Answer:
The height of the box with the smaller base is 4 times that of the box with the larger base
Step-by-step explanation:
The volume of a box is the product of the base area and the height of the box, it is given as:
Volume = base area × height
For the smaller base box, it has a base of 5 cm by 5 cm, therefore the base area of the smaller base box = 5 cm × 5 cm = 25 cm². Let the height of the smaller base box be [tex]h_1[/tex]The volume of the small box = [tex]25*h_1[/tex]
For the larger base box, it has a base of 10 cm by 10 cm, therefore the base area of the larger base box = 10 cm × 10 cm = 100 cm². Let the height of the large base box be [tex]h_2[/tex]The volume of the larger base box = [tex]100*h_2[/tex]
Since both boxes have the same volume, therefore:
[tex]100*h_2[/tex] = [tex]25*h_1[/tex]
[tex]\frac{h_1}{h_2} =\frac{100}{25} \\\\\frac{h_1}{h_2}=4\\\\h_1=4h_2[/tex]
The height of the box with the smaller base is 4 times that of the box with the larger base
We can use the formula V=lwh to compare the volume in the two boxes.
First let's compare the volume of both boxes to see if they have the same height. To make it simple, let's use a height of 1 centimeter.
First the box with the smaller base.
V=lwh
V=5⋅5⋅1
V=25
Now the box with the larger base
V=lwh
V=10x10x1
V=100
We can set up an equation to find out how many times as tall the smaller box needs to be to have the same volume as the box with the larger base.
25·h=100
h=4
The boz with the smaller base is 4 times tall
hope it helped :)
A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive".
(a) Using Bayes’ Theorem, when a person tests positive, determine the probability that the person is infected.
(b) Using Bayes’ Theorem, when a person tests negative, determine the probability that the person is not infected.
Answer:
A) P(A|B) = 0.01966
B) P(A'|B') = 0.99944
Step-by-step explanation:
A) We are told that A is the event "the person is infected" and B is the event "the person tests positive".
Thus, using bayes theorem, the probability that the person is infected is; P(A|B)
From bayes theorem,
P(A|B) = [P(A) × P(B|A)]/[(P(A) x P(B|A)) + (P(A') x P(B|A'))]
Now, from the question,
P(A) = 1/400
P(A') = 399/400
P(B|A) = 0.8
P(B|A') = 0.1
Thus;
P(A|B) = [(1/400) × 0.8)]/[((1/400) x 0.8) + ((399/400) x (0.1))]
P(A|B) = 0.01966
B) we want to find the probability that when a person tests negative, the person is not infected. This is;
P(A'|B') = P(Not infected|negative) = P(not infected and negative) / P(negative) = [(399/400) × 0.9)]/[((399/400) x 0.9) + ((1/400) x (0.2))] = 0.99944
If the wavelength of the violet color is 400 nm, what is the value of its frequency?
Hi there! Hopefully this helps!
-------------------------------------------------------------------------------------------------- The frequency is ~7.5*1014 Hz
Since visible light has a wavelength spectrum of ~400 nm to ~700 nm, Violet light has a wavelength of ~400 nm and a frequency of ~7.5*1014 Hz.
Step-by-step explanation:
Speed = wavelength × frequency
3×10⁸ m/s = (400×10⁻⁹ m) f
f = 7.5×10¹⁴
The current l in an electrical conductor varies inversely as the resistance R of the conductor. The current is 1/6 ampere when the resistance is 32400 ohms. What is the current when the resistance is 22500 ohms
Answer:
I=0.24ampere
Step-by-step explanation:
Assuming that the voltage is the same:
I=V/R (V- voltage, I-current, R-resistance)
1/6ampere=V/3240ohms
V=1/6*3240
= 5400v
Voltage across =V=5400v
Since the voltage is the same when the resistance is 22500ohms
I=V/R
=5400/22500
=6/25
=0.24ampere
if sqrt((2GM)/r) = 11 km/h, what does sqrt(((8G)(M/81))/r) equal?
