{-\lambda t}[/tex]
∴ Decay constant, λ = [tex]\frac{ln2}{t_{1/2}}[/tex]
λ = [tex]\frac{ln2}{5}[/tex]
On putting values, we get
⇒ [tex]0.100=N_{0} \ e^{-\frac{ln2}{5}}\times 10[/tex]
⇒ [tex]0.1=N_{0} \ e^{-2ln2} = N_{0} \ e^{-ln4}[/tex]
⇒ [tex]0.1=N_{0} \ e^{ln\frac{1}{4}}[/tex]
⇒ [tex]0.1=\frac{N_{0}}{4}[/tex]
⇒ [tex]N_{0}=0.1\times 4[/tex]
⇒ [tex]MX_{e}=0.400 \ gm[/tex]
A researcher classifies firefighters according to whether their gloves fit well or poorly and by gender. They want to know if there is a difference in the proportion of poorly fitted gloves and gender. At alpha = 0.01, use the chi-square test to determine if there is a difference in the population proportion of glove fitness for the two genders.
Observed data Males Females Total
Gloves fit poorly 132 20 152
Gloves fit well 415 19 434
Total 547 39 586
Expected data Males Females Total
Gloves fit poorly
Gloves fit well
Total
Answer:
Step-by-step explanation:
Hello!
The objective is to test if the proportion of "X: gloves fitness, categorized: Fit poorly and Fit well" is the same for two populations of interest, "male firefighters" and "female firefighters"
To do this you have to conduct a Chi-Square test of Homogeneity.
In the null hypothesis you have to state that the proportion of the categories of the variable are the same for all the populations of interest.
Be
M: the firefighter is male
F: the firefighter is female
Y: represents the category that the gloves "fit poorly"
W: represents the category that the gloves "fit well"
The null hypothesis will be:
H₀: P(Y|M)=P(Y|F)=P(Y)
P(W|M)=P(W|F)=P(W)
H₁: At least one of the statements in the null hypothesis is false.
α: 0.01
To calculate the statistic under the null hypothesis you have to calculate the expected frequencies first:
[tex]E_{ij}= O_{.j}*\frac{O_{i.}}{n}[/tex]
O.j= total of the j-column
Oi.= total of the i-row
n= total of observations
[tex]E_{11}= 547*\frac{152}{586} = 141.88[/tex]
[tex]E_{12}=39*\frac{152}{586}= 10.12[/tex]
[tex]E_{21}= 547*\frac{434}{586} = 405.12[/tex]
[tex]E_{22}= 39*\frac{434}{586} = 28.88[/tex]
[tex]X^2= sum \frac{(O_{ij}-E_{ij})^2}{E_{ij}} ~~~X^2_{(r-1)(c-1)}[/tex]
r= number of rows (in this case 2)
c=number of columns (in this case 2)
[tex]X^2_{H_0}= \frac{(132-141.88)^2}{141.88} +\frac{(20-10.12)^2}{10.12} +\frac{(415-405.12)^2}{405.12} +\frac{(19-28.88)^2}{28.88} = 13.95[/tex]
Using the critical value approach, you have to remember that this test is always one-tailed to the right, meaning that you'll have only one critical value from which the rejection region is defined:
[tex]X^2_{(r-1)(c-1);1-\alpha }= X^2_{1;0.99}= 6.635[/tex]
The decision rule is then:
If [tex]X^2_{H_0}[/tex] ≥ 6.635, reject the null hypothesis.
If [tex]X^2_{H_0}[/tex] < 6.635, do not reject the null hypothesis.
The calculated value is greater than the critical value, the decision is to reject the null hypothesis.
So at a 1% level you can conclude that this test is significant. This means that the proportions of gloves fitness, categorized in "Fit poorly" and "Fit well" are different for the male and female firefighters populations.
I hope this helps!
Answer:
The Chi - Square Test Statistics is 13.98
p-value = 0.0002
CONCLUSION: Since the p-value is less than the level of significance ; (i.e p-value < ∝) we reject the null hypothesis and accept the alternative hypothesis.
