The 95% confidence interval based on the same data is 5.15 < μ < 6.05
Because it has a longer interval, the 95 percent confidence interval offers more details.
What is a confidence interval?The likelihood that a parameter will fall between two values near the mean is shown by a confidence interval.
Confidence intervals quantify how certain or uncertain a sampling technique is.
Confidence intervals are used by statisticians to gauge the degree of uncertainty in a sample variable.
The 90% confidence interval is given by:
Mean - 1.645(S.D./[tex]\sqrt{n}[/tex]) < μ < Mean + 1.645(S.D./[tex]\sqrt{n}[/tex])
2μ = 5.22 + 5.98 = 11.2
μ = 11.2 / 2 = 5.6
Thus,
5.6 - 5.22 = 1.645(S.D./[tex]\sqrt{n}[/tex]) = 0.38
S.D./[tex]\sqrt{n}[/tex] = 0.38 / 1.645 = 0.231
The 95% confidence interval is given by:
Mean - 1.96(S.D./[tex]\sqrt{n}[/tex]) < μ < Mean + 1.96(S.D./[tex]\sqrt{n}[/tex])
=5.6 - 1.96(0.231) < μ < 5.6 + 1.96(0.231)
= 5.6 - 0.4528 < μ < 5.6 + 0.4528
= 5.15 < μ < 6.05
The 95% confidence interval provides more information because it has a larger interval.
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The prism shown in the diagram has a volume of 39 units^3. What is the volume of the pyramid? Explain your reasoning. I WILL GIVE BRAINLIEST ASAP FOR A QUICK ANSWER
The volume of the pyramid is 13 units³.
What is the volume of the pyramid?
A pyramid is a 3-dimensional shape that is made up of a rectangular base and 4 triangular faces. The volume of a pyramid is one-third that of a prism.
Volume of a pyramid = 1/3 x prism
1/3 x 39 = 13
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The graph of f(x) = 1/3
is reflected vertically, compressed horizontally by a factor of 5, shifted
right 2 units and down 6 units. Write the equation of the new graph.
The transformed function is defined by:
g(x) = -f(x/5 - 2) - 6
Where f(x) is the given function.
How to get the equation of the transformed function?Here we start with the function:
f(x) = (1/3)*x
(I don't know if this is the actual function, but that does not matter, I will solve it in a general way).
If first, we reflect it vertically, then the new function is:
g(x) = -f(x).
If now we compress it horizontally by a factor of 5, then we get:
g(x) = - f(x/5)
Now we shift it 2 units to the right, then:
g(x) = -f(x/5 - 2)
Finally, we shift it down 6 units, then we get:
g(x) = -f(x/5 - 2) - 6
That is the general form of the function g(x).
Replacing f(x) by what is defined above, we get:
g(x) = -(1/3)*(x/5 - 2) - 6
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Two boys, John and Peter, are running a 100-meter race. In the first race that they run John beats Peter by 5 meters. To make things fair, the next time they race John stands 5 meters behind the starting line. If they run at the same speed as the first race, who will win the second race
Second time john wins the race because he runs in the race with constant speed as same speed they run in 1st race.
According to the statement
We have given that the John and Peter, are running a 100-meter race.
In the first race that they run John beats Peter by 5 meters. and the next time they race John stands 5 meters behind the starting line.
Here the both participant's speed remain same in both races.
So, We have to find that the If they run at the constant speed as the first race, who will win the second race
So, for this purpose
According to the statement
in first race john beats the peter and wins the race and if they start the second race with the same speed then it is clear that the second time john won the race.
So, Second time john wins the race because he runs in the race with constant speed as same speed they run in 1st race.
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Find the midpoint between
-7 + 4i
and
3 - 2i
Answer:
-2+i
Step-by-step explanation:
-7+4i represents (-7,4) and 3-2i represents (3,-2).
So, the midpoint is (-2,1), which represents -2+i.
Which statement can you use to conclude that quadrilateral xyzw is a parallelogram
Answer: Option (4)
Step-by-step explanation:
A quadrilateral with two pairs of opposite congruent sides must be a parallelogram.
The Hartman family is saving $400 monthly for Ronald’s college education. The family anticipates they will need to contribute $20,000 toward his first year of college, which is in 4 years. Which best explains whether the family will have enough money in 4 years?
