expand (x-2)^7 using binomial theorem​

Answer:

True

Explanation:

Bridget Riley was one of the most prominent artists associated with the 1960s 'Op Art' movement, which was an art movement that explored optical illusions and effects to create abstract art that played with the viewer's perception. However, there were many other artists associated with this movement, including Victor Vasarely, Richard Anuszkiewicz, and Yaacov Agam, among others.

The best estimate for the number of fish is that there are 82 yellow fish and 18 green fish, which you can calculate using the rule of three. This estimate is expected to be accurate.

This can be calculated using a rule of three as follows. Let's start with the yellow fish:

53 = 65

x    = 100

53 x 100 / 65 = 82 yellow fish

Green fish:

12 = 65

x = 100

12 x 100 / 65= 18 green fish

This estimate is expected to be accurate; however, there might be small differences in real life such as 80 yellow fish and 20 green fish.

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The value that would have the most dots on a line plot is given as follows:

4.25.

The dot plot gives a dot to each measure for each time that it appears, hence it says the same thing as a table, in a different format.

A line plot is built from the dot plot, in which:

Hence the value 4.25 is the value in this problem that would have the most dots in a line plot, as it is the value that appears the most times in the data-set (only value to appear three times).

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Answer:

A way for one of the toddler triplets to end up with their coat is if the other two toddler triplets each get one another coat.

making it a 33% chance of one of the toddler triplets to end up with their own coat.

100% divided by 3 = 0.33

The slope of the graph of this linear function is -1/2 in decimal form.

What is slope?

The formula to find the slope between 2 coordinates of a line is given by;

m = (y₂ - y₁)/(x₂ - x₁)

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (6, 1) and (x2, y2) = (-6, -5)

slope = (-5 - 1) / (-6 - 6)

slope = -6/12

slope = -1/2

Therefore, the slope of the graph of this linear function is -1/2 in decimal form.

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The obtained stress which is acting from every direction is at 45 degree.

The transformation equations will be used to calculate the stresses acting on an inclined element.

(σ x+σ y )/2  =75 MPa

(σ x-σ y )/2  =35 MPa

Tor xy = 28 MPa

sin 2θ = sin 90° = 1          

cos 2θ = cos 90° = 0

Substituting these values into Eqs

σ x1 =(σ x+σ y )/2+ (σ x-σ y )/2 cos2θ+ τxy sin2θ      

= 130 MPa

τ x 1 y 1 =  (σ x-σ y )/sin2θ + τxy cos2θ

σ y 1=  (σ x+σ y )/2- (σ x-σ y )/cos2θ+ τxy sin2θ    

= 47Mpa

Elements of stress

We can easily obtain the stresses acting on all sides of an element oriented at = 45° from these results.

The arrows indicate the true directions of the stresses. Take special note of the shear stress directions, which all have the same magnitude. Also, keep in mind that the sum of the normal stresses remains constant at 150 MPa.

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Answer:

75

Step-by-step explanation:

f(4) means to use 4 in place of x.

f(x) = 3(5)^(x-2)

fill in 4 for

f(4) = 3(5)^(4-2)

do the 4-2 subtraction first

f(4) = 3(5)^2

do the 5 to the 2nd power next.

f(4) = 3(25)

last, multiply.

f(4) = 75

This is just following the typical order of operations.

Answer:

2500

Step-by-step explanation:

Dimensions of first level

Length = Breadth = 75 ft (since it is a square)

It is assumed that a person will occupy \(2.25\ \text{ft}^2\)

Area of first level

\(75\times 75=5625\ \text{ft}^2\)

When the area of the level is divided by the area of one person then we will get the number of people that can occupy the room or the number of tickets that can be sold.

\(\dfrac{5625}{2.25}=2500\)

The number of tickets that can be sold for the first level is 2500.

The absolute value function that matches the graph is given as follows:

y = -|x + 1| + 1.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex in this problem are given as follows:

(-1, 1).

Hence:

y = a|x + 1| + 1.

The function is reflected over the x-axis with a slope of -1, hence the leading coefficient a is given as follows:

a = -1.

Thus the function is:

y = -|x + 1| + 1.

