At the beginning of a snowstorm, Kaj had 7 inches of snow on her lawn. The snow
then began to fall at a constant rate of 0.5 inches per hour. Assuming no snow was
melting, how much snow would Kaj have on her lawn 3 hours after the snow began to
fall? How much snow would Kaj have on her lawn after t hours of snow falling?

Using the definition of congruent triangles, the missing values are:

x = 35

y = 30°

Given that the two triangles in the image above are congruent, it implies that all its corresponding angles and corresponding side lengths have equal measure.

Therefore, we have:

2x - 10 = x + 25

Solve for x:

2x - x = 10 + 25

x = 35

Plug in the value of x to find the missing angles:

y + 90 + (2x - 10) = 180 [triangle sum theorem]

y + 90 + (2(35) - 10) = 180

y + 90 + 60 = 180

y = 30°

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The pair of functions f(x) and g(x) below that equals 0 as the limit as x goes to infinity of the quotient of f of x and g of x will be C. f(x) = ln(x); g(x) = ex

For the limit of the quotient of f(x) and g(x) to equal 0 as x approaches infinity, it is necessary for f(x) to grow more slowly than g(x).

Out of the options given, the only pair of functions where this is true is f(x) = ln(x) and g(x) = ex. As x approaches infinity, ex grows much faster than ln(x), so the limit of the quotient of these two functions as x approaches infinity is 0.

In conclusion, the correct option is C.

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Answer: the number is 6

Step-by-step explanation: First, set up an equation. Two more means +2, 3 times a number means 3x. So your equation would be 3x+2=20. Then solve the equation for x.

Answer:

x = 6

Step-by-step explanation:

Let the number be 'x'

Then, the equation becomes,

2 + 3x = 20
3x = 20 - 2
3x = 18
x = 18/3
x = 6

Hope it helped :)

By applying the Pythagorean theorem to the provided question, we can say that in this triangle =>

AC =[tex]\sqrt{115}[/tex]

Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.

Pythagorean theorem applies here, in this triangle

AC = [tex]A^2 + B^2[/tex]

AC  = [tex]\sqrt{14^2 -9^2}[/tex]

AC = [tex]\sqrt{115}[/tex]

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Sipho earned R33.15 in simple interest.

The balance of the account at the end of the first 30 days was R2 133.15.

a. To calculate the simple interest earned by Sipho, we need to calculate the total amount deposited and the interest earned on that amount.

Total amount deposited = R600 + R1 000 + R500 = R2 100

Interest earned = R2 100 x 4.5% x 30/365 = R33.15 (rounded to the nearest cent)

Therefore, Sipho earned R33.15 in simple interest.

b. The balance of the account at the end of the first 30 days can be calculated by adding the total amount deposited and the interest earned to the initial deposit:

Balance = R600 + R1 000 + R500 + R33.15 = R2 133.15

Therefore, the balance of the account at the end of the first 30 days was R2 133.15.

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The only way to completely eliminate the risk of arc flash is to de-energize the equipment before performing any maintenance or testing.

Racking a circuit breaker in energized gear poses a significant arc flash hazard to workers due to the potential for electrical energy to be released and cause an arc flash.

If it is not possible to de-energize the equipment, the following means could be used to reduce the arc flash hazard to 0 incident energy exposure to a worker:

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Answer:

y = -2x + 8

When x = 4, Mark has no more money , so when x is greater than 4, Mark is in debt or is not able to give his sister any more money.

Step-by-step explanation:

Danielle's sales last week were $. At her job at an electronics store, Danielle receives a  $4,295.16 commission on every sale.

What is an electronics store?

Let's start by first finding out how much commission Danielle earned last week. We know that her total earnings were $1,058.25 and her base salary was $725 per week. Therefore, her commission must have been:

                          $1,058.25 - $725 = $333.25

We also know that Danielle earns a 7.75% commission on everything she sells. Let's use "x" to represent her total sales last week. Then we can set up an equation to solve for x:

                                   0.0775x = $333.25

Solving for x, we get:

x = $333.25 / 0.0775

x = $4,295.16

Therefore, Danielle's sales last week were $4,295.16.

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Answer: Region Z

Step-by-step explanation: Region X is smaller than Region Y, while Region Y is smaller than Region Z.

Answer:

The value of the investment in 5 years.

Step-by-step explanation:

The description of the function states that it tells us the value of an investment at some point in the future (t), measured in years.  In other words, f(t).  When the time is 5 years, it would be written as f(5), and the t term in the function will be set to 5 for the calculation, which will yield the value of the investment at that time.

Answer: x is anything from the set {2, 3, 5, 7, 11}

This is the list of primes between 1 and 11. The value 1 is not prime.

Answer:

Step-by-step explanation:

7/x^-8 = 7x^8

The number of strings where exactly two of the ones are next to each other, while the third one is not next to the other two, is (n-1) x (n-2).

In combinatorics, one of the fundamental concepts is counting the number of strings or sequences of symbols that satisfy certain conditions.

Let us first consider the case where the two ones that are next to each other are at the beginning of the string. In this case, we can place the third one in any of the remaining positions, which are n-2, where n is the total length of the string. Therefore, the number of such strings is (n-2).

Similarly, if the two ones are at the end of the string, we can place the third one in any of the n-2 remaining positions, and the number of such strings is again (n-2).

Now let us consider the case where the two ones are in the middle of the string. In this case, we can place the two adjacent ones in (n-2) ways, and the third one can be placed in any of the remaining n-3 positions, since it cannot be adjacent to the other two ones. Therefore, the number of such strings is (n-2) x (n-3).

To get the total number of strings that satisfy the given condition, we need to add up the number of strings in each of the three cases:

Total number of strings = (n-2) + (n-2) + (n-2) x (n-3)

Simplifying this expression, we get:

Total number of strings = (n-1) x (n-2)

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The number of miles Ling Jog than Trent can be written as the expression 2.8x - 8

Trent's expression:

2.2x + 8

Ling's expression:

5x

Where,

Number of hours= x

Number of hours Ling Jog than Trent =Ling's expression - Trent's expression

= 5x - (2.2x + 8)

= 5x - 2.2x - 8

= 2.8x - 8

Therefore, Ling jog 2.8x - 8 miles than Trent.

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We can make advantage of the distributive property of multiplication over addition, which says that a(b + c) = ab + ac. As a result, -55 is the simplified expression.

When you multiply a value by a sum, the distributive property of multiplication over addition is put to use. For instance, you wish to multiply 5 by the product of 10 plus 3. Since the numbers are similar terms, we typically add the numbers first and then multiply by 5=> 5(10 + 3) = 65.

An algebraic principle known as the distributive property indicates that it is necessary to multiply each of the two integers by the factor being multiplied by the sum or difference of two terms.

Using this property, we can expand the expression as follows:

(2 − 3)(7 2 − + 8) = 2(7 2 − + 8) − 3(7 2 − + 8)

Now we can simplify each term separately:

2(7 2 − + 8) = 2(49 − 2 + 8) = 2(55) = 110

and

−3(7 2 − + 8) = −3(49 − 2 + 8) = −3(55) = −165

Therefore, putting the results together, we have:

(2 − 3)(7 2 − + 8) = 110 − 165 = -55

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Answer:

Step-by-step explanation:

4 = d

5=1/5

3 the first one is 4x1/12 and 2x3/12

Answer:

Step-by-step explanation:

take length as x,

perimeter= 28cm

Answer:

28cm

Step-by-step explanation:

7+7+7+7

Answer: To find the ordered pair that is a solution of the equation y = 4x - 7, we need to substitute the values of x and y into the equation and see if it is true.

If (x, y) is a solution, then y = 4x - 7 must be true for that particular x and y.

Option A: (2, 1)

Substituting x = 2 and y = 1 into the equation, we get:

1 = 4 * 2 - 7

1 = 8 - 7

1 = 1

Since the equation is true for x = 2 and y = 1, (2, 1) is not a solution of the equation.

Option B: (4, 9)

Substituting x = 4 and y = 9 into the equation, we get:

9 = 4 * 4 - 7

9 = 16 - 7

9 = 9

Since the equation is true for x = 4 and y = 9, (4, 9) is a solution of the equation.

Option C: Both (2, 10) and (4, 9)

Substituting x = 2 and y = 10 into the equation, we get:

10 = 4 * 2 - 7

10 = 8 - 7

10 = 3

Since the equation is not true for x = 2 and y = 10, (2, 10) is not a solution of the equation.

So, the only ordered pair that is a solution of the equation y = 4x - 7 is (4, 9). The answer is B) only (4, 9).

Step-by-step explanation:

Answer: look at the image for the answer and solution

Step-by-step explanation:

Answer: x = 365

Step-by-step explanation:

find the angle bisector and divide and multiply it

The value of ∠E = 31 degrees and the value of ∠G = 149 degrees for the given triangle.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "."

The two triangles are similar thus the measure of its angle are also equal.

Using the similar triangle we have:

Angle D = Angle A = 82 degrees.

