Answer:
a) We reject H₀
b) The manager won´t be satisfied with nominal filling its cup
c) See step-by-step explanation
Step-by-step explanation:
Normal distribution n < 30, therefore, we should use t - student table
Sample size n = 16
degree of freedom = df = n - 1 df = 15
Sample mean μ = 5,85 ou
Sample standard deviation is s = 0,2 ou
Hypothesis test
Null hypothesis H₀ μ >= μ₀
Alternative hypothesis Hₐ μ < μ₀
CI = 95 % then α = 5 % α = 0,05 α/2 = 0,025
Then in t-student table we find t(c) = 1,753
To calculate t(s)
t(s) = ( μ - μ₀ ) s/√n
t(s) = ( 5,85 - 6 ) / 0,2/√16
t(s) = - 0,15* 4 / 0,2
t(s) = - 3
To compare t(s) and t(c)
|t(s)| > |t(c)| 3 > 1,753
Then t(s) is in the rejection region. We should reject H₀. Data indicate that at 95 % of CI μ seems to be smaller than 6 ou
b) The manager won´t be satisfied with nominal filling its cup
I
Ifm DGF = 72, what equation can you use to find mZEGF?
Answer:
see explanation
Step-by-step explanation:
∠ DGE + ∠ EGF = ∠ DGF , that is
∠ EGF = ∠ DGF - ∠ DGE
∠ EGF = 72° - ∠ DGE
Enter an expression that is equivalent to (6x2−1)+(x2+3)−2(x2−5)−15x2, combining all like terms. Use the on-screen keyboard to type the correct polynomial in the box below.
Answer:
Its 10x^2+12
Step-by-step explanation:
Answer:
-10X^2+12
Step-by-step explanation:
determine the results of the following operations
Answer:
[tex]\sqrt[3]{4}\times (\sqrt[3]{16}-10 )[/tex]
Step-by-step explanation:
Let be [tex]\sqrt[3]{64}-\sqrt[3]{32} \times \sqrt[3]{125}[/tex], this expression is simplified as follows:
1) [tex]\sqrt[3]{64}-\sqrt[3]{32} \times \sqrt[3]{125}[/tex] Given
2) [tex]\sqrt[3]{4^{3}}-\sqrt[3]{2^{5}}\times \sqrt[3]{5^{3}}[/tex] Definition of power
3) [tex](4^{3})^{1/3}-(2^{2}\cdot 2^{3})^{1/3}\times (5^{3})^{1/3}[/tex] Definition of n-th root/[tex]a^{b+c}= a^{b}\cdot a^{c}[/tex]/[tex](a^{b})^{c} = a^{b\cdot c}[/tex]
4) [tex]4 - (2^{2})^{1/3}\times 2\times 5[/tex] [tex]a^{b+c}= a^{b}\cdot a^{c}[/tex]/[tex](a\cdot b)^{c} = a^{c}\cdot b^{c}[/tex]
5) [tex]4 - 10\times 4^{1/3}[/tex] Multiplication/Definition of power
6) [tex]4^{1/3}\cdot (4^{2/3}-10)[/tex] Distributive property/[tex]a^{b+c}= a^{b}\cdot a^{c}[/tex]
7) [tex]\sqrt[3]{4}\times [(4^{2})^{1/3}-10][/tex] [tex](a^{b})^{c} = a^{b\cdot c}[/tex]/Definition of n-th root
8) [tex]\sqrt[3]{4}\times (\sqrt[3]{16}-10 )[/tex] Definition of power/Result
The MCAT is the admission exam that medical schools use as one of the criteria for accepting students. The exam is based on a scale of 0-45. The following data shows the MCAT scores for nine students.
32 36 29 31 30 35 34 26 30
The 35th percentile of this data set is:________
a. 31
b. 32
c. 31.5
d. 30
Answer:
d. 30
Step-by-step explanation:
The computation of the 35th percentile of this data set is shown below:
Before that first we have to series the number in ascending number
S. No Numbers
1 26
2 29
3 30
4 30
5 31
6 32
7 34
8 35
9 36
Now use the formula
Here n = 9
Percentile = 100
[tex]= \frac{35(9 + 1)}{100} \\\\[/tex]
= 3.5th
= 3th + 0.5 (4th - 3th)
= 3th + 0.5 (30 - 30)
= 3th + 0
= 30
Prove that for all integers m and n, m - n is even if, and only if, both m and n are even or both m and n are odd.
