Ben sat outside his school in cambridge and made a note of the colour of the first 100 cars that passed.
27 of the cars were red
in Britain there are around 35 million cars on the road
use bens findings to give an estimate of how many cars on the road are red

Answer:

D. 2019

Step-by-step explanation:

So I started by rewriting the function f(x)

1000 = 10^3 so

    f(x)=10^3 times 1.03^x

1.03 = 103/100 so

     f(x)= 10^3 times (103/100)^x

to raise a fraction to a power you just raise the numerator and denominator to that power so

      f(x)= 10^3 times 103^x/100^x

change it to exponential form with a base of 10

     f(x)=10^3 times 103^x/10^2x

then you can reduce it with the 10^3

     f(x)=103^x/10^2x-3

so now that thats in more of a standard form you can find the intersection of the two functions

which is at (9.012,1305.244)

x is the number of years after 2010, so they will be equal ~9 years after 2010, which is 2019.

The probability that is within $500 of the population mean if a sample of size 60 is used is 0.6680.

The probability that is within $500 of the population mean if a sample of size 120 is used is 0.8294

z = (x - μ)/σ

z1 = (71300 - 71800)/516.3978 = -0.97

z2 = (72300 - 71800)/516.3978 = 0.97

Therefore, we get

P(71300 <= X <= 72300) = P((72300 - 71800)/516.3978) <= z <= (72300 - 71800)/516.3978)

= P(-0.97 <= z <= 0.97) = P(z <= 0.97) - P(z <= -0.97)

= 0.834 - 0.166

= 0.6680

b)

Here, μ = 71800, σ = 365.1484, x1 = 71300 and x2 = 72300. We need to compute P(71300<= X <= 72300). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ

z1 = (71300 - 71800)/365.1484 = -1.37

z2 = (72300 - 71800)/365.1484 = 1.37

Therefore, we get

P(71300 <= X <= 72300) = P((72300 - 71800)/365.1484) <= z <= (72300 - 71800)/365.1484)

= P(-1.37 <= z <= 1.37) = P(z <= 1.37) - P(z <= -1.37)

= 0.9147 - 0.0853

= 0.8294

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Answer:not sure what u talking about

Step-by-step explanation:

Answer:

Since the ratios are constant, the sequence is geometric. The common ratio is –1. Since the ratios are constant, the sequence is geometric.

The original APR needed to reach Prof. ME's goal was approximately 15.87%.

To calculate the original annual rate of return (APR) needed to reach Prof. ME's goal of $440,000, we can use the present value formula and solve for the APR.

a. Using the present value formula:

PV = FV / (1 + r)^n

Where:

PV = Present value ($140,000)

FV = Future value ($440,000)

r = Annual interest rate (APR)

n = Number of years (10)

Rearranging the formula and substituting the given values:

r = (FV / PV)^(1/n) - 1

r = (440,000 / 140,000)^(1/10) - 1

r ≈ 0.1587 or 15.87%

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The relationship between a dependent and an independent variable expressed as a logarithmic equation is as follows X = Y/2

At times, the relationship between a dependent and an independent variable is expressed as a logarithmic equation. For this question, given a positive constant € and the two equations below, we can find the relationship between X and Y. Equation 1: Log(c) = X/2 Equation 2: Log(c^2) = Y.We can use the basic properties of logarithms to solve this problem. To do so, we need to understand what logarithms are first.Logarithms are the opposite of exponentials. They allow us to find the exponent needed to produce a given value. For instance, log base 2 of 8 is 3 since 2^3 = 8.

A logarithm is represented as log_bx where b is the base and x is the argument or the number being passed to the logarithm.In equation 1, we are given that log(c) = x/2. To isolate x, we need to exponentiate both sides with base e.e^(log(c)) = e^(x/2)This gives us c = e^(x/2).We can rewrite this expression as c^2 = e^x. Now we use equation 2 which states that log(c^2) = y. This is equivalent to 2log(c) = y.Using equation 1, we can substitute log(c) for x/2.2log(c) = y2(x/2) = yx = y/2So the relationship between X and Y is X = Y/2. Therefore, we can conclude that the relationship between a dependent and an independent variable expressed as a logarithmic equation is as follows: X = Y/2.