Answer:
((23GM)
Step-by-step explanation:
it goes for this because 23gm = 40pm
Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. (Round your answer to four decimal places. Enter your answers as a comma-separated list.)
f(x)=5√x,[4,9]
Answer:
25/4Step-by-step explanation:
The mean value theorem for integrals for the function f(c) over a given interval [a, b] is expressed as g prime(c) = g(b) - g(a)/b-a. The idea is that there is a value c in between the interval [a, b] for the function given.
Given the function g(x) = 5√x within the interval [4,9]
g prime (c) = g(9) - g(4)/9-4
g(9) = 5√9
g(9) = 5*3 = 15
g(4) = 5√4
g(4) = 5*2 = 10
g prime c) = 15-10/9-4
g prime (c) = 5/5
g prime(c) = 1
So we are to find the number for which g prime (x) = g prime(c)
If g(x) = 5√x = [tex]5x^{1/2}[/tex]
g prime (x) = [tex]5/2 \ x^{-1/2}[/tex]
g prime (x) = 5/2√x
Since g prime (c) = 1 then;
5/2√x = 1
5 = 2√x
√x = 5/2
x = (5/2)²
x = 25/4
The value of c guaranteed by the mid value theorem is 25/4
The possible value of c for [tex]\mathbf{f(x) = 5\sqrt x\ [4,9]}[/tex] is 6.25
The function is given as:
[tex]\mathbf{f(x) = 5\sqrt x\ [4,9]}[/tex]
Calculate f(4) and f(9)
[tex]\mathbf{f(4) = 5\sqrt 4 = 10}[/tex]
[tex]\mathbf{f(9) = 5\sqrt 9 = 15}[/tex]
Substitute c for x in f(x)
[tex]\mathbf{f(c) = 5\sqrt c }[/tex]
Calculate f'(c)
[tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]
So, we have:
[tex]\mathbf{f'(c) = \frac{f(9) - f(4)}{9 - 4}}[/tex]
[tex]\mathbf{f'(c) = \frac{f(9) - f(4)}{5}}[/tex]
This gives
[tex]\mathbf{f'(c) = \frac{15 -10 }{5}}[/tex]
[tex]\mathbf{f'(c) = \frac{5 }{5}}[/tex]
[tex]\mathbf{f'(c) = 1}[/tex]
Also, we have:
[tex]\mathbf{f'(x) = \frac 52x^{-1/2}}[/tex]
Substitute c for x
[tex]\mathbf{f'(c) = \frac 52c^{-1/2}}[/tex]
Substitute 1 for f'(c)
[tex]\mathbf{\frac 52c^{-1/2} = 1}[/tex]
Multiply through by 2/5
[tex]\mathbf{c^{-1/2} = \frac 25}[/tex]
This gives
[tex]\mathbf{c^{1/2} = \frac 52}[/tex]
Square both sides
[tex]\mathbf{c = \frac{25}4}[/tex]
[tex]\mathbf{c = 6.25}[/tex]
Hence, the possible value of c is 6.25
Read more about mean value theorem at:
https://brainly.com/question/3957181
solve the rational equation 5/x = 4x+1/x^2
Answer:
x = 1
Step-by-step explanation:
Set up the rational expression with the same denominator over the entire equation.
Since the expression on each side of the equation has the same denominator, the numerators must be equal
5x =4x+1
Move all terms containing x to the left side of the equation.
Hope this can help you
There are two frozen yogurt stores in the mall. Both stores sell frozen yogurt by the ounce. Hammy's Froyo charges $2.40 for the container and $0.40 for each ounce of yogurt. Yogurt Palace charges $0.80 for each ounce of yogurt (no charge for the container). Graph the line that shows the cost of frozen yogurt at Hammy's Froyo. Graph the line that shows the cost of frozen yogurt at Yogurt Palace.
Answer:
The graphs for the lines of the costs are in the attachment. For this answer you have to first determine the equations for each cost. Since Hammy's Froyo charges $2.40 for the container and $.40 for each ounce, the equation would be y=.40x+2.40. For Yogurt Palace, which charges $0.80 for each ounce, the equation would be y=.80x.
