Answer:
1) There exists a real number x such that for all real numbers y, xy ≤ y.
Step-by-step explanation:
Given the statement:
"There exists a real number x such that for all real numbers y, xy > y"
The negation of the statement is:
"There exists a real number x such that for all real numbers y, xy ≤ y"
The correct option is 1
You want to put a 2 inch thick layer of topsoil for a new 14 ft by 26 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Answer:
2 1/4
Step-by-step explanation:
The volume of soil needed is ...
(14/3 yd)(26/3 yd)(2/36 yd) = 728/324 yd³ = 2.247 yd³
The nearest higher quarter-yard is 2.250 yd³. That's how much you need to order.
You need to order 2 1/4 cubic yards.
___
There are 3 ft or 36 inches to a yard.
a patient is taking 65 grams of medicine if it is increased by 20% how many grams are they taking
Answer:
78 grams
Step-by-step explanation:
20% is 1/5
1/5 of 65 is 13
65 + 13 = 78
brainliest?
The Demon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginning of the growing season to protect against various insects. Two new insecticides have just been marketed: Pernod 5 and Action. To test their effectiveness, three long rows were selected and sprayed with Pernod 5, and three other were sprayed with Action. When the grape ripened, 400 of the vines treated with Pernod 5 and 400 of the vines treated with Action were checked for infestation. The number of infested vines treated with Pernod 5 and Action are 24 and 40 respectively.
At 0.05 significance level, can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action?
Answer:
At a significance level of 0.05, there is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.
Then, the null and alternative hypothesis are:
H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0
The significance level is 0.05.
The sample 1 (Pernod 5), of size n1=400 has a proportion of p1=0.06.
[tex]p_1=X_1/n_1=24/400=0.06[/tex]
The sample 2, of size n2=400 has a proportion of p2=0.1.
[tex]p_2=X_2/n_2=40/400=0.1[/tex]
The difference between proportions is (p1-p2)=-0.04.
[tex]p_d=p_1-p_2=0.06-0.1=-0.04[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{24+40}{400+400}=\dfrac{64}{800}=0.08[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.08*0.92}{400}+\dfrac{0.08*0.92}{400}}\\\\\\s_{p1-p2}=\sqrt{0.000184+0.000184}=\sqrt{0.000368}=0.019[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.04-0}{0.019}=\dfrac{-0.04}{0.019}=-2.085[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]\text{P-value}=2\cdot P(z<-2.085)=0.037[/tex]
As the P-value (0.037) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.
Find the length of KC
Answer:
54
give me brainliest please please please and follow my page
Step-by-step explanation:
To find length of KC...we need to find the length of HM and MU first ...
so....HM= 96- 78 = 14
JU = 96 + HM = 96 + 14 = 110
....
KU = 110 - JK = 110 - 82 = 28
....
UN = 105+ 82 -( 96 + 14 )
187 - 110
= 77
UC = 77 - 51 = 26
KC = UC + KU = 26 + 28 = 54
The length of [tex]\overline{KC}[/tex] along line [tex]\overline{JN}[/tex] is given as 54 (Option A) See the computation below.
How do you compute the length of [tex]\overline{KC}[/tex]?To determine the length of [tex]\overline{KC}[/tex], the length of [tex]\overline{HM}[/tex] and [tex]\overline{MU}[/tex]must first be derived.
