Evaluate
\(lim \: \frac{ \frac{1}{ \sqrt{x} } - 1}{ \sqrt{x} - 1} \: as \: x \: approaches \: 1\)
​

Answer:

2x^2 - 6x

Step-by-step explanation:

2x(x-3)

= 2x^2 - 6x

(c) The argument is valid, and we can conclude that Penelope missed class because she got a detention.

(e) The argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.

(c) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:

Let "M(x)" be the predicate "x missed class", and "D(x)" be the predicate "x got a detention".

Hypotheses: M(Penelope), D(Penelope)

Conclusion: M(Penelope)

Using modus ponens, which states that if P implies Q and P is true, then Q must be true, we can conclude that M(Penelope) is true:

From M(Penelope) and "Every student who missed class got a detention", we have D(Penelope)

From D(Penelope), we have M(Penelope)

So, the argument is valid, and we can conclude that Penelope missed class because she got a detention.

(e) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:

Let "M(x)" be the predicate "x missed class", "D(x)" be the predicate "x got a detention", and "A(x)" be the predicate "x got an A".

Hypotheses: A(Penelope), ~D(Penelope)

Conclusion: ~M(Penelope)

Using modus tollens, which states that if P implies Q and Q is false, then P must be false,

we can conclude that M(Penelope) is false:

From A(Penelope) and "Every student who missed class or got a detention did not get an A",

we have ~M(Penelope) & ~D(Penelope)

From ~D(Penelope), we have ~M(Penelope)

So, the argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.

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Answer:

b, a, c

Step-by-step explanation:'

The side opposite of the smallest angle(50) is always the smallest, which means b is the smallest

Hope this helps!

Answer:

b ,a ,c

Step-by-step explanation:

The side opposite the smallest angle is the shortest

The smallest

x = 180 - 70 -62 = 48

48 is the smallest angle so b is the smallest side

The side opposite the largest angle is the longest side

70 is the largest angle so c is the longest side

b ,a ,c

Answer:

\((5+3\sqrt{2} )^{2} =43+30\sqrt{2}\)  

≈85.43

Step-by-step explanation:

apply the binomial theorem to the square

\(=(5)^{2} +2(5)(3\sqrt{2} )+(3\sqrt{2} )^{2}\)

\(=25+30\sqrt{2} +18\\\)

\(=43+30\sqrt{2}\)

≈85.43

Hope this helps

Hello!

Here, we apply the algebraic identity :

\(\boxed {(a + b)^{2} = a^{2} + 2ab + b^{2}}\)

Let's solve!

⇒ (5 + 3√2)²

⇒ (5)² + 2(5)(3√2) + (3√2)²

⇒ 25 + 30√2 + 18

⇒ \(\boxed {43 + 30\sqrt{2}}\)

∴ The final answer will be 43 + 30√2.

Answer:

A) 144 yd²

Step-by-step explanation:

Base= 8x8=64

Side = 1/2*8*5=20

64+20+20+20+20=144 yd²

Answer:

168 sq yds

Step-by-step explanation:

5x8/2x2=40

8x8/2x2=64

8x8=64

40+64+64=168

Answer: 297

Step-by-step explanation:

a=6n-3

a=6(50)-3

a=300-3

a=297

Answer:

15

Step-by-step explanation:

The circumference of a circle is 2*pi*radius. Divide the circumference by 2pi to find the radius.

Answer:

The answer is 15 cm

Step-by-step explanation:

Now,

C = 2πr

r = C ÷ 2π

r = 94.20 ÷ 2 × 3.14 cm

r = 94.20 ÷ 6.28 cm

r = 15 cm

Thus, The Radius is 15 cm

-TheUnknownScientist 72

The bootstrap method is considered to be more accurate because it uses the actual data, while the conservative estimate for the standard error is considered to be more conservative because it assumes a normal distribution.

A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain degree of confidence.

There are two methods for calculating the confidence interval for p: bootstrap and a conservative estimate for the standard error.