A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape.
389 357 359 364 375 424 326 395 402 373
374 371 365 367 365 326 339 393 392 369
374 359 357 403 335 397
A normal probability plot of the n 26 observations on escape time given above shows a substantial linear pattern; the sample mean and sample standard deviation are 371.08 and 24.45, respectively. (Round your answers to two decimal places.)
Required:
a. Calculate an upper confidence bound for population mean escape time using a confidence level of 95%.
b. Calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%.
Answer:
The upper confidence bound for population mean escape time is: 379.27
The upper prediction bound for the escape time of a single additional worker is 413.64
Step-by-step explanation:
Given that :
sample size n = 26
sample mean [tex]\bar x[/tex] = 371.08
standard deviation [tex]\sigma[/tex] = 24.45
The objective is to calculate an upper confidence bound for population mean escape time using a confidence level of 95%
We need to determine the standard error of these given data first;
So,
Standard Error S.E = [tex]\dfrac{\sigma }{\sqrt{n}}[/tex]
Standard Error S.E = [tex]\dfrac{24.45 }{\sqrt{26}}[/tex]
Standard Error S.E = [tex]\dfrac{24.45 }{4.898979486}[/tex]
Standard Error S.E = 4.7950
However;
Degree of freedom df= n - 1
Degree of freedom df= 26 - 1
Degree of freedom df= 25
At confidence level of 95% and Degree of freedom df of 25 ;
t-value = 1.7080
Similarly;
The Margin of error = t-value × S.E
The Margin of error = 1.7080 × 4.7950
The Margin of error = 8.18986
The upper confidence bound for population mean escape time is = Sample Mean + Margin of Error
The upper confidence bound for population mean escape time is = 371.08 + 8.18986
The upper confidence bound for population mean escape time is = 379.26986 [tex]\approx[/tex] 379.27
The upper confidence bound for population mean escape time is: 379.27
b. Calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%.
The standard error of the mean = [tex]\sigma \times \sqrt{1+ \dfrac{1}{n}}[/tex]
The standard error of the mean = [tex]24.45 \times \sqrt{1+ \dfrac{1}{26}}[/tex]
The standard error of the mean = [tex]24.45 \times \sqrt{1+0.03846153846}[/tex]
The standard error of the mean = [tex]24.45 \times \sqrt{1.03846153846}[/tex]
The standard error of the mean = [tex]24.45 \times 1.019049331[/tex]
The standard error of the mean = 24.91575614
Recall that : At confidence level of 95% and Degree of freedom df of 25 ;
t-value = 1.7080
∴
The Margin of error = t-value × S.E
The Margin of error = 1.7080 × 24.91575614
The Margin of error = 42.55611149
The upper prediction bound for the escape time of a single additional worker is calculate by the addition of
Sample Mean + Margin of Error
= 371.08 + 42.55611149
= 413.6361115
[tex]\approx[/tex] 413.64
The upper prediction bound for the escape time of a single additional worker is 413.64
RVLC2019] IC/Off
In AMNO, m = 20, n = 14, and mZM = 51°. How many distinct triangles can be formed given these measurements?
O There are no triangles possible.
VX
O There is only one distinct triangle possible, with m N= 33º.
O There is only one distinct triangle possible, with mZN 147º.
O There are two distinct triangles possible, with m2N 33° or mZN-147º.
Done
) Intro
DO
There is only one distinct triangle possible, with m N= 33º. Therefore, option B is the correct answer.
What is sine rule?Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
The formula for sine rule is sinA/a=sinB/b=sinC/c
Given that, in ΔMNO, m = 20, n = 14, and m∠M = 51°.
Now, sin51°/20=sinN/14
0.7771/20=sinN/14
0.038855=sinN/14
sinN=14×0.038855
sinN=0.54397
N=33°
Therefore, option B is the correct answer.
Learn more about the sine rule here:
https://brainly.com/question/22288720.
