Answer:
Step-by-step explanation:
A complex number is a number that contains a real part and an imaginary one .
Mathematical expression : a+bi xhera a and b are real numbers and i the solution of an equation like x²) -1 ..
Answer:a complex number is a number that can be shown in a form a+bi when a and b are real numbers and i is the answer to the equation x^2=-1
Find the slope-intercept form of the line with slope 6 that passes through the point (3,5).
Answer:
y=6x-13
Step-by-step explanation:
Since we are given a point and a slope, we can use the slope intercept formula.
[tex]y-y_{1} = m(x-x_{1} )[/tex]
where (x1, y1) is a point and m is the slope.
We know that the slope is 6 and the point is (3,5). Therefore,
x1= 3
y1= 5
m=6
Substitute these into the formula.
[tex]y-5 = 6(x-3 )[/tex]
Distribute the 6. Multiply each term inside the parentheses by the number outside the parentheses.
[tex]y-5= (6*x) + (6*-3)[/tex]
[tex]y-5=6x-18[/tex]
We want to find the slope-intercept form, or y=mx+b. Therefore, we must get y by itself.
5 is being subtracted from y. The inverse of subtraction is addition. Add 5 to both sides.
[tex]y-5+5=6x-18+5[/tex]
[tex]y= 6x-18+5[/tex]
[tex]y= 6x -13[/tex]
The tread life of a particular brand of tire is normally distributed with mean 60,000 miles and standard deviation 3800 miles. Suppose 35 tires are randomly selected for a quality assurance test. Find the probability that the mean tread life from this sample of 35 tires is greater than 59,000 miles. You may use your calculator, but show what you entered to find your answer. Round decimals to the nearest ten-thousandth (four decimal places).
Answer:
P [ x > 59000} = 0,6057
Step-by-step explanation:
We assume Normal Distribution
P [ x > 59000} = (x - μ₀ ) /σ/√n
P [ x > 59000} = (59000 - 60000)/ 3800
P [ x > 59000} = - 1000/3800/√35
P [ x > 59000} = - 1000*5,916 /3800
P [ x > 59000} = - 5916/3800
P [ x > 59000} = - 1,55
We look for p value for that z score n z-table and find
P [ x > 59000} = 0,6057
Please answer this correctly
Answer:
Option 2
Step-by-step explanation:
Last month the change in water level was -13 mm. This month, the water level increase by 13 mm.
-13 + 13 = 0
which linear function is represented by the graph below?
A) f(x) = -2x + 1
B) f(x) = -1/2x + 1
C) f(x) = 1/2x + 1
D) f(x) = 2x + 1
Answer:
The answer is answer choice b.
Step-by-step explanation:
b/c its a negative line
meg mows 20% of a lawn in 10 minutes how much more time will she need to finish mowing the lawn
Answer: 40 mins
Step-by-step explanation:
10=20%
20=40%
30=60%
40=80%
50=100%
A travel agent is booking trips for tourists who travel from New York to Chicago. Tourists have three choices for how to travel from New York to Chicago. They can take an airplane for $350, a bus for $150, or a train for $225. Once they arrive in Chicago, they can travel by van to their hotel for $60 or take a cab for $40. If each option is equally likely to occur, what is the probability that a tourist will spend more than $275 on these 2 legs of the trip?
Answer:
P = 1/2
Step-by-step explanation:
If the tourist spends more than 275$, they must not arrive in Chicago by bus.
