Answer:
[tex]\mathbf{ \sqrt{\dfrac{15.7}{4} + \dfrac{10.6}{3}} }[/tex]
Step-by-step explanation:
Given that:
[tex]\overline x_1 =[/tex] the average diameter of 4 randomly select sequoia trunk from giant trees
[tex]\overline{x_2}[/tex] = the average diameter of 3 randomly selected trunk in California trees.
Thus;
sample size [tex]\mathbf{n_1 = 4 \ \ \& \ \ n_2 = 3}[/tex]
Variance:
[tex]\mathbf{\sigma_1^2 = 15.7 }[/tex]
[tex]\mathbf{\sigma_2^2 = 10.6 }[/tex]
Recall that:
[tex]\mathbf {( \overline x_1 - \overline x_2) \sim Normal \Big ( \mu_1 -\mu_2 \ , \ \dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma_12^2}{n_2} \Big )}[/tex]
[tex]\mathbf{Mean ( \overline x_1 - \overline x_2) = \mu_1 - \mu_2}[/tex]
Therefore:
The standard deviation [tex]\mathbf{ \overline x_1 - \overline x_2 = \sqrt{\dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma_2^2}{n_2} } }[/tex]
[tex]\mathbf{ \overline x_1 - \overline x_2 = \sqrt{\dfrac{15.7}{4} + \dfrac{10.6}{3}} }[/tex]
The standard deviation of the sampling distribution of the difference in the sample means is 9.95
The given parameters are:
Variance: [tex]\sigma_1 ^2 = 15.7[/tex], [tex]\sigma_2 ^2 = 10.6[/tex]Sample size: [tex]n_1 = 4[/tex], [tex]n_2 = 3[/tex].For a normal distribution we have:
[tex]\bar x_1 - \bar x_2 = \sqrt{\frac{\sigma_1^2}{n_1} +\frac{\sigma_2^2}{n_2}}[/tex]
So, the equation becomes
[tex]\bar x_1 - \bar x_2 = \sqrt{\frac{15.7^2}{4} +\frac{10.6^2}{3}}[/tex]
Evaluate the exponents
[tex]\bar x_1 - \bar x_2 = \sqrt{\frac{246.49}{4} +\frac{112.36}{3}}[/tex]
[tex]\bar x_1 - \bar x_2 = \sqrt{61.62+37.45}[/tex]
Evaluate the sums
[tex]\bar x_1 - \bar x_2 = \sqrt{99.07}[/tex]
Evaluate the square roots
[tex]\bar x_1 - \bar x_2 = 9.95[/tex]
Hence, the standard deviation of the sampling distribution of the difference in the sample means is 9.95
Read more about sampling distribution at:
https://brainly.com/question/17218784
Can someone help, marking Brainly ! Thank you if you do help .
Answer:
in order
y=0
y=1
y=2
y=3
y=4
y=5
Which line , or solid , is the best line of best fit ? What evidence can you provide to prove this is the best line of best fit ?
someone help , i’ll give you brainliest !
Answer:
It is y^5 + 15y^4 + 90y^3 + 270y^2 + 405y + 243
Step-by-step explanation:
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 160 engines and the mean pressure was 5.3 pounds/square inch (psi). Assume the population standard deviation is 0.6. The engineer designed the valve such that it would produce a mean pressure of 5.4 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.1 will be used. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
Test statistic Z = 2.1097
Step-by-step explanation:
Step(i):-
Given that size of the sample 'n' = 160
Given that mean of the Population(μ) = 5.3pounds/square inch
The Standard deviation of the population(σ) = 0.6
Mean of the sample(x⁻) = 5.4
Level of significance =0.1
Step(ii):-
Test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{5.4-5.3}{\frac{0.6}{\sqrt{160} } }[/tex]
Z = 2.1097
Final answer:-
Test statistic Z = 2.1097
HELP PLEAASE I WILL GIVE BRAINLIEST PLSSSSSS I WILL GIVE BRAINLIEST
Answer:
It is B
Step-by-step explanation: n is -1.5 and m is 2.5
-1.5 + 2.5 = 2
Answer:
I feel like it is the second one B
Step-by-step explanation:
Because it is the one that makes sense and is true.
the ratio of marks age to reeta's age is 3:5 marks age is 24 work out reeta's age
Answer:
40
Step-by-step explanation:
Set up a ratio. Solve for x.
3/5 = 24/x
3x = 120
x = 40
Reeta is 40 years old.
Answer:
40
Step-by-step explanation:
For every three years mark has, reeta has five.
Find out how many 'three years' mark has: 24/3 = 8
For every 'three years' he has, reeta has five. 5*8=40
6) A sample of water is being cooled according to the formula is given by
C(t)= 80 – 2t, where t represents the number of minutes the water is cooled,
and C measures the corresponding temperature in degrees Centigrade. The
cooling period ends when the water freezes (0°). Determine the relevant
domain and range for this function.
Determine the relevant Domain and relevant Range for this function. Use
interval notation.
Answer:
Relevant domain: [0 40]
Relevant range: [0 80]
Step-by-step explanation:
We have the following function:
[tex]C(t) = 80 - 2t[/tex]
In which C(t) is the water temperature.
t is the time.
The colling period ends when the water freezes (0°).
So it freezes after t minutes, and t is found when C(t) = 0. So
[tex]C(t) = 80 - 2t[/tex]
[tex]80 - 2t = 0[/tex]
[tex]2t = 80[/tex]
[tex]t = \frac{80}{2}[/tex]
[tex]t = 40[/tex]
Relevant domain:
Input value of the function, which is in minutes. So between 0(initial) and 40(when the water freezes).
Relevant range:
Initial temperature, which is C(0) = 80, until it freezes, 0. So from 0 to 80.
Imagine that you have the opportunity to purchase a large piece of land for $100,000, after taking out a loan. You have decided to take out a loan for $135,000 in order to cover the cost of the land purchase and building your park. You have hired a financial adviser to help you explore different loan options and decide which one is best for you. Below you will see the different loan options. You will need to calculate the total cost of each loan with interest. Once you have do this you and your group members will need to decide which of the loan options is best for you and why.
Option #1 – charges 5% simple interest per year; this is a short-term loan for only 5-years.
Option #2 – charges 7% simple interest per year; this is a short-term loan for only 3-years.
Option #3 – charges 3.2% simple interest per year; there is no time limit on this loan (as a group determine how long you think it will take you to make enough money to be able to pay back the loan with interest)
Option #4 - charges 10% simple interest per year; only lasts 10 months
Option #5 - charges 12% simple interest per year; only lasts 6 months
Written Response
You will be meeting with your financial adviser in two days. Write out which loan option your group is choosing to use and why. You really want to impress her with how much thought you have put into this decision so be as detailed as possible.
what is this
Step-by-step explanation:
Option #1 – charges 5% simple interest per year; this is a short-term loan for only 5-years.
Option #2 – charges 7% simple interest per year; this is a short-term loan for only 3-years.
Option #3 – charges 3.2% simple interest per year; there is no time limit on this loan (as a group determine how long you think it will take you to make enough money to be able to pay back the loan with interest)
Option #4 - charges 10% simple interest per year; only lasts 10 months
Option what is this
Answer:
Its option one
Step-by-step explanation:
Because 135,000/5=27000 then x5=135,000
Which expression represents the phrase " the difference of 18 and 12"?
Given:
The statement is "the difference of 18 and 12".
To find:
The expression for the given statement.
Solution:
We have,
Given statement = The difference of 18 and 12.
We use subtraction, to find the different between two numbers and subtraction is represented by negative sign. So, we need to subtract second number form the first number.
The difference of 18 and 12 = 18 - 12
Therefore, the required expression for the given statement is 18-12.
the doctor recommended that Matt increase the number of calories you consume from 2000 to 2800 by what percent did the number of calories increase
Answer:
40% number of calories have increased
Step-by-step explanation:
Old Value ( Calories consume before) = 2000
New Value (increase in Calories consumed) = 2800
We need to find by what percent did the number of calories increase
To find percent increase, the formula used is:
[tex]Percent\: increase=\frac{New\:Value-Old\:Value}{Old\:Value}\times 100%[/tex]
Putting values in formula and finding percent increase
[tex]Percent\: increase=\frac{New\:Value-Old\:Value}{Old\:Value}\times 100\%\:\\Percent\: increase=\frac{2800-2000}{2000}\times 100\%\: \\Percent\: increase=\frac{800}{2000}\times 100\%\: \\Percent\: increase=0.4\times 100\%\: \\Percent\: increase=40\%[/tex]
So, 40% number of calories have increased
Including a 9% sales tax, an inn charges $114.45 per night. Find the inn's nightly cost before tax is added.
Answer:
$10.34
Step-by-step explanation:
9/100 x $114.95= $10.34
Simplify
3/4a - 2/3 - 1/2a + 5/6= ????
Answer:
3a + 2
——————
12
Step-by-step explanation:
Let LaTeX: x = \text{-}\frac {11} 8x = - 11 8 and LaTeX: y = \text{-}\frac {11} 4y = - 11 4.
Which expression has a negative value?
Group of answer choices
LaTeX: x + yx + y
LaTeX: x - yx − y
LaTeX: x \cdot yx ⋅ y
LaTeX: \frac x y
Answer:
This makes no sense
Step-by-step explanation:
The ratio of 15 and a number.
Answer:
15 to 20
Step-by-step explanation: hope this helps! have a supercalifragilisticexpialidocious day ◑﹏◐
Answer:
15:x or 15 to x
Step-by-step explanation:
it depends on what the question is asking, so if they want you to fill in a number, you could replace x with any number you'd like. but its probably a word problem they want you to put as numbers, so bc you dont know what 'a number' is, you can pick a variable such as x to replace it with.
hope this helps :)
9x^2+25 Can someone doble this
Answer:
Since both terms are perfect squares, factor using the difference of squares formula, a2−b2=(a+b)(a−b) where a=3x and b=5.
(3x+5)(3x−5)
Step-by-step explanation:
2. Angela deposited $600 into an account paying a simple interest rate of 3.6% for 4.5 years. How
much interest did she earn? What was the balance of her account after the 4.5 years (assuming she made no deposits of withdrawals during the time)
Answer:
Step-by-step explanation:
to find out how much Angela she would have in the bank,
(600*3.6*1)100=21.60 she gains in one year
6 months 21.60/2=10.80
in 4.5 years
(21.60*4)+10.80=86.40+10.80=97.20 interest
the balance=600+97.20=697.20
f(x) = 16x^3- 20х^2 - 4х + 15
Answer:
hopes this helps
Step-by-step explanation:
Records kept for a period of 30 weeks by a
dietician at a cafeteria show the following
weekly consumption of milk ( in gallons).
200
205
210
215
220
225
230
235
240
Milkin
gallons
Probability
3/30
4/30
6/30
5/30
4/30
3/30
2/30
2/30
1/30
Find the average number of gallons of milk
consumed per week.
Answer:
216
Step-by-step explanation:
LCD = 30
200(3/30) = 600/30
^ do this process for each number
Answer: 216
Step-by-step explanation:
What is the measure of 2X?
х
1240
Select the best answer from the choices provided.
A.56
B.66
C.114
D.124
Answer:
D
Step-by-step explanation:
1240/10
A given angle measures 30° and the measure of its vertical angle is expressed as (5x + 5).
Part A
Write an equation to determine the value of x. Solve for 2.
Enter the correct answers in the boxes.
Answer:
Equation: 5x+5 = 30
x = 5
Step-by-step explanation:
Since vertically opposite angles are equal, then;
5x+5 = 30
Subtract 5 from both sides
5x +5-5 = 30-5
5x = 25
x = 25/5
x = 5
The required equation is 5x+5 = 30 (vertically opposite angles are equal)
The value of x is 5
Graph? Which is linear
Answer:
Below
Step-by-step explanation:
1. Linear because it is of the form y = mx + b. The variable x is of the first degree.
The coefficient of x (1/3) ( = slope) is positive so it is increasing.
2. This is non-linear because the variable x is an exponent.
3. Because its of the second degree (x^2) - it is non-linear.
Eighteen percent of apples grown in an orchard have defects. Let X = the number of apples that are randomly inspected from the orchard until a defective one is found.
