Answer:
The answer is below
Step-by-step explanation:
The box contains 5 red and 4 white balls.
A) The probability that at least 1 ball was red = P(both are red) + P(first is red and second is white) + P(first is white second is red)
Given that the first ball was (Upper A )Replaced before the second draw:
P(both are red) = P(red) × P(red) = 5/9 × 5/9 = 25/81
P(first is red and second is white) = P(red) × P(white) = 5/9 × 4/9 = 20/81
P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/9 = 20/81
The probability that at least 1 ball was red = 25/81 + 20/81 + 20/81 = 65/81
B) The probability that at least 1 ball was red = P(both are red) + P(first is red and second is white) + P(first is white second is red)
Given that the first ball was not Replaced before the second draw:
P(both are red) = P(red) × P(red) = 5/9 × 4/8 = 20/72 (since it was not replaced after the first draw the number of red ball remaining would be 4 and the total ball remaining would be 8)
P(first is red second is white) = P(red) × P(white) = 5/9 × 4/8 = 20/72
P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/8 = 20/72
The probability that at least 1 ball was red = 20/72 + 20/72 + 20/72 = 60/72
Question 15 please and i will mark the brainliest!!! And thank you to whoever answers
Explanation:
We have 4 options for the first choice and 3 options for the next. So there are 4*3 = 12 different combos possible. The tree diagram below shows 12 different paths to pick from. For instance, the right-most path has us pick the number 4 and the color yellow.
Determine the number of degrees of freedom for the two-sample t test or CI in each of the following situations. (Round your answers down to the nearest whole number.)a. m = 12, n = 15, s1 = 4.0, s2 = 6.0b. m = 12, n = 21, s1 = 4.0, s2 = 6.0c. m = 12, n = 21, s1 = 3.0, s2 = 6.0d. m = 10, n = 24, s1 = 4.0, s2 = 6.0
Answer:
Part a ) The degrees of freedom for the given two sample non-pooled t test is 24
Part b ) The degrees of freedom for the given two sample non-pooled t test is 30
Part c ) The degrees of freedom for the given two sample non-pooled t test is 30
Part d ) The degrees of freedom for the given two sample non-pooled t test is 25
Step-by-step explanation:
Degrees of freedom for a non-pooled two sample t-test is given by;
Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}
Now given the information;
a) :- m = 12, n = 15, s₁ = 4.0, s₂ = 6.0
we substitute
Δf = {[ 4²/12 + 6²/15 ]²} / {[( 4²/12)²/12-1] + [(6²/15)²/15-1]}
Δf = 30184 / 1241
Δf = 24.3223 ≈ 24 (down to the nearest whole number)
b) :- m = 12, n = 21, s₁ = 4.0, s₂ = 6.0
we substitute using same formula
Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}
Δf = {[ 4²/12 + 6²/21 ]²} / {[( 4²/12)²/12-1] + [(6²/21)²/21-1]}
Δf = 56320 / 1871
Δf = 30.1015 ≈ 30 (down to the nearest whole number)
c) :- m = 12, n = 21, s₁ = 3.0, s₂ = 6.0
we substitute using same formula
Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}
Δf = {[ 3²/12 + 6²/21 ]²} / {[( 3²/12)²/12-1] + [(6²/21)²/21-1]}
Δf = 29095 / 949
Δf = 30.6585 ≈ 30 (down to the nearest whole number)
d) :- m = 10, n = 24, s₁ = 4.0, s₂ = 6.0
we substitute using same formula
Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}
Δf = {[ 4²/10 + 6²/24 ]²} / {[( 4²/10)²/10-1] + [(6²/24)²/24-1]}
Δf = 1044 / 41
Δf = 25.4634 ≈ 25 (down to the nearest whole number).
If y varies directly with x and y = -11.7 when x = -3, find the value of y when x = 7.
Answer:
y = 27.3Step-by-step explanation:
To find the value of y when x = 7 we must first find the relationship between them.
