Answer:
[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]
And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55.
Step-by-step explanation:
Information given
We have the following data: 54 55 58 59 59 60 61 61 62 65
The sample mean and deviation can be calculated with the following formulas:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s=\sqrt{\frac{\sum_{i=1}^n (X-i -\bar x)^2}{n-1}}[/tex]
[tex]\bar X=59.4[/tex] represent the sample mean
[tex]s=3.239[/tex] represent the sample standard deviation
[tex]n=10[/tex] sample size
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true mean is higher than 55, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 55[/tex]
Alternative hypothesis:[tex]\mu > 55[/tex]
Replacing the info given we got:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing the info given we got:
[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]
And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55
According to a report released by CIBC entitled "Women Entrepreneurs: Leading the Charge," the average age for Canadian businesswomen in 2008 was 41. In the report, there was some indication that researchers believed that this mean age will increase. Suppose now, a few years later, business researchers in Canada want to test to determine if, indeed, the mean age of Canadian businesswomen has increased. The researchers randomly sample 97 Canadian businesswomen and ascertain that the sample mean age is 43.4. From past experience, it is known that the population standard deviation is 8.95. Test to determine if the mean age of Canadian businesswomen has increased using a 1% level of significance. What is the p-value for this test? What is the decision? If the null hypothesis is rejected, is the result substantive?
Answer:
We conclude that the mean age of Canadian businesswomen has increased.
Step-by-step explanation:
We are given that according to a report released by CIBC entitled "Women Entrepreneurs: Leading the Charge," the average age for Canadian businesswomen in 2008 was 41.
The researchers randomly sample 97 Canadian businesswomen and ascertain that the sample mean age is 43.4. From past experience, it is known that the population standard deviation is 8.95.
Let [tex]\mu[/tex] = mean age of Canadian businesswomen.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 41 {means that the mean age of Canadian businesswomen has decreased or remained same}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 41 {means that the mean age of Canadian businesswomen has increased}
The test statistics that would be used here One-sample z-test statistics because we know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean age of Canadian businesswomen = 43.4
[tex]\sigma[/tex] = population standard deviation = 8.95
n = sample of Canadian businesswomen = 97
So, the test statistics = [tex]\frac{43.4-41}{\frac{8.95}{\sqrt{97} } }[/tex]
= 2.64
The value of z test statistic is 2.64.
Also, P-value of the test statistics is given by;
P-value = P(Z > 2.64) = 1 - P(Z < 2.64)
= 1 - 0.99585 = 0.00415
Now, at 1% significance level the z table gives critical value of 2.33 for right-tailed test.
Since our test statistic is more than the critical value of z as 2.64 > 2.33, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the mean age of Canadian businesswomen has increased.
A solid lies between planes perpendicular to the x-axis at xequals=0 and xequals=1212. The cross-sections perpendicular to the axis on the interval 0less than or equals≤xless than or equals≤1212 are squares with diagonals that run from the parabola y equals negative 2 StartRoot x EndRooty=−2x to the parabola y equals 2 StartRoot x EndRooty=2x. Find the volume of the solid.
Question:
A solid lies between planes perpendicular to the x-axis at x=0 and x=12. The cross-sections perpendicular to the axis on the interval 0≤x≤12 are squares with diagonals that run from the parabola y=-2√x to the parabola y=2√x. Find the volume of the solid.
Answer:
576
Step-by-step explanation:
Given:
Length of diagonal square:
[tex] D = 2\sqrt{x} - (-2\sqrt{x}) [/tex]
[tex] D = 4\sqrt{x} [/tex]
Here, the diagonal is the hypotenus of a right angle triangle, with leg S, where the square has a side of length S.
Using Pythagoras theorem:
[tex] S^2 + S^2 = D^2 [/tex]
[tex] S^2 + S^2 = (4\sqrt{x})^2 [/tex]
[tex] 2S^2 = 16x [/tex]
Divide both sides by 2
[tex] S^2 = 8x [/tex]
Thus,
Area, A = S² = 8x
Take differential volume, dx =
dV = Axdx
dV = 8xdx
Where limit of solid= 0≤x≤12
Volume of solid, V:
V =∫₀¹² dV
V = 8 ∫₀¹² xdx
V = [4x²]₀¹²
V = 4 (12)²
V = 12 * 144
= 576
Volume of solid = 576
Find the volume of the prism.
