If the sample mean is close to 32 ounces or the sample standard deviation is large, it is less likely that we will reject the null hypothesis.
To determine if there is sufficient evidence to conclude that the mean amount of milk in cartons is less than 32 ounces, we would conduct a hypothesis test. The null hypothesis (H0) would state that the mean amount of milk in cartons is at least 32 ounces, while the alternative hypothesis (Ha) would state that the mean amount is less than 32 ounces.
The null hypothesis: [tex]\( H_0: \mu \geq 32 \)[/tex]
The alternative hypothesis: [tex]\( H_a: \mu < 32 \)[/tex]
Here is the step-by-step process to conduct the hypothesis test:
1. **Identify the sample mean [tex](\( \bar{x} \))[/tex] and the sample standard deviation (s).** These values would be calculated from the sample of 22 cartons.
2. **Calculate the test statistic (t-score).** The formula for the t-score in a one-sample t-test is:
[tex]\[ t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}} \][/tex]
where [tex]\( \mu_0 \)[/tex] is the hypothesized mean (32 ounces in this case), [tex]\( \bar{x} \)[/tex] is the sample mean, [tex]\( s \)[/tex] is the sample standard deviation, and [tex]\( n \)[/tex] is the sample size.
3. **Determine the degrees of freedom (df).** For a one-sample t-test, the degrees of freedom are [tex]\( n - 1 \)[/tex], where [tex]\( n \)[/tex] is the sample size. In this case, [tex]\( df = 22 - 1 = 21 \)[/tex].
4. **Find the critical t-value or p-value.** Using the degrees of freedom, we can find the critical t-value from a t-distribution table or calculate the p-value. The significance level (α) is typically set at 0.05 for such tests.
5. **Make a decision.** If the test statistic is less than the critical t-value or if the p-value is less than α, we reject the null hypothesis in favor of the alternative hypothesis. This would mean there is sufficient evidence to conclude that the mean amount of milk in cartons is less than 32 ounces.
6. **Calculate the p-value.** The p-value is the probability of observing a sample mean at least as extreme as the one observed, assuming the null hypothesis is true. It can be calculated using statistical software or a t-distribution table.
7. **Report the results.** If the p-value is less than α, we report that there is sufficient evidence to conclude that the mean amount of milk in cartons is less than 32 ounces. If the p-value is greater than α, we report that there is not enough evidence to conclude that the mean amount is less than 32 ounces.
Without the actual sample data (sample mean and sample standard deviation), we cannot perform the calculations or make a conclusion. However, if the sample mean is substantially less than 32 ounces and the sample standard deviation is small, it is more likely that we will reject the null hypothesis. Conversely, if the sample mean is close to 32 ounces or the sample standard deviation is large, it is less likely that we will reject the null hypothesis.
Sarah is fighting a sinus infection her doctor prescribed a nasal spray and I know a biotic to fight the infection the active ingredient in milligrams remaining in the bloodstream from the nasal spray in, tea, and the anabiotic a comity, our models in the functions below where tea is the time in hours and some medications were taken
Answer:
a) The antibiotic is made with a greater initial amount of active ingredient
b) The two medications will have the same amount of active ingredients in the blood stream at exactly 8 hours after first taking the medication.
Step-by-step explanation
Active ingredient of Nasal spray left in the bloodstream is modelled as
n(t) = ((t + 1)/(t + 5)) + (18/(t² + 8t + 15))
Active ingredient of Antibiotic left in the bloodstream is modelled as
a(t) = 9/(t+3)
with t in hours.
a) At the instance of usage, the active ingredient for both drugs are at their initial concentration as they appear in the drugs.
So, we find the amount of active ingredient for each drug in the bloodstream at t=0 and compare.
