Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it.

lim (√1 + 8x-√1-10x)/x
x → 0

Step-by-step explanation:

At t = 0   the graph shows the initial height to be 12 544 ft

The area of the composite figure by adding the areas of the rectangle and the triangle is 375 cm, option (C) is correct.

Let the height of the rectangle and the triangle be 'h', and let the base of the triangle be 'b'. Then, the base of the rectangle is '2b' since it is twice the base of the triangle.

Area of the rectangle = base x height

A₁ = 2b x h

A₁ = 2bh

Area of the triangle = (1/2) x base x height

A₂ = (1/2) x b x h

A₂ = (b/2) x h

Total area of the composite figure = A₁ + A₂

Aₙ = 2bh + (b/2)h

Aₙ = (5/2)bh

Substituting the given values, we get:

A(total) = (5/2)(b x h)

A(total) = (5/2)(15 x 10) [given values: b=15, h=10]

A(total) = 375 cm

Hence, option (C) is correct.

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Answer:

rail, lap, pal, pail

Step-by-step explanation:

Answer:

the length of each leg of the isosceles right triangle is 15√2 centimeters

Step-by-step explanation:

In an isosceles right triangle, the two legs are congruent (i.e., have equal length) and the hypotenuse is √2 times the length of each leg.

Given that the hypotenuse is 30 centimeters, we can set up the following equation to find the length of each leg, denoted by "x":

√2 * x = 30

To solve for "x", we can divide both sides of the equation by √2:

x = 30 / √2

To simplify the result, we can rationalize the denominator by multiplying both the numerator and denominator by √2:

x = (30 / √2) * (√2 / √2)

x = (30√2) / 2

x = 15√2

So, the length of each leg of the isosceles right triangle is 15√2 centimeters.

Answer:

To find n if the mean of 30n, 12, 40, and 10 is n, we can use the formula for the mean of a set of numbers:

mean

=

sumofnumbers

numberofnumbers

mean=

numberofnumbers

sumofnumbers

​

In this case, we have four numbers: 30n, 12, 40, and 10. The mean is n. So we can write:

�

=

30

�

+

12

+

40

+

10

4

n=

4

30n+12+40+10

​

Simplifying the right-hand side:

�

=

30

�

+

62

4

n=

4

30n+62

​

Multiplying both sides by 4:

4

�

=

30

�

+

62

4n=30n+62

Subtracting 30n from both sides:

−

26

�

=

62

−26n=62

Dividing both sides by -26:

�

=

−

31

13

n=−

13

31

​

Therefore, if the mean of 30n, 12, 40, and 10 is n, then n is approximately -2.381.

Answer:

[tex]3k = 36[/tex]

[tex]k = 12[/tex]

Answer:

12

Step-by-step explanation:

If y = 36 and X = 3 then K would = (y divided by x) so it would be 36 divide 3

that being 12 so, therefore, the answer is 12.

K= 12

Answer: $1040

Step-by-step explanation:

There are 52 weeks in a year so they will get 26 haircuts in the year at every 2 weeks.

26x$40 =$1040

Using the definition of supplementary angles, we can see that x = 60

Im just answering the first question.

We know that two angles A and B are supplementary if the sum of their measures is equal to 180°.

Then:

A + B = 180°

In this case, we know taht:

m∠A = (3x + 21)° and m∠B = (6x − 21)°

We can replace that in the equation to get:

3x + 21 + 6x - 21 = 180

Now solve that for x:

9x =180

x = 180/9

x = 60

That is the value of x.

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Answer:

The total cost of registration fee and equipment is $572 + $1,240 = $1,812.

After raising $786 from the car wash, the team still needs to raise $1,812 - $786 = $1,026 from selling candles.

To find out how many candles each player must sell, we need to divide the total amount needed by the number of players:

$1,026 ÷ 12 = $85.50

So each player needs to sell candles for a total of $85.50.

To find out how many candles that is, we need to divide the total amount by the price per candle:

$85.50 ÷ $9.50 = 9

Therefore, each player needs to sell 9 candles to cover the remaining costs.

The scale factor of the dilation is 1/3.

Scale factor is a numerical scale that represents the ratio of the dimensions of two similar geometric figures. It is used in geometry to compare the size of two similar figures.

To determine whether the dilation is an enlargement or a reduction, we need to compare the size of the solid and dashed triangles.

We can calculate the lengths of the sides of the solid triangle using the distance formula:

[tex]Side 1: \sqrt{[(6 - (-6))^2 + (3 - 0)^2]} = \sqrt{(12^2 + 3^2)} = \sqrt{(144 + 9)} = \sqrt153\\\\Side 2: \sqrt{[(6 - (-6))^2 + ((-6) - 0)^2]} = \sqrt{(12^2 + 6^2)} = \sqrt{(144 + 36)} = \sqrt{180}\\\\Side 3: \sqrt{[(6 - 6)^2 + ((-6) - 3)^2]} = \sqrt{(0 + 81)} = \sqrt81 = 9[/tex]

So, the solid triangle has side lengths of √153, √180, and 9.

