A ladder leans against the wall at the point B
(window end) from a ground level and makes an
angle horizontally at 52º. The height of ladder is 15
m. When the same ladder leans above the point B
at point A (window start) and makes an angle of 85°
horizontally. The distance between point A and
point B is

GET THEM ALL RIGHT!?

Answer:

i think x=3

Step-by-step explanation:

5x+14=19x-28

- 14=19x−28−5x

- 14+28=14x

- 42=14x

(divide)

x=3

The statement is false because the element 2 does not meet the criteria of being an integer greater than 13.

To determine if {2} is an element of the set of integers greater than 13, we need to analyze the statement.

The set of integers greater than 13 can be represented as {x | x ∈ ℤ, x > 13}. This set contains all integers that are greater than 13.

Now, let's check if the element 2 is in this set. Since 2 is not greater than 13, it does not satisfy the condition x > 13. Therefore, {2} is not an element of the set of integers greater than 13.

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Answer:

141

Step-by-step explanation:

It is a 7 sided shape

first find the sum of interior angles

7-2 x 180 = 900

so 122 +125 +131 +107+ x-15+x+x+7 = 900

477 +3x =900

3x= 423

x=141

It Is Going To Be 5 Because 15÷3=5 And 15÷5=3 And 5×3=15 3×5=15

Answer:

90 i think im sorry if its wrong

Step-by-step explanation:

Answer:

(-2,2)     see attached diagram

Step-by-step explanation:

see graph

Answer:

Step-by-step explanation:

Given  x^2 - 16x + 60 = -12

Using the completing the square method to find x;

subtract 60 from both sides

x2 - 16x + 60-60 = -12-60

x2 - 16x  = -72

Add square of the half of the coefficient of x to both sides

x2 - 16x + (1/2(-16))²  = -72 +  (1/2(-16))²

x^2 - 16x +64 = -72+64

(x-8)² = -8

Take the square root of both sides

√(x-8)² = √-8

x - 8 = ±√8i

x =  ±√8i+8

x =  ±2√2i+8

The solution of the given equation is:  \(x = 8+\sqrt{-8}\)  and  \(\\x = 8-\sqrt{-8}\).

Given that:

Equation:  \(x^2 - 16x + 60 = -12\)

Simplify the above equation as:

x² - 16x + 60 = -12

x² - 16x = -12 - 60

x² - 16x = -72

Add 64 to each side of the equation to complete the square.

x² - 16x + 64 = -72 + 64

x² - 16x + 64 = -8

Write x² - 16x + 64 as (x - 8)² since it is a perfect square trinomial.

(x - 8)² = -8

Take the square root of both sides to get the solutions.

\(x - 8 = \±\sqrt{-8}\\x = 8\±\sqrt{-8}\\x = 8+\sqrt{-8}\\x = 8-\sqrt{-8}\)

where i is the imaginary unit.

Hence, the value of x are:  \(x = 8+\sqrt{-8}\)  and  \(\\x = 8-\sqrt{-8}\).

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Answer:

84%

Step-by-step explanation:

2940+560=3,500

\(\frac{2940*100}{3500} =\)\(\frac{84}{100}\)

=84%

Answer: answer is a

Step-by-step explanation:

The given data can be used to test the hypothesis that the proportion of preterm births among twins has increased from 1990 to 2000 and the conclusion is that the proportion of preterm births among twins has increased from 1990 to 2000.

Using a two-proportion z-test, with the null hypothesis that the proportions are equal, we find that the test statistic is approximately 1.89, with a p-value of 0.029. This suggests that there is evidence to reject the null hypothesis at the 5% significance level, and conclude that the proportion of preterm births among twins has increased from 1990 to 2000.

However, it's important to note that this conclusion is based on the assumption that the two samples are independent and representative of the population of interest. Other factors, such as changes in the population or hospital policies, may have also contributed to the observed increase in preterm births among twins.

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Answer:

W can be 3, 4, and 5

Step-by-step explanation:

If it is less than 18 and higher than 6 then I think those, 3 times 3, 4, and 5, would be in between your range.

9514 1404 393

Answer:

  (3) y + 1 = -1/2(x + 6)

Step-by-step explanation:

The slope of the line between the two points can be found from the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -1)/(6 -2) = -2/4 = -1/2

Then the point-slope form of the equation of the line through the given points can be written as either of ...

  y -1 = -1/2(x -2)

  y +1 = -1/2(x -6)

We note that only choices (2) and (3) have slopes of -1/2, so are parallel. Choice (2) matches the first equation above, so is the identical line, not one that is parallel.

Choice (3) matches neither of the equations of the line through the given point, so that is the choice of interest.

As per the question, the complexity that ranks between the other two is O(n^2) - Quadratic (or Polynomial).

As we compare the run-time complexities, it's crucial to examine the function’s growth with an increase in input size (n).

Let us analyze the growth rates:

Exponential (O(2^n)): The function doubles for each increment in n. This is very fast growth.

Quadratic (O(n^2)): The function grows proportional to the square of n. This is slower growth compared to exponential but faster than logarithmic.

Logarithmic (O(log n)): The function grows very slowly as n increases. The growth rate is less than linear (O(n)).

So the ranking, from slowest to fastest growth, is:

O(log n) - Logarithmic

O(n^2) - Quadratic (or Polynomial)

O(2^n) - Exponential

As per the question, the complexity that ranks between the other two is O(n^2) - Quadratic (or Polynomial).

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The probability that all 3 cards are clubs will be 0.0129

To find the chance that all three cards are clubs,

We can use the following formula:

\(P(\text{all 3 are clubs}) = \frac{\text{number of favorable outcomes}}{\text{number of possible outcomes}}\)

The number of favorable outcomes is the number of ways to choose 3 clubs from the 13 clubs in the deck, which is given by the given binomial coefficient \({13 \choose 3} = 286\)

The number of possible outcomes is the number of ways to choose 3 cards from the deck, which is given by the binomial coefficient \({52 \choose 3} = 22,!100\)

Therefore, the value of the probability that all 3 cards are clubs is:

\(P(\text{all 3 are clubs}) = \frac{\text{number of favorable outcomes}}{\text{number of possible outcomes}} \\= \frac{286}{22,!100} \\\approx 0.0129\)

Rounding to 3 decimal places, the answer is 0.013.

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The complete questions should be:

A standard deck of cards has 52 cards. There are 4 suits clubs, diamonds, hearts, and spades each of which has 13 cards. Suppose you draw 3 cards without replacement. What is the chance that all three are clubs? Round your answer to 3 decimal places

The sytem of liner equation are that satisfies the given conditon are:

L1 : 2x-y=5

L2 : 3x - y = 10

Given that one of the line of the sytem of equations passes through (2,-1) and also given that solution of system of equations is (5,5) so it justifies that  the 1st line passes through (2.-1) and (5,5) so the equation of 1st line is given by:

To find the equation of a line that passes through the points (2, -1) and (5, 5), we can use the point-slope form of a line, which is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line.

To find the slope of the line, we can use the formula:

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

Substituting the coordinates of the two given points and the formula for the slope into the point-slope form, we get:

y - (-1) = ((5 +1) / (5 - 2))(x - 2)

= (6 / 3)(x - 2)

= 2(x - 2)

= 2x - 4

=> 2x- y =5

so the equation of line 1 is 2x-y=5

And as mentioned that equation of line that passes through (5,5) but as given it won't pass through (2,-1)

so let m be the slope of 2nd line and passes through (5,5)

so the equation of line is given by:

y-5 = m (x-5)

and if this  line won't pass through (2,-1) then

-1 - 5 ≠ m (2 -5)

m  ≠ 2

so the equation of 2nd line is given by:

y - 5 = 3(x-5)

=> 3x - y = 10

So the equation of sytem of liner equation are

L1 : 2x-y=5

L2 : 3x - y = 10

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The area of the floor in the scale drawing will be equal to 150 in².

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given information in the question,

Length of the classroom, l = 30 feet and,

The width of the classroom, w = 20 feet.

As per the scale drawing, the length of the classroom, l' = 15 feet

Let the scale width, w' = x feet

As we can see that the original length is twice the scale drawing.

Then, the original width also is twice the scale drawing.

So, w' = 20/2 = 10 feet.

Now, the area of the floor in the scale drawing will be,

A = wl

A = (15)(10)

A = 150 in².  

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Answer:

6566

Step-by-step explanation:

The answer is 6566.

Answer:

Step-by-step explanation:

I can't get to act correctly either.

The answer is 1 day and 7 items.

Ariana

y = 5x + 2

Julie

y = 7x

The ys have to be the same so equate the right hand side.

7x = 5x + 2                      Subtract 5x from both sides.

7x - 5x = 5x - 5x + 2

2x = 2                             Divide by 2

2x/2 = 2/2

x = 1

1 day

7 items

The depth of the well is 190 feet.