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URGENT)
In the figure, ABCDE is a regular pentagon and DEFG is a square. CD
produced and GF intersect at H. Find x.
Answer:
108 degrees
Step-by-step explanation:
angle CDE is 108 degrees, which is supplementary to angle EDH, so EDH must be 72 degrees
then put it into an equation
90+90+72+x=360
solve
x=108
Answer:
The answer is 108
You are dealt two card successively without replacement from a shuffled deck of 52 playing cards. Find the probability that the first card is a king and the second is a queen. Round to nearest thousandth
Answer:
0.078
Step-by-step explanation:
The probability P(A) of an event A happening is given by;
P(A) = [tex]\frac{number-of-possible-outcomes-of-event-A}{total-number-of-sample-space}[/tex]
From the question;
There are two events;
(i) Drawing a first card which is a king: Let the event be X. The probability is given by;
P(X) = [tex]\frac{number-of-possible-outcomes-of-event-X}{total-number-of-sample-space}[/tex]
Since there are 4 king cards in the pack, the number of possible outcomes of event X = 4.
Also, the total number of sample space = 52, since there are 52 cards in total.
P(X) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]
(ii) Drawing a second card which is a queen: Let the event be Y. The probability is given by;
P(Y) = [tex]\frac{number-of-possible-outcomes-of-event-Y}{total-number-of-sample-space}[/tex]
Since there are 4 queen cards in the pack, the number of possible outcomes of event Y = 4
But then, the total number of sample = 51, since there 52 cards in total and a king card has been removed without replacement.
P(Y) = [tex]\frac{4}{51}[/tex]
Therefore, the probability of selecting a first card as king and a second card as queen is;
P(X and Y) = P(X) x P(Y)
= [tex]\frac{1}{13} * \frac{4}{51}[/tex] = 0.078
Therefore the probability is 0.078
Brainliest for the correct awnser!!! In general, when solving a radical equation with square roots, you should first isolate the radical and then _____ both sides.A.addB.squareC.multiplyD.subtract
Answer:
B
Step-by-step explanation:
Answer:
The answer for this Question is Elementary
It is B.
Write these numbers in standard form 0.000 04
Answer:
4/ 100000
hope it was useful for you
stay at home stay safe
pls mark me as brain.....m
keep rocking
Bart bought a digital camera with a list price of $219 from an online store offering a 6 percent discount. He needs to pay $7.50 for shipping. What was Bart's total cost? A. $205.86 B. $211.50 C. $213.36
Answer:
Barts total cost is (c)213.36
Step-by-step explanation:
First, you subtract 6% from $219
=204.92
add shipping,
+7.50
=213.36
Hope this helps <3
Answer:
C. $213.36
Step-by-step explanation:
The original price is $219 and the discount is 6% which is equal to $13.14
$219 - $13.14 + $7.50 (shipping cost) = $213.36
Please help a girl out !!!!
Answer:
work is shown and pictured
Find the area of the kite below. POSSIBLE ANSWERS: 168 mm 2 or 216 mm 2 or 195 mm 2 or 228 mm 2
Answer:
168 mm²
Step-by-step explanation:
Let A be the area of this shape
the kite is made of two triangles
Let A' and A" be the areas of the triangles
let's calculate A' and A" :
The area of a triangle is the product of the base and the height over 2
A' = [tex]\frac{(12+12)*5}{2}[/tex] = 60 mm² A"= [tex]\frac{(12+12)*9}{2}[/tex] = 108 mm²Let's calculate A
A = A' + A" A = 108+ 60 A = 168 mm²An open-top rectangular box is being constructed to hold a volume of 350 in3. The base of the box is made from a material costing 8 cents/in2. The front of the box must be decorated, and will cost 10 cents/in2. The remainder of the sides will cost 4 cents/in2. Find the dimensions that will minimize the cost of constructing this box.
Answer:
the dimensions that will minimize the cost of constructing the box is:
a = 5.8481 in ; b = 5.848 in ; c = 10.234 in
Step-by-step explanation:
From the information given :
Let a be the base if the rectangular box
b to be the height and c to be the other side of the rectangular box.
