The value of Double integral will be [tex]\mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}[/tex]
A two-dimensional region can be integrated using double integrals. They enable us to, among other things, calculate the volume beneath a surface.
The integrals of a function in two variables over a region in R2, or the real number plane, are referred to as double integrals in mathematics. It is possible to write the double integral of a function of two variables, such as f(x, y), over a rectangular region as: R f (x, y) d A = R f (x, y) d x d y.
We know that by the property of integral [tex]$\int u \mathrm{udv}=u v-v \int d u$[/tex]
[tex]$$\begin{aligned}& \mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}=\left[\mathrm{x} \ln (1+\mathrm{x})-\int \mathrm{x} \frac{.1}{1+\mathrm{x}} \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4\left[\mathrm{x} \ln (1+\mathrm{x})-\int\left(1-\frac{1}{1+\mathrm{x}}\right) \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4[\mathrm{x} \ln (1+\mathrm{x})-\mathrm{x}+\ln |1+\mathrm{x}|]_0^4 \\& \mathrm{I}=[4 \ln (5)-4+\ln (5)]-[0-0+0] \\& \mathrm{I}=4[5 \ln 5-4] \\& \mathrm{I}=20 \ln 5-16\end{aligned}$$[/tex]
We have to evaluate the given double integral
[tex]$$\iint_{\mathrm{R}} \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dA} \text { where } \mathrm{R}=[0,4] \times[0,1]$$[/tex]
[tex]$$\begin{aligned}& \mathrm{I}=\int_0^4 \int_0^1 \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dydx}=\int_0^4 4 \mathrm{x}\left[\frac{|1+\mathrm{xy}|}{\mathrm{x}}\right]_0^1 \mathrm{dx} \\& \mathrm{I}=\int_0^{44}[\ln |1+\mathrm{x}|-0] \mathrm{dx}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}\end{aligned}$$[/tex]
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pls help super simple!!!
The minimum and the maximum of the linear equation - 2 · a + b are - 4 and - 1, respectively.
How to find the possible values of a given expression
In this question we find an algebraic expression that comprises two variables (a, b) and each variable is defined by following inequalities:
3 < a < 4
4 < b < 5
Herein we must determine the minimum and the maximum associated with linear equation - 2 · a + b:
Minimum (a = 4, b = 4)
m = - 2 · 4 + 4
m = - 4
Maximum (a = 3, b = 5)
M = - 2 · 3 + 5
M = - 1
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what is 131.4 divided by 6 equal?
21.9 is the answer to 131.4/6
Answer:
21.9
Step-by-step explanation:
learn how to use a calculator.
the perimeter of a rectangle is 34 centimenters the length is two more than twice the width. write and solve a system of linear equations to find the width of the rectanlge.
The linear equation that can be used to find the width of the rectangle is 34 = 6w, and w = 5.67cm
What is linear equation?A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.
The length of the rectangle is twice the width. Therefore, l = 2w
The perimeter of a rectangle is expressed as : P = 2(l+w)
l = 2w
P= 2(2w + w)
P = 6w
34 = 6w
therefore the equation that can be used to find the width of the rectangle is 34 = 6w
and the value of w = 34/6 = 5.67cm
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please help me find the positive and negative.. thank you :)
The positive intervals are the y values over (0,∞ )
The negative intervals are the y values over (0,9]
What is Function?
A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.
The periods where a function is above the x-axis are considered its positive regions. Where the y-values are positive is where it is (not zero). Periods where a function is below the x-axis are referred to as its negative regions. This is the case when the y-values are negative (not zero).
The graph extends to infinity from the origin above x-axis
So, the positive intervals are the y values over (0,∞ )
The graph extends to y=9 from the origin below x-axis
So, the negative intervals are the y values over (0,9]
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I WILL MARK BRAINLIST!! HELP IMMEDIATELY
Answer: 25°F is approximately $375.
Step-by-step explanation:
The scatter plot shows a positive correlation between the average monthly temperature (x) and the family's monthly heating cost (y). The line of best fit appears to be a linear equation, and it can be approximated by the equation y = mx + b, where m is the slope and b is the y-intercept.
(a) One possible equation of the line of best fit for the data is y = 15x + 300. This equation is only an approximation as it is hard to determine the exact line of best fit without more data points.
(b) Using the equation y = 15x + 300, the predicted monthly heating cost for a month with an average temperature of 25°F can be found by plugging in x = 25 into the equation.
y = 15(25) + 300 = 375
Therefore, the predicted monthly heating cost for a month with an average temperature of 25°F is approximately $375.
PWEASE PWEASE PWEASE
Answer:
-2
a open bracket
and then a and - a negate each other to give -2
y=30m+12t
y=15m+15t
how many minutes can you use your phone on both plans for the same cost?
what is the cost?
Answer:
1/5 of a minute they are equal.
The cost would be $18
Step-by-step explanation:
Something does not look right. You would not have 3 variables.
Set the two equations equal to each other and solve for m. I think that the variables t may be an error.
30m + 12 = 15m + 15 Subtract 15 m from both sides
30m -15 m + 12 = 15m -15m + 15
15m + 12 = 15 Subtract 12 from both sides
15m + 12 - 12 = 15 - 12
15m = 3 Divide both sides by 15
[tex]\frac{15m}{15}[/tex] = [tex]\frac{3}{15}[/tex]
m = [tex]\frac{1}{5}[/tex]
Cost:
y = 30m + 12
y = 30(1/5) + 12
y = 18
y = 15m + 15
y = 15(1/5) + 15
y = 3 + 15
y = 18
What is the equation of the tangent to the parabola y=4+2x-x^2 such that:
PLEASE HELP 100 POINTS+ BRAINLIEST
Answer:
[tex]\textsf{1)} \quad y=x+\dfrac{17}{4}[/tex]
[tex]\textsf{2)} \quad y=2x+4[/tex]
Step-by-step explanation:
Differentiation is an algebraic process that finds the gradient (slope) of a curve.
At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.
Given function:
[tex]y=4+2x-x^2[/tex]
Differentiate the given function:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2-2x[/tex]
If the tangent to the parabola forms an angle of 45° with the negative direction of the x-axis, then the gradient of the tangent is 1.
Set the differentiated function to 1 to find the x-value of the point where the gradient of the tangent is 1:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=1[/tex]
[tex]\implies 2-2x=1[/tex]
[tex]\implies -2x=-1[/tex]
[tex]\implies x=\dfrac{1}{2}[/tex]
Substitute x = 1/2 into the given function to find the y-value of the point:
[tex]\implies y=4+2\left(\dfrac{1}{2}\right)-\left(\dfrac{1}{2}\right)^2=\dfrac{19}{4}[/tex]
Therefore, the point at which the tangent of the parabola forms an angle of 45° with the negative direction of the x-axis is:
[tex]\left(\dfrac{1}{2},\dfrac{19}{4}\right)[/tex]Substitute the found point and slope into the point-slope formula to create an equation of the tangent:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-\dfrac{19}{4}=1\left(x-\dfrac{1}{2}\right)[/tex]
[tex]\implies y=x+\dfrac{17}{4}[/tex]
--------------------------------------------------------------------------------------
Given function:
[tex]y=4+2x-x^2[/tex]
Differentiate the given function:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2-2x[/tex]
If the tangent to the parabola is parallel to the line y = 2x - 4 then the gradient of the tangent is 2 (since parallel lines have the same gradient).
Set the differentiated function to 2 to find the x-value of the point where the gradient of the tangent is 2:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2[/tex]
[tex]\implies 2-2x=2[/tex]
[tex]\implies -2x=0[/tex]
[tex]\implies x=0[/tex]
Substitute x = 0 into the given function to find the y-value of the point:
[tex]\implies y=4+2\left(0\right)-\left(0\right)^2=4[/tex]
Therefore, the point at which the tangent of the parabola is parallel to the line y = 2x - 4 is:
(0, 4)Substitute the found point and slope into the point-slope formula to create an equation of the tangent:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-4=2\left(x-0\right)[/tex]
[tex]\implies y=2x+4[/tex]
Find y' and y''.
y = √x ln(x)
y' = ...?
y'' = ...?
Therefore , the solution of the given problem of equation comes out to be y" = -1/4 *√x * ln(x) + 1/2√x -1/2 * √x .
What is the equation?A mathematical equation looks to be a formula that joins two statements and indicates equality when it uses the equals symbol (=). In algebra, an equation is a statement of fact that demonstrates the equality of different mathematical variables . For instance, the result obd + 6 = 12 has an equal sign between quantities ptdc + 6 and 12. There is a mathematical formula that describes the connection between the syllables on either side of each letter. The emblem and the statement are frequently the same.
Here,
y = √x ln(x)
To find the y'
=> dy/dx = d(√x ln(x)) /dx
=> dy/dx = 1/2√x * ln(x) + 1/x *√x
=> dy/dx = 1/2√x * ln(x) + 1/√x
To find the value of y ''
=> dy'/dx = d(1/2√x * ln(x) + 1/√x ) / dx
=> dy'/dx = 1/2 * (-1/2* √x * ln(x) + 1/√x ) -1/2 * √x
=>dy'/dx = -1/4 *√x * ln(x) + 1/2√x -1/2 * √x
Therefore , the solution of the given problem of equation comes out to be y" = -1/4 *√x * ln(x) + 1/2√x -1/2 * √x .
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the length of a puppy on a scale drawing is 6 cm. if the scale is 1:9 cm, what is the actual length of the puppy?
Despite appearing to be 6 cm long on a scale drawing, puppies are actually 54 cm long.
what is length ?Distance between two sites can be determined by a measurement called length. Aside from height and width, it also determines how long an object is. In math classes, kids will study about length to assist them in solving real-world problems both as a part of their education and outside of it. the largest or longest dimension of a thing; a measurable length or width. Dimensions: 10 ft. Table of the Metric System, Weights and Measures Table: the characteristic of length. The definition of length is the distance or measurement between two points. In other terms, the largest two or highest three dimensions of a geometric shape or item.
given
Puppy drawn to scale measures 6 cm in length.
due to the scale's 1:9 cm
Utilize the ratio approach to determine the puppy's true length.
1 = 6 cm
9 = 6×9 = 54 cm
Despite appearing to be 6 cm long on a scale drawing, puppies are actually 54 cm long.
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Which function is shown on the graph?
ANSWER OPTIONS
A: f(x) = - 1/2 cos x
B: f(x) = -1/2 sin x
C: f(x) = 1/2 cos x
D: f(x) = 1/2 sin x
The function shown on the graph is f(x) = - 1/2 cos x.
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
Here,
We have given a graph and we have to determine which function is shown on the given graph.
We concluded that
The amplitude of the first graph is (1/2) which is the height from the midline to the peak.
The value of the function at x = 0 is -(1/2), where sin(0) = 0, therefore, the function is a cosine function
The period of the graph is 2·π, which is the period of the parent cosine function.
Hence, the function shown on the graph is f(x) = - 1/2 cos x.
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parallel to x-2y=17 through (-10,4)
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]x-2y=17\implies -2y=-x+17\implies y=\cfrac{-x+17}{-2} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}} x-\cfrac{17}{2}\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is 1/2 and that it passes through (-10 , 4)
[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{(-10)}) \implies y -4= \cfrac{1}{2} (x +10) \\\\\\ y-4=\cfrac{1}{2}x+5\implies {\Large \begin{array}{llll} y=\cfrac{1}{2}x+9 \end{array}}[/tex]
Which of the following can be the sides of a right triangle?
(i) 2.5 cm, 6.5 cm, 6 cm
(ii) 2 cm, 2 cm, 5 cm
(iii) 1.5 cm, 2cm, 2.5 cm
In the case of right-angled triangles, identify the right angles
(i) 2.5 cm, 6.5 cm, 6 cm and (iii) 1.5 cm, 2cm, 2.5 cm can be the sides of a right triangle.