( 150 + 60 < 275, 150 + 40 < 275)
The total options the tourist can make:
3 x 2 = 6
(1st leg: 3 possible options, 2nd leg: 2 possible options)
The number of options the tourist can make after excluding bus option:
2 x 2 = 4
(1st leg: 2 remaining possible options, 2nd leg: 2 possible options)
The number of options the tourist can make after excluding the bus option and spend more than 275$:
4 - 1 = 3
(excluding the case of selecting train and cab, because 225 + 40 < 275)
=> The probability that the tourist will spend more than 275$ on these 2 legs of the trip:
P = 3/6 = 1/2
Probability helps us to know the chances of an event occurring. The probability that a tourist will spend more than $275 on these 2 legs of the trip is 0.5.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that Tourists have three choices for how to travel from New York to Chicago. They can take an aeroplane for $350, a bus for $150, or a train for $225. Also, when they arrive in Chicago, they can travel by van to their hotel for $60 or take a cab for $40. Therefore, the cost of different routes is,
Aeroplane($350) + Van($60) = $410Aeroplane($350) + Cab($40) = $390Bus($150) + Van($60) = $210Bus($150) + Cab($40) = $190Train($225) + Van($60) = $285Train($225) + Cab($40) = $265As it can be seen that there are 3 cases where a tourist will spend more than $275, while the total number of cases is 6. Therefore, the probability that a tourist will spend more than $275 on these 2 legs of the trip is,
Probability = 3/6 = 1/2 =0.5z
Hence, the probability that a tourist will spend more than $275 on these 2 legs of the trip is 0.5.
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On the "Compiled Information" tab, a VLOOKUP formula has been pre-entered into cell E3. This formula was written correctly, and it uses references to the numbers in cells E1 through G1 to determine the correct index_number parameter. Fill in cells F1 and G1 with the correct index numbers, then copy the formula in cell E3 down to all the rows in columns E, F, and G. What number did you enter into cell G1?
Answer:
3
Step-by-step explanation:
Vlookup is a technique in excel which enables users to search for criterion values. It is vertical lookup function in excel which return a value from a different column. The formula for Vlookup function is:
=Vlookup'select cell you want to look up in' select cell you want to lookup from' select column index number' true/false.
where true is approximate match and false is exact match.
On a piece of paper Graph Y=-3x-2
Answer:
hope it helps uh......
In professor Hoepker's class, there are X tests and a final. At the end of the semester, the lowest Y test scores are dropped and the remaining test scores and the final (which has twice the weight of a test) are averaged to compute the average score for the entire class. The final cannot be dropped. Going into the final, student Kaytee has an average of W on the X tests. The sum of her lowest Y test scores is L. Her final exam score is S. Find her average score G in the class in terms of X, Y, W, L, and S.
Step-by-step explanation:
Kaytee's total points are WX + 2S − L. The total number of exams is W − Y + 2. Therefore:
G = (WX + 2S − L) / (X − Y + 2)
The total number of exams is W − Y + 2.
We have given that,
In professor Hoepker's class, there are X tests and a final. At the end of the semester, the lowest Y test scores are dropped and the remaining test scores and the final (which has twice the weight of a test) are averaged to compute the average score for the entire class. The final cannot be dropped.
Going into the final, student Kaytee has an average of W on the X tests. The sum of her lowest Y test scores is L. Her final exam score is S.
What is the sum?The sum brings two or more numbers together to make a new total.
We have to determine her average score of G in the class in terms of X, Y, W, L, and S.
Kaytee's total points are WX + 2S − L.
The total number of exams is W − Y + 2.
Therefore:G = (WX + 2S − L) / (X − Y + 2)
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18 is divisible by both 2 and 3 it is also divisible by 2 into 36 similarly a number is divisible by both 4 and 6 can we say that the number must also be divided by 4 and 2 6 24 if not give an example to justify your answer
Answer:
no; 12
Step-by-step explanation:
A number divisible by 4 and 6 will be divisible by their least common multiple, 12. If it is an odd multiple of 12, it will not be divisible by 24.
Examples:
12÷4 = 3; 12÷6 = 2; 12 is not divisible by 24
24÷4 = 6; 24÷6 = 4; 24 is divisible by 24
36÷4 = 9; 36÷6 = 6; 36 is not divisible by 24
Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas's fastest-moving inventory item has a demand of 6,100 units per year. The cost of each unit is $101, and the inventory carrying cost is $8 per unit per year. The average ordering cost is $31 per order. It take about 5 days for an order to arrive, and the demand for 1 week is 120 units. (This is a corporate operation, and the are 250 working days per year.)A) What is the EOQ?B) What is the average inventory if the EOQ is used?C) What is the optimal number of orders per year?D) What is the optimal number of days in between any two orders?E) What is the annual cost of ordering and holding inventory?F) What is the total annual inventory cost, including cost of the 6,100 units?
