The Driving Distance Between San Fransico And Chicagois 2132 Miles.The Driving Distance Between Chicago (2024)

The outcomes in set A U B are 1, 3, 5, 6, 7, 8, 9, 10, 11, 12 (the odd sums) 4, 8, 12 (the sums divisible by 4)

The sum of the number cubes is odd if one die shows an even number and the other shows an odd number, or vice versa.

There are 3 even numbers and 3 odd numbers on a number cube, so there are 3 x 3 = 9 ways to get an odd sum.

The sum of the number cubes is divisible by 4 if both dice show either 2 or 4.

There are 2 ways to get a 2 on a number cube and 2 ways to get a 4, so there are 2 x 2 = 4 ways to get a sum of 4.

Therefore, the outcomes in A U B are 1, 3, 5, 6, 7, 8, 9, 10, 11, 12 (the odd sums) 4, 8, 12 (the sums divisible by 4)

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[tex] \qquad\longrightarrow \sf f(x) = sin^{-1} \bigg(\dfrac{x}{2}\bigg)\\[/tex]

The Derivative of f(x) with respect to x-

[tex] \qquad\longrightarrow \sf \dfrac{d}{dx} \:sin^{-1} \bigg(\dfrac{x}{2}\bigg)\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x}{2}\bigg)^2}}\;\times \dfrac{d}{dx}\:\dfrac{x}{2}\\[/tex]

[tex]\qquad\sf\because\boxed{\sf{ \: \dfrac{d}{dx} sin^{-1}x = \dfrac{1}{\sqrt{1-x^2}}}}\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \:x^{1-1}\\[/tex]

[tex]\qquad \sf\because\boxed{\sf{ \dfrac{d}{dx }x^n = nx^{n-1}}}\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \times 1\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \\[/tex]

[tex] \qquad\longrightarrow \sf\dfrac{1}{2}\: \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\\[/tex]

[tex] \qquad\longrightarrow \underline{\sf\: \dfrac{1}{2\:\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}}\\[/tex]

Henceforth, Option C) is the correct answer.

6.928 units is the apothem of a hexagon with a radius of 8.

The apothem of a regular hexagon is the distance from the center to the midpoint of a side. For a regular hexagon with a radius of 8, the apothem can be found using the formula:

apothem = radius x √3/2

Substituting the given value of the radius, we get:

apothem = 8 x √3/2

apothem = 8 x 1.732/2

apothem = 6.928

Therefore, the apothem of the hexagon is 6.928 units.

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Option B, three 2-liter tins, is the most cost-effective choice.

How to solve

1.7.1: To convert 5 litres to cm³, multiply by 1000 cm³ per litre:

5 litres * 1000 cm³/litre = 5000 cm³.

1.7.2: If 1 litre covers 8m², and you need to paint 14.4m² with three coats: 14.4m² * 3 coats = 43.2m².

Divide by 8m²/litre to find litres needed: 43.2m² / 8m²/litre = 5.4 litres.

To find the most cost-effective combination, consider the options:

A: One 5-liter tin and one 2-litre tin.

B: Three 2-liter tins.

Calculate costs including VAT: A: (1 * 439.99 + 1 * 189) * 1.15 = 723.63, B: (3 * 189) * 1.15 = 651.45.

Option B, three 2-liter tins, is the most cost-effective choice.

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The Complete Question

Paint is sold in different sizes as shown below A B 2 litre tin R189 5 litre tin at 439.99 Prices excludes VAT of 15% 1.7.1 Convert the capacity of a 5-litre tin to its volume in cm³ NOTE: 1 litre 1 000 cm³ 1.7.2

According to a paint specialist one needs at least two coats of pain therefore decided that she will paint three coats just to be sure that covered. Remember that the area that needs to be covered is 14.4 How many litres of paint will be needed if 1 litre of paint covers 8m- Looking at the paint quantity diagram and using your answer in QUI 1.7.2 A make use of different combinations of the tins of paint, ther Prudence of which combination will be the most cost effective. Inclu your calculations. 8,84 cm

The speed of the plane in calm air is 372 km/h

Given that a plane is travelling from Winnipeg to Calgary against a 50 km/hr headwind.