To check if the given measurements are possible sides of a right triangle, it must follow the Pythagorean theorem, where the square of the hypotenuse is equal to the sum of the squares of the legs.
c² = a² + b²
where c is the hypotenuse(longest side)
and a and b are the two other sides
(i) 2.5 cm, 6.5 cm, 6 cm
6.5² = 2.5² + 6²
42.25 = 6.25 + 36
42.25 = 42.25
(ii) 2 cm, 2 cm, 5 cm
5² = 2² + 2²
25 = 4 + 4
25 ≠ 8
(iii) 1.5 cm, 2cm, 2.5 cm
2.5² = 1.5² + 2²
6.25 = 2.25 + 4
6.25 = 6.25
Hence, (i) 2.5 cm, 6.5 cm, 6 cm and (iii) 1.5 cm, 2cm, 2.5 cm can be the sides of a right triangle.
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5 log(2) rewrite in log(c)
The solution to the given logarithmic equation is log32
Law of logarithmsThe logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which b must be raised in order to obtain a number x is its logarithm to the base b.
One of the law of logarithm is expressed as:
bloga = log a^b
Applying this law to the given question;
5 log(2) =log2⁵
Since 2⁵ = 32, hence the given expression is equivalent to log32.
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A handyman wants to build a fence round a garden in the shape of a triangle. He plans to use a 6-ft-longpiece of fencing and a 7-ft-long piece of fencing. What could be the length of the third piece of fencing?
Answer:
1 < x < 13
Step-by-step explanation:
The longest leg of a triangle must be less than the sum of the shorter legs.
c < a + b
If the third piece is the longest leg, then:
x < 6 + 7
x < 13
If the 7-ft piece is the longest leg, then:
7 < 6 + x
x > 1
Therefore, the third leg is between 1 ft and 13 ft.
please help me fast no w!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
A
Step-by-step explanation:
A run-on sentence occurs when independent clauses are not joined properly.
students in mrs. barnes class determined the probability that she will check homework on a randomly chosen day is 0.42. they also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9. the probabilities are displayed in the tree diagram. a tree diagram. random day goes to checks homework and does not check homework. the arrow to checks homework is 0.42, and does not check homework is 0.58. checks homework to pop quiz, 0.60; checks homework to no pop quiz, 0.40. does not check homework to pop quiz, 0.90; does not check homework to no pop quiz, 0.10. what is the probability that the students will have a pop quiz on a randomly selected day? 0.25 0.52 0.77 0.90
The probability that the students will have a pop quiz on a randomly selected day 0.77
Mrs. Barnes’s class determined the probability that she will check homework on a randomly chosen day is 0.42.
They also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9.
Then the probability that Mrs. Barnes does not check homework if the students take a pop quiz will be
P= 0.42*0.60 + 0.58*0.90
P = 0.252 + 0.522
P = 0.774
P ≈ 0.77
The probability that the students will have a pop quiz on a randomly selected day 0.77
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four fair six-sided dice are rolled. what is the probability that at least two dice show a 3? express your answer as a common fraction.
Four fair six-sided dice are rolled. The probability that at least two dice show a 3 is 1/36.
In the given question, four fair six-sided dice are rolled.
We have to find the probability that at least two dice show 3.
There are four dice and each have 6 numbers to come.
So total number of cases = 6×6×6×6
Total number of cases = 1296
At least two dice show 3. So
The favorable outcome = 6 × 5
The favorable outcome = 30
The possible outcome = aabc, abac, abca, baac, baca, bcaa = 6
Total of outcomes = 30 + 6
Total of outcomes = 36
The probability that at least two dice show a 3 = 36/1296
The probability that at least two dice show a 3 = 1/36
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A rectangle ha a perimeter of 112. If the ide are 5x & 3x 5, what i x and what are each of the ide?
As a result, the rectangle's sides measure 5x = 5(6.375) = 31.875 inches and 3x+5 = 3(6.375) + 5 = 20.125 inches, respectively.
We may utilize the knowledge that the rectangle's perimeter is 112 and that its sides are 5x and 3x+5 to determine the value of x and the lengths of each side. We can put up the following equation because the perimeter of a rectangle is equal to the sum of its four sides:
2(5x) + 2(3x + 5) = 112
We must simplify and account for x in order to solve for x. We'll start by allocating the two on the left side of the equation:
10x + 6x + 10 = 112
We'll then mix similar terms:
16x + 10 = 112
To get x alone, we will now deduct 10 from both sides, giving us 16x = 102.
Next, multiply both sides by 16 times to get 6.375.