For nasal spray,
n(t) = ((t + 1)/(t + 5)) + (18/(t² + 8t + 15))
At t = 0
n(0) = (1/5) + (18/15) = 1.4
For antibiotics,
a(t) = 9/(t+3)
At t=0
a(0) = (9/3) = 3
3 > 1.4
Hence, the antibiotic is made with a greater initial amount of active ingredient.
b) when both medications will have the same amount of active ingredients in the bloodstream, n(t) = a(t)
n(t) = ((t + 1)/(t + 5)) + (18/(t² + 8t + 15))
a(t) = 9/(t+3)
Note that (t² + 8t + 15) = (t + 3)(t + 5)
When n(t) = a(t)
((t + 1)/(t + 5)) + (18/(t² + 8t + 15)) = 9/(t+3)
Multiplying through by (t² + 8t + 15) or more properly written as (t + 3)(t + 5)
(t+1)(t+3) + 18 = 9(t+5)
t² + 4t + 3 + 18 = 9t + 45
t² - 5t - 24 = 0
Solving the quadratic equation
t = 8 or t = -3
Time can't be negative, hence, t = 8 hours.
Hope this Helps!!!
Graham sold 6 magazines less than double what Adrianne sold, a. Which of the following expressions represents Graham's sales?
6a − 2
2(a − 6)
a^2 − 6
2a − 6
The video store is having a sale on movie videos. They normally sell for $24.99, but are on sale for $12.99. Mr. Berger purchased 3 videos on sale. How much did he save?
How are the archetypes presented in these two passages
different?
The first passage shows Antigone as a warrior, and the
second passage shows Boadicea as a tragic heroine.
The first passage shows Antigone as a tragic heroine,
and the second passage shows Boadicea as a sage.
The first passage shows Antigone as a rebel, and the
second passage shows Boadicea as a warrior.
The first passage shows Antigone as a villain, and the
second passage shows Boadicea as a sage.
Answer: the third answer. Explanation below.
Step-by-step explanation:
The first passage shows Antigone as a rebel because she chooses to defy the State. The second passage shows Boadicea as a warrior because she "herself led the soldiers, encouraging them with her brave words."
Antigone and Boadicea are presented with different archetypal roles across the passages; Antigone as a warrior, tragic heroine, rebel, and villain; and Boadicea as a tragic heroine, sage, warrior, and sage again.
Explanation:The archetypes presented in these passages are different in the roles and characteristics assigned to Antigone and Boadicea. In the first set of passages, Antigone is depicted as a warrior, then as a tragic heroine, next as a rebel, and lastly as a villain. Conversely, Boadicea is presented as a tragic heroine, followed by a sage, then as a warrior, and finally as a sage once again. These variations represent unique depictions of these mythical figures, giving us different lenses to interpret their actions and significance within their respective narratives.
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A right triangle whose hypotenuse is 3 centimeters long is revolved about one of its legs to generate a right circular cone. Find the radius, height, and volume of the right cone that will have the greatest volume when constructed this way.
Answer:
The height of the right circular cone when constructed this way is [tex]\sqrt3[/tex] cm.
The radius of the right circular cone when constructed this way is [tex]\sqrt6[/tex] cm.
The volume of the right circular cone when constructed this way is [tex]6\sqrt3 \pi[/tex] cm³.
Step-by-step explanation:
Given that,
A right triangle whose hypotenuse is 3 cm long is revolved .
Then other two legs of the triangle will be radius and height of the cone.
Assume the height and radius of the cone be h and r respectively.
From Pythagorean Theorem :
h²+r²=3²
⇒ r²= 9 - h²
Then the volume of the cone is
V= π r²h
⇒ V= π(9-h²)h [ ∵ r²= 9 - h²]
⇒V= π(9h - h³)
Differentiating with respect to h
V'=π(9 - 3h²)
Again differentiating with respect to h
V''= π(-6h)
⇒V''= (-6πh)
To maximum or minimum ,we set V'=0
π(9 - 3h²)=0
⇒3h²=9
⇒h²=3
[tex]\Rightarrow h=\sqrt3[/tex]
Now, [tex]V''|_{h=\sqrt3}=-6\pi (\sqrt3)<0[/tex].
