There are [tex]\binom62=15[/tex] ways of selecting any two fruit from the basket, where
[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]
is the so-called binomial coefficient.
If the baby picks out [tex]k[/tex] oranges, where [tex]k\in\{0,1,2\}[/tex], it can do so in
[tex]\dbinom 3k \dbinom3{2-k} = \dfrac{3!}{k!} \dfrac{3!}{(2-k)! (1 + k)!}[/tex]
ways.
Then the PMF (probability mass function) of [tex]X[/tex] is
[tex]P(X=x) = \begin{cases} \dfrac{\binom30 \binom32}{\binom62} = \dfrac3{15} & \text{if }x=0 \\\\ \dfrac{\binom31 \binom31}{\binom62} = \dfrac9{15} & \text{if }x = 1 \\\\ \dfrac{\binom32 \binom30}{\binom62} = \dfrac3{15} & \text{if }x=2 \\\\ 0 &\text{otherwise}\end{cases}[/tex]
Find a solution to dA/dt=-6A if A(0)=6. A(t)=
This equation is separable,
[tex]\dfrac{dA}{dt} = -6A \implies \dfrac{dA}A = -6\,dt[/tex]
Integrate both sides and solve for [tex]A[/tex] :
[tex]\displaystyle \int \frac{dA}A = -6 \int dt[/tex]
[tex]\ln|A| = -6t + C[/tex]
[tex]e^{\ln|A|} + e^{-6t+C}[/tex]
[tex]\implies A(t) = Ce^{-6t}[/tex]
Solve for [tex]C[/tex] using the initial value.
[tex]A(0) = 6 \implies 6 = Ce^0 \implies C=6[/tex]
Then the particular solution is
[tex]\boxed{A(t) = 6e^{-6t}}[/tex]
Simplify 1-4 can you show how you got the answer on a sheet of paper.
Answer:
to solve fractions such as
1 1/3
first multiple the denominator with the whole no.
and then add with the numerator
here 3 * 1 + 1 /3
= 4/3
1 2/3
= 3*1 + 2 /3
5/3
which matrix equation represents the system of equations
Answer:
option B is correct
To write any equations in the form of matrix
first make a matrix of all coefficients of that equations.. here coefficients of first equation is 4 and - 2 and that of second is 0 ( as there is no value of X) and 3
then make second matrix of X and y
last of answer of the equations, here (-7 ) and 5
A restaurant offers 7 appetizers and 8 main courses. In how many ways can a person order a two-course meal?
There are ways a person can order a two-course meal.
Answer:
56
Step-by-step explanation:
so 7 appetizers times 8 main courses
I do a easy trick where I multiple so
7×8=56
24. Show and explain clearly, how you would solve the following problem using John Mason's Model for problem solving: A lady rears goats and fowls in her backyard. She observed that there were 42 eyes and 66 legs in her backyard. How many fowls and how many goats are in the yard?
The number of fowls is 9, and the number of goats is 12 if there were 42 eyes and 66 legs in her backyard.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x be the number of fowls and
y be the number of goats
Then total eyes = 2x + 2y
Because both have two eyes
2x + 2y = 42 ..(1)
Total legs = 2x + 4y
fowl has two legs and a goat has 4 legs
2x + 4y = 66 ..(2)
After solving two linear equation:
-2y = -24
y = 12
x = 9
Thus, the number of fowls is 9, and the number of goats is 12 if there were 42 eyes and 66 legs in her backyard.