[tex]\overline{HM}[/tex] = 96 - 78
[tex]\overline{HM}[/tex] = 14
[tex]\overline{JU}[/tex] = 96 + [tex]\overline{HM}[/tex]
= 96 + 14
[tex]\overline{JU}[/tex]= 110
[tex]\overline{KU}[/tex] = 110 - [tex]\overline{JK}[/tex]
= 110 - 82
[tex]\overline{KU}[/tex]= 28
[tex]\overline{UN}[/tex] = 105+ 82 -( 96 + 14 )
=187 - 110
[tex]\overline{UN}[/tex]= 77
[tex]\overline{UC}[/tex] = 77 - 51
[tex]\overline{UC}[/tex]= 26
Thus,
[tex]\overline{KC}[/tex] = [tex]\overline{UC}[/tex] + [tex]\overline{KU}[/tex]
[tex]\overline{KC}[/tex]= 26 + 28
[tex]\overline{KC}[/tex]= 54
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find the area of the shaded region. 27.8 in and 150 degrees
Answer: 57769.8 in²
Let A be the area of the shaded region
We have a relation that can help us calculate its area
A= 0.5*(θ-sin(θ))*r² where r is the radius and θ the angle
A= 0.5*(150-sin(150°))* 27.8² =57769.79≈57769.8 in²
Answer:
818.4
Step-by-step explanation:
Which property is displayed in the example below: 4(x + 3) = 4x + 12
Answer:
This equation displays the distributive property which states that a(b + c) = a(b) + a(c).
Answer:
Distributive property
Step-by-step explanation:
4(x+3)=4x+12
This example shows distributive property because 4 is distributed (multiplied) to x +3. When 4 is distributed, it will equal 4x+12!!
Hope it helps!!!!
This is not an incomplete question, it has come from a very reliable source, please dont delete. If 60% of the students in Mr. Bobby's class are bio majors, which of the following could be the total number of students in his class? 28 32 35 39 PLZHELPTHANKS
Answer:
35 students
Step-by-step explanation:
Take the number of students in the class and multiply by 60% and see if you get an integer number
28 * .60 =16.8 not an integer
32 * .6 =19.2
35 * .6 =21 yes
39*.6 =23.4
please help hurryyyyyyy
Answer:
Hey there!
40 is 25% of 120.
We can see that 30 is 25% of 120, because 0.25(120)=30.
Hope this helps :)
Answer:
30 is 25% of 120
Step-by-step explanation:
What is 25% of 120
Is means equals and of means multiply
What = 25% * 120
What = .25 * 120
What =30
30 is 25% of 120
According to the Stack Overflow Developers Survey of 20184 , 25.8% of developers are students. The probability that a developer is a woman given that the developer is a student is 7.4%, and the probability that a developer is a woman given that the developer is not a student is 76.4%. If we encounter a woman developer, what is the probability that she is a student
Answer:
3.26%
Step-by-step explanation:
The computation of the probability that she is a student is shown below:
Percentage of student developers = 25.8% = SD
The Percentage of the developer is student = 7.4% = DS
The percentage of the developer is not student = 76.4% = ND
Based on this, the probability is
[tex]= \frac{SD \times DS}{SD \times DS + DS \times ND}[/tex]
[tex]= \frac{25.8\% \times 7.4\%}{25.8\% \times 7.4\% + 7.4\% \times 76.4\%}[/tex]
=3.26%
we simply considered all the elements
Not sure how to graph this
Answer:
y=2x+6
Step-by-step explanation:
The slope is 2x and the y-intercept is 6. It is shown how to graph it in the attachment.
perform the indicated operations a. 3/10+6/10. b. 1/3+2/4+1/6. c. 5/6-3/6 d. 2/3-6/10 e. 4/10×3/7 f. 1/6x6/15 g. 1/8÷4/9 h. 1/5÷3/4
Answer:
A. [tex]\frac{9}{10}[/tex]
B. 1
C. [tex]\frac{2}{6}[/tex] or [tex]\frac{1}{3}[/tex]
D. [tex]\frac{2}{30}[/tex] or [tex]\frac{1}{15}[/tex]
E. [tex]\frac{12}{70}[/tex] or [tex]\frac{6}{35}[/tex]
F. [tex]\frac{6}{90}[/tex] or [tex]\frac{1}{15}[/tex]
G. [tex]\frac{9}{32}[/tex]
H. [tex]\frac{4}{15}[/tex]
Answer:
Step-by-step explanation:
Reducing the given expressions to the lowest terms:
A. 3/10 + 6/10:
B. 1/3 + 1/4 + 1/6:
C. 5/6-3/6:
D. 2/3-6/10:
E. 4/10*3/7:
F. 1/6*6/15:
G. 1/8 divided by 4/9:
H. 1/5 divided by 3/4:
Which are the roots of the quadratic function f(b) = 62 – 75? Select two options.