The family will not have enough money. They will have saved only $16,000.
The family will not have enough money. They will have saved only $19,200.
The family will likely have enough money. They will have saved $16,000 and have accumulated interest.
The family will likely have enough money. They will have saved $19,200 and have accumulated interest.
The statement which best explains whether the family will have enough money in 4 years is; The family will not have enough money. They will have saved only $19,200.
SavingsAmount Hartman family saves monthly = $400Amount needed = $20,000Number of years = 4Number of months = 4 × 12 = 48Amount saved in 4 years = Amount Hartman family saves monthly × Number of months
= $400 × 48
= $19,200
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The statement which best explains whether the family will have enough money in 4 years is; The family will not have enough money. They will have saved only $19,200.
SavingsAmount Hartman family saves monthly = $400Amount needed = $20,000Number of years = 4Number of months = 4 × 12 = 48Amount saved in 4 years = Amount Hartman family saves monthly × Number of months
= $400 × 48
= $19,200
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Riley bought a 7 1/2 pounds of clay for the students in her pottery class. She then divided the clay into 4 equal pieces for her students to use for making vases and pots. How much did each piece weigh?
Answer:
1.857 pounds
Step-by-step explanation:
If the clay is divided into 4 equal parts, we divide 7.5lbs by 4: 7.5/4 = 1.857 lbs
The math team wraps gifts as a way to raise money for traveling to competitions. They offer two choices: a plain wrapping or a decorative wrapping with bows. The table represents the money raised over a busy shopping weekend.
A 3-column table titled Gift-Wrapping Fundraiser has 3 rows. The first column is labeled Plain Gifts Wrapped with entries 10, 25, 16. The second column is labeled Decorative Gifts Wrapped with entries 9, 12, 12. The third column is labeled Total Raised in dollars with entries 47, 86, 68.
Which statement describes the amounts the team charged for wrapping gifts?
Answer:
Step-by-step explanation:
We will assume that the first two columns are the numbers sold for Plain Wrapping and Decorative Wrapping. The third colum does not equal the sum of the first two, so we'll assume it is the total paid for both options. Let set the price of Plain Wrapping to x and the Decorative Wrapping to y. The number of gift wrappings times the cost per warpping is the product of x or y timers the number wrapped as shown in columns 1 and 2.
Take the first row and set it as an equation:
10x+9y = 47 [10 Plain Wraps and 9 Decorative Wraps bring a total of $47]
Do the same for the second and third rows:
25x + 12y = 86, and
16x +12y = 68
===========
We can take any equation and rearrange it to isolate one of the 2 variables, x or y. I'll pick 10x = 47-9y and isolate x:
10x = 47-9y
x = (47-9y)/10
-------------------
Now use this definition of x in another equation. I'll use 25x + 12y = 86.
25x + 12y = 86
25(47-9y)/10 + 12y = 86 [since x = (47-9y)/10 from above]
117.5 - 22.5y + 12y = 86
-10.5y = -31.5
y = 3 [the price for decorative wrapping is $3]
If y = 3, then we can use this in any of the equations to find x:
x = (47-9y)/10
x = (47-9(3))/10 [Use y = 3]
x = (47-27)/10
x = 2 [The price for plain wrapping is $3]
======================
Check to see if these values will expalin the total value of the three rows of numbers:
CHECK:
______UNITS____ $2 each $3 each
PlainW DecG Total PlainW ($) DecG ($) Total ($)
x y x y
10 9 $47 $20 $27 $ 47 OK
25 12 $86 $50 $36 $ 86 OK
16 12 $68 $32 $36 $ 68 OK
The values work. Merry Christmas.
Answer:
The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.
Step-by-step explanation:
just did it in edg
Which algebraic expression has a term with a coefficient of 9?
• A. 6 + X- 9
• B. 6x - 9
C. 6(x + 5)
• D. 9x ÷ 6
Answer:
D
Step-by-step explanation:
Coefficient is the number next to the variable, and D is the only one where that number is 9. All the others are 6.
Johnny created a chart using stick people to depict the frequency of the data. What type of chart did Johnny create
Johnny created a Tally marks chart.
A frequency distribution table displays the frequency of each data set in an organized way. It helps us to find patterns in the data and also enables us to analyze the data using measures of central tendency and variance. The first step that a mathematician does with the collected data is to organize it in the form of a frequency distribution table. All the calculations and statistical tests and analyses come later.
