Find the 4th term of the expansion of (2a - b)^7.

a.
-560a^4b^3

c.
560a^4b^3

b.
-560a^3b^4

d.
560a^3b^4

For this problem, you need to know how to use sin, cos, and tan or 'SOH-CAH-TOA' sin- opposite/hypotenuse cos-adjacent/hypotenuse toa- opposite/adjacent

in this case, you can use tan or toa

the equation should be set up like this:

4/x=1/0.848

solve, and you will get 3.39...

(you need to use the sin,cos,tan degree chart to find 0.848)

In the equation F=kx, F is the force, k is the spring constant, and x is the displacement.  Plug in and solve:

F=0.3(1.5)

F=0.45N

Hope this helps!!

Check the picture below.

Answer:

1

Step-by-step explanation:

-2(1) = -2

then -2 - 4 = -6

-6 = -6

Answer:

1

Step-by-step explanation:

Move all terms that don't contain x to the right side & solve.

[tex]\textrm{97 percent accurate for individual with the virus}[/tex]

[tex]\text{3 percent inaccurate}[/tex]

[tex]\textrm{99 percent accurate for an individual}[/tex]

[tex]\textrm{1 percent inaccurate probability}[/tex]

[tex]\textrm{Probability of infected:}[/tex]

[tex].0055[/tex]

[tex]\textrm{Probability of not being infected}[/tex]

[tex]1 - .0055 = .9945[/tex]

[tex]\textrm{Combine it all together}[/tex]

[tex]0.0055 * 0.03 + 0.9945 * 0.01 = 0.01011[/tex]

[tex]\textrm{The probability that a randomly chosen person gets an incorrect result is 0.01011}[/tex]

[tex]\textbf{Answer}[/tex]

[tex]\textrm{0.01011}[/tex]

The probability of an incorrect result for the test to detect respiratory syncytial virus is calculated by considering the test's sensitivity and specificity, along with the prevalence of the virus in the population.

In order to calculate the probability that a randomly chosen person gets an incorrect result, we first need to understand how test accuracy works. Sensitivity refers to how often the test correctly identifies the presence of a disease when it is indeed there, while specificity refers to how often it correctly identifies the absence of a disease when it isn't there. In this case, the sensitivity is 97%, meaning it correctly identifies the virus in 97% of individuals who have the virus; the specificity is 99%, meaning it correctly identifies no virus in 99% of individuals who do not have the virus.

For the given population, 0.55% are infected. Hence, the probability of an incorrect result for a person with a virus is 3% (100% - 97%), and for a person without the virus is 1% (100% - 99%). Therefore, the total probability of getting an incorrect result is (0.55%/100 * 3%) + [(1 - 0.55%/100) * 1%].

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ANSWER

[tex]S_{26}=1300[/tex]

EXPLANATION

The sum of an arithmetic sequence whose first term and last terms are known is calculated using

[tex]S_{n}= \frac{n}{2} (a + l)[/tex]

From the given information, the first term of the series is

[tex]a = 7[/tex]

and the last term of the series is

[tex]l = 93[/tex]

The sum of the first 26 terms is

[tex]S_{26}= \frac{26}{2} (7 + 93)[/tex]

[tex]S_{26}= 13 (100)[/tex]

[tex]S_{26}=1300[/tex]

The sum of the first 26 terms of the given arithmetic series is 1300, obtained using the sum formula S = n/2 * (a1 + an) for arithmetic series.

To find the sum of the first 26 terms of an arithmetic series whose first term (a1) is 7 and the 26th term (a26) is 93, you can use the formula for the sum of an arithmetic series: S = n/2*(a1 + an). Here, n is the number of terms, a1 is the first term, and an is the nth term. In this case, we have n = 26, a1 = 7, and a26 = 93.

The sum, S, of the series is calculated as follows:
S = 26/2 * (7 + 93) = 13 * (100) = 1300.

Therefore, the sum of the first 26 terms of the arithmetic series is 1300.

I don’t know what answer Is I wish I could help

Answer:

4.22 meters per second.

Step-by-step explanation:

First multiply the revs per second by pi:

= 11pi = 34.558.

