Use the binomial theorem to find specified term of the given power of binomial ( remember that r starts at 0 in the binomial theorem so finding say the second term means that r=1)
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The fourth term in the expanded form of (x - 1)⁶ is -20x³.
What is the fourth term in the expanded form of (x - 1)⁶?The fourth term in the expanded form of (x - 1)⁶ using the binomial theorem is calculated as follows;
The expanded form of (x - 1)⁶ using the binomial theorem is;
(x - 1)⁶ = 1x⁶ + (-6)x⁵ + 15x⁴ + (-20)x³ + 15x² + (-6)x + 1
(x - 1)⁶ = x⁶ -6x⁵ + 15x⁴ -20x³ + 15x² -6x + 1
To find the fourth term, we look for the fourth term from the left side to right side, which is -20x³.
Therefore, the fourth term in the expanded form of (x - 1)⁶ is -20x³.
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Related Questions
Fernando wants to know how much interest he will earn on the $4000 he puts into a savings account. He has the interest rate. What other information does he need to know?
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Answer:
the time period, and what compounding is usedStep-by-step explanation:
You want to know what else Fernando needs to know to figure how much interest he will earn on $4000, if he has the interest rate.
InterestThere are two interest formulas. One is for simple interest, and one is for compound interest. So, one bit of information Fernando needs is whether interest is being compounded.
The formulas are ...
I = P·r·t . . . . . . . simple interest
I = P((1 +r/n)^(nt) -1) . . . . . . compound interest
If Fernando knows the invested amount P and the interest rate r, then he needs to know 'n' and 't' to be able to choose and use the correct interest formula.
Fernando needs to know ...
the time period of concernthe number of times per year interest is compoundedHow many centimeters are in x meters
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Answer:
multiply the number of meters by 100
how to do I solve this
Answers
Answer:
the answer is 80
Step-by-step explanation:
1pound=16ounces
Question 10: The graph below shows a company's profits f(x), in dollars, depending on the price of 8.01 & 8.04
pens x, in dollars, sold by the company.
Part A (2pts): Highlight your answer below
150
90
00
30
f(x)
What does the maximum value represent?
A The point where no profit is made
B.
C.
D.
The point where the most profit is made
The point where the most pens are made
The point where no pens are made.
Part B (2 pts) Highlight/circle your answer What do the x-intercepts represent?
A.
The price per pen where the most profit is made
B.
The price per pen where no profit is made.
C.
D.
The point where the most pens are made.
The point where no pens are made.
Part C (3 pts): What is an approximate average rate of change of the graph from
x=3 to x = 6? Show your work.
Part D (3 pts) Drag & Drop into the blanks to describe the constraints of the
domain.
The domain of this graph given the situation is
because
beyond those points.
+
Z
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The x-intercepts represent a zero profit, the maximum value of the graph represents the maximum profit, An approximate average rate of change of the graph from x=3 to x=5 represents the reduction in profit from 3 to 5 and the domain is constrained by x=0.
Part A:
The x-intercepts represent a zero profit.
The maximum value of the graph represents the maximum profit.
The function increases up till the vertex and decreases after it.
This means that the profit increases as it reaches the peak at the vertex.
It decreases after the vertex up till it reaches zero.
On the left of the first zero and on the right of the second zero, the profits are negative.
Part B:
An approximate average rate of change of the graph from x=3 to x=5 represents the reduction in profit from 3 to 5.
Part C:
Simply, the domain is constrained by x=0.
We are obliged at x=6 .
This is because we have to avoid a negative profit.
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1. Define, compare and contrast common stock and preferred stock.