We can also calculate the lengths of the sides of the dashed triangle using the distance formula:

[tex]Side 1: \sqrt{[(2 - (-2))^2 + (1 - 0)^2]} = \sqrt{(4^2 + 1^2)} = \sqrt17\\\\Side 2: \sqrt{[(2 - (-2))^2 + ((-2) - 0)^2]} = \sqrt{(4^2 + 2^2)} = \sqrt20\\\\Side 3: \sqrt{[(2 - 2)^2 + ((-2) - 0)^2]} = \sqrt{(0 + 4)} = 2[/tex]

So, the dashed triangle has side lengths of √17, √20, and 2.

Comparing the side lengths, we can see that the dashed triangle is smaller than the solid triangle. Therefore, the dilation is a reduction.

To find the scale factor of the dilation, we can choose any corresponding side lengths from the solid and dashed triangles and divide them. For example, we can choose side 1:

Scale factor = (length of corresponding side in dashed triangle) / (length of corresponding side in solid triangle)

= √17 / √153

= √(17/153)

= (√17) / (3√17)

= 1/3

Therefore, the scale factor of the dilation is 1/3.

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The first term of a geometric sequence is 2, and the common ratio is 3.
Therefore, the 8th term of the sequence is 4,374.

To find the 8th term of a geometric sequence with the first term 2 and a common ratio of 3, you can use the formula:
T_ n = a * r^(n-1)
where T_ n is the nth term, a is the first term, r is the common ratio, and n is the position of the term you're looking for.

In this case, you want to find the 8th term (n = 8), the first term (a) is 2, and the common ratio (r) is 3. Plug these values into the formula:
T_8 = 2 * 3^(8-1)
T_8 = 2 * 3^7
T_8 = 2 * 2,187
T_8 = 4,374
So, the 8th term of the geometric sequence is 4,374.

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To solve the equation 135°·(7x-10)=(11x+10)·(7x) is x ≈ -0.203 or x ≈ 1.567.

To solve the equation 135°·(7x-10)=(11x+10)·(7x), we can use the distributive property to expand the right side of the equation and then simplify.

First, convert the angle measure of 135 degrees to radians:

135° = 135/180π = 3π/4

Then substitute and simplify;

3π/4(7x - 10) = (11x + 10)(7x)

21πx/4 - 15π/4 = 77x² + 70x

Move all the terms to one side:

77x² + 70x - 21πx/4 + 15π/4 = 0

Next, we can solve for x using the quadratic formula;

x = (-b ± √(b² - 4ac))/2a

where a = 77, b = 70 - 21π/4, and c = 15π/4.

Plugging in these values, we get;

x = (-[70 - 21π/4] ± √[(70 - 21π/4)² - 4(77)(15π/4)])/(2(77))

Simplifying this expression gives two possible solutions for x;

x ≈ -0.203 or x ≈ 1.567

Therefore, the solution to the equation 135°·(7x-10)=(11x+10)·(7x) is x ≈ -0.203 or x ≈ 1.567.

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The expression uses to find the product 6300, are 7×900, 700×9, 70×90.

Given is a number 6300, we need to write it as a product of numbers,

So, the factors of 6300 = 2, 2, 3, 3, 7, 5, 5

We cannot write the, (7 × 9) + (10 × 10), (63) + (100) as a product of 6300,

(7× 9) + (10 × 10) = 63 + 100 = 163

(63) + (100) = 163

But,

7×900 = 6300

700×9 = 6300

70×90 = 6300

Hence, the expression uses to find the product 6300, are 7×900, 700×9, 70×90.

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Using the Z-table, you can find the z-score that corresponds to a cumulative probability of 0.70, which is approximately 0.52. So, the z-score for the 7th decile on the standard normal curve is 0.52.

To find the z-score that corresponds to the 7th decile of the standard normal curve, we first need to determine the cumulative probability up to that point.

The 7th decile represents the point where 70% of the data lies below it and 30% lies above it. Using a standard normal distribution table or calculator, we can find the z-score that corresponds to a cumulative probability of 0.70.

The z-score that corresponds to a cumulative probability of 0.70 is approximately 0.524. Therefore, the z-score that corresponds to the 7th decile of the standard normal curve is 0.524.

To find the z-score corresponding to the 7th decile on the standard normal curve, you'll need to use the cumulative probability distribution function (also known as the Z-table or standard normal table). The 7th decile represents the point where 70% of the data is below it, so you'll be looking for a cumulative probability of 0.70.