b=573
Ob= -573
b=35
b= -35
Ob= 253
Answer:
[tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]
Step-by-step explanation:
Given
[tex]f(b) = b^2 - 75[/tex]
Required
Determine the roots
To get the root of the function, then f(b) must be 0;
i.e. f(b) = 0
So, the expression becomes
[tex]0 = b^2 - 75[/tex]
Add 75 to both sides
[tex]75 + 0 = b^2 - 75 + 75[/tex]
[tex]75 = b^2[/tex]
Take square roots of both sides
[tex]\sqrt{75} = \sqrt{b^2}[/tex]
[tex]\sqrt{75} = b[/tex]
Reorder
[tex]b = \sqrt{75}[/tex]
Expand 75 as a product of 25 and 3
[tex]b = \sqrt{25*3}[/tex]
Split the expression
[tex]b = \sqrt{25} *\sqrt{3}[/tex]
[tex]b = \±5 *\sqrt{3}[/tex]
[tex]b = \±5 \sqrt{3}[/tex]
[tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]
The options are not clear enough; however the roots of the equation are [tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]
Scott has eight CDs, and he picks two to take to work each day. How many different ways can Scott choose two CDs?
Answer:
The total number of ways to select 2 CDs from 8 CDs is 28.
Find the total area of the prism.
Answer:
864
Step-by-step explanation:
AT= 2Area base+ph
AT= 2(12*12) +(12*4)12
AT=2 (144)+576
AT= 288+576
AT=864"
Galina had two boxes with pieces of paper in each. In the first box, each piece of paper had one possible outcome from flipping a coin 4 times (e.g. HHTH). There was one piece of paper for every possible outcome.
How many pieces of paper were in the first box?
Answer:
B
Step-by-step explanation:
For each ordered pair, determine whether it is a solution to the system of equations. y=6x-7 9x-2y=8
Answer:
x = 2, y = 5
Step-by-step explanation:
Hello,
y=6x-7
9x-2y=8
can be written as
(1) 6x - y = 7
(2) 9x -2y = 8
(2)-2*(1) gives
9x -2y -12x +2y = 8 - 2*7 = 8 - 14 = -6
<=> -3x=-6
<=> x = 6/3=2
and we replace it in (1)
y = 6*2-7=12-7=5
hope this helps
Periodically, customers of a financial services company are asked to evaluate the company's financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use
α = 0.05
and test to see whether the consultant with more experience has the higher population mean service rating.
Consultant A Consultant B
n1 = 16
n2 = 10
x1 = 6.82
x2 = 6.28
s1 = 0.65
s2 = 0.75
(a)
State the null and alternative hypotheses.
H0:
μ1 − μ2 ≤ 0
Ha:
μ1 − μ2 = 0
H0:
μ1 − μ2 > 0
Ha:
μ1 − μ2 ≤ 0
H0:
μ1 − μ2 ≠ 0
Ha:
μ1 − μ2 = 0
H0:
μ1 − μ2 ≤ 0
Ha:
μ1 − μ2 > 0
H0:
μ1 − μ2 = 0
Ha:
μ1 − μ2 ≠ 0
(b)
Compute the value of the test statistic. (Round your answer to three decimal places.)
(c)
What is the p-value? (Round your answer to four decimal places.)
p-value =
(d)
What is your conclusion?
Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.Do not reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating. Do not Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.Reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating.
Answer:
A) Null hypothesis; H0: μ1 − μ2 ≤ 0
Alternative hypothesis; Ha: μ1 − μ2 > 0
B) Test statistic = t = 1.878
C) p-value is 0.038823.