2. Define, compare and contrast dividends and dividends in arrears.
3. Define, compare and contrast bond premium and discount.
4. What are the 3 main fee structures of mutual funds?
5. What is NAV and how is it calculated?
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Common Stock:
- Represents ownership in a company and a claim on a portion of the company's assets and earnings.- Has voting rights, allowing shareholders to participate in corporate decision-making.- Dividends are not guaranteed and can fluctuate.- In the event of liquidation, common stockholders are paid after preferred stockholders.Preferred Stock:
- Represents partial ownership in a company but typically does not carry voting rights.- Typically has a fixed dividend rate, which is paid before dividends to common stockholders.- In the event of liquidation, preferred stockholders have priority over common stockholders.- Can be converted to common stock or have a callable feature, allowing the company to redeem shares at a predetermined price.Comparison:
- Common stockholders have voting rights, while preferred stockholders generally do not.- Preferred stock usually has a fixed dividend rate, while common stock dividends can fluctuate.- Preferred stockholders have priority in receiving dividends and in the event of liquidation.2. Dividends vs Dividends in Arrears:Dividends:
- Payments made by a corporation to its shareholders, usually in the form of cash or additional shares.- Typically paid from a company's profits or retained earnings.- Can be regular (e.g., quarterly) or special (one-time) dividends.Dividends in Arrears:
- Unpaid dividends owed to preferred stockholders.- Occur when a company does not pay the full dividend amount it has committed to for preferred stockholders.- Must be paid before any dividends can be paid to common stockholders.Comparison:
- Dividends are regular or special payments to shareholders, while dividends in arrears are unpaid dividends owed to preferred stockholders.- Dividends in arrears must be paid before any dividends can be paid to common stockholders.3. Bond Premium vs Bond Discount:Bond Premium:
- Occurs when a bond's market price is higher than its face value.- Usually results from a decrease in market interest rates, making the bond's fixed interest payments more attractive to investors.- Bond premium is amortized over the life of the bond, reducing the bond's book value.Bond Discount:
- Occurs when a bond's market price is lower than its face value.- Usually results from an increase in market interest rates, making the bond's fixed interest payments less attractive to investors.- Bond discount is amortized over the life of the bond, increasing the bond's book value.Comparison:
- A bond premium represents a bond selling for more than its face value, while a bond discount represents a bond selling for less than its face value.- Bond premiums typically occur when market interest rates decrease, while bond discounts occur when market interest rates increase.4. 3 Main Fee Structures of Mutual Funds:1. Sales Loads: Fees paid when buying or selling shares of a mutual fund. They can be front-end loads (charged when buying shares) or back-end loads (charged when selling shares).
2. Expense Ratio: The annual fee that covers the fund's operating expenses, including management fees, administrative fees, and other costs. It is expressed as a percentage of the fund's average net assets.
3. 12b-1 Fees: Annual fees charged by some mutual funds to cover marketing and distribution expenses. These fees are included in the fund's expense ratio.
5. NAV (Net Asset Value):- NAV represents the per-share value of a mutual fund, calculated by dividing the fund's total net assets by the number of outstanding shares.- Total net assets are calculated by subtracting the fund's liabilities from its total assets.- NAV is typically calculated at the end of each trading day and is the price at which investors can buy or sell shares of the mutual fund.A recycling bin contained 40 pounds of plastic in October and 50 pounds of plastic in
November. By what percentage did the amount of plastic increase from October to
November?
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The percentage increase by the given data is 25%.
We are given that;
Weight of plastic in october= 40
Weight of plastic in november= 50
Now,
To find the percentage increase of the amount of plastic from October to November, we need to find the absolute increase and divide it by the original amount, then multiply by 100 to get the percentage.
The absolute increase is the difference between the final amount and the initial amount, which is 50 - 40 = 10 pounds.
The original amount is the initial amount, which is 40 pounds.
10/40×100=25%.
Therefore, by the percentage the answer will be 25%.
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Sue likes to skate at a skate park that is due south of her school and due west of her favorite ice cream parlor. If the skate park is 4 miles from her school and the straight-line distance between the school and the ice cream parlor is 5 miles, how far is the skate park from the ice cream parlor?
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The skate park is approximately 6.4 miles from the ice cream parlor.
We can use the Pythagorean theorem to find the distance between the skate park and the ice cream parlor.
As per the information, we can see that the distance we're looking for is the hypotenuse of a right triangle with legs of length 4 miles (distance from school to skate park) and 5 miles (distance from school to ice cream parlor).