The statement
y varies directly with x is written as
y = kx
where k is the constant of proportionality
From the question
when y = - 11.7
x = - 3
We have
- 11.7 = -3k
Divide both sides by - 3
k = 3.9
So the formula for the variation is
y = 3.9kWhen x = 7
y = 3.9(7)
y = 27.3Hope this helps you
Answer: 27.3
Step-by-step explanation:
Joint Variation
How many positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13
Answer:
10,000
Step-by-step explanation:
There are 2970 positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13
What is Number system?A number system is defined as a system of writing to express numbers.
We need to find
positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13
Let all 9 numbers ae
a+b+c+d+e+f+g+h+9=13
a+b+c+d+e+f+g+h=13-9
a+b+c+d+e+f+g+h=4
Then we use combinations
(n+k-1)Ck
¹¹C₄
11!/(11-4)!4!
11!/7!4!
330
Three hundred thirty times of nine is two thousand nine hundred seventy.
Now 330 ×9=2970
Hence there are 2970 positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13
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One number is twice another. The sum of their reciprocals is 3/2 . Find the numbers.
Answer:
The two numbers are 1 and 2.
Step-by-step explanation:
Let the two numbers be a and b.
One number is twice another, so let's let b=2a.
Their reciprocals are 3/2. Thus:
[tex]\frac{1}{a}+\frac{1}{b} =\frac{3}{2}[/tex]
Substitute and solve for a:
[tex]\frac{1}{a}+\frac{1}{2a} =\frac{3}{2}\\[/tex]
Combine the fractions by forming a common denominator by multiplying the left term by 2:
[tex]\frac{2}{2a} +\frac{1}{2a}=\frac{3}{2}[/tex]
Combine and cross-multiply:
[tex]3/2a=3/2\\6a=6\\a=1\\b=2(1)=2[/tex]
Thus, the two numbers are 1 and 2.
For a certain casino slot machine, the odds in favor of a win are given as 17 to 83. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Step-by-step explanation:
83P (E)=17-17P (E),
P (E)=17/100=0.17
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find the width and height of an older 35-inch television whose screen has an aspect ratio of 4:3.
Answer:
The Width = 28 inches
The Height = 21 inches
Step-by-step explanation:
We are told in the question that:
The width and height of an older 35-inch television whose screen has an aspect ratio of 4:3
Using Pythagoras Theorem
Width² + Height² = Diagonal²
Since we known that the size of a television is the length of the diagonal of its screen in inches.
Hence, for this new TV
Width² + Height² = 35²
We are given ratio: 4:3 as aspect ratio
Width = 4x
Height = 3x
(4x)² +(3x)² = 35²
= 16x² + 9x² = 35²
25x² = 1225
x² = 1225/25
x² = 49
x = √49
x = 7
Hence, for the 35 inch tv set
The Width = 4x
= 4 × 7
= 28 inches.