D) Reject the Null hypothesis H0
Step-by-step explanation:
We are given;
α = 0.05
n1 = 16
n2 = 10
bar x1 = 6.82
bar x2 = 6.28
s1 = 0.65
s2 = 0.75
A) The hypothesis is as follows;
Null hypothesis; H0: μ1 − μ2 ≤ 0
Alternative hypothesis; Ha: μ1 − μ2 > 0
B) Formula yo determine the test statistic is;
t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))
Plugging in the relevant values, we have;
t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))
t = 0.54/√(0.02640625 + 0.05625)
t = 0.54/0.2875
t = 1.878
C) The formula for the degree of freedom is;
Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))
Plugging in the relevant values, we have;
Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))
Δ = 0.00683205566/(0.000046486 + 0.0003515625)
Δ ≈ 17
Thus, the P-value;
From online p-value calculator from t-score and DF which i attached, we have the p-value as;
The p-value is 0.038823.
D) The p-value result is significant at p < 0.05
Thus, we reject the Null hypothesis H0
A) Null hypothesis: μ1 − μ2 ≤ 0
B) Test statistic = t = 1.878
C) The p-value is 0.038823.
D) Reject the Null hypothesis H0.
HypothesisWhat all information we have ?
α = 0.05
n1 = 16
n2 = 10
bar x1 = 6.82
bar x2 = 6.28
s1 = 0.65
s2 = 0.75
Part A)
The hypothesis is as follows;
Null hypothesis; H0: μ1 − μ2 ≤ 0
Alternative hypothesis; Ha: μ1 − μ2 > 0
Part B)
The formula to determine the test statistic is :
t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))
t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))
t = 0.54/√(0.02640625 + 0.05625)
t = 0.54/0.2875
t = 1.878
The formula to determine the test statistic is t = 1.878.
Part C)
The formula for the degree of freedom is;
Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))
Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))
Δ = 0.00683205566/(0.000046486 + 0.0003515625)
Δ ≈ 17
Thus, the P-value is 0.038823.
Part D)
The p-value result is significant at p < 0.05 is :
Thus, we reject the Null hypothesis H0.
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The table shows claims and their probabilities for an insurance company.
O A. (a)
O B. (a)
Amount of Claim
$0
$50,000
$100,000
$150,000
$200,000
$250,000
Probability
0.60
0.25
0.09
0.04
0.01
0.01
O c. (a) $
OD. (a) $
(a) Calculate the expected value.
(b) How much should the company charge as an average premium so that it breaks even on its claim
costs?
(c) How much should the company charge to make a profit of $60 per policy?
Answer:
a) Expected Value of Claims = $32,000
b) Average premium per claim, in order to break-even on claim costs
= $5,333.33
c) To make a profit of $60 per policy (i.e. a total profit of $360 ($60 x 6), it must charge:
= $5,393.33 per policy
Step-by-step explanation:
a) Data and Calculations:
Amount of Claim Probability Expected Value
$0 0.60 $0
$50,000 0.25 $12,500
$100,000 0.09 9,000
$150,000 0.04 6,000
$200,000 0.01 2,000
$250,000 0.01 2,500
Expected Cost of claims = $32,000
b) Average premium per claim, in order to break-even on claim costs
= Total Claim cost divided by number of policies
= $32,000/6 = $5,333.33
c) To make a profit of $60 per policy (i.e. a total profit of $360 ($60 x 6), it must charge:
Total Claim cost + Total profit / 6 or Average Premium plus Profit per policy =
= ($32,000 + $360)/6 or $5,333.33 + $60
= $32,360/6 or $5,393.33
= $5,393.33
The total expected value is $32000, the average premium so that it breaks even on its claim costs are $5333.33 and the company charge to make a profit of $60 per policy is $5393.33.
Given :
The table shows claims and their probabilities for an insurance company.