Using the Pythagorean theorem, we get:
c² = a² + b²
where c is the distance between the skate park and the ice cream parlor, and a and b are the distances from the school to the skate park and ice cream parlor, respectively.
Substituting the values we know, we get:
c² = 4² + 5²
c² = 16 + 25
c² = 41
Taking the square root of both sides, we get:
c = √41
c ≈ 6.4
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Write the standard form of the equation of the circle with radius 7 and center at (0, 0).
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The standard form of the equation of the circle with a radius of 7 and center at (0, 0) will be x² + y² = 49.
Given that:
The center is at the origin.
Radius, r = 7
Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,
(x - h)² + (y - k)² = r²
Substitute h = 0, k = 0, and r = 7, then we have
(x - 0)² + (y - 0)² = 7²
x² + y² = 49
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PLS HELP ME OUT! A sporting event has a promotion in which the first 1,000 fans to enter the arena receive either a blue cap or a red cap. A random number generator is used to simulate the color of a cap given to a person where indicates a blue cap and indicates a red cap. Ten simulations, each consisting of ten random numbers, are conducted, and the results are shown in the following table:
Based on the simulations, what is the probability that ten hats given to ten people will consist of more blue caps than red caps? a. 0.20
b. 0.40 c. 0.60 d. 0.80
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The probability that ten hats given to ten people will consist of more blue caps than red caps is given as follows:
a. 0.2.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The outcomes in which there are more blue than red caps are those in which the number of zeros is greater than the number of ones, hence the number of desired outcomes is of:
2. (simulation number 7 and simulation number 10).
Hence the probability is of:
p = 2/10
p = 0.2.
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A right prism with a triangular base has a volume of 195 mm3 . The right prism is 13 mm tall. The triangular base of the prism has a base length of 5 mm .
What is the base height of the triangular base of the right prism? Round your answer to the nearest whole millimeter, if necessary.
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Complete the ratio table
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Answer: do u need help
Step-by-step explanation: ask a teacher dont cheat
Justify Results Hector was asked to simplify the expression (5^-3/5^-1) He gave the answer 1/25 Did Hector give the correct answer? Explain.
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Answer:
To simplify the expression (5^-3/5^-1), we need to use the rule of exponents that states when dividing two powers with the same base, we can subtract the exponents.
Using this rule, we get:
(5^-3/5^-1) = 5^-3 ÷ 5^-1 = 5^-3 × 5^1 = 5^-2 = 1/25
Therefore, Hector gave the correct answer.
Let h(x) = x² - 8x.
(a) Find the average rate of change from 3 to 9.
(b) Find an equation of the secant line containing (3,h(3)) and (9, h(9))
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(a) Find the average rate of change from 3 to 9.
(b) Find an equation of the secant line containing (3,h(3)) and (9, h(9))
your avatar
(a) The average rate of change from 3 to 9 can be found by calculating the slope of the secant line connecting the points (3, h(3)) and (9, h(9)).
The formula for the slope of a line passing through two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Applying this formula, we have:
m = (h(9) - h(3)) / (9 - 3)
To find the values of h(9) and h(3), we need to substitute 9 and 3 into the function h:
h(9) = 9² - 8(9) = -27 h(3) = 3² - 8(3) = -9
Substituting into the formula for slope, we have:
m = (-27 - (-9)) / (9 - 3) = -18 / 6 = -3
Therefore, the average rate of change from 3 to 9 is -3.
(b) To find the equation of the secant line containing (3, h(3)) and (9, h(9)), we need to find the slope of the line and its y-intercept.
We've already calculated the slope in part (a) as -3. To find the y-intercept, we can use the point-slope form of a line:
y - y1 = m(x - x1)
where m is the slope, (x1, y1) is a point on the line, and (x, y) are any other points on the line. We can choose either (3, h(3)) or (9, h(9)) as our point.
Let's use (3, h(3)):
y - h(3) = -3(x - 3)
Simplifying, we get:
y = -3x + 18 - 9 y = -3x + 9
Therefore, the equation of the secant line is y = -3x + 9.
What is the measure of y (angle AXB)?
