Answer:
the first step is to subtract the 2W from each sides of the equal sides
Step-by-step explanation:
P=2L+2W
the first step is to subtract the 2W from each sides of the equal sides
P-2W=2L+2W-2W
P-2W=2L
To test H0: μ=100 versus H1:≠100, a simple random sample size of nequals=24 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d).(a) If x =104.2 and s=9.6, compute the test statistic.t= _ (Round to three decimal places as needed.)(b) If the researcher decides to test this hypothesis at the α=0.01 level of significance, determine the critical values.The critical values are __ .(c) Draw a t-distribution that depicts the critical region(s). Which of the following graphs shows the critical region(s) in thet-distribution?(d) Will the researcher reject the null hypothesis?
Answer:
a) Test statistic = 1.960
b) The critical values include -2.50 and 2.50.
The critical regions of rejection are thus
t < -2.50 or t > 2.50
c) The sketch of the curve is presented in the attached image to this solution. The shaded parents indicate the rejection regions.
d) The t-statistic obtained (1.96), lies within the acceptance region (-2.50 ≤ x ≤ 2.50), we fail to reject the null hypothesis.
Step-by-step explanation:
a) Test statistic is computed using the expression
t = (x - μ₀)/σₓ
x = Sample mean = 104.2
μ₀ = the standard we are comparing Against
σₓ = standard error of the mean = (σ/√n)
σ = 9.6
n = Sample size = 24
σₓ = (9.6/√24) =
t = (0.425 - 0.35) ÷ 0.07816
t = 1.9595917942 = 1.960
b) To obtain these critical values, we first find the degree of freedom
Degree of freedom = n - 1 = 24 - 1 = 23
The critical values for significance level of 0.01 and degree of freedom of 23 is given as
t(0.01, 23) = 2.50
So, since the test is two-tailled (we are testing in both directions; greater than or less than), the regions of rejection include
t < -2.50 and t > 2.50
c) since the test is two-tailled (we are testing in both directions; greater than or less than), the regions of rejection include
t < -2.50 and t > 2.50
The t-distribution curve is very similar to the normal distribution curve. The t-distribution curve is also a bell shaped curve, but it is heavier at the limits indicating that the t-distribution favours outliers more than the normal distribution.
The sketch of the curve is presented in the attached image with the shaded regions indicating the rejection region.
d) Since the t-statistic obtained (1.96), lies within the acceptance region (-2.50 ≤ x ≤ 2.50), we fail to reject the null hypothesis.
Hope this Helps!!!
a. What is a residual? b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? a. What is a residual?
Answer:
a. A residual is how far off a point is from the expected value. For example, if I were to estimate the weight of my Southeastern Lubber Grasshopper, I would say it's maybe 5 ounces. But, in reality, it might be 4 ounces. So, the residual would be the reality minus the prediction, or 4 - 5, or -1 ounce.
b. The regression line is the line of predicted values for the points in the scatterplot. It tries to predict the points and make all the points be on the line.
Hope this helps!
SOMEONE HELP! (b+3)(c-4)
Answer
[tex]bc - 4b + 3c - 12[/tex]
solution,
[tex](b + 3)(c - 4) \\ = b(c - 4) + 3(c - 4) \\ = bc - 4b + 3c - 12[/tex]
hope it helps..
Answer:
[tex]bc - 4b + 3c - 12[/tex] apply de disruptive property by multiplying each term of b+3 by each term of c -4
In the figure angle G measures 102° and angle B measures 30° what is the measurement of angle B
Answer:
I hope this helps
Step-by-step explanation:
AHH!! PLEASE HELP ME IM STUCK :(
Answer:
x = 6
Step-by-step explanation:
Compare the given formula to the equations shown in the attachment. First of all, you see that all of the numbers are scaled by a factor of 4. Removing that gives ...
[tex]r=\dfrac{6.6}{1+1.1\cos{\theta}}=\dfrac{1.1\cdot6}{1+1.1\cos{\theta}}[/tex]
This matches the formula for the hyperbola with e=1.1 and d=6, for a directrix of x = 6.
The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 95% of the lead to decay?