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Which expression is equivalent to the given expression? 4lh x + lh 3 - lh x
my sis needs help asap SHOW WORK! :)
Step-by-step explanation:
el resultado le puedo ayudar si sabe Spanish
Answer:
see below
Step-by-step explanation:
White = 1 1/3 = 4/3 = 16/12
Color = 3/4 = 9/12
white - color == 16/12 - 9/12 = (16-9) / 12 = 7/12 of a scoop more for the white load
The linear function that is represented by which table has the same slope as the graph? On a coordinate plane, a line goes through points (0, negative 3) and (2, 1). a A 2-column table with 5 rows. Column 1 is labeled x with entries negative 25, negative 21, negative 17, negative 13, negative 9. Column 2 is labeled y with entries negative 9, negative 7, negative 5, negative 3, negative 1. b A 2-column table with 5 rows. Column 1 is labeled x with entries negative 25, negative 21, negative 17, negative 13, negative 9. Column 2 is labeled y with entries 9, 7, 5, 3, 1. c A 2-column table with 5 rows. Column 1 is labeled x with entries negative 9, negative 7, negative 5, negative 3, negative 1. Column 2 is labeled y with entries negative 25, negative 21, negative 17, negative 13, negative 9. d A 2-column table with 5 rows. Column 1 is labeled x with entries 1, 3, 5, 7, 9. Column 2 is labeled y with entries negative 9, negative 13, negative 17, negative 21, negative 25.
Option C. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 9, negative 7, negative 5, negative 3, negative 1. Column 2 is labeled y with entries negative 25, negative 21, negative 17, negative 13, negative 9. This labeled is correct.
According to the linear function,
Every linear function is characterized by a constant rate of change; the slope. The slope of a linear function is a measure of the “steepness” of the line. We use the symbols Δx and Δy which mean respectively the “change in x ” and the “change in y ”.
So Option C is correct after all assumptions.
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given the formula p=k*2 w, find the value of p if k= 5 and w= - 3
A condominium is taxed based on its $78,584 value. The tax rate is $3.49 for every $100 of value. If the tax is paid before March 1, 4%
of the normal tax is given as a discount. How much tax is paid if the condominium owner takes advantage of the discount?
The tax paid by the condominium owner is $2,632.88.
What is the tax paid?
Tax is a compulsory levy that is paid to the government. The type of tax that is paid by the condominium owner is known as property tax.
Tax paid = (78,584 / 100) x $3.49 x (1 - 0.04) = $2,632.88.
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The movement of the progress bar may be uneven because questions can be worth more or less (including zera
Round 608 to the nearest hundred.
O 610
Type here to search
O 700
O 500
O 600
4
Oi
1
Answer:
600
Step-by-step explanation:
Because the tens digit is less than 5, round down to 600
A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compare over the interval
The exponential function decays at one-half the rate of the quadratic function.
The exponential function decays at the same rate as the quadratic function.
The exponential function decays at two-thirds the rate of the quadratic function.
The exponential function decays at three-fourths the rate of the quadratic function.
The exponential function decays at three-fourths the rate of the quadratic function.
The given inequality is -2≤x≤0.
We need to determine how do the decay rates of the functions compare over the interval.
What is the quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.
We calculate the average slope of each graph in the indicated interval, the slope can be calculated as [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
Now, for the exponential function:
[tex]m_{c} =\frac{4-1}{-2-0} =\frac{3}{-2}[/tex]
For the quadratic function:
[tex]m_{q} =\frac{4-0}{-2-0} =\frac{4}{-2}=-2[/tex]
Now, the ratio of both average slopes is[tex]\frac{m_{c} }{m_{q}} =\frac{\frac{3}{-2} }{-2} =\frac{3}{4}[/tex].
Therefore, the exponential function decays at three-fourths the rate of the quadratic function.
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How do I graph y−3=1/2(x+3) on this graph? :c
From point (0, 9/2) and (-9, 0) we get a straight line.
What is Straight line?A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extend to infinity.
Here, given equation:
(y − 3) = 1/2(x + 3)
at x = 0,
y - 3 = 1/2 (0 + 3)
y - 3 = 1/2 X 3
y = 3/2 + 3
y = 9/2
at y = 0,
0 - 3 = 1/2 (x + 3)
-3 = 1/2 (x + 3)
-6 = x + 3
x = -6 - 3
x = -9
Thus, from point (0, 9/2) and (-9, 0) we get a straight line.
