The 95% confidence interval (in minutes) for the population mean is of:
(2.55, 3.83).
What is a t-distribution confidence interval?The bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the parameters are described as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The distribution is used when the standard deviation of the population is not known, only for the sample.
In the context of this problem, the values of the parameters are given as follows:
[tex]\overline{x} = 3.19, s = 0.77, n = 8[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 8 - 1 = 63 df, is t = 2.3646.
Then the lower bound of the confidence interval is calculated as follows:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 3.19 - 2.3646\frac{0.77}{\sqrt{8}} = 2.55[/tex]
The upper bound is calculated as follows:
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 3.19 + 2.3646\frac{0.77}{\sqrt{8}} = 3.83[/tex]
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A growing number of thieves are using keylogging programs to steal passwords and other personal information from Internet users. The number of keyloggingprograms reported grew approximately exponentially from 0.3 thousand programs in 2001 to 11.0 thousand programs in 2008. Predict the number of keyloggingprograms that will be reported in 2013
Exponential growth (EG):
2001 = 0.3
2008 = 11
2013 = ?
[tex]n\text{ = }a\times b^t[/tex]a = initial amount = 0.3
b= growth factor = ?
t = period = 7
n = 11
[tex]\begin{gathered} 11=0.3\times b^7 \\ b^7=\frac{11}{0.3} \\ b\text{ = }\sqrt[7]{\frac{11}{0.3}} \\ b=1.67 \end{gathered}[/tex]b = 1.67
Solving the number of keylogging programs that will be reported in 2013:
[tex]\begin{gathered} n\text{ = }0.3\times1.67^{12} \\ n=144.12 \end{gathered}[/tex]Determine the perimeter of this shape. Use 3.14 for pi. the numbers are 12m and 15 m
We are asked to find the perimeter of the figure. To do that we will add the perimeters of the semi-circle and the rectangle.
To determine the perimeter of the semi-circle we will use the following formula:
[tex]P_{c\text{ }}=\frac{\pi D}{2}[/tex]The diameter is 12 m. Replacing in the formula we get:
[tex]P_c=\frac{\pi(12m)}{2}[/tex]Solving the operations:
[tex]P_c=\frac{3.14(12)}{2}=6.28m[/tex]Now we will find the perimeter of the rectangle by adding the length of all of its sides:
[tex]P_R=15m+12m+15m=42m[/tex]Now, the perimeter of the figure is the sum of the perimeters we found:
[tex]\begin{gathered} P=P_c+P_R \\ \end{gathered}[/tex]Replacing:
[tex]P=6.28m+42m=48.28m[/tex]Therefore, the perimeter of the figure is 48.28m
Describe the complement of the given event. 73% of nineteen year old males are at least 166 pounds
Solution
- The event is "73% of nineteen year old males are at least 166 pounds"
- The complement of this event is the set of all 19 year old males not in the event described above.
- These set of 19 year olds, must represent the remaining 27% of the population.
- Also, they would weigh less than 166 pounds.
- Thus, the complement of the event is:
"27% of nineteen year old males weigh less than 166 pounds"
h(x)= -1/2 (x+4)^2 +10Writing quadratics in standard form
`Answer:
h(x) = -x^2/2 - 4x + 32
Explanation:
The standard form of a quadratic equation is expresssed as
ax^2 + bx+c
Writing the given equation h(x)= -1/2 (x+4)^2 +10 in stabdard form will give;
h(x)= -1/2 (x+4)^2 +10
h(x)= -1/2 (x^2+8x+16)+40
h(x)= -x^2/2 - 4x - 8 + 40
h(x) = -x^2/2 - 4x + 32
Hence the equation in standard form is expressed as h(x) = -x^2/2 - 4x + 32
if the author sells x Books per day his profit will be : J(X)= (-0.001x^2)+3x-1800Find the max profit per dayFind the amount of books the author must sell for the most profit
The given function in a quadratic function in standard form where
a = -0.001, b = 3, and c = -1800
It is a parabola that is facing downwards, therefore, the vertex of this parabola, (x,y) is the maximum of the function where
x is the amount of books that the author must sell for the most profit, and
y is the max profit per day.
