A car travels 19 mph slower in a bad rain storm than in sunny weather. The car travels the same distance in 2 hr in sunny weather as it does in 3 hr in rainy weather.

Find the speed of the car in sunny weather.

Using the concept of change of subject of formula, we can express the radius r₁ and r₂ as r₁ = r₂² / 18π

The formula of volume of a cylinder is given as;

V = πr²h

The equation for the volume of the cylindrical tank is V1 = 36πr₁ and the equation for the volume of the neighborhood pool is V2 = 1/2(4/3πr₂²).

Since V₁ = V₂, we can set the two equations equal to each other and solve for r₁:

36πr₁ = 1/2(4/3πr₂²)

To solve for r₁, we can first multiply both sides of the equation by 2/4/3, which gives:

18πr₁ = r₂²

Then we can divide both sides of the equation by 18π to get:

r₁ = r₂² / 18π

So we can say that r₁ is a function of r₂ because it can be expressed in terms of r₂.

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We can conclude that -

Given are the inequality signs as : >, < and =.

An inequality is used to make unequal comparisons between two numbers or expressions.

Therefore, we can conclude that -

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The probability using the same formula as before: P(X>=3) = 1 - P(X<=2), which gives us 1 - 0.8530p = 0.08, or p = 0.0934.

Let p be the probability of a rivet being defective.  In order for 19% of all seams to need reworking, at least 4 of the 23 rivets must be defective.  This means that the probability of at least 4 of the rivets being defective must be 0.19.  We can calculate this probability using the formula P(X>=4) = 1 - P(X<=3), where X is a binomial random variable with parameters n = 23 and p = p.  This gives us 1 - 0.9920p = 0.19, or p = 0.1984.

To ensure that only 8% of all seams need reworking, at least 3 of the 23 rivets must be defective.  This means that the probability of at least 3 of the rivets being defective must be 0.08.  We can calculate this probability using the same formula as before: P(X>=3) = 1 - P(X<=2), which gives us 1 - 0.8530p = 0.08, or p = 0.0934.

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A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number.

How do you explain logarithm?

The exponent or power that must be added to a base to produce a particular number is called the logarithm. If bx = n, then the mathematical expression for x is x = logb n, where x is the logarithm of n to the base b. For instance, since 23 = 8, 3 is the logarithm of 8 in base 2, or 3 = log2 8.

The opposite of exponentiation in mathematics is the logarithm. The exponent to which b must be raised in order to obtain a number x is hence the logarithm of a number x to the base b. For instance, since 1000 = 103, log10 of 1000 is 3, or log10 = 3.

Common logarithms, with a base of 10, binary logarithms, with a base of 2, and natural logarithms, with a base of e 2.71828, are the four most popular varieties of logarithms.

Say you have n=4 and k=2. (Next, we might look at n=8 and k=3). Let f[(x-list_),y] be the expected value of the number of random trials needed to get from a list of thus and so many hits already, to completion with y or more hits in every slot. We want f[(0,0,0,0),2].

Note that f[anylist,0]=0, and that f[(0),1]=1.

Now f[0000,2]=1+f[0001,2], because the first random number has to go somewhere and whichever one it lands on is symmetric to the case where it lands on 4.

Next, f[0001,2]=1+(1/4)f[0002,2]+(3/4) f[0011,2]=1+(1/3)f[000,2]+(3/4)f[0011,2], the second step because once one slot is filled, it just takes 4/3 times as long to finish because 1/4 of your shots will be wasted on the saturated target.

By and by, you’ll encounter f[1111,2] among other situations, and this will be equal to f[0000,1].

It’s a finite calculation, it can be written up as a recursive program, and you’ll be able to get an exact answer for any f[(however many zeros), (whatever value counts as saturation)]. The calculation will, unfortunately, run into geometric expansion of time and space as there are going to be a lot of subcases to consider even for f[00000000,3]. Still, it’s nice to have the actual exact answer for a number of representative small cases.

As to the long term situation, once you’ve fired, say, n log n shots, you theoretically might be done, having `wasted no shots’. But consider the number of hits that “1” has got. This is a binomial distribution, with the probability of k hits out of n log n shots each at odds 1/n of hitting being Binomial[n log n, k](1/n)^k((n-1)/n)^(n log n-k). This should work out to roughly a Poisson distribution, with density something like (x/log n)e^{-x/log n} being the probability that you got x hits. The saturated targets would be the ones with x greater than log n, and you’d expect a typical target would need  ( log n - x )  e x / log n dx further hits.