The bootstrap method involves resampling the data from the 400 tosses and computing the estimate of p for each resample.

This process is repeated a large number of times to create a distribution of estimates for p.

The 95% confidence interval for p is then defined as the range of values that includes the middle 95% of the estimates of p.

The formula is:

SE = √(p(1-p)/n)

Where p is the observed number of heads and n is the number of tosses. The 95% confidence interval for p is then defined as:

=> p ± 1.96 * SE

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The height of the tower is 2358 feets.

David is standing 500 feet away from the base of a cell phone tower.

The angle of elevation from his eyes to the top of the tower is 78°. David eyes are 6 feet above the ground . The height of the tower can be found as follows:

This situation forms a right angle triangle. Therefore,

using trigonometric ratios,

tan 78° = opposite / adjacent

tan 78° = x / 500

cross multiply

x = 500 tan 78°

x = 500 × 4.70463010948

x = 2352.31505474

Therefore,

height of the tower = 2352 + 6

height of the tower = 2358 ft.

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The trigonometric Identity proof (sec²θ - 1)cot²θ = 1 is as explained below.

We want to prove that;

(sec²θ - 1)cot²θ = 1

Now, we know from trigonometric identities that;

sec²θ - 1 = tan²θ

Thus, the left hand side of our original equation can be written as;

tan²θ * cot²θ

We also know in trigonometric identities that 1/tan θ = cot θ. Thus;

tan²θ * cot²θ can be written as;

tan²θ * (1/ tan²θ)

The above will cancel out to give us 1 which is also equal to the right hand side and as such our trigonometric proof is complete.

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By considering these rules and properties of integers, the correct result of 6 was obtained.

When writing the response, I considered the following information:

The product or quotient of two integers with different signs is negative. This rule was used to determine that 2(-12) equals -24, not 24.

To subtract an integer, add its opposite. This rule was applied when subtracting -30 from -24, resulting in -24 - (-30) = -24 + 30.

To add integers with opposite signs, subtract the absolute values. The sum has the same sign as the integer with the greater absolute value.

This rule was used to calculate -24 + 30 = 6, where the absolute value of 30 is greater than the absolute value of -24.

By considering these rules and properties of integers, the correct result of 6 was obtained.

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The  equation of the parabola with the following properties y = (-1/4)(x+3)^2 -1

To find the equation of a parabola, we can use the formula f(x) = ax^2 + bx + c, where a, b and c are congruent vertices.

Alternatively, we can use PF = PM to find the equation of the parabola.

vertex is half way between the focus and directrix

It's a downward opening parabola, general form

y= a(x-h)^2 + k

where (h,k) = vertex= (-3,-1)

plug in another point on the parabola to solve for a which gives

am answer with either x coefficient = -1'/4 or =4 Check the math.

one or the other is right another point is the y intercept = 9a-1

Another point is directly to the right of the focus  (-1, -2)  It's 2 down from the directrix and 2 to the right of the focus, equidistant.   plug that point into y= a(x+3)^2 -1 and solve for "a"  

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

-2 = 4a -1

4a = -

a = -1/4

The parabola is y = (-1/4)(x+3)^2 -1

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Answer:

-2

Step-by-step explanation:

-4+2=-2

Answer:

f(4) = -2

Step-by-step explanation:

\(f(x)=-x+2\\\\f(4)=-(4)+2\\\\f(4)=-4+2\\\\\boxed{f(4)=-2}\)

Hope this helps!

Answer:

\(\displaystyle \int\limits^8_1 {\frac{3}{x}} \, dx = 9 \ln 2\)

General Formulas and Concepts:

Calculus

Integration

Integration Rule [Fundamental Theorem of Calculus 1]:                                     \(\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)

Integration Property [Multiplied Constant]:                                                         \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Area of a Region Formula:                                                                                     \(\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx\)

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle f(x) = \frac{3}{x} \\\left[ 1 ,\ 8 \right]\)

Step 2: Integrate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

The average weight of carry-on luggage by passengers in airplanes is (15.7, 20.3) pounds.

