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The given equation has been solved in the table.
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In step 4, the
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The distance the ball drops in the next 8 second is: 640 m. Using the concept of equation of motion.

An item is considered to be at rest when its position doesn't alter throughout time. An item is considered to be in motion if, over time, its location changes.

It is possible to build a relationship using a series of equations between the body's velocity, acceleration, and the distance it travels in a given amount of time when the body is travelling in a straight line with uniform acceleration. The term "motion equations" refers to these equations.

D = kt²  where D is the constant of proportionality.

D = 80 m

t = 4 seconds

Putting the values we get -

80 = k(4)²

or, k = 80 / 16

or, k = 5.

So the equation of motion is D = 5t²

When t = 8+4 = 12 seconds

now, D = 5(12)² =  5×144

or, D =  720 m

So, the distance the ball drops in the next 8 seconds = 720 - 80

= 640 m.

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[tex]\displaystyle\\Answer:\ sin(2\theta)=-\frac{4\sqrt{21} }{25} ,\ cos(2\theta)=\frac{17}{25}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\sin(\theta)=-\frac{2}{5} \ \ \ \ \ \ \ \ 270^0 < \theta < 360^0\\\\sin^2(\theta)+cos^2(\theta)=1\\\\cos^2(\theta)=1-sin^2(\theta)\\\\Hence,\\\\cos^2(\theta)=1-(-\frac{2}{5})^2 \\cos^2(\theta)=1-\frac{4}{25} \\\\cos^2(\theta)=\frac{25(1)-4}{25} \\\\cos^2(\theta)=\frac{21}{25} \\\\[/tex]

Extract the square root of both parts of the equation:

[tex]\displaystyle\\cos(\theta)=б\sqrt{\frac{21}{25} } \\\\cos(\theta)=б\frac{\sqrt{21} }{5} \\\\270^0 < \theta < 360^0\\\\Hence,\\\\cos(\theta)=\frac{\sqrt{21} }{5}[/tex]

[tex]\displaystyle\\a)\ sin(2\theta)=2sin(\theta)cos(\theta)\\\\sin(2\theta)=2(-\frac{2}{5})(\frac{\sqrt{21} }{5})\\\\sin(2\theta)=-\frac{4\sqrt{21} }{25}[/tex]

[tex]\displaystyle\\b)\ cos(2\theta)=cos^2(\theta)-sin^2(\theta)\\\\cos(2\theta)=(\frac{\sqrt{21} }{5})^2-(-\frac{2}{5})^2 \\\\cos(2\theta)=\frac{21}{25}-\frac{4}{25} \\\\cos(2\theta)=\frac{17}{25}[/tex]

Answer:

-------------------------------------

For each tree you need 3 + 12 = 15 feet space.

On one side of the street you can plant:

Same number is applicable for the opposite side, so the total number is:

The matching choice is D.

The graph of the parabola declines through (-5, 2), (-3, 0), (-2, 0), (0, 1), (1, 2), (2, 3), (3, 5) on the x y coordinate plane represents the function.

A function is defined as the relation between the x and y coordinates such that no value of x maps to two values of y.

A vertical line test is a test used to determine whether the graph given is a function or not. This is a test where we draw a vertical line passing through a point x. If the graph is a function, then the vertical line will not intersects the graph at two points.

That is, no x coordinate maps to more than 1 y coordinate.

In the first graph of ellipse, the value -5 maps to two values 3 and 5. So this is not a function.

In the parabola all x values only maps to one y value. So this graph represents a function.

In the third graph, the value 3 maps to three values of y, 3, 2, and 1. So this is also not a function.

In the fourth graph, -2 maps to both 4 and 2, which also indicates that the given graph is not a function.

Hence the second graph of the parabola represents a function.

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Answer: B. X

Step-by-step explanation; I JUST DID IT(;

Rotation of a shape is a type of transformation. The required answers are:

1. AB=A'B'  (YES)

2.  AC II BD, then A'C' II B'D'    (YES)

3. m<ABC < m<A'B'C'   (NO)

A quadrilateral is a family of shapes which have four sides. Examples are square, rectangle, rhombus etc.

Transformation is a process which can be used to change the orientation or dimensions of a given figure or shape called an object. Some types of transformation are: rotation, translation, reflection, and dilation.

Rotation implies turning an object at a certain angle in a specific direction. The direction could be either clockwise or counterclockwise.

NB: Rotating an object changes only its orientation, but not the length of its dimensions or angles.

So that the required answers to the questions are:

1. AB=A'B'  (YES)

2.  AC II BD, then A'C' II B'D'    (YES)

3. m<ABC < m<A'B'C'   (NO)

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Answer:

1 & 3, 2 & 4, 5 & 7, and 6 & 8 are vertically opposite angles

4 & 8, 3 & 7, 1 & 5, and 2 & 6 are corresponding angles

4 & 6 and 3 & 5 are alternate angles

1 & 2, 2 & 3, 3 & 4, 1 & 4, 5 & 6, 6 & 7, 7 & 8, and 5 & 8 are supplementary angles

The function that matches the graph is y(x)=(1-x)(x+2)^2

a function from a set X to the  set of Y assigns to each other element of X exactly one  element of Y. The set X is the  called the domain of to the  function of  the set Y is called as  the condominium of the functions.

From the graph the curve cross the x -axis at X=1

Therefore the expression is (x-1)

And at (-) x axis at X=-2 it is the turning point.

Therefore the expression is

(X+2)^2

And the point on y axis is (0,4)

Therefore the function can be written as

Y(x)=a(x-1)(x+2)^2

4= -4a≈a=-1

Therefore the function is y(x)

(-1)(x-1)(x+2)^2

= y(x)=(1-x)(x+2)^2

Therefore the function that matches the graph is y(x)=(1-x)(x+2)^2

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Yes, the starting position of these players form a perpendicular line.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Using Trigonometry

sin [tex]\theta[/tex] = 33.33/100

sin [tex]\theta[/tex] = 0.3333

[tex]\theta[/tex] = [tex]sin^{-1}[/tex] (0.3333)

[tex]\theta[/tex] = 19.469

cos 19.469 = B/ 100

0.9428 = B/ 100

B= 94.28

tan  [tex]\theta[/tex] = P/B

tan  [tex]\theta[/tex] = 94.28/ 33.33

[tex]\theta[/tex] = 70.5

Using Angle Sum property

< 3= 180 - (70.5 + 19.5)

<3 = 180 - 90

<3 = 90

Hence, they form perpendicular line.

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Answer:

k = (-55) / 8

k = (-3005) / 8

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510((-255 + sqrt(65025 - 510(0.309016^2))) / 2)^2)) / 2)^2)) / 2

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510((-255 + sqrt(65025 - 1469.59)))))^2)) / 2)

To find the acute angle between two vectors, we can use the dot product formula:

angle = arccos((a * b) / (||a|| * ||b||))

where a and b are the vectors, * is the dot product, and ||a|| and ||b|| are the magnitudes of the vectors a and b, respectively.

In this case, the dot product of a and b is (i - kj) * (i + j) = i^2 - kj * i + kj * i + kj^2 = 2i - k^2j

The magnitudes of the vectors a and b are ||a|| = sqrt(i^2 + (-kj)^2) = sqrt(1 + k^2) and ||b|| = sqrt(i^2 + j^2) = sqrt(2).

Substituting these values into the formula above, we get:

angle = arccos((2i - k^2j) / (sqrt(1 + k^2) * sqrt(2)))

Since the angle is given to be 60 degrees, we can set this equal to 60 degrees and solve for k:

60 = arccos((2i - k^2j) / (sqrt(1 + k^2) * sqrt(2)))

We can use the inverse cosine function to solve for k:

k = sqrt(1 / (cos(60)^2 - (2i / sqrt(1 + k^2) * sqrt(2))^2))

Since cos(60) = 0.5, we can substitute this value in and solve for k:

k = sqrt(1 / (0.5^2 - (2i / sqrt(1 + k^2) * sqrt(2))^2))

k = sqrt(1 / (0.25 - (2i / sqrt(1 + k^2) * sqrt(2))^2))

k = sqrt(1 / (0.25 - (4i^2 / (1 + k^2) * 2)^2))

k = sqrt(1 / (0.25 - (16 / (1 + k^2))^2))

k = sqrt(1 / (0.25 - 256 / (1 + k^2)^2))

k = sqrt((1 + k^2)^2 / (256 - (1 + k^2)^2))

k = sqrt((1 + k^4) / (256 - 1 - 2k^2 - k^4))

k = sqrt((k^4 + 1) / (255 - 2k^2))

We can then solve for the roots of this equation to find the possible values of k:

k = sqrt((k^4 + 1) / (255 - 2k^2))

k^4 - (255 - 2k^2)k^2 + 1 = 0

This is a quartic equation and can be solved using the quartic formula:

k = sqrt((-b +- sqrt(b^2 - 4ac)) / 2a)

where a, b, and c are the coefficients of the polynomial. In this case, a = 1, b = -(255 - 2k^2), and c = 1.

Substituting these values into the quartic formula, we get:

k = sqrt((-(-(255 - 2k^2)) +- sqrt((-(255 - 2k^2))^2 - 4 * 1 * 1)) / 2 * 1)

k = sqrt((255 - 2k^2 +- sqrt((255 - 2k^2)^2 - 4)) / 2)

k = sqrt((255 - 2k^2 +- sqrt(255^2 - 510k^2 + 4k^4)) / 2)

k = sqrt((255 - 2k^2 +- sqrt(255^2 - 510k^2)) / 2)

k = sqrt((255 - 2k^2 +- sqrt(65025 - 510k^2)) / 2)

Solving for the roots of this equation gives us the possible values of k:

k = (-255 + sqrt(65025 - 510k^2)) / 2

k = (-255 - sqrt(65025 - 510k^2)) / 2

The first equation gives us one possible value of k:

k = (-255 + sqrt(65025 - 510k^2)) / 2

Substituting k = (-255 + sqrt(65025 - 510k^2)) / 2 into the second equation gives us the second possible value of k:

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510k^2)) / 2)^2)) / 2

Simplifying this expression gives us the final possible value of k:

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510((-255 + sqrt(65025 - 510k^2)) / 2)^2)) / 2)^2)) / 2

Therefore, the possible values of k are:

k = (-255 + sqrt(65025 - 510k^2)) / 2

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510k^2)) / 2)^2)) / 2

solve for k in each

To solve for k in the first equation, we can isolate k by moving everything else to the right side of the equation:

k = (-255 + sqrt(65025 - 510k^2)) / 2

2k = -255 + sqrt(65025 - 510k^2)

2k + 255 = sqrt(65025 - 510k^2)

(2k + 255)^2 = 65025 - 510k^2

4k^2 + 1020k + 65025 = 65025 - 510k^2

4k^2 + 1530k + 65025 = 0

This is a quadratic equation, and we can use the quadratic formula to solve for k:

k = (-b +- sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the polynomial. In this case, a = 4, b = 1530, and c = 65025.

Substituting these values into the quadratic formula gives us:

k = (-1530 +- sqrt(1530^2 - 4 * 4 * 65025)) / 2 * 4

k = (-1530 +- sqrt(3080400 - 2601000)) / 8

k = (-1530 +- sqrt(477900)) / 8

k = (-1530 +- sqrt(222725)) / 8

k = (-1530 + 1475) / 8

k = (-55) / 8

k = (-1530 - 1475) / 8

k = (-3005) / 8

Therefore, the solutions to the first equation are:

k = (-55) / 8

k = (-3005) / 8

Answer:

y = 4

Step-by-step explanation:

substitute x = 3 into the equation

y = 6(3) - (9 + 5) = 18 - 14 = 4

Answer: y=4

Step-by-step explanation:

y=6(3)-(9+5)

y=18-14

y=4

Answer:

t= 2.52 hours

Step-by-step explanation:

it is given that for first 30 km, the speed of bicyclist is v km/hour

time taken to cover first 30 km is given by

          ( )

for next 17 km the speed of bicyclist is 2 km/hour greater than his original speed

so the speed to cover next 17 km = v+2

time taken to cover next 17 km is given by

now total time t spent by the bicyclist to cover entire trip is given by

now if v=18 , we have

now to add fractions we make the denominator same

Hence we will find the LCM of 18 and 20

LCM of 18 and 20 = 180

now we need to make both the denominator equal to 180

hours (approx)

Hope it helps :) Make me as brainlest!

Answer:

PART A

x-intercept: (-7,0)

y-intercept: (0,9)

PART B

Answer is A (Top Left One)

Step-by-step explanation:

I left a desmos explanation on my previous answer

Answer:

find the size of unknown angle in the following figure

Step-by-step explanation:

the solve by putting the given valu

Answer:

Step-by-step explanation:

18/2 = 9

36/4 = 9

72 / 8 = 9

each dollar spent appears to earn the same number of points

points / dollars = 9

points = 9 · dollars

dollars = points / 9

dollars = 81/9

dollars = 9

Answer: B

Step-by-step explanation:t+4+3−2.2t

Add 4 and 3 to get 7.

t+7−2.2t

Combine t and −2.2t to get −1.2t.

−1.2t+7

a) A recurrence relation for the number of bit strings of length n that contain three consecutive 0s :

a_n = a_(n-1) + a_(n-2) + a_(n-3) + 2^(n-3)   for n ≥ 3

b) The initial conditions are:

a_0 = a_1 = a_2 = 0 and a_3 = 1

c) There are 47 bit strings of length seven contain three consecutive 0s

Let s_n be a string of length n that does not have 3 consecutive 0's, and a_n be the number of strings  that contain three consecutive 0's

Consider a string of length n -1 that does not have 3 consecutive 0's, s_(n-1)

If we add 1 to this string, then we get a string s_n.

Consider a string s_(n-2)

If we add 10 at the end, then we get a string s_n

Now consider a string s_(n-3)

If we add 100 at the end we get a string s_n.

Now we got all possible strings s_n: that end in 1 (i.e. the last 3 digits could be 001, 011, 101 and 111),

Those strings that end in 10 (i.e. the last 3 digits could be 010 and 110)

and those strings  that end in 100. There are no other possibilities without having 3 consecutive zeros.

In the third case, there are a_(n-3) possibilities. And, in the fourth case, there are 2^(n-3) possibilities.

Hence the recurrence relation is

So, a_n = a_(n-1) + a_(n-2) + a_(n-3) + 2^(n-3)   for n ≥ 3

The initial conditions are a_0 = a_1 = a_2 = 0 and a_3 = 1

The recurrence gives the sequence of positive integers 0, 0, 0, 1, 3, 8, 20, 47, 107, 238, 520, 1121, 2391, . . . .

Hence there are a_7 = 47 bit strings of length seven that contain

three consecutive 0's.

Therefore, a) the recurrence relation:

a_n = a_(n-1) + a_(n-2) + a_(n-3) + 2^(n-3)   for n ≥ 3

b) Initial conditions: a_0 = a_1 = a_2 = 0 and a_3 = 1

c) there are 47 bit strings of length seven

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Answer:

h

Step-by-step explanation:

because it shifts the graph to the left by 6 units

Step-by-step explanation:

subtract the area of the phone from that of the phone

The rate of interest for simple compounding if Louis is offered an interest rate of 6.35% for an investment with continuous compounding, is 0.0656 or 6.56%, so option D is correct.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

Louis is offered an interest rate of 6.35% for an investment with continuous compounding,

Here, P will be the same, the amount will be the same and the time period will be the same then,

The amount in simple compounding = The amount in continuous compounding

[tex]P(1 + r)^t = Pe^{Rt}[/tex]

Here, r is the rate of interest for simple compounding,

[tex]1 + r = e^{0.0635}[/tex]

r = 1.0656 - 1

r = 0.06556

r = 0.0656

r = 6.56%

Thus, the rate of interest for simple compounding is 6.56%.

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Step-by-step explanation:

3.1×10⁵ ÷ 5.4×10⁵

= (3.1/5.4) × 10^5-5

=0.5741 × 10⁰

= 5.7 × 10^-1

The total value of the sales today is £1581 and the total value of the sales for each salesperson today is:

Mo = £330 +  £247 = £577,

Daz = £180 + £259 = £439,

Colin = £300 + £265 = £565,

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

The value of sales each salesperson made this morning from the bar chart:

Mo = £330,  Daz = £180,  Colin = £300,

The value of sales each salesperson made this afternoon from the table given:

Mo = £247,  Daz = £259,  Colin = £265,

so, the total value of the sales today is :

= £330 + £180 + £300 + £247 + £259 + £265

= £1581.

also the total value of the sales for each salesperson today is:

Mo = £330 +  £247 = £577,

Daz = £180 + £259 = £439,

Colin = £300 + £265 = £565,

Hence, the total value of the sales today is £1581 and the total value of the sales for each salesperson today is:

Mo = £330 +  £247 = £577,

Daz = £180 + £259 = £439,

Colin = £300 + £265 = £565,

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Answer:

---------------------------------

Given function:

Find f(-7) by plugging in the value of x:

Answer:

Median: 85.5

Step-by-step explanation:

Knowledge Needed

Median is the middlemost value of the data set.

For example, we have a data set:

1, 7, 5

Line up in least to greatest.

1, 5, 7

Median is 5.

If there is an even amount of terms, the value of the median is the average of the 2 middlemost terms. For example:

1, 7, 16, 8

Line up in least to greatest.

1, 7, 8 , 16

(7 + 8)/2, average: 7.5

Median is 7.5

Question

Test Scores:

79 88 83 93 79 88 83 93 79 88 83 93 79 88 83 93 79 88

Line them up in least to greatest.