Since at [tex]h=\sqrt3[/tex],V''<0.
The volume of cone is maximum at [tex]h=\sqrt3[/tex] cm when constructed this way.
The height of the right circular cone when constructed this way is [tex]\sqrt3[/tex] cm.
The radius of the right circular cone when constructed this way [tex]r=\sqrt{9-(\sqrt3)^2[/tex]
= [tex]\sqrt{9-3}[/tex]
[tex]=\sqrt6[/tex] cm.
The volume of the right circular cone when constructed this way is
=π r²h
[tex]=\pi (\sqrt6)^2\sqrt3[/tex]
[tex]=6\sqrt3 \pi[/tex] cm³
What is the equation of the line that passes through the point (-5,3)(−5,3) and has a slope of fraction -6/5
Answer:
Step-by-step explanation:
Use the point-slope formula.
y - y_1 = m(x - x_1) when : x_1 = -5 and y_1 =3 and m= -6/5
the equation : y - 3 = -6/5(x +5)
Answer:
y=-6/5x-3
Step-by-step explanation:
A bonsai tree is 18 inches wide and stands 2 feet tall. What is the ration of the width of the bonsai to its height?
Answer:
3:4
Step-by-step explanation:
Before we start to deal with the ratio, we need all lengths in the same units.
The width is 18 inches.
The height is 2 feet.
Let's convert the height to inches. Then we will have both dimensions in the same units, inches.
2 ft * (12 in.)/ft = 24 in.
Now we have:
width = 18 in.
height = 24 in.
ratio of width to height = 18 in. to 24 in. = 18/24 = 3/4 = 3:4
The ratio of the width to the height of the bonsai tree is 3:4 after converting the height into inches and simplifying the ratio.
Explanation:The question asks to find the ratio of the width of a bonsai tree to its height. Since the width is given in inches and the height in feet, we first need to convert the height into inches to have a consistent unit of measure. There are 12 inches in 1 foot, so the bonsai tree's height is 2 feet times 12 inches/foot, which equals 24 inches.
Now, we can write the ratio of the width to height as 18 inches (width) to 24 inches (height). This simplifies to 3:4 after dividing both terms by the greatest common factor, which is 6.
Fill in the numbers that go into the blank boxes. The numbers have to multiply to be the top number and add to be the bottom number.
Answer: 6 and 6
Step-by-step explanation:6x6=36
6+6=12
What word goes with the image?
Answer:
Wavelength
Step-by-step explanation:
The picture below is an example of a wavelength which is very similar.
Step-by-step explanation:
In a right triangle, the value of cos B = 3/5. What is the value of sin B?
[Leave your answer as a fraction]
Answer:
4/5
Step-by-step explanation:
cos B = 3/5
cos Ф = adjacent/hypothesis
hypothesis ² = adjacent² + opposite²
5²= 3²+ o²
25 = 9+o²
25-9=o²
16 = o²
√16 = o = 4
Sin B = opposite/hypothesis = 4/5
simplify (x -3)(x + 7) using the table method, and identify the resulting expression in standard form.
Factor this expression completely.
-21x + 28
7 (3x - 4)
-7(3x – 4)
- 7 (3x + 4)
- (21x - 4)
Answer:
− 21 x + 28 , 7 , 3 x − 4 , − 7 ( 3 x − 4 ) , − 7 , 3 x + 4 , − ( 21 x − 4 )
Step-by-step explanation:
too much to explain sorry
Hope this helped!
The factor of the expression -21x + 28 is equal to -7(3x – 4). The correct option is B.
What is an expression?The numerical variables and operations denoted by the addition, subtraction, multiplication, and division signs are combined in the mathematical expression.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols. They can also denote the operation order and other properties of the logical syntax.