Answer:
[tex] N(t) =N_o (\frac{1}{2})^{\frac{t}{t_{1/2}}}[/tex]
Where [tex]t_{1/2}= 3.3 hr[/tex] represent the half life and the intial amount would be [tex] N_o = 1[/tex]
And we want to find the time in order to have a 95% of decay so we can set up the following equation:
[tex] 0.05 = 1 (0.5)^{t/3.3}[/tex]
If we apply natural log on both sides we got:
[tex] ln(0.05) = \frac{t}{3.3} ln (0.5)[/tex]
And solving for t we got:
[tex] t= 3.3 *\frac{ln(0.05)}{ln(0.5)}= 14.26[/tex]
So then would takes about 14.26 hours in order to have 95% of the lead to decay
Step-by-step explanation:
For this case we can define the variable of interest amount of Pb209 and for the half life would be given:
[tex] N(t) =N_o (\frac{1}{2})^{\frac{t}{t_{1/2}}}[/tex]
Where [tex]t_{1/2}= 3.3 hr[/tex] represent the half life and the intial amount would be [tex] N_o = 1[/tex]
And we want to find the time in order to have a 95% of decay so we can set up the following equation:
[tex] 0.05 = 1 (0.5)^{t/3.3}[/tex]
If we apply natural log on both sides we got:
[tex] ln(0.05) = \frac{t}{3.3} ln (0.5)[/tex]
And solving for t we got:
[tex] t= 3.3 *\frac{ln(0.05)}{ln(0.5)}= 14.26[/tex]
So then would takes about 14.26 hours in order to have 95% of the lead to decay
A certain group of test subjects had pulse rates with a mean of 80.9 beats per minute and a standard deviation of 10.7 beats per minute. Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. Is a pulse rate of 142.3 beats per minute significantly low or significantly high?
Answer:
We want to find the usual limits using the rule of thumb and for this case rule states that we have most of the values within 2 deviations from the mean so then we can find the usual limits like this:
[tex] \mu -2*\sigma = 80.9 -2*10.7= 59.5[/tex]
[tex] \mu +2*\sigma = 80.9 -2*10.7= 102.3[/tex]
And for this case a value of 142.3 is higher than the upper limti so then we can conclude that would be significantly high with the rule of thumb criteria
Step-by-step explanation:
For this case we have the follwing info given:
[tex] \mu = 80.9[/tex] represent the mean
[tex]\sigma = 10.7[/tex] represent the deviation
We want to find the usual limits using the rule of thumb and for this case rule states that we have most of the values within 2 deviations from the mean so then we can find the usual limits like this:
[tex] \mu -2*\sigma = 80.9 -2*10.7= 59.5[/tex]
[tex] \mu +2*\sigma = 80.9 -2*10.7= 102.3[/tex]
And for this case a value of 142.3 is higher than the upper limti so then we can conclude that would be significantly high with the rule of thumb criteria
The figure below is a rhombus. What is the answer?
Answer:
w = 28°
Step-by-step explanation:
• The opposite angles of a rhombus are congruent.
• The diagonals bisect the angles.
• All sides are congruent by definition.
Thus in the lower triangle w and y are congruent ( isosceles triangle ), thus
w = [tex]\frac{180-124}{2}[/tex] = [tex]\frac{56}{2}[/tex] = 28
That is w = 28°
The value of angle w in the given rhombus is equal to 28° if one angle is 124 degrees.
What is a rhombus?It is a 2 dimensional figure whose all sides are equal and whose diagonals bisect each other at 90 degrees.
How to calculate the value of an angle?We know that the opposite angles of a rhombus are congruent and the diagonals bisect the angles, and by the definition above all sides are equal. Thus w and y angles will be congruent as both triangles are isosceles triangles. thus the value of w=180-124/2=56/2
=28 degrees.
Hence the value of angle w in the given rhombus will be equal to 28°
Learn more about rhombus at https://brainly.com/question/20627264
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the distance around the edge of a circular pond is 88m. the radius in meters is ?
