(a) The scale of a map is 1:75 000. The length of the road on the map is 18 cm. Calculate the actual distance of the road in km.​

The closest increase in the distance of the Olympic marathon, in miles, is 1.25 miles. The correct option is B.

Given the Olympic marathon has been extended from 40 km to about 42 km.

Option B is correct. In 1908, the marathon was extended by  42 - 40 = 2 km. Since 1 mile is equal to 1.6 km, the  2 km increment can be converted to miles by multiplying as illustrated:

2 km × (1 mile / 1.6 km) = 1.25 miles

The options other than B are A, C, and D are incorrect and may be due to errors in applying conversion rates or other calculation errors.

Hence, an increase in the distance of the Olympic marathon when the Olympic marathon was lengthened from 40 kilometers to approximately 42 kilometers is 1.25 miles.

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The fraction of stars in the milky way having an earth-size planet in the habitable zone are around 10-20%.

Milky way is the galaxy comprising our solar system and therefore marking Earth's location in the universe. The milky way galaxy is just one among billions of different galaxies in the universe.

It contains numerous stars and the planets revolving it. Thus, the milky way galaxy can said to contain thousands of planetary systems. The planets in turn can be habitable or non-habitable owing to atmospheric conditions.

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Answer:

QR=2x=16

Step-by-step explanation:

2x+8= 3x

8=3x-2x

8=x

QR=2x= 8*2=16

Answer:

obvious answer, no

Step-by-step explanation:

specific and scientific answer:

the first input 1 equals 2, which could mean both +1 or times 2

but when there is input of 4 and an out-put of -1, it starts to not make sense

basically the first input is always going to be your control group for science experiments or the one that stays the same and judges

Answer:

125 Dolphins

Step-by-step explanation:

The number of dolphins varied linearly with the number of fish.

The number of dolphins = D

The number of fish = F

Hence:

D ∝ F

D = kF

When 400 fish were present 250 dolphins appeared

Solving for k

250 = 400k...... Equation 1

Also

when 300 fish were present, 200 dolphins appeared.

200 = 300k...... Equation 2

So: we find k = Constant of Proportionality

250 = 400k...... Equation 1

200 = 300k...... Equation 2

We Subtract Equation 2 from Equation 1

50 = 100k

k = 50/100

k = 1/2

How many dolphins would appear if 250 fish were present?

D = kF

D = 1/2 × 250

D = 125 Dolphins

Answer:

3g=x-2

Step-by-step explanation:

3g+2=x then, move 2 to the other side(nb*change to negative) then it will be 3g=x-2 finally divide both sides by 3 then it will be g=x-2

3

Using the trapezoid rule with n=4 subintervals, the approximate value of the definite integral is 3.64. Using Simpson's rule with n=4 subintervals, the approximate value of the definite integral is 3.141.

Using the trapezoid rule, the formula for the approximation of the definite integral is:

∆x/2 * [f(x0) + 2f(x1) + 2f(x2) + 2f(x3) + f(x4)]

where ∆x = (b-a)/n, a=0, b=π/4 and n=4. Evaluating the expression, we get 3.64 as the approximate value of the integral.

Using Simpson's rule, the formula for the approximation of the definite integral is:

∆x/3 * [f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + f(x4)]

where ∆x = (b-a)/n, a=0, b=π/4 and n=4. Evaluating the expression, we get 3.141 as the approximate value of the integral.

To find the exact value of the integral, we can evaluate it directly:

∫0π4sin⁡xdx = [-cos(x)]_0^π/4 = 1-1/√2 = (√2-1)/√2 ≈ 0.4142. Therefore, the exact value of the integral is (√2-1)/√2 ≈ 0.4142.