Answer and Step-by-step explanation:
The computation is shown below:
a. The economic order quantity is
[tex]= \sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}[/tex]
[tex]= \sqrt{\frac{2\times \text{6,100}\times \text{\$31}}{\text{\$8}}}[/tex]
= 217 units
b. The average inventory used is
[tex]= \frac{economic\ order\ quantity}{2}[/tex]
[tex]= \frac{217}{2}[/tex]
= 108.5 units
c. The optimal order per year
[tex]= \frac{annual\ demand}{economic\ order\ quantity}[/tex]
[tex]= \frac{6,100}{217}[/tex]
= 28 orders
d. The optima number of days is
[tex]= \frac{working\ days}{optimal\ number\ of\ orders}[/tex]
[tex]= \frac{250}{28}[/tex]
= 8.9 days
e. The total annual inventory cost is
= Purchase cost + ordering cost + carrying cost
where,
Purchase cost is
[tex]= \$6,100 \times \$101[/tex]
= $616,100
Ordering cost = Number of orders × ordering cost per order
= 28 orders × $31
= $868
Carrying cost = average inventory × carrying cost per unit
= 108.50 units × $8
= $868
So, the total would be
= $616,100 + $868 + $868
= $617,836
g In R simulate a sample of size 20 from a normal distribution with mean µ = 50 and standard deviation σ = 6. Hint: Use rnorm(20,50,6) to get one random sample of size 20. Determine the mean and standard deviation from this sample, compare these with the population mean and standard deviation.
Answer:
> a<-rnorm(20,50,6)
> a
[1] 51.72213 53.09989 59.89221 32.44023 47.59386 33.59892 47.26718 55.61510 47.95505 48.19296 54.46905
[12] 45.78072 57.30045 57.91624 50.83297 52.61790 62.07713 53.75661 49.34651 53.01501
Then we can find the mean and the standard deviation with the following formulas:
> mean(a)
[1] 50.72451
> sqrt(var(a))
[1] 7.470221
Step-by-step explanation:
For this case first we need to create the sample of size 20 for the following distribution:
[tex] X\sim N(\mu = 50, \sigma =6)[/tex]
And we can use the following code: rnorm(20,50,6) and we got this output:
> a<-rnorm(20,50,6)
> a
[1] 51.72213 53.09989 59.89221 32.44023 47.59386 33.59892 47.26718 55.61510 47.95505 48.19296 54.46905
[12] 45.78072 57.30045 57.91624 50.83297 52.61790 62.07713 53.75661 49.34651 53.01501
Then we can find the mean and the standard deviation with the following formulas:
> mean(a)
[1] 50.72451
> sqrt(var(a))
[1] 7.470221
Answer:
b
Step-by-step explanation:
Solve by completing the square. x2−12x=−27 Select each correct answer. −9 −3 3 9 15
Answer:
x=9,3
Step-by-step explanation:
x²-12x=-27
x²-12x+(12/2)²=-27+(12/2)²
x²-12x+6²=-27+36
(x-6)²=9
x-6=[tex] \frac{ + }{ - } \sqrt{9} [/tex]
x-6=+3 and x-6=-3
x=9 and 3
a rectangular playing field measure 350 by 200m if kolade stroll 11 times around what is the answer in km
Answer:
12.1 km
Step-by-step explanation:
350 * 2 = 700
200 * 2 = 400
700 + 400 = 1100
1100 * 11 = 12100
12100 / 1000 = 12.1
12.1 km
The table shows three unique functions. (TABLE IN PIC) Which statements comparing the functions are true? Select three options. Only f(x) and h(x) have y-intercepts. Only f(x) and h(x) have x-intercepts. The minimum of h(x) is less than the other minimums. The range of h(x) has more values than the other ranges. The maximum of g(x) is greater than the other maximums.