The Height = 3x
= 3 × 7
= 21 inches
6x - 10 = 4(x + 3) x = ? x = 9 x = 10 x = 11 x = 12
Answer:
x=11
Step-by-step explanation:
Answer:
x = 11
Step-by-step explanation:
6x - 10 = 4(x+3)
6x - 10 = 4*x + 4*3
6x - 10 = 4x + 12
6x - 4x = 12 + 10
2x = 22
x = 22/2
x = 11
check:
6*11 - 10 = 4(11+3)
66 - 10 = 4*14 = 56
Express the quotient of z1 and z2 in standard form given that [tex]z_{1} = -3[cos(\frac{-\pi }{4} )+isin(\frac{-\pi }{4} )][/tex] and [tex]z_{2} = 2\sqrt{2} [cos(\frac{-\pi }{2} )+isin(\frac{-\pi }{2} )][/tex]
Answer:
Solution : [tex]-\frac{3}{4}-\frac{3}{4}i[/tex]
Step-by-step explanation:
[tex]-3\left[\cos \left(\frac{-\pi }{4}\right)+i\sin \left(\frac{-\pi \:}{4}\right)\right]\:\div \:2\sqrt{2}\left[\cos \left(\frac{-\pi \:\:}{2}\right)+i\sin \left(\frac{-\pi \:\:\:}{2}\right)\right][/tex]
Let's apply trivial identities here. We know that cos(-π / 4) = √2 / 2, sin(-π / 4) = - √2 / 2, cos(-π / 2) = 0, sin(-π / 2) = - 1. Let's substitute those values,
[tex]\frac{-3\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)}{2\sqrt{2}\left(0-1\right)i}[/tex]
=[tex]-3\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)[/tex] ÷ [tex]2\sqrt{2}\left(0-1\right)i[/tex]
= [tex]3\left(-\frac{\sqrt{2}i}{2}+\frac{\sqrt{2}}{2}\right)[/tex] ÷ [tex]-2\sqrt{2}i[/tex]
= [tex]\frac{3\left(1-i\right)}{\sqrt{2}}[/tex]÷ [tex]2\sqrt{2}i[/tex] = [tex]-3-3i[/tex] ÷ [tex]4[/tex] = [tex]-\frac{3}{4}-\frac{3}{4}i[/tex]
As you can see your solution is the last option.
A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. Social Activity Education Above Average Average Below Average College 30 20 10 High School 20 40 90 Grade School 10 50 130 Using 0.05 as the significance level, what is the critical value for the test statistic
Answer:
9.488
Step-by-step explanation:
The critical value is found by first assessing which statistical test should be used.
We are interested in investigating relationship between social activity and education so chi-square test would be appropriate.
We have 3 rows and 3 columns. The degree of freedom for chi-square critical value is (r-1)(c-1)=(3-1)(3-1)=2*2=4
Chi-square critical value(0.05,4)= 9.488
An angle is 100° angle. how many degrees will you add it to make it a linear pair ?
Answer:
80
Step-by-step explanation:
linear pair = 180
Now,
100 + 80 = 180
Of the three properties, reflexive, symmetric, and transitive that define the relation "is equal to," which one could also apply to "is less than" and "is greater than?" transitive reflexive symmetric
Answer: Transitive property.
Step-by-step explanation:
First, for the equality we have:
Reflexive:
For all real numbers x, x = x.
Symmetric:
For all real numbers x, y
if x= y, then y = x.
Transitive:
For reals x, y and z.
if x = y, and y = z, then x = z.
Now, let's talk about inequalities.
first, the reflexive property will say that:
x > x.
This has no sense, so this property does not work for inequalities.
Now, the reflexive.
If x > y, then y > x.
Again, this has no sense, if x is larger than y, then we can never have that y is larger than x. This property does not work for inequalities.
Not, the transitive property.
if x > y, and y > z, then x > z.
This is true.
x is bigger than y, and y is bigger than z, then x should also be bigger than z.
x > y > z.
And this also works for the inverse case:
x < y and y < z, then x < z.
So the correct option is transitive property.
what is the distance between the first and third quartiles of a data set called?
Answer:
Interquartile range is the distance between the first and third of a data.
Step-by-step explanation:
Hope it will help you :)
Find the length of FT¯¯¯¯¯¯¯ A. 77.71 B. 72.47 C. 56.84 D. 49.42
Answer:
D, 49.42
Step-by-step explanation:
ΔVFT=180-90-43=47
formula
a/sin A = b/sin B/ = c/sin C
So,
FV/sin90=53/sin47
FV=72.4684
FT=√(72.4684)^2-(53)^2
FT=49.4234
Ans:D
The length FT in the given right-angle triangle is 49.42.
So option D is the correct answer.
We are given a right-angle triangle and to find the length of any side we can use Pythagoras theorem or trigonometric identities.