79 79 79 79 79 83 83 83 83 88 88 88 88 88 93 93 93 93

Middle of the set: 83 & 88 (Because there is an even amount of terms).

83 + 88 = 171

171/ 2= 85.5

Median: 85.5

Answer:

7 feet

Step-by-step explanation:

Because they divided the length by 5 to get the scaled length so you would do the same for the width.

Answer:

26 inches squared

Step-by-step explanation:

If the real length is 30 feet and the scale drawing is 6 inches its 5:1

So if the actual width is 35 feet the scale drawing will be 7 inches

The perimeter is the sum of all sides of the rectangle, 2 sides have 6 inches and the other 2 sides are 7 inches

6+6+7+7= 26

The equation of function for the given problem is y = 3x + 12.

What is point slope form of the line?

For linear equations, the general form is y - y1 = m(x - x1).

It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

Given:

A bathtub has some water in it. Mia turns on the faucet to add more water.

The total amount of water in gallons, y, is a function of the time in minutes since Mia turns on the faucet, a.

The graph of the linear function passes through the points (4, 24) and

(6, 30).

We have to find the equation of function.

Let the linear function passes through the points (4, 24) and (6, 30).

First to find the slope of equation using given points.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{30-24}{6-4} = \frac{6}{2} = 3[/tex]

Now to find the equation of function.

Consider the point slope form of the line,

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

Plug the values of m = 3 and [tex](x_1,, y_1) = (4, 24)[/tex]

⇒

[tex]y-24=3(x-4)\\y-24=3x-12\\y=3x-12+24\\y=3x+12[/tex]

Hence, the equation of function for the given problem is y = 3x + 12.

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Type I errors (also known as a "false positive") occur when a test erroneously rejects a true null hypothesis. In other words, the test incorrectly concludes that the observed effect is significant or real when, in fact, it is not.

A type I error is a statistical mistake where the null hypothesis is rejected, despite it being true. This is also known as a false positive. This means that the test concluded that the observed effect was significant when in reality, it was not. Type I errors are more likely to occur when the sample size is small or when too many tests are conducted at once. To avoid type I errors, it is important to use an appropriate sample size and to consider the power of the test before conducting it.

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Answer:

Step-by-step explanation:

We need to graph all the given constraints(inequalities). The intersection of the of all the graphed system of inequalities gives the vertices of the feasible region.

The first inequality is .  

This is very simple to graph. It is the region bounded by the horizontal lines,

and .

The next constraint or inequality is

To graph this inequality, we need to graph the corresponding linear equation .  

We plot the intercepts  and .

We then draw a solid line through the points.

Next, we test the origin to determine which half plane to shade.

This statement is true so we shade the lower half plane.

We now graph the inequality,

To graph this inequality, we need to graph the corresponding linear equation .  

We plot the intercepts  and .

We then draw a solid line through the points.

Next, we test the origin to determine which half plane to shade.

This statement is true so we shade the lower half plane.

The feasible region is shown in the above diagram.

The vertices of the feasible region are;

We substitute the vertices into the objective function to obtain;

Therefore the maximum value is  and it occurs at .

The minimum value is  and it occurs a

ANSWER TO QUESTIONS 14 We need to graph all the - 1

Writing the fraction 7/11 as a decimal gives a repeating decimal 0.636363 the sum of the first two digits is 90

The fraction 7/11 is written in fraction to give a repeating deicmal

Where decimal with repeats. Recurring decimal, often known as repeating  decimal, is a decimal number made up only of digits that repeat after the decimal at regular intervals.

The division inform of fraction when converted to decimal gives

0.636363

the sum of the first 20 decimals is 90

this is 6 ten times and 3 ten times

6 * 10 + 3 * 10

60 + 30

90

the sum is 20

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When we divide the 464 by 60 we get the following remainder in our answer that is 44.

The Remainder is the name for the value that is left behind after division. If an amount (reward) cannot be divided completely with another number, we are left with only a meaning (divisor). The remaining is the name for this amount. For instance, 10 is not precisely divisible by 3. We can calculate 3 x 3 = 9 because that is the closest value.

7.733333333333333

=7 44/60 ⇔ 7 R 44

464 divided by 60

=7 with a remainder of 44

Here, we provide you the outcome of the dividing with remainder, often known as the Euclidean division, along with a brief explanation of the following terms:

464 divide by 60 yields a quotient and residual of 7 R 44.

464 is the dividend & 60 is the divisor; the division (numeric division) of 464/60 is 7; the remainder ("left over") is 44.

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