aki ola In the figure below AB=24cm,BD=17cm,AD=13cm and ACD=90Degrees. find CD

Answer:

75

Step-by-step explanation:

300/4 = 75

Change of y/ change of x = gradient

The dimensions of the new pyramid is 8 times the original volume.

The area of the pyramid's base and its height are exactly proportional to its volume, hence the volume of any pyramid is equal to the area of the base times the height of the pyramid divided by three.

Knowing the formula of the pyramid is:

1/3 x a x b x h

If the dimensions are doubled, it will be :

1/3 x 2a x 2b x 2h

So:

v2= 1/3 x 2a x 2b x 2h

v2 = 1/3 x 8 x a x b x h

Hence, The new volume is 8 times more than the original.

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Answer:

[tex]\frac{62}{9}[/tex] or  6.8888889

Step-by-step explanation:

The explanation is on the attachment below

Answer:

2(9(5) + 5(3) + 9(3)) = 2(45 + 15 + 27) = 2(87) = 174 square inches

Boolean algebra is a type of algebra that deals with binary variables and logical operations. In this case, we're simplifying expressions using Boolean algebra.

1. ABC +(A+B+7)

First, let's simplify the expression in the parentheses:
A + B + 7 = 1 (since any input to a Boolean function that is not 0 is considered 1)
Now, let's substitute this value back into the original expression:
ABC + 1
This is the simplified expression.

2. (A+Ā)(AB+ ABC)

Using the identity A + Ā = 1, we can simplify the first set of parentheses:
(A + Ā)(AB + ABC) = AB + ABC

3. (B+BC)(B+ BC)(B+D)

Using the distributive property of Boolean algebra, we can simplify the first set of parentheses:
(B + BC)(B + BC)(B + D) = (B + BC)(B + D)
Using the distributive property again, we can simplify this further:
(B + BC)(B + D) = BB + BCD
Simplifying further, we know that B + BC = B and BB = B, so we can simplify to:
B + BCD

So, the simplified expressions are:
1. ABC + 1
2. AB + ABC
3. B + BCD

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Answer:

2nd and 4th

Step-by-step explanation:

In the second quadrant, the x-coordinate is negative and the y-coordinate is positive. If we let the x-coordinate be -a, then the y-coordinate will be a. Therefore, the point will have the form (-a, a), and the y-coordinate will be the opposite of the x-coordinate.

In the fourth quadrant, the x-coordinate is positive and the y-coordinate is negative. If we let the x-coordinate be a, then the y-coordinate will be -a. Therefore, the point will have the form (a, -a), and again, the y-coordinate will be the opposite of the x-coordinate.

The hexagon's apothem is approximately 13.856 inches long. The hexagon's perimeter is 96 inches. The hexagon has a surface area of approximately 665.088 square inches.

A hexagon is a six-sided polygon in geometry. The sum of any simple (non-self-intersecting) hexagon's internal angles is 720°.

Given that the length of a side is = 16 in

So half a side = 8 in

Using the Pythagorean theorem, calculate the area of the given right triangle.

Apothem = [tex]\sqrt{16^{2} - 8^{2} }[/tex]

= [tex]\sqrt{256 - 64}[/tex]

= √192

= 13.856 inches.

Now, we will calculate the perimeter of the hexagon. We have been given 6 sides of hexagon and each side length is 16 in, so

Perimeter = 16 × 6 = 96 inches

Area of hexagon = 1/2 × apothem × perimeter

= 1/2 × 13.856 × 96

= 665.088 inches

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Correct question:

Find the missing measures in this regular hexagon.

A regular hexagon has side lengths of 16 inches. The radius is 16 inches. An apothem is shown.

The length of the apothem of the hexagon is about ___inches.

The perimeter of the hexagon is ___ inches.

The area of the hexagon is about ___ square inches.

In order to find the probability of the intersection of two events, P(A ∩ B), we can use the formula: P(A ∩ B) = P(A) + P(B) - P(A ∪ B) Therefore, the correct answer is c. 0.2100.

In order to find the probability of the intersection of two events, P(A ∩ B), we can use the formula:

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

Given the probabilities P(A) = 0.62, P(B) = 0.47, and P(A ∪ B) = 0.88, we can plug these values into the formula:

P(A ∩ B) = 0.62 + 0.47 - 0.88

P(A ∩ B) = 1.09 - 0.88

P(A ∩ B) = 0.21

Therefore, the correct answer is option (c) 0.2100.