1. 90°
2. 60°
3. 45°
4. 30°
Answers
Answer:
4. 30°
Step-by-step explanation:
Sum of interior angles of a triangle = 180
y° + ∠XYZ + ∠YZX = 180
y° = 180 - 90 - 60 = 30°
Write a quadratic function with zeros -9 and 7
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The quadratic function with roots -9 and 7 is f(x) = x² + 2x - 63
What is the quadratic function with zeros -9 and 7?First, recall that a quadratic function has the form:
f(x) = ax² + bx + c
where a, b, and c are constants.
Given the roots of the quadratic function:
-9 and 7
x = -9 and x = 7 are the two distinct solutions to the quadratic equation.
Hence:
x + 9 and x - 7 are the factors of the quadratic equation.
( x + 9 ) ( x - 7 )
Expanding this expression Using FOIL method:
x( x - 7 ) + 9( x - 7 )
x² - 7x + 9x - 63
Collect and add like terms
x² + 2x - 63
Therefore, the function is f(x) = x² + 2x - 63.
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Find the perimeter of this shape
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Answer:
3y+8x
Step-by-step explanation:
To solve this problem we first have to add similar terms
Adding like terms:
So let us add up the sides that have the same variable. Let us solve for the variable y first ->
[tex]4+y+2y-2\\\\(y+2y)+(4-2)\\\\3y+2[/tex]
Now we have the simplified form of the y. Now let us solve for x ->
[tex]6x+2+2x-4\\\\(6x + 2x) + (2 - 4)\\\\8x - 2[/tex]
Combine both expressions:
To combine these expressions we add the constants and leave the variables. (We do this because different variables cannot be added together)
[tex]8x - 2 +3y +2\\\\8x + 3y + (-2 + 2)\\\\8x+3y+0\\\\8x+3y[/tex]
So 3y + 8x is the asnwer
Two ramps are placed back to back as shown. What is the length of the ramp labeled x?
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The value of the x as shown in the graph will be 16.61 ft.
From the sine rule in the triangle,
In a triangle ABC, where a, b, and c are the side lengths opposite to the angles A, B, and C respectively, and where the opposite angles A, B, and C are opposite to sides a, b, and c respectively, the Sine Rule states:
[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}[/tex]
Use the Law Of Sines to solve this:
(Sin 7)/9 = (Sin 13)/x
Cross multiply...
x(Sin 7) = 9(Sin 13)
Divide both sides by Sin 7
x = [9(Sin 13)]/(Sin 7)
x = 16.61254121
therefore, for the ramp, the value of the x will be 16.612 ft.
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A circular arc has measure 6cm and is intercepted by a central angle of 40° . Find the radius r of the circle
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The radius of the circle with central angle θ = 40° is r = 8.594 cm
Given data ,
A circular arc has measure 6cm and is intercepted by a central angle of 40°
Now , the radius r of the circle is given by
r = L / θ
where θ is in radians
So , 40° = 0.6981317007977318 radians
On simplifying , we get
r = 40 / 0.6981317007977318
Now , the measure of r = 8.594 cm
Hence , the radius is r = 8.594 cm
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Help!
The surface area of this rectangular prism is __ square centimeters.
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The surface area of the rectangular prism is 216 square cm
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
10 cm by 3 cm by 6 cm
The surface area of the rectangular prism is calculated as
Area = 2 * (3 * 10 + 3 * 6 + 10 * 6)
Evaluate
Area = 216
Hence, the area is 216 square cm
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6+3(-2x - 3y). Please help mee
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the diagram shows a right angled triangle
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Answer:
34.8°
Step-by-step explanation:
You want the angle opposite a side of length 8 cm in a right triangle with hypotenuse 14 cm.
SineThe sine relation is the one of interest in this geometry:
Sin = Opposite/Hypotenuse
sin(x°) = (8 cm)/(14 cm)
The angle can be found using the inverse sine function:
x° = arcsin(8/14) ≈ 34.8°
The size of the angle x° is 34.8°.
