For some real number a and some positive integer n, the first few terms in the expansion of (1 + ax)^n are [1 - 20x + 150x^2 + cx^3 ]. find c?

The contrapositive of the given statement is "If it is not a cat, then it is a lion."

The contrapositive of the statement "If it is not a lion, then it is a cat" can be obtained by negating the original statement and switching the positions of the antecedent (the "if" part) and the consequent (the "then" part).

The contrapositive takes the form:

"If it is not a cat, then it is a lion."

So, the contrapositive of the given statement is "If it is not a cat, then it is a lion."

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Answer:

0% (0/40)

Step-by-step explanation:

I feel like this is a trick question. since chicken is not indicated on the graph, I believe chicken is nobodies favorite food

a. S = {(1, -1), (2, 1)}Let's begin by calculating the determinant of the matrix composed of the vectors of S, and checking if it is equal to 0. Because the two vectors are not colinear, they should span R2.|1 -1||2 1| determinant is not 0, therefore S spans R2. No geometric description is required for this example.

b. S = {(1, 1)} The set S contains one vector. A set containing only one vector cannot span a plane because it only spans a line. Therefore, S does not span R2. Geometric description: S spans a line that passes through the origin (0, 0) and the point (1, 1).c. S = {(0, 2), (1, 4)} Let's again begin by calculating the determinant of the matrix composed of the vectors of S, and checking if it is equal to 0.|0 2||1 4| determinant is 0, thus S does not span R2. In this scenario, S only spans the line that contains both vectors, which is the line with the equation y = 2x.

Geometric description: S spans a line that passes through the origin (0, 0) and the point (1, 2).

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The length of the altitude of the equilateral triangle with side lengths of 28 meters is 14[tex]\sqrt{3}[/tex] meters.

Define equilateral.

Equilateral is an adjective used to describe a geometric figure, such as a triangle, that has all sides of equal length. In an equilateral triangle, all three sides are of equal length, and all three angles are also equal, measuring 60 degrees each.

To find the altitude of an equilateral triangle, we can use the following formula:

altitude = ([tex]\sqrt{3}[/tex]/2) x side length

Since the side length of the equilateral triangle is 28 meters, we can substitute it in the formula and simplify:

altitude = ([tex]\sqrt{3}[/tex]/2) x 28

= 14[tex]\sqrt{3}[/tex] meters (rounded to two decimal places)

Therefore, the length of the altitude of the equilateral triangle is approximately 14.00 meters.

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The length of Line FG is 13.5 inch

A parallelogram is a four-sided, geometric form in two dimensions. It is a quadrilateral, which means it has four vertices (corners) and four angles.

Area of parallelogram = base × height

As per given diagram, base, GH = 9inch and height, FP = 12inch

So, Area of parallelogram = 9 × 12 = 108 inch²

and also, Area of parallelogram = EQ × FG

put values here, 108 = 8 × FG

FG = 13.5 inch

Therefore, the length of Line FG is 13.5 inch

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The person must leave the money in the bank for approximately 13.6 years to reach 13300 dollars.

Using the formula A=P(1+r/n)⁽ⁿᵗ⁾, where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years, we can solve for t.

We have P = 4500, A = 13300, r = 0.0625, n = 2. Plugging these values into the formula and solving for t, we get t ≈ 13.6 years. Therefore, the person must leave the money in the bank for approximately 13.6 years to reach 13300 dollars.

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There will be a total of 28 handshakes when the 3 late members arrive.

The first n-1 positive integers are added together using the formula n(n-1)/2, where n is the total number of terms being added together.

The number of combinations or arrangements of a given collection of items may be determined using this formula, which can be obtained using the process of mathematical induction. It is often used in combinatorics and discrete mathematics. For instance, the formula was used to determine how many times a group of individuals shook hands in the scenario above. It might also be used to determine the number of pathways in a network of nodes or vertices or the number of ways to choose a portion of an object set from a bigger set in other settings.

Given that, 3 members arrive late, and 5 members are already present.

The total members are 5 + 3 = 8.

Now, using the sum of positive integer formula:

n(n-1)/2

We can determine the number of handshakes.

8(8-1)/2 = 28

Hence, there will be a total of 28 handshakes when the 3 late members arrive.

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The percentage of customers who do not purchase clubs or balls is 0.66 or 66%.

Ten percent of customers who walk into a golf store purchase a golf club and 30% of customers purchase golf balls. Six percent of customers purchase both clubs and balls. The percentage of customers who do not purchase clubs or balls is 0.66.

Given that, The percentage of customers who purchase golf clubs = 10%The percentage of customers who purchase golf balls = 30%The percentage of customers who purchase both clubs and balls = 6%To find out the percentage of customers who do not purchase clubs or balls, we have to subtract the percentage of customers who purchase either clubs or balls or both from 100%.