Amount of Claim Probability Expected Value
$0 0.60 0
$50000 0.25 $12500
$100000 0.09 $9000
$150000 0.04 $6000
$200000 0.01 $2000
$250000 0.01 $2500
A) So, the total expected value is = 12500 + 9000 + 6000 + 2000 + 2500
= $32000
B) The average premium is given by:
[tex]=\dfrac{32000}{6}[/tex]
= $5333.33
C) The company charge to make a profit of $60 per policy is:
[tex]= \dfrac{32000+360}{6}[/tex]
[tex]=\dfrac{32360}{6}[/tex]
= $5393.33
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need help asap! what is the value of x given that figure MNOP is a trapezoid with median QR
Answer:
x = 8
Step-by-step explanation:
To find the possible value of x in the given trapezoid MNOP with median QR, recall that one of the properties of a trapezoid is that the median length = ½ of the sum of the length of the parallel bases
Thus, ½ of [x + (3x + 8)] = 20
Let's find x
½*[x + (3x + 8)] = 20
½*[x + 3x + 8)] = 20
½*[4x +8] = 20
Multiply both sides by 2
4x + 8 = 20*2
4x + 8 = 40
Subtract 8 from both sides
4x = 40 - 8
4x = 32
Divide both sides by 4
x = 32/4
x = 8
Answer:
I think its 8 ♂️
Step-by-step explanation:
A sample of size 42 college students produced a 95% confidence interval of (3.1, 5.2) for the mean number of coats owned. Then there is a 95% chance that these 42 students own on average between 3.1 and 5.2 coats.
a. True
b. False
Answer:
b. False.
Step-by-step explanation:
According to the presented information, at the 95% confidence level, the mean number of coats owned will be between 3.1 and 5.2. That does not mean that there is a 95% chance that they will own that many coats; just that you are 95% confident that they will own the coats.
Hope this helps!
Travis bought $9.45 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 5 fewer than the number of 49-cent stamps. Solve the equation 0.49s+0.21(s−5)=9.45 for s to find the number of 49-cent stamps Travis bought.
Answer:
15 49-cent stamps
Step-by-step explanation:
We can solve this problem with the equations 0.49(x) + 0.21(y) = 9.45 and x - 5 = y. Well, 0.49(15) + 0.21(10) = 9.45, so we know that there are 15 49-cent stamps and 10 21-cent stamps. The question is asking for the number of 49-cent stamps, so we can tell Travis bought 15 49-cent stamps.
Hope this helps! Plz give me brainliest, it will help me achieve my next rank.
The number of 49-cent stamps that Travis bought given the equation is 15.
What he number of 49-cent stamps Travis bought?Given this equation: 0.49s+0.21(s−5)=9.45 take the following steps to determine the value of s
Expand the bracket: 0.49s + 0.21s - 1.05 = 9.45Combine similar terms : 0.49s + 0.21s = 9.45 + 1.05Add similar terms: 10.50 = 0.70sDivide both sides of the equation by 0.70: s = 15To learn more about mathematical equations, please check: https://brainly.com/question/26427570
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{3, 6, 9, 12, 15} {1, 6, 12, 18, 24}Which of the following shows the intersection of the sets?
Answer:
{ 6,12}
Step-by-step explanation:
The intersection is what the two sets have in common
{3, 6, 9, 12, 15}∩ {1, 6, 12, 18, 24}
= { 6,12}
Forty one people were riding bus number 527. At 8:45 am,it arrived at the 109th street stop. There,19 people got off and then 20 people boarded. How many riders were on the bus when it traveled to the next stop?
Answer:
1 because jahahdhekskdbsks
Find the volume of the region between the planes x plus y plus 2 z equals 2 and 4 x plus 4 y plus z equals 8 in the first octant.
Find the intercepts for both planes.
Plane 1, x + y + 2z = 2:
[tex]y=z=0\implies x=2\implies (2,0,0)[/tex]
[tex]x=z=0\implies y=2\implies(0,2,0)[/tex]
[tex]x=y=0\implies 2z=2\implies z=1\implies(0,0,1)[/tex]
Plane 2, 4x + 4y + z = 8:
[tex]y=z=0\implies4x=8\implies x=2\implies(2,0,0)[/tex]
[tex]x=z=0\implies4y=8\impliesy=2\implies(0,2,0)[/tex]
[tex]x=y=0\implies z=8\implies(0,0,8)[/tex]
Both planes share the same x- and y-intercepts, but the second plane's z-intercept is higher, so Plane 2 acts as the roof of the bounded region.