We can find the vertex using
[tex]x=\frac{-b}{2a}[/tex]Substitute the following values, and we get
[tex]\begin{gathered} x=\frac{-b}{2a} \\ x=\frac{-3}{2(-0.001)} \\ x=\frac{-3}{-0.002} \\ x=1500 \end{gathered}[/tex]Now that we have x, plug it in the original function to solve for y
[tex]\begin{gathered} J(x)=\mleft(-0.001x^2\mright)+3x-1800 \\ J(1500)=-0.001(1500)^2_{}+3(1500)-1800 \\ J(1500)=-2250+4500-1800 \\ J(1500)=450 \end{gathered}[/tex]We have determine that the vertex of the function is at (1500,450). We can now conclude that
The max profit per day is $450.
The amount of of books the author must sell for the most profit is 1500 books.
I would like to learn the long multiplication so I can teach my fifth grader this math problem
352x20=
Answer: 7040
Step-by-step explanation:
1
352
x20
——-
000
7040
+
———
7040
Find the equation of the line that is parallel to the line y = -2x +3 and passes through the point (5,4).y = − 1/2x + 6.5y = 2x - 14y = -2x + 14y = 1/2x + 1.5
lets remember how to find the equation of a parallel line
two lines are parallel if they don"t intersect, that means they slopes are the same
y=-2x+3
slope as we see is m=-2
the other line has to pass through point (5,4)
y-y1=m(x-x1)
y-4=-2(x-5)
we solve the equation
y= 4-2x+10
y= -2x+14
i will send you a picture
green line is y=-2x+14
solving right triangle find the missing side. round to the nearest tenth
Apply trigonometric functions:
Cos a = adjacent side / hypotenuse
Where:
a = angle = 59°
adjacent side = 34
Hypotenuse = x
Replacing:
Cos 59 = 34 / x
Solve for x:
x = 34 / cos 59
x = 66
On the desmos app can you have more standard forms or only one?
Answer: I am pretty sure you can only have one.
Step-by-step explanation:
What are all the factors of 54?
To find the factors of a number, we can look for factors to divide it by subsequently.
It is easier to start with lower factors.
Let's start by "2".
Since "54" is even, it is divisable by "2":
[tex]\frac{54}{2}=27[/tex]So "2" is one of the factors.
Now, we have got 27. It is not even anymore, but it is divisable by "3":
[tex]\frac{27}{3}=9[/tex]So "3" is another factor.
Now we have got "9" and it is also divisable by "3":
[tex]\frac{9}{3}=3[/tex]So there is another "3" factor.
And since we have got now another "3", we know it is divisable by "3":
[tex]\frac{3}{3}=1[/tex]Now we have got to "1", so we found all the prime factors:
[tex]54=2\cdot3\cdot3\cdot3[/tex]Now,, we need to combine them to find all possible combinations.
We will start from low to high.
"1" is always a factor.
There is "2" there, so it is also a factor.
Then we have "3" as another factor.
There is no need to combine "1" with another factor, so we will start b combining 2 and 3:
[tex]2\cdot3=6[/tex]So, "6" is another factor.
We can combine 3 with 3:
[tex]3\cdot3=9[/tex]"9" is another factor.
Now we start combining three of them:
[tex]\begin{gathered} 2\cdot3\cdot3=6\cdot3=18 \\ 3\cdot3\cdot3=9\cdot3=27 \end{gathered}[/tex]So, "18" and "27" are factors.
And now we combine 4 of them, but this is get us back to "54" which is the last factor.
So, the factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54.
Answer:
Step-by-step explanation:
1 × 54 = 54, (1, 54) is a pair factor of 54.