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URGENT!! ILL GIVE BRAINLIEST! ALONG WITH 100 POINTS
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You currently have $6,500 that you would plan to deposit into an investment account that has an anticipated growth factor of 1.03 per year. Use guess and check to estimate the number of years that it will take for this investment to grow to $10,000. Show your work.
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Answer:
Using guess and check, we can estimate the number of years it will take for the investment to grow to $10,000 as follows:
First, we'll assume that it will take 5 years for the investment to grow to $10,000.
After 5 years, the investment would grow to:
$6,500 x 1.03^5 = $7,960.35
Since this is still less than $10,000, we need to increase the number of years.
Next, we'll assume that it will take 10 years for the investment to grow to $10,000.
After 10 years, the investment would grow to:
$6,500 x 1.03^10 = $9,020.14
Since this is still less than $10,000, we need to increase the number of years again.
Finally, we'll assume that it will take 15 years for the investment to grow to $10,000.
After 15 years, the investment would grow to:
$6,500 x 1.03^15 = $10,005.58
Since this is slightly more than $10,000, we can estimate that it will take around 15 years for the investment to grow to $10,000.
Therefore, the estimated number of years it will take for the investment to grow to $10,000 is about 15 years.
A water park has pools, slides, and rides that, in total, make use of 8.8 × 1 0 5 8.8×10 5 gallons of water. They plan to add a ride that would make use of an additional 51 , 000 51,000 gallons of water. Use scientific notation to express the total gallons of water made use of in the park after the new ride is installed.
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[tex]9.31*10^5[/tex] gallons are the total gallons of water used by the water park after adding the new ride.
To express the total gallons of water used by the water park after adding the new ride in scientific notation, we need to add the two values together and then convert them to scientific notation.
[tex]8.8*10^5[/tex] gallons + 51,000 gallons = [tex]9.31*10^5[/tex] gallons
Therefore, the total gallons of water used by the water park after adding the new ride is [tex]9.31*10^5[/tex] gallons.
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the sonar system then detects a sunken ship 1500 meters ahead, with an angle of elevation of 19° to the highest part of the sunken ship. how many meters must the submarine rise to pass over the sunken ship?
Answers
Step-by-step explanation:
Tan Φ = opposite leg / adjacent leg
tan 19 = height / 1500
1500 * tan 19 = height = 516 m <==== must rise this much
Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Refer to the accompanying data set. Use a 0.01 significance level to test the claim that women and men have the same mean diastolic blood pressure.
Answers
The null and alternative hypothesis is represented by option A.
The test statistic is 0.153.
How to explain the informationWe want to test the claim that women and men have the same mean diastolic blood pressure.Let μ1 be the mean diastolic blood pressure for women and let μ2 be the mean diastolic blood pressure for men.
The t-statistic value will be:
= (69.81 - 69.53) / (✓10.46²/26 + 11.24²/26)
=0.153
Since p-value for two tail test=0.879 which is greater than =0.05(0.879>0.05) So we do not reject H0.
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Autumn's Pumpkin Patch started the day with 432 pumpkins, each priced at $5. Most of
the pumpkins sold. At the end of the day, there were only 129 pumpkins left. How much
money did the pumpkin patch make today?
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Answer:
It's very simple you just subtract 432 and 129. And you get 303. Then you just multiple 303 by 5 and you get 1515.
1515
What is the midpoint of line segment Ab (-3,-5) (-1,-7)
Answers
Answer:
(-2, -6)
Step-by-step explanation:
Midpoint = (x1 + x2)/2, (y1 + y2)/2
= (-3 + -1)/2, (-5 + -7)/2
= (-4/2), (-12/2)
= (-2, -6)
What is the value of x?
34°
(-1/2 x) °
Answers
Answer:
The expression "34° (-1/2 x) °" can be simplified by multiplying 34° by the quantity (-1/2 x):
34° (-1/2 x) ° = (34°) * (-1/2 x)
To multiply two values with units, we can simply multiply the numerical parts and keep the units. Therefore, we get:
(34°) * (-1/2 x) = -17x°
So the value of "34° (-1/2 x) °" is simply -17x°.
solve for x in the diagram
Answers
Answer:
see attatched picture
Step-by-step explanation: