Question 1: The director of a green energy company is interested in comparing two different methods of installing solar light panels. An experiment is conducted with 31 technicians using the old method and the other 46 technicians using the new method. For the 31 technicians using the old method, the average time was 525 minutes with 47.7 standard deviation. For the 46 technicians using the new method, the average time was 520 minutes with 48.2 standard deviation. Conduct an analysis to determine whether there is a difference in the average time to complete the installation of the solar panels. Provide the test statistic value.
Question 2:
The director of a green energy company is interested in comparing two different methods of installing solar light panels. An experiment is conducted with 39 technicians using the old method and the other 55 technicians using the new method.
For the 39 technicians using the old method, the average time was 582 minutes with 63.8 standard deviation.
For the 55 technicians using the new method, the average time was 542 minutes with 97.8 standard deviation.
Conduct an analysis to determine whether there is a difference in the average time to complete the installation of the solar panels. Provide the degrees of freedom.
Answer:
Question 1
The test statistics is [tex]t = 0.44[/tex]
The decision rule is
Fail to reject the null hypothesis
The conclusion
There is no sufficient evidence to show that there is a difference in the average time to complete the installation of the solar panels
Question 2
The degree of freedom is [tex]df = 92 [/tex]
The decision rule is
Reject the null hypothesis
The conclusion
There is sufficient evidence to show that there is a difference in the average time to complete the installation of the solar panels
Explanation:
Considering Question 1
Here we are told to provide the test statistics
From the question we are told that
The first sample size is [tex]n_1 = 31[/tex]
The second sample size is [tex]n_ 2 = 46[/tex]
The first sample mean is [tex]\= x_1 = 525 \ minutes[/tex]
The first standard deviation is [tex]\sigma_1 = 47.7[/tex]
The second sample mean is [tex]\= x_2 = 520 \ minutes[/tex]
The second standard deviation is [tex]\sigma_2 = 48.2[/tex]
The null hypothesis is [tex]H_o : \mu_1 - \mu_2 = 0[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 \ne 0[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n_1 + n_2 -2[/tex]
=> [tex]df = 31 + 46 -2[/tex]
=> [tex]df = 75 [/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{(\= x_1 - \= x_2 )-0}{ \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2} } }[/tex]
=> [tex]t = \frac{( 525- 520 )-0}{ \sqrt{\frac{47.7^2}{31} + \frac{48.2^2}{46} } }[/tex]
=> [tex]t = 0.44[/tex]
Let assume that the level of confidence is [tex]\alpha = 0.05[/tex]
Generally the probability of t at a degree of freedom of is [tex]df = 75[/tex]
[tex]P(t > 0.44 ) = 0.33060124 [/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 * P(t > 2.398)[/tex]
=> [tex]p-value = 2 * 0.33060124[/tex]
=> [tex]p-value = 0.66120[/tex]
From the value obtain we see that [tex]p-value > \alpha[/tex] hence we fail to reject the null hypothesis
The conclusion is that there is no sufficient evidence to show that there is a difference in the average time to complete the installation of the solar panels
Considering Question 2
Here we are told to provide the degree of freedom
From the question we are told
The first sample size is [tex]n_1 = 39[/tex]
The first sample mean is [tex]\= x_1 = 582 \ minutes[/tex]
The first standard deviation is [tex]\sigma_2 = 63.8[/tex]
The second sample size is [tex]n_ 2 = 55[/tex]
The second sample mean is [tex]\= x_2 = 542 \ minutes[/tex]
The second standard deviation is [tex]\sigma_2 = 97.8 [/tex]
The null hypothesis is [tex]H_o : \mu_1 - \mu_2 = 0[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 \ne 0[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n_1 + n_2 -2[/tex]
=> [tex]df = 39 + 55 -2[/tex]
=> [tex]df = 92 [/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{(\= x_1 - \= x_2 )-0}{ \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2} } }[/tex]
=> [tex]t = \frac{( 582 - 542 )-0}{ \sqrt{\frac{63.8^2}{39} + \frac{97.8^2}{55} } }[/tex]
=> [tex]t = 2.398[/tex]
Let assume that the level of confidence is [tex]\alpha = 0.05[/tex]
Generally the probability of t at a degree of freedom of is [tex]df = 92 [/tex]
[tex]P(t > 2.398 ) = 0.00925214[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 * P(t > 2.398)[/tex]
=> [tex]p-value = 2 * 0.00925214[/tex]
=> [tex]p-value = 0.0185[/tex]
From the value obtain we see that [tex]p-value < \alpha[/tex] hence we reject the null hypothesis
The conclusion is that there is sufficient evidence to show that there is a difference in the average time to complete the installation of the solar panels
The country of Honduras has a population of 8.2 million. There were 7,172 homicide deaths there in 2014.