Given expression is -21x + 28, The value of the expression will be calculated as,
E = -21x + 28
Take -7 common from the whole expression,
E = -21x + 28
E = -7 ( 3x - 4 )
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Convert the angle \theta=\dfrac{17\pi}{18}θ= 18 17π theta, equals, start fraction, 17, pi, divided by, 18, end fraction radians to degrees. Express your answer exactly. \theta=θ=theta, equals ^\circ ∘
Answer:
θ = 170°
Step-by-step explanation:
Given angle is in radian as,
[tex]\theta^{c} = \dfrac{17 \pi}{18}[/tex]
Here, [tex]\theta^{c}[/tex] symbol represents the angle is in radian.
To convert given angle into degree, multiply the given angle with conversion factor as follows,
[tex]\theta^{\circ} = \theta^{c} \times \left(\frac{180}{\pi }\right)^{\circ}[/tex]
Substituting the values,
[tex]\theta^{\circ} = \dfrac{17 \pi}{18} \times \left(\dfrac{180}{\pi }\right)[/tex]
Cancelling out the common terms,
[tex]\theta^{\circ} =17\times \left(10\right)[/tex]
Therefore,
[tex]\theta^{\circ} =170^{\circ}[/tex]
Therefore the value of given angle in degree is 170°
To convert radians to degrees, utilize the conversion factor 180/π. In this instance, we have the angle (17π / 18) radians, which simplifies to 170 degrees when converted to the degree format.
Explanation:The subject topic of this conversation is about converting radians to degrees. Specifically, we're looking at how to convert the radian measurement = 17 / 18 into degrees.
One radian is equivalent to 180/ degrees. As such, to convert radians to degrees, you multiply the radian measurement by this conversion factor (180/).
Have a look at the calculation: = (17 / 18) * (180/).
The cancels out leaving us with / * . This calculation gives us = 170 degrees.
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For a school fundraiser, Ayana needs to sell 40 rolls of wrapping paper. So far, she has sold 7 rolls to her grandmother, 2 rolls to her uncle, and 9 rolls to a neighbor. How many more rolls of wrapping paper does Ayana need to sell?
Answer:
22?
Step-by-step explanation:
Just take 40 and subtract the 7 to get 33 and then 2 to get 31 and 9 to get 22.
Answer:
22 more rolls
Step-by-step explanation:
if she needs to sell 40 and she has sold 9+7+2=18 than you subtract 18 from 40 getting 22 more rolls
A green die and a red die are tossed. What is the probability that a "4" shows on the green die and a "5" shows on the red die?
Answer:
1 out of 6 for green die and 1 out of 6 for red die
Step-by-step explanation:
As we know there are six numbers on both of the dices
so if we toss a die there is a 1 out of 6 outcomes that a 4 comes out for the green die and 1 out of 6 outcomes again for the red die
The probability that a 4 shows on the green die and a 5 shows on the red die is given by P ( C ) = 1/36
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability that a 4 shows on the green die and a 5 shows on the red die be represented as P ( C )
Now , the number of outcomes in a roll of die = { 1 , 2 , 3 , 4 , 5 , 6 } = 6 outcomes
And , probability that a 4 shows on the green die P ( A ) = 1/6
The probability that a 5 shows on a red die P ( B ) = 1/6
Now , it is an independent experiment
So , the compound probability is P ( C ) = P ( A ) . P ( B )
And , the probability that a 4 shows on the green die and a 5 shows on the red die P ( C ) = ( 1/6 ) ( 1/6 )
The probability that a 4 shows on the green die and a 5 shows on the red die P ( C ) = 1/36
Hence , the probability is P ( C ) = 1/36
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!3 3/4 as an inproper fraction
Answer:
55/4
Step-by-step explanation:
13 3/4
(13×4 + 3)/4
55/4
Answer:
hope this helps!