Then ;
the area of the base is ac
area for the front of the box is ab
area for the remaining other sides ab + 2cb
The base of the box is made from a material costing 8 ac
The front of the box must be decorated, and will cost 10 ab
The remainder of the sides will cost 4 (ab + 2cb)
Thus ; the total cost C is:
C = 8 ac + 10 ab + 4(ab + 2cb)
C = 8 ac + 10 ab + 4ab + 8cb
C = 8 ac + 14 ab + 8cb ---- (1)
However; the volume of the rectangular box is V = abc = 350 in³
If abc = 350
Then b = [tex]\dfrac{350}{ac}[/tex]
replacing the value for c in the above equation (1); we have :
[tex]C = 8 ac + 14 a(\dfrac{350}{ac}) + 8c(\dfrac{350}{ac})[/tex]
[tex]C = 8 ac + \dfrac{4900}{c}+\dfrac{2800}{a}[/tex]
Differentiating C with respect to a and c; we have:
[tex]C_a = 8c - \dfrac{2800}{a^2}[/tex]
[tex]C_c = 8a - \dfrac{4900}{c^2}[/tex]
[tex]8c - \dfrac{2800}{a^2}=0[/tex] --- (2)
[tex]8a - \dfrac{4900}{c^2}=0[/tex] ---(3)
From (2)
[tex]8c =\dfrac{2800}{a^2}[/tex]
[tex]c =\dfrac{2800}{8a^2}[/tex] ----- (4)
From (3)
[tex]8a =\dfrac{4900}{c^2}[/tex]
[tex]a =\dfrac{4900}{8c^2}[/tex] -----(5)
Replacing the value of a in 5 into equation (4)
[tex]c = \dfrac{2800}{8*(\dfrac{4900}{8c^2})^2} \\ \\ \\ c = \dfrac{2800}{\dfrac{8*24010000}{64c^4}} \\ \\ \\ c = \dfrac{2800}{\dfrac{24010000}{8c^4}} \\ \\ \\ c = \dfrac{2800*8c^4}{24010000} \\ \\ c = 0.000933c^4 \\ \\ \dfrac{c}{c^4}= 0.000933 \\ \\ \dfrac{1}{c^3} = 0.000933 \\ \\ \dfrac{1}{0.000933} = c^3 \\ \\ 1071.81 = c^3\\ \\ c= \sqrt[3]{1071.81} \\ \\ c = 10.234[/tex]
From (5)
[tex]a =\dfrac{4900}{8c^2}[/tex] -----(5)
[tex]a =\dfrac{4900}{8* 10.234^2}[/tex]
a = 5.8481
Recall that :
b = [tex]\dfrac{350}{ac}[/tex]
b = [tex]\dfrac{350}{5.8481*10.234}[/tex]
b =5.848
Therefore ; the dimensions that will minimize the cost of constructing the box is:
a = 5.8481 in ; b = 5.848 in ; c = 10.234 in
The dimensions that will minimize the cost of constructing this box are: a = 5.8481 inches, b = 5.848 inches, and c = 10.234 inches and this can be determined by using the given data.
Given :
An open-top rectangular box is being constructed to hold a volume of 350 inches cube.The base of the box is made from a material costing 8 cents/inch square.The front of the box must be decorated and will cost 10 cents/inch square. The remainder of the sides will cost 4 cents/inch square.According to the given data the total cost is given by:
C = 8ac + 14ab + 8cb --- (1)
The volume of the rectangular box is (V = abc = 350 inch cube). So, the value of b is given by:
[tex]\rm b = \dfrac{350}{ac}[/tex]
Now, substitute the value of 'b' in the equation (1).
[tex]\rm C = 8ac + \dfrac{4900}{c}+\dfrac{2800}{a}[/tex]
First differentiating the above equation with respect to c.
[tex]\rm C_c = 8a-\dfrac{4900}{c^2}[/tex] --- (2)
Now, differentiating the above equation with respect to a.