In the triangle, we see that TV = 53 and ∠ FVT = 43°
We will find the length FT by using Pythagoras theorem or trigonometric identities.
What are trigonometric functions?
There are some commonly used trigonometric identities:
SinФ = Perpendicular / hypotenuse
Cos Ф = Base / hypotenuse
Tan Ф = Perpendicular / Base
We will use Tan Ф = Perpendicular / Base to find the length FT.
Because we need to use trigonometric identities that have TV and FT.
Tan Ф = FT / TV
Tan 43° = FT / 53
FT = Tan 43° x 53
FT = 0.932515 X 53
FT = 49.42
Thus we got FT = 49.42 using the tan function.
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The double number lines show the ratio of cups to gallons. How many cups are in 333 gallons? _____ cups
Answer:
5328 cups.
Step-by-step explanation:
Given that 333 gallons
We know that
1 gallons = 16 cups
1 cups = 0.0625 gallons
Therefore,from the above conversion we can say that
Now by putting the values in the above conversion
333 gallons = 16 x 333 cups
333 gallons = 5328 cups
So , we can say that 333 gallons is equal to 5328 cups.
Thus the answer will be 5328 cups.
Answer:
48 cups(BTW he meant 33 galons, IVE had this before). lol you need to put the double number line image. first u have to divide 64/4 to get 16, Then it says "How many cups are in 3 gallons". There fore, U multiply 16 to 3 to get ur answer "48".
Which option is correct and how would one solve for it?
Answer:
102
Step-by-step explanation:
We have the sum for k = 1 to 4 of 3 ^ ( k-1) * ( k-1)
k =1 3 ^ (1-1) * ( 1-1) = 3^0 * 0 = 0
k =2 3 ^ (2-1) * ( 2-1) = 3^1 * 1 = 3
k =3 3 ^ (3-1) * ( 3-1) = 3^2 * 2 = 9*2 = 18
k =4 3 ^ (4-1) * ( 4-1) = 3^3 * 3 = 27 *3 = 81
Add these together
0+3+18+81 =102
━━━━━━━☆☆━━━━━━━
▹ Answer
102
▹ Step-by-Step Explanation
Convert the notation into a sum and substitute values from 1-4:
(3¹⁻¹ *(1 - 1)) + (3²⁻¹ * (2 - 1)) + (3³⁻¹ * (3 - 1)) + (3⁴⁻¹ * (4 - 1))
0 + 3 + 18 + 81
= 102
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
What is the value of 20 + 3 (7 + 4) + 5 + 2 (7 + 9)?
Answer:
90
Step-by-step explanation:
Answer:
90
Step-by-step explanation:
Here is the equation
[tex]20+3\times(7+4)+5+2\times(7+9)[/tex]
In the order of operations parentheses go first so we get
[tex]20+3\times11+5+2\times16[/tex]
Next we do the multiplication
[tex]20+33+5+32\\[/tex]
And finally we add them all up
[tex]20+33+5+32=90\\[/tex]
Thus, 90 is the answer of [tex]20+3\times(7+4)+5+2\times(7+9)[/tex] or [tex]20+3(7+4)+5+2(7+9)[/tex]
Identify the equivalent expressions of 4(2x + x-3) - 3x + 3 by substituting x = 2 and x = 3.
9x - 9
9x - 1
9x + X-9
9(x - 1)
4(3x - 3) + 3 - 3x
Answer:
9x -9
9(x - 1)
4(3x-3) - 3x + 3
Step-by-step explanation:
4(2x + x-3) - 3x + 3
Combine like terms
4(3x-3) - 3x + 3
Distribute
12x -12 -3x+3
Combine like terms
9x -9
Factor out 9
9(x-1)
Answer:
9
18
Step-by-step explanation:
x = 2:
4(4 + 2 - 3) - 6 + 3 = 12 - 6 + 3 = 9
x = 3:
4(6 + 3 - 3) - 9 + 3 = 24 - 9 + 3 = 18
We have seen how to convert specified odds from a "fair bet" into the gamblerâs belief about the likelihood of an event happening. The following are related.a. Torik gives 5:3 odds that someone will walk in late for class tomorrow. What probability does lie assign for this event? b. Mikko believes there is a 60% chance that at least five students from this class will be at the next basketball game. If he were to set up odds, what would they be? c. Change the 60% to 75%. Now would would be the odds?