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In a direct proof, evidence is used to support a claim, On the other hand, a counterexamples is a single example that show the contradictions in a claim.

Evidence means any piece of information that supports the argument being made in a proof which could include mathematical formulas, logic, or theorems that have been previously proven.

Counterexamples are specific examples that disprove a statement made in a proof and are used to show that a proof is not valid and that the argument being made is flawed.

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The weight of the ice after 10 hours is 1217 lb

A 523 lb mass of ice melts at 4.3 hours

The first step is to calculate the weight after one hour

523= 4.3

x= 1

cross multiply both sides

4.3x= 523

x= 523/4.3

x= 121.7

The weight after 10 hours can be calculated as follows

121.7= 1

y= 10

y= 121.7 × 10

y= 1217

Hence the weight after 10 hours is 1217 lb

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The area of the parallelogram formed by the given vertices A(1, 0, -1), B(1, 7, 2), C(2, 4, -1), and D(0, 3, 2) is 2√21 square units.

To calculate the area of a parallelogram, we can use the cross product of two vectors formed by the sides of the parallelogram. The vectors AB and AD can be calculated by subtracting the coordinates of the initial and final points.

The cross product of these vectors gives us a vector representing the area of the parallelogram. Taking the magnitude of this vector gives us the area of the parallelogram. The magnitude of the cross product of AB and AD is 24, so the area of the parallelogram is 24 square units.

In this case, the vector AB is (-3, 7, 3), and the vector AD is (-1, 3, 3). Taking the cross product of these vectors gives us the vector (-12, 6, 24). The magnitude of this vector is √(12² + 6² + 24²) = √756 = 2√21. Therefore, the area of the parallelogram is 2√21 square units.

Complete Question:

Find the area of the parallelogram whose vertices are A(1, 0, −1), B(1, 7, 2), C(2, 4, −1), D(0, 3, 2).

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The longer leg of the triangle is 17✓3 yards based on the information of triangle and shorter leg length.

We will use law of sines relating an angle and it's opposite side -

sin shorter angle/shorter side = sin longer angle/longer side

The formula is as per the known fact that wide angle will have wider side opposite to it

Keep the values in formula -

sin 30/17 = sin 60/longer side

Longer side = 17 sin 60/sin 30

Substitute the values of sin 30 and sin 60

Longer side = (17 × ✓3/2)/(1/2)

Longer side = 17✓3 yards.

Thus, the longer leg of the right triangle is 17✓3 yards.

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The probability that in a given week the airline will lose less than 20 suitcases is approximately 0.8186 or 81.86%.

We are given that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with a mean of [tex]$\mu = 16.9$[/tex] and standard deviation of [tex]$\sigma = 3.3$[/tex]. We need to find the probability that in a given week the airline will lose less than 20 suitcases.

Let X be the number of suitcases lost in a week. Then we need to find P(X < 20).

Using the Z-score formula, we can standardize the variable X as:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

Substituting the given values, we get:

[tex]Z=\frac{20-16.9}{3.3}=0.91[/tex]

Now, we need to find the probability that Z is less than 0.91. We can use a standard normal distribution table or calculator to find this probability, which is approximately 0.8186.

Therefore, the probability that in a given week the airline will lose less than 20 suitcases is approximately 0.8186 or 81.86%.

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The value of the variable x is 24

To determine the value of the variable, it is important that we know;

From the information given, we have;

<NLM ≅ <NOP

We have the values;

NLM = x + 12

NOP = 20 + 16

Now, substitute the values

x + 12 = 20 + 16

add the values

x + 12 = 36

collect the like terms

x = 36 - 12

subtract the values

x = 24

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To answer your question about the inhomogeneous differential equation.

a) To guess a solution for the inhomogeneous equation f''(x) = e^x, we first observe that the right side of the equation is e^x. A function whose second derivative is e^x is a linear combination of e^x, x*e^x, and x^2*e^x. Therefore, we can guess the solution to be f(x) = A*x^2*e^x + B*x*e^x + C*e^x, where A, B, and C are constants to be determined.

b) To describe all solutions of the homogeneous equation f''(x) = 0, we can note that the second derivative of a linear function is zero. Therefore, the general solution of the homogeneous equation is f(x) = Ax + B, where A and B are constants.

c) To describe all solutions of the inhomogeneous equation f'''(x) = e^x, we combine the particular solution from part a) with the general solution from part b). This gives us the general solution for the inhomogeneous equation: f(x) = A_1*x^2*e^x + B_1*x*e^x + C_1*e^x + A_2*x + B_2, where A_1, B_1, C_1, A_2, and B_2 are constants.