Therefore as a result, the rectangle's sides measure 5x = 5(6.375) = 31.875 inches and 3x+5 = 3(6.375) + 5 = 20.125 inches, respectively.
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Replace variables wit values and evaluate using order of operations D= wt² W=70 T=4 give your answer in simplest form
The value of variable d is 1120
How to determine the value of variable d from the known valuesFrom the question, we have the following parameters that can be used in our computation:
D= wt²
Where W = 70 and T = 4
Substitute the known values in the above equation, so, we have the following representation
D = 70 * 4²
Evaluate the exponent
D = 70 * 16
Evaluate the products
D = 1120
Hence, the solution is 1120
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What is stable solution Class 9?
A stable solution is a solution to a problem that does not change when the parameters of the problem are slightly varied. It is a point at which there is no net change, or a point of equilibrium.
A stable solution is a solution to a problem that does not change when the parameters of the problem are slightly varied. The parameters of a problem can refer to the data, assumptions, constraints, or other factors that are used to define the problem. When the parameters are changed, a stable solution will remain intact, indicating that it is the best solution to the problem.
For example, if a mathematics problem has a solution of 3, this solution is considered to be stable, as changing any of the parameters of the problem will not alter the solution of 3.
Stable solutions are important as they provide a point of equilibrium, or a point at which there is no net change. This can help to ensure that the solution is the most effective one to the problem.
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amy has 4 pounds of ground turkey to make meatballs. she uses 3/8 pound per meatball to make 9 meatballs. how many 1/8 meatballs can amy make with the remaining turkey
As per the unitary method, the number of meatballs made using the the remaining turkey is 29 meatballs
The term unitary method is known as the way to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.
Here we have know that Amy has 4 pounds of ground turkey to make meatballs
And here we also know that she uses 3/8 pound per meatball to make 9 meatballs
Then in order to find the remaining we have to subtract 3/8 from 4
Then we get,
=> 4 - 3/8
=> 29/8
Therefore, here we have identified that there are 21/8 pounds of ground turkey left
As here we have given that the number of 1/8 pound meatball that can be produced from 21/8 pounds of ground turkey can be calculated as follows,
=> 29/8 ÷ 1/8
When we simplify this one then we get,
=> 29
So, Amy can make 29 meatballs
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Look at the cups shown below (please note images are not drawn to scale):
A cone is shown with width 2 inches and height 4 inches, and a cylinder is shown with width 2 inches and height 6 inches.
How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth.
8.8 cubic inches
10.1 cubic inches
14.7 cubic inches
22.3 cubic inches
Answer
22.3 is correct i believe :)
Step-by-step explanation:
Construct a vertical transversal and horizontal transversal to lines AB and DC that intersect each other at F. Label the points of intersection to the parallel lines A, B, C, and D.
Pls help!!
The missing statement in the given proof is ΔFDC ≅ Δ FAB, reason SAS. Option C is correct.
What is congruent geometry?In congruent geometry, the shapes that are so identical. can be superimposed on themselves.
here,
As given in the quesiton,
Consider the triangle formed by the given construction,
ΔFDC and Δ FAB
AB║CD
∠FAB = ∠FCD
∠FBA = ∠FDC
So, ΔFDC ≅ Δ FAB, by SAS congruency.
Thus, the missing statement in the given proof is ΔFDC ≅ Δ FAB, reason SAS. Option C is correct.
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mi use structure ji builds a right rectangular prism with 14 centimeter cubes in the bottom layer with no gaps or pverlaps. if there are 8 layers, what is the volume of the right ectangular prism?
Mi use structure ji builds a right rectangular prism with 14-centimeter cubes in the bottom layer with no gaps or overlaps. if there are 8 layers, The volume of the right rectangular prism is 14 x 14 x 8 = 1,536 cm3.
To get this answer, I first determined the number of cubes in the bottom layer. Since the bottom layer contains 14 cubes, the total length of the base of the prism is 14 cm. The height of the prism is 8 layers, so the total height of the prism is 8 cm. To calculate the volume of a right rectangular prism, you need the base length, the width, and the height. Since all three of these measurements are given, the volume can be calculated by multiplying the base length (14 cm) by the width (14 cm) by the height (8 cm). The result is 1,536 cm3.