Angle F = 67 degrees

Using the sum of interior angles of triangle we have:

∠D + ∠F + ∠E = 180

82 + 67 + ∠E = 180

∠E = 31

From the figure we observe that,

∠E + ∠G = 180 (straight line)

31 + ∠G = 180

∠G = 149

Hence, the value of ∠E = 31 degrees and the value of ∠G = 149 degrees for the given triangle.

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If Kirk had worked for 7 hours he would have made 42 kg of dough.

A unit rate means a rate for one of something.

Given that, Kirk prepared 24 kilograms of dough after working 4 hours, we need to find the amount of dough if he worked for 7 hours.

Calculating the unit rates,

Since, he worked for 4 and made 24 kg,

So, in 1 hour = 24/4 = 6 kg

Therefore, in 1 hour he will make 6 kg

Therefore, in 7 hours he will make = 7x6 = 42 kg

Hence, If Kirk had worked for 7 hours he would have made 42 kg of dough.

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The estimate for the mean book thickness is 3.2 mm.

What is mean?

In arithmetic, mean is the sum of all the added values of all the data in a set divided by the number of data in the set.

To find the mean book thickness, we can use the formula for the mean (also known as the average):

mean = (sum of all data points) / (number of data points)

Since we don't have the exact thickness of each book, but rather intervals of thickness and the number of books in each interval, we can use a weighted mean to estimate the mean thickness.

Here is the calculation:

First, we'll find the midpoint of each interval:

Interval 1: [0, 2]  -> midpoint: x1 = 1

Interval 2: [2, 4]  -> midpoint: x2 = 3

Interval 3: [4, 6]  -> midpoint: x3 = 5

Next, we'll find the weight of each interval by multiplying the midpoint by the frequency:

Interval 1: x1 * f1 = 1 * 5 = 5

Interval 2: x2 * f2 = 3 * 8 = 24

Interval 3: x3 * f3 = 5 * 7 = 35

Finally, we'll sum up the weights and divide by the total frequency to find the weighted mean:

Weighted mean = (5 + 24 + 35) / (5 + 8 + 7) = 64 / 20 = 3.2

So, the estimate for the mean book thickness is 3.2 mm.

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To make two hexagons out of pattern blocks, you would need a total of 12 triangles. Six triangles are needed for each hexagon.

To make two hexagons out of pattern blocks, you would need a total of 12 triangles. Each hexagon requires six triangles to make it, so two hexagons would need double that amount. Since the pattern blocks come in the shapes of triangles, you can easily construct the hexagons by placing the triangles together. Each triangle has two sides that fit together and two sides that overlap, so the six triangles will create a complete hexagon when they are all put together. Once you have two hexagons constructed, they will fit together to make a larger shape, depending on how you place them. With this method, you can easily make two hexagons out of pattern blocks.

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25 random students are asked how much they spent on books  is an example of a statistic.

The primary areas of study in statistics include data collection, organization, organization, analysis, interpretation, and presentation. It is customary to begin with a statistical population or a statistical model that will be examined when applying statistics to a scientific, industrial, or social problem. There are many different groups of people or things that can be referred to as populations, such as "each person living in a country" or "each atom making up a crystal." Every aspect of data is covered by statistics, including the planning of data collection in terms of survey and experiment design. Statisticians gather data using custom experiment designs and survey samples in the absence of census data.

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The requried solutions are as follows,
(1) the original price is $450.   (2)  the original price is $172.40.

Sale price is defined as the price of a product marked including of various price cut such as discounts.

Here,
If the percent of discount is 80% and the sale price is $90, we can use the following formula to find the original price x (let)

Sale price = Original price - Discount

$90 = x - 0.8x

Simplifying the right-hand side:

$90 = 0.2x

x = $450

Therefore, the original price is $450.

If the percent of discount is 15% and the sale price is $146.54, we can use the same formula:

Sale price = Original price - Discount

$146.54 = x - 0.15x

Simplifying the right-hand side:

$146.54 = 0.85x

x = $172.40

Therefore, the original price is $172.40.

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Answer:

Step-by-step explanation:

Let's call the number of boys "b" and the number of girls "g". From the ratio, we know that b/g = 11/9.

Also, we know that b = g + 124, so we can substitute the second equation into the first:

b/g = 11/9

b = g + 124

g + 124 / g = 11/9

Cross multiply:

9g + 1112 = 11g

Solve for g:

-2g = -1112

g = 556

So there are 556 girls and 556 + 124 = 680 boys at the school.

The total number of students at the school is 556 + 680 = 1236.

Answer:5/8

Step-by-step explanation: you put the numbers in a fraction the smallest goes on top and the more enormous number at the bottom you simply by finding the most significant standard number between the 2 numbers which is in this case 6 divide it by that and that is how you get your answer

Answer:

Step-by-step explanation:

is this a bot or girl