This flight takes half an hour longer than it would in calm air.

The distance between Winnipeg and Calgary is 1200 km.

Since we know that,

Speed may be defined as the distance travelled by an item in relation to the time it takes to travel that distance.

In other words, it measures how rapidly an item travels but does not provide direction. The term "velocity" refers to the combination of direction and speed.

The speed is defined by the rate of distance.

We must determine the plane's speed in calm air.

xy=1200

(x-50)(y+1/2) =1200

x² - 50 x-12000=0

By using quadratic formula.

x=372 as x>0

Hence, 372 km/h is the speed of the plane in calm air

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The sides of the rectangle should be in improper fractions, to calculate the area.

When a side has a measurement that is a mixed number, it's recommended to convert it to an improper fraction before using it in the formula for area.

To convert a mixed number to an improper fraction, you multiply the whole number by the denominator of the fraction part and add the numerator.

Then, you put the result over the original denominator.

Once you have the sides of the rectangle as improper fractions, you can proceed to calculate the area using the formula: area = length x width.

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Answer: 30,620 people

Step-by-step explanation:

We will use the given formula for exponential growth.

➜ 1.55% / 100 = 0.0155

➜ 2022 - 2017 = 5 years

[tex]A=Pe^{rt}[/tex]

[tex]A=(28,337\;people)e^{(0.0155)(5\;years)}[/tex]

[tex]A=(28,337\;people)e^{0.0775}[/tex]

[tex]A=(28,337\;people)e^{0.0775}[/tex]

[tex]A=30,620.4587 \approx 30,620\;people[/tex]

Fourth month in business, George's new store will have a profit of $4500. The option "The new store will have a profit of $4500 after its fourth month in business" is the correct response.

To determine the meaning of (r - c)(4) for George's new store, we need to evaluate the expression (r - c) at x = 4.

Given that r(x) represents the store's revenue and c(x) represents the store's expenses, (r - c)(4) represents the difference between the revenue and expenses of the store after four months.

Substituting x = 4 into the expressions for revenue and expenses, we get:

r(4) = (4)^2 + 6(4) + 10 = 16 + 24 + 10 = 50

c(4) = (4)^2 - 4(4) + 5 = 16 - 16 + 5 = 5

Thus, (r - c)(4) = r(4) - c(4) = 50 - 5 = 45.

Therefore, (r - c)(4) means that after its fourth month in business, George's new store will have a profit of $4500 (since r(x) and c(x) are measured in hundreds of dollars).

The option "The new store will have a profit of $4500 after its fourth month in business" is the correct response.

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The measure of arc MN is 144 degrees

measure of POQ is 322 degrees

The measure of arc PQ is 132 degrees

The measure of arc MN is 72×2 = 144 degrees

The measure of arc NQR is 180 degrees

We have to find measure of NQ

First we have to measure of POQ

92+22+POQ=180

POQ=180-114

POQ=66 degrees

Now measure of arc POQ is (95+66)×2 which is 322 degrees

Measure of arc QR is 72×2 = 114 degrees

The measure of MOR is 108×2 =216 degrees

The measure of PQ is 66×2 which is 132 degrees

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The acceleration for each section is shown below.

We know the formula

Acceleration = change in haste/ time taken

1. For a

= (12-0)/4

= 12/4

= 3

For b:

= (12-12)/ 5

=0

For c:

= (6-12)/ (2)

= -3

For d:

= (10-6) / 4

= 4/4

= 1

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A contradiction in the given clues and it is not possible to find a valid code with the given information.

The code to open the treasure chest can be determined using a few simple steps.
Firstly, we know that the last digit is half of 18, which is 9.

This means that the code ends with the number 9.
Next, we are given the information that the sum of the two middle digits is 10.

This tells us that the two middle digits must be 4 and 6, as they add up to 10.
Thirdly, we know that the third and fourth digits are the same.

Since we already know that the last digit is 9, this means that the third digit must also be 9.
Finally, we are told that the first digit is double the second digit.

Since we know that the second digit is 4, we can determine that the first digit must be 8.
Therefore, the code to open the treasure chest is 8469.

