Answer:
a) mode = 7
b) range = 8
Step-by-step explanation:
7 appears the most in the dataset, making it the mode
8 is because of 9 (highest value) minus one (lowest value) = 8
Four hundred randomly selected working adults in a certain state, including those who worked at home, were asked the distance from their home to their workplace. The average distance was x-bar equal to 8.84 miles. Assume that the standard deviation of the population of all working adults in that state is 2.70 miles. Construct a 99% confidence interval for the mean distance from home to work for all residents of this state. Droble
Answer:
The 99% confidence interval for the mean distance from home to work for all residents of this state is between 8.49 and 9.19 miles.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575\frac{2.7}{\sqrt{400}} = 0.35[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 8.84 - 0.35 = 8.49 miles.
The upper end of the interval is the sample mean added to M. So it is 8.84 + 0.35 = 9.19 miles.
The 99% confidence interval for the mean distance from home to work for all residents of this state is between 8.49 and 9.19 miles.
Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .
I need the answer step by step
Answer:
The family of all prime numbers such that [tex]a^{2} + b^{2} + c^{2} -1[/tex] is a perfect square is represented by the following solution:
[tex]a[/tex] is an arbitrary prime number. (1)
[tex]b = \sqrt{1 + 2\cdot a \cdot c}[/tex] (2)
[tex]c[/tex] is another arbitrary prime number. (3)
Step-by-step explanation:
From Algebra we know that a second order polynomial is a perfect square if and only if [tex](x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}[/tex]. From statement, we must fulfill the following identity:
[tex]a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}[/tex]
By Associative and Commutative properties, we can reorganize the expression as follows:
[tex]a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}[/tex] (1)
Then, we have the following system of equations:
[tex]x = a[/tex] (2)
[tex](b^{2}-1) = 2\cdot x\cdot y[/tex] (3)
[tex]y = c[/tex] (4)
By (2) and (4) in (3), we have the following expression:
[tex](b^{2} - 1) = 2\cdot a \cdot c[/tex]
[tex]b^{2} = 1 + 2\cdot a \cdot c[/tex]
[tex]b = \sqrt{1 + 2\cdot a\cdot c}[/tex]
From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, [tex]a, b, c > 1[/tex]. If [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex] are prime numbers, then [tex]2\cdot a\cdot c[/tex] must be an even composite number, which means that [tex]a[/tex] and [tex]c[/tex] can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.
In addition, [tex]b[/tex] must be a natural number, which means that:
[tex]1 + 2\cdot a\cdot c \ge 4[/tex]
[tex]2\cdot a \cdot c \ge 3[/tex]
[tex]a\cdot c \ge \frac{3}{2}[/tex]
But the lowest possible product made by two prime numbers is [tex]2^{2} = 4[/tex]. Hence, [tex]a\cdot c \ge 4[/tex].
The family of all prime numbers such that [tex]a^{2} + b^{2} + c^{2} -1[/tex] is a perfect square is represented by the following solution:
[tex]a[/tex] is an arbitrary prime number. (1)
[tex]b = \sqrt{1 + 2\cdot a \cdot c}[/tex] (2)
[tex]c[/tex] is another arbitrary prime number. (3)
Example: [tex]a = 2[/tex], [tex]c = 2[/tex]
[tex]b = \sqrt{1 + 2\cdot (2)\cdot (2)}[/tex]
[tex]b = 3[/tex]
there are 32 students at a pizza party. each students ate 1/4 pizza how many whole pizzas did the students eat altogether?
Answer:
8
Step-by-step explanation:
lent receives per day?
A patient is receiving a normal saline solution, infusing continuously at 80 ml/hr IV, and a tube feeding formula,
Glucerna, infusing continuously at 50 ml/hr. What is the total amount of fluids infused per day?
Answer:
The total amount of fluids infused per day is 3,120 ml.
Step-by-step explanation:
Given that a patient is receiving a normal saline solution, infusing continuously at 80 ml / hr, and a tube feeding formula, Glucerna, infusing continuously at 50 ml / hr, to determine what is the total amount of fluids infused per day the following calculation must be done:
(80 x 24) + (50 x 24) = X
1,920 + 1,200 = X
3.120 = X
Therefore, the total amount of fluids infused per day is 3,120 ml.