Compute the flux H F of F(x,y) = hxy, x − yi across the boundary of the square given by −1 ≤ x ≤ 1, −1 ≤ y ≤ 1.
Answer:
4i.
Step-by-step explanation:
To find the flux through the square, we use the divergence theorem for the flux. So Flux of F(x,y) = ∫∫divF(x,y).dA
F(x,y) = hxy,x - yi
div(F(x,y)) = dF(x,y)/dx + dF(x,y)dy = dhxy/dx + d(x - yi)/dy = hy - i
So, ∫∫divF(x,y).dA = ∫∫(hy - i).dA
= ∫∫(hy - i).dxdy
= ∫∫hydxdy - ∫∫idxdy
Since we are integrating along the boundary of the square given by −1 ≤ x ≤ 1, −1 ≤ y ≤ 1, then
∫∫divF(x,y).dA = ∫₋₁¹∫₋₁¹hydxdy - ∫₋₁¹∫₋₁¹idxdy
= h∫₋₁¹{y²/2}¹₋₁dx - i∫₋₁¹[y]₋₁¹dx
= h∫₋₁¹{1²/2 - (-1)/2²}dx - i∫₋₁¹[1 - (-1)]dx
= h∫₋₁¹{1/2 - 1)/2}dx - i∫₋₁¹[1 + 1)]dx
= 0 - i∫₋₁¹2dx
= - 2i[x]₋₁¹
= 2i[1 - (-1)]
= 2i[1 + 1]
= 2i(2)
= 4i
What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question.
A normal curve with a peak at 0 is shown. The area under the curve shaded is 1 to 2.
z
Probability
0.00
0.5000
1.00
0.8413
2.00
0.9772
3.00
0.9987
0.14
0.16
0.86
0.98
Answer:
0.14
Step-by-step explanation:
The z score is a score used in statistics to determine by how many standard deviations ti the raw score above or below the mean. If the raw score is above the mean then the z score is positive while If the raw score is below the mean then the z score is negative, It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
From the normal distribution table, The area under the curve shaded is 1 to 2 = P(1 < z < 2) = P(z < 2) - P(z < 1) = 0.9772 - 0.8413 = 0.1359 ≈ 0.14
The area under the curve shaded is 1 to 2 is 0.14
What are probabilities?Probabilities are used to determine the chances of an event
The shaded region represents the probability of the z-scores
The shaded region 1 to 2 is represented as:
P(1 < z < 2) =
Using the probability of z-score, we have the formula
P(1 < z < 2) = P(z < 2) - P(z < 1)
From the given standard normal table:
P(z < 2) = 0.9772
P(z < 1) = 0.8413
So, we have:
P(1 < z < 2) = 0.9772 - 0.8413
P(1 < z < 2) = 0.1359
Approximate
P(1 < z < 2) = 0.14
Hence, the area under the curve shaded is 1 to 2 is 0.14
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Find the equation of a parabola that has a vertex (3,5) and passes through the point (1,13).
Oy= -27 - 3)' +5
Oy=2(x + 3) - 5
Oy=2(0 - 3)' + 5
Oy= -3(2 – 3) + 5
PLEASE HELP ME!!