Tally Marks are used to keep a track of numbers in the quickest possible way. Tally marks are used for counting and are represented as a set of five lines in which there are four vertical lines (one vertical line is made for each of the first four numbers) and the fifth number is represented by a diagonal line across the previous four numbers. It can be understood through the given figure
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Alex scored 40 marks out of 60 in a spelling test pet scored 65% in the same test who did better
Based on the test by result, Alex did better in the test by scoring 66.67%
PercentageAlex = 40 out of 60Percentage scored by Alex = 40/60 × 100
= 0.66666666666666 × 100
= 66.6666666666666
= 66.67%
my Percentage scored by pet = 65%Therefore, Alex did better in the test
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Consider the expansion of (x^2+px-3)(3x-5),where p is a constant.If the coefficient of x of the expansion is -44,find the value of p
Answer:
p = 7
Step-by-step explanation:
(x² + px - 3)(3x - 5)
each term in the second factor is multiplied by each term in the first factor, that is
x²(3x - 5) + px(3x - 5) - 3(3x - 5) ← distribute parenthesis
= 3x³ - 5x² + 3px² - 5px - 9x + 15 ← collect like terms
= 3x³ +x²(3p - 5) - x(5p + 9) + 15
given the coefficient of the x- term is - 44 , then
-(5p + 9) = - 44 ← - (5p + 9) is th coefficient of x in the expansion
- 5p - 9 = - 44 ( add 9 to both sides )
- 5p = - 35 ( divide both sides by - 5 )
p = 7
There are 26 prize tickets in a bowl, labeled A to Z. What is the probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen? Does this represent an independent or dependent event? Explain.
The probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen is 0.031 or 3.1%. So, this represents a dependent event.
What are independent and dependent events?Independent events are the events in which the outcome of one event does not affect the outcome of the other event.Dependent events are the events in which the outcome of one event affects the outcome of the other event.Calculation:It is given that there are 26 prize tickets in a bowl, labeled A to Z.
There are 5 vowels- A, E, I, O, U
So, the probability of choosing a ticket with a vowel will be - (5/26)
Another ticket with a vowel will be chosen without replacing the first ticket. Then, its probability is (4/25)
So, the required probability is,
(5/26) × (4/25) = 2/65 = 0.031
The event of choosing the first ticket with a vowel effect the event of choosing the second ticket with a vowel and vice-versa. So, this represents dependent events.
Therefore, the probability is 3.1 %.
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Find the surface area of a rectangular prism with a height of 16 feet, a width of 10 feet, and a length of 13 feet.
The surface area of a rectangular prism with a height of 16 feet, a width of 10 feet, and a length of 13 feet is 996 ft².
A = Surface area
l = Length
w = Width
h = Height
A = 2 ( w l + h l + h w )
= 2 · ( 10 · 13 + 16 · 13 + 16 · 10 )
= 996 ft²
The gap occupied by using a dimensional flat surface is referred to as the region. it's far measured in rectangular gadgets. The location occupied by using a 3-dimensional object by means of its outer floor is referred to as the surface location.
The surface vicinity of a strong object is a degree of the total vicinity that the surface of the item occupies.
The floor location is the overall location included via all of the faces of a 3-d item. As an example, if we need to discover the amount of paint required to paint a cube, then the surface on which the paint will be implemented is its floor place. it is continually measured in square gadgets.
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Which expression can be used to find 52% of 230?
Hello,
52% of 230 = 52/100 × 230 = 0,52 × 230 = 119,6
Answer:
230 : 100 * 52 =
Step-by-step explanation:
Which expression can be used to find 52% of 230?
The expression is: 230 : 100 * 52 =
Which expression is equivalent to 4x^2sqrt 5x^4 times 3sqrt 5x^8 , if x ≠ 0?
The expression which is equivalent to 4x²√5x⁴ × 3√5x^8 is; 60x^8.
Which expression is equivalent to the given expression?The expression given in the task content is; 4x²√5x⁴ × 3√5x^8.
Hence, upon evaluation of the product; we have;
= 12x²√25x¹².
= 60x^8.
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A cylinder has a height of 17 feet and a radius of 6 feet. What is its volume? Use ≈ 3.14
and round your answer to the nearest hundredth.