[tex]\rm C_a = 8c-\dfrac{2800}{a^2}[/tex] --- (3)
Now, equate equation (2) and equation (3) to zero.
From equation (2):
[tex]\rm a=\dfrac{4900}{8c^2}[/tex] ----- (4)
From equation (3):
[tex]\rm c=\dfrac{2800}{8a^2}[/tex] ----- (5)
Now, from equations (4) and (5).
[tex]\rm c = \dfrac{2800}{8\left(\dfrac{4900}{8c^2}\right)^2}[/tex]
Now, simplifying the above expression in order to get the value of c.
c = 10.234
Now, put the value of 'c' in equation (5) in order to get the value of 'a'.
a = 5.8481
The value of 'b' is given by:
[tex]\rm b = \dfrac{350}{5.8481\times 10.234}[/tex]
b = 5.848
So, the dimensions that will minimize the cost of constructing this box are: a = 5.8481 inches, b = 5.848 inches, and c = 10.234 inches.
For more information, refer to the link given below:
https://brainly.com/question/19770987
HELP PLEASE! A Blue Jay wanted to store some acorns for the winter. If she hides 18 acorns per tree, she will be left with four acorns; if she hides 20 acorns per tree, there will be extra space for an additional four acorns (the number of trees is always the same). How many acorns is the Blue Jay going to store for the winter, and in how many trees?
Answer:
Step-by-step explanation:
Let
T = number of trees
A = number of acorns
Given:
A = 18T + 4 ...........................(1)
A = 20T -4 .........................(2)
Equate A from (1) and (2)
20T-4 = 18T+4
simplify and solve for T
20T - 18T = 4+4
2T = 8
T = 4 trees
A = 18T + 4 = 72+4 = 76 acorns, or
A = 20T - 4 = 80 - 4 = 76 acorns.
Question 3
Which of the following best describes the solution to the system of equations below?
-6x + y=-3
7x-y=3
The system of equations has exactly one solution where x = 6 and y = 3.
The system of equations has no solution.
The system of equations has infinitely many solutions.
The system of equations has exactly one solution where x = 0 and y=
-3
Answer:
The system has exactly one solution where x = 0 and y = -3.
Step-by-step explanation:
-6x + y = -3
7x - y = 3
(7x - 6x) + (y - y) = 3 - 3
x + 0 = 0
x = 0
7(0) - y = 3
0 - y = 3
-y = 3
y = -3
-6(0) + y = -3
0 + y = -3
y = -3
So, the system has exactly one solution where x = 0 and y = -3.
Hope this helps!
Wina drove 282 miles on 10 gallons of gas. At this same rate, how many miles could she drive on 12 gallons of gas?
Hey there! I'm happy to help!
Let's set this up a proportion (two equal ratios) to find out how many miles Wina can drive on 12 gallons gas.
[tex]\frac{miles}{gallons} =\frac{282}{10} =\frac{m}{12}[/tex]
What do we multiply the bottom 10 by to get to 12? Well, to find out, we can divide 12 by 10 below.
12÷10=1.2
This means that we multiply the numbers in the first fraction by 1.2 to have the same numerator and denominator as the second fraction.
If we multiplied our 10 b y 1.2 to get the denominator in the second fraction, we should be able to multiply 282 by 1.2 to get the numerator in the second fraction!
282×1.2=338.4
If you use 338.4 in this proportion, the ratios will be equal.
Therefore, Wina could drive 338.4 miles on 12 miles of gas at this same rate.
Have a wonderful day!
Express the following ratio in the simplest form vii) 4.5km: 450m
Answer:
4.5 ×1000 =4500m
Step-by-step explanation:
450/1000=0.45km
Answer: 10 : 1
Step-by-step explanation: Now first let’s convert this to the same units, for instance, the SI unit for length meters. 4.5 x 1000 = 4500m. Then put the ratio 4500m : 450m. You can divide 4500 by 450 as it is divisible so you get 10 as the answer.
Even if you have converted them to kilometers before, nevermind, still 4.5 divide by 0.45 is 10 and there the answer is 10 : 1 or shortly the ratio is just 10.