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9)Rover the dog is on a 60-foot leash. One end of the leash is tied to Rover, who is 2 feet tall. The
other end of the leash is tied to the top of an 8-foot pole. How far can Rover roam from the
pole?
The dog can roam 59.7 feet if the dog is on a 60-foot leash. One end of the leash is tied to Rover, who is 2 feet tall.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
We have:
Rover the dog is on a 60-foot leash. One end of the leash is tied to Rover, who is 2 feet tall. The other end of the leash is tied to the top of an 8-foot pole.
After drawing a right-angle triangle from the above information.
Applying Pythagoras' theorem:
60² = 6² + x²
After solving:
x = 59.69 ≈ 59.7 foot
Thus, the dog can roam 59.7 feet if the dog is on a 60-foot leash. One end of the leash is tied to Rover, who is 2 feet tall.
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Question 6 of 15
Gloria invested $1200 in an account that earns 2.5% interest, compounded
annually. The formula for compound interest is A(t) = P(1 + i)t. How
much did Gloria have in the account after 5 years?
O A. $3662.11
OB. $6150.00
OC. $1470.00
OD. $1357.69
Answer:
D
Step-by-step explanation:
[tex]1200( {1.025}^{5} ) = 1357.69[/tex]
someone help solve asap for points
Answer:
[tex]\textsf {p(-4) = -134}[/tex]
Step-by-step explanation:
[tex]\textsf {Given :}\\[/tex]
[tex]\mathsf {p(x) = x^{3} - 3x^{2} + 7x + 6}[/tex]
[tex]\textsf {Substitute x = -4 to find p(-4) :}[/tex]
[tex]\mathsf {p(-4) = (-4)^{3} - 3(-4)^{2} + 7(-4) + 6}[/tex]
[tex]\mathsf {p(-4) = -64 - 48 - 28 + 6}[/tex]
[tex]\textsf {p(-4) = 6 - 140}[/tex]
[tex]\textsf {p(-4) = -134}[/tex]
Identify the value of the variable in the equivalent expressions.
What is the value of n in the simplified expression?
(4k7)3= 4n ·(k7) 3= 64k21
n =
What is the value of m in the simplified expression?
(Negative 3 r Superscript negative 4 Baseline) Superscript negative 4 Baseline = (negative 3) Superscript negative 4 Baseline times (r Superscript negative 4 Baseline) Superscript negative 4 Baseline = StartFraction 1 Over 81 EndFraction r Superscript m
m =
The value of expression is n=3 and r= 16
What is expression?An expression is a set of terms combined using the operations +, – , x or , /.
Given:
[tex](4k^{7})^{3} = 4^{n}* (k^{7})^{3} = 64 k^{21}[/tex]
[tex](64 k^{21}) = 4^{n}* k^{21} = 64 k^{21}[/tex]
[tex]4 ^{3} * k^{21}= 4^{n}* k^{21}[/tex]
On comparing
n=3
Now,
[tex](-3r^{-4})^{-4} = (-3)^{-4} * (r^{-4})^{-4} = 1/81* r^{m}[/tex]
[tex](-3)^{-4} * (r^{-4})^{-4} = 1/81* r^{m}\\1/ (-3)^{4} * 1/(r^{-4})^{4} = 1/81* r^{m}\\1/ (-3)^{4} * (r^{16}) = 1/81* r^{m}[/tex]
1/81 * r^16 = 1/81 * r^{m}
On compairing
r = 16.
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Answer:
answer in picture
Step-by-step explanation:
Set up a linear system and solve. A cash register contains $5 bills and $50 bills with a total value of $345. If there are 15 bills total, then how many of each does the register contain?