Answer:
(A)Only f(x) and h(x) have y-intercepts.
(C)The minimum of h(x) is less than the other minimums.
(E)The maximum of g(x) is greater than the other maximums.
Step-by-step explanation:
From the table
f(0)=0 and h(0)=0, therefore, Only f(x) and h(x) have y-intercepts. (Option A)
Minimum of f(x)=-14Minimum of g(x)=1/49Minimum of h(x)=-28Therefore, the minimum of h(x) is less than the other minimums. (Option C).
Maximum of f(x)=14
Maximum of g(x)=49
Maximum of h(x)=0
Therefore, the maximum of g(x) is greater than the other maximums. (Option E)
Answer: It's B,C, and E
Step-by-step explanation:
Use the table to identify values of p and g that can be used to factor X2 - x - 12
as (x + 2)(x + 9).
e
р
2
-2
ptq
-4
9
-6
6
-4
4
4
6
3
-3
-1
1
O A. -3 and 4
unctions
ving
O B-2 and 6
O C. 2 and -6
deling
O D. 3 and 4
Answer:
D. 3 and -4
Step-by-step explanation:
Given the expression, x² - x - 12, let's factorise to find the value of p and q using the table, for which we would have the expression simplified as (x + p)(x + q)
From the table, let's find the values of p and q that would give us -12 when multiplied together, and would also give us -1 when summed together.
Thus, from the table given, the row containing the values of p(3) and q(-4) gives us = -1 (p+q) . p = 3, q = -4 would be our values to use to factor x² - x - 12, as multiplying both will also give us "-12".
Thus, x² - x - 12 would be factorised or simplified as (x + 3)(x - 4)
Therefore, the answer is: D. 3 and -4
Answer:
D a p e x
Step-by-step explanation:
WILL GIVE BRAINLIEST What is the perimeter of the track, in meters? Use π = 3.14 and round to the nearest hundredth of a meter. plz help me
Answer:
P ≈ 317.08 m
Step-by-step explanation:
Circumference: C = πd
Step 1: Find circumference of both domes
C = π(50)
Since it's a dome, we divide by 2
50π/2 = 25π
Since we have 2 domes, we simply multiply by 2 again
25π(2) = 50π
Step 2: Find perimeter of track
50π + 80(2)
P = 50π + 160
P = 317.08 m
can someone help asAP!
Answer:
Option 3
Step-by-step explanation:
Interior angles of a triangle add up to 180 degrees. So to find a missing angle we just need to subtract the rest of the angles from 180.
So,
[tex]\theta = 180-(\alpha +\beta )[/tex]
HELP!!
Which Platonic solid has four faces that are equilateral triangles?
A. Hexahedron
B. Dodecahedron
C. Tetrahedron
D. Icosahedron
Answer:
C. Tetrahedron
Step-by-step explanation:
In figure
The Platonic solid that has four faces that are equilateral triangles is the Tetrahedron. The correct option is C.
What is Tetrahedron?A Tetrahedron is a three-dimensional shape made up of four equilateral triangles. It is one of the five Platonic solids, which are regular, convex polyhedra with identical vertices and faces.
Each vertex in a Tetrahedron is connected to the other three vertices by an edge, resulting in a pyramid-like structure.
The Tetrahedron is a unique shape with numerous applications in mathematics, engineering, and chemistry.
The Tetrahedron is a Platonic solid with four equilateral triangle faces. It has four faces, four vertices, and six edges in total. It is the most basic of the Platonic solids and the only one with no parallel faces.
Thus, the correct option is C.
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Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h
Answer:
C
Step-by-step explanation:
We know that A is not true because we know that h(8) is 19, not 21. B is also not true because the value of h(x) can't be -1. D can't be true because x can't be 13, therefore the answer is C.
work out the following, giving your answer to the simplest form 5 3/5/2 2/3
Answer:
2 1/10
Step-by-step explanation:
We suppose you want the quotient of the mixed numbers 5 3/5 and 2 2/3.