Using the Z-table, you can find the z-score that corresponds to a cumulative probability of 0.70, which is approximately 0.52. So, the z-score for the 7th decile on the standard normal curve is 0.52.

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Answer:

x= 21

Step-by-step explanation:

(x+6)^1/3-5=-2

Solve for x

Add 5 to each side

(x+6)^1/3-5+5=-2+5

(x+6)^1/3=3

Cube each side.

((x+6)^1/3)^3=3^3

x+6 = 27

Subtract 6 from each side

x+6-6 = 27-6

x= 21

Answer:

x = 21

Step-by-step explanation:

[tex]\sf(x+6)^\frac{1}{3} -5=-2[/tex]

First, add 5 to both sides.

[tex]\sf(x+6)^\frac{1}{3} =-2+5\\\\\sf(x+6)^\frac{1}{3} =3\\\\\sqrt[3]{(x+6)} =3[/tex]

Cube both sides.

[tex]\sqrt[3]{(x+6)} =3\\\\x+6=3^3\\\\x+6=27[/tex]

Subtract 6 from both sides.

[tex]x+6=27\\\\x=27-6\\\\x=21[/tex]

Thus, the probability that two people picked at random both own a dog is 0.1296 or 1296/10000.

To solve this problem, we need to use the formula for calculating the probability of independent events: P(A and B) = P(A) x P(B).

In this case, let A be the event that the first person owns a dog and B be the event that the second person owns a dog.

We know that P(A) = 0.36, or 36% chance that the first person owns a dog. Since the events are independent, P(B) is also 0.36.

So, the probability of both events occurring (both people owning dogs) is:

P(A and B) = P(A) x P(B)
= 0.36 x 0.36
= 0.1296

This can also be expressed as a fraction:

P(A and B) = 36/100 x 36/100
= 1296/10000

Therefore, the probability that two people picked at random both own a dog is 0.1296 or 1296/10000.

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Answer: 24 clothing items

Step-by-step explanation:

The total is 120.

1/5 of 120 is the same as saying 120 divided by 5.

120 divided by 5 is 24.

Answer : 24

Answer:

The given function is:

f(x) = -3x^2 + 12

To find the interval over which the function is increasing, we need to find the critical points of the function.

f'(x) = -6x

The critical point is where f'(x) = 0

-6x = 0

x = 0

Now, we need to check the sign of f'(x) on either side of the critical point to determine whether the function is increasing or decreasing.

If x < 0, then f'(x) < 0, so the function is decreasing.

If x > 0, then f'(x) > 0, so the function is increasing.

Therefore, the interval over which the function is increasing is:

(0, infinity)

Step-by-step explanation:

gg

The product of the zeros in the given polynomial is 5.

Given is a polynomial p(x) = (a+1)x² + (2a+3)x + (3a+4), the sum of zeros is -1,

We need to find the product of its zeros,

So,

We know that in the polynomial ax²+bx+c = 0,

the sum of the roots = -b/a

Product of the roots = c/a

Therefore,

Here a = a+1, b = 2a+3 and c = 3a+4

So,

-(2a+3)/a+1 = -1

-2a-3 = -a-1

-a = 2

a = 2

Put a = 2 in value of c,

c = 3(2)+4 = 10

So, the product of the zeros is = 10/2 = 5

Hence the product of the zeros in the given polynomial is 5.

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As per the unitary method, the duration of the movie is 1 hour and 10 minutes.

To solve this problem, we can use a mathematical concept called the "unitary method."

Now, let's take a closer look at the information given in the problem. We have two analog clocks: one labeled "start" and the other labeled "end." The hour and minute hands on each clock provide information about the time.

Since the minute hand has moved halfway between the 6 and 7 marks, we can say that it has moved 30 minutes (since each mark represents 5 minutes). Therefore, the time on the start clock is 11:30 + 30 minutes = 12:00.

To determine the duration of the movie, we can subtract the start time from the end time.

End time - start time = 1:10 - 12:00

First, we need to convert the end time to 24-hour format for easier calculation. Since the hour hand is between 1 and 2, we know that the time is in the afternoon or evening. Therefore, we can add 12 to the hour value to convert it to 24-hour format.

1:10 + 12 hours = 13:10 (in 24-hour format)

Now, we can subtract the start time from the end time:

13:10 - 12:00 = 1 hour and 10 minutes

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The equation of line passes through the points (-2, 1) and (0, 5). will be;

⇒ y = 2x + 5

And, Slope = 2

And, Y - intercept  = 5

Given that;

Two points on the line are (-2, 1) and (0, 5).