(a)88π
(b)176π
(c)88/π
(d)88/2π
Answer: (d) 88/ 2π
Step-by-step explanation:
Perimeter = 88m
Perimeter of a circle = 2πr
88 = 2π x r
r = 88 / 2π
Answer:
88/2π = r
Step-by-step explanation:
The circumference is 88 m
The circumference is given by
C = 2*pi*r
88 = 2 * pi *r
Divide each side by 2 pi
88 / 2pi = 2 * pi *r / 2 * pi
88 / 2 pi = r
The electric field in the xy-plane due to an infinite line of charge along the z-axis is a gradient field with a potential function
V(x,y)equals=c ln (ro/√ x²+y²)
where c > 0 is a constant and r0 is a reference distance at which the potential is assumed to be 0.
Required:
Find the components of the electric field in the x- and y-directions, where E(x,y) =∇V (x,y )
Answer:
c(x,y)/(x²+y²)
Step-by-step explanation:
Since E(x,y) = -∇V (x,y ) and V(x,y) =c ln (ro/√ x²+y²)
Let ro/√(x²+y²) = u and √(x²+y²) = v
dV/du = c/u = c√(x²+y²)/ro,
du/dv = -ro/(x²+y²) = -ro/² and dv/dx = x/√(x²+y²)
Using the chain rule,
So dV/dx = dV/du × du/dv × dv/dx
= c√(x²+y²)/ro × -ro/(x²+y²) × x/√(x²+y²)
dV/dx = -cx/(x²+y²)
- dV/dx = -(-cx/(x²+y²)) = cx/(x²+y²)
Also, dv/dy = y/√(x²+y²)
Using the chain rule
dV/dy = dV/du × du/dv × dv/dy
= c√(x²+y²)/ro × -ro/(x²+y²) × y/√(x²+y²)
dV/dy = -cy/(x²+y²)
- dV/dy = -(-cy/(x²+y²)) = cy/(x²+y²)
E(x,y) = -∇V (x,y )
= -(dV/dx)i + [-(dV/dy)]j
= [cx/(x²+y²)]i +[ cy/(x²+y²)]j
= c(x,y)/(x²+y²)
Need Assistance With This Problem
Answer:
not sure how to really answer this question.
Answer:
4.56, 4.65, 5.46, 5.64, 6.45, 6.54
Step-by-step explanation:
First we have to compare the first digits in each number as less is this digit as less is the number. So the least off all are
4.56 and 4.65
which of these two numbers is least ? Now we have to look to the 2-nd digits of these numbers:
they are 5 and 6 . 5<6 so 4.56<4.65
Lets select next numbers whicj first digit is 5. They are:
5.46 and 5.64. However the second digit of the number 5.64 -6 is bigger than the second digit of number 5.46 -4. That is why 5.46<5.64
Similarly 6.45< 6.54
convert 3days to minutes
Answer:
4320 minutes
Step-by-step explanation:
Recall,
1 day ---> 24 hours
but each hour has 60 minutes, hence 1 day can also be expressed:
1 day -----> 24 x 60 = 1440 minutes
3 days -----> 1440 min/day x 3 days = 4320 minutes
Answer: 4,320 minutes
Step-by-step explanation: 1 day = 1440 days. 1440 * 3 = 4,320 minutes
6. Create a probability distribution for a coin flipping game. That is, toss a coin at least 25 times and keep up with the number of heads and the number of tails. (8 points for each part) a. Compile your data into a probability distribution. Be sure to show that your distribution meets the properties for a probability distribution. Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Res. T H H H T H H H H T H H T H T H T T H T T H H T H H 15/25=3/5 T 10/25=2/5 3/5+2/5=1 Can anyone help with part a im lost!
Answer:
Event Probability
Heads [tex]\dfrac{3}{5}[/tex]
Tails [tex]\dfrac{2}{5}[/tex]
Step-by-step explanation:
If a coin is tossed 25 times, then from the given table it is clear that
Number of heads = 15
Number of tails = 10
Total number of tosses = 15+10 = 25
We know that,
[tex]Probability=\dfrac{\text{Favorable outcomes}}{\text{Total number of outcomes}}[/tex]
[tex]P(H)=\dfrac{\text{Number of heads}}{\text{Total number of tosses}}=\dfrac{15}{25}=\dfrac{3}{5}[/tex]
[tex]P(T)=\dfrac{\text{Number of tails}}{\text{Total number of tosses}}=\dfrac{10}{25}=\dfrac{2}{5}[/tex]
So, probability distribution table is
Event Probability
Heads [tex]\dfrac{3}{5}[/tex]
Tails [tex]\dfrac{2}{5}[/tex]
According to the properties for a probability distribution, the sum of probability of all events is 1.