Now multiply this by the diameter which is 2*6.1 = 12.2 cm = 0.122 m.

Linear velocity =  0.122 * 34.558

= 4.22 m/s.

Linear velocity of the gear in meters per second is  4.22 m/s.

Linear velocity is the measure of “the rate of change of displacement with respect to time when the object moves along a straight path.” It is a vector quantity.

Given

Gear of radius = 6.1 cm

Gear of diameter = [tex]2 \times 6.1 = 12.2 cm[/tex] = 0.122 m

Revolutions per second = [tex]11\pi[/tex] = 34.558

Linear velocity of the gear  =  diameter × Revolutions per second

Linear velocity = 0.122 × 34.558

= 4.22 m/s

Linear velocity of the gear in meters per second is  4.22 m/s.

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[tex]\bf (\stackrel{x}{1},\stackrel{y}{8})\qquad y=2x^3\implies 8=2(1)^3\implies 8\ne 2~~\bigotimes \\\\\\ (\stackrel{x}{-1},\stackrel{y}{-2})\qquad y=2x^3\implies -2=2(-1)^3\implies -2=-2~~\checkmark \\\\\\ (\stackrel{x}{0},\stackrel{y}{0})\qquad y=2x^3\implies 0=2(0)^3\implies 0=0~~\checkmark \\\\\\ (\stackrel{x}{2},\stackrel{y}{16})\qquad y=2x^3\implies 16=2(2)^3\implies 16=16~~\checkmark[/tex]

x + y = 16

x = y^2 x 4

i hope this helps :)

good luck

Answer:

27.90

Step-by-step explanation:

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The amount of money that is left with Lisa after buying tickets is $27.90.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The total number of members in the family is 5 (Parents+2sisters+Lisa). Also, the cost of a single ticket in Atlanta is $14.42, therefore, the cost of five tickets will be,

The cost of 5 tickets = $14.42 × 5 = $72.10

The amount Lisa has to spend is $100, therefore, the money left with Lisa after buying the tickets is,

Amount left = $100 - $72.10 = $27.90

Hence, the amount of money that is left with Lisa after buying tickets is $27.90.

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Answer:

The inverse of f(x) is  [tex]f ^ {- 1}(x) = x + 2[/tex]

Step-by-step explanation:

To find the inverse of the function [tex]f (x) = x-2[/tex], perform the following steps:

1) do [tex]y = f (x)[/tex]

[tex]y = x-2[/tex]

2) Solve the equation for the variable x.

[tex]y + 2 = x -2 +2[/tex]

[tex]y + 2 = x[/tex]

3) exchange the variable x with the variable y

[tex]y + 2 = x[/tex] ----> [tex]x + 2 = y[/tex]

4) Change the variable y by [tex]f ^{- 1}(x)[/tex]

Finally the inverse function is:

 [tex]f ^ {- 1} (x) = x + 2[/tex]

Answer:

f-1(x)=x+2

Step-by-step explanation:

Answer:

The answer is 62208

Step-by-step explanation:

The reason is because 18*2=36 12*2=24 and 36*2=72

36*24*72=62208

Can I get brainliest

Answer:

$35

Step-by-step explanation:

since it is 60% off, $14 is 40% of original price.

1% of original price (original price is 100%)

= $14 ÷ 40

= $0.35

original price

= $0.35 × 100

= $35

Answer:

The area of ABCD is 50 units²

The area IJKL is 80 units²

The area of QRST is 100 units²

The area of UVWX is 300 units²

Step-by-step explanation:

* Lets revise the area of the rectangle

- The area of any rectangle = its length × its width

- To solve the problem find the lengths of two adjacent sides and

  consider that one of them is the length and the other is the width

- Use the rule of the distance between two points (x1 , y1) and (x2 , y2)

 the distance = √[(x2 - x1)² + (y2 - y1)²]

# In rectangle ABCD

∵ A = (-9 , 8) , B = (-5 , 5) , C = (1 , 13)