Answer:
6 $50 bills and 9 $5 bills
Step-by-step explanation:
Let's let x = the number of $5 bills, and y = the number of $50 bills. With this, we can set up two equations:
5x + 50y = 345
x + y = 15
Because there is $345 total in the register, that means that 5 times the number of $5 bills plus 50 times the number of $50 bills would equal 345. And there are 15 bills total, so the numbers added is 15. Now, we can solve these equations through substitution:
x + y = 15
x = 15 - y
Now, plug in (15 - y) for x into the other equation, and solve for y:
5(15 - y) + 50y = 345
75 - 5 y + 50y = 345
75 + 45y = 345
45y = 270
y = 6
Since y is 6, that means we have 6 $50 bills. And there are 15 bills total, so there are 9 $5 bills. (15 - 6 = 9)
In which expression would you complete the operation first and then find the absolute value of the sum?
a |11/8+2/3|
b|-17.3| - |9.05|
c|-35| - |22|
d|-18.531| + |19.2894|
enita is factoring the expression 32 a b minus 8 b. She determines the GCF and writes the factored expression as 8 b (4 a minus 0). Which best describes Venita’s error?
a. She incorrectly determined the GCF.
b. She subtracted the GCF from the second term in the expression instead of dividing.
c. She divided the GCF into the first term in the expression instead of subtracting.
d. She divided each piece of the expression by different factors.
This shows that the greatest common factor is 8, Hence Venita's error is that she incorrectly determined the GCF.
Greatest common factorGiven the following expression
32ab - 8
Find the factors of each terms
32ab = 8 * 4. * a * b
8 = 8 * 1
Since 8 is common to both factors, hence
32ab - 8 = 8(4ab -1)
This shows that the greatest common factor is 8, Hence Venita's error is that she incorrectly determined the GCF.
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Line m passes through the points (-4,3) and (-4,7). What is the slope of the line that is parallel to line m?
Answer:
undefined
Step-by-step explanation:
Since line m passes through two points that have the same x-value but different y values, line m is horizontal to the y-axis which has an undefined slope.
PLEASEEEE PLEASEEEEEEEEE HELPPPPPPPPPP
how do i solve this equation?
Answer:
360
Step-by-step explanation:
using the definition
n [tex]P_{r}[/tex] = [tex]\frac{n!}{(n-r)!}[/tex]
where n! = n(n - 1)(n - 2)..... × 3 × 2 × 1
then
6[tex]P_{4}[/tex]
= [tex]\frac{6!}{(6-4)!}[/tex]
= [tex]\frac{6!}{2!}[/tex]
= [tex]\frac{6(5)(4)(3(2)(1)}{2(1)}[/tex] ← cancel 2(1) on numerator / denominator
= 6 × 5 × 4 × 3
= 360
a rhombus has perimeter 120 M and one of its diagonal is 50 M find the area of the Rhombus
The area of the rhombus is 829.1562m².
What is the area of the rhombus?A rhombus is a four sides quadrilateral with the four sides equal in length
The area of a rhombus = [tex]\frac{1}{4}d[/tex] ×√(p² - 4d²)
where p is the perimeter and d is the diagonal
1/4(50) x √(120² - 4 x 50²) =829.1562m²
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Find f(x) and g(x) so that the
function given can be described
as y = f(g(x)).
y = e^sin x
Answer:
g(x) = sin(x)
f(x) = e^x
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]f(x)=e^x\\g(x)=sin~x\\y=f(g(x))=f(sin~x)=e^{sin~x}[/tex]
Problem 5. Utility Bills The monthly utility bills in a city are normally distributed and
represented by the variable X, with a mean of $100 and a standard deviation of $12. Find the
probability that a randomly selected utility bill is
(a) less than $70,
(b) between $90 and $120,
(c) more than $140.
(2 points)
(2 points)
(2 points)
Hint: Convert the normal distribution X to Standard normal using Z formula Z =
and then look the Z-values from the table and then find the probability.
