Answer:
1000 * 10th sqrt of 10 or about 12589 times more powerful?
Step-by-step explanation:
Answer:v 31623
Step-by-step explanation:
2. Suppose the 90% confidence interval for the mean SAT scores of applicants at a business college is given by [1690, 1810]. This confidence interval uses the sample mean and sample standard deviation based on 25 observations. What are the sample mean and sample standard deviation used for this interval
Answer:
The sample mean used for this interval is 1750.
The sample standard deviation used for this interval was of 175.34
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The margin of error is the subtraction of these two bounds divided by two.
In this question:
Lower bound: 1690
Upper bound: 1810
Sample mean
[tex]\frac{1690 + 1810}{2} = 1750[/tex]
The sample mean used for this interval is 1750.
Sample standard deviation:
The first step is finding the margin of error:
[tex]M = \frac{1810 - 1690}{2} = 60[/tex]
Now we have to develop the problem a bit.
We want the sample standard deviation, so we use the T-distribution.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 25 - 1 = 24
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.711
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
We have that: [tex]M = 60, T = 1.711, n = 25[/tex]
We have to find s
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
[tex]60 = 1.711\frac{s}{\sqrt{25}}[/tex]
[tex]1.711s = 60*5[/tex]
[tex]s = \frac{60*5}{1.711}[/tex]
[tex]s = 175.34[/tex]
The sample standard deviation used for this interval was of 175.34
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = ln(x), [1, 5]
Answer:
Yes, the function satisfies the hypothesis of the Mean Value Theorem on the interval [1,5]
Step-by-step explanation:
We are given that a function
[tex]f(x)=ln(x)[/tex]
Interval [1,5]
The given function is defined on this interval.
Hypothesis of Mean Value Theorem:
(1) Function is continuous on interval [a,b]
(2)Function is defined on interval (a,b)
From the graph we can see that
The function is continuous on [1,5] and differentiable at(1,5).
Hence, the function satisfies the hypothesis of the Mean Value Theorem.
A concession-stand manager buys bottles of water and soda to sell at a football game. The manager needs to buy a total of 4,500 drinks and have 25% more water than soda. Let w be the number of bottles of water and let s be the number of bottles of soda. Create a system of equations for w in terms of s that the manager could use to find out how many bottles of water and soda to bu
Answer: The equations are
w + s = 4500
2.25s = 4500
Step-by-step explanation:
Let w represent the number of bottles of water that the football manager bought.
Let s represent the number of bottles of soda that the football manager bought.
The manager needs to buy a total of 4,500 drinks. This means that
w + s = 4500
He also needs to have 25% more water than soda.
25% of soda = 25/100 × s = 0.25s
25% more of water than soda = s + 0.25s = 1.25s
The equation would be
1.25s + s = 4500
2.25s = 4500
can someone help me with this please?!?
Answer:
The answer is 60cm^2.
hope it helps..
Consider the accompanying matrix as the augmented matrix of a linear system. State in words the next two elementary row operations that should be performed in the process of solving the system.
(1 -4 4 0 -2
0 2 -6 0 5
0 0 1 2 - 4
0 0 4 5 -1]
(Type an integer or a simplified fraction)
A. Replace row 4 by its sum with - 4 times row 3.
(Type an integer or a simplified fraction)
B. Replace row 2 by its sum with times row 4.
(Type an integer or a simplified fraction.)
C. Interchange row 3 and row 2.
Answer:
The correct option is (A)
A. Replace row 4 by its sum with - 4 times row 3.
[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&0&-3&15\end{array}\right][/tex]
w = 8
x = 17/2
y = 6
z = -5
Step-by-step explanation:
The given matrix is
[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&4&5&-1\end{array}\right][/tex]
To solve this matrix we need to create a zero at the 4th row and 3rd column which is 4 at the moment.
Multiply 3rd row by -4 and add it to the 4th row.
Mathematically,
[tex]R_4 = R_4 - 4R_3[/tex]
So the correct option is (A)
A. Replace row 4 by its sum with - 4 times row 3.
So the matrix becomes,
[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&0&-3&15\end{array}\right][/tex]
Now the matrix may be solved by back substitution method.
Bonus:
The solution is given by
Eq. 1
-3z = 15
z = -15/3
z = -5
Eq. 2
y + 2z = -4
y + 2(-5) = -4
y - 10 = -4
y = -4 + 10
y = 6
Eq. 3
2x - 6y + 0z = 5
2x - 6(6) = 5
2x - 12 = 5
2x = 12 + 5
2x = 17
x = 17/2
Eq. 4
w - 4x + 4y + 0z = -2
w - 4(17/2) + 4(6) = -2
w - 34 + 24 = -2
w - 10 = -2
w = -2 + 10
w = 8
Please help asap!!!!!!!
Answer:Yes indeed!
Step-by-step explanation:
Your right!
In a recent study of 42 eighth graders, the mean number of hours per week that they watched television was 19.6. Assume the population standard deviation is 5.8 hours. Find the 98% confidence interval for the population mean.
a. (17.5, 21.7)
b. (14.1, 23.2)
c. (18.3, 20.9)
d. (19.1, 20.4)
Answer:
[tex]19.6-2.42\frac{5.8}{\sqrt{42}}=17.43[/tex]
[tex]19.6+2.42\frac{5.8}{\sqrt{42}}=21.77[/tex]
And the best option for this case would be:
a. (17.5, 21.7)
Step-by-step explanation:
Information given
[tex]\bar X= 19.6[/tex] represent the sample mean
[tex]\mu[/tex] population mean
[tex]\sigma= 5.8[/tex] represent the population deviation
n=42 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom, given by:
[tex]df=n-1=42-1=41[/tex]
Since the Confidence is 0.98 or 98%, the significance would be [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.1[/tex], and the critical value would be [tex]t_{\alpha/2}=2.42[/tex]
Replacing we got:
[tex]19.6-2.42\frac{5.8}{\sqrt{42}}=17.43[/tex]
[tex]19.6+2.42\frac{5.8}{\sqrt{42}}=21.77[/tex]
And the best option for this case would be:
a. (17.5, 21.7)
Answer:
The 98% confidence interval for the population mean is between 17.5 hours and 21.7 hours.
At work, Brett must check and record the internal temperature of the freezer on an hourly basis. When working properly, the temperature should remain constant over time. What word describes the slope of a line showing the temperature of the freezer as a function of time in hours when the freezer is working properly?
a.positive
b.zero
b.negative
c.undefined
Answer:
B. zero
Step-by-step explanation:
If the temperature is supposed to remain constant over time (the same) when working properly, then this means that there is no increase or decrease over time.
If there were a line to represent this, then it would be a straight line with a slope of 0 because the temperature would remain the same.
The valve was tested on 250 engines and the mean pressure was 7.3 pounds/square inch (psi). Assume the population standard deviation is 0.8. The engineer designed the valve such that it would produce a mean pressure of 7.2 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answe
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 7.2
For the alternative hypothesis,
H1: µ ≠ 7.2
This is a two tailed test.
Since the population standard deviation is given, the test statistic would be the z score determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 7.2
x = 7.3
σ = 0.8
n = 250
z = (7.3 - 7.2)/(0.8/√250) = 1.976
Test statistic is 1.976
Follow the properties of the equality given for the steps to solve the following equation:
-3(x-4)+5=-x-3
(answers and steps in photo)
Answer:
Step-by-step explanation:
-3x+12+5= -x-3 -3x+17 = -x-317 = 2x-320 =2xx=10how much would $100 invested at 6% interest compounded monthly be worth after 20 years? Round your answer to the nearest cent a(t)=p(1+r/n)^nt
Answer:
Amount after 12 years is $205.42
Step-by-step explanation:
Fibal amount a is not given and to be found
Principal amount p = $100
Rate r = 6% ° 0.06
Years t = 20
Number if times computed n = 20*12
n = 240
a(t)=p(1+r/n)^nt
a = 100(1+0.06/240)^(240*12)
a = 100(1+0.00025)^(2880)
a= 100(1.00025)^2880
a= 100(2.054248)
a= 205.4248
To the nearest cent
a =$ 205.42
Amount after 12 years is $205.42
Suppose you pick 4 cards randomly from a well-shuffled standard deck of 52 playing cards. The probability that you draw the 2, 4, 6, and 8 of spades in that order is
Answer: 1/52 x 1/51 x 1/50 x 1/49
= 1/ 6,497,400
Step-by-step explanation:
Identify the parts (include: terms, coefficients, variables and
constants) of the following expression and translate it into a
verbal expression:
2(3x - 2y) + 7
Answer:
x=9
Step-by-step explanation:
3x subtracted by 2y
is 1 then 1 multiplied by 2 is 2 then 7 + 2 is 9
PEMDAS
As part of a larger project to study the behavior of stressed-skin panels, a structural component being used extensively in North America, an article reported on various mechanical properties of Scotch pine lumber specimens. Data on the modulus of elasticity (MPa) obtained 1 minute after loading in a certain configuration and 4 weeks after loading for the same lumber specimens is presented here.
Observatio 1 min 4 Week Difference
1 16,620 9,110 1380
2 17,300 13,250 3370
3 15,480 14,720 2580
4 12,970 12,740 2740
5 17,260 10,120 2850
6 13,400 14,570 2690
7 13,900 11,220 2180
8 13,630 11,100 2800
9 13,260 11,420 2210
10 14,370 10,910 2350
11 11,700 12,110 2260
12 15,470 8,620 3080
13 17,840 12,590 2880
14 14,070 15,090 2750
15 14,760 10,550 3520
Required:
Calculate and interpret an upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus; first check the plausibility of any necessary assumptions. (Use α = 0.05. Round your answer to the nearest whole number.)
Answer:
The upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus is 2933.82.
Step-by-step explanation:
Compute the mean difference and standard deviation of the difference as follows:
[tex]\bar d=\frac{1}{n}\sum d_{i}=\frac{1}{15}\times [1380+3370+2580+...+3520]=2642.67\\\\S_{d}=\sqrt{\frac{1}{n-1}\sum (d_{i}-\bar d)^{2}}\\=\sqrt{\frac{1}{15-1}[(1380-2642.67)^{2}+(3370-2642.67)^{2}+...}=525.69[/tex]
The degrees of freedom is:
df = n - 1
= 15 - 1
= 14
Th critical value of t is:
[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, 14}=2.145[/tex]
*Use a t-table.
Compute the upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus as follows:
[tex]\text{Upper Confidence Bound}=\bar d+t_{\alpha/2, (n-1)}\cdot \frac{S_{d}}{\sqrt{n}}[/tex]
[tex]=2642.67+2.145\cdot \frac{525.69}{\sqrt{15}}\\\\=2642.67+291.15\\\\=2933.82[/tex]
Thus, the upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus is 2933.82.
The point ( -3, -5 ) is on the graph of a function. which equation must be true regarding the function?
Answer:-4-5
Step-by-step explanation:
Answer:
f(–3) = –5
Step-by-step explanation:
y and z are whole numbers y<70 z 60 work out the largest possible value of y and z
Answer:
a) 12
b) 129
Step-by-step explanation:
a)
[tex]w, x \in \mathbb{Z}_{\ge 0}[/tex]
[tex]w>50\\x<40[/tex]
For the smallest value of [tex]w-x[/tex], we gotta figure out the smallest value for w and the highest value for x.
[tex]w>50 \Rightarrow \text{ smallest value is } 51[/tex]
For [tex]x[/tex], once [tex]-(-x)=x[/tex], we conclude that [tex]x[/tex] cannot be negative and therefore, [tex]x=39[/tex].
[tex]51-39=12[/tex]
b)
[tex]y, z \in \mathbb{Z}_{\ge 0}[/tex]
[tex]y<70\\z\leq 60[/tex]
For the largest value of [tex]y+z[/tex], we gotta figure out the highest value for y and z.
[tex]y<70 \Rightarrow \text{ highest value is } 69[/tex]
[tex]z\leq 60 \Rightarrow \text{ highest value is } 60[/tex]
[tex]y+z=69+60=129[/tex]
Help me pls I need help
Answer:
C
Step-by-step explanation:
If two lines are parallel, their slopes are the same.
Since the slope of line l is 4/9, this means that the slope of line m must also be 4/9.
Answer:
C. 4/9
Step-by-step explanation:
Parallel lines have equal slopes.
Since line l and line m are parallel, then their slopes must be the same.
[tex]m_{l} =m_{m}[/tex]
We know that the slope of line l is 4/9
[tex]\frac{4}{9} = m_{m}[/tex]
Line l has a slope of 4/9, therefore line m must also have a slope of 4/9.
The correct answer is C. 4/9
In a lecture of 100 students, there are 29 women and 23 men. Out of these students, 4 are teachers and 24 are either men or teachers. Find the number of women teachers attending the lecture.
Answer:
1 woman Teacher
Step-by-step explanation:
We proceed as follows;
Let W and M represent the set of women and men respectively , and T represent teachers
from the information given in the question we have
n(W)=29
n(M)=23
n(T)=4
n(M U T)=24
Mathematically;
n(MUT)=n(M)+n(T)-n(MnT)
24=23+4-n(Mn T)
n(MnT)=3
that is number of men teachers is 3,
so out of 4 teachers there are 3 men ,
and remaining 1 is the women teacher .
so the number of women teachers attending the lecture is 1
Can somebody please help me with this question?
Answer: 6x^2
Step-by-step explanation:
The area of a triangle is 1/2bh
Thus, simply multiply 2x*3x = 6x^2
Hope it helps <3
Answer:
[tex]3 {x}^{2} [/tex]Solution,
Base(b)= 3x
Height(h) = 2x
Now,
Finding the area of triangle:
[tex] \frac{1}{2} \times b \times h[/tex]
[tex] \frac{1}{2} \times 3x \times 2x[/tex]
[tex] \frac{1}{2} \times 6 {x}^{2} [/tex]
[tex]3 {x}^{2} [/tex]
Hope this helps....
Good luck on your assignment....
pls help help help hepl
Answer:
C
Step-by-step explanation:
undefined slope means tat the denominator=0 in the equation
m=y2-y1/x2-x1
A: m=-1-1/1+1=-2
B;2-2/2+2=0
C: 3+3/-3+3 = 6/0 undefined
D: 4+4/4+4=1
The voltage in a circuit is the product of two factors, the resistance and the current. If the voltage is 6ir + 15i + 8r+20, find the expressions for the current and resistance
Answer:
resistance: (2r +5)current: (3i +4)Step-by-step explanation:
The factors of the given expression are ...
6ir +15i +8r +20 = (3i +4)(2r +5)
Which factor is current and which is resistance is not clear. Usually, resistance is referred to using the variable r, so we suppose the expressions are supposed to be ...
resistance: (2r +5)
current: (3i +4)
What is the greatest common factor of 36 and 44?
Answer:
GCF - 4
Step-by-step explanation:
36 - 1, 2, 3, 4, 6, 9, 12, 18, 36
44 - 1, 2, 4, 11, 44
Hope this helps! :)
The sum of Joe's and Sheila's ages is 115. Fourteen years ago, Joe was twice as old as Sheila. How old is Sheila now?
Answer: Sheila today = [tex]46\dfrac{1}{3}[/tex] yrs old
Step-by-step explanation:
J + S = 115 v⇒ J = 115 - S
Current Ages Ages 14 years ago
Joe (J) = 115 - S J - 14 = 2(S - 14)
Sheila (S) = S
Substitute J = 115 - S into the "14 years ago" equation
J - 14 = 2(S - 14)
(115 - S) - 14 = 2(S - 14)
111 -S = 2S - 28
111 = 3S - 28
139 = 3S
46 [tex]\frac{1}{3}[/tex] = S
It is odd that the result was not an integer. I wonder if you meant to type "Joe was twice as old as Sheila is today. That would change the equation to:
J - 14 = 2S
111 - S = 2S
111 = 3S
37 = S
Need Help With This
Answer/Step-by-step explanation:
Let x = 4 (you and 3 friends)
Ticket cost per head = $5.50
Drink cost per head = $2.50
Popcorn cost per head = $4.00
Expression representing total amount of money spent = $5.50(x) + $2.50(x) + $4.00(x)
Evaluate the expression by plugging in the value of x = 4
Total amount of money spent = $5.50(4) + $2.50(4) + $4.00(4)
= $22 + $10 + $16 = $48
Total amount of money spent = $48
Suppose you invest $ 2,000 at 45% Interest
compounded daily. F(t) represents value of investments
in t years
A) Find equation For F(+)
B) use equation to find how much account will
be worth in 30 years round to nearest cent
C) How much you should invest now in
order to have 14.000 in 9 years round to the nearest cent
Answer:
You will have $29,000 in 30 years, and you need to start with about $2,772.28 to make $14,000 in 9 years
Step-by-step explanation:
To find the total investment use the equation [tex]A = P(1 + rt)[/tex]
Where A equals total investment, P is your start investment, r is your rate, and t is time.