∴ AB = √[(-5 - -9)² + (5 - 8)²] = √[(4)² + (-3)²] = √[16 + 9] = √25 = 5 units

∴ BC = √[(1 - -5)² + (13 - 5)²] = √[(6)² + (8)²] = √[36 + 64] = √100 = 10 units

∴ The area of ABCD = 5 × 10 = 50 units²

# In rectangle EFGH

∵ E = (30 , 20) , F = (39 , 29) , G (49 , 19)

∴ EF = √[(39 - 30)² + (29 - 20)²] = √[9² + 9²] = √[81 + 81] = √162 unit

∴ FG = √[(49 - 39)² + (19 - 29)²] = √10² + (-10)²] = √[100 + 100] = √200 units

∴ The area of EFGH = √162 × √200 = 180 units²

# In rectangle IJKL

∵ I = (-6 , 2) , J = (2 , 2) , K = (2 , -8)

∴ IJ = √[(2 - -6)² + (2 - 2)²] = √[8² + 0²] = √8² = 8 units

∴ JK = √[(2 - 2)² + (-8 - 2)²] = √[0² + (-10)²] = √10² = 10 units

∴ The area IJKL = 8 × 10 = 80 units²

# In rectangle MNOP

∵ M = (5 , 5) , N = (11 , 5) , O = (11 , -5)

∴ MN = √[(11 - 5)² + (5 - 5)²] = √[6² + 0²] = √6² = 6 units

∴ NO = √[(11 - 11)² + (-5 - 5)²] = √[0² + (-10)²] = √10² = 10 units

∴ The area of MNOP = 6 × 10 = 60 units²

# In rectangle QRST

∵ Q = (10 , 0) , R = (15 , 5) , S = (25 , -5)

∴ QR = √[(15 - 10)² + (5 - 0)²] = √[5² + 5²] = √[25 + 25] = √50 units

∴ RS = √[(25 - 15)² + (-5 - 5)²] = √[10² + (-10)²] = √[100 + 100] = √200 units

∴ The area of QRST = √50 × √200 = 100 units²

# In rectangle UVWX

∵ U = (0 , 5) , V = (15 , 20) , W = (25 , 10)

∴ UV = √[(15 - 0)² + (20 - 5)²] = √[15² + 15²] = √[225 + 225] = √450 units

∴ VW = √[(25 - 15)² + (10 - 20)²] = √[10² + (-10)²] = √100 + 100 = √200 units

∴ The area of UVWX = √450 × √200 = 300 units²

Answer:

2. simplifying multiplication property of equality

3. x - 2 = 8

5. x = 10 , addition property of equality

Step-by-step explanation:

* Lets explain how to solve the problem

- The equation is [tex]\frac{x-2}{4}=2[/tex]

- The value of x is 10

- We want to a statement reason to each step to complete the proof

* Lets write each step with statement reason

1. [tex]\frac{x-2}{4}=2[/tex]  ⇒ Given

2. [tex]4(\frac{x-2}{4})=4*2[/tex]  ⇒ simplifying multiplication property of equality

3. x - 2 = 8  ⇒ Simplifying

4. x - 2 + 2 = 8 + 2                      

5. x = 10  ⇒  addition property of equality

- In step 2 we multiply both sides by 4 to cancel the denominator of

 the left hand side (simplifying multiplication property of equality)

- Then we simplify the two sides to get (x - 2 = 8)

- Then we add two to both sides to cancel -2 in the left hand side

- Then after adding we find (x = 10) , (addition property of equality)

* The answer is:

2. simplifying multiplication property of equality

3. x - 2 = 8

5. x = 10 , addition property of equality

x = 180° - 67° - 52°

x = 61°

So, the value of x is 61°

D. Normal distributions are symmetric, so the mean is the same as the median.

Answer:

18

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

The circumcenter is the center of the circumscribing circle, the circle that intersects each of the vertices. Since the points on a circle are equidistant from its center, the vertices of a triangle are equidistant from the circumcenter.

Final answer:

The circumcenter of a triangle is the point that is equidistant from the vertices of the triangle.

Explanation:

True

The circumcenter of a triangle is the point that is equidistant from the vertices of the triangle. This means that the distance from the circumcenter to each vertex of the triangle is the same.