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The area of the rectangle is A = 172.5 m^2

The area of a rectangle can be found by using the formula A = lw, where l is the length and w is the width. In this case, we are given that the length is 8 meters more than twice the width, so we can let l = 2w + 8. We are also given the perimeter, which is the sum of the length and width multiplied by two, or 2l + 2w. We can set this equal to 46 and solve for w:

2(2w + 8) + 2w = 46

4w + 16 = 46

4w = 30

w = 7.5

Therefore, the width of the rectangle is 7.5 meters and the length is 2(7.5) + 8 = 23 meters. The area of the rectangle can then be found by substituting these values into the area formula:

A = lw

A = (23)(7.5)

A = 172.5 m^2

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The bar diagram representing 150% of the price 5 years ago would be a bar with a height of $4.50.

What is the percentage?

Percentage is a way to express a number as a fraction of 100. It is often used to describe the relationship between two quantities, or to express a rate or change in a quantity over time. The symbol for percent is "%".

For example, if a pizza is marked up by 20%, it means the price has increased by 20/100 or 1/5 of the original price. If a student scores 80% on a test, it means they got 80 out of 100 questions correct. If a stock's value increases by 10%, it means the value has gone up by 10/100 or 1/10 of the original value.

The current admission price is $3 + $3 * 50% = $3 + $1.50 = $4.50.

150% of the price 5 years ago is $3 * 150% = $3 * 1.5 = $4.50.

So, the bar diagram representing 150% of the price 5 years ago would be a bar with a height of $4.50.

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Answer:

10.8

Step-by-step explanation:

using Sine Law

a/sin A = b/sin B = c/sinC

a = 8

A = 40°

b = ?

B = 120

substitute the values and you will get the answer 10.778370842670, rounding to the nearest 10ths.

10.8 is the measure of the value of x to the nearest tenth.

The given diagram is a triangle with side 8 and angles 40 and 120 degrees.

Applying the sine rule, we will have:

x/sin120 = 8/sin40

Cross multiply to have:

8sin120 = xsin40

x = (8sin120)/sin40

x = 6.9282/0.6428

x = 10.8

Hence the measure of the value of x to the nearest tenth is 10.8.

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the cost of direct materials used for the current year i.e the direct material used is $122,000

The computation of the direct material used is shown below:

= Opening raw material inventory + material purchased - ending raw material inventory

January 1 Raw materials inventory $6,000

Add Materials purchased $123,500

Raw material available for production $129,500

($6,000+$123,500)

Less December 31 Raw material Inventory $7,500

Cost of direct materials used $122,000

= $6,000 + $123,500 - $7,500

= $122,000

Hence, the direct material used is $122,000

the cost of direct materials used for the current year i.e the direct material used is $122,000

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So, the trade discount for 15 boxes of computer paper if the unit price is $14.26, and a single trade discount rate of 45% allowed is $96.255.

Trade discount refers to the reduction in list price known as a discount, allowed by a supplier to the consumer while selling the product generally in bulk quantities to the concerned consumer to increase the sales of the business as more customers are attracted when the discount is given on the list price of the product.

We have to calculate the trade discount for 15 boxes of computer paper.

the unit price of computer paper is $ 14.26, and a single trade discount rate is 45% allowed.

The trade discount on one unit computer paper is.

= 45%×14.26

= $6.417

now, trade discount on 15 unit of computer paper box is.

=6.417×15

=$96.255.

So, the trade discount for 15 boxes of computer paper if the unit price is $14.26, and a single trade discount rate of 45% allowed is $96.255.

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Answer: Let's call the smallest of the 3 consecutive natural numbers "n". The other two numbers are "n+1" and "n+2". The sum of these 3 numbers is "3n + 3"

Also, the sum of the two numbers following these 3 consecutive natural numbers is (n+3) + (n+4) = 2n + 7

We know that these two expressions are equal:

3n + 3 = 2n + 7

By solving this equation we can find the value of n.

Subtracting 3 from both sides: 3n = 4

Dividing by 3: n = 4/3

Since n is a natural number, n has to be the integer 1.

So the three consecutive natural numbers are 1, 2, 3 and the sum of the students in the class is 6, which is also the sum of the next two natural numbers 4 and 5.

Therefore, there are 6 students in her class.