(5 3/5)/(2 2/3) = (28/5)/(8/3) = (28/5)(3/8) = (4)(7)(3)/(5(4)(2)) = 21/10
= 2 1/10
If possible, find AB, BA, and A2.
First product:
[tex]AB=\begin{bmatrix}3&-3\\-7&0\\2&4\end{bmatrix}\begin{bmatrix}1&0\\0&1\end{bmatrix}=\begin{bmatrix}\begin{bmatrix}3&-3\end{bmatrix}\begin{bmatrix}1\\0\end{bmatrix}&\begin{bmatrix}3&-3\end{bmatrix}\begin{bmatrix}0\\1\end{bmatrix}\\\begin{bmatrix}-7&0\end{bmatrix}\begin{bmatrix}1\\0\end{bmatrix}&\begin{bmatrix}-7&0\end{bmatrix}\begin{bmatrix}0\\1\end{bmatrix}\\\begin{bmatrix}2&4\end{bmatrix}\begin{bmatrix}1\\0\end{bmatrix}&\begin{bmatrix}2&4\end{bmatrix}\begin{bmatrix}0\\1\end{bmatrix}\end{bmatrix}=\begin{bmatrix}3&-3\\-7&0\\2&4\end{bmatrix}[/tex]
Notice how multiplying A by B produces A again, because B is an identity matrix.
The second product cannot be carried out because A has more columns that B has rows.
The third product also cannot be computed because A is not a square matrix.
Before the pandemic cancelled sports, a baseball team played home games in a stadium that holds up to 50,000 spectators. When ticket prices were set at $12, the average attendance was 30,000. When the ticket prices were on sale for $10, the average attendance was 35,000.
(a) Let D(x) represent the number of people that will buy tickets when they are priced at x dollars per ticket. If D(x) is a linear function, use the information above to find a formula for D(x). Show your work!
(b) The revenue generated by selling tickets for a baseball game at x dollars per ticket is given by R(x) = x-D(x). Write down a formula for R(x).
(c) Next, locate any critical values for R(x). Show your work!
(d) If the possible range of ticket prices (in dollars) is given by the interval [1,24], use the Closed Interval Method from Section 4.1 to determine the ticket price that will maximize revenue. Show your work!
Optimal ticket price:__________ Maximum Revenue:___________
Answer:
(a)[tex]D(x)=-2,500x+60,000[/tex]
(b)[tex]R(x)=60,000x-2500x^2[/tex]
(c) x=12
(d)Optimal ticket price: $12
Maximum Revenue:$360,000
Step-by-step explanation:
The stadium holds up to 50,000 spectators.
When ticket prices were set at $12, the average attendance was 30,000.
When the ticket prices were on sale for $10, the average attendance was 35,000.
(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)
Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).
[tex]\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500[/tex]
Therefore, we have:
[tex]y=-2500x+b[/tex]
At point (12,30000)
[tex]30000=-2500(12)+b\\b=30000+30000\\b=60000[/tex]
Therefore:
[tex]D(x)=-2,500x+60,000[/tex]
(b)Revenue
[tex]R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2[/tex]
(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.
[tex]R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12[/tex]
The critical value of R(x) is x=12.
(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]
Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.
[tex]R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0[/tex]
Therefore:
Optimal ticket price:$12Maximum Revenue:$360,000The following observations were made on fracture toughness of a base plate of 18% nickel maraging steel (in ksi √in, given in increasing order)].
68.6 71.9 72.6 73.1 73.3 73.5 75.5 75.7 75.8 76.1 76.2
76.2 77.0 77.9 78.1 79.6 79.8 79.9 80.1 82.2 83.7 93.4
Calculate a 90% CI for the standard deviation of the fracture toughness distribution. (Give answer accurate to 2 decimal places.)
Answer:
A 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].
Step-by-step explanation:
We are given the following observations that were made on fracture toughness of a base plate of 18% nickel maraging steel below;
68.6, 71.9, 72.6, 73.1, 73.3, 73.5, 75.5, 75.7, 75.8, 76.1, 76.2, 76.2, 77.0, 77.9, 78.1, 79.6, 79.8, 79.9, 80.1, 82.2, 83.7, 93.4.