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The Reinventing Government (REGO) approach to public administration and bureaucracy emphasizes a mission-driven approach to public service delivery, rather than a rule-driven approach. REGO advocates argue that this approach is beneficial to bureaucracies for several reasons.

Firstly, a mission-driven approach allows for improved budget management, as resources can be allocated more efficiently based on the organization's priorities and goals. This can lead to cost savings and better use of public funds.

Secondly, a mission-driven approach fosters greater employee creativity and flexibility. By focusing on the overarching objectives, employees have more freedom to innovate and develop new strategies to achieve those goals. This can lead to increased productivity and better outcomes for the public.

There may be certain types of agencies that are more open to adopting the REGO approach. Generally, agencies with a clear and well-defined mission, as well as those that can easily measure their performance, might be more receptive to the idea of a mission-driven approach. Additionally, agencies with a culture of innovation and adaptability might also be more inclined to embrace this approach.

In summary, the Reinventing Government approach aims to improve public service delivery by focusing on the mission of an organization. Its benefits include better budget management, increased employee creativity and flexibility, and overall improved outcomes for the public. The suitability of the REGO approach may vary depending on the agency's mission, performance measurement capabilities, and culture.

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5, instances of the number 5 will be stored in this 2D array. Option B.

To count the instances of the number 5 in the 2D array, we need to iterate through all the elements of the array and count the occurrences of 5.

Starting from the top-left element, we see that it is not a 5. Moving to the right, we find a 5 in the second column. Continuing to the right, we find another 5 in the same row. So far, we have counted 2 instances of 5.

Moving to the next row, we find no 5s in the first column. In the second column, we find two 5s in the same row. This brings our total count to 4. Moving to the last row, we find a single 5 in the second column, bringing our final count to 5.

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The account will be worth $39,847.15 in 40 years.

Given,

P = 8500 is the amount deposited

r = 0.039 is the decimal form of the 3.9% interest rate

n= 2 is the number of times the money is compounded per year

t = 40 is the number of years

We know that the amount  calculated semi-annually is:

[tex]A = 8500 (1 + \frac{0.039}{2})^{2*40}[/tex]

[tex]A = 8500( 1 + 0.0195)^{80}[/tex]

[tex]A = 8500 * 4.6875[/tex]

A = $39,847.15

As a result, The account will be worth $39,847.15 in 40 years.

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The correct answer is (a) $160.

The prediction equation, Spending = 60 + 5(Age of Consumer), suggests that there is a linear relationship between the age of a consumer and their spending. The equation can be interpreted as follows: for every additional year in age, the consumer's spending is expected to increase by $5, and the baseline spending for a consumer of any age is $60.

To find the model's prediction for spending when the consumer is 20 years old, we simply substitute 20 for Age of Consumer in the equation:

Spending = 60 + 5(20) = 60 + 100 = $160

Therefore, the correct answer is (a) $160.

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Farah's team runs a total of 3.2 kilometers in the relay race.

We have,

First, let's start with the number of laps each student runs:

2 laps per student x 4 students

= 8 laps in total

Next, let's convert the number of laps to the total distance:

8 laps x 400 meters per lap = 3200 meters

Finally, let's convert the distance from meters to kilometers:

3200 meters ÷ 1000 meters per kilometer

= 3.2 kilometers

Thus,

Farah's team runs a total of 3.2 kilometers in the relay race.

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The probability that both event will occur is 1/6

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 which is equivalent to 100%.

Probability = sample space/ total outcome

the probability that a coin will lands on head = 1/2 since a coin has two faces.

Also the probability that when a die is rolled , the probability of getting 5 or greater = 2/6, since die has 6 sides and 2 sides has 5 and greater.

Therefore the probability of getting both event = 1/2 × 2/6 = 1/6

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The expanded form of the series [tex]\sum_{n=6}^{13}(2)^{n -1}[/tex] is given by  (2⁵) + (2⁶) + (2⁷) + (2⁸) + (2⁹) + (2¹⁰) + (2¹¹) + (2¹²) and the sum of the given series is equal to 8160.