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Answer:

1  4(3-r)  or  12-4r

2.  7( 8-m) or 56-7m

3.   -2

Step-by-step explanation:

1) |4r−12| , if r<3

|4r-12|

Factor out a 4

4|r-3|

|r-3| will be less than 0 since r is less than 3

So we can rewrite it as 3-r to remove the absolute value signs and make it positive

4 (3-r)

12 -4r

2.   |7m–56| , if m<8

Factor out a 7

7| m-8|  

|m-8| will be less than 0 since m is less than 8

So we can rewrite it as  8-m to remove the absolute value signs and make it positive

7( 8-m)

56-8m

3) |z−7|−|z−9| , if z<7

|z-7| will be less than 0 since z is less than 7  and |z-9| will be less than 0 since z is less than 7

So we can rewrite it as  7-z  and 9-z to remove the absolute value signs and make it positive

7-z - (9-z)

Distribute the minus sign

7-z-9+z

-2

11 packs of 3 tennis ball was sold .

An equation is a mathematical statement formed when two algebraic expressions are equated by an equal sign.

It is given that

A store sells

A pack of 3 tennis ball at $5

A pack of 8 tennis ball at $12

Let the pack of 3 sold is x

and the pack of 8 sold is y

It is given that

3x + 8y = 97

5x +12y = 151

Solving these equations

x = 11

and y = 8

Therefore 11 packs of 3 tennis ball was sold .

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Answer:

x-9y=1

Step-by-step explanation:

Answer:

If real GDP in a particular year is $80 billion and nominal GDP is $240 billion, the GDP price index for that year is: 300.

Step-by-step explanation:

Answer:

height = 15 inches

Step-by-step explanation:

the volume (V) of a cylinder is calculated as

V = Ah ( A is the base area and h the height )

given V = 1650 and A = 110 , then

1650 = 110h ( divide both sides by 110 )

15 = h

\(numerical \: coefficient \: = > 7 \\ \\ literal \: coefficient \: = > \: xy\)

hope that helps uh..☺

1000 cubic millimeters are in a cubic centimeter.

'What is cubic centimeter?'

There are 1000 cubic millimeters in one cubic centimeter (cm³) (mm³). Add 1000 to the cubic cm number to convert it to cubic mm.

For instance, multiplying 10 by 1000 results in 10000 mm3, or how many cubic mm there are in 10 cubic cm.

The volume of small items is measured in cubic centimeters, a tiny unit of measurement. Discover standard units of measurement, the definition of cubic centimeters, how to convert them, and how to measure volume using cubic centimeters. A little cube with sides that are 1 cm long occupies the same amount of space as a cubic centimeter.

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The ninth term of the series \(80,60,45.....\)  is \(50\).

We need to determine the relationship between the consecutive terms of the series to evaluate the succeeding terms of the series.

How to find the terms in a series?

The difference between the first and second terms is \(60-80=-20\).

The difference between the second and the third terms is \(45-60=-15\)

So, the difference between the third and the fourth terms will be \(-10\). So, the fourth term will be \(45-10=35\).

Similarly, the difference between the eighth and the ninth terms will be \(-15\). So, the ninth term will be \(35-(-15)=50\).

Thus, the ninth term of the series is \(50\).

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Answer:

3 2/3 cups

Step-by-step explanation:

1 1/3 for one recipe.

2/3 cups for the second recipe.

1 2/3 for the third recipe.

Add all of the amount of cups used to get the total amount of sugar used.

1 1/3 + 2/3 + 1 2/3 = 3 2/3

She used 3 2/3 cups of sugar in all.

hope this helps!! p.s. i really need brainliest :)

We have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

To solve the given equations for the equilibrium values of C, NX, CF, r, and ε, let's go step by step.

First, we'll substitute equations (2), (3), (4), (5), (6), (7), (8), and (9) into equation (2) to eliminate the variables C, I, G, NX, CF, and T.

Equation (2) becomes:
Y = (1/2)(Y - T) + (2,000 - 100r) + 1,500 + (500 - 500ε)

Next, let's simplify the equation:

Y = (1/2)(Y - 1,000) + 2,000 - 100r + 1,500 + 500 - 500ε

Distribute (1/2) to the terms inside the parentheses:

Y = (1/2)Y - 500 + 2,000 - 100r + 1,500 + 500 - 500ε

Combine like terms:

Y = (1/2)Y + 3,500 - 100r - 500ε

Now, let's isolate Y by subtracting (1/2)Y from both sides:

(1/2)Y = 3,500 - 100r - 500ε

Multiply both sides by 2 to get rid of the fraction:

Y = 7,000 - 200r - 1,000ε

We now have one equation (10) in terms of Y, r, and ε.

Next, let's substitute equation (1) into equation (10) to solve for Y:

5,000 = 7,000 - 200r - 1,000ε

Subtract 7,000 from both sides:

-2,000 = -200r - 1,000ε

Divide both sides by -200:

10 = r + 5ε

This gives us equation (11) in terms of r and ε.