Step-by-step explanation:

The dimensions of the rectangle that will produce the largest area of the window are x = (12 - √3) / 2 and y = 3 / √3.

Let x be the length of the rectangle, and y be the width of the rectangle. The perimeter of the window is 12m, and since the triangle is equilateral, we know that all 3 sides of the triangle are equal to x.

Therefore, we can set up the following equation to represent the perimeter of the window: x + y + x = 12

The area expression is:

A = x*y + (x^2 * √3)/4

After substituting x = (12-y)/2, the area expression becomes:

A = [((12-y)/2)*y] + [(12-y)^2 * √3]/16

Which can be simplified to:

A = 6y - 3y^2 + (9-3y)√3 / 4

To find the maximum value of this expression, we can differentiate it with respect to y and set it to zero:

dA/dy = -3y + (9-3y)√3/4 = 0

and solve for y:

-3y + (9-3y)√3/4 = 0

-3y = (3y-9)√3/4

-3y = 3y-9 / 2√3

3y = 9 / 2√3

y = 3 / √3

To find x, we can substitute this value of y back into x = (12-y)/2:

x = (12 - 3 / √3) / 2 = (12 - √3) / 2

So the dimensions of the rectangle that will produce the largest area of the window are x = (12 - √3) / 2 and y = 3 / √3.

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On applying higher-order thinking skills, it can be seen that Joel does not count the numbers 82 82 62 80 while counting backwards from 79 to 65.

What is Higher-Order Thinking?

Higher-order thinking is a concept of educational reform based on learning taxonomies (like Bloom's taxonomy). Higher-order thinking skills are also known as higher order thinking skills (HOTS). The theory holds that some forms of learning have more universal advantages while requiring more cognitive effort than others.

Joel counts back from 79 to 65.

The numbers in descending order from 79 to 65 is -

79 78 77 76 75 74 73 72 71 70 69 68 67 66 65

The numbers go from right to left on a number line.

The options for the numbers are -

77 72 70 82 70 82 67 62 80

After applying HOTS the numbers which do not lie in between 79 and 65 when counting backwards is -

82 82 62 80

Therefore, the numbers which can be eliminated are 82 82 62 80.

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Step-by-step explanation:

The given system of equations models the scenario where Jason spent all of his money on buying CDs and magazines, and that if he had bought one more CD, he would have run out of money. The system of equations is:

4x + 2y = 32 (Equation 1)

5x + 2y = 36 (Equation 2)

The first equation represents the total amount of money Jason spent on 4 CDs (x dollars each) and 2 magazines (y dollars each). The second equation represents the total amount of money Jason would have spent if he had bought one more CD. By subtracting equation 1 from equation 2, we get:

x = 4 (Equation 3)

This equation tells us that each CD costs $4.

By substituting this value into equation 1, we get:

4(4) + 2y = 32

16 + 2y = 32

2y = 16

y = 8 (Equation 4)

This equation tells us that each magazine costs $8.

So, Jason spent $4 for each CD and $8 for each magazine.

Answer:

H = 3

K = 0

Step-by-step explanation:

To solve the system of linear equations using elimination by multiplication, we can first multiply the first equation by 3. This gives us:

3(H+2k)=3*3=9

3H+6k=9

Now we have the same coefficient (6k) on the second variable in both equations. We can now subtract the first equation from the second equation to eliminate the second variable:

3H+6k=9

-3H-6k=-9

0H=0

This tells us that the system of equations is consistent and has infinitely many solutions. To find the specific solution, we can use either equation and substitute in a value for one of the variables. For example, we can use the first equation and substitute in H=3. This gives:

3+2k=3

2k=0

k=0

Now we can substitute this value for k back into either equation to find the value of H. For example, using the first equation:

H + 2(0) = 3

H = 3

So the solution to the system of equations is:

H = 3, k = 0

Answer: 27 28 29

Step-by-step explanation:

The lithosphere is: a. the rigid outer part of the earth, consisting of the crust and upper mantle.

The Lithosphere is the solid outer shell of the Earth that forms the Earth's surface, including the continents and the ocean floor. It is the uppermost layer of the Earth's solid surface, composed mostly of the minerals, such as silicon and oxygen, that form rocks like granite and basalt.

The lithosphere is composed of the Earth's crust and the uppermost part of the Earth's mantle. It is broken up into tectonic plates that are in constant motion and are responsible for the earthquakes, volcanoes, and the creation and destruction of land masses. The lithosphere is also the layer that supports all life on Earth.