A hypothesis will be used to test that a population mean equals 9 against the alternative that the population mean is less than 9 with known variance . What is the critical value for the test statistic for the significance level of 0.020
Answer:
-2.05
Step-by-step explanation:
From the given information,
Let consider [tex]\mu[/tex] to represent the population mean
Therefore,
The null and alternative hypothesis can be stated as :
[tex]H_o :\mu=9[/tex]
[tex]H_1 :\mu<9[/tex]
From the hypothesis , the alternative hypothesis is one tailed (left)
when the level of significance = 0.020, the Z- critical value can be determined from the standard normal distribution table
Hence, the Z-critical value at ∝ = 0.020 is -2.05
Identify the value of the TEST STATISTIC used in a hypothesis test of the following claim and sample data:
Claim: "The average battery life (between charges) of this model of tablet is at least 12 hours."
A random sample of 80 of these tablets is selected, and it is found that their average battery life is 11.58 hours with a standard deviation of 1.93 hours. Test the claim at the 0.05 significance level.
a. -0.218
b. -1.645
c. -1.946
d. -1.667
Answer:
-1.946 ; C
Step-by-step explanation:
Here, we want to identify the value of the z-statistic
Mathematically;
z = (x -mean)/SD/√n
Thus we have ;
Z = (11.58-12)/1.93/√80
z = -1.946
HELP:How many ways can four
students be seated in a row of
four seats? (answer is not 4 or 16)
Answer:
24 ways.
Step-by-step explanation:
In this case, you just need a factorial.
For the first seat, you have 4 students you can place.
For the second seat, you have 3 students.
For the third, you have 2.
For the fourth, you have 1.
So, you can arrange the students by doing 4 * 3 * 2 * 1 = 12 * 2 = 24 ways.
Hope this helps!
Answer:
There are 24 ways you can seat the people.Explantation:
First seat: 4 seats
Second seat: 3 seats
Third: 2 seats
Fourth seat: 1 seat remaining
4 * 3 * 2 * 1 = 12 * 2 * 1 = 24 * 1 = 24
There are 24 ways you can seat the people.PLEASE HELP I DO NOT UNDERSTAND AT ALL ITS PRECALC PLEASE SERIOUS ANSWERS
You want to end up with [tex]A\sin(\omega t+\phi)[/tex]. Expand this using the angle sum identity for sine:
[tex]A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi[/tex]
We want this to line up with [tex]2\sin(4\pi t)+5\cos(4\pi t)[/tex]. Right away, we know [tex]\omega=4\pi[/tex].
We also need to have
[tex]\begin{cases}A\cos\phi=2\\A\sin\phi=5\end{cases}[/tex]
Recall that [tex]\sin^2x+\cos^2x=1[/tex] for all [tex]x[/tex]; this means
[tex](A\cos\phi)^2+(A\sin\phi)^2=2^2+5^2\implies A^2=29\implies A=\sqrt{29}[/tex]
Then
[tex]\begin{cases}\cos\phi=\frac2{\sqrt{29}}\\\sin\phi=\frac5{\sqrt{29}}\end{cases}\implies\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)[/tex]
So we end up with
[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]
Answer:
y(t) = √29·sin(4πt +1.1903)amplitude: √29angular frequency: 4πphase shift: 1.1903 radiansStep-by-step explanation:
In the form ...
y(t) = Asin(ωt +φ)
you have ...
Amplitude = Aangular frequency = ωphase shift = φThe translation from ...
y(t) = 2sin(4πt) +5cos(4πt)
is ...
A = √(2² +5²) = √29 . . . . the amplitude
ω = 4π . . . . the angular frequency in radians per second
φ = arctan(5/2) ≈ 1.1903 . . . . radians phase shift
Then, ...
y(t) = √29·sin(4πt +1.1903)
_____
Comment on the conversion
You will notice we used "2" and "5" to find the amplitude and phase shift. In the generic case, these are "coefficient of sin( )" and "coefficient of cos( )". When determining phase shift, pay attention to whether your calculator is giving you degrees or radians. (Set the mode to what you want.)