Answer:
Below
Step-by-step explanation:
Suppose that m and n are both even numbers.
So we can express them as the product of 2 and another number.
● n = 2×a
● m = 2×b
● m-n = 2b-2a
● m-n = 2(b-a)
m-n is an even number since it is divisible by 2.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Suppose that both n and m are odd numbers.
● n = 2a+1
● m = 2b+1
● m-n = 2b+1-(2a+1)
● m-n = 2b+1-2a-1
● m-n = 2b-2a
● m-n = 2(b-a)
So m-n is even since it is divisible by 2.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Suppose that m is odd and n is even ir vice versa
● n = 2a or n= 2a+1
● m = 2b+1 or m = 2b
● m-n = 2b+1-2a or m-n = 2b-2a-1
● m-n = 2(b-a) +1 or m-n = 2(b-a)-1
In both cases m-n isn't even.
■■■■■■■■■■■■■■■■■■■■■■■■■■
So m-n is even if and only if m and n are odd or m and are even
Answer:
Case 1
both m and n are even
Therefore m/2 and n/2 are integers
Then,
m-n
=2(m/2 - n/2)
Since m/2 and n/2 are integers
Then m/2 - n/2 will be an integer
Therefore,
m-n = 2(Z)
Where Z is an integer
Since 2 is a factor of m-n
Therefore m -n is even
Case 2
Both m and n are odd
m-n
= 2(½m - ½n)
When an odd number is divided by 2 it gives an integer and a remainder of 1
Therefore
½m = Y + ½
And
½n = Z + ½
Where Y and Z are integers
Then
m-n = 2(Y+½-Z-½)
= 2(Y-Z)
Y-Z will also be an integer
m-n= 2A
Therefore m-n is even
Case 3
One is odd and the other even
m-n = 2(m/2 - n/2)
Assume m is even and n is odd
From the discussions above
m-n = 2(Y - Z - ½)
m-n = 2(A - ½)
Hence m-n is not even because when is divided by two it doesn't give an integer.
Therefore for all integers m and n, m - n is even if, and only if, both m and n are even or both m and n are odd.
What is the distance between the two endpoints in the graph below? If necessary, round your answer to two decimal places.
A.
16.45 units
B.
13 units
C.
15.81 units
D.
22 units
Answer:
C. [tex] d = 15.81 units [/tex]
Step-by-step explanation:
Given:
2 end points on a graph => (5, 6) and (-4, -7)
Required:
Distance between them
SOLUTION:
Distance between two points in a graph can be calculated using [tex] distance (d) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Where,
[tex] (-4, -7) = (x_1, y_1) [/tex]
[tex] (5, 6) = (x_2, y_2) [/tex]
Plug in the values into the formula and solve
[tex] d = \sqrt{(5 - (-4))^2 + (6 - (-7))^2} [/tex]
[tex] d = \sqrt{(5 + 4))^2 + (6 + 7))^2} [/tex]
[tex] d = \sqrt{(9)^2 + (13)^2} [/tex]
[tex] d = \sqrt{81 + 169} [/tex]
[tex] d = \sqrt{250} [/tex]
[tex] d = 15.81 units [/tex]
Answer:
15.81
Step-by-step explanation:
Which equation will solve the following word problem? In a given amount of time, Jamie drove four times as far as Rhonda. Altogether they drove 125 miles. Find the number of miles driven by each. 4T + T = 125 4T = 125/T T = 125/4T 4T - T = 12
Answer:
1) 4T+T=125
2) Rhonda drove 25 miles
and Jamie drove 100 miles
Step-by-step explanation:
1) Rhonda drove = T
Jamie drove = 4T
4T+T=125
2) 5T=125
T=125/5
T=25
So Rhonda drove T = 25
And Jamie drove 4T = 100
simplify -3(2g - 6) +4g
-3-2g+6+4g
3+2g
hope it helps
Answer:
-2g + 18
Step-by-step explanation:
-3(2g - 6) + 4g
First we use distributive property.
