10
Velocity (m/s)
8-
6-
4
2-
of
0-
0 2 4 6 8 10
10 12 14 16 18 20
Time (seconds)
a) Work out the total distance travelled on the cycle.
b) Work out the acceleration in the last 8 seconds.

The transformation for the graph f(x) to h(x) is a vertical transformation of 2 units.

The graph is given below.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

f(x) = x

h(x) = x + 2

h(x) = f(x) + 2

Now,

f(x) → h(x)

The transformation from f(x) to h(x) is a vertical translation of 2 units.

i.e

f(x) → f(x) + 2

The graph is given below.

The blue line is the function.

The red line is the parent function.

Thus,

The transformation of the function is f(x) → f(x) + 2.

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A collector offers to buy state quarters for 2000% of their face value. The face value of each quarter is 25 cents. At that rate 20 dollars Bryden will get for his four state quarters.

In the given question, a collector offers to buy state quarters for 2000% of their face value.

The face value of each quarter is 25 cents.

We have to find at that rate how many dollars Bryden will get for his four state quarters.

As given that,

Collector buy state quarters = 2000% of their face value

We can write 2000% as 20×100%.

It means that state quarters is 20 times of their face value.

As we know that, 4 quarter is equal to the one dollar. So,

Bryden get for his four state quarters = 20×1 dollars

Bryden get for his four state quarters = 20 dollars

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9,900 codes that are available for reckha.

There are a total of 10,000 possible three-digit codes when each digit is in the set {0,1,2,3,4,5,6,7,8,9}. Since each digit can take 10 different values, we can use the formula 10^3 = 1000 to calculate the total number of codes.

However, since reckha cannot choose a code that is the same as yours or one that is the same as yours except for switching the positions of two digits, we have to subtract these possibilities from the total. We can calculate the number of codes forbidden by subtracting the number of codes with the same digits in all three positions (10) and the number of codes with the same digits but different positions (90) from the total. This leaves us with 10,000 - (10 + 90) = 9,900 codes that are available for reckha.

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Answer:

410cm^3

Step-by-step explanation:

The Volume of the upper rectangular prism is 10x3x8 which is 240

The volume of the middle prism is 6x5x3 which is 90

And the volume of the bottom prism is 8x2x5 which is 80

If you add them all up, the total volume is 410

Note(The volume of a rectangular prism is base x height x width)

Answer:

60

Step-by-step explanation:

there are three sides to a triangle so 20x3 is 60 which is the perimeter

The ratio of 2 or more integers is known as fraction. The answer to the given expression is 3 13/16

Fractions are written as a ratio of two integers. Fractions are written in the form a/b

Given the expression below:

15/4 + 7/12 x 3/28

Required

Simplified form of the expression

On solving, we will have;

15/4 + (7/12 x 3/28)

15/4 + (1/4 x 1/4)

15/4 + 1/16

Find the LCM of the resulting sum

15/4 + 1/16= [4(15)+1]/16

15/4 + 1/16 = 61/16

15/4 + 1/16 = 3 13/16

Hence the answer to the given expression is 3 13/16

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Answer:

1.2

Step-by-step explanation:

[tex]\frac{v}{5}[/tex] = [tex]\frac{3}{13}[/tex]  Cross multiply and solve for v

13v = 15  Divide both sides by 13

[tex]\frac{13v}{13}[/tex] = [tex]\frac{15}{13}[/tex]

v = 1.2 rounded to the nearest tenth

Why  this works

[tex]\frac{v}{5}[/tex] = [tex]\frac{3}{13}[/tex]  we can clear the fraction by multiplying both sides of the equal sign by (5·13)

[tex]\frac{(5x13)}{1}[/tex] · [tex]\frac{v}{5}[/tex] = [tex]\frac{(5x13)}{1}[/tex] ·[tex]\frac{3}{13}[/tex]  On the left of the equal sign the 5's cancel out and the on the right of the equal sign the 13's cancel out.

13v = 5(3)

13v = 15

1 kilograms is equal to 2.205 pounds, which leads to the conversion factor of 2.205. The conversion factor is based on both the Avoirdupois system of measurement, which is used in the United States and the United Kingdom to measure weight or mass, and the International System of Units (SI).

  The basis for the Avoirdupois system is the pound, which is equal to 0.45359237 kilos. Consequently, 0.45359237 kilograms equal one pound.

  Finding the weight in pounds of 1 kilograms is necessary to convert kilograms to pounds. We can divide 1 kilograms by 0.45359237 kilograms/pound to get this equivalent weight.

1 kg / 0.45359237 kg/lb = 2.20462262 lb

 This is the kilograms to pound conversion factor. The value is rounded to the widely regarded and employed value of 2.205.

 Therefore, to convert kilograms to pounds, we multiply the weight in kilograms by 2.205.

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The solution to the system of equations for 3x+6y=18 and X-12y=31 are:

X=37/7 and Y=25/14

A system of equations is a set of one or more equations involving a number of variables.

A system of equations is also known as a set of simultaneous or equation systems.

Now, consider the given equations:

3x+6y=18--------(1)

X-12y=31---------(2)

the equation can be rewritten as 3x+6y-18=0, by taking the common number in the equation we get:

x+2y-6=0 as x+2y=6----(3)

To solve the equations add them (2)+(3)

X-12y=31

X+2y=6

changing the signs we get

14y=25

y=25/14

Now substitute y value equation(3)

X+2(25/14)=6

7X+25=42

7X=37

X=37/7

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Answer: hoped this help. bye.:)

Length of KL is 31.5 unit.

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points. The sum of interior angles of quadrilaterals is always equal to 360 degrees.

Given in the figure

GJ = 15

GH = 8

KN = 59

KL = x

GHIJ and KLMN are similar

therefore, ratio of the sides will be equal

GJ/GH = KN/KL

15/8 = 59/x

x = 59 × 8/15

x = 472/15

x = 31.4667

Hence,31.5 is length of KL.

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The price per square foot of a vacant lot that measures 50' x 102' and sold for $108,250 is $21.23.

To find the price per square foot of the vacant lot, we need to divide the total price by the total area of the lot.

We can find the area of the lot by multiplying the length by the width:

Area = 50' x 102' = 5100 sq.ft

Then, we can divide the total price by the total area to find the price per square foot:

Price per sq.ft = Total Price / Total Area

Price per sq.ft = 108,250 / 5100

Price per sq.ft = 21.23

Therefore, the price per square foot of the vacant lot is $21.23.

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Answer:

80 grow into plants

Step-by-step explanation:

Fraction word problems:

   Out of 13 seeds, 8 grew into plants.

[tex]\sf \text{Number of seeds grown out of 130 okra seeds} = \dfrac{8}{13}*130[/tex]

                                                                       = 8 * 10

                                                                       = 80

Out of 130 seeds, 80 grow into plants.

In order to have negative correlation between two variables the covariance must be negative.

What is correlation?

The degree to which two variables are linearly related is expressed by the statistical concept of correlation (meaning they change together at a constant rate). It is a typical technique for outlining straightforward connections without stating cause and effect.

The correlation between two variables x and y is,

[tex]r = \frac{Cov(x, y)}{S_x*S_y}[/tex]

where,

Cov(x, y) is the covariance between x and y.

[tex]S_x[/tex] and [tex]S_y[/tex] respectively denotes the standard deviation of x and y.

If the correlation is negative then  r < 0.

Now r < 0

[tex]\frac{Cov(x, y)}{S_x*S_y} < 0\\Cov(x, y) < 0\\Sx > 0, S_y > 0[/tex]

If r < 0 the Cov(x, y) < 0.

In order to have negative correlation between two variables the covariance must be negative.

Hence, in order to have negative correlation between two variables the covariance must be negative.

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Answer:

0.00746696035

Step-by-step explanation:

3.39/454 = 0.00746696035

Rounded that would only be 1 cent per kg.  Hummmppp....

The value of (x + y) is 25.

What is solving an equation?

We must use arithmetic operations to separate the variables in order to solve any equation.

The same number is added on both sides.

Taking away the same number from both sides.

using the same number on both sides of the multiplication.

using the same number on both sides to divide.

Consider, the given equations

2x^2 - 2y^2 = 125              ..(1)

x - y = 2.5                           ..(2)

From equation (1)

x^2 - y^2 = 125/2

By using:  [tex]a^2 - b^2 = (a - b)(a + b)[/tex]

⇒  (x - y)(x + y) = 125/2

Given:  (x - y) = 2.5

⇒ 2.5*(x + y) = 125/2

           (x + y) = 125/(2*2.5)

            x + y = 125/5

            x + y = 25

Hence, the value of (x + y) is 25.

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The solution is, The perimeter is 37inches.

The perimeter of a figure is the sum of the whole sides of the figure.

Therefore, the perimeter of the entire shape can be calculated as follows:

The shape is made of one half-circle attached to an equilateral triangle

Therefore,

circumference of the semi-circle = πr

r = 8 / 2 = 4 inches

circumference of the semi-circle = 4π

Hence,

perimeter of the shape = 8+8+8+4π

perimeter of the shape = 24+ 4(3.14)

perimeter of the shape = 24 + 12.56

                                       = 36.56

Therefore, perimeter of the shape = 37 inches (approx)

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-7.4 degrees celsius is less than the temperatures Susan recorded.

To explain, temperatures are measured on a scale, with 0 degrees celsius being the point at which water freezes and 100 degrees celsius being the point at which water boils. A temperature of -7.4 degrees celsius is therefore less than the recorded temperatures of -7.4 and 1.8 degrees celsius.

The temperature is a measure of the thermal energy of a substance or system, and is typically measured on a scale, such as the Celsius scale or the Fahrenheit scale.

In other words, the number -7.4 is less than 1.8 and -7.4 on the scale of temperature, meaning that -7.4 degrees celsius is less than the temperatures Susan recorded.

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Answer: Assuming the conditions for inference are met, we can use the difference in proportions of red beads in the two samples to estimate the difference in proportions of red beads in the population. The 95% confidence interval for the difference in proportions of red beads in the two containers is calculated as follows:

Difference in sample proportions = p1 - p2 = (13/50) - (16/50) = -0.03

Standard error of the difference in sample proportions = sqrt{(p1*(1-p1)/n1) + (p2*(1-p2)/n2)} = sqrt{(13/50)(37/50)/50 + (16/50)(34/50)/50} = 0.079

Margin of error = z* * standard error of the difference in sample proportions = 1.96 * 0.079 = 0.155

95% Confidence interval for the difference in proportions of red beads in the two containers = (difference in sample proportions - margin of error, difference in sample proportions + margin of error) = (-0.03 - 0.155, -0.03 + 0.155) = (-0.185, 0.125)

So, we can be 95% confident that the difference in the proportion of red beads in the two containers is between -0.185 and 0.125.

Step-by-step explanation:

The probability of 30 random people having weight more than 6000 pounds is 0.3134 or 31.34%.

To find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds, we can use the Central Limit Theorem (CLT) which states that the sum of a large number of independent and identically distributed random variables will tend to be normally distributed, regardless of the underlying distribution of the individual variables.

Since we know the average weight of a passenger (190 pounds) and a reasonable standard deviation (35 pounds), we can use this information to calculate the mean and standard deviation of the total weight of 30 passengers.

The mean weight of 30 passengers is:

30*190 = 5700 pounds

The standard deviation of the weight of 30 passengers is:

sqrt(30)*35 = 59.8076211353316

Now we can use the standard normal distribution table, or z-score formula to find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds.

z = (6000-5700)/59.8076211353316

z = 0.50251572

The probability of a z-score being greater than 0.50251572 is 0.3134, this means that there is a 31.34% chance that the total weight of 30 randomly selected passengers will exceed 6000 pounds.

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(A) P(AB) = P(A B) = 0.5 denotes that there is a 0.5 chance that occurrences A and B will occur simultaneously. We cannot tell whether this relationship holds true for these specific events because the provided information does not specify whether A and B are independent or mutually exclusive.

(b) P(A'B) = P(A') + P(B') - P(A'B') = 0.6 denotes that there is a 0.6 chance that events A and B will occur together.

(c) The chance that either the complement of event A or the complement of event B will occur is 0.5. P(A'B') = 1 - P(AB) = 1 - 0.5 = 0.5.

(d) P(A|B) = P(AB) / P(B) = 0.5 / 0.2 = 2.5 denotes that there is a 2.5 percent chance that event A will occur provided that event B has already occurred.

If P(A) = 0.4 and P(B) = 0.2, respectively, then A and B are independent events.

(a) P(AB) is the probability that both occurrences A and B will occur at the same time. It is calculated as P(A) * P(B) = 0.4 * 0.2 = 0.08. The likelihood that A will occur is independent of the likelihood that B will occur since the two events are unrelated.

(b) P(A'B) = P(A') * P(B) = (1-0.4) * 0.2 = 0.12 is the likelihood that events A and B will occur in complement.

(c) The probability that either the complement of event A or the complement of event B will occur, or both, is given by P(A'B') = 1 - P(A'B) = 1 - 0.08 = 0.92.

(d) P(A|B) = P(AB) / P(B) = 0.08 / 0.2 = 0.4, which represents the likelihood that event A will occur in the absence of event B.

if P(A) = 0.4 and P(B) = 0.2, respectively, and A and B are events that cannot coexist.

(a) P(AB) = 0 (by definition of mutual exclusion), indicating that there is no chance that events A and B will occur simultaneously.

(b) The probability that event A's complement, event B, will occur is P(A'B) = P(B) = 0.2.