The margin of error to be used is 2.3 pounds.

where z is the Z-score that corresponds to the desired confidence level (95% confidence corresponds to a Z-score of 1.96), standard deviation is the population standard deviation (7.5 pounds), and sample size is the number of items in the sample (25).

       Margin of Error = 1.96 * (7.5 / sqrt(25)) = 2.3 pounds

        (average weight - margin of error, average weight + margin of error)

         = (18 - 2.3, 18 + 2.3) = (15.7, 20.3) pounds.

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Answer:

The denominators of the fractions are 2 and 10.

The fractions with numerators of 1 that have sum of 3 / 5  is calculated below

The sum of the fractions are 3 / 5. Each of the fractions have a numerator of 1. Therefore, let the denominators be x and y

1 / x + 1 / y = 3 / 5

Therefore,

1 / x  + 1 / y = 3 / 5

y + x / xy = 3 / 5

cross multiply

5y + 5x = 3xy

Using hit and trial method,

5(2) + 5(10) = 3(10)(2)

10 + 50 = 60

60 = 60

The values are same.

Therefore, the denominators are 2 and 10.

Step-by-step explanation:

Answer: 12 is the awnser

Step-by-step explanation: simple math.

The adjusted balance of Blossom's inventory account is $214,680.

The rate of interest, also known as the interest rate, is the percentage amount charged by a lender or financial institution for the use of borrowed money or for the extension of credit. It is the cost of borrowing money, typically expressed as an annual percentage of the amount borrowed or owed.

Therefore, the adjusted balance of Blossom's inventory account is $214,680.

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The restrictions on the width is that it must be between 14.1 yards and 17.3 yards

From the question, we have the following parameters that can be used in our computation:

Area = between 240 yd² and 360 yd²

Also, we have

Length = 1.2 times the width

This means that

l = 1.2w

The area is then calculated as

Area = lw

So, we have

Area = 1.2w²

This means that

240 < 1.2w² < 360

Divide through by 1.2

200 < w² < 300

Take the square roots

14.14 < w < 17.32

Approximate

14.1 < w < 17.3

Hence, the width must be between 14.1 yards and 17.3 yards

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Answer:

C. The items have different y-intercepts and different rates of change

Step-by-step explanation:

Figure I shows a linear equation in the form y = mx + b, where "m" is the rate of change and "b" is the y-intercept. That means for y = 1/4 * x - 1/2, 1/4 is the slope and 1/2 is the y-intercept.

Figure II shows a table. The y-intercept is when x = 0, so look at where x = 0 is in the table and see the y-value which corresponds to it. The y-value in this case would be -0.25. To find the rate of change, assuming Table II is changing at a constant rate, subtract the subsequent y-value from a proceeding y-value and divide that by subtracting the corresponding x-values (any two sets of x and y-values should work): (3.75 - 7.75)/(-1 - -2) = -4/(-1 + 2) = -4/-1 = 4.

Thus, we know that the rates of change are different and the y-intercepts are different for both functions.

Answer:

The slopes are perpendicular.

Step-by-step explanation:

First we are going to find the slope-inercept form from the equation, -5x + 10y = 5.

Solve for y.

-5x + 10y = 5

+5x. =+5x

10y = 5x + 5

\( \frac{10y}{10} = \frac{5x + 5}{10} \\ y = \frac{1}{2}x + \frac{1}{2} \)

So we now have

\(y = \frac{1}{2}x + \frac{1}{2} \\ and \\ y = - 2x + 4 \)

Looking at the equation above, the slopes are perpendicular.

The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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Answer:

the answer would be 139000

Answer:139000

Step-by-step explanation:

Answer:

54.7

Step-by-step explanation:

19% of 288

0.19 * 288 = 54.72

54.72 = 54.7

Answer:

Estimated 60 and rounded 55 and normal 54.72.