Firstly, the pivotal quantity for finding the confidence interval for the standard deviation is given by;
P.Q. = [tex]\frac{(n-1) \times s^{2} }{\sigma^{2} }[/tex] ~ [tex]\chi^{2} __n_-_1[/tex]
where, s = sample standard deviation = [tex]\sqrt{\frac{\sum (X - \bar X^{2}) }{n-1} }[/tex] = 5.063
[tex]\sigma[/tex] = population standard deviation
n = sample of observations = 22
Here for constructing a 90% confidence interval we have used One-sample chi-square test statistics.
So, 90% confidence interval for the population standard deviation, [tex]\sigma[/tex] is ;
P(11.59 < [tex]\chi^{2}__2_1[/tex] < 32.67) = 0.90 {As the critical value of chi at 21 degrees
of freedom are 11.59 & 32.67}
P(11.59 < [tex]\frac{(n-1) \times s^{2} }{\sigma^{2} }[/tex] < 32.67) = 0.90
P( [tex]\frac{ 11.59}{(n-1) \times s^{2}}[/tex] < [tex]\frac{1}{\sigma^{2} }[/tex] < [tex]\frac{ 32.67}{(n-1) \times s^{2}}[/tex] ) = 0.90
P( [tex]\frac{(n-1) \times s^{2} }{32.67 }[/tex] < [tex]\sigma^{2}[/tex] < [tex]\frac{(n-1) \times s^{2} }{11.59 }[/tex] ) = 0.90
90% confidence interval for [tex]\sigma^{2}[/tex] = [ [tex]\frac{(n-1) \times s^{2} }{32.67 }[/tex] , [tex]\frac{(n-1) \times s^{2} }{11.59 }[/tex] ]
= [ [tex]\frac{21 \times 5.063^{2} }{32.67 }[/tex] , [tex]\frac{21 \times 5.063^{2} }{11.59 }[/tex] ]
= [16.48 , 46.45]
90% confidence interval for [tex]\sigma[/tex] = [[tex]\sqrt{16.48}[/tex] , [tex]\sqrt{46.45}[/tex] ]
= [4.06 , 6.82]
Therefore, a 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].
Use implicit differentiation to find an equation of the tangent line to the curve at the given points. (x2 + y2)2 = 3x2y − y3;
(a) (0, −1),
(b) (−1/2, 1/2)
Answer:
a.[tex]y+1=0[/tex]
b.[tex]2x+4y=1[/tex]
Step-by-step explanation:
We are given that
[tex](x^2+y^2)^2=3x^2y-y^3[/tex]
a.(0,-1)
Differentiate w.r.t x
[tex]2(x^2+y^2)(2x+2yy')=6xy+3x^2y'-3y^2y'[/tex].....(1)
Substitute x=0 and y=-1 in equation (1)
[tex]2(0+1)(-2y')=-3y'[/tex]
[tex]-4y'+3y'=0[/tex]
[tex]-y'=0[/tex]
[tex]y'=0[/tex]
[tex]m=y'=0[/tex]
Point-slope form:
[tex]y-y_0=m(x-x_0)[/tex]
Using the formula
[tex]y+1=0[/tex]
This is required equation of tangent line to the given curve at point (0,-1).
b.(-1/2,1/2)
Substitute the value in equation (1)
[tex]2(1/4+1/4)(-1+y')=6(-1/2)(1/2)+3(1/4)y'-3(1/4)y'[/tex]
[tex]2(2/4)(-1+y')=-3/2+3/4y'-3/4y'[/tex]
[tex]-1+y'=-3/2[/tex]
[tex]y'=-3/2+1=\frac{-3+2}{2}=-\frac{1}{2}[/tex]
[tex]m=y'=-1/2[/tex]
Again using point-slope formula
[tex]y-1/2=-1/2(x+1/2)[/tex]
[tex]\frac{2y-1}{2}=-\frac{1}{4}(2x+1)[/tex]
[tex]2y-1=-\frac{1}{2}(2x+1)[/tex]
[tex]4y-2=-2x-1[/tex]
[tex]2x+4y=2-1[/tex]
[tex]2x+4y=1[/tex]
Abox in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12
cubes measuring 6 inches on each side.