Answer:
y = 2(x - 3)² + 5
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (3, 5), thus
y = a(x - 3)² + 5
To find a substitute (1, 13) into the equation
13 = a(1 - 3)² + 5 ( subtract 5 from both sides )
8 = 4a ( divide both sides by 4 )
a = 2, then
y = 2(x - 3)² + 5 ← equation of parabola in vertex form
Using fluorescent imaging techniques, researchers observed that the position of binding sites on HIV peptides is approximately Normally distributed with a mean of 2.45 microns and a standard deviation of 0.35 micron. What is the standardized score for a binding site position of 2.03 microns? (Enter your answer rounded to one decimal place.)
Answer:
The values is
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 2.45[/tex]
The standard deviation is [tex]\sigma = 0.35 \ mi[/tex]
The random value is [tex]x = 2.03[/tex]
The standardized score for a binding site position of 2.03 microns is mathematically represented as
[tex]z-score = \frac{x - \mu}{ \sigma }[/tex]
=> [tex]z-score = \frac{2.03 - 2.45}{ 0.35}[/tex]
=> [tex]z-score = -1.2[/tex]
An ‘in shuffle’ is a perfect shuffle on a standard deck of 52 playing cards that splits the deck in half, then interleaves cards starting with the top half.
Required:
a. What is the position of the first card after the 7th shuffle?
b. How many times must one perform the shuffle so that the top card becomes the bottom card?
c. When do the first and last cards in the deck touch?
Answer:
a) position 22
b) 26
c) shuffle 25
Step-by-step explanation:
Assuming the shuffling occurs so that the bottom card of the top half of the deck (card 26) becomes the bottom card (card 52), while the top card of the bottom half (card 27) becomes the top card (card 1), the sequence of card 1 positions with successive shuffles is ...
{2, 4, 8, 16, 32, 11, 22, 44, 35, 17, 34, 15, 30, 7, 14, 28, 3, 6, 12, 24, 48, 43, 33, 13, 26, 52, 51, 49, 45, 37, 21, 42, 31, 9, 18, 36, 19, 38, 23, 46, 39, 25, 50, 47, 41, 29, 5, 10, 20, 40, 27, 1}
That is, after the first shuffle, card 1 is at position 2; after the second shuffle, it is at position 4; and so on.
(a) Hence the position of card 1 after the 7th shuffle is 22.
__
(b) The top card is in position 52 after 26 shuffles.
__
(c) The top card is in position 26 after 25 shuffles; the bottom card is in position 27 after 25 shuffles. That is when they first touch. (They touch again after 51 shuffles.)
The balances in two separate bank accounts that grow each month at different rales are represented by the functions f(x) and gix) In what month do the funds in the f(x) bank account exceed those in the glx)
bank account?
Month (x) f(x) = 2* g(x) = 4x + 12
1
2
16
2.
4
20
O Month 3
O Month 4
O Month 5
O Month 6
Answer:
The balance in two separate bank accounts grows each month at different rates. the growth rates for both accounts are represented by the functions f(x) = 2x and g(x) = 4x 12. in what month is the f(x) balance greater than the g(x) balance?
Answer:
6 months
A function is a relationship between inputs where each input is related to exactly one output.
x = 5,
f(5) = [tex]2^5\\[/tex] = 32
g(5) = 4 x 5 + 12 = 20 + 12 = 32
x = 6,
f(6) = [tex]2^6[/tex] = 64
g(6) = 4 x 6 + 12 = 24 + 12 = 36
At month 6 the funds in the f(x) bank account exceed those in the g(x) bank account.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = [tex]2^{x}[/tex]
g(x) = 4x + 12
x = number of months
Now,
x = 3,
f(3) = 2³ = 8
g(3) = 4 x 3 + 12 = 12 + 12 = 24
x = 4,
f(4) = [tex]2^4[/tex] = 16
g(4) = 4 x 4 + 12 = 16 + 12 = 28
x = 5,
f(5) = [tex]2^5\\[/tex] = 32
g(5) = 4 x 5 + 12 = 20 + 12 = 32
x = 6,
f(6) = [tex]2^6[/tex] = 64
g(6) = 4 x 6 + 12 = 24 + 12 = 36
We see that,
At x = 6,
f(5) = 64
g(5) = 36
Thus,
At month 6 the funds in the f(x) bank account exceed those in the g(x) bank account.