The volume is cubic meters.
which equation represents a line perpendicular to the line shown on the graph
Answer:
y = 1/4x + (any number)
Step-by-step explanation:
m = -8/2 = -4, the equation shown is y = -4x + 8
perpendicular is y = 1/4x + (any number), you didn't say where the line was perpendicular.
The tree diagram below shows all of the possible outcomes for flipping three coins.
What is the probability of one of the coins landing on tails and two of them landing on heads?
A) 1/4
B) 3/8
C) 1/2
D) 3/4
Answer:
B
Step-by-step explanation:
In that scenario, you would have one T and two H's, in any order. Looking at the chart, this happens in 3 different scenarios. Since there are a total of 8 possible outcomes, the probability of this happening is 3/8 or answer choice B. Hope this helps!
Answer:B
Step-by-step explanation: the number of event is 3 event={HHT, HTH,THH }
And the number of sample space is 8
By using 2^n formula our n is 3 2^3 = 8
The probability = 3/8
Hope it helps
Brainliest please
Use the distributive property to remove the parentheses .
-8(y-v-3)
Answer:
-8y +8v +24
Step-by-step explanation:
-8(y-v-3)
Multiply each term inside the parentheses by -8
-8y -v*-8 -3*-8
-8y +8v +24
___________________________________
Hey!!!
solution,
-8(y-v-3)
= -8y+8v+24
_________________________________
Here,
You have to remember these things:
(+)*(+)=(+)(+)*(-)=(-)(-)*(-)=(+)(-)*(+)=(-)Hope it helps.
Good luck on your assignment
What is the y coordinate of the point that divides the directed line segment from j to k into a ratio of 2 to 3
Answer:
y = [tex]y_{1}[/tex] + rise * 2/5
Step-by-step explanation:
5.44 Teaching descriptive statistics: A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures, computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam. (a) What are the hypotheses for evaluating if the average test scores are different for the different teaching methods?
Answer:
The null hypothesis is that all the different teaching methods have the same average test scores.
H0: μ1 = μ2 = μ3 = μ4 = μ5
The alternative hypothesis is that at least one of the teaching methods have a different mean.
Ha: at least one mean is different. (μ1 ≠ μi)
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
For the case above, let μ represent the average test scores for the teaching methods:
The null hypothesis is that all the different teaching methods have the same average test scores.
H0: μ1 = μ2 = μ3 = μ4 = μ5
The alternative hypothesis is that at least one of the teaching methods have a different mean.
Ha: at least one mean is different. (μ1 ≠ μi)
Only answer if you know geometry or if you know this
Answer:
SAS
Step-by-step explanation:
the angles are congruent, and the 2 pairs of sides are proportional.
200/150 is 4/3 and 320/240 is 4/3 as well.
therefore Side-Angle-Side
Choose the equation of the graph shown below:
y = |x - 1| - 3
y = |x + 1| - 3
y = |x - 1| + 3
Answer:
y=[x+1]-3 because it's at the end of the line
the length of a ruler is 170cm,if the ruler broke into four equal parts.what will be the sum of the length of three parts
Answer:
127.5
Step-by-step explanation:
Multiply 170 by 0.75
127.5
Answer:
3 divided by 4 = 0.75 = 3/4
0.75 x 170 = 127.5
or
170/1 x 3/4 = 510/4 = 127 1/2
1/2 = 0.5 = 1 divided by 2
127 + 0.5 = 127.5
127.5 is the answer
Hope this helps
Step-by-step explanation:
Find the median of the following set of data: 4, 7, 2, 1, 4, 6,
2,6
Answer:
(4+4)/2 = 4
Hope this helps
Answer:
4
Step-by-step explanation:
1,2,2,4,4,6,6,7
The median is the number in the middle however there are an even amount of numbers so you get the number between 4 and 4 which is just 4
If the selected consumer is 70 years old, what is the probability that he/she likes crunchicles
Answer:
The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.