Express the deaths per capita as a decimal rounded to 6 decimal places.
Express the deaths per capita in Scientific Notation.
Type your answer as though you were typing it into your calculator--either with "E" or "x10^" notation-- no spaces in your answer!
The United States has a population of about 320 million. If our homicide deaths were proportional to that of Honduras, how many deaths would we expect in the
Answer:
a)Express the death per capita as a decimal rounded to 6 decimal places
0.000875 death per capita
b) Express the death per capita in Scientific notation
8.75 × 10^-4 death per capita
c) 279883 deaths
Step-by-step explanation:
a) Express the death per capita as a decimal rounded to 6 decimal places
The formula for Death Per capita is given as
Number of deaths/ Total population
Measurement : 7172 homicide deaths
Total population : 8.2 millon= 8,200,000
Death per capita = 7172/8200000
Death per capita = 0.00087463414 death per capita.
Approximately to 6 decimal places
= 0.000875 death per capita.
b) Express the death per capita in Scientific notation
The death per capita = 0.000875
In Scientific notation = 8.75 × 10^-4 death per capita
c) The United States has a population of about 320 million. If our homicide deaths were proportional to that of Honduras, how many deaths would we expect in the United States due to homicides? Round to the nearest person.
Measurement : 7172 homicide deaths
Total population : 8.2 millon= 8,200,000
The United States has a population of about 320 million
Death per capita in Honduras : Death per capita in United States
7172/8200000 : x/320,000,000
7172/8,200,000 = x/320,000,000
Cross Multiply
7172 × 320,000,000 = 8,200,000 × x
x = 7172 × 320,000,000/8,200,000
x = 279882.926829 deaths
Approximately to the nearest person = 279883 deaths
¾ divid ⅖=n
Pleas answer i need a answer
Which equation represents the vertical line passing through (7,-3)?
A
X=-3
B. y=-3
C.
x=7
D.y= 7
Answer:
a
Step-by-step explanation:
(0,-3)
-3 x axis form a vertical line
Answer:
c. x=7
Step-by-step explanation:
Store B sells a set for $27.00 and offers a 20% discount
Answer:
22.50
and you can pleasent do 22.50
Step-by-step explanation:
I don’t understand what this means
Answer:
This means that if you have that amount of those and you do whatever the rest of the question is.
Step-by-step explanation:
Answer:
120 different ways
Step-by-step explanation:
So Fundamental Counting Principle helps understand probability. So for this question, they are asking how many different ways there are.
To do that, we have to split into sets.
Set A: 4 Theme Parks
Set B: 6 Passes
Set C: 5 Food Options
Now we have to multiply the sets.
4 x 6 x 5 = 120
Therefore, the answer is 120 different ways.
10a^2b^0 for a=–3, b=–8
Answer:
90Step-by-step explanation:
Substitute a = -3 and b = -8 to the expression 10a²b⁰:
10(-3)²(-8)⁰ = 10(9)(1) = 90
a⁰ = 1 for any real number
Answer:
90
Step-by-step explanation:
10a^2b^0
Let a=–3, b=–8
10 (-3)^2 ( -8)^0
10 * 9 *1
90
What’s 1.2983 rounded to the nearest hundredth
Answer:
1.30 :)
All you have to do is see if the number on your left is greater than 5 or not if it’s is round up 1 if not it stays the same !
Hope this helped !!!
Step-by-step explanation:
Darren and Carl each go for a morning jog before work. Darren's jogging pace
is represented by the equation y = 5x where y is the number of miles he jogs
and x is the number of hours he jogs. Carl's pace is given by the graph.
35
28
Distance (miles)
21
14
2
3
5
Time (hours)
Choose the statement that correctly compares their unit rates.
O A. Carl's unit rate is equal to Darren's unit rate.
O B. Carl's unit rate is 2 fewer miles per hour than Darren's unit rate.