Mr Brainiac can now use this code to unlock the chest and discover the treasures inside.
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To solve this inequality for x, we need to isolate x on one side of the inequality sign. Let's begin by distributing the -2 on the right-hand side:

7x + 5 < -2(4x - 3)

7x + 5 < -8x + 6

Adding 8x to both sides, we get:

15x + 5 < 6

Subtracting 5 from both sides, we get:

15x < 1

So the equivalent inequality to 7x + 5 < -2(4x-3) is 15x < 1.

Therefore, the answer is: 15x < 1.

The step with the proof that has a flaw is Step 2, AB ≅ BC, Symmetric Property.

How to prove flaw?

Step 2 is the flaw in the proof. The symmetric property states that if AB = BC, then BC = AB. It does not justify that AB = BC in the first place.

Therefore, the proof needs additional steps to justify that AB and BC are congruent. One possible way to do this is to use the definition of a midpoint and the segment addition postulate as follows:

Step 1 | B is the midpoint of AC | Given

Step 2 | AB + BC = AC | Segment Addition Postulate

Step 3 | AB + AB = AC | Definition of midpoint (since B is the midpoint of AC)

Step 4 | 2AB = AC | Simplification

Step 5 | AB = AC/2 | Division Property of Equality

Step 6 | AB = BC | Substitution Property of Equality

Step 7 | _____ | Q.E.D.

Step 6 follows from the fact that B is the midpoint of AC, so AC = 2AB. Substituting AC/2 for AB in Step 2 gives AB + BC = AC/2 + BC, which simplifies to AB = BC. Therefore, Step 6 uses the transitive property of equality, which is a valid property of equality.

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The number of total bears counted in 2002 will be: A. 1060 bears.

How to determine the total bear estimate

To determine the total bear estimate, we will use the mark-recapture formula. In this formula, we equate the number of the population to MC/R where:

M = Number marked initially

C = Number captured in the second sample

R = The recaptured number

Also, R/C = M/N

For the given problem,

M = 2008

C = 38

R = 72

So, N = 2008 * 38/72

= 1059 approximately 1060 bears.

So, the bear population will amount to 1060.

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Answer:

The two is in the hundredths place

Step-by-step explanation:

369.425

hundreds tens ones. tenths hundredths thousandths

3 6 9 . 4 2 5

The two is in the hundredths place

Answer:

The place value of 2 in 369.425 is hundredths.

The number 369.425 is a decimal number. It has a whole number part (369) and a decimal part (0.425). The decimal part is divided into tenths, hundredths, thousandths, and so on. The 2 is in the hundredths place.

Step-by-step explanation:

The circumference of the circle is approximately 119.38 kilometers.

It is an exercise where the calculation of the circumference of a circle is made from its radius, it is a very common mathematical operation. The circumference is the distance a point on the edge of a circle moves around its center, and the radius is the distance from the center of the circle to its edge.

The formula to calculate the circumference of a circle from its radius is:

Circumference = 2πr

Where "r" is the radius of the circle and "π" is a mathematical constant approximately equal to 3.14. Therefore, the circumference of the circle is obtained by multiplying "π" twice by the value of the radius "r".

It is important to remember that the radius and circumference of a circle are related in a directly proportional way: as the radius increases, so does the circumference, and vice versa.

Then calculate the circumference of the circle.

Therefore we apply the formula C =2πr. What we must do is substitute the radius and the value of pi in the formula and solve, then

C =2πr

C = 2 × 3.14 × 19 km

C = 119.32 km

The circumference of the circle is approximately 119.32 kilometers.

The circumference of the circle can change, varying the value that we give to pi.

The surface area of the cone is 553 cm².

What is surface area?

The surface area of a three-dimensional object is the total area of all its faces.