Step-by-step explanation:

To get the estimated answer, first convert the percentage to a decimal: 19% = 0.19. Second, you have to round the 2 numbers so they are easier to multiply: 0.19 = 0.20 and 288 = 300. Now that you have the 2 rounded numbers, you can multiply them to get the estimated answer: 0.20 x 300 = 60 so 60 is your estimated answer.

To get the rounded answer, you first have to multiply the 2 given numbers, the whole number and the percentage (as a decimal), together: 0.19 = 54.72. Now that you have the answer to the multiplication problem, you can round the answer to the nearest whole number: 54.72 = 55 so the rounded answer is 55.

To get the exact answer, all you have to do is multiply the percentage (as a decimal), by the whole number to get the answer: 0.19 x 288 is 54.72 so the exact answer is 54.72.

I hope I helped and please mark this answer as brainliest if so!

Answer:

Step-by-step explanation:

The equation 7x +10 = -x² describes two points on a number line: x = -5 and x = -2.

Perhaps you want points to help you plot ...

  y = x² +7x +10

__

The y-intercept is easy to find: set x=0. What's left is the constant, y = 10. So, the point (0, 10) is one point on the graph.

__

The vertex form of the equation is ...

  y = a(x -h)² +k . . . . . . . . where (h, k) is the vertex, and 'a' is the vertical scale factor

If you expand this equation, you get ...

  y = a(x² -2hx +h²) +k = ax² -2ahx +ah² +k

Comparing the coefficients to the equation you have, you can see that ...

  1 = a

  7 = -2ah

  10 = ah² +k

Solving for h and k, we find ...

  7 = -2(1)h   ⇒   h = -7/2

  10 = (1)(-7/2)² +k   ⇒   k = 10 -49/4 = -9/4

With these values, we can write the vertex form equation as ...

  y = (x +7/2)² -9/4

The vertex is (x, y) = (-7/2, -9/4).

__

The equation can be factored by looking for factors of 10 that have a sum of 7. Such values are 2 and 5.

  y = x² +7x +10 = (x +2)(x +5)

The x-intercepts are the values of x that make these factors zero.

  x +2 = 0   ⇒   x = -2

  x +5 = 0   ⇒   x = -5

This tells you two other points on the graph are (-2, 0) and (-5, 0).

An equation to represent the total cost of a job that takes "x" hours is "total cost = $50 + ($150 × x)". The situation can be described as linear.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the cost of consulting is $50, while the cost of labour is $150 per hour.

A.) An equation to represent the total cost of a job that takes "x" hours.

Total cost = $50 + ($150 × x)

B.) Total cost is the labour works for 40 hours,

Total cost = $50 + ($150 × 40) = $6,050

C.) As found above the cost of working 40 hours is $6,050, therefore, the amount of $5,000 will not be enough.

D.) The situation can be described as linear.

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Answer:

multiply 65 by 5 and divide by 1 fourth

Step-by-step explanation:

The triangles which are right triangles in the given three are none.

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

|AC|^2 = |AB|^2 + |BC|^2    

We are given that;

Sides of the triangles

Now,

For Triangle 1, the side lengths are 12, 14, and 16. To check if it is a right triangle, we can see if the Pythagorean theorem holds for any two sides:

12^2 + 14^2 = 144 + 196 = 340

16^2 = 256

Since 340 is not equal to 256, Triangle 1 is not a right triangle.

For Triangle 2, the side lengths are 6, 11, and \($\sqrt{160}$\). To check if it is a right triangle, we can see if the Pythagorean theorem holds for any two sides:

6^2 + 11^2 = 36 + 121 = 157

\($\sqrt{160}^2 = 160$\)

Since 157 is not equal to 160, Triangle 2 is not a right triangle.

For Triangle 3, the side lengths are 8, 11, and 15. To check if it is a right triangle, we can see if the Pythagorean theorem holds for any two sides:

8^2 + 11^2 = 64 + 121 = 185

15^2 = 225

Since 185 is not equal to 225, Triangle 3 is not a right triangle.

Therefore, by Pythagoras theorem none of the given triangles are right triangles.

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