O C. Carl's unit rate is 1 more mile per hour than Darren's unit rate.
D. Carl's unit rate is 2 more miles per hour than Darren's unit rate.
Answer: d
Step-by-step explanation:
Answer:
D. Carl's unit rate is 2 more miles per hour than Darren's unit rate.
Step-by-step explanation:
Identify next 3 numbers in this sequence 2,6,3,9,6,18,15
How long does it take for the baseball to reach its maximum height? (2)
b. What was the initial height of the ball? (2)
form A : h(t)= -16t^2 + 96t +7
form b: -16(t-3)^2 +151
help please
Answer: ha no way have the same question
Step-by-step explanation:
Am gonna give branliest!!!
Quadrilateral GHJK has vertices G(2, 3), H(8, 2), J(6, 8), and K(3, 6). It is transformed according to the rule T(–4, –5).
What are the coordinates of G”?
(–7, 3)
(–2, 2)
(–1, –7)
(2, –2)
Answer:
the transformation T(a, b) can be change the pre image to the final image by following the rule as we explain below
if A(x, y) is a pre image, then A ' ( x', y') is its image, and x' = a+x, y' = b + y, where because of T(a, b) transformation
in our case Quadrilateral GHJK has vertices G(2, 3), so the coordinates of G”
can be found with
T(-4, -5) applied to G(2, 3) ⇒ G' (-4 +2, -5+3)=G' (-2, -2)
T(-4, -5) applied to G' (-2, -2) ⇒ G"(-4-2, -5-2) =G"(-6, -7)
the coordinates of G” are (-6, -7)
Step-by-step explanation:
i hope it helps?Answer:
its c on edg (-1, -7)
Step-by-step explanation:
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.35°F and a standard deviation of 0.64°F. Using the empirical rule, find each approximate porcent
a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 96.43°F and 100.27°F?
b. What is the approximate percentage of healthy adults with body temperatures between 97 71°F and 98.99°F?
a. Approximately % of healthy adults in this group have body temperatures within 3 standard deviations of the mean, or between 96.43°F and 100.27°F
(Type an integer or a decimal. Do not round)
Answer:
a) 99.97%
b) 65%
Step-by-step explanation:
• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.
• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.
• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.
Mean of 98.35°F and a standard deviation of 0.64°F.
a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 96.43°F and 100.27°F?
μ - 3σ
98.35 - 3(0.64)
= 96.43°F
μ + 3σ.
98.35 + 3(0.64)
= 100.27°F
The approximate percentage of healthy adults with body temperatures is 99.97%
b. What is the approximate percentage of healthy adults with body temperatures between 97 .71°F and 98.99°F?
within 1 standard deviation from the mean - that means between μ - σ and μ + σ.
μ - σ
98.35 - (0.64)
= 97.71°F
μ + σ.
98.35 + (0.64)
= 98.99°F
Therefore, the approximate percentage of healthy adults with body temperatures between 97.71°F and 98.99°F is 65%
Valerie runs track and field. At meets, Valerie lkes to buy protein bars, bananas and sports drinks Protein bars are $1. bananas are S0.50, and sports drinks are S2. Valerie has S10 to spend. She will spend no more than twice as much on sports drinks as bananas and at least three times as much on bananas as protein bars. Let represent the number of protein bars. represent the number of bananas. and represent the number of sports drinks that Valerie buys. Which statements are true regarding Valerie's situation? Select all that apply A: p + 0.5b + 2d < 10 B: 0.5d + b + 3p < 10. C: d < 2b. D: b > 3p. E: 2d < b. F: 3b > p
Complete Question
Valerie runs track and field. At meets, Valerie likes to buy protein bars, bananas, and sports drinks. Protein bars are $1, bananas are $0.50, and sports drinks are $2. Valerie has $10 to spend. She will spend no more than twice as much on sports drinks as bananas and at least three times as much on bananas as protein bars.
Let p represent the number of protein bars, b represent the number of bananas, and d represent the number of sports drinks that Valerie buys.
Which statements are true regarding Valerie's situation? Select all that apply A: p + 0.5b + 2d < 10 B: 0.5d + b + 3p < 10. C: d < 2b. D: b > 3p. E: 2d < b. F: 3b > p
Answer:
The statements that are true regarding Valerie's situation:
A: p + 0.5b + 2d < 10
C: d < 2b
D: b > 3p
Step-by-step explanation:
Lets represent
The number of protein bars as p.