Percentage of customers who purchase either clubs or balls or both = 10% + 30% - 6% = 34% Percentage of customers who do not purchase clubs or balls = 100% - 34% = 66%.

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Answer:

Step-by-step explanation:

Kind of like rema from the song calm down calm down!!

you an find it on youtub

The linear approximation error when using the linear approximation to estimate the cube root of 8.25 is 0.0593.

When we want to find the linear approximation error, we can use the formula

Error = f(x) - L(x),

Where `f(x)` is the actual value of the function at `x`, and `L(x)` is the linear approximation of the function at `x`.

The linear approximation of a function f(x) near x=a is given by:

L(x) = f(a) + f'(a)(x-a)

In this case, we want to find the linear approximation of the function f(x) = cube root of x near x=8. To do so, we first need to find the value of f(8) and f'(8).

f(8) = cube root of 8 ⇒ 2

To find f'(8), we take the derivative of f(x) with respect to x:

f(x) = x^(1/3)

f'(x) = (1/3)x^(-2/3)

So, f'(8) = (1/3)(8)^(-2/3) ⇒ 1/12

Therefore, the linear approximation of f(x) near x=8 is:

L(x) = 2 + (1/12)(x-8)

Now, we want to use this linear approximation to estimate the value of the cube root of 8.25. To do so, we substitute x=8.25 into the linear approximation:

L(8.25) = 2 + (1/12)(8.25-8) ⇒ 2.0208

The actual value of the cube root of 8.25 is:

∛8.25 ⇒ 2.0801

So, the error in the linear approximation is:

2.0801 - 2.0208 ⇒ 0.0593

Therefore, the linear approximation error when using the linear approximation to estimate a cube root of 8.25 is approximately 0.0593.

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The option in the question that is equivalent to 3/8 is 2/5.

We can simplify 3/8 and 2/5 so that they have a common denominator:

3/8 = 3*(5/5)/(85/5) = 15/40

2/5 = 2(8/8)/(5*8/8) = 16/40

Since 15/40 and 16/40 have the same denominator, we can compare their numerators to see which is larger:

15/40 < 16/40

Since 16/40 is larger, we can conclude that 2/5 is greater than 3/8.

Therefore, the option that is equivalent to 3/8 is 2/5.

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To find:-

Answer:-

To find out the equation of the line , we need to find out the slope first. It can be calculated as ,

[tex]\implies m =\dfrac{\Delta y}{\Delta x }=\dfrac{y_2-y_1}{x_2-x_1} \\[/tex]

And here ,

On substituting the respective values, we have;

[tex]\implies m =\dfrac{25-20}{8-3} \\[/tex]

[tex]\implies m=\dfrac{5}{5}\\[/tex]

[tex]\implies m=\boxed{1} \\[/tex]

Hence the slope of the line is 1 . Now we may use point slope form of the line to find out the equation of the line. Point slope form of the line is,

[tex]\implies y - y_1 = m(x-x_1) \\[/tex]

Take any of the given two points. Here i am taking (3,20) . So here we have;

On substituting the respective values, we have;

[tex]\implies y - 20 = 1(x - 3) \\[/tex]

[tex]\implies y -20 = x - 3 \\[/tex]

[tex]\implies x - 3 - y +20 = 0 \\[/tex]

[tex]\implies \underline{\underline{\green{ x - y +17=0}}}\\[/tex]

Hence the equation of the line in standard form is x - y + 17 = 0 .

and we are done!

Since only 25% of the variability in y is explained, Julie's actual score could have been much higher than the predicted value.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. When the standard deviation is low, the data are concentrated around the mean, and when it is large, the data are widely dispersed.

(a) Slope, b = r*(sy/sx) = 0.5*(8/40) = 0.1

Intercept = y - bx = 75 - 0.1*280 = 47

The regression equation is:

y = 47 + 0.1*x

(b) Put x = 300

y = 47 + 0.1*300

y = 77

(c) r2 = 0.5*0.5 = 0.25

Since only 25% of the variability in y is explained, Julie's actual score could have been much higher than the predicted value.

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Answer:

The observer deck of a ship is located at the origin of a coordinate system. Find the bearing of an object located at the point (5, 5).

Step-by-step explanation:

To find the bearing of an object located at the point (5, 5) relative to the observer deck at the origin of a coordinate system, we need to find the angle between the positive x-axis and the line connecting the observer deck to the object.

First, we calculate the slope of the line connecting the observer deck at (0, 0) to the object at (5, 5):

slope = (change in y) / (change in x)

= (5 - 0) / (5 - 0)

= 1

Next, we use the inverse tangent function to find the angle whose tangent is equal to the slope:

angle = arctan(slope)

= arctan(1)

= 45°

Therefore, the bearing of the object located at (5, 5) relative to the observer deck at the origin is 45 degrees.