Since,
[tex]\dfrac{3}{5}+\dfrac{2}{5}=\dfrac{3+2}{5}=\dfrac{5}{5}=1[/tex]
Hence, the distribution meets the properties for a probability distribution.
What is the sum?
StartFraction x Over x + 3 EndFraction + StartFraction 3 Over x + 3 EndFraction + 2 Over x + 3 EndFraction
Five-thirds
StartFraction x + 5 Over x + 3 EndFraction
StartFraction x + 5 Over 3 x + 27 EndFraction
StartFraction 6 x Over x + 3 EndFraction
Answer:
4 i think
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
If f(x) = x² + x - 4, evaluate f(2i).
Can anyone show a step by step process to get the answer?
Answer:
-6+2i
Step-by-step explanation:
f(2i)=2i^2+2i-4
2i^2 is -2 because i^2 is-1, times 2 is -2.
Therefore, the equation becomes -2+2i-4, leaving the answer of -6+2i.
Solve the two-step equation.-0.45x + 0.33 = -0.66What is the solution?x = -2.2x = -1.4x = 1.4x = 2.2f
Answer:
x = 2.2
Step-by-step explanation:
-0.45x + 0.33 = -0.66
Subtract .33 from each side
-0.45x + 0.33-.33 = -0.66-.33
-.45x = -.99
Divide each side by -.45
-.45x./-.45 = -.99/-.45
x = 11/5
x = 2.2
Which expression is the simplest form of -(x + 5) - 3(x + 2)?
Answer:
-4x -11
Step-by-step explanation:
-(x + 5) - 3(x + 2)
Distribute
-x -5 -3x -6
Combine like terms
-x-3x -5-6
-4x -11
Answer:
[tex] = - (4x + 11)[/tex]
Step-by-step explanation:
[tex]-(x + 5) - 3(x + 2) \\ -x - 5 - 3x - 6 \\ -x - 3x -5 - 6 \\ - 4x - 11 \\ = -(4x + 11)[/tex]
Fourth term of (x − 2)^5
Answer:
-80x²
Step-by-step explanation:
When you expand the binomial, you should get:
[tex]x^5-10x^4+40x^3-80x^2+80x-32[/tex]
To find the 4th term, you must put the expression in standard form (which it is already) and find the 4th by counting left to right. Once you do so you should see your answer as -80x².
Assume that adults have IQ scores that are normally distributed with a mean of 94 and a standard deviation of 14. Find the probability that a randomly selected adult has an IQ greater than 107.1. (Hint: Draw a graph.) To help visualize the area of interest, draw a standard normal curve. Label the given values for x and mu . x 94107.1
Answer:
0.6517
Step-by-step explanation:
z = (x - μ)/σ
Z= standard score
x= observed value
μ= mean of the sample
σ= standard deviation of the sample
z = (x - μ)/σ = (107.1 - 94 )/ 14 = 0.9357
probability that a randomly selected adult has an IQ greater than 107.1. = P(Z > 0.935) = 0.6517
NB: the value is 0.6517 is pulled from the z table which can be found at the back of most math text.
Mary invested $200 for 3 years at 5% per annum. John invested $300 at the same rate. If they both received the same amount of interest how much did john invest???
Answer:
Step-by-step explanation:
calculating the five number summary
Answer:
2) 43
4) 65
Step-by-step explanation:
The first and third quartile of the data can be found by calculating the median of the first and second halves of the data. For example, the first quartile of the data can be calculated thus:
40,41,43,50,56
41,43,50
43
and the third quartile thus:
62,63,65,78,97
63,65,78
65
Hope it helps <3
Answer:
A) 43
B) 65
Step-by-step explanation:
A) First Quartile = [tex](N+1)\frac{1}{4}[/tex]
Where N is the number of observations
=> 1st Quartile = (11+1)(1/4)
=> 1st Quartile = (12)(1/4)
=> 1st Quartile = 3rd number
=> 1st Quartile = 43B) Third Quartile = [tex](N+1)\frac{3}{4}[/tex]
=> 3rd Quartile = (11+1)(3/4)
=> 3rd Quartile = (12)(3/4)
=> 3rd Quartile = 3*3
=> 3rd Quatile = 9th number
=> 3rd Quartile = 65If 5ex = 300, x = A) ln (300) = 5.703 . . . B) 5 ln (60) = 20.471 . . . C) ln (300)∕5 = 1.140 . . . D) ln (60) = 4.094 . . .