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A semicircle has been cut out of a rectangular paperboard that is 20 inches long and 12 inches broad, as seen below. After the semicircle is taken out, the paperboard's remaining perimeter is 34.58 inches.

The paperboard has a length of 20 inches and a width of 12 inches. A semicircle is cut out of it, which means we need to find the perimeter of the remaining part.

The diameter of the semicircle is equal to the width of the paperboard, which is 12 inches. So, the radius of the semicircle is half of the diameter, which is 6 inches.

The perimeter of the remaining part will be the sum of the length of the paperboard and the two straight sides of the semicircle.

The length of the paperboard is 20 inches, and the two straight sides of the semicircle are equal to the diameter of the semicircle, which is 12 inches. So, the perimeter of the remaining part is:

P = 20 + 12 + 12 = 44 inches

However, we also need to subtract the length of the curved part of the semicircle from the perimeter. The length of the semicircle can be found using the formula:

C = πr

where C is the circumference of the semicircle and r is the radius.

Since we have a semicircle, we need to divide the circumference by 2. So, the length of the curved part of the semicircle is:

C/2 = (π x 6) / 2 = 9.42 inches (rounded to two decimal places)

Therefore, the perimeter of the remaining part is:

P = 44 - 9.42 = 34.58 inches (rounded to two decimal places)

So, the perimeter of the remaining paperboard is 34.58 inches.

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Answer: 0.50b + 1.50p ≤ 9

Hope this helped =)

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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The amount Stefan spent originally to buy the bike is; $100.91.

The amount Stefan made in profit by selling the bicycle and helmet to Jin is; $10.09.

According to the task content;

Stefan sold the bicycle and helmet for a total of;

104 + 17 = $111.

Also, since the total cost ($111) for Jin is 110% of what Stefan spent to buy the bicycle and helmet, x originally; we have

110% × x = 111

x = (111 × 100) / 110

x = $100.91.

Therefore, Stefan spent $100.91 originally to buy the bike and helmet.

Consequently, the money Stefan made by selling the bicycle and helmet to Jin is; 111 - 100.91 = $10.09.

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Answer:

\(1 \frac{1}2}\)

Step-by-step explanation:

The question is asking \(\frac{1}{2}\) times 2. You multiply 6 with the numerator to get \(\frac{6(1)}{4}\) Simplify it and get 6/4, or one and one-half

The probability expression when converted from odd's expression is 8/17

From the question, we have the following odd parameters

Odd = 8 to 9

To start with, we need to express the odd as ratio

So, we have the following representation

Odds ratio = 8 : 9

Solving further, we need to express the ratio as fraction

So, we have the following representation

Odds fraction = 8/9

To convert the above odd's expression to probability expression, we make use of the following equation

This is represented as

P = Odds/(Odds + 1)

Substitute the known values in the above equation

So, we have the following equation

P = (8/9)/(8/9 + 1)

Evaluate the sum

This gives

P = (8/9)/(17/9)

Express the quotient as product

P = (8/9) * (9/17)

Evaluate

P = 8/17

Hence, the probability is 8/17

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Set up equation

\( {x}^{2} - 2bx\)

Factor out an x

\(x(x - 2b)\)

Set x-2b=0

\(x - 2b = 0\)

\(x = 2b\)

So our zeroes are

\(0\)

\(2b\)

When we graph our parabola, our y intercept will be at (0,0) and (0,2b).

Our axis of symmetry will be at

\( {b}\) since we did -b/2a

Our extreme values for this function is a minimum value since our leading factor coefficient (1) is greater than zero.

so plug in b f

into the equation at the very top will give us our minimum.

\( {b}^{2} - 2b(b)\)

\( {b}^{2} - 2 {b}^{2} \)

\( - {b}^{2} \)

so our miniumum value is

\( - {b}^{2} \)

Answer:57

Step-by-step explanation:

Answer:

\(\rm\implies y = 4x + 3 \)

Step-by-step explanation:

Given :-

And we need to find the equation of the line. On looking at the graph we see that , it cuts y axis at (0,3) .So the y Intercept of the equation is 3 .