2 × 27 = 54, (2, 27) is a pair factor of 54
3 × 18 = 54, (3, 18) is a pair factor of 54
6 × 9 = 54, (6, 9) is a pair factor of 54
Therefore, the positive pair factors are (1, 54), (2, 27),(3, 18) and (6, 9).
Rewrite the equation in Ax+By=C form.Use integers for A, B, and C.y-4=-5(x+1)
The given equation is
[tex]y-4=5(x+1)[/tex]To write the equation in standard form, first, we have to use the distributive property.
[tex]y-4=5x+5[/tex]Now, we subtract 5x and 5 on both sides.
[tex]\begin{gathered} y-4-5x-5=5x+5-5x-5 \\ -5x+y-9=0 \end{gathered}[/tex]Now, we add 9 on each side
[tex]\begin{gathered} -5x+y-9+9=0+9 \\ -5x+y=9 \end{gathered}[/tex]Therefore, the standard form of the given equation is[tex]-5x+y=9[/tex]Where A = -5, B = 1, and C = 9.3. Suppose an investment of $5000 doubles every 12 years. How much is the investment worth after: 24 years?
Money = $5000
time = 12 years
investment after 24 years
If the investment doubles every 12 years after 24 years the total amount of money will be $10000.0
8. Three consecutive even numbers have a sum where one half of that sum is between 90 and 105. a. Write an inequality to find the three numbers. Let n represent the smallest even number. b. Solve the inequality. a. (n+(n+2)+(n+4) < −90 or −(n+(n+2)+(n+4)) > 105 b. n-62 or n > 68 a. 90 < 2(n + (n + 2) + (n + 4)) < 105 b. 13 ≤ n ≤ 15.5 a. 90 < ¹² (n + (n +2)+(n+ 4))
Given:
Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.
Required:
To write an inequality to find the three numbers and to solve the inequality.
Explanation:
(a)
Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.
[tex]90<\frac{1}{2}(n+(n+2)+(n+4))<105[/tex](b)
[tex]undefined[/tex]12x÷4yif x=-8 and y=3
To solve 12x÷4y, first, let's evaluate the products on both sides of the ÷ symbol, we know that x = -8, then we have:
[tex]12\times(-8)=-96[/tex]We have -96 on the left side of the ÷ symbol.
We know that y = 3, then, on the right side, we have:
[tex]4\times3=12[/tex]Then, we have 12 on the right side of the ÷ symbol, now the expression looks like this:
-96 ÷ 12. what we have to do is to divide -96 by 12, then we get:
[tex]-96\text{ }\div12=\frac{-96}{12}=-8[/tex]Then, the answer is 8
find the slop of the line passing through the points (1,-1) and (-1,1)
Answer:
I think its done this way. But I don't know if the answer is correct.
a scuba diver descended 19 5/12 feet blow sea level. Then he descended another 3 3/5 feet. Which of the following is true about the scuba diver after both descents?
The position of the scuba diver is 23 1/60 feet.
How to calculate the fraction?From the information, the scuba diver descended 19 5/12 feet blow sea level and then he descended another 3 3/5 feet.
The position of the diver will be. the addition of the fraction for descending. This will be:
= 19 5/12 + 3 3/5
= 19 25/60 + 3 36/60
= 22 61/60
= 23 1/60
Note that your information is incomplete as the question was answered based on information given.
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Which of the following tables shows a uniform probability model?
The answer is the third choice
Where all probability are equal
NO LINKS!! Please help me with this probability question 2a
====================================================
Work Shown:
A = he eats pizza
B = he drinks cola
P(A) = 0.40
P(B) = 0.60
P(A and B) = 0.30
Then apply the conditional probability formula.
P(A given B) = P(A and B)/P(B)
P(A given B) = 0.30/0.60
P(A given B) = 0.5 exactly
P(A given B) = 50%
If we know for certain he drinks cola, then there's a 50% chance of him eating pizza.
Find the exact value of sin,cos, and tan for the angle while simplifying all roots.