Answer:

45° north of east

Step-by-step explanation:

tan⁻¹(y/x) = tan⁻¹(5/5) = tan⁻¹(1) = 45°

Answer:

x=15°,  ∠A=75°,  ∠B=60°,  ∠C=45°

Step-by-step explanation:

As we know that sum of the angle of a triangle is 180°

Therefore ∠A+∠B+∠C=180°

                5x+4x+3x=180°     {  ∵ ∠A=5x   ∠B=4x ∠C=3x   }

              ⇒   12x=180°

              ⇒      x=15°

Hence ∠A=5x=5×15°=75°

           ∠B=4x=4×15°=60°

and      ∠C=3x=3×15°=45°

to verify your answer 75°+60°+45°=180°

The histogram that most likely represents a country with a declining population growth rate is one where the bars to the right (representing higher numbers of births or deaths) are lower than the bars to the left.

A declining population growth rate means that the rate at which the population is growing is decreasing, which suggests that the number of births is decreasing or the number of deaths is increasing.

In other words, the shape of the histogram would be skewed to the left, with a long tail on the left-hand side and shorter bars on the right-hand side. This shape suggests that there are fewer births or more deaths, leading to a declining population growth rate.

It is worth noting that a histogram alone may not provide enough information to make definitive conclusions about population growth rates. Other factors such as migration rates and changes in life expectancy can also affect population growth. Therefore, it is important to consider multiple sources of data and statistical methods when analyzing population trends.

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The first game brought in more money than the last game.

Any number of equal parts is represented by a fraction, which also symbolizes a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many pieces of a particular size there are when spoken in everyday English.

According to question:

The baseball team made more money at their first game because 6/7 is less than 1. This means that they made less money at their last game than at their first game. For example, if they made $100 at their first game, then they made 6/7 x $100 = $85.71 at their last game, which is less than $100.

Therefore, the first game brought in more money than the last game.

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The bank statement  that is shown in the question shows a loss of £285.00 and calculated by subtracting the total expenses (money out) from the total revenue (money in).

Profit or loss is a measure of the financial performance of a business, organization, or individual over a given period of time.

Profit refers to the positive difference between the revenue earned by a business or individual and the expenses incurred during a given period.

A loss occurs when the expenses incurred exceed the revenue earned during a given period.

To calculate the profit or loss, you need to subtract the total expenses (money out) from the total revenue (money in).

In this case, the total revenue is £315.00 + £265.00 + £190.00 = £770.00, and the total expenses are £210.00 + £30.00 + £450.00 + £100.00 = £790.00.

So, the calculation would be:

Total revenue - total expenses = profit/loss

£770.00 - £790.00 = -£20.00

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There are 720 different choices if order matters and there are 120 different choices if order does not matter.

a) If order matters,

The player can choose the first number in 10 ways (any of the digits 0-9), the second number in 9 ways (since one digit has already been chosen), and the third number in 8 ways (since two digits have already been chosen).

So the total number of choices is:

10 x 9 x 8 = 720

Therefore, there are 720 different choices if order matters.

b) If order does not matter,

We need to divide the number of choices by the number of ways the three numbers can be arranged.

Since there are 3 numbers, they can be arranged in 3! = 6 ways.

So the number of choices when order does not matter is:

(10 x 9 x 8) / 6 = 120

Therefore, there are 120 different choices if order does not matter.

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ANSWER:

The Pythagorean theorem is used to find the hypotenuse of a triangle.

=> AC² = AB² + BC²

In squares, the length of the side can be calculated by finding the square root of the area.

Answer:

X = 3

Step-by-step explanation:

I can't really draw the diagram for you.

$9 is always charged so just add that to the end of your equation.

x is what they charge for skates and their are 7 skates so 7x

$30 is the total

7x + 9 = 30

subtract 9 from both sides

7x = 21

divide by 7 on both sides

x = 3

Sara’s hair was 25 inches long. Three years later it was 43 inches long. The percentage increase rounded to the nearest hundredth will be 72.

Percentage:

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we need to calculate the percentage of a number, we divide the number by the whole number and multiply by 100. So , percent means one hundredth and the word percent means every 100th. It is represented by the symbol "%".

Calculate the percentage of a total value:

Since percent implies 100, we will split the total portion into 100 parts and then multiply it by b to gather b things per 100 items.

The percentage increase is found as:

   [tex]% increase = \frac{change in value}{original value}[/tex][tex]%increase = \frac{change in value}{original value}[/tex][tex]%[/tex]% increase = Change in value/ Original value

⇒ % increase = [tex]\frac{13-25}{25} * 100[/tex]

⇒ % increase = 72

Hence, the percent increase rounded to the nearest hundredth will be 72.

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The Rico ride his bike at a speed of 6 miles per hour.