[tex]A=2,000(1+(0.45 * 30))[/tex]
[tex]A=2,000(1+13.5)[/tex]
[tex]A=2,000*14.5[/tex]
[tex]A=29,000[/tex]
To find the start investment use the equation [tex]P = A / (1 + rt)[/tex]
[tex]P=14,000/(1+(0.45*9))[/tex]
[tex]P=14,000/(1+4.05)[/tex]
[tex]P=14,000/5.05[/tex]
[tex]P=2,772.28[/tex]
What is the value of x?
Enter your answer in the box.
X=
Answer:
3
Step-by-step explanation:
Triangle ABC is an isosceles triangle, so
[tex]x^2+x^2=(6\sqrt{2} )^2\\2x^2=6^2*2\\x^2=6^2\\x=6.[/tex]
Triangle BCD is a notable triangle and the sides are
BD=x, CD=[tex]x\sqrt{3}[/tex],BC=2x=6
2x=6
x=3
The time to assemble the first unit on a production line is 8 hours. The learning rate is 0.81. Approximately how long will it take for the seventh unit to be assembled?
Answer:
4.428 hours
Step-by-step explanation:
If the learning rate is 0.81, the slope of the learning curve is:
[tex]b=\frac{ln(0.81)}{ln(2)} \\b=-0.304[/tex]
The time it takes to produce the n-th unit is:
[tex]T_n=T_1*n^b[/tex]
If T1 = 8 hours, the time required to produce the seventh unit will be:
[tex]T_n=8*7^{-0.304}\\T_n=4.428\ hours[/tex]
It will take roughly 4.428 hours.
divide 15 root 20 by 6 root 125
Answer:
15√20/6√125
=√20/√5
=2
Step-by-step explanation:
If x=3 then what is y the equation is 2x -y=5 if you have the answer lets d a t e I m f e m a l e. T a n g ie_man 18 snap without spaces.
Answer:
y = 1Step-by-step explanation:
Given the equation, 2x- y = 5, if x = 3, to get y we will simply substitute the value of x into the expression given as shown;
[tex]2x - y = 5\\\\Substituting \ x = 3\ into \ the \ equation\\\\2(3) - y = 5\\\\6 - y = 5\\\\subtracting\ 6\ from\ both\ sides\\\\6-6-y = 5- 6\\\\-y = -1\\\\multiplying\ both\ sides\ by \ -1\\-(-y) = -(-1)\\\\y = 1[/tex]
Hence, the value of y is 1
How do you write 0.0026 in scientific notation? ___× 10^____
Answer:
It's written as
[tex]2.6 \times {10}^{ - 3} [/tex]
Hope this helps you
Answer:
2.6 × 10⁻³
Step-by-step explanation:
To write a number in scientific notation, move the decimal to the right or left until you reach a number that is 1 or higher.
In the decimal 0.0026, the first number that is 1 or higher is 2.
0.0026 ⇒ 2.6
When trying to figure out the exponent, here are some things to keep in mind:
- when you move the decimal to the right, the exponent is negative
- when you move the decimal to the left, the exponent is positive
You moved the decimal to the right three places. So the exponent will be -3.
The result is 2.6 × 10⁻³.
Hope this helps. :)