Given that Lisa raises her arm very high and drops a ball from a height of 6.0 feet. Her stopwatch measured a time of 3.5 seconds. And the polynomial equation that models this situation is -16t² + 0t + h, where h is the height from which the ball was dropped. So we need to find the value of h. Using the formula, h = -16t² + 0t + h Substituting the given values, we get h = -16 × 3.5² + 0 × 3.5 + 6h = -196 + 6h = -190 feet.

Therefore, the depth of the well is 190 feet.

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In this scenario, Tony is the one who comes out behind, and by $14. Tony's loss of $14 is smaller than Dave's loss of $20, making Tony the one who comes out behind by a smaller amount.

Tony initially purchases a hat for $14 and gives Dave a $20 bill. Since Dave doesn't have any change, he goes to Laura at Watson's Hardware store and exchanges the $20 bill for twenty $1 bills. Dave gives Tony $6 in change, which means Tony effectively paid $8 for the hat ($14 - $6).

However, it is later discovered that the $20 bill given to Laura by Dave was counterfeit. As a result, Dave compensates Laura by giving her a genuine $20 bill from the store's till. This means that Dave essentially lost $20 in the process.

So, in total, Tony ends up $14 behind because he paid $8 for the hat and received $6 in change, while Dave ends up $20 behind due to the counterfeit $20 bill. Tony's loss of $14 is smaller than Dave's loss of $20, making Tony the one who comes out behind by a smaller amount.

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To calculate the inclusion probability for unit 6 (PSU level) in the first stage of PPS without replacement, we need to divide the number of sampling units in the population by the total number of sampling units selected in the first stage.

Looking at the provided data, we can see that there are a total of 10 sampling units (Mi) in the dataset.

In PPS without replacement, the first sampling unit is selected with certainty. So, the inclusion probability for unit 6 (PSU level) is:

Inclusion probability = 1 / Total number of sampling units selected in the first stage

                    = 1 / 10

                    = 0.1

Therefore, the inclusion probability for unit 6 (PSU level) in the first stage of PPS without replacement is 0.1 or 10%.

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Answer:

x = 14

Step-by-step explanation:

Two angles a, b are complentary if a+b = 90.

Therefore, 4x + (2x+6) = 90

6x + 6 = 90

6x = 84

x = 84/6 = 14.

Answer:

x=14°

Step-by-step explanation:

Complementary angles are angles that add to 90°.

4x+2x+6=90

add like terms

6x+6=90

subtract 6 on both sides

6x=84

divide 6 on both sides

x=14

x is 14°.

Part a: The equation of the tangent line is: y - 5 = -15(x - 0)

Part b:The second derivative is a constant value, -15. Since the second derivative is negative, it means the function is concave down at (0, 5).

Part c:The particular solution is y = -10cos(x² + 3x + π) + 15(x² + 3x + π) - 5 - 15π

Part A: To find the equation of the line tangent to the solution curve at the point (0, 5), to follow these steps:

Step 1: Find the derivative of the given differential equation.

Given differential equation: dy/dx = 5(2x + 3)sin(x² + 3x + π)

Differentiate both sides with respect to x:

dy/dx = d/dx (5(2x + 3)sin(x²+ 3x + π))

dy/dx = 5 × (2(sin(x² + 3x + π)) + (2x + 3)cos(x² + 3x + π))

Step 2: Evaluate the derivative at the point (0, 5).

To find the slope of the tangent line at (0, 5), substitute x = 0 into the derivative:

dy/dx = 5 × (2(sin(π)) + (2×0 + 3)cos(π))

dy/dx = 5 × (2(0) + 3(-1)) = -15

Step 3: Use the point-slope form of the equation to write the equation of the tangent line.

The point-slope form of the equation is: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point (0, 5).

Simplifying, we get: y = -15x + 5

Part B: To find the second derivative at (0, 5) and determine the concavity of the solution curve at that point, follow these steps:

Step 1: Find the second derivative of the given differential equation.

Given differential equation: dy/dx = 5(2x + 3)sin(x² + 3x + π)

Differentiate the previous result for dy/dx with respect to x to get the second derivative:

d²y/dx² = d/dx (-15x + 5)

d²y/dx² = -15

Step 2: Determine the concavity.