4. 4csc^2x+3cscx-1=0
Answer: 8cxs^c= -3 csc (x) +1
Step-by-step explanation:
To solve for c you need to simplify both sides of the equation, then isolating the variable
Answer:
x = - π/2 or x = - π/2 + 2nπ n = integer
Step-by-step explanation:
4csc²x+3cscx-1=0
(csc x + 1) (4csc x - 1) = 0
csc x = - 1 or csc x = 1/4
1/ sin x = - 1 or 1 / sin x = 1/4
sin x = - 1 or sin x = 4 (x no solution when sin x = 4)
sin x = - 1
x = - π/2 or x = - π/2 + 2nπ n = integer
Consider a system to be one train car moving toward
another train car at rest. When the train cars collide, the
two cars stick together.
What is the total momentum of the system after the
collision?
800 kg. m
1,600 kg. m
2,400 kg. m
4,000 kg. m
Step-by-step explanation:
I just finished the assignment and got everything right ;)
Hope i helped!
Answer:
c
Step-by-step explanation:
In your own words, describe what an exponential function is.
An exponential function is a mathematical concept characterized by a constant base elevated by a variable exponent. The rate of growth or decay of the function is proportional to its current value, leading to exponential growth or decay.
Explanation:An exponential function is a mathematical concept where a constant base is elevated by a variable exponent. The base could be any positive value different from one. A simple example of this type of function is f(x) = 2^x, where 2 is the constant base and x is the variable exponent.
The unique property of an exponential function is that the rate of growth or decay is proportionate to its current value. This means, as the variable x increases, the function value increases exponentially when the base is greater than one - thus showing exponential growth. Conversely, if the base is less than one but greater than zero, the function value decreases as x increases - thus representing exponential decay.
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6x squared plus 2x minus 20 equals 0
Answer:
x=2 or 5/3
Step-by-step explanation:
the explanation is in the picture
please like and Mark as brainliest
Answer:
x = 5/3
x = -2
Step-by-step explanation:
6x² + 2x - 20 = 0
(6x - 10)(x + 2)
= 6x² + 12x - 10x - 20
= 6x² + 2x - 20
6x - 10 = 0
6x = 10
x = 10/6
x = 5/3
x + 2 = 0
x = -2
PLEASE HELP!!! AND EXPLAIN IF YOU CAN !!!
sin(-295°) = _____. sin 65° sin 295° sin 25° -sin 65°
Answer:
Step-by-step explanation:
sin(-295°)=-sin (295)=-sin (360-65)=-(-sin 65°)=sin (65°)
Angles! It's Urgent Pleasee help me
Answer:
<1 and <2 are alternate exterior angles
<3 and <4 are consecutive interior angles
Step-by-step explanation:
<1 and <2 are alternate exterior angles
Alternate exterior angles are on opposite outside of the lines
<3 and <4 are consecutive interior angles
Consecutive interior angles are on the same side on the inside of the line
FASST PLZZZ!! It’s really important!!!
Answer:
The second, third and fifth are true.
Step-by-step explanation:
1) False, the radius is d÷2=8÷2=4 cm
2) True, C = 2×π×r = π×d = 8π
3) True, C = 8π = 8 × 22/7 = 176÷6 ≈ 25,14
4) False, C = 25,14 ≈ 25
5) True, C = 8π = 8×3,14 = 25,12
Answer: B,C,E
Step-by-step explanation:
How much carbon dioxide is produced from running a microwave (1500 watts) for 10 minutes per day for one month? (round to the tenths place)
HINT: 1.37 pounds CO2 per kWh
Answer: 10.3 pounds of CO2 is produced
Step-by-step explanation:
Assuming there are 30 days in a month, if the microwave is run for 10 minutes per day, then the number of minutes for which the microwave is run in a month is
30 × 10 = 300 minutes
We would convert from minutes to hours
60 minutes = 1 hour
Therefore,
300 minutes = 300/60 = 5 hours
Also,
1000 watts = 1 kW
Therefore,
1500 watts = 1500/100 = 1.5kw
Therefore, the number of kWh is
1.5 × 5 = 7.5 kWh
If 1.37 pounds CO2 per kWh, then
If 1kWh = 1.37 pounds CO2, then
7.5 kWh = 7.5 × 1.37 = 10.3 pounds rounded to the nearest tenth
Final answer:
A 1500-watt microwave running for 10 minutes per day for one month emits approximately 10.3 pounds of CO2 when rounding to the tenths place.