The number of bananas as b.
The number of sports drinks that Valerie buys as d.
From the question:
We are told
Protein bars are $1
Bananas are $0.50
Sports drinks are $2.
She will spend no more than twice as much on sports drinks as bananas
d ≤ 2b = d < 2b
At least three times as much on bananas as protein bars.
b ≥ 3p = b > 3p
We are also told that:
Valerie has $10 to spend.
Hence:
$1 × p + $0.50 × b + $2 × d < $10
= p + 0.5b + 2d < 10
Therefore, the statements that are true regarding Valerie's situation:
A: p + 0.5b + 2d < 10
C: d < 2b
D: b > 3p
I need help with this
Answer: B. 8 x 10^3
Step-by-step explanation:
b. 8 x 10³
hope this helps
Pls pls Pls pls Pls Pls help me pls pls pls pls pls pls ASAP pls pls pls Pls pls Pls pls Pls Pls help me pls pls pls pls pls pls ASAP pls pls pls Pls I WILLL BRAINLIEST!!!!
Answer:
y = -3x - 8
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
m - slope
b - y-intercept
Step 1: Define
slope m = -3
y-intercept = -8
Step 2: Plug into equation
y = -3x - 8
A table marked at ₹ 15,000 is available for ₹ 14,400. Find the discount given and the discount percentage.
Answer: ₹ 600 and 15% discount rate i believe
Step-by-step explanation:
Drove 260 km using 12 liters of gas at this rate how many liters of gas would he need to drive 286km
Answer:
We calculate the amount of gas used per km and multiply it by 286
Step-by-step explanation:
If we drive for 260km and use 12 litres of gas that means that we use
[tex]\frac{12}{260}[/tex] litres per km.
Now we multiply it by 286:
[tex]\frac{12}{260} *286 = \frac{858}{65} = 13.2[/tex]
So, the answer is 13.2 litres.
Helppppppp lol idk what I’m doing
Answer:
C
Step-by-step explanation:
Step 1: Translate word to math
"Five" = 5
"times" means multiplication
"a number" = n
"plus" means addition
"3" = 3
"is" means equal
"12" = 12
Step 2: Set up equation (combine)
5n + 3 = 12
Answer:
C
Step-by-step explanation:
a number represents n
is represents =
times represents multiplication
plus represents addition
5 times n plus 3 is 12
so this means
5n+3=12
The table gives the numbers of teachers and students in grades 6 to 8 at Earhart Middle School.
Grade Teachers Students
6 1 25
7 2 50
8 3 75
Which teacher-to-student ratio maintains the proportional relationship described in the table?
Teachers Students
5 125
Teachers Students
4 120
Teachers Students
4 100
Teachers Students
6 130
Teachers Students
7 125
Answer:
no one and i am doing time pass and
6 130 will be a right answer
whe it is rong i am sorry
Answer:
6 teachers, and 130 student's
Step-by-step explanation:
NEED HELP ASAP Ann, Ben, and Cindy were eating strawberries. The ratio of the numbers of berries they ate is 5:5:7. If Cindy ate 30 strawberries less than Ann and Ben together, what is the total number of strawberries the three of them ate?
Answer:
170Step-by-step explanation:
given:
Ann, Ben, and Cindy were eating strawberries.
The ratio of the numbers of berries they ate is 5:5:7.
If Cindy ate 30 strawberries less than Ann and Ben together,
find:
what is the total number of strawberries the three of them ate?
solution:
add the ratios 5 + 5 + 7 = 17
since Cindy ate 30, less than Ann and Ben together so, the equation is
7x = 5x + 5x - 30
7x - 10x = -30
x = 30/3
x = 10
ann 5 x 10 = 50
ben 5 x 10 = 50
cindy 7 x 10 = 70
total = 170
==============================================
Explanation:
A = number Ann ate
B = number Ben ate
C = number Cindy ate
Let x be some positive whole number
Since A,B,C is in the ratio 5:5:7, this means
A = 5x
B = 5x
C = 7x
Note how A:B:C = 5x:5x:7x = 5:5:7. We divide all parts by x to simplify the ratio.