Part C: To find the particular solution y = f(x) with the initial condition f(0) = 5,  to integrate the given differential equation:

dy/dx = 5(2x + 3)sin(x² + 3x + π)

Step 1: Integrate the equation with respect to x:

∫dy = ∫5(2x + 3)sin(x² + 3x + π) dx

y = ∫(10x + 15)sin(x² + 3x + π) dx

Step 2: Use u-substitution:

Let u = x² + 3x + π, then du = (2x + 3) dx

Now the integral becomes:

y = ∫(10x + 15)sin(u) du

Step 3: Integrate with respect to u:

y = -10cos(u) + 15u + C

Step 4: Substitute back for u:

y = -10cos(x² + 3x + π) + 15(x² + 3x + π) + C

Step 5: Apply the initial condition f(0) = 5:

Substitute x = 0 and y = 5 into the equation:

5 = -10cos(π) + 15(0² + 3(0) + π) + C

5 = 10 + 15π + C

Simplifying,

C = 5 - 10 - 15π

C = -5 - 15π

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The denominator 6 in 3/6 is should not be changed when adding fractions if other fractions have a denominator of 6, to make the addition easy because 6 will be the lowest common multiple.

One of the reasons why the denominator will always stay the same when adding fraction is because the size of the equal pieces does not change when you combine the two fractions together.

For example say you want to add 3/6 + 1/6 + 2/6,

you will notice that all the fractions have equal denominator, so adding the fractions together will have the following result.

3/6 + 1/6 + 2/6 = (3 + 1 + 2 ) / 6

= 6/6

= 1

So the 6 in 3/6 should not be changed if all other fractions you wish to add to 3/6 have 6 as their denominator, because the 6 is lowest common multiple.

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The solution to the limits (a) and (b) are 24 and 4 respectively.

Given

lim f(x)=8

lim g(x)=-2

lim h(x)=0

Using the properties of limits and basic arithmetic operations, we can find the limit of the following:

(a) \(\lim_{x \to \ 3} [2f(x) - 4g(x)]\)

We can apply the properties of limits to each term separately:

lim [2f(x)] - lim [4g(x)] as x approaches 3.

Using the given information:

2 * lim f(x) - 4 * lim g(x) as x approaches 3.

Substituting the known limits:

2 * 8 - 4 * (-2) = 16 + 8 = 24.

Therefore, lim [2f(x) - 4g(x)] as x approaches 3 is equal to 24.

(b) \(\lim_{n \to \ 3} [2g(x)^{2} ]\)

We can apply the property of limits to the entire expression:

[lim (2g(x))]² as x approaches 3.

Using the given information:

[lim g(x)]² as x approaches 3.

Substituting the known limit:

(-2)² = 4.

Therefore, lim [2g(x)]² as x approaches 3 is equal to 4.

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a. Present value of $400 per year for 14 years at 14%: $2,702.83
b. Present value of $200 per year for 7 years at 7%: $1,155.54
c. Present value of $400 per year for 7 years at 0%: $2,800
d. Present value of $400 per year for 14 years at 14% (annuity due): $2,943.07
  Present value of $200 per year for 7 years at 7% (annuity due): $1,233.24
  Present value of $400 per year for 7 years at 0% (annuity due): $2,800

To find the present values of the ordinary annuities, we can use the formula for the present value of an annuity:

PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present value
PMT = Payment per period
r = Interest rate per period
n = Number of periods

a. $400 per year for 14 years at 14%:
PV = $400 * [(1 - (1 + 0.14)^(-14)) / 0.14]

≈ $2,702.83

b. $200 per year for 7 years at 7%:
PV = $200 * [(1 - (1 + 0.07)^(-7)) / 0.07]

≈ $1,155.54

c. $400 per year for 7 years at 0%:
Since the interest rate is 0%, the present value is simply the total amount of payments over the 7 years:
PV = $400 * 7

= $2,800

d. Reworking previous parts assuming they are annuities due:
For annuities due, we need to adjust the formula by multiplying it by (1 + r):

a. Present value of $400 per year for 14 years at 14%:
PV = $400 * [(1 - (1 + 0.14)^(-14)) / 0.14] * (1 + 0.14)

≈ $2,943.07

b. Present value of $200 per year for 7 years at 7%:
PV = $200 * [(1 - (1 + 0.07)^(-7)) / 0.07] * (1 + 0.07)

≈ $1,233.24

c. Present value of $400 per year for 7 years at 0%:
Since the interest rate is 0%, the present value remains the same:
PV = $400 * 7

= $2,800

In conclusion:
a. Present value of $400 per year for 14 years at 14%: $2,702.83
b. Present value of $200 per year for 7 years at 7%: $1,155.54
c. Present value of $400 per year for 7 years at 0%: $2,800
d. Present value of $400 per year for 14 years at 14% (annuity due): $2,943.07
  Present value of $200 per year for 7 years at 7% (annuity due): $1,233.24
  Present value of $400 per year for 7 years at 0% (annuity due): $2,800

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The quotients of both are equal.