(c) The probability that either the complement of event A or the complement of event B will occur, or both, is P(A'B') = P(A') + P(B') = 0.6.

(d) Since P(AB) = 0, the probability of event A occurring provided that event B has already occurred is undefined. P(A|B) = P(AB) / P(B) = 0 / 0.2 = undefined.

 Roll a die once. The event of getting a "2" and the event of getting a "5" are mutually exclusive.

Roll a die twice. The event of getting a "2" on the first roll and the event of getting a "5" on the second roll are independent events.

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Therefore ,on solving the provided question we can say that - Simple Interest after 5 year the car value is £7,689.6

Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it.

here,

rate = 10%

Time = 1 year

Principle = 12000

=>SI = PRT/100

=> SI =  10*1*12000/100

=> SI = 1200

and

=>  After 1 year = 12000 -1200 = 10800

and

for five  years

=> SI = PRT/100

=> SI = 10800 * 7.2 * 4 / 100

=> SI = 3110.4

After 5 year = 10800 - 3110.4  = 7,689.6

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Answer:

it is 28 cm^2 ig

you got to solve it in the same way as the first question ( divide the shape into rectangles and find the area of each then add them )

Answer:

1.) x=1; y=1

2.) x=1; y=5

3.) No solution

Step-by-step explanation:

1.) To start off with number one, we see that in both equations the x and y are positive, and the sums aren't equal to each other, this means we have to do something to make them equivalent. For example, we can multiply the top equation by 8 and the bottom equation by 7, so we get the equations 32x + 24y = 56 and the bottom equation to be 21x+35y=56. From here we can just make the equations equal each other to get 32x+ 24y = 21x +35y. From here we can just get a certain amount of x to equal certain amount of y by taking away the smaller amount of each and bringing it to the other side by subtracting. From that we get 11x = 11y. We can simplify this to be x=y. Now we can substitute either x or y in either equation to get 4x + 3(x) = 7. Then you solve algebraically and you get x=1. Now since we established that x was already equal to y, both x AND y are equal to 1.

2.) For this problem, we have an x that is negative in one equation and positive in the other. This means we can use the method of multiplying the bottom equation by 3 to get 3x +3y = 18. Now we are able to add both equations to each other crossing out the x's because they cancel out. From this we get 4y=20, Which means y=5. We can now plug this back into the equation to get x+(5) = 6. Which means y=5 and x=1.

3.) For this problem, we have both equations equal to y. However the x's are also equal to each other. Meaning if we were to solve them like in problem one, we would get the issue of cancelling the x's out and just getting 13/2=9/2 which is a problem because they do not equal each other. But, we can notice that both of the given systems are linear lines, meaning we could plot them off a graph. But to save time, we can notice that both equations have the exact same slope but different starting positions. Meaning that both lines would be parallel to each other. Since both lines are parallel to each other, There will never be an intersection, or answer between them. Making x and y null (no answer)

a) The velocity and position functions are given as follows:

b) The particle is at rest when: t = kπ, k = ± 1, ± 2, ± 3, ...

The acceleration function for this problem is defined as follows:

a(t) = cos(t).

The velocity function is the integral of the acceleration function, hence it is given as follows:

v(t) = sin(t).

(as the integral of cos(t) is sin(t).)

The particle will be at rest when:

v(t) = 0.

Hence:

sin(t) = 0

t = arcsin(0)

t = kπ, k = ± 1, ± 2, ± 3, ...

The position function is the integral of the velocity function, hence it is given as follows:

s(t) = -cos(t) + 3.

As:

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The sum of the measures of the interior angles, in degrees, of a decagon (10-sided polygon) is 1440°

A polygon having ten sides (or a ten-sided polygon) is called a decagon or ten-gon, in geometry. Also, it has ten vertices and ten angles.

The summation of the interior angles of a polygon is ( n - 2 ) x 180 where n is the number of sides.

The sum of interior angles = (10 - 2) x 180

The sum of interior angles = 1440º

Therefore the measure of each angle is

10 angles = 1440

1 angle = 1440 ÷ 10 = 144º

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By square root, power and sign properties, the expression - 16 · y is the square root of 16 · y² for y < 0.

Let be n a real number, x is the square root of n if and only if n = x², that is:

x = √n

In addition, we find by sign properties the following two cases according to sign of variable y:

Now we proceed to find the square root of 16 · y² for y < 0. First, write the square root described in statement:

√(16 · y²)

Second, use square root and power properties:

√16 · √y², where y < 0.

- 16 · y

In conformity with square root, power and sign properties, the square root 16 · y² for y < 0 is the expression - 16 · y.

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