-3 × 2g = -6g
-3 × -6 = 18
now we have
-6g + 18 + 4g
Now we combine the like terms
-6g + 4g = -2g
Finally we have
-2g + 18
and they are not like terms so we leave them and the equation is solved.
In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is
Complete Question
In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is:
A -1.645
B -2.066
C -2.000
D-1.960
Answer:
The correct option is C
Step-by-step explanation:
From the question we are told that
The population mean is [tex]p = 0.50[/tex]
The sample size is [tex]n = 64[/tex]
The number that met the standard is [tex]k = 24[/tex]
Generally the sample proportion is mathematically evaluated as
[tex]\r p = \frac{24}{64}[/tex]
[tex]\r p =0.375[/tex]
Generally the standard error is mathematically evaluated as
[tex]SE = \sqrt{ \frac{p(1- p )}{n} }[/tex]
=> [tex]SE = \sqrt{ \frac{0.5 (1- 0.5 )}{64} }[/tex]
=> [tex]SE = 0.06525[/tex]
The test statistics is evaluated as
[tex]t = \frac{ \r p - p }{SE}[/tex]
[tex]t = \frac{ 0.375 - 0.5 }{0.0625}[/tex]
[tex]t = -2[/tex]
What is the solution (x, y) to this system of linear equations? 2x – 3y = –6 x + 2y = 11
Answer:
x = 3, y = 4
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
32 x 42 is equal to how much
Answer:
1,344
Step-by-step explanation:
Hope i am marked as brainliest answer
the rainfall R(t) (inmm) over the course of a year in bali, indonesia as a function of time t(in days) can be modeled by a sinusoidal expression of the form a*sin(b*t)+d. At t=0, in mid april, the expected daily rainfall is 2.3mm, which is the daily average value throughout the year. 1 quarter of the year leter, at t=91.25, when the rainfall is at its minimum, the expected daily value is 1.4mm. find R(t).
[tex]\bold{\text{Answer:}\quad R(t)=-0.96\sin\bigg(\dfrac{\pi}{182.5}t}\bigg)+2.3}[/tex]
Step-by-step explanation:
The equation of a sin function is: y = A sin (Bx - C) + D where
Amplitude (A) is the distance from the midline to the max (or min)Period (P) = 2π/B --> B = 2π/PC/B is the phase shift (not used for this problem)D is the vertical shift (aka midline)D = 2.3
It is given that t = 0 is located at 2.30. The sin graph usually starts at 0 so the graph has shifted up 2.3 units. --> D = 2.3
A = -0.96
The amplitude is the difference between the maximum (or minimum) and the centerline. A = 2.30 - 1.44 = 0.96
The minimum is given as the next point. Since the graph usually has the next point as its maximum, this is a reflection so the equation will start with a negative. A = -0.96
B = π/182.5
It is given that [tex]\frac{1}{4}[/tex] Period = 91.25 --> P = 365
B = 2π/P
= 2π/365
= π/182.5
C = 0
No phase shift is given so C = 0
Input A, B, C, & D into the equation of a sin function:
[tex]R(t)=-0.96\sin\bigg(\dfrac{\pi}{182.5}t-0}\bigg)+2.3[/tex]
Write 11 numbers in a row so that the sum of any 3 consecutive numbers is negative, while the sum of all the numbers is positive.
Answer:
Step-by-step explanation:
Hello, if I take the following
2, 2, -5, 2, 2, -5, 2, 2, -5, 2, 2
The sum is 8*2-5*3=16-15=1 > 0
and
2 + 2 -5 < 0
2 - 5 + 2 < 0
-5 + 2 + 2 < 0
2 + 2 -5 < 0
2 - 5 + 2 < 0
-5 + 2 + 2 < 0
2 + 2 -5 < 0
2 - 5 + 2 < 0
-5 + 2 + 2 < 0
2 + 2 -5 < 0
2 - 5 + 2 < 0
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
. A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential model for the population.
Answer: [tex]A=6000(1.012)^t[/tex]
Step-by-step explanation:
General exponential function:
[tex]A=P(1+r)^t[/tex]
, where P= current population
r= rate of growth
t= time period
A= population after t years
As per given , we have P=6,000
r= 1.2% = 0.012
Then, the required exponential function: [tex]A=6000(1+0.012)^t[/tex]
or [tex]A=6000(1.012)^t[/tex]
Algebraic Expressions
Evaluate
The weight of a bag of oranges is 1.3 pounds. There are 9 bags of oranges. What is the total weight?