We can solve these values using the next triangle:
First, we need to label the sides using the angle of 30 degrees.
- The largest side is always the hypotenuse, h = 1.
- The opposite side is opposite to the angle, opp = 1/2.
- The adjacent side is between the angle of 30 degrees and the right angle,
adj = √3/2.
Now, we can solve the trigonometric expressions:
For sin:
sin θ = opposite side / hypotenuse
sin 30 = (1/2) / 1
sin 30 = 1/2
For cos:
cos θ = adjacent side / hypotenuse
cos 30 = (√3/2)/1
cos 30 =√3/2
For tan:
tan θ = opposite side / adjacent side
tan 30 =(1/2) / (√3/2)
Simplify the fractions:
tan 30 = 1/√3
Tony is a hiring director at a large tech company in Chicago, and he gets hundreds of resumes each week. How long does Tony MOST likely spend looking over each resume?30 seconds50 seconds3 minutes30 minutes
The time needed to look over the resumes depends on how many papers is the resume
But it is convenient to have a speed looking on each one
so, the answe will be 50 seconds
how many inches are in 20 centimeters?
We know that an inch is equivalent to 2.54 centimeters, then if we want to know how many inches are in a centimeters we do this:
[tex]a\times\frac{1inch}{2.54\operatorname{cm}}[/tex]In this case, we have 20 centimeters, then replacing a by 20 we find the equivalent inches to 20 like this:
[tex]20\text{cm}\times\frac{1inch}{2.54\operatorname{cm}}\approx7.87\text{inches}[/tex]find the first second and third derivatives of the function
Given the function
[tex]f(x)=\frac{8}{5}x-9[/tex]Finding the derivative we have
[tex]f^{^{\prime}}(x)=\frac{8}{5}[/tex]Also
[tex]f^{\doubleprime}(x)=0^{}[/tex]Finally
[tex]f^{^{\doubleprime}^{\prime}}(x)=0[/tex]Write an equation of the line passing through the point (8,-3) that is parallel to the line y= -x -1. An equation of the line is
The equation of the line, in slope-intercept form, that is parallel to the line y = -x - 1 is: y = -x + 5.
How to Write the Equation of Parallel Lines?Parallel lines have equal slope value, "m". In slope-intercept form, the equation y = mx + b represents a line, where the slope is "m" and the y-intercept is "b".
The slope of y= -x -1 is -1. This means the line that is parallel to y= -x -1 will also have a slope that is equal to -1.
Substitute m = -1 and (x, y) = (8, -3) into y = mx + b to find the value of b:
-3 = -1(8) + b
-3 = -8 + b
-3 + 8 = b
5 = b
b = 5
Substitute b = 5 and m = -1 into y = mx + b to wrote the equation of the line that is parallel y = -x -1:
y = -x + 5
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what is the volume of a cube with sides 3 cm.be sure to include correct units with your answer
Answer:
27 cubic feet
Explanation:
The volume of a cube with side length L is given by
[tex]V=L^3[/tex]Now in our case, L = 3 ft; therefore, the volume is
[tex]V=3^3[/tex]which simplifies to give
[tex]\boxed{V=27\text{ ft}^3.}[/tex]which is our answer!
Hence, the volume of the cube with the side length of 3 cm is 27 cubic cm.
Solve the triangle: a = 25, C = 25, B = 25°. If it is not possible, say so.A=25*,b= 25, C = 250A=77.5*,b=10.8, C = 77.5eA=77.5', b = 24.1, C = 77.5This triangle is not solvable.
We will have the following:
First:
Since we have that sides a & c have the same length by theorem angles A & C are equal, so the following is true:
[tex]A+B+C=180\Rightarrow2A+B=180[/tex][tex]\Rightarrow2A=180-25\Rightarrow A=77.5[/tex]so, angles A & C have a measure of 77.5°.