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Answer:

5 and 6

Step-by-step explanation:

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

a. The mean as 11 grams and the standard deviation as 2 grams.

b. The percent of spiders that weigh between 7 grams and 13 grams is approximately 81%.

c. The percent of spiders that weigh less than 9 grams is approximately 16%.

d. The weight values between 9 and 13 grams include approximately 68% of all the spider weights.

e. The z-score of a spider that weighs 15 grams is 2.

f. The percent of spiders that weigh more than 15 grams is approximately 2.28%.

a. To sketch a normal curve, we start with a horizontal axis representing the weight of the spiders. The vertical axis represents the frequency or probability density of the weights. We label the mean as 11 grams and the standard deviation as 2 grams. Then we mark one, two, and three standard deviations on either side of the mean, which are 9, 13, 15, 7, and 5 grams, respectively.

b. To find the percent of spiders that weigh between 7 grams and 13 grams, we need to calculate the z-scores for these weights. The z-score formula is z = (x - μ) / σ, where x is the weight, μ is the mean, and σ is the standard deviation.

For x = 7, z = (7 - 11) / 2 = -2.

For x = 13, z = (13 - 11) / 2 = 1.

The area under the curve between z = -2 and z = 1 represents the percentage of spiders in this range. Using a standard normal distribution table or a calculator, we find this area to be approximately 81%.

c. To find the percent of spiders that weigh less than 9 grams, we need to calculate the z-score for this weight. For x = 9, z = (9 - 11) / 2 = -1. The area under the curve to the left of z = -1 represents the percentage of spiders that weigh less than 9 grams. Using a standard normal distribution table or a calculator, we find this area to be approximately 16%.

d. We know that approximately 68% of all the spider weights fall within one standard deviation of the mean. Therefore, the weight values between 9 and 13 grams include approximately 68% of all the spider weights.

e. To find the z-score of a spider that weighs 15 grams, we use the z-score formula as z = (x - μ) / σ. For x = 15, μ = 11, and σ = 2, we get z = (15 - 11) / 2 = 2. The z-score of a spider that weighs 15 grams is 2.

f. To find the percent of spiders that weigh more than 15 grams, we need to calculate the area under the curve to the right of z = 2. Using a standard normal distribution table or a calculator, we find this area to be approximately 2.28%. Therefore, approximately 2.28% of all the spiders in the colony weigh more than 15 grams.

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If lisa is on her way home in her car, she has driven 24 miles so far, which is three-fourths of the way home, Lisa's total drive is 32 miles.

Let's represent the total length of Lisa's drive as x. We know that she has driven 24 miles so far, which is three-fourths of the total length. We can write this information as:

24 = (3/4) x

To find x, we need to isolate it on one side of the equation. We can start by multiplying both sides by 4/3 to get rid of the fraction:

24 * (4/3) = x

Simplifying, we get:

32 = x

We can say that Lisa has already driven 24 miles, which is three-fourths of the total distance. To find the total distance, we use the equation 24 = (3/4) x, where x represents the total distance.

To solve for x, we multiply both sides of the equation by 4/3 to cancel out the fraction, giving us 32 = x. Therefore, Lisa's total drive is 32 miles.

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The most accurate estimated sum of 181 and 204 is 380

The given numbers are 181 and 204

The compatible numbers are defined as the numbers that are easy to do the arithmetic operations. The arithmetic operations are addition, subtraction, division and multiplication etc.

To find the sum of the compatible numbers first we have to round the given numbers to the nearest tens or hundreds and do the the arithmetic operation

Round 181 to the nearest tens = 180

Round 204 to the nearest tens = 200

Then the sum of compatible numbers will be

180 + 200 = 380

Therefore, the most accurate estimation is 380

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Answer:

V ≈ 68.63 cm³

Step-by-step explanation:

the volume (V) of a sphere is calculated as

V = \(\frac{4}{3}\)πr³

the volume of a hemisphere is half the volume of a sphere, so

V = \(\frac{1}{2}\) × \(\frac{4}{3}\) πr³ = \(\frac{2}{3}\) πr³ , then

V = \(\frac{2}{3}\) π × 3.2³

  = \(\frac{2}{3}\) π × 32.768

  ≈ 68.63 cm³ ( to 2 dec. places )

The rate at which the area of the triangle is increasing when the angle between the sides of fixed lengths is π/3 is 0.3 m²/s.

If the lengths a and b for two sides of the triangle, as well as the included angle θ, are known, the area of a triangle can be calculated using the sine formula.

\(\text { Area }=\frac{1}{2} a b \sin \theta\)

Now, according to the question;

The two sides of the triangle are given;

Let a = 4m and b = 5m.