For example, in an equilateral triangle, the circumcenter is the point where all the perpendicular bisectors of the sides intersect.

Step-by-step explanation:

x = a cos t, y = b sin t

cos t = x / a, sin t = y / b

cos² t + sin² t = 1

(x / a)² + (y / b)² = 1

If a = b, the conic section is a circle.

If a and b are different, the conic section is an ellipse.

Answer:

h=20

Step-by-step explanation:

h=3 (V/lw)

h= 3 (960/12*12)

D.All interior angles are 90 degrees

Let's analyze each choice to determine which one is the exception, that is, a property that is not shared between a square and a rhombus:
A. Opposite pairs of sides are parallel:
This is true for both a square and a rhombus. By definition, both a square and a rhombus have opposite sides that are parallel.
B. Opposite pairs of sides are congruent:
This property also holds true for both squares and rhombi. In a square, all four sides are equal in length. In a rhombus, opposite sides are equal in length.
C. Pairs of interior and exterior angles are supplementary:
Again, this is a common feature of both squares and rhombuses. In any parallelogram (which includes both squares and rhombuses), each pair of interior and exterior angles on the same side are supplementary, totaling 180 degrees.
D. All interior angles are 90 degrees:
This is where we can find the exception. In a square, all four interior angles are indeed 90 degrees. However, this is not the case for a rhombus. A rhombus does not necessarily have right angles; its angles can be of any measure as long as opposite angles are equal and the sum of the angles is 360 degrees, which is true for any quadrilateral.
Therefore, the correct answer to the question is:
D. All interior angles are 90 degrees
This is the property that is not common between a square and a rhombus, making it the exception.

[tex]\bf (\stackrel{a}{2}~,~\stackrel{b}{-1})\qquad \begin{cases} r=\sqrt{a^2+b^2}\\\\ \theta =tan^{-1}\left( \frac{b}{a} \right) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ r=\sqrt{2^2+(-1)^2}\implies r=\sqrt{5} \\\\\\ \theta =tan^{-1}\left( \cfrac{-1}{2} \right)\implies \theta \approx -26.57^o\implies \theta \approx 333.43^o \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (\sqrt{5}~~,~~333.43^o)~\hfill[/tex]

Answer:

[tex](r,\theta); (\sqrt{5} , tan^{-1}(\frac{x}{y}))\\(r,\theta); (-\sqrt{5} , -tan^{-1}(\frac{x}{y}))[/tex]

Step-by-step explanation:

Here we are given our rectangular coordinates as (2,-1) . We have to convert this into polar coordinates. The formula for conversion into polar form is

[tex]r=\sqrt{x^2+y^2}[/tex]

[tex]\theta=tan^{-1}(\frac{x}{y})[/tex]

Substituting the values of x and y in the above formulas we get

[tex]r=\sqrt{2^2+(-1)^2}\\r=\sqrt{4+1}\\r=\sqrt{5}\\r=-\sqrt{5}\\[/tex]

[tex]\theta=tan^{-1}(\frac{-1}{2})[/tex]

Hence our polar coordinates are

[tex]r=(\sqrt{5},tan^{-1}(\frac{-1}{2}) )\\r=(-\sqrt{5},tan^{-1}(\frac{-1}{2}) )\\[/tex]

Answer:

none of the above

Step-by-step explanation:

All of the answer choices agree that the magnitude of the components is 150/√2 ≈ 106.1. The units of these components should be "mph", the same as the units of the magnitude of the given vector.

We only know the angle with respect to horizontal. We don't know whether that angle is measured with respect to the positive x-axis or the negative x-axis. Both of those are horizontal, and there is nothing in the problem statement that restricts the airplane to be traveling in one direction or the other.

Possible answers are ...

<106.1 mph, -106.1 mph> . . . . . . "horizontal" is +x direction

<-106.1 mph, -106.1 mph> . . . . . "horizontal" is -x direction

(The units are not degrees (°).)

- The equation of this line is x=3.

- And I think it's also, This graph is a function of whose range is set at {3}.

Answer:

D. The equation of this line is x=3

E. This graph is not a function because the value x=3 is assigned to mre than one y-value.

Step-by-step explanation:

The range is all real numbers.