*Second: We determine the measurement f the segment b, that is:
[tex]\frac{b}{\sin(25)}=\frac{25}{\sin(77.5)}\Rightarrow b=\frac{25\sin (25)}{\sin (77.5)}[/tex][tex]\Rightarrow b=10.8219807\Rightarrow b\approx10.8[/tex]So we will have that the measurements are:
A = 77.5°
b = 10.8
C = 77.5°
[Option B]
Mai must choose a number between 49 and 95 that is a multiple of 3, 8, and 12. Write all the numbers that she could choose. If there is more than one number, seperate them with commas.
Answer:
72
Explanation:
To choose a number between 49 and 95 that is a multiple of 3, 8, and 12, the first step is to find the lowest common multiple of the three numbers.
Begin by expressing them as a product of their prime factors:
[tex]\begin{gathered} 3=3 \\ 8=2^3 \\ 12=2^2\times3 \\ \text{LCM}=2^3\times3=24 \end{gathered}[/tex]Next, we find multiples of the L.C.M in between 49 and 95.
[tex]\begin{gathered} 24\times2=48 \\ 24\times3=72 \\ 24\times4=96 \end{gathered}[/tex]The only number that she could choose is 72.
Laura needs summer blouses. She bought 1 blouseand 2 sweaters. How much did she spend? Did shebuy clothes that matched her summer needs?
Given:-
Cost of blouse is $27.50
Cost of sweater is $34.99
To find the cost if laura bought :-
So since laura bought one blouse and two sweaters, we get
[tex]27.50+2(34.99)=97.48[/tex]So the cost is $97.48 and she bought the cloths of her summer needs.
6. Express the given function h as a composition of two functions f and g
such that H(x) = (fog)(x).
a) H(x) = |3x +2|
b) H(x) = √√√√5x +4
The given function can be represented f(x) and g(x) as below
What are functions?
A function from X to Y is an assign of each constituent of Y to each variable of X. The set X is known as the function's scope, while the set Y is known as the function's image domain. The notation f: XY denotes a function, its domain, and its codomain, and the value of a function f at an element x of X, indicated by f(x), is known as the image of x under f, or the value of f applied to the argument x. When defining a function, the domains and codomain are not often explicitly specified, and without performing some (complicated) calculation, one may only know that perhaps the domain is included in a larger package.
The functions are
(a) f(x) = 3x+2 and g(x) = |x|
so, H(x) = f(g(x)) = |3x+2|
(b) f(x) = 5x+4 and g(x) = √√√√x
so, H(x) = f(g(x)) = √√√√5x+4
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Write the decimal as a quotient of two integers in reduced form.
0.513
The given decimal can be written as a quotient of 513/1000.
What is quotient?
In maths, the result of dividing a number by any divisor is known as the quotient. It refers to how many times the dividend contains the divisor. The statement of division, which identifies the dividend, quotient, and divisor, is shown in the accompanying figure. The dividend 12 contains the divisor 2 six times. The quotient is always less than the dividend, whether it is larger or smaller than the divisor.
we can write the decimal given 0.513 as a answer of of 513 divided by 1000.
I.e.
[tex]0.513 = \frac{513}{1000}[/tex]
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Coffee Shop PricesCup CostSmall $2Regular $4Large $5David and Jon are placing coffee orders for their friends.David orders 10 large cups of coffee. Jon orders 4 fewer large cups than David. Jon pays for his orders with a $50 bill.Jon wants to know how much he spent on coffee.What is a good plan to find the amount Jon spent on coffee?3rd grade student
Step 1:
Cost of large cup = $5
Step 2:
Number of large David orders = 10 cups
A good plan to find the amount Jon spent is to find the number of large cups Jon orders from the number of large cups David orders.
Jon order 4 fewer large cups
Therefore,
Jon order = 6 cups
Step 3:
A good plan to find the amount Jon spent is to find the number of large cups Jon orders from the number of large cups David orders.
The amount Jon spent on coffee = 6 x $5 = $30