The series is equal to,

[tex]\sum_{n=6}^{13}(2)^{n -1}[/tex]

First expand the series by plugging in the values of n from 6 to 13,

= 2⁶⁻¹ + 2⁷⁻¹ + 2⁸⁻¹ + 2⁹⁻¹ + 2¹⁰⁻¹ + 2¹¹⁻¹ + 2¹²⁻¹ + 2¹³⁻¹

= (2⁵) + (2⁶) + (2⁷) + (2⁸) + (2⁹) + (2¹⁰) + (2¹¹) + (2¹²)

Now,  use the formula for the sum of a geometric series to find the sum of this series,

S = a(1 - rⁿ)/(1 - r)

Here, a is the first term of the series,

r is the common ratio which is equals to 2 ,

and n is the number of terms in the series = 8.

Using this formula,  find the sum of the series we have,

S = (2⁵)(1 - 2⁸)/(1 - 2)

  = 32( 1-256 ) / (-1)

  = 8160

Therefore, the expanded form of the series is equal to (2⁵) + (2⁶) + (2⁷) + (2⁸) + (2⁹) + (2¹⁰) + (2¹¹) + (2¹²) and the sum of the series is 8160.

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The above question is incomplete, the complete question is:

What are the expanded form and sum of the series

[tex]\sum_{n=6}^{13}(2)^{n -1}[/tex]

A quadrilateral is a shape with four sides: The indicated measures are A = 56, B = 128, C = 100 and D = 76.

The indicated measures:

The angles in a quadrilateral add up to 360 degrees.

So, we have:

4n + 5n + 6 + 9n + 2 + 8n - 12 = 360

Collect like terms

4n + 5n + 9n + 8n = 360 - 6 - 2 + 12

Evaluate the like terms

26n = 364

Divide through by 26

n = 14

From the figure, we have:

A = 4n

B = 9n + 2

C = 8n - 12

D = 5n + 6

So, we have:

A = 4 * 14 = 56

B = 9*14 + 2 = 128

C = 8*14 - 12 = 100

D = 5*14 + 6 = 76

Hence, the indicated measures are

A = 56, B = 128, C = 100 and D = 76

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Correct Question:

A window is the shape of a quadrilateral. Find the indicated measure

Answer:

16 science problems

26 math problems

Step-by-step explanation:

m = number of math problems

s = number of science problems

m = s + 10

m + s = 42

(s + 10) + s = 42

2s + 10 = 42

2s = 42 - 10 = 32

s = 32/2 = 16

m = s + 10 = 16 + 10 = 26

Where the logistic growth function is f( t) = 116000/(1+5200e⁻t)

a) 22 people were initially affected

b) after 4 weeks the numbers increased to 1,205 approximately

c) the limiting size of the population that becomes ill is 116,000.

The logistic equation (also known as the Verhulst model or logistic growth curve) is a population growth model developed by Pierre Verhulst (1845, 1847).

a) since when the epidemic began, the initial number of infection will always be zero, thus:

f( t) = 116000/(1+5200e⁻t )

Note that e is the mathematical constant known as Euler's number or the natural base. e = 2.71828

f(0) = 116000/(1+5200e⁻0 )

f(0) = 116000/(1+5200 (2.71828)⁻0 )

f(0) = 116000/(1+5200 (1) )

f(0) = 116000/(1+5200 )

f(0) = 116000/(5201 )

f(0) = 22.3034031917

f (0) [tex]\approx[/tex] 22

B) by the fourth week,

the expression became f(4) = 116000/(1+5200e⁻4 )

f (4) = 116000 /(1+5200 (e)⁻4 )
f (4) = 1205.30347384
f (4)  [tex]\approx[/tex] 1205

C)

Since the logistic curve is given as....

f(t) = 116000/(1+5200e⁻t )

as t becomes smaller and smaller nearing 0, the denominator will be almost 1

So
f(t) = 116000/(1+5200e⁻ ∞ )

f(t) = 116000/(1+0 )

f(t) = 116,000

As you can see, the limit to the size of the population that can fall ill is 116,000 peple.

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Sam lives in either a small house or a yellow house.

Mutually exclusive:

Maya chooses either red or yellow when taking one crayon from a set of 16.

Raymond draws a 2 or a 3 when taking a single card from a deck.

Hannah gets either heads or tails when she flips a coin.

Not mutually exclusive:

Sally wears a blue shirt or blue pants.

Jack either goes to his friend's house or does his homework.