Let θ = π/3. be the angle between the two sides;

Then,

Differentiate the area with respect to time (as rate of change of area)

\(\begin{aligned}\frac{\mathrm{d} A}{\mathrm{~d} t}=\frac{\mathrm{d}}{\mathrm{d} t} \frac{1}{2} a b \sin \theta &=\frac{1}{2} * 4 * 5 * \frac{\mathrm{d}(\sin \theta)}{\mathrm{d} \theta} \cdot \frac{\mathrm{d} \theta}{\mathrm{d} t} \\&=10 *(\cos \theta) * 0.06 \frac{\mathrm{m}^{2}}{\mathrm{~s}}=0.6 \cos (\pi / 3) \frac{\mathrm{m}^{2}}{\mathrm{~s}} \\&=0.6 * 0.5 \frac{\mathrm{m}^{2}}{\mathrm{~s}}=0.3 \frac{\mathrm{m}^{2}}{\mathrm{~s}}\end{aligned}\)

Therefore, the area of the triangle as a function of angle is 0.3 m²/s.

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The complete question is-

Two sides of a triangle are 4m and 5 m in length and the angle between them is increasing at a rate of 0.06 rad/sec. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed lengths is π/3.

Step-by-step explanation:

If you put some quantities for theta, you reach to B option

The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a conversion factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn.

(a) The given units can be converted as follows: 6 glints = 1 filn...

(1)12 grees = 1 zool...

(2)2 grees = 10 twibbs...

(3)5 grees = 1 bic...

(4)Note that the grees are in both the numerator and denominator of the second unit conversion factor (3). Hence we can cancel out the grees by using it twice in the numerator and denominator. Now using the given conversion factors in equation (1), we get:

7 glint/twibb=7 glint/ (10 grees/2 grees)=14 glint/10 grees=14 glint/ (5 grees/12 grees)=16.8 filn/strord

(b) We need to convert the result of part (a) from filn/strord to megafiln/strord.

1 mega = 106

Thus 1 megafiln = 106 filn

16.8 filn/strord = (16.8 filn/strord) x (1 megafiln/106 filn) = 1.68 x 10-5 megafiln/strord

The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn. Similarly, going 1 foot-per-hour would mean going a smaller number of feet-per-hour than going 1 mile-per-hour since there are 5280 feet in a mile.

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AJ, this is the solution to the exercise:

Applying one of the exponents property, we have:

(2^2t

Using the z-distribution, as we have the standard deviation for the population, it is found that 8 stores must be analyzed.

The confidence interval is:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

The margin of error is given by:

\(M = z\frac{\sigma}{\sqrt{n}}\)

In this problem, we have an 82% confidence level, hence\(\alpha = 0.82\), z is the value of Z that has a p-value of \(\frac{1+0.82}{2} = 0.91\), so the critical value is z = 1.34.

The standard deviation for the population is of \(\sigma = 0.06\), and we want a margin of error of M = 0.03, hence we solve for n to find the sample size needed.

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(0.03 = 1.34\frac{0.06}{\sqrt{n}}\)

\(0.03\sqrt{n} = 1.34 \times 0.06\)

Simplifying by 0.03:

\(\sqrt{n} = 1.34 \times 2\)

\((\sqrt{n})^2 = (1.34 \times 2)^2\)

\(n = 7.2\)

Rounding up, 8 stores must be analyzed.

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The value of P(Ac ∩ B) is found using the complement rule is  0.6250 .The correct option is A) 0.6250

To find P(B | Ac ) given the events A and B in a sample space S, and where P(A) = 7⁄25, P(B) = 1/2, and P(A ∩ B) = 1/20, and we have to find P(B | Ac ), we follow the following steps:

Step 1: Find P(Ac) and P(Ac ∩ B)

Step 2: Find P(B | Ac )

We use the formula P(B|Ac) = P(Ac ∩ B) / P(Ac)

Step 1: Find P(Ac) and P(Ac ∩ B)