Step-by-step explanation:
The question is incomplete:
Three hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.
18–24 25–34 35–55 55 and over Total
Liked Crunchicles 4 9 3 23 39
Disliked Crunchicles 5 27 28 64 124
No Preference 7 27 10 93 137
Total 16 63 41 180 300
One consumer from the survey is selected at random. If the selected consumer is 70 years old, what is the probability that he/she likes crunchicles .
If the consumer is 70 years old is included in the category "55 and over" from this survey. There are 180 subjects in that category.
The number that likes Crunchicles and are 55 and over is 23.
If we calculate the probability as the relative frequency, we have:
[tex]P(\text{L }|\text{ 55+})=\dfrac{P(\text{L \& 55+})}{P(5\text{5+})}=\dfrac{23}{180}=0.1278[/tex]
L: Likes Crunchicles.
The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.
What is the solution set of the quadratic inequality x2+x-2
Answer:
The solution set is x = 1 and x = -2
Step-by-step explanation:
Math Is TU parallel to VW explain
Answer: C ( yes, both lines have a slope of 2/3. )
Step-by-step explanation:
Answer: C
Step-by-step explanation:
how much alcohol must be added to 480grams of hand sanitizer that is 24% alcohol to make it a hand sanitizer that is 40% alcohol?
Answer:
what she/he said
Step-by-step explanation:
Graph the equation below by plotting the
y-intercept and a second point on the
line.
Answer:
Step-by-step explanation:
On the y-axis, graph the point on (0,4). Then from there, go up one, and to the right 4.
Line segment ON is perpendicular to line segment ML
What is the length of chord ML?
0
20 units
24 units
26 units
30 units
13
P
8
M
N
Mark this and return
Answer:
The correct answer is B (24 units)
Step-by-step explanation:
What is the length of AC
Answer:
5.8
Step-by-step explanation:
The angle bisector makes the triangle sides on either side of it proportional.
AC/CD = AB/BD
AC = CD·AB/BD
AC = 2(8.1/2.8) = 8.1/1.4 ≈ 5.7857 . . . . substitute shown values, evaluate
AC ≈ 5.8
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Help please !!!
Answer:
y=2x-4
Step-by-step explanation:
Which of the following is an arithmetic sequence?
2.4.8. 16.
2.4.-6.8.
-8, -6,-4,-2
Answer:
-8,-6,-4,-2 is an Arithmetic sequence, because there common difference is 2.
adiocarbon dating of blackened grains from the site of ancient Jericho provides a date of 1315 BC ± 13 years for the fall of the city. What is the relative amount of 14C in the old grain vs the new grain in 2007 AD? (A0 = original radioactivity; At = radioactivity in 2007 AD).
Answer:
[tex]\left(\frac{m(t)}{m_{o}} \right)_{min} \approx 0.659[/tex] and [tex]\left(\frac{m(t)}{m_{o}} \right)_{max} \approx 0.661[/tex]
Step-by-step explanation:
The equation of the isotope decay is:
[tex]\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]
14-Carbon has a half-life of 5568 years, the time constant of the isotope is:
[tex]\tau = \frac{5568\,years}{\ln 2}[/tex]
[tex]\tau \approx 8032.926\,years[/tex]
The decay time is:
[tex]t = 1315\,years + 2007\,years \pm 13\,years[/tex] (There is no a year 0 in chronology).
[tex]t = 3335 \pm 13\,years[/tex]
Lastly, the relative amount is estimated by direct substitution:
[tex]\frac{m(t)}{m_{o}} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{\mp\frac{13\,years}{8032.926\,years} }[/tex]
[tex]\left(\frac{m(t)}{m_{o}} \right)_{min} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{-\frac{13\,years}{8032.926\,years} }[/tex]
[tex]\left(\frac{m(t)}{m_{o}} \right)_{min} \approx 0.659[/tex]
[tex]\left(\frac{m(t)}{m_{o}} \right)_{max} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{\frac{13\,years}{8032.926\,years} }[/tex]
[tex]\left(\frac{m(t)}{m_{o}} \right)_{max} \approx 0.661[/tex]
are supplementary angles, then
A) Both should be acute B) Both should be obtuse C) one acute other right D) None of these
Answer:
D
Step-by-step explanation:
Answer:
D) None of these
Step-by-step explanation:
Supplementary pairs must equal to 180 degrees. They can either be made up of two right angles, or one acute and one obtuse angle.