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mi use structure ji builds a right rectangular prism with 14-centimeter cubes in the bottom layer with no gaps or overlaps. if there are 8 layers, what is the volume of the right rectangular prism?
−11 + |−5| − |−15| help
The expression −11 + |−5| − |−15| containing modulus sign is solved to get -21
What are absolute values?Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.
A number can never have a negative absolute value.
How to solve the absolute value equationThe equation is written in the form below
= −11 + |−5| − |−15|
removing the absolute value sign
= −11 + 5 − 15
performing the mathematical operations (addition and subtraction)
= -11 - 10
= -21
The absolute value equation was solved to get -10
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a business organization needs to make up a 8 member fund-raising committee. the organization has 6 accounting majors and 9 finance majors. what is the probability that at least 4 accounting majors are on the committee?
The probability that at least 4 accounting majors are on the committee is P(at least 4 accounting majors) = 1 - P(less than 4 accounting majors)
We can use the complement rule to solve this problem. The complement rule states that the probability of an event happening plus the probability of the event not happening is equal to 1.
In this case, we can find the probability that less than 4 accounting majors are on the committee and then subtract that from 1 to find the probability that at least 4 accounting majors are on the committee.
There are 6 accounting majors and 9 finance majors, for a total of 15 students.
To find the probability that fewer than 4 accounting majors are on the committee, we can use the binomial probability formula:
P(k) = (combination(8,k)) [tex]\times (6/15)^k \times (9/15)^{(8-k)[/tex]
where k is the number of accounting majors on the committee.
To find the probability that fewer than 4 accounting majors are on the committee, we need to sum the probabilities for k = 0, 1, 2, and 3.
P(less than 4 accounting majors) = P(0) + P(1) + P(2) + P(3)
Finally, we can use the complement rule to find the probability that at least 4 accounting majors are on the committee:
P(at least 4 accounting majors) = 1 - P(less than 4 accounting majors)
You can calculate the exact probability using the binomial coefficient and the binomial probability formula and then subtract that from 1 to get the final probability.
To learn more about the probability, visit:
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what does 안녕하세요 mean??
Answer:
I hope my answer is helpful!
"안녕하세요" is a formal and polite way of saying "hello" in Korean. It is commonly used as a greeting, both when meeting someone for the first time and when meeting someone again after a period of time. The literal translation of 안녕하세요 is "Are you at peace?"
Bonnie is making a dipping sauce. She mixes 150150150 milliliters of soy sauce with 100100100 milliliters of vinegar.
How much soy sauce does Bonnie mix with every 111 milliliter of vinegar?
milliliters
How much vinegar does Bonnie mix with every 111 milliliter of soy sauce?
milliliters
Answer:
We need 166.5 ml of soy sauce when we have 111 ml of vinegar.
We need 74 ml of vinegar when we have 111 ml of soy sauce.
Step-by-step explanation:
I think that you meant 150 and not 150150150 and 100 and not 100100100
[tex]\frac{soy sauce}{vinegar}[/tex] = [tex]\frac{soy sauce}{vinegar}[/tex]
[tex]\frac{150}{100}[/tex] is the same as [tex]\frac{3}{2}[/tex] (simplified by dividing the top and the bottom by 50)
[tex]\frac{3}{2}[/tex] = [tex]\frac{x}{111}[/tex] Cross multiply and solve for x
2x = 3(111)
2x = 333 Divide both sides by 2
[tex]\frac{2x}{2}[/tex] = [tex]\frac{333}{2}[/tex]
x = 166.5
We need 166.5 ml of soy sauce when we have 111 ml of vinegar.
[tex]\frac{3}{2}[/tex] = [tex]\frac{111}{x}[/tex] Cross multiply and solve for x
3x = 2(111)
3x = 222 Divide both sides by 3
[tex]\frac{3x}{3}[/tex] = [tex]\frac{222}{3}[/tex]
x = 74
We need 74 ml of vinegar when we have 111 ml of soy sauce.
Expand out of brackets: 5(4d+f+h)
Answer: If you mean simplify then here: 20d+5f+5h
Step-by-step explanation:
Use distributive property to remove the parentheses.
20d+5f+5h
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