Slope Intercept Form :-

\(\rm\implies y = mx + c\)

Substituting the respective values :-

\(\rm\implies y = 4*x + 3 \\\\\rm\implies y = 4x + 3 \)

Hence the equation of line is y = 4x + 3

The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Answer:

1 can sing but cannot play keyboard.

Step-by-step explanation:

There are six members in the rock band. We need to identify how many person can sing, play guitar and play keyboard. To identify this we will find out number of member for each activity,

Total 6 members

4 can play guitar

3 can pay keyboard

All singers play guitar but one guitarist cannot sing.

There will be 1 singer who cannot play keyboard.

Answer:

a. P(x≤9)=0.9999

b. P(x=6)=0.0430

c. P(x≥6)=0.0611

Step-by-step explanation:

The question is incomplete:

a.At most 9 will come to a complete stop?

b.Exactly 6 will come to a complete stop?

c.At least 6 will come to a complete stop?

d.How many of the next 20 drivers do you expect to come to a complete stop?

The amount of drivers from the sample that will come to a complete stop can be modeled by a binomial random variable with n=15 and p=0.2.

The probability that exactly k drivers from the sample come to a complete stop is:

\(P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}\)

a. We have to calculate the probability that at most 9 come to a complete stop:

\(P(x\leq9)=\sum_{k=0}^9P(x=k)\\\\\\P(x=0) = \dbinom{15}{0} p^{0}q^{15}=1*1*0.0352=0.0352\\\\\\P(x=1) = \dbinom{15}{1} p^{1}q^{14}=15*0.2*0.044=0.1319\\\\\\P(x=2) = \dbinom{15}{2} p^{2}q^{13}=105*0.04*0.055=0.2309\\\\\\P(x=3) = \dbinom{15}{3} p^{3}q^{12}=455*0.008*0.0687=0.2501\\\\\\P(x=4) = \dbinom{15}{4} p^{4}q^{11}=1365*0.0016*0.0859=0.1876\\\\\\P(x=5) = \dbinom{15}{5} p^{5}q^{10}=3003*0.0003*0.1074=0.1032\\\\\\P(x=6) = \dbinom{15}{6} p^{6}q^{9}=5005*0.0001*0.1342=0.043\\\\\\\)

\(P(x=7) = \dbinom{15}{7} p^{7}q^{8}=6435*0*0.1678=0.0138\\\\\\P(x=8) = \dbinom{15}{8} p^{8}q^{7}=6435*0*0.2097=0.0035\\\\\\P(x=9) = \dbinom{15}{9} p^{9}q^{6}=5005*0*0.2621=0.0007\\\\\\P(x\leq9)=0.0352+0.1319+0.2309+0.2501+0.1876+0.1032+0.043+0.0138+0.0035+0.0007\\\\P(x\leq9)=0.9999\)

b. We have to calculate the probability that exactly 6 will come to a complete stop:

\(P(x=6) = \dbinom{15}{6} p^{6}q^{9}=5005*0.0001*0.1342=0.043\\\\\\\)

c. We have to calculate the probability that at least 6 will come to a complete stop:

\(P(x\geq6)=\sum_{k=6}^{15}P(x=k)\\\\\\P(x=6) = \dbinom{15}{6} p^{6}q^{9}=5005*0.0001*0.1342=0.043\\\\\\P(x=7) = \dbinom{15}{7} p^{7}q^{8}=6435*0*0.1678=0.0138\\\\\\P(x=8) = \dbinom{15}{8} p^{8}q^{7}=6435*0*0.2097=0.0035\\\\\\P(x=9) = \dbinom{15}{9} p^{9}q^{6}=5005*0*0.2621=0.0007\\\\\\P(x=10) = \dbinom{15}{10} p^{10}q^{5}=3003*0*0.3277=0.0001\\\\\\P(x=11) = \dbinom{15}{11} p^{11}q^{4}=1365*0*0.4096=0\\\\\\P(x=12) = \dbinom{15}{12} p^{12}q^{3}=455*0*0.512=0\\\\\\\)

\(P(x=13) = \dbinom{15}{13} p^{13}q^{2}=105*0*0.64=0\\\\\\P(x=14) = \dbinom{15}{14} p^{14}q^{1}=15*0*0.8=0\\\\\\P(x=15) = \dbinom{15}{15} p^{15}q^{0}=1*0*1=0\\\\\\P(x\geq6)=0.043+0.0138+0.0035+0.0007+0.0001+0+0+0+0\\\\P(x\geq6)=0.0611\)