Thus; there is a difference in the population proportion of glove fitness for the two genders.
Step-by-step explanation:
From the information given ; the structure of the table can be well represented as follows;
Observed data Males Females Total
Gloves fit poorly 132 20 152
Gloves fit well 415 19 434
Total 547 39 586
Expected data Males Females Total
Gloves fit poorly
Gloves fit well
Total
The objective of this question is to use the chi-square test to determine if there is a difference in the population proportion of glove fitness for the two genders.
We call represent the hypothesis as follows:
The null hypothesis: [tex]H_o:[/tex] states that there is no difference in the population proportion of glove fitness for the two genders.
The alternative hypothesis: [tex]H_a[/tex] states that there is difference in the population proportion of glove fitness for the two genders.
The expected frequency of a particular cell can be calculated by multiplying the sum of the rows and columns together, then dividing it by the Total sum
For row 1 column 1 (gloves fit poorly (male) ; we have:
[tex]= \dfrac{547*152}{586} =141.884\\[/tex]
For row 2 column 1 (gloves fit well(male) ; we have:
[tex]= \dfrac{547*434}{586} =405.116[/tex]
For row 1 column 2 (gloves fit poorly (female)) ; we have:
[tex]= \dfrac{39*152}{586} =10.116[/tex]
For row 2 column 2 ( gloves fit well ( female ) ; we have:
[tex]= \dfrac{39*434}{586} =28.884[/tex]
Thus; we can have the complete table to now be:
Observed data Males Females Total
Gloves fit poorly 132 20 152
Gloves fit well 415 19 434
Total 547 39 586
Expected data Males Females Total
Gloves fit poorly 141.884 10.116 152
Gloves fit well 405.116 28.884 434
Total 547 39 586
The Chi - Square Test Statistics can be calculated via the formula:
[tex]X^2 = \dfrac{\sum (f_o-f_e)^2}{f_e}[/tex]
where;
[tex]f_o[/tex] = observed data frequency
[tex]f_e[/tex] = expected data frequency
∴
The Chi - Square Test Statistics is as follows:
[tex]=\dfrac{(131-141.884)^2}{141.884} + \dfrac{(20-10.116)^2}{10.116}+ \dfrac{(415-405.116)^2}{405.116}+ \dfrac{(39-28.884)^2}{28.884}[/tex]
= 0.68+9.6+0.2+3.5
= 13.98
We are given the level of significance ∝ to be = 0.01
numbers of rows = 2; number of column = 2
Thus; the degree of freedom = (2-1)(2-1) = 1×1 = 1
Using the Excel Function : [ = CHISQ.DIST.RT²(X²,df)]
p-value = 0.0002
CONCLUSION: Since the p-value is less than the level of significance ; (i.e p-value < ∝) we reject the null hypothesis and accept the alternative hypothesis.
Thus; there is a difference in the population proportion of glove fitness for the two genders.
Triangles E F G and K L M are shown. Angles E F G and K L M are congruent. The length of side K L is 6, the length of side M L is 5, and the length of K M is 8. The length of E G is 24, the length of G F is 15, and the length of E F is 18. Can the triangles be proven similar using the SSS or SAS similarity theorems? Yes, △EFG ~ △KLM only by SSS. Yes, △EFG ~ △KLM only by SAS. Yes, △EFG ~ △KLM by SSS or SAS. No, they cannot be proven similar by SSS or SAS.?
Answer:
The Answer is C: Yes, △EFG~ △KLM by SSS or SAS
Step-by-step explanation:
SSS is for side-side-side
Both triangles have all three sides given, so the SSS similarity theorem is one way to prove these triangles are similar.
SAS is for side-angle-side
Both triangles have one angle measurement given, and two side lengths given, therefore we can also use the SAS similarity theorem to prove the two triangles are similar.