Speed is a measure of how quickly an object moves, calculated as the distance traveled per unit of time.

Let's take Rico's speed on his bicycle is 'r'.

So, Luis's speed can be expressed as 4r.

Time = Distance / Speed

For Luis, the time it takes to travel 24 miles is:

Time = 24miles / 4r

For Rico, the time it takes to travel 24miles is:

Time = 24miles / r

Since Rico takes 3 hours longer than Luis to travel the same distance (24miles), we can set up an equation:

24miles / r = (24miles / 4r) + 3hour

Simplifying this equation, we get:

⇒ 24 = 6 + 3r

⇒ r = 6

Therefore, Rico can ride his bike at a speed of 6 miles per hour.

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The resulting double-line graph should show the sales data for desktop and laptop computers over the five days, with a line for each type of computer.

A double-line graph is a graph that displays two sets of data on the same graph, using two lines to show how each set of data changes over time or some other variable.

To create a double-line graph of the sales data for desktop and laptop computers over five days, follow these steps:

Draw a graph with two perpendicular axes, the horizontal axis (x-axis) representing the days, and the vertical axis (y-axis) representing the number of computers sold.

Label the horizontal axis with the days from Day 1 to Day 5.

Label the vertical axis with the heading "Number of Computers Sold".

Plot the data points for desktop computer sales. For Day 1, plot a point at (1, 4), for Day 2 plot a point at (2, 1), for Day 3 plot a point at (3, 2), for Day 4 plot a point at (4, 5), and for Day 5 plot a point at (5, 1).

Connect the data points for desktop computer sales with a line.

Plot the data points for laptop computer sales. For Day 1, plot a point at (1, 5), for Day 2 plot a point at (2, 2), for Day 3 plot a point at (3, 3), for Day 4 plot a point at (4, 7), and for Day 5 plot a point at (5, 3).

Connect the data points for laptop computer sales with a line.

Use a different color or style for the line representing desktop sales and the line representing laptop sales.

Add a legend to the graph to indicate which line corresponds to desktop sales and which corresponds to laptop sales.

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Answer:

9.5x + 8 = 65

Step-by-step explanation:

Let x = number of sandwiches.

The cost of x sandwiches is 9.5x.

The delivery fee is $8.

The total cost of an order is the price of the sandwiches, 9.5x plus the delivery fee, 8.

In this case, the total cost is $65.

9.5x + 8 = 65

Answer:

$65

Step-by-step explanation:

X=9.50 because you add the $8 delivery fee to equal 65 in total.

Answer:

9.5 decimal

espero y te ayude

The system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.

To solve the system of equations:

1x + 0y + 60z = 1

1x + 10y + 0z = 0

0x + 0y + 0z = 0

The third equation is an identity, implying that it does not give us any new information. The first two equations can be used to solve for x, y, and z:

From the first equation, we get x = 1 - 60z

From the second equation, we get y = 0 - 10x = -10(1 - 60z) = -10 + 600z

Therefore, the solution to the system can be written as a point in terms of z as:

(x, y, z) = (1 - 60z, -10 + 600z, z)

Since z can take on any value, there are infinitely many solutions to the system, which can be parameterized as:

(x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.

he system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.

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When the radius of circle 2 is twice the radius of circle 1, the size of circle 2 is larger than circle 1.

In geometry, a triangle is a polygon with three sides and three angles. The sum of the angles in a triangle is always 180 degrees. Triangles are one of the most basic and fundamental shapes in geometry and are used in many mathematical and real-world applications, such as in architecture, engineering, and physics. There are different types of triangles based on the length of their sides and the measures of their angles, such as equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles.

Here,

2. This is because the circumference and area of a circle are directly proportional to the radius.

3. To determine if triangles ABC and DEF are similar, we need to check if their corresponding angles are congruent and if their corresponding sides are in proportion. From the diagram, we can see that angle A is congruent to angle D, angle B is congruent to angle E, and angle C is congruent to angle F. This satisfies the angle-angle (AA) similarity criterion. Additionally, we can use the side-side-side (SSS) similarity criterion to determine if the corresponding sides are in proportion. From the diagram, we can see that side AB is parallel to side DE, side AC is parallel to side DF, and side BC is parallel to side EF. Therefore, we can conclude that triangles ABC and DEF are similar.

4. To find the coordinates of D using the coordinates of A, we need to determine the translation from A to D. From the diagram, we can see that A is translated two units to the right and three units down to get to D. Therefore, we can find the coordinates of D by adding two to the x-coordinate of A and subtracting three from the y-coordinate of A. If the coordinates of A are (x1, y1), then the coordinates of D would be (x1 + 2, y1 - 3).

A= (-0.87,0.5)

D=(-0.87 + 2, 0.5 - 3)

D=(1.13,-2.5)

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