Explanation:
The question is how much carbon dioxide is produced from running a 1500-watt microwave for 10 minutes a day for a month. To solve this, we first need to calculate the total energy used by the microwave in kWh. Since the microwave uses 1500 watts and is used for 10 minutes daily, we convert this to hours:
10 minutes = 10/60 hours = 1/6 hour
Power in kWh = Power in watts / 1000
Energy used per day in kWh = (1500 watts / 1000) x (1/6 hour) = 0.25 kWh
Next, we need to calculate the monthly energy use:
Energy used per month in kWh = 0.25 kWh/day x 30 days = 7.5 kWh
Using the given conversion factor of 1.37 pounds of CO2 per kWh, the total CO2 emissions can be calculated:
CO2 emissions = 7.5 kWh x 1.37 pounds CO2/kWh = 10.275 pounds of CO2
Finally, rounding to the tenths place:
CO2 emissions for the month = 10.3 pounds (rounded)
One of the largest cookies on record had a diameter of 78.75 feet. What is the approximate circumference of the cookie? Use 3.14 for n. Round to tenths place.
Answer:
247.3 Ft
Step-by-step explanation:
c=3.14(78.75)
c=247.245 *rounded*
The question was about calculating the circumference of a circle using its diameter. The diameter was given, and the formula for circumference 'C = πd' was used, where 'd' was 78.75 feet and 'π' was approximated at 3.14. The circumference comes out to be approximately 247.35 feet when rounded to the nearest tenth.
Explanation:The subject in this question is the measurement of the circumference of a cookie given its diameter, a basic concept in geometry in the field of Mathematics. Circumference which is the distance around a circle can be calculated using the formula 'C = πd', where 'C' is the circumference, 'd' is the diameter and 'π' is a constant approximately equal to 3.14.
In this case, the diameter 'd' of the cookie is 78.75 feet. So, by substituting the values into the formula, we get: C = 3.14 * 78.75.
After performing this calculation, you'll find that the approximate circumference of the cookie is 247.35 feet when rounded to the nearest tenth.
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The graph of the function f(x) = (x − 3)(x + 1) is shown. Which describes all of the values for which the graph is positive and decreasing?
all real values of x where x < −1
all real values of x where x < 1
all real values of x where 1 < x < 3
all real values of x where x > 3
Answer:
option a all real values of x where x < −1
Step-by-step explanation:
suppose you have a 4-liter bucket and a 7-liter bucket. you need 5-liters for an aquarium. Explain how to get 5liters if neither bucket is marked?
Answer:
it is a 7 step process explained in explanation section
Step-by-step explanation:
Step one
fill 7 litre bucket then pour it in 4 liter bucket
output: 7 litre bucket has 3 litres and 4 litres bucket has 4 liter in it
Step two
drain four liter bucket and pour 3 liter from 7 litre bucket in it
output: 7 litre bucket has 0 litres and 4 litres bucket has 3 liter in it
step 3
fill 7 litre bucket and transfer water from it in 4 liter bucket which has already 3 liter in it
output: 7 litre bucket has 6 litres and 4 litres bucket has 4 liter in it
step 4
drain four liter bucket and pour 4 liter from 7 litre bucket which has 6 litre in it
output: 7 litre bucket has 2 litres and 4 litres bucket has 4 liter in it
step 5
drain 4 litre bucket and pour 2 litre from 7 litre bucket
output: 7 litre bucket has 0 litres and 4 litres bucket has 2 liter in it.
step 6
fill 7 liter bucket fully
output: 7 litre bucket has 7 litres and 4 litres bucket has 2 liter in it.
step 7
pour water from 7 liter bucket in 4 litre bucket which has already 2 litre in it
output: 7 litre bucket has 5 litres and 4 litres bucket has 4 liter in it.