-------------------
Cindy ate 30 strawberries less than Ann and Ben, so
C = A+B-30
C = 5x+5x-30
C = 10x-30
Earlier in the last section we had C = 7x, and now we found C = 10x-30
Since we're talking about the same C value, we can equate and solve
C = 7x
10x-30 = 7x ... replace C with 10x-30
10x-7x = 30
3x = 30
x = 30/3
x = 10
------------------
With this x value, we now know that...
A = 5x = 5*10 = 50
B = 5x = 5*10 = 50
C = 7x = 7*10 = 70
Cindy's count (70) is 30 less than Ann and Ben's combined count (50+50 = 100), so that helps confirm the answer.
Further confirmation comes from 50:50:70 reducing to 5:5:7 when you divide all parts by the GCF 10.
--------------------
The last step is to add the values of A, B and C.
A+B+C = 50+50+70
A+B+C = 100+70
A+B+C = 170
---------------------
Side note: since A+B+C = 5x+5x+7x = 17x, this means that the final answer is a multiple of 17.
Complete the statement. If a transversal intersects two parallel lines, then _____
A) alternate interior angles are always congruent.
B) same-side interior angles are always complementary.
C) same-side exterior angles are always complementary.
D) corresponding angles are always supplementary.
Answer:
B)
Step-by-step explanation:
They are intersected to make a same side interior angle.
Answer:
A) alternate interior angles are always congruent.
Anthony wants to make a discretionary purchase of a basic laptop computer. He checks the prices of a particular make and model listed by seven different venders on a shopping comparison website. He found these prices: $850, $798, $2,400, $790, $836, $700, and $780. He computes the mean as $1022.
Answer:
He computes the mean as $1,022.
Step-by-step explanation:
2x2 + x + 5 = 0 i don’t know how to do this please help
9514 1404 393
Answer:
x = -0.25+√2.4375i or -0.25-√2.4375i
Step-by-step explanation:
The quadratic formula works for this. The quadratic equation ...
ax² +bx +c = 0
has solutions given by the quadratic formula:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Your equation ...
2x² +x +5 = 0
has coefficients a=2, b=1, c=5, so the quadratic formula tells you the solutions are ...
[tex]x=\dfrac{-1\pm\sqrt{1^2-4\cdot2\cdot5}}{2\cdot2}=\dfrac{-1\pm\sqrt{-39}}{4}\\\\x=\left\{-\dfrac{1}{4}+\dfrac{\sqrt{39}}{4}i, -\dfrac{1}{4}-\dfrac{\sqrt{39}}{4}i\right\}[/tex]
The decimal equivalents are ...
x = -0.25+√2.4375i or -0.25-√2.4375i . . . . . . the 'i' is outside the radical
Make 3 1/2 cakes in 20 minutes how many cakes can you make in two hours
Answer:
17
Step-by-step explanation:
3 1/2+3 1/2=5 which is 40 min
5=40mins
5+3 1/2=81/2
1 hour=8 1/12
8 1/2+8 1/2= 17
17 in two hours
1 5/16 divided by 7/12
The US emerged as a world power because of its success in
A. the Korean War
B. World War I
C. World War II
D. the Cold War
Answer:
its c
Step-by-step explanation:
trust and dont vote me out! its not me i sware its cyan he sus!
Answer:
It's C
Step-by-step explanation:
Dean walked from the library to the mall. For the
first 12 minutes, he walked at a speed of 80
m/min, but then he slowed his speed to 68
m/min for next 7 minutes. If he was still 130 m
away from the mall, what was the distance
between the library and the mall?
Find the limit
(calculus)
Answer:
0
Step-by-step explanation:
Step 1: Define
[tex]\lim_{x \to \infty} e^{x-x^2}[/tex]
Step 2: Substitute in infinity
[tex]\lim_{x \to \infty} e^{\infty-\infty^2}[/tex]
We know that the second exponent is always going to be bigger than the 1st exponent, so we would get a negative exponent.
[tex]\lim_{x \to \infty} e^{-\infty}[/tex]
We can simplify a negative exponent into a fraction.
[tex]\lim_{x \to \infty} \frac{1}{e^{\infty}}[/tex]
We know that if we keep plugging in larger numbers for x, the denominator is going to be infinitely big. And bigger the number we are dividing by, the smaller the entire fraction is going to be.
Therefore, we would be approaching 0.