Now,

Since, The equation of line passes through the points (-2, 1) and (0, 5).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (5 - 1) / (0 - (-2))

m = 4 / 2

m = 2

Thus, The equation of line with slope 2 is,

⇒ y - 1 = 2 (x - (-2))

⇒ y - 1 = 2 (x + 2)

⇒ y - 1 = 2x + 4

⇒ y = 2x + 5

Therefore, The equation of line passes through the points (-2, 1) and (0, 5). will be;

⇒ y = 2x + 5

And, Slope = 2

And, Y - intercept  = 5

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Answer:

18 different outfits

Step-by-step explanation:

Hector can make 18 different outfits.

To see why, simply multiply the number of options for each item:

3 shirts x 3 shorts x 2 shoes = 18 possible outfits

The appropriate measure of variability depends on the characteristics of the data and the research question being addressed and the IQR is a more robust measure than the range if the data is skewed, and a large IQR indicates a wide range of expenses, requiring more funds. (option c)

Firstly, the IQR of 10 is the most accurate to use if the data is skewed. IQR is a measure of variability that measures the spread of the middle 50% of the data, thus, reducing the influence of outliers. Therefore, if the data is skewed, the IQR provides a more robust measure of variability than the range. The range is the difference between the largest and smallest value in a dataset and is sensitive to extreme values, which can distort the results.

Secondly, the IQR of 45 is the most accurate to use if the charity wants to show that they need more money. If the IQR is large, it means that there is a large variation in the data, and the spread is significant. Therefore, in this scenario, a large IQR indicates that the charity has a wide range of expenditures, and some expenses are significantly higher than others. Thus, the charity needs more funds to cover these expenses adequately.

Finally, the range of 45 is the most accurate to use if the charity wants to show that they have plenty of money. A large range indicates that the data points are spread out, and there is a significant variation in the expenses.

Therefore, in this scenario, a large range indicates that the charity has a wide range of expenses, and some expenses are higher than others, but overall, they have enough money to cover these expenses.

Hence the correct option is (c).

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The proportion of identity theft complaints in the state is significantly higher than 23%.

The random variable for this scenario is the proportion of identity theft complaints out of the total number of complaints received by the state. The population parameter is the true proportion of identity theft complaints in the entire population of complaints in the state.

The null hypothesis (H0) is that the proportion of identity theft complaints in the state is equal to or less than 23%. The alternative hypothesis (Ha) is that the proportion of identity theft complaints in the state is greater than 23%.

To test this hypothesis, the state needs to conduct a one-tailed hypothesis test with a significance level (alpha) of 0.05. They can use the z-test statistic to compare the sample proportion with the population proportion. If the test statistic is greater than the critical value, they can reject the null hypothesis.

It is important to note that this test assumes that the sample of 1245 complaints is randomly selected and representative of the entire population of complaints in the state. If there is any bias or non-representativeness in the sample, the results of the test may not be accurate.

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The statement which is true about the function of the temperature of the soup over time is D. As time increases, the temperature of the soup approaches 72 °F.

Given a table of values which shows the temperature of a bowl of soup left out on the kitchen counter with the time.

Here the time shown are ranged from 5, 10, 20, 30, 45, 60, 80.

Corresponding temperature of the soup left ranges from 139.503, 109.047, 83.158, 75.361, 72.556, 72.092, 72.008 respectively.

It is clear that as the time increases, the temperature of the soup is decreasing and at last approaches to 72 °F.

Hence the correct statement is D.

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Answer:

186

Step-by-step explanation:

7 / 100 = 0,07

20 / 0,07 = 285,7142 - 100 = 185,7142 ≈ 186

The average rate of change of the substance is given as -2.4

When the value of t is ten years, the radioactive substance in grams is given as 6

When t is 0 on the graph, the gram is given as 3o grams

The rate of change would be

6 - 30 / 10 - 0

= -24 / 10

= - 2.4

The average rate of change is not a good measure. This is because what we have here is an exponential decay

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Answer:

Set your calculator to degree mode.

The measure of angle Q is

[tex] {cos}^{ - 1} \frac{29}{63} = 62.6 \: degrees[/tex]

Angle Q measures 62.6°.

Answer:

x^2 - 4x + 24 cannot be factored.

The measures of central tendency of the first psychology exam in a semester are the average score, which was an 85.

The correlation coefficient and the range of scores from 95 to 65 are not measures of central tendency either.

The standard deviation is a measure of variability, not central tendency, that the measures of central tendency of the first psychology exam are the average and median scores. This states that the mode, correlation coefficient, range of scores, and standard deviation are not measures of central tendency.

Hence, the measures of central tendency for the first psychology exam in a semester are the average score (85) and the median score (80).

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The measures of central tendency for the psychology exam scores include the average, median, and mode.

The measures of central tendency of the first psychology exam in a semester include the average score, median score, and mode (most frequently occurring score).

The average score on the exam was 85, which represents the mean of all the scores.

The median score on the exam was 80, which represents the middle value when all the scores are arranged in order.

The most frequently occurring score was 82, which represents the mode of the scores.

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