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A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F. (Let y be measured in degrees Fahrenheit, and t be measured in seconds.) (a) Determine the cooling constant k. k = s−1 (b) What is the differential equation satisfied by the temperature y(t)? (Use y for y(t).) y'(t) = (c) What is the formula for y(t)? y(t) = (d) Determine the temperature of the bar at the moment it is submerged. (Round your answer to one decimal place.)
Answer:
a. k = -0.01014 s⁻¹
b. [tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]
c. [tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]
d. y(t) = 130.485°F
Step-by-step explanation:
A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F.
(Let y be measured in degrees Fahrenheit, and t be measured in seconds.)
We are to determine :
a. Determine the cooling constant k. k = s−1
By applying the new law of cooling
[tex]\dfrac{dT}{dt} = k \Delta T[/tex]
[tex]\dfrac{dT}{dt} = k(T_1-T_2)[/tex]
[tex]\dfrac{dT}{dt} = k (T - 60)[/tex]
Taking the integral.
[tex]\int \dfrac{dT}{T-60} = \int kdt[/tex]
㏑ (T -60) = kt + C
T - 60 = [tex]e^{kt+C}[/tex]
[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]
After 20 seconds, the temperature of the bar submersion is 120°F
T(20) = 120
From equation (1) ,replace t = 20s and T = 120
[tex]120 = 60 + C_1 e^{20 \ k}[/tex]
[tex]120 - 60 = C_1 e^{20 \ k}[/tex]
[tex]60 = C_1 e^{20 \ k} --- (2)[/tex]
After 1 min i.e 60 sec , the temperature = 100
T(60) = 100
From equation (1) ; replace t = 60 s and T = 100
[tex]100 = 60 + c_1 e^{60 \ t}[/tex]
[tex]100 - 60 =c_1 e^{60 \ t}[/tex]
[tex]40 =c_1 e^{60 \ t} --- (3)[/tex]
Dividing equation (2) by (3) , we have:
[tex]\dfrac{60}{40} = \dfrac{C_1e^{20 \ k } }{C_1 e^{60 \ k}}[/tex]
[tex]\dfrac{3}{2} = e^{-40 \ k}[/tex]
[tex]-40 \ k = In (\dfrac{3}{2})[/tex]
- 40 k = 0.4054651
[tex]k = - \dfrac{0.4054651}{ 40}[/tex]
k = -0.01014 s⁻¹
b. What is the differential equation satisfied by the temperature y(t)?
Recall that :
[tex]\dfrac{dT}{dt} = k \Delta T[/tex]
[tex]\dfrac{dT}{dt} = \dfrac{- In (\dfrac{3}{2})}{40}(T-60)[/tex]
Since y is the temperature of the body , then :
[tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]
(c) What is the formula for y(t)?
From equation (1) ;
where;
[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]
Let y be measured in degrees Fahrenheit
[tex]y(t) = 60 + C_1 e^{-\dfrac{In (\dfrac{3}{2})}{40}t}[/tex]
From equation (2)
[tex]C_1 = \dfrac{60}{e^{20 \times \dfrac{-In(\dfrac{3}{2})}{40}}}[/tex]
[tex]C_1 = \dfrac{60}{e^{-\dfrac{1}{2} {In(\dfrac{3}{2})}}}[/tex]
[tex]C_1 = \dfrac{60}{e^ {In(\dfrac{3}{2})^{-1/2}}}}[/tex]
[tex]C_1 = \dfrac{60}{\sqrt{\dfrac{2}{3}}}[/tex]
[tex]C_1 = \dfrac{60 \times \sqrt{3}}{\sqrt{2}}}[/tex]
[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]
(d) Determine the temperature of the bar at the moment it is submerged.