Could 1.5, 2.5, 3.5 and 6, 10, 12 be the corresponding sides of two similar triangles
Answer:
No
Step-by-step explanation:
If the ratios of the corresponding sides are equal then they would be the sides of 2 similar triangles.
Calculate the ratio of corresponding sides.
[tex]\frac{6}{1.5}[/tex] = 4
[tex]\frac{10}{2.5}[/tex] = 4
[tex]\frac{12}{3.5}[/tex] ≠ 4
Thus the sides are not the corresponding sides of similar triangles.
A small accounting firm has 444 accountants who each earn a different salary between \$50{,}000$50,000dollar sign, 50, comma, 000 and \$60{,}000$60,000dollar sign, 60, comma, 000, and a 5^{\text{th}}5 th 5, start superscript, start text, t, h, end text, end superscript accountant who works part-time for tax season and earns \$10{,}000$10,000dollar sign, 10, comma, 000. [Show data] 1010 5252 5454 5656 5858 The firm decides to get rid of the part-time accountant and keep the other 444 salaries the same. How will getting rid of the part-time accountant affect the mean and median? Choose 1 answer: Choose 1 answer: (Choice A) A Both the mean and median will increase, but the median will increase by more than the mean. (Choice B) B Both the mean and median will increase, but the mean will increase by more than the median. (Choice C) C The mean will increase, and the median will decrease. (Choice D) D The median will increase, and the mean will decrease.
Answer:
The correct option is;
(Choice B) Both the mean and median will increase, but the mean will increase by more than the median.
Step-by-step explanation:
Here, we are expected to show the differences (advantages/properties) of the mean and median
Note that the definition of the mean is the sum of the value of all data points divided by the number of data points
Assuming the four accountants each earn $ 55,000.00
Therefore, initial mean before getting rd of the part-time accountant is
(55+ 55+ 55 + 55 + 10)/5 = 46
Final mean after the part-time accountant is gone =(55+ 55+ 55 + 55 )/4 = 55
Therefore the mean increases
However, the median is given by the middle value when the list of values are arranged in increasing order as
55, 55, 55, 55, 10
Therefore the initial median is 55
Final median after the part-time accountant is gone is
55, 55, 55, 55
Therefore, final = (55 + 55)/2 = 55
That is the median remains the same that is little or increase.
Therefore, since the range of values for the full time accountants salaries weigh less than the difference between the average full time salary and a single part time, both the mean and the median will increase but the mean will increase more than the median
Answer:
b
Step-by-step explanation:
Researchers are interested in the effect of a certain nutrient on the growth rate of plant seedlings. Using a hydroponics grow procedure that utilized water containing the nutrient, they planted six tomato plants and recorded the heights of each plant 14 days after germination. Those heights, measured in millimeters, were as follows: 53.1, 60.2, 60.6, 62.1, 64.4, 68.6. Given a margin of error of 5.4 mm, construct a 95% confidence interval for the population mean height.
Answer: The required confidence interval is (56.1,66.9).
Step-by-step explanation:
Since we have given that
53.1, 60.2, 60.6, 62.1, 64.4, 68.6
[tex]\bar{x}=\dfrac{53.1+60.2+60.6+62.1+64.4+68.6}{6}=\dfrac{369}{6}=61.5[/tex]
n = 6
Margin of error = 5.4
At 95% level of confidence, z = 1.96
So, the confidence interval would be
[tex]\bar{x}\pm \text{Margin of error}\\\\=61.5\pm 5.4\\\\=(61.5-5.4,61.5+5.4)\\\\=(56.1,66.9)[/tex]
Hence, the required confidence interval is (56.1,66.9).