Answer:
D) ln (60) = 4.094...
Step-by-step explanation:
Let's solve for x
We'll be careful because it's exponential.
5ex = 300
ex= 300/5
ex= 60
x = e^-1(60)
Let's note that this expression e^-1 is equal to In
x= In (60)
x = 4.0943
So the value of x is equal to 4.0943
Thank you.
The hourly rate for a staff nurse is £13.75.
A staff nurse works 30 hours a week and 6 hours overtime at time-and-a-half.
What is her total pay for the week?
Answer:
P = £536.25
Her total pay for the week is £536.25
Step-by-step explanation:
The total pay can be written as;
P = t1(r1) + t2(r2)
Where;
t1 = normal time
r1 = normal time pay rate
t2 = overtime
r2 = overtime pay rate
Given;
t1 = 30 hours
t2 = 6 hours
r1 = £13.75
r2 = 1.5(r1) = 1.5(£13.75)
Substituting the given values into the equation 1;
P = 30(£13.75) + 6(1.5(£13.75))
P = £536.25
Her total pay for the week is £536.25
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Answer:
the first box and the second box
9) BRAINLIEST & POINTS!
Answer:
no supplement
Step-by-step explanation:
Supplementary angles add to 180 degrees
312 is greater than 180 degrees by itself, so it has no supplement
solve for x.
x/3 < -6
Answer: x < -18
Step-by-step explanation:
Simply multiply both sides by three to get x < -18
Step-by-step explanation:
x/3 < - 6
x < - 18
This should be the answer
Given the equation y = 7 sec(6x– 30)
The period is:
The horizontal shift is:
Answer:
The period is of [tex]\frac{\pi}{3}[/tex] units.
The horizontal shift is of 30 units to the left.
Step-by-step explanation:
The secant function has the following general format:
[tex]y = A\sec{(Bx + C)}[/tex]
A represents the vertical shift.
C represents the horizontal shift. If C is positive, the shift is to the right. If it is negative, it is to the left.
The period is [tex]P = \frac{2\pi}{B}[/tex]
In this question:
[tex]y = 7\sec{6x - 30}[/tex]
So [tex]B = 6, C = -30[/tex]
Then [tex]P = \frac{2\pi}{6} = \frac{\pi}{3}[/tex]
The period is of [tex]\frac{\pi}{3}[/tex] units.
The horizontal shift is of 30 units to the left.
PLS HELP. The question is in the photo :)
Answer:
So each strawberry is 4 calories
Step-by-step explanation:
First find the slope of the line
Two points on the line are
(0,0) and (3,12)
m = (y2-y1)/(x2-x1)
= (12-0)/(3-0)
= 12/3
= 4
So each strawberry is 4 calories
Parallelogram A B C D is shown. Diagonals are drawn from point A to C and from point D to B and intersect at point E. Line segment D E is 2 x + 9 and line segment E B is 3 x minus 21. What is the length of segment EB in parallelogram ABCD? 30 units 34.5 units 69 units 138 units
Answer:
(C)69 units
Step-by-step explanation:
The diagonals of a parallelogram bisect each other.
Therefore, point E divides diagonal BD into DE and EB such that:
DE = EB
2x+9=3x-21
3x-2x=9+21
x=30
Therefore:
DE=2(30)+9=69 Units
EB=3x-21=3(30)-21=69
Therefore, the length of segment EB in parallelogram ABCD is 69 Units
The correct option is C.
Answer:69
Step-by-step explanation:
I want to fence in a rectangular vegetable patch. The fencing for the east and west sides costs $2 per foot, and the fencing for the north and south sides costs only $1 per foot. I have a budget of $40 for the project. What is the largest area I can enclose
Answer:
largets area is 32 feet cubed
Step-by-step explanation:
8=4 foot 2 for each side w and e and 32feet n and s 16 each side