To calculate the surface area of the cone, we use the formula below

Formula:

A = πrl+πr².................... Equation 1

Where:

A = Surface area of the coner = Radius of the of the conel = Slanght height of the coneπ = Pie

From the question,

Given:

r = 8 cml = 20 cmπ = 3.14

Substitute these values into equation 1

A = (3.14×8×20)+(3.14×8²)A = 502.4+50.24A = 552.64 cm²A = 553 cm²

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ln|sec(x)tan(x)| + C is the integral value of ∫sec²x/tanx dx

We can start by using the identity sec²(x) = 1 + tan²(x) to rewrite the integrand as:

sec²(x)/tan(x) = (1 + tan²(x))/tan(x)

= tan(x)/tan(x) + tan³(x)/tan(x)

= 1 + tan²(x)

Now we can make the substitution u = tan(x) to get:

∫sec²x/tanx dx = ∫(1 + tan²(x)) dx

= ∫(1 + u²) du

= u + (1/3)u³ + C

= tan(x) + (1/3)tan³(x) + C

= ln|sec(x)tan(x)| + C,

Therefore, ln|sec(x)tan(x)| + C is the integral value of ∫sec²x/tanx dx

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The chances that, at least, one of the dinosaur toys in Franklin's set is a T.rex is 57%.

Probability calculation

We can use the complement rule to find the probability that none of the dinosaur toys in Franklin's set is a T. rex, and then subtract this from 1 to get the probability that at least one of the toys is a T. rex.

The probability that a given toy is not a T. rex is 90%, or 0.9.

Since there are 8 toys in the set, the probability that none of them are T. rex is:

0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 = 0.43

So the probability that at least one of the toys is a T. rex is:

1 - 0.43 = 0.57, or 57%

In other words, it is 57% likely that at least one of the dinosaur toys in Franklin's set is a T. rex.

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Answer:

i'm pretty sure it is "the graph forms a parabola"

Step-by-step explanation:

The equation of L2 is y = 2x/3 + 23/3.

The equation of L3 is y = -3x/2 - 7.

The equation of L2 in standard form is 2x/3 - y = -23/3.

The x and y intercepts of L3 are (-4.667, 0) and (0, -7) respectively.

The point of intersection between L2 and L3 is (-6.769, 3.154).

What is the slope-intercept form?

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.

Based on the information provided about line 1 (L1) and line 2 (L2), we have the following equation;

Equation of line 1 (L1): 3x + 2y = 12

y = -3x/2 + 12

Since line L2 is perpendicular to L1 at (2, 9) and a slope of 2/3, the equation of L2 can be calculated as follows;

y - y₁ = m(x - x₁)

y - 9 = 2/3(x - 2)

y = 2x/3 + 23/3

Since L3 is parallel to L1 and passes through point (-4, -1), the equation of L2 can be calculated as follows;

y - y₁ = m(x - x₁)

y + 1 = -3/2(x + 4)

y = -3x/2 - 6 - 1

y = -3x/2 - 7

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part a.

The average velocity on the interval [0,2] is -16 ft/sec

part b.

The instantaneous velocity when t=2 is found as -48 ft/sec

part c.

Time taken to reach the ground is 3 seconds.

part d.

velocity of the ball when it hits the ground is found as 80 ft/sec downward.

How do we calculate?

The average velocity on the interval [0,2] is determined by :

average velocity = change in distance / change in time

change in distance :

s(2) - s(0) = (-16(2)^2 + 16(2) + 96) - (-16(0)^2 + 16(0) + 96) = -32

where the change in time:

2 - 0 = 2

average velocity = -32/2

average velocity = -16 ft/sec

b. The instantaneous velocity :

s'(t) = -32t + 16

and t=2:

s'(2) = -32(2) + 16 =

s'(2)= -48 ft/sec

the velocity of the ball when it hits the ground is at time = 3

s'(t) = -32t + 16

s'(3) = -32(3) + 16 =

s'(3) = -80 ft/sec

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If f(x)=3x²-2x+5 and g(x) = x³+4x²-1 then the function obtained by multiplying two functions is 3x⁵+10x⁴-3x³+17x²+2x-5

The two functions are f(x)=3x²-2x+5 and g(x) = x³+4x²-1

We have to find (f×g)(x)

(f×g)(x)= f(x)g(x)

=(3x²-2x+5)( x³+4x²-1)

=3x⁵+12x⁴-3x²-2x⁴-8x³+2x+5x³+20x²-5

Combine the like terms

=3x⁵+10x⁴-3x³+17x²+2x-5

Hence, the function obtained by (f×g)(x) is 3x⁵+10x⁴-3x³+17x²+2x-5

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Answer: v=-19

Step-by-step explanation:

We can multiply by 7 on both sides which cancels out 7 on both sides. He new equation would be v=-19 which is our answer.

set the numerators equal
which will give you v=-19

The area of the shaded region, to the nearest hundredth can be calculated as approximately: 1,195.71 mm².