Answer:

Step-by-step explanation:

2(3n-5)-4n+7=

6n-10-4n+7=

-3+2n

Answer:

2n-3

Step-by-step explanation:

2(3n-5)-4n+7

6n-10-4n+7

6n-4n-10+7

2n-10+7

2n-3

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Answer:

Value of x = 11 ° , ∠B = 108° ,∠C = 36° ,∠D = 36°

Step-by-step explanation:

Given :

In ΔBCD , BC = BD And ∠B= (13x-35)° , ∠C= (5x-19)° ,∠D=(2x+14)°

To Find :

value of x and ∠D , ∠B and ∠C

Solution:

∵ BC=BD , So ∠C = ∠D

Therefore 5x-19 = 2x+14

3x = 33 , ∴ x=11°

So, ∠B = (13×11) - 35 = 108°

∠C = (5×11)-19 = 36°

∠D= (2×11) +14 =36°

Answer: 23.76 sq yds

Step-by-step explanation:

0.5*9.9*4.7=23.76

Area of triangle: 0.5*b*h

Answer:

\(x = 3.6\)

Step-by-step explanation:

To find the area of a rectangle, you multiply its length by its width. The formula is \(lw = a\).

We already know the length, 5, and the area, 18, so we can plug it into the equation.

\(5\cdot w=18\)

We can simplify this equation by dividing both sides by 5.

\(5\cdot w \div5 = 18\div5\\\\w = 3.6\)

Hope this helped!

Answer: x= 13

Step-by-step explanation:

The proof demonstrates that given a well-ordered set W, an isomorphic ordinal can be found using the function F. The uniqueness of this ordinal is established using the Replacement Axioms. The set F(W) is shown to exist for each x in W, and if the least F(W) exists, it serves as an isomorphism of VV onto -y.

Lemma 2.7: This is a previously stated lemma that is referenced in the proof. Unfortunately, without the specific details of Lemma 2.7, it's difficult to provide further explanation for its role in the proof.

Well-ordered set W: A well-ordered set is a set where every non-empty subset has a least element. In this proof, W is assumed to be a well-ordered set.

Isomorphic ordinal: An ordinal is a mathematical concept that extends the notion of natural numbers to represent order and magnitude. An isomorphic ordinal refers to an ordinal that has a one-to-one correspondence or mapping with another ordinal, preserving their order and magnitude properties.

Function F: The function F is defined to assign an ordinal o to each element x in W. This means that for every x in W, there is a corresponding ordinal o.

Existence and uniqueness: The proof asserts that if there exists an ordinal o that is isomorphic to a specific initial segment of the ordinal VV (the set of all ordinals), then this ordinal o is unique. In other words, there is only one ordinal that can be mapped to the initial segment of VV given by x.

Replacement Axioms: The Replacement Axioms are principles in set theory that allow the construction of new sets based on existing ones. In this case, the Replacement Axioms are used to assert that the set F(W) exists, which is the collection of all ordinals that can be assigned to elements of W.

For each x in W: The proof states that for every x in W, there exists an ordinal o that can be assigned to it. If there is no such ordinal, the proof suggests considering the least x for which such an ordinal does not exist.

The least F(W): The proof introduces the concept of the least element in the set F(W), denoted as the least F(W). If this least element exists, it serves as an isomorphism (a one-to-one mapping) of the set of all ordinals VV onto the ordinal -y.

Overall, the proof outlines the existence and uniqueness of an isomorphic ordinal that can be obtained from a well-ordered set W using the function F, and it relies on the Replacement Axioms and the concept of least element to establish this result.

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Answer:

$143.82

Step-by-step explanation:

423 x 0.34 = 143.82

423 + 143.82 = 566.82

The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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Answer:

Your answer is: \(x=\frac{b}{9}\)

or if you are solving for b:  \(b=9x\)

Isolate the variable by dividing each side by factors that don't contain the variable.

Step-by-step explanation:

Hope this helped : )