Help please :)
Answer:
11.7 pounds
Step-by-step explanation:
Multiply the weight of one bag of oranges by 9 bags.
Candice spent 5 1/4 hours doing her homework. Her brother, Ronald, spent 1/2 that number of hours doing his homework. How many hours did Ronald spend on his homework?
Answer:
Step-by-step explanation:
½ of 5¼
½×(21/4)
=21/8
=2⅝ hours
Answer:
2 5/8
Step-by-step explanation:
you would divide 5 1/4 by 2 :
5 divided by 2 =2 1/2
1/4 divided by 2=1/8
then make the numbers have the same denomanator
1/2, 2/4, 4/8
1/8,
then you add
2 4/8+1/8=2 5/8
Identify the slope and y-intercept of the function y = –2x+1.
Answer:
Below
Step-by-step explanation:
The function is y= -2x +1
● the slope is -2
● the y-intercept is 1
A box is 90 cm long. Which of these is closest to the length of this box in feet?{1 inch= 2.54cm} (1 point)
Answer:
2.952755906 ft
Step-by-step explanation:
We need to convert 90 cm to inches
90 cm * 1 inch / 2.54 cm =35.43307087 inches
Now convert inches to ft
12 inches = 1ft
35.43307087 inches * 1 ft/ 12 inches =2.952755906 ft
5.39 jings =15.4 hings
4.9 hings = 2.8 gings
According to the conversion rates above, how
many jings equal 1 ging?
E. 7/40
F. 5/8
G. 49/80
H. 20/7
Step-by-step explanation:
It is given that,
5.39 jings =15.4 hings ....(1)
4.9 hings = 2.8 gings ...(2)
From equation (2), the value of 1 ging is :
[tex]1\ \text{ging} = \dfrac{4.9}{2.8}\ \text{hing}\ .....(3)[/tex]
From equation (1), the value of 1 jing is :
[tex]1\ \text{jing} = \dfrac{15.4}{5.39}\ \text{hing}\ .....(4)[/tex]
From equation (3) and (4), we get :
[tex]\dfrac{\text{1 ging}}{\text{1 jing}}=\dfrac{4.9}{2.8}\times \dfrac{5.39}{15.4}\\\\\dfrac{\text{1 ging}}{\text{1 jing}}=\dfrac{49}{80} \\\\1\ \text{ging}=\dfrac{49}{80}\ \text{ jings}[/tex]
Hence, the correct option is (g) "49/80"
Simplify 6.92 to the exponent of 1000
Answer:
Whatever is raised to the power of 0 is 1
SO the answer is 1
Prove that if a and b are integers, then for any integer k one has (a,b) = (a + kb,b). (Hint: Show that they are mutually divisible.)
Answer:
The operation:
(a,b) is equal to the rest of the division of a by b.
Now, if we have:
(a + kb,b) = (a,b) + (k*b,b)
But if we have that k and b are integers, then:
(k*b)/b = k
So b divides k*b into a whole number, this means that (k*b,b) = 0
then:
(a + kb,b) = (a,b) + (k*b,b) = (a,b) + 0 = (a,b)
In a factory there are 100 units of a certain product, 5 of which are defective. We pick three units from the 100 units at random. What is the probability that none of them are defective
Answer:
Probability of picking all three non-defective units
= 7372/8085 (or 0.911812 to six decimals)
Step-by-step explanation:
Let
D = event that the picked unit is defective
N = event that the picked unit is not defective
Pick are without replacement.
We need to calculate P(NNN) using the multiplication rule,
P(NNN)
= 97/100 * 96/99 * 95/98
=7372/8085
= 0.97*0.969697*0.9693878
= 0.911812
The probability that none of the picked products are defective is;
P(None picked is defective) = 0.856
We are told that 5 are defective out of 100.This means the number of good products that are not defective are 95.