Since both SSS and SAS work to prove the triangles are similar, the correct answer is C: Yes, △EFG~ △KLM by SSS or SAS
(I also just answered this question on the assignment and got it correct)
Answer:
Answer is C
Step-by-step explanation:
Took it on Edg
A polygraph (lie detector) is an instrument used to determine if the individual is telling the truth. These tests are considered to be 86% reliable. In other words, if an individual lies, there is a 0.86 probability that the test will detect a lie. Let there also be a 0.070 probability that the test erroneously detects a lie even when the individual is actually telling the truth. Consider the null hypothesis, "the individual is telling the truth," to answer the following questions.
a. What is the probability of Type I error? (Round your answer to 3 decimal places.)
Probability
b. What is the probability of Type II error? (Round your answer to 2 decimal places.)
Probability
Answer:
Step-by-step explanation:
a) The probability of a Type I error in a lie detection test would be the probability that the lie detection machine incorrectly detected lie for the truth tellers. This is already given in the problem as 0.07.
Therefore,
[tex]P(Type-I) = 0.07[/tex]
Therefore 0.07 is the required probability here.
b) The probability of a Type II error in a lie detection test would be the probability that the lie detection machine incorrectly detected truth for the the people who are actually liars. This is thus 1 - reliability.
[tex]P(Type-II) = 1 - Reliability = 1- 0.86 = 0.14[/tex]
Therefore 0.14 is the required probability here.
Answer:
a) 0.070
b) 0.14
Step-by-step explanation:
Given that the tests are 86% reliable, i.e a probability of 0.86 a lie would be detected.
Probability of error = 0.070
a) For type I error, we have:
The probability of a type I error in this lie detector is the probability that the test erroneously detects a lie even when the individual is actually telling the truth, i.e
P(type I error) = P(rejecting true null)
= 0.070
b) The probability of a Type II error this lie detectot is the probability that the test erroneously detected truth insteax of lie.
i.e = 1 - reliability
P (Type II error) = P(Failing to reject false Null)
= P(Not detecting a lie)
= 1-0.86
= 0.14
Solve for x
A) 5
B) 6
C)7
D)8
Answer:
[tex]7x+1+6x+101=180\\13x=78\\x=6[/tex]
How would I start this?
Answer:
(0, ∞)
Step-by-step explanation:
A good place to start is by visualizing what the graph looks like on a number line.
For x > 0, it is an open circle at x=0, and shading to the right extending to infinity.
__
So, the left end of the interval is 0, but 0 is not included in the interval.
The right end of the interval is infinity, but there is no such number, so "infinity" is not included in the interval.
"Not included" means you use round brackets ( ) for the corresponding end of the interval. ("Included" would mean you use square brackets [ ].)
So, the interval 0 < x < ∞ is written in interval notation as ...
(0, ∞)
HELP PLEASE!!!!!!!!
Answer:
3¹²
Step-by-step explanation:
Move 3⁻² to the numerator using the negative exponent rule
1/b-n = bⁿ
(3⁵)² ⋅ 3²
Multiply the exponents
3¹⁰ · 3²
Multiply by adding the exponents
3¹⁰⋅ 3²
3¹²
WHAT IS A VOLUME OF THE BOX WITH A HEIGHT OF 3\2 WIDTH OF 5\2 AND LENGHT OF 7\2
Answer:
13.125 or 105/8u^3
Step-by-step explanation:
To find the volume of the box, you can use the formula of length times width time height.
3 * 5 = 15
2*2=4
15/4*7/2=105/8 which can be divided to become 13.125
I Need help ASAP!!!
Answer:
x = 15, AOB = 15, BOC = 165
Step-by-step explanation:
Assume that this is a straight line
2x - 15 + 11x = 180
Combine like terms
13x - 15 = 180
Add 15 on both sides
13x = 195
Divide 13 on both sides
x = 15
Substitute x for 15 in both equations
2(15) - 15 = 15
11(15) = 165
(For checking purposes, 165 + 15 = 180)
When planning road development, the road commission estimates the future population using the function represented in the table, where x is the time in years and f(x) is the total population. What is the significance of 160,000 in the function . Graph is x: 0, 1, 2, 3, 4, 5 f(x):160,000, 163,200, 166,464, 169,793, 173,189, 176,653
Answer:C
Step-by-step explanation:
Answer:
The answer is C
Step-by-step explanation:
Source: Dude trust me