The domain of this graph is x=3, but it is not a function

The graph is a vertical line whose equation is x=3 because the graph passes through (3,y).

This graph cannot represent a function because it will not pass the vertical line test.

In other words, the x-value of 3 is assigned to more than one y-value.

Therefore the correct answers are:

Option D and E

Answer:

  8

Step-by-step explanation:

The minus sign outside parentheses changes the sign of what's inside parentheses when parentheses are eliminated:

  7 -(-1) = 7 +1 = 8

_____

Alternate way to think about it

Subtraction is the same as addition of the opposite. The opposite of -1 is +1, so subtracting -1 is the same as adding +1.

Answer:

Step-by-step explanation:

This is a third degree polynomial because we are given three roots to multiply together to get it.  Even though we only see "2 + i" the conjugate rule tells us that 2 - i MUST also be a root.  Thus, the 3 roots are x = -4, x = 2 + i, x = 2 - i.

Setting those up as factors looks like this (keep in mind that the standard form for the imaginary unit in factor form is ALWAYS "x -"):

If x = -4, then the factor is (x + 4)

If x = 2 + i, then the factor is (x - (2 + i)) which simplifies to (x - 2 - i)

If x = 2 - i, then the factor is (x - (2 - i)) which simplifies to (x - 2 + i)

Now we can FOIL all three of those together, starting with the 2 imaginary factors first (it's just easier that way!):

(x - 2 - i)(x - 2 + i) = [tex]x^2-2x+ix-2x+4-2i-ix+2i-i^2[/tex]

Combining like terms and canceling out the things that cancel out leaves us with:

[tex]x^2-4x+4-i^2[/tex]

Remembr that [tex]i^2=-1[/tex], so we can rewrite that as

[tex]x^2-4x+4-(-1)[/tex] and

[tex]x^2-4x+4+1=x^2-4x+5[/tex]

That's the product of the 2 imaginary factors.  Now we need to FOIL in the real factor:

[tex](x+4)(x^2-4x+5)[/tex]

That product is

[tex]x^3-4x^2+5x+4x^2-16x+20[/tex]

which simplifies down to

[tex]x^3-11x+20[/tex]

And there you go!

Answer:

B. 25

Step-by-step explanation:

In order to find out the value of x + 2, you need to know what x is.  Let's solve for it then sub it back in to evaluate the expression.

3(x+2)=5(x-8) distributes out to give you

3x + 6 = 5x - 40.  Get like terms together on opposite sides of the equals sign:

46 = 2x and divide to get x = 23.  Now that we know that x = 23, that means that x + 2 is the same as 23 + 2 which is 25.

Final answer:

The probability that Judy guesses at least 3 questions correctly in a multiple-choice test is calculated using the binomial probability formula. For the survey question, the hypergeometric distribution is used to find the probability of 4 or fewer out of 9 people entering a profession related to their major. Exact probabilities require mathematical computation.

Explanation:

Probability of Answering Multiple-Choice and Survey Questions Correctly

For question 1, we must calculate the probability that Judy guesses at least 3 questions correctly on a 7-question multiple-choice test, where each question has 4 possible answers. Since only one answer is correct per question, her probability of guessing a question correctly is 1/4. To find the total probability of answering 3 or more questions correctly, we use the binomial probability formula which considers the probability of success (1/4) and the number of trials (7 questions). We sum the probabilities of getting exactly 3, 4, 5, 6, or all 7 questions correct.

For question 2, regarding the survey of 300 college graduates, we use the hypergeometric distribution since the samples are taken without replacement. We need to determine the probability that 4 or fewer of the randomly selected 9 survey subjects entered a profession closely related to their college major. We know that 63% of the entire group, which is 189 individuals, entered a relevant profession. We sum the probabilities of 0, 1, 2, 3, and 4 people from our sample of 9 falling into the group who are working in their field.

The correct probabilities from the provided choices are not directly calculable without doing the necessary computations using the respective formulas for each scenario, which are beyond the scope of this response as we do not have the calculations or the respective formulas provided within the context of this interaction.

The answer should be 3840