Answer:
1921.68 [tex]ft^{3}[/tex]
Step-by-step explanation:
V = pi*r*r*h
= 3.14*6*6*17
= 1921.68
Point W is located at (-5, -3).
Select all of the following that are 5 units from point W.
Choose all answers that apply:
A. (-5, 2)
B. (−8,−5)
C. (-5, 0)
The point that is 5 units from W is (A) (-5, 2)
How to determine the points?The point is given as:
W= (-5, -3)
A point 5 unit from W can be any of the following
W' = (-5 ± 5, -3)
W' = (-5, -3 ± 5)
When the above expressions are evaluated, we have:
W' = (0, -3), (-10, -3), (-5, 2) and (-5, -8)
Hence, the point that is 5 units from W is (A) (-5, 2)
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The table above represents what type of function?
A.
linear and nonlinear
B.
linear
C.
neither linear nor nonlinear
D.
nonlinear
B because it’s a linear graph.
Find the nth term of the arithmetic sequence (an) whose initial term a and common difference d are given below. What is the forty-fifth term?
a₁ = 2; d = 1/4
Answer:
a₄₅ = 13
Step-by-step explanation:
The n-th term of an arithmetic sequence with first term a₁ and common difference d is given by the formula ...
aₙ = a₁ +d(n -1)
SetupYou want the 45th term where a₁ = 2 and d = 1/4. Putting these values into the formula gives ...
a₄₅ = a₁ +d(n -1) = 2 +(1/4)(45 -1)
SolutionEvaluating this expression, we have ...
a₄₅ = 2 +44/4 = 2 +11
a₄₅ = 13
The 45th term of the sequence is 13.
The forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]
How to find the nth term of the Arithmetic series?
The nth term of the arithmetic series is find by [tex]Tn = a+(n-1)d[/tex] where Tn is the nth term of the series a is called the initial number and is the common difference between two number. n is the number of term of that arithmetic series.
In the given series initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex]
We have the find the forty-fifth term of the given series.
= [tex]Tn=a+(n-1)d[/tex]
= [tex]Tn = 2+(45-1)\frac{1}{4}[/tex]
= [tex]Tn=2+44\cdot\frac{1}{4}[/tex]
= [tex]Tn = 2+11[/tex]
= [tex]Tn = 13[/tex]
So, the forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]
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Use the fact that 1.5 is the same as 3/2 to select all of the equations below that are equivalent toT
The equivalent expressions of T=A^1.5 are: T= (A)^3/2 and T= ((A)^1/2)^3
According to the statement
we have to show that the 1.5 is same as 3/2 are equivalent to T.
So,
Equivalent expressions are expressions with the same value.
The Given expression is
T=A^1.5
we can write it as a
T= (A)^3/2
Because we know that the
1.5 = 3/2
So, it become T= (A)^3/2.
And From
T=A^1.5
we can write it as a
T= ((A)^1/2)^3
because we know that the
3/2 = (1/2)^3.
So, The equivalent expressions of T=A^1.5 are: T= (A)^3/2 and T= ((A)^1/2)^3.
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6.6x 10⁵ in standard notation
Answer:
660000
Step-by-step explanation:
Shawn graphed the points listed below.
(0, 0) (1, -1) (3, 0) (4, 4) (4, 5) (5, 4) (6, -2)
Which pair of points could be used to show that the points Shawn graphed do not represent a function?
A. (4, 4) and (4, 5)
B. (4, 4) and (5, 4)
C. (0, 0) and (3, 0)
D. (1, -1) and (6, -2)
Answer: A. (4, 4) and (4, 5)
Step-by-step explanation:
The same x value maps onto more than one y value.
A partition of a positive integer $n$ is any way of writing $n$ as a sum of one or more positive integers, in which we don't care about the order of the numbers in the sum. For example, the number 4 can be written as a sum of one or more positive integers (where we don't care about the order of the numbers in the sum) in exactly five ways: \[4,\; 3 1,\; 2 2,\; 2 1 1,\; 1 1 1 1.\] So 4 has five partitions. What is the number of partitions of the number 7
There are 15 partitions for the number 7. Where the partitions are nothing but writing an integer in different ways as a sum of two or more integers.
What is a partition?A partition of a positive integer is the way of writing the integer as a sum of one or more positive integers. Where the order of the integers in the sum is not considered.