X-μ
6
The probabilities in the question are
0.00620.74990.000429How to solve for the probabilitiesa. For x < 70
we have
z< 70 - 100/12
= z < -30/12
= -2.5
Such that p (x<70) = 0.0062
Hence the probability that is is less than $70 = 0.0062
b. between $90 and $120,90 - 100/12. 120 - 100/12
= -0.8333 <z< 1.67
p(90<x<120) = 0.95224 - 0.20234
= 0.7499
0.7499 is the probability of between $90 and $120.
c. more than $140140-100/12
= P(Z>3.3333)
= 0.000429
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How is the two point formula used to find the equation of a line when 2 points are known? a. taking the change in y over the change in x c. dividing the first y by the first x b. taking the change in x over the change in y d. dividing the first x by the first y Please select the best answer from the choices provided A B C D
Taking the change in y over the change in x. Then the correct option is A.
What is the equation of a line passing through two points?Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by
[tex]\rm (y - y_1) = \left [ \dfrac{y_2 - y_1}{x_2 - x_1} \right ] (x -x_1)[/tex]
The equation of the line can be determined by the two known points.
Taking the change in y over the change in x.
Then the correct option is A.
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Solve the problem.
Determine dy/dt for x^3 + y^3 = 9 given x = 1, y = 2, and dx/dt= -3
Differentiate both sides with respect to [tex]t[/tex], treating both [tex]x[/tex] and [tex]y[/tex] as functions of [tex]t[/tex].
[tex]x^3 + y^3 = 9 \implies 3x^2 \dfrac{dx}{dt} + 3y^2 \dfrac{dy}{dt} = 0[/tex]
Then when [tex]x=1[/tex], [tex]y=2[/tex] and [tex]\frac{dx}{dt}=-3[/tex], we get
[tex]3\times1^2\times(-3) + 3\times2^2\dfrac{dy}{dt} = 0 \implies \dfrac{dy}{dt} = \dfrac9{12} = \boxed{\frac34}[/tex]
Dominic had a coupon for 15 off his purchase at Save4You. At DiscountsRUs, there was a sale of 40% off on any purchase. Which store offered the better discount, and how much is the difference?
The better option will be at DiscountsRUs 40% off on any purchase.
What is the discount?The amount of money which is reduced on any product below its actual selling price is called the discount.
here we have two offers from the two stores Dominic had a coupon for 15 off his purchase at Save4You. At DiscountsRUs, there was a sale of 40% off on any purchase.
For a Dominic, the discount is fixed for any purchase that is if you purchase a $50 product or a $1000 product you will be getting only a $15 discount.
Now for the second store, the discount is given as 40% so if you purchase $50 your discount will be $20. If you purchase $1000 so 40% discount will be $400.
Therefore better option will be at DiscountsRUs 40% off on any purchase.
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a. d(7) 6
b. Interpret the meaning of d(7):
OA. In the first 6 seconds, the particle moved a total of 7 feet.
B. The particle was 7 feet away from the starting line 6 seconds since timing started.
OC. The particle was 6 feet away from the starting line 7 seconds since timing started.
D. In the first 7 seconds, the particle moved a total of 6 feet.
c. Solve d(t) = 2 for t. Use commas to separate your answers if there are more than one solution. t =
d. Interpret the meaning of part c's solution(s):
OA. The article was 2 feet from the starting line 9 seconds since timing started.
OB. The article was 2 feet from the starting line 1 seconds since timing started.
C. The article was 2 feet from the starting line 1 seconds since timing started, or 9 seconds since timing started.
D. The article was 2 feet from the starting line 1 seconds since timing started, and again 9 seconds since timing started.
dit on this problem.
Answer:
Step-by-step explanation:
The temperature is dropping at a rate of five degrees per hour.
Let d represent the number of degrees the temperature drops.
Let t represent the number of hours that pass.
Which is the dependent variable?
Othe number of hours
Othe number of degrees the temperature drops
O the rate at which the temperature drops
the day of the week
Answer:
The rate at which the temperature drops.
Step-by-step explanation:
In science, the dependent variable is what you are measuring.
In math, the dependent variable is what you are evaluating.
Same idea, different topic.
Answer:
d=temp drop
t=hours
dependent variable is the temperature drops because the number of hours will tell you how much the temprature drops
this is the equation
total temp drops=t x 5
hope this helps!?