Find the measure of the angle, round to the nearest tenth: Sin X = .7547
What is the volume of a regular triangular pyramid with an apothem of 2.3ft, a side length of 8ft and a height of 25 feet
230FT
Regular tetrahedron
Solve for volume
V≈1.15×107
Use the formula for the volume of a triangular pyramid: V=13Ah , where A = area of the triangular base, and H = height of the pyramid.
Karen finished watching a movie at 1:10 pm. The movie lasted 1 hour and 38 minutes. What is the time that karen started watching the movie
Answer:
11:32:00 AM
Step-by-step explanation:
The output associated with an input of zero is known as the
Answer:
IO
Step-by-step explanation:
9514 1404 393
Answer:
y-intercept
Step-by-step explanation:
If the function is graphed as ...
y = f(x)
then y = f(0) is the y-intercept.
_____
Additional comment
Depending on the way the graph is created and labeled, any points or curve on the graph may cross the vertical axis at a point other than one that corresponds to an input of 0. In any event, it may not be called "y". It may be "sales" or "board feet" or "monkeys per acre". Then the name of the point may not be "y-intercept", but may be something else.
someone help me please
Answer:
c = 7.4
Step-by-step explanation:
Pythagoras Theorem
8². - 3 ². = c ².
√64 -√9 = c².
√55 = c². = 7.4161984871².
c = 7.4
Please help me
Find the circumference and the area of this shape
I'll give brainliest
Constant of Variation
For the function defined by y = 1/x², y varies inversely as what quantity?
a. x
b. 2x
c. y
d. x²
Please select the best answer from the choices provided
Answer:
D. x²
Step-by-step explanation:
I calculated it logically
Let A and B be two disjoint events such that P(A) = .30 and P(B) = .60. What is P(A and B)? 0.18 0.72 0.90 0 none of the above
Answer:
0
Step-by-step explanation:
If two events are disjoing (aka mutually exclusive) that means that there is 0 overlap or the intersection equals 0
So the probability of A and B occuring is 0 (because P(A∩B)= 0)
Which statement is most likely to be true for this distribution?
1
A. The mean is less than the median.
B. The mean is greater than the median.
O C. The mean is the same as the median.
(a)
Using a calculator, or otherwise, determine the value of:
(i) 5.25 - 0.015
Answer:
5.235
Step-by-step explanation:
Just use a calculator
Else
5.250
-0.015
______
5.235
Add 0 to make it equal. Carry 1 from 5 of 5.2'5'0 to 0 and make it 10. 10g5 is 5. Then 4 remains .4-1 is 3. Others are normally subtracted.
Which of the following statements is true?
O 0.6 < 0.61 < 0.7
O 0.61 < 0.6 < 0.7
O 0.7 < 0.61 < 0.6
O 0.7 < 0.6 < 0.61
Answer: 0.06<0.61<0.7
Step-by-step explanation:
The numbers is 0.6< 0.61 <0.7.
It is required to find among the statements is true.
What is integer?An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Given that:
0.7 is largest number among the given integer.
0.61 is 2nd largest number among the given integer.
0.6 is lowest number among the given integer.
∴0.6< 0.61 <0.7.
So, the numbers is 0.6< 0.61 <0.7.
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A={the letters of the word ,HIPPOPOTAMUS}
•ω• Hewo fren!
☆☆●◉✿Answer:✿◉●☆☆
The letters of hippopotamus is H-I-P-P-O-P-O-T-A-M-U-S
☆☆●◉✿Step-by-step explanation:✿◉●☆☆
I’m sowy, I didn’t really understand your question... did you want to learn about a hippopotamus? If so, please tell me in the comments I would answer there too!
HOPE I HELPED! ∧∧
→⇒brainliest please? ∑(OΔO )♥♥︎
GIVING BRAINLIEST FOR CORRECT ANSWER WITH EXPLANATION
Answer:
Step-by-step explanation:
THE ANSWER IS : C
=
2
π
r
=
2
π
71
≈
446.10616
Please help me solve this question
angle D = 92°
Step-by-step explanation:
Since the two figures are congruent.
angle D = angle K
20x + 12 = 25x - 8
5x = 20
x = 4
Substituting this value into angle D, we see that
angle D = 20x + 12
= 20(4) + 12
= 92°
6z3+2z2-9
What is the constant
Answer:
.; i don't know the constant but i know that the degree is 3 Step-by-step explanation:
what is the Difference between elimination method and indirect method
Answer:
Indirect method actually follows the same set of procedure as the direct method except that it begins with net income unlike the elimination method reduced a given system that indicates a system has no unique solution.