Choose the function that is a "parent function".
Answer:
f(x)=√x
Step-by-step explanation:
A parent function is something simple with just x
Answer:
f(x)=Square Root of x (choice B or the second one down)
Step-by-step explanation:
All the other choices have either a plus 3 or minus 3. A parent function is not going to have any type of number being added or subtracted to it.
URGENT!! EASY IM DUMB MY LAST QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
YOU HAVE TO LOOK CLOSLY TO SEE THE NUMBERS ON THE TRIANGLE
IN CASE YOU CANNOT ON THE LEFT IT IS 15CM AND ON THE BOTTOM IT IS 14 CM
Find the unknown side of the triangle below (round to the nearest tenth).
A) 20.5 cm
B) 210.5 cm
C) 5.4 cm
D) 16 cm
Answer:
A. 20.5
Step-by-step explanation:
We can use the Pythagorean theorem to solve this equation for the missing side length, X.
a^2 + b^2 = c^2
We have a and b, we just need c, the hypotenuse.
14^2 + 15^2 = c^2
196 + 225 = c^2
421 = c^2
Now, we will square both sides:
The answer is about 20.5
Dominique is thinking about buying a hosue for 286000
Answer:
is this supposed to be a question?
Answer:
yah so
Step-by-step explanation:
If the measure of the angle in the southwest corner of the intersection of Broadway and 21st Street is approximately 105ºwhat is the measure of the angle in the southwest corner of the intersection of Broadway and 22nd Street?
A: 85 degrees
B: 95 degrees
C: 120 degrees
D: 105 degrees
Answer:
95°
Step-by-step explanation:
The angle on the 20TH street and 22ND street must add up to 180° so the answer is 95°
Answer:
This isnt right. Good try though
Step-by-step explanation:
Anyone know the answer?
Which is the value of this expression when a = negative 2 and b = negative 3? (StartFraction 3 a Superscript negative 3 Baseline b squared Over 2 a Superscript negative 1 Baseline b Superscript 0 Baseline EndFraction) squared
Answer:
27/8
Step-by-step explanation:
You seem to want to evaluate ...
[tex]\dfrac{3a^{-3}b^2}{2a^{-1}b^0}[/tex]
I like to simplify the expression first, even though the order of operations would have you evaluate it as is.
[tex]=\dfrac{3}{2}a^{-3-(-1)}b^{2-0}=\dfrac{3b^2}{2a^2}[/tex]
Substitute the given values for "a" and "b" and do the arithmetic.
[tex]=\dfrac{3(-3)^2}{2(-2)^2}=\dfrac{3\cdot 9}{2\cdot 4}=\boxed{\dfrac{27}{8}}[/tex]
When the health department tested private wells in a county for two impurities commonly found in drinking water, it found that 10% of the wells had neither impurity, 90% had impurity A, and 20% had impurity B. (Obviously, some had both impurities.) If a well is randomly chosen from those in the county, find the probability distribution for Y, the number of impurities found in the well.
Answer:
P(Y= 0) = 0.1
P(Y= 0) = 0.7
P(Y= 0) = 0.2
Step-by-step explanation:
Let Y be number of impurities that can be found in the well,
Let A denote the event that impurity A is randomly found in the well
Here Y can have three values i.e 0 , 1 and 2
✓It will take take the value of 0 when there is no impurity found in the well
✓It will take the value of 1 when when exactly one impurity vis found in the well
✓It will take the value of 2 when when both impurities vis found in the well
CHECK THE ATTACHMENT FOR DETAILED EXPLATION
Please answer this correctly
Answer:
0
Step-by-step explanation:
No one is there which satisfies the condition
Answer:
0 or 0/9 of the club members
Step-by-step explanation:
The only part of the data of members that have logged more than 1 1/5 but less than 1 3/5 hours is the members that logged 1 2/5 hours. There are no members that have logged 1 2/5 hours so our answer is 0 or 0/9.