What is the number of partitions of the number 7?There are 15 partitions. They are as follows:
71+62+53+41+1+51+2+41+3+32+2+31+1+1+41+1+2+31+2+2+21+1+1+1+31+1+1+2+21+1+1+1+1+21+1+1+1+1+1+1These are the 15 possible partitions of the number 7.
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Using the quadratic formula, solve the
equation below to find the two possible
values of t.
6x^2-35=-11x
Give each value as a fraction in its
simplest form.
Answer:
x= 19/12, -41/12
Step-by-step explanation:
I'm guessing x is "t".
The quadratic formula is x=(-b+-sqrtb^2-4ac)/2a I know that this is hard to read sorry!
Plug in a, b, and c.
Oh yeah, first convert it to the form Ax^2+bx+c
so 6x^2-35=-11x
6x^2+11x-35=0
(-11+-sqrt11^2-(-4*6*35))/2*6
Simply: (-11+-sqrt 121+840)/12
(-11+-sqrt961)/12
(-11+-31)/12
-11+30=19
-11-30=-41
x= 19/12, -41/12
Do the points (1,2) , (51,27) and (91,48) lie on a straight line? give reason for your answer
Answer:
No. They cannon be on the same straight line.
Step-by-step explanation:
As explained in the attached graphic, the slopes are slightly different between the three points.
Jenny made $120 for 8 hours of work. How much would jenny make for 40 hours of work? Use a proportion to show your work in the space provided.
Answer:
$600
Step-by-step explanation:
For 8 hours she makes $120
For 1 hour she makes $120÷8 = $15
For 40 hours she makes $15 × 40 = $600
Our final answer is $600
Hope this helped and have a good day
I NEED HELP NOW PLSSS!!! Daredevil Robbie Knievel is building a ramp to attempt to jump his motorcycle over 35 school buses. The surface of the ramp will be 40 feet long and the ramp must stand 11 feet tall in order to clear the buses. What angle will the ramp form with the ground?
A. 7°
B. 15°
C. 16°
D. 74°
The angle that the ramp makes with the ground is 16 degrees.
What angle does the ramp make with ground?We can see that the ramp is and its support now constitutes a right angled triangle.
Thus, the hypotenuse of the triangle is 40feet while the opposite of the angle is 11 feet.
The angle made with the ground is;
sin x = 11/40
x = sin-1(11/40)
x = 16 degrees
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You’re taking a 33 question multiple choice test. Each question has 4 choices. Clueless on 1 question, you decide to guess. What’s the chance you’ll get it right?
Let theta be an angle in quadrant iv such as sin theta = -5/8. find the exact value of sec theta and cot theta
Using a trigonometric identity, it is found that the secant and the cotangent of the angles are given as follows:
[tex]\sec{\theta} = \frac{8\sqrt{39}}{39}[/tex][tex]\cot{\theta} = -\frac{\sqrt{39}}{5}[/tex]Which trigonometric identity relates the sine and the cosine of an angle?The following identity is used, considering an angle [tex]\theta[/tex].
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
In this problem we are given the sine, then the cosine can be found as follows:
[tex]\left(-frac{5}{8}\right)^2 + \cos^2{\theta} = 1[/tex]
[tex]\cos^2{\theta} = 1 - \frac{25}{64}[/tex]
[tex]\cos^2{\theta} = \frac{39}{64}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{39}{64}}[/tex]
In the fourth quadrant, the cosine is positive, hence:
[tex]\cos{\theta} = \frac{\sqrt{39}}{8}[/tex].
What is the secant of an angle?The secant of an angle [tex]\theta[/tex] is one divided by the cosine of the angle, hence:
[tex]\sec{\theta} = \frac{1}{\cos{\theta}} = \frac{1}{\frac{\sqrt{39}}{8}} = \frac{8}{\sqrt{39}} \times \frac{\sqrt{39}}{\sqrt{39}} = \frac{8\sqrt{39}}{39}[/tex]
What is the cotangent of an angle?The cotangent of an angle [tex]\theta[/tex] is the cosine divided by the sine of the angle, hence:
[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}} = \frac{\frac{\sqrt{39}}{8}}{-\frac{5}{8}} = -\frac{\sqrt{39}}{5}[/tex]
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