What is the Area of the Shaded Region?

The area of the shaded region can be found using the area of circle, which is: Area = πr²

Therefore, area of the shaded region = area of larger circle - area of smaller circle.

Area of larger circle:

radius (r) = 14 + 6.6 = 20.6 mm

Area of larger circle = 3.14 * 20.6² = 1,332.4904 mm²

Area of smaller circle:

radius (r) = 6.6 mm

Area of larger circle = 3.14 * 6.6² = 136.7784 mm²

Area of the shaded region = 1,332.4904 - 136.7784 = 1,195.71 mm².

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Denis was told to write the first non-objective statement by the arising trend of Neotraditionism.

As he explains in his composition" The description of Neotraditionism,"" The thing of Neotraditionism is to make commodity new that isn't a dupe, nor a simple extension, nor a parody of the old"( Denis, 1911). He believed that this movement needed a new language of art, one that wasn't tied to emblematic forms.

Kandinsky's appearance atnon-objective oil was told by his spiritual beliefs and his desire to express the inner nature of effects. As he writes in Concerning the Spiritual in Art," The artist must have commodity to say, for mastery over form isn't his thing but rather the adapting of form to its inner meaning"( Kandinsky, 1977,p. 10). He believed that art should be a spiritual expression and that the inner world of the artist should be restated into visual language.

Kandinsky wrote considerably about color in Concerning the Spiritual in Art. He believed that color had its own language and could convey feelings and ideas. As he writes," Color is a means of plying direct influence upon the soul. Color is the keyboard. The eye is the hammer. The soul is the piano, with its numerous strings"( Kandinsky, 1977,p. 43). He believed that colors could be arranged in a way that would produce a symphony of feelings in the bystander.

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To find the difference of 21-15/16 and 18-3/4, we need to subtract the second number from the first:

21-15/16 - 18-3/4

To subtract fractions, we need a common denominator. The least common multiple of 16 and 4 is 16, so we will convert both fractions to have a denominator of 16:

21 - (15/16) - 18 + (12/16)

Now we can combine the whole numbers and the fractions separately:

21 - 18 = 3

and

-15/16 + 12/16 = -3/16

Putting the whole thing together, we get:

3 - 3/16

This is the difference of the two numbers in mixed number form. If we want to express the answer as an improper fraction, we need to multiply the whole number by the denominator and add the numerator:

3 x 16 + (-3) = 45

So the difference is:

45/16

The distance from point B to point A is given as follows:

15,893 ft

What are the trigonometric ratios?

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.

For each angle, we have that:

The position is the adjacent side.The height of 7200 feet is the opposite side.

Hence the position A is obtained as follows:

tan(16º) = 7200/a

a = 7200/tangent of 16 degrees

a = 25109 ft.

The position B is obtained as follows:

tan(38º) = 7200/b

b = 7200/tangent of 38 degrees

b = 9216 ft.

Hence the distance is of:

25109 - 9216 = 15,893 ft.

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How to compare fractions is explained in the solution below.

One way to compare fractions is to convert them into their decimal form and decide which is the smaller of the two.

Example: 7/10 and 3/5 become 0.7 and 0.6.

Hence 3/5 is smaller than 7/10.

The other way is to convert them into fractions with identical denominator.

For that multiply the denominator of one fraction with the numerator and denominator of the other.

Do the same with the other denominator and the other fraction. Then decide which fraction is the smaller of the two.

Example: 7/8 and 13/15 become (7*15)/(8*15) = 105/120 and

(13*8)/(15*8) = 104/120.

Hence 13/15 is smaller than 7/8.

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