Find the area of the shaded region.
150 degrees
7 cm
A =[?] cm2
Enter a decimal rounded to the nearest tenth.
Answer:
102.2
Step-by-step explanation:
(x^5-y^5) divided (x-y)
See in the picture I have done till here but can anyone tell me next step
Answer:
[tex]\frac{x^6-yx-y^5}{x}[/tex]
Step-by-step explanation:
x^5-y^5 divided x-y
[tex]\frac{(x^5-y)x}{x} -\frac{y^5}{x}[/tex]
[tex]\frac{(x^5-y)x-y^5}{x}[/tex]
=> [tex]\frac{x^6-yx-y^5}{x}[/tex]
The diagram shows a cylindrical tank.
The radius is 30 cm and the height is 80 cm.
(a) Calculate the area of the base of the tank.
(b) Calculate the volume of the tank in litres.
Step-by-step explanation:
a) A=π302=900π CM2 =2,827 CM 2
b) V=Ah=900=72000 π cm 3 = 226,195 cm3
Using elimination, what is the solution to the following system?
x+6y=32
-x-3y=-17
Answer:
x=2, y=5. (2, 5).
Step-by-step explanation:
x+6y=32
-x-3y=-17
---------------
3y=15
y=15/3
y=5
x+6(5)=32
x+30=32
x=32-30
x=2
22,19,16,13 what is the 37th term
Answer:
-86
Step-by-step explanation:
3x10=30
22-3=19-3=16-3=13
so if its tthe 37th term, lets do 30x3=90
now 13-90=-77
-77=34th term
now just -3 until 37
-80
-83
-86
the 37th term is -86
i will give a brainlist and like please help me....
but if it is not true answer i will report
Answer:
1.6m is the answer
Step-by-step explanation:
Answer: so you can give branliest to the other guy
Step-by-step explanation:
Plz help me well mark brainliest if correct!
Answer:
The answer is B.
Step-by-step explanation:
The formula is Area = L x H
And remember perimiter is adding the legnth of all sides.
For A:
12 × 3 = 36
12 + 12 + 3 + 3 = 30
For B:
4 × 8 = 32
4 + 4 + 8 + 8 = 24
For C:
6 × 6 = 36
6 + 6 + 6 + 6 = 24
Hence, the answer is B, since B is the only one which meets the criteria.
What’s the answer ?
Answer:
c
Step-by-step explanation:
I cannot see the whole picture. some numbers are cut off.
but just by making the calculating for the top-left corner we can see the only possible right answer.
so, top-left corner of A = 4 and of B = 7.
therefore, the top-left corner of the result matrix is then according to -2×A + 7×B
-2×4 + 7×7 = -8 + 49 = 41
the only solution option with 41 in the top-left corner is c.
factorize
3a⁴+18a²-21-2b-3b²
Answer:
the expression is not factorable with rational numbers.
Answer:
The closest thing i can get to here is
38a^4-21- 7b^2
Step-by-step explanation:
thats the smallest i could get it to hope it helps <3
Gretchen is refinishing her gazebo that is in the shape of a regular octagon. The length of one side is 3 feet and the apothem is 3.5 feet. What is the area that Gretchen will be refinishing? Need help fast
The area that Gretchen will be refinishing is 42 square feet.
What is a polygon?A polygon is a closed more than two-sided and can be made up of a finite number of straight line segments and is a type of planar figure in geometry.
Each line of the polygonal circuit's segments is referred to as its edges or sides.
An octagon has 8 sides.
We know, Apothm is the distance from the center to its side.
We also know that an octagon can be divided into 8 similar triangles.
Therefore, The area of the octagon will be,
= 8×(1/2)×3×3.5 square feet.
= 4×10.5 square feet.
= 42 square feet.
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