Probability of the first picked product not being defective is written as; P(First picked not defective) = 95/100Since the good ones have been picked, there will be 99 left of which the good ones are now 94. Thus, probability of second one not being defective = 94/99Since two good ones have been picked, there will be 98 left and 93 good ones left. Thus, probability of third one not being defective = 93/98Finally, Probability of none of the three being defective is;95/100 × 94/99 × 93/98 = 0.856
Read more at; https://brainly.com/question/14661097
The double number line shows how many meters a dragonfly can fly in 1 second.
Answer: It's B
Step-by-step explanation:
The table that represents the double number line is (b)
How to determine the table of the number line?On the double number line, we have the following points
x: 0 1
y: 0 25
This means that as x increases by 1, y increases by 25.
So, we have:
x: 0 1 2 3 4
y: 0 25 50 75 100
The above is represented by the second table
Hence, the table that represents the double number line is (b)
Read more about number lines at:
https://brainly.com/question/4727909
#SPJ2
Please answer this correctly without making mistakes
Answer:
5/12
Step-by-step explanation:
3/4-1/3=
9/12-4/12=
5/12
10/7p+13/8+15/2p=909/56 i NEED THiS solving multi step equations w fractions and #8 PLEASE
Answer:
P= 2
Step-by-step explanation:
10/7p+13/8+15/2p=-909/56
Combine like terms
10/7p+15/2p=-909/56-13/8
20p+105p/14=-909-13*7/56
125/14p=-909-91/56
125/14p= -1000/56
125/14p*14/125= -1000/56*14/125
simplify
P= 8/4=2
And for #8 n =1 I answered this question it
Search
What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is 1.25
Complete Question
What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is 1.25? The standard deviation in a pre-selected sample is 7.5
Answer:
The minimum sample size is [tex]n =97[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 1.25[/tex]
The standard deviation is [tex]s = 7.5[/tex]
Given that the confidence level is 90% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha =10\%[/tex]
[tex]\alpha =0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is [tex]Z_{\frac{ \alpha }{2} } = 1.645[/tex]
The minimum sample size is mathematically evaluated as
[tex]n = \frac{Z_{\frac{\alpha }{2} * s^2 }}{E^2 }[/tex]
=> [tex]n = \frac{1.645^2 * 7.5^2 }{1.25^2 }[/tex]
=> [tex]n =97[/tex]
A piece of buttered toast falls to the floor 17 times. The toast landed buttered side up 6 times. What is the probability that the toast lands buttered side down?
Step-by-step explanation:
Given that,
A piece of buttered toast falls to the floor 17 times. The toast landed buttered side up 6 times.
It means that the total number of outcomes are 17
We need to find the probability that the toast lands buttered side down. Favourable oucome is 17-6 = 11
So, probability is given by :
[tex]P(E)=\dfrac{\text{favourable outcomes}}{\text{total no of outcomes}}[/tex]
[tex]P(E)=\dfrac{11}{17}[/tex]
So, the probability that the toast lands buttered side down is 11/17.
On a map, two locations are 0.75 centimeter apart. Their actual distance is 15 kilometers apart. What scale could be
shown on the map? Select three options.
Answer:
20
Step-by-step explanation:
It is 20 because 0.75 is on the map and its actualy distance is 15 so 15/0.75 is 20
Many drugs used in treating schizophrenia block the reception of dopamine by neurons. (Dopamine is a neurotransmitter, which, when released by the axons of one nerve, inhibits the firing of the next nerve.) This fact led to the idea that schizophrenia occurs when too much dopamine is produced. Suppose the following data on dopamine production were obtained.
Schizophrenics Control Group
42 33
31 27
29 18
The study described above is an example of:_______
a. an independent-samples design;
b. a paired-samples design;
c. comparing a sample mean to a known population mean;
d. unknown; more information is required in order to decide.
Answer:
a. an independent-samples design.
Step-by-step explanation:
Independent sample design is the one in which samples are selected randomly. It is the observation which is not dependent on any other value. The statistical analysis is based on the assumption that the samples are independent. The study in this scenario is not dependent on any other variable and is based on independent sample design.
The formula for the area of a square is s2, where s is the side length of the square. What is the area of a square with a side length of 6 centimeters? Do not include units in your answer.
Answer:
36
step by step
given length=6
so area of square is given by s2 i.e 6^2
=6×6
=36 (Ans)