If you have a negative coefficient for sin( ), you will need to add 180° (π radians) to the phase shift value given by the arctan( ) function.
Select the equation that could represent the relationship between f(x) and g(x).
Answer:
Option C.
Step-by-step explanation:
We have to see the common things we have in both graphs and express them:
1. There is a value x=a≠0, where g(a)=f(a)=0
2. The slope of g(x) is of opposite sign of the slope of f(x). Then f(x)=m*g(cx) with m<0.
3. The slope of f(x) seems to be higher than the slope of g(x)
A. As the slopes are different, this is not adequate.
B. As the slopes are different, this is not adequate.
C. This can be adequate, as it applies to all the observations we have made.
D. This is not adequate because f(0)≠g(-2*0).
The only adequate option then is C.
A bag contains balls colored in 7 different colors. What is the minimum no of balls one need to pick in order to get three balls of same color
Answer:
twenty one balls.
Step-by-step explanation:
there would be three of each colour.
Answer:
the real answer is 15
Step-by-step explanation:
Identify the type of observational study (cross-sectional, retrospective, or prospective) described below. A research company uses a device to record the viewing habits of about 25002500 households, and the data collected todaytoday will be used to determine the proportion of households tuned to a particular children's children's program.. Which type of observational study is described in the problem statement
Answer: cross-sectional study
Step-by-step explanation:
A cross-sectional study is a kind of research study in which a researcher collects the data from many different persons at a single point in time. In this study researcher observes the variables without influencing them.Here, A research company uses a device to record the viewing habits of about 2500 households (that includes different persons such as adults , children and seniors )
The data collected today(at a single point in time).
If it is used to determine the proportion of households tuned to a particular children's children's program.
The type of observational study is described in the problem statement : "cross-sectional"
Gabriella drives her car 360 miles and averages a certain speed, If the average speed had been 6 mph less, she could have traveled only 330 miles in the same length of time. What is her average speed?
Answer:
72mile/hr
Step-by-step explanation:
Let d be distance in mile
Let r be average rate in mile/hr
Let t be time in hr
d = r × t
t = d/r
360/r = t ........1
Also
The question stated that the average speed was 6 less to travel a distance of 330mile at the same time.
Since the average speed is r, hence 6 less that r = r-6 at the same time
Therefore
330/r-6 = same time ( t ) .......2
Equate 1 and 2
360/r = 330/r-6
Cross multiply
360(r-6) = 330(r)
360r - 360×6 = 330r
360r - 2160 = 330r
Collecting like terms
- 2160 = 330r - 360r
- 2160 = - 30r
Divide both sides by - 30
- 2160/ - 30 = - 30r/ - 30
r = 72mile/hr
Hence the average speed is 72mile/hr
The summer has ended and it’s time to drain the swimming pool. 20 minutes after pulling the plug, there is still 45 000L of water in the pool. The pool is empty after 70 minutes.
Calculate the rate that the water is draining out of the pool.
b) Calculate how much water was in the pool initially.
c) Write an equation for this relationship.
d) Use your equation to calculate how much water is in the pool at
62 minutes.
Answer:
a) -900 L/min
b) 63000 L
c) v = -900t +63000
d) 7200 L
Step-by-step explanation:
a) You are given two points on the curve of volume vs. time:
(t, v) = (20, 45000) and (70, 0)
The rate of change is ...
Δv/Δt = (0 -45000)/(70 -20) = -45000/50 = -900 . . . . liters per minute
__
b) In the first 20 minutes, the change in volume was ...
(20 min)(-900 L/min) = -18000 L
So, the initial volume was ...
initial volume -18000 = 45000
initial volume = 63,000 . . . . liters
__
c) Since we have the slope and the intercept, we can write the equation in slope-intercept form:
v = -900t +63000
__
d) Put the number in the equation and do the arithmetic.
When t=62, the amount remaining is ...
v = -900(62) +63000 = -55800 +63000 = 7200
7200 L remain after 62 minutes.