Using the complement rule, P(Ac) = 1 - P(A)P(Ac) = 1 - (7⁄25)P(Ac) = 18⁄25

Using the formula P(A ∩ B) = P(A) + P(B) - P(A ∪ B) to find P(A ∪ B),

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)P(A ∪ B) = (7⁄25) + (1/2) - (1/20)

P(A ∪ B) = (14⁄50) + (25/50) - (2⁄100)P(A ∪ B) = (39/50)

P(Ac ∩ B) = P(B) - P(A ∩ B)P(Ac ∩ B) = (1/2) - (1/20)

P(Ac ∩ B) = (9/40)

Step 2: Find P(B | Ac )P(B | Ac ) = P(Ac ∩ B) / P(Ac)

P(B | Ac ) = (9/40) / (18⁄25)P(B | Ac ) = 5/8P(B | Ac ) = 0.6250

The correct option is A) 0.6250

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Answer:

(-2,1)

Step-by-step explanation:

P' = (-5+3,2-1)

P' = (-2,1)

Answer: C

Step-by-step explanation:

:)

There are 125,970 ways to choose a dozen donuts from 20 varieties if there are no two donuts of the same variety.

a) If there are no two donuts of the same variety, the problem is equivalent to choosing 12 distinct objects from 20. This is because each variety of donut is distinct and cannot be repeated, so we can think of each variety as a unique object.

To calculate the number of ways to choose 12 distinct objects from 20, we use the combination formula, which is:

C(20,12) = 20! / (12! * (20-12)!)

Here, 20! represents the total number of ways to order all 20 objects, 12! represents the number of ways to order the selected 12 objects, and (20-12)! represents the number of ways to order the remaining 8 objects that were not selected. Dividing the total number of orders by the number of ways the selected objects can be ordered and the remaining objects can be ordered gives us the number of distinct combinations of 12 objects that can be chosen from 20.

Plugging in the numbers, we get:

C(20,12) = 20! / (12! * (20-12)!)

= (20 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9) / (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)

= 125,970

Therefore, there are 125,970 ways to choose a dozen donuts from 20 varieties if there are no two donuts of the same variety.

b) If all donuts are of the same variety, there is only one way to choose a dozen donuts - simply choose any 12 donuts from the available 12.

c) If there are no restrictions, we can choose any combination of 12 donuts from 20. This is equivalent to choosing 12 objects from 20 where the order of selection does not matter. We can again use the combination formula:

C(20,12) = 20! / (12! * (20-12)!)

Here, the formula calculates the number of ways to choose 12 objects from 20 without considering the order of the objects. We get the same answer as part a), which is 125,970.

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The second wheel has a smaller circumference compared to the first wheel. The second wheel completes a revolution when the wheel turns 75.40 inches, but the odometer reads 84.82 inches.

There are two types of odometers

In the case of a mechanical odometer, the worm gear is used to make the gear train, and the overall gear ratio is 1690:1, which means that when the vehicle travels a distance of 1 mile, the mechanical odometer input shaft makes 1690 revolutions during this time. In the case of a digital odometer, a magnetic sensor is used to receive pulses, each of which counts as one revolution. We now have a bicycle odometer designed for 27 wheels. Thus, d₁ = 27 inches is the diameter of the first wheel

d₂= 24 inches is the diameter of the second wheel

The odometer is the distance traveled by the vehicle, given as the number of revolutions of the wheel multiplied by the circumference of the wheel. So for the first wheel, Therefore, in case of first

wheel, \(C_1 = πd_1 \)

= π × 27

= 84.82 inches

In case of second wheel,

\(C_2 = π × d_2\)

= π × 24 inches

= 75.40 inches

So, \(C_1 - C_2 = \) 84.82 inches - 75.40 inches

= 9.42 inches

So we can see that the second wheel has circumference is less as compared to the first wheel.

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Complete question:

bicycle odometer is designed for 27 wheels. what happens if you use it on a bicycle with 24 wheels?