Therefore, we can state that the correct description of the lithosphere is: a. the rigid outer part of the earth, consisting of the crust and upper mantle.

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Answer:

Sum of two polynomials:
[tex]3x^2 - x - 4[/tex]        Choice C   (read explanation carefully)

Product of the two polynomials:
[tex]2x^4-5x^3-14x^2+30x-12\\\\[/tex]     Choice C   (read explanation carefully)

In both cases, your answer choice copy/paste messed up the formatting. I looked at the coefficients and came up with the choices.

You should compare the actual terms with the choices I have provided to make sure they match

Step-by-step explanation:

The two polynomials are
2x² + 3x - 6

and

x² - 4x + 2

Addition

To add these two polynomials together group like terms and add their coefficients:

(2x² + 3x - 6) + (x² - 4x + 2)

= 2x² + 3x - 6 + x² - 4x + 2

= (2x² + x²) + (3x -4x) + (-6 + 2)

= 3x² - x - 4

Your answer choices have lost formatting during copy paste. You will have to compare and choose the right one. I think it is C because it has a 3x² term and the last term is - 4

Multiplication

[tex]\left(2x^2\:+\:3x\:-\:6\right)\cdot \left(x^2-4x\:+\:2\right)\\\\\\[/tex]
Distribute the parentheses - multiply each term in the second polynomial by each term in the first polynomial and simplify

[tex]\left(2x^2\:+\:3x\:-\:6\right)\cdot \left(x^2-4x\:+\:2\right)\\\\= 2x^2x^2+2x^2\left(-4x\right)+2x^2\cdot \:2+3xx^2+3x\left(-4x\right)+3x\cdot \:2-6x^2-6\left(-4x\right)-6\cdot \:2\\\\= 2x^4-8x^3+4x^2+3x^3-12x^2+6x-6x^2+24x-12\\\\\textrm{Add similar terms}\\=2x^4 +(-8x^3+3x^3)+ (4x^2-12x^2-6x^2) + (6x+24x) -12\\\\[/tex]

[tex]=2x^4-5x^3-14x^2+30x-12\\\\[/tex]    (Answer)

Again your answer choices have lost formatting but my best guess from looking at the coefficients is that it is choice C

Answer:

she is 0 blocks away from home because you said she started at home

Answer:

a) Malavika is 8 blocks west from home

b) Traveled 20 blocks total

Step-by-step explanation:

a) According to a compass: 3 west (left), then 6 east (right) and that puts you at 3 east (right). Then back 11 west (left) puts you at 8 west (left)

b) Add up all blocks traveled: 3 + 6 + 11 = 20

The height of the candle after 9 hours can be written as 23.4 cm.

What is a linear relationship?

The linear relationship is the relationship between two variables such that it follows a straight line.

As it is given that the height of the candle is linear to the amount of time. Now, let's the time be on the x-axis and the y-axis be the height of the candle. therefore, the slope of the linear relationship can be represented as,

Point1 of the slope, (x₁, y₁) = (6, 24.6)

Point2 of the slope, (x₂, y₂) = (21, 18.6)

Now, since we know the two points of the linear relationship, therefore, the slope can be written as,

m = (y2 - y1)/(x2-x1)

m = (18.9 - 24.6) / (21 - 6)

m = -0.4

Thus, the slope of the linear relationship is -0.4.

Now, the equation of the linear relationship can be written as,

y = mx + c

y1 = mx1 + c

24.6 = (-0.4 * 6) + c

24.6 = -2.4 + c

Thus, the Linear relationship of the candle height and the amount of time can be written as y = -0.4x + C.

Now, In order to calculate the height of the candle after 9 hours, we will substitute the value of the x as 9.

y = -0.4x + 27.

y = -0.4(9) + 27.

y = -3.6 + 27.

y = 23.4

Hence, the height of the candle after 9 hours can be written as 23.4 cm.

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Answer:

Cayley earned per day: 4 x 5 = 20

: Her earning per week-  3 x 20 = 60

: Her earning for 8 weeks- 8 x 60 = 480

Cayley earns $480 per week.

Each measure in a 4/4 time signature has four quarter note beats; each measure in a ¾ time signature has three quarter note beats; and each measure in a 2/4 time signature has two quarter note beats.