Now, let's substitute equation (11) into equation (5) to solve for NX:

NX = 500 - 500ε

Substitute r + 5ε for ε:

NX = 500 - 500(r + 5ε)

Simplify:

NX = 500 - 500r - 2,500ε

This gives us equation (12) in terms of NX, r, and ε.

Finally, let's substitute equation (12) into equation (6) to solve for CF:

CF = -100r

Substitute 500 - 500r - 2,500ε for NX:

CF = -100(500 - 500r - 2,500ε)

Simplify:

CF = -50,000 + 50,000r + 250,000ε

This gives us equation (13) in terms of CF, r, and ε.

To summarize, we have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

These equations represent the equilibrium values of Y, r, ε, NX, and CF in the given open economy.

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Answer:

C

Step-by-step explanation:

Angle Bisector means the line is being split in half evenly. So, when angle 3 is 60, so is angle 4. Angles 1 and 2 are both 30 degrees because 30 + 60 equals to 90 degrees.

I hope this helps!

Answer:

60⁰..................

Answer:

y = 2x + 2

Step-by-step explanation:

6x -3y = -6 (get y on one side of the equals sign by substracting 6x from both sides)

-3y = -6x - 6 (divide each side by -3 to get final value of y)

y = 2x + 2

The value of x for this problem is given as follows:

x = 5.

Hence the angle measures are given as follows:

We have that angles A and D are congruent for this problem, meaning that they have the same measure.

Hence the value of x is obtained as follows:

7x - 3 = 5x + 7

2x = 10

x = 5.

Hence the angle measures are given as follows:

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Answer:  A

Step-by-step explanation: I think it's point A.

The appropriate test statistic for conducting a hypothesis test to determine if the current process mean fill is less than the target mean weight of 5.3 oz at a 95% confidence level is -8.37.

To test whether the current process mean fill is less than the target mean weight, we can use a one-sample t-test. The test statistic is calculated by subtracting the target mean from the sample mean, and then dividing it by the standard error of the sample mean.

In this case, the sample mean is 4.8 oz, the target mean is 5.3 oz, and the sample standard deviation is 0.3 oz. The standard error of the sample mean is calculated by dividing the sample standard deviation by the square root of the sample size. Since the sample size is 28, the standard error is 0.3/sqrt(28).

The test statistic is then calculated as (4.8 - 5.3) / (0.3/sqrt(28)), which simplifies to -8.37 (rounded to two decimal places). This test statistic is used to determine the p-value or compare with critical values to make a conclusion about the hypothesis test.

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Answer:

y=1/3x+4

Step-by-step explanation:

Answer:

1/10

Step-by-step explanation:

Percent spent on cable TV = 10%

Percent means "per hundred".

So, we can write 10% as,

10/100

= 1/10

So the family spent 1/10 of their total budget on cable TV.

The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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The results are different because the simulated data is based on random numbers and may not perfectly match the probability distribution.

To simulate the emergency calls for 3 days, we need to use a cumulative hourly clock and generate random numbers to determine when the calls will occur. Let's use the following table of random numbers:

Random Number Call Time

57 1 hour

23 2 hours

89 3 hours

12 4 hours

45 5 hours

76 6 hours

Starting at 12:00 AM on the first day, we can generate the following sequence of emergency calls:

Day 1:

12:00 AM - Call

1:00 AM - No Call

3:00 AM - Call

5:00 AM - No Call

5:00 PM - Call

Day 2:

1:00 AM - No Call

2:00 AM - Call

4:00 AM - No Call

7:00 AM - Call

8:00 AM - No Call

11:00 PM - Call

Day 3:

12:00 AM - No Call

1:00 AM - Call

2:00 AM - No Call

4:00 AM - No Call

7:00 AM - Call

9:00 AM - Call

10:00 PM - Call

The average time between calls can be calculated by adding up the times between each call and dividing by the total number of calls. Using the simulated data from part a, we get:

Average time between calls = ((2+10+10+12)+(1+2+3)) / 7 = 5.57 hours

The expected value of the time between calls can be calculated using the probability distribution:

Expected value = (1/6)x1 + (1/6)x2 + (1/6)x3 + (1/6)x4 + (1/6)x5 + (1/6)x6 = 3.5 hours

The results are different because the simulated data is based on random numbers and may not perfectly match the probability distribution. As more data is generated and averaged, the simulated results should approach the expected value.

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To prove that X(=0), we need to show that when X is a scalar function, its derivative with respect to time is zero.