Answer:

He will make a lot of money

Step-by-step explanation:

The recursive formula of the geometric sequence is \(b(1) = -0.25\), \(b(n) = b(n-1)\cdot 8\)

The sequence is given as:

\(-0.25\,,-2\,,-16\,,-128,..\)

The first term of the above sequence is

\(b(1) = -0.25\)

Calculate the common ratio using

r = b(2)/b(1)

So, we have:

r = -2/-0.25

Evaluate

r = 8

So, we have:

\(b(n) = b(n-1)\cdot 8\)

Hence, the recursive formula of the geometric sequence is \(b(1) = -0.25\), \(b(n) = b(n-1)\cdot 8\)

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Complete question

Complete the recursive formula of the geometric sequence

\(-0.25\,,-2\,,-16\,,-128,..\)

\(b(1) =\)

\(b(n) = b(n-1)\cdot\)

Distribute

-6(8p+3)

-48p-18

Solution

-48p-18

Even function:

A function is said to be even if its graph is symmetric with respect to the , that is:

Odd function:

A function is said to be odd if its graph is symmetric with respect to the origin, that is:

So let's analyze each question for each type of functions using examples of polynomial functions. Thus:

FOR EVEN FUNCTIONS:

1. When  becomes  

1.1 Effects on the y-intercept

We need to find out the effects on the y-intercept when shifting the function  into:

We know that the graph  intersects the y-axis when , therefore:

So:

So the y-intercept of  is one unit less than the y-intercept of

1.2. Effects on the regions where the graph is increasing and decreasing

Given that you are shifting the graph downward on the y-axis, there is no any effect on the intervals of the domain. The function  increases and decreases in the same intervals of

1.3 The end behavior when the following changes are made.

The function is shifted one unit downward, so each point of  has the same x-coordinate but the output is one unit less than the output of . Thus, each point will be sketched as:

FOR ODD FUNCTIONS:

2. When  becomes  

2.1 Effects on the y-intercept

In this case happens the same as in the previous case. The new y-intercept is one unit less. So the graph is shifted one unit downward again.

An example is shown in Figure 1. The graph in blue is the function:

and the function in red is:

So you can see that:

2.2. Effects on the regions where the graph is increasing and decreasing

The effects are the same just as in the previous case. So the new function increases and decreases in the same intervals of

In Figure 1 you can see that both functions increase at:

and decrease at:

2.3 The end behavior when the following changes are made.

It happens the same, the output is one unit less than the output of . So, you can write the points just as they were written before.

So you can realize this concept by taking a point with the same x-coordinate of both graphs in Figure 1.

FOR EVEN FUNCTIONS:

3. When  becomes  

3.1 Effects on the y-intercept

We need to find out the effects on the y-intercept when shifting the function  into:

As we know, the graph  intersects the y-axis when , therefore:

And:

So the new y-intercept is the negative of the previous intercept shifted one unit upward.

3.2. Effects on the regions where the graph is increasing and decreasing

In the intervals when the function  increases, the function  decreases. On the other hand, in the intervals when the function  decreases, the function  increases.

3.3 The end behavior when the following changes are made.

Each point of the function  has the same x-coordinate just as the function  and the y-coordinate is the negative of the previous coordinate shifted one unit upward, that is:

FOR ODD FUNCTIONS:

4. When  becomes  

4.1 Effects on the y-intercept

In this case happens the same as in the previous case. The new y-intercept is the negative of the previous intercept shifted one unit upward.

4.2. Effects on the regions where the graph is increasing and decreasing

In this case it happens the same. So in the intervals when the function  increases, the function  decreases. On the other hand, in the intervals when the function  decreases, the function  increases.

4.3 The end behavior when the following changes are made.

Similarly, each point of the function  has the same x-coordinate just as the function  and the y-coordinate is the negative of the previous coordinate shifted one unit upward.

The equation to determine the length and width of the rug is

28 = w² + 12w

Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.

What is a rectangle?

Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

We are given a rectangular rug with an area of 28 square feet.

Also, the rug is 12 feet longer than it is wide.

So,

Let 'l' be the length of the rug and 'w' be the width of the rug

As given, Length is 12 feet longer than its width

Therefore, l = w + 12

We know Area of rectangle = Length * Width and area is given to be 28 square feet.

So,

⇒28 = (w + 12)w

⇒28 = w² + 12w

Hence, the equation to determine the length and width of the rug is

28 = w² + 12w.

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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.

Create an equation to determine the length and the width of the rug.