A 4/4 time signature does not imply that each measure contains simply four quarter notes. It signifies that each measure only contains four beats. These beats may comprise half notes, quarter notes, eighth notes, pauses, or whatever the composer desires, but all note and rest values must add up to no more or less than the time signature’s top number (or numerator).

The most popular musical meter is 4/4. Because it is so widespread, it is also known as common time, and the two numerals in the time signature are sometimes substituted with the letter C. The stacking digits in 4/4 indicate that each measure comprises four quarter note beats. To count 4/4 meter, tap the beat every time you tap the beat.

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The solution of the system of equations is:

(-3/2, 1/2)

Here we have two lines of the form:

y = a*x + b

one passes through (0, 0) and (1, -3)

For the first point we know that the constant is 0, and replacing the values of the second point we get:

1 = a*-3

1/-3 = a

The line is:

y = (-1/3)*x

The second line passes through (0, 2) and (-1, 1) from the first point we can see that:

y = a*x + 2

And replacing the values of the second point we get:

1 = a*-1 + 2

1 - 2 = -a

-1 = - a

1 = a

This line is y = x + 2

Then the system of equations is:

y = x + 2

y = (-1/3)*x

We can replace use the substitution method to write:

x + 2 =  (-1/3)*x

x + 1/3*x = -2

(4/3)*x = -2

x = -2*(3/4)

x = -3/2

And the y-value is:

y = -3/2 + 2

y = 1/2

The solution is (-3/2, 1/2)

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$1.15

Let's call the cost of the bike horn "x".

Dirk paid $5.33 and received $4.18 in change, so he must have paid x + $4.18 = $5.33.

Solving for x, we get x = $5.33 - $4.18 = $1.15.

Therefore, the bike horn cost $1.15.

Answer:

To solve the equation 9x² = 3³x-2, we can follow these steps:

First, we need to simplify the right side of the equation. 3³ = 27, so we can replace 3³ with 27. The equation now becomes: 9x² = 27x - 2

Next, we'll want to get all the x terms on one side of the equation and all the constants on the other side. To do this, we'll add 2 to both sides of the equation: 9x² = 27x - 2 + 2 = 27x. This gives us: 9x² = 27x

Next, we'll divide both sides of the equation by 9. This will give us x² = 3x.

Finally, we can divide both sides by 3. This will give us x = 1.

So the solution is x = 1

The starting pay was $ 168.6 and has climbed by $ 3,000 annually since 2008 at a consistent rate.

Since it is a percent increase, they will receive a 2% salary raise in year two, which will amount to $30,000. As a result, it would be 1.2, and we'll now try to identify a pattern. We know that the pay will be 30,000 because of the 2% increase because the power in this situation is one and the salary is in the eleventh year.

At this moment, I would have accepted ten times the 2% rise. During the first year, it would not have occurred. If you want to proceed, divide it by one less than 1.2 to get the temperature. After we calculate it, we'll receive a value for their entire compensation for the next 10 years.

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The side length of the square will be 1 unit.

What is a square?

A square is a two-dimensional plane figure with four equal sides and all the four angles are equal to 90 degrees. The properties of rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.

The most important properties of a square are listed below:

Now

As given

1=√A (A=area)

Hence,

A=1

Now because A=side^2

Therefore,

Side=√1

side=1

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The incorrect code contained two errors. The first was that the variable 'resistance' was initialized with a string value from the prompt, and the second was that the inverse value was not rounded off to two decimal places.

// incorrect code

//

// let resistance = prompt("Enter the resistance: ");

// inverse = 1.0 / resistance;

// console.log("The inverse of resistance is " + inverse);

// correct code

let resistance = parseFloat(prompt("Enter the resistance: "));

let inverse = 1.0 / resistance;

console.log("The inverse of resistance is " + inverse.toFixed(2));

1. In the incorrect code we have a variable 'resistance' that is initialized with a string value from the prompt. To fix this we have used the parseFloat function to convert this string to a float value.

2. In the incorrect code the inverse value is not rounded off to 2 decimal places. To do this we have used the toFixed(2) method to round off the inverse value to 2 decimal places.

The incorrect code contained two errors. The first was that the variable 'resistance' was initialized with a string value from the prompt, and the second was that the inverse value was not rounded off to two decimal places. To fix these errors, the parseFloat function was used to convert the string value of 'resistance' to a float value, and the toFixed(2) method was used to round off the inverse value to two decimal places.

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