Meanwhile, in the (x, y)-plane where z = 0, we see the bounded region projects down to the triangle in the first quadrant with legs x = 0, y = 0, and x + y = 2, or y = 2 - x.
So the volume of the region is
[tex]\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx[/tex]
[tex]=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx[/tex]
[tex]=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}[/tex]
Charlotte is running at a rate of 9 (km)/(h) what is charlotte speed in (m)/(s)
Answer:
2.5 meters per second
Step-by-step explanation:
9x1000=9000m/h
9000/60/60=2.5m/s
Answer:
2.5 m/s
Step-by-step explanation:
convert kilometers to meters and then use a conversion calc to do the rest
Hi, what trigonometry is?
Trigonometry is the study of the properties of triangles and trigonometric functions and of their applications.
I'm not sure how you'd want me to answer your question though, but stay safe!!
- eli <3
in QRS, m Q = 70°, m R = 44", and m S = 66º. Which side of QRS is the shortest?
Answer:
QS
Step-by-step explanation:
The side opposite to the smallest angle must be the shortest side. The smallest angle is ∠R so the opposite side is QS.
Answer:
Hey there!
Smaller angles are opposite smaller sides, so the side opposite to angle R would be the shortest. (Or side SQ)
Hope this helps :)
Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. The sample standard deviation is 7.309. Adam reads that the average speed that cars drive on the highway is 65 mph. The t-test statistic for a two-sided test would be __________. Answer choices are rounded to the hundredths place.
Answer:
We accept null hypothesis
Step-by-step explanation:
We assume a normal distribution
The population mean μ₀ = 65 mph
Sample mean μ = 63,2 mph ( calculated from data )
Sample standard deviation σ = 7,309
Sample size n = 8
Degree of freedom is n - 1 8 - 1 = 7
As n < 30 we have to use the t-student test
We will do our test with a confidence interval of 95 % that means α = 5 %
or α = 0,05 and as we are going through a two-tail test α/2 = 0,025
Test Hypothesis:
Null Hypothesis: H₀ μ = μ₀
Alternate Hypothesis Hₐ μ ≠ μ₀
From t-student table for the degree of freedom 7, α/2 = 0,025 two-tail test we find tc
tc = 2,365
And calculate ts as
ts = ( μ - μ₀ ) / σ /√n
ts = ( 63,2 - 65 ) / 7,309/ √8
ts = - 1,8 *2,828/ 7,309
ts = - 5,091 /7,309
ts = - 06965
Now we compare ts and tc
tc = 2,365 or tc = - 2,365 ( by simmetry) tc = -2,37
and ts = -0,06965 ts = - 0,07
As |ts| < |tc|
ts is in the acceptance zone so we accept null hypothesis
Answer:
-0.70
Step-by-step explanation:
For the tabulated value the mean is calculated as:
Mean = (60.5 + 63.2 + 54.7 + 51.6 + 72.3 + 70.7 + 67.2 + 65.4)/8
= 505.6/8
Mean \bar{x}= 63.2
and population mean as assumption u= 65
and given that the sample standard deviation is: s= 7.309
The test statistic is calculated as:
Ζ = Τ –μ 63.2 - 65 = -0.696 -0.70 S
Hence the T statistic would be -0.70
is -17 a natural number
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▹ Answer
-17 isn't a natural number
▹ Step-by-Step Explanation
Positive integers are only natural numbers, meaning negative numbers aren't natural numbers.
Hope this helps!
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Brainliest is greatly appreciated!
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help :(( i am very confused and if the screenshot says 25 just know its 26 not 25
Answer:
9/26
Step-by-step explanation:
Answer:
Step-by-step explanation:
25-3 =22 have a cat or a dog
15 +16 =31 students are in the class if every person has either a cat or a dog
But we have 22
so 31 - 22 = 9 have both cat and dog
the probability is 9/25