What is the probability that the first defective apple found is the 10th one inspected? Round to 2 decimal places.
a). 0
b). 0.03
c). 0.14
d). 0.86
*it’s not c). 0.14*
Answer: It’s B. I guessed and it’s right.
Step-by-step explanation:
Answer:
0.03 edge2021
Step-by-step explanation:
The human body consist 1/10 hydrogen 16/25 oxygen 1/5 carbon
Answer:
ok? whats the question Imao
Step-by-step explanation:
11
12
What is that fraction decimal
Answer:
0.91666666666...
The equation c = 0.25n can be used to find the cost (c) of buying n number of apples.
A) What is the constant of proportionality in this equation?
B) What information does the constant of proportionality provide us?
C) How many apples can you buy for $3?
Be sure to answer A, B and C. Make sure that you label each answer.
PLEASE HELP ME!
Answer:
a) Constant of proportionality = 0.25
b) The constant of proportionality provides the cost of one apple.
c) n = 12
Step-by-step explanation:
It is given that:
c = 0.25n
a) Here,
c = cost of apples
n = number of apples
As the proportion varies directly.
c ∝ n
c = kn
Comparing the equations
k = 0.25
b) The constant of proportionality provides the cost of one apple.
c) Putting c = $3
3 = 0.25n
Dividing both sides by 0.25
n = 12
Thus,
a) Constant of proportionality = 0.25
b) The constant of proportionality provides the cost of one apple.
c) n = 12
108x25^2divided by
2^6 x 5^2
Answer:
108 x 25² divided by 2⁶ x 5² is equal to [tex]42\frac{3}{16}[/tex]
Step-by-step explanation:
Given;
108 x 25² divided by 2⁶ x 5²
The expression is simplified as follows;
[tex]\frac{108\times 25^2}{2^6 \times 5^2} = \frac{108\times 625}{64\times25} =\frac{675}{16} = 42\frac{3}{16}[/tex]
Therefore, 108 x 25² divided by 2⁶ x 5² is equal to [tex]42\frac{3}{16}[/tex]
Mrs. Bush has a carpet remnant left from putting carpet down in her living room.
The carpet remnant was 4 1/8 square units. If the remnant was 3/4 units wide,
what was the length? *
Answer: The length = [tex]5\dfrac12[/tex] units
Step-by-step explanation:
Given: Area of carpet = [tex]4\dfarc18 \text{ sq. units}=\dfrac{33}{8}\text{ sq. units}[/tex]
Width of carpet = [tex]\dfrac34[/tex] units
Shape of carpet = Rectangle
Area of rectangle = length x width
So,
length = [tex]\dfrac{Area}{width}[/tex]
[tex]=\dfrac{\dfrac{33}{8}}{\dfrac34}\\\\=\dfrac{33}{8}\times\dfrac43\\\\=\dfrac{11}{2}\\\\=5\dfrac12\text{ units}[/tex]
Hence, the length = [tex]5\dfrac12[/tex] units
The ratio of the sides of a triangle is 2:6:7. If the perimeter of the triangle is 195 meters, what is the length of the shortest side?
Answer:
The shortest side is 26 units.
Step-by-step explanation:
(2×13)+(6×13)+(7×13) = 195
2×13 = 26
Martin has read 40% of a book. He has 30 more pages to finish. How many pages are there in the book?
Answer:
75
Step-by-step explanation:
Answer:
There are 50 pages in the book.
Step-by-step explanation:
Given that:
Martin has read 40% of the book.
Remaining percent = (100 - 40)% = 60%
Number of pages left to finish = 30
Let,
x be the total number of pages in the book.
60% of x = 30
[tex]\frac{60}{100}x=30[/tex]
0.6x = 30
Dividing both sides by 0.6
[tex]\frac{0.6x}{0.6}=\frac{30}{0.6}\\x= 50[/tex]
Hence,
There are 50 pages in the book.
Solve for y: 3x + 2y = 5y + 9
Answer:
y = x - 3
Step-by-step explanation:
First you want to combine like terms (so get x on one side and y on the other).
2y = 5y + 9 - 3x
-3y = -3x + 9
Then just solve for y by dividing by -3
y = (-3x + 9)/-3
y = x - 3