Let's consider a scalar function X(t). The derivative of X(t) with respect to time is denoted as dX/dt. To prove that X(=0), we need to show that dX/dt = 0.

The derivative of a scalar function X(t) is computed as dX/dt = AX(t), where A is a constant matrix and X(t) is a vector function.

Since X(=0), the derivative becomes dX/dt = A(0) = 0. Thus, the derivative of X(t) is zero, which proves that X(=0).

Now, let's consider the second part of the question. We are given that X1, X2, and X3 are linearly independent solutions of the differential equation X'=AX. We need to prove that 2X1-X2+3X3 is also a solution of the same differential equation.

We can verify this by substituting 2X1-X2+3X3 into the differential equation and checking if it satisfies the equation.

Taking the derivative of 2X1-X2+3X3 with respect to time, we get:

d/dt (2X1-X2+3X3) = 2(dX1/dt) - (dX2/dt) + 3(dX3/dt)

Since X1, X2, and X3 are linearly independent solutions, we know that dX1/dt = AX1, dX2/dt = AX2, and dX3/dt = AX3.

Substituting these expressions, we get:

2(dX1/dt) - (dX2/dt) + 3(dX3/dt) = 2(AX1) - (AX2) + 3(AX3)

Using the properties of matrix multiplication, this simplifies to:

A(2X1-X2+3X3)

Thus, we can conclude that 2X1-X2+3X3 is also a solution of the differential equation X'=AX.

The proof shows that for a scalar function X(=0), the derivative is zero. Additionally, for the given linearly independent solutions X1, X2, and X3, the expression 2X1-X2+3X3 is also a solution of the differential equation X'=AX.

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Answer:

Area = 12

Step-by-step explanation:

Given

See attachment

Required

Area of \(\triangle PQR\)

From the attached image, we have:

\(P = (6,10)\)

\(Q = (10,8)\)

\(R = (6,4)\)

The area is then calculated as:

\(A = \frac{1}{2}|(x1y2 - x2y1) + (x2y3 - x3y2) + (x3y1 - x1y3)|\)

So, we have:

\(A = \frac{1}{2}|(6*8 - 10*10) + (10*4 - 6*8) + (6*10 - 6*4)|\)

Using a calculator:

\(A = \frac{1}{2}|-24|\)

Remove absolute bracket

\(A = \frac{1}{2} * 24\)

\(A = 12\)

Parallel lines are defined as lines that do not intersect or meet at any point in a plane. They are always parallel and equidistant from one another.

What is answer parallel line?

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical.

Parallel lines are two lines in the same plane that are equal distance apart and never intersect.

Real-world parallel line examples include railroad tracks, sidewalk edges, street markings, zebra crossings, the surface of pineapple and strawberry fruit, staircases and railings, and so on.

Parallel lines are lines in a plane that never meet, no matter how far they are extended. The distance between the parallel lines is constant because they never meet.

Parallel lines are defined as lines that do not intersect or meet at any point in a plane. They are always parallel and equidistant from one another.

these are 8 parallel lines

2x+3y = 6

2x+3y = 4

2x+3y = 1

2x+3y = 2

2x+3y = 3

2x+3y = 8

2x+3y = 7

2x+3y = 5

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Answer: 25

Step-by-step explanation:

part of a low is anything lower than 1oo

twice of 1/8 = 2/8 = 1/4

Answer:

25%

Step-by-step explanation:

"twice" means two times.

"twice the value of 1/8" is

2 × 1/8

(to multiply a whole number times a fraction, multiply the big number × the top number)

2 × 1/ 8 is 2/8

2/8 is 1/4.

1/4 = .25 = 25%

Since the answer is a percent, change 1/4 to a decimal, .25, change the decimal to a percent.

Or you could change 1/4 to 25/100. Percent means "per hundred" 25/100 is 25%.

Answer: 2

Step-by-step explanation:

(x - 7)² + (y - 3)² = 33 is the  equation of the circle with center (7,3) containing the point (5,10).

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

A circle with center (a,b) and radius r has the equation:

(x - a)² + (y - b)² = r²

We are given that the center of the circle is (7,3), so we can substitute a=7 and b=3:

(x - 7)² + (y - 3)² = r²

We are also given that the point (5,10) lies on the circle.

Since any point on the circle is r units away from the center, we can use the distance formula to find the value of r:

r = √(5-7)² + (10-3)²

=  √4+49

=√33

(x - 7)² + (y - 3)² = r²

(x - 7)² + (y - 3)² = 33

Hence, (x - 7)² + (y - 3)² = 33 is the  equation of the circle with center (7,3) containing the point (5,10).

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