If the length and width of the base are doubled, how many cubes could the new box hold?
18
0 24
48
o 96
Answer:
48
Step-by-step explanation:
You are doubling 2 dimensions, so you just multiply the volume by 2 each time. Since you are doing it twice, you multiply the volume by 4. 12*4=48. You could also brute force it and just do 24*36*12/216(the volume of the 6 inch cube).
Given that, a box in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12 cubes measuring 6 inches on each side.
We need to find that how many cubes it holds if the length and width of the base are doubled,
We know that,
Volume of a rectangular prism = length × width × height
Volume of the new rectangular prism, = 2length × 2width × height
= 4(length × width × height)
= 4(12·12·18)
= 4×2592
= 10,368
Volume of the cube = side³
= 6³ = 216
The number of cube that the new rectangular prism can hold = Volume of the rectangular prism / Volume of the cube
= 10,368 / 216
= 48
Hence, the new rectangular prism, can hold 48 cubes.
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The average duration of labor from the first contraction to the birth of the baby in women over 35 who have not previously given birth and who did not use any pharmaceuticals is 16 hours. Suppose you have a sample of 29 women who exercise daily, and who have an average duration of labor of 17.8 hours and a sample variance of 77.4 hours. You want to test the hypothesis that women who exercise daily have a different duration of labor than all women. Calculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is s M
Answer:
There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women.
Standard error sm = 1.634
Test statistic t = 1.102
P-value = 0.28
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that women who exercise daily have a significantly different duration of labor than all women.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=16\\\\H_a:\mu\neq 16[/tex]
The significance level is 0.05.
The sample has a size n=29.
The sample mean is M=17.8.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√77.4=8.8.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{8.8}{\sqrt{29}}=1.634[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{17.8-16}{1.634}=\dfrac{1.8}{1.634}=1.102[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=29-1=28[/tex]
This test is a two-tailed test, with 28 degrees of freedom and t=1.102, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t>1.102)=0.28[/tex]
As the P-value (0.28) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women.
Can u pls tell the pythagroes thearom formula plsss
Answer:
a² + b² = c²
Step-by-step explanation:
The sum of the legs squared is equal to the hypotenuse squared.
a² + b² = c²
Where a and b are legs.
c is the hypotenuse.
Answer:
Trigonometry: Hypotenuse^2 = Opposite^2+ Adjacent^2General: a² + b² + c²Step-by-step explanation:
Pythagoras Theorem(used in trigonometry) :
[tex]Hypotenuse^2 = opp^2 + adj ^2 \: [/tex]
Pythagoras Theorem (General)
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
A sample consists of every 30th worker from a group of 1000 workers. What sampling technique was used?
Answer:
Systematic sampling
Step-by-step explanation:
We have the following sampling technique:
-Random sampling is analogous to putting everyone's name in a hat and extracting several names. Each element of the population has the same probability of occurring.
-Systematic sampling, here the list of elements is "counted". That is, each element k is taken. This is similar to aligning everyone and listing "1,2,3,4; 1,2,3,4; etc."
-Convenience sampling, easily available data is used here. That is, the first people the surveyor meets.
-Cluster sampling is achieved by dividing the population into groups, generally geographically.
-Stratified sampling also divides the population into groups called strata. However, this time it is for some feature, not geographically
In the case of the statement it is systematic because every 30th multiple is picked up which is in a system order members
Not sure how to solve this
Answer:
-3/17
Step-by-step explanation:
(7,1) and (-10,4)
slope formula: m = (y₂ - y₁) / (x₂ - x₁)
plug in data: m = (4 - 1) / (-10 - 7)
solve: 3 / -17
simplify: -3/17 (written as a fraction)