Sam lives in either a small house or a yellow house.

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The equation of the ellipse is

Calculate the distance between the foci (2c):

2c = |8 - (-2)| = 10

c = 5

Determine the length of the semi-major axis (a):

a = 26 / 2 = 13

Solving for the center of the ellipse, denoted by (h, k):

h = (5 + 5)/2 = 5

k = (8 + -2)/2 = 3

hence, center of the ellipse is (5, 3).

solving for the length of the semi-minor axis denoted by (b):

a^2 = b^2 + c^2

knowing that the values of parameter a and c, so we can solve for b:

13^2 = b^2 + 5^2

169 = b^2 + 25

b^2 = 144

b = 12

equation of the ellipse:

((x - h)^2) / b^2 + ((y - k)^2) / a^2 = 1

Plugging in the values:

((x - 5)^2) / 12^2 + ((y - 3)^2) / 13^2 = 1

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a) The value of circumference of circle is,

C  = 219.8 Inches

b) The value of area of circle is,

A = 3,846.5 in²

Given that;

The diameter of circle is, 70 inches

a) Circumference of circle is,

C = π × diameter,

So, We get;

C = 3.14 × 70

C  = 219.8 Inches

b) The area of circle is,

A = πr²,

And, Radius is 1/2 of diameter,

Hence, Radius = 70/2 = 35 inches

Thus, We get;

A =  3.14 × 35²

A = 3.14 × 1225,

A = 3,846.5 in²

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we conclude that the helicopter will land in a finite amount of time if and only if p <= 0.

The differential equation dh/dt = [tex]-h^{p}[/tex], where h is the height of the helicopter, represents the rate of change of the height with respect to time. To find the value of p that results in predictions that the helicopter will land in a finite amount of time, we need to consider the behavior of the solution as h approaches zero.

If we assume that the helicopter will eventually land, then the height h will approach zero as time goes to infinity. Therefore, we can consider the behavior of the solution near the origin. To do this, we will use a technique called separation of variables.

Separation of variables involves writing the differential equation in the form dh/[tex]h^{p}[/tex] = -dt and then integrating both sides. This gives:

∫h_[tex]0^{h}[/tex] dh / [tex]h^{p}[/tex] = ∫0^t -dt

where h_0 is the initial height of the helicopter.

The left-hand side can be evaluated using the power rule of integration:

[tex][1/(1-p)] [h^{(1-p)}]_h_0^{h} = -t[/tex]

where [f(x)]_aᵇ denotes the value of f(x) evaluated at b minus the value of f(x) evaluated at a.

We can simplify this expression by using the fact that h_0 is nonzero, so h^(1-p)_0 approaches infinity as h approaches zero. Therefore, we can neglect the term h^(1-p)_0 and write:

[tex][1/(1-p)] h^{(1-p)} = -t[/tex]

If p > 1, then h^(1-p) approaches zero as h approaches zero. Therefore, the left-hand side of the equation approaches infinity as t approaches a finite value. This implies that the helicopter will never land, which contradicts our assumption that it will eventually land. Therefore, we must have p <= 1.

If p = 1, then the left-hand side of the equation becomes ln(h), which approaches negative infinity as h approaches zero. Therefore, the equation cannot hold for any finite value of t. This implies that the helicopter will not land in a finite amount of time.

If p < 1, then the left-hand side of the equation approaches infinity as h approaches zero. Therefore, the equation cannot hold for any finite value of t. This implies that the helicopter will not land in a finite amount of time.

Therefore, we conclude that the helicopter will land in a finite amount of time if and only if p <= 0.

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The standard error of the mean is 1.16. At 95% confidence, the margin of error is 2.27.

(a) The standard error of the mean, σx, can be calculated using the formula:
σx = σ/√n
where σ is the population standard deviation, and n is the sample size.
Substituting the given values, we get:
σx = [tex]\frac{9}{ \sqrt{60} }[/tex]
σx = 1.16
Therefore, the standard error of the mean is 1.16.

(b) To find the margin of error, we need to use the formula:
The margin of error = z(σx)
where z is the z-score corresponding to the level of confidence. For 95% confidence, the z-score is 1.96 (using a standard normal distribution table).
Substituting the values we get:
Margin of error = 1.96(1.16)
Margin of error = 2.27

Therefore, at 95% confidence, the margin of error is 2.27. This means that we can be 95% confident that the true population means falls within 2.27 units of the sample mean of 25.

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