At the moment it is submerged t = 0
[tex]\mathbf{y(0) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ 0}{40}}}[/tex]
[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} }[/tex]
y(t) = 60 + 70.485
y(t) = 130.485°F
Calculate how many different sequences can be formed that use the letters of the given word. Leave your answer as a product of terms of the form C(n, r). HINT [Decide where, for example, all the s's will go, rather than what will go in each position.]
georgianna
A) C(10, 7)
B) C(2, 10)C(1, 8)C(1, 7)C(1, 6)C(1, 5)C(2, 4)C(2, 2)
C) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 1)C(3, 1)C(2, 1)C(1, 1)
D) 10 · C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
Answer: E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
Step-by-step explanation:
According to the combinations: Number of ways to choose r things out of n things = C(n,r)
Given word: "georgianna"
It is a sequence of 10 letters with 2 a's , 2 g's , 2 n's , and one of each e, o,r, i.
If we think 10 blank spaces, then in a sequence we need 2 spaces for each of g.
Number of ways = C(10,2)
Similarly,
1 space for 'e' → C(8,1)
1 space for 'o' → C(7,1)
1 space for 'r' → C(6,1)
1 space for 'i' → C(5,1)
1 space for 'a' → C(4,2)
1 space for 'n' → C(2,2)
Required number of different sequences = C(10,2) ×C(8,1)× C(7,1)× C(6,1)×C(5,1)×C(2,2).
Hence, the correct option is E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
You are starting a sock company. You must determine your costs to manufacture your product. The start-up cost is $2000 (which helps you purchase sewing machines). Material and labor is $2.50 per pair of socks.
a. Write an equation to model your company’s cost for manufacturing the socks. (i.e. y=mx+b)
b. Which variable represents the domain? Explain your answer.
c. What is the domain for this situation?
d. Which variable represents the range? Explain your answer.
e. What is the range for this situation?
f. Using your equation, what would be the cost of manufacturing 25 pairs of socks?
g. How many socks could you make with $2500?
h. Create a coordinate graph on a sheet of paper to represent this situation. Describe the graph. Include the dimensions you would use for the x and y axes.
PLS HELP ASAP!
a. y = 2.5x + 2000
b. The variable x represents the domain because the domain is the range of the possible x values.
c. x ≥ 0
d. The variable y represents the range because the range is the range of the possible y values.
e. y ≥ 2000
f. y = 2.5(25) + 2000
y = 62.5 + 2000
y = $2062.50
g. 2500 = 2.5x + 2000
2.5x = 500
x = 200
h. I am sorry I cannot make the graph but hopefully you can figure out how to make it using the info I have given in the above parts of the problem :)
Express the function F in the form f∘g. (Enter your answers as a comma-separated list. Use non-identity functions for f(x) and g(x).)
F(x) = (x − 1)4
Answer:
[tex]f(x) = x^{4}[/tex], [tex]g(x) = x-1[/tex]
Step-by-step explanation:
Let be [tex]F(x) = f\circ g (x) = (x-1)^{4}[/tex], then expression for [tex]f(x)[/tex] and [tex]g(x)[/tex] are, respectively:
[tex]f(x) = x^{4}[/tex] and [tex]g(x) = x-1[/tex]
What is the answer -13.62-(27.9)
Answer:
− 1049
Step-by-step explanation:
-13.62-(27.9)
primero haremos los paréntesis y después las demás multiplicaciones de izquierda a derecha.
-13.62-243
-806-243
Finalmente tenemos − 1049
Espero te ayude :)
Answer:
-41.52
Step-by-step explanation:
-13.62 - (27.9) = -13.62 - 27.9When you subtract from a negative, the answer will be smaller than the starting number:
-13.62 - 27.9 = -41.52Therefore, the answer is -41.52.
