The tatue i 4. 6 meter high. The angle of elevation from the oppoite corner of the courtyard to the top of the tatue i 8

Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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Answer: 25 Plays Total.

60% of 25 is 15

10% of 25 = 2.5

2.5x6=15

Hope This Helps.

The Geometric Mean between the pair of numbers 8 and 12 is 4√6   .

Geometric Mean between the numbers x and y is calculated using the formula ,

GM = √(x * y),

where GM represents the Geometric Mean

In the question ,

it is given that ,

the pair of numbers are 8 and 12 .

we need to find the geometric mean between them ,

By using the Geometric Mean formula from above ,

we get ,

GM = √(8 × 12)

GM = √96

GM = 4√6

Therefore , The Geometric Mean between the pair of numbers 8 and 12 is   4√6  .

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Answer:

Step-by-step explanation:

Volume of the figure = Base area * height

Base area:

Base area = area of trpezium + area of triangle

Trapezium:

a, b area the length of parallel sides and h is the height of trapezium.

a = 8 m ; b =  5 m & h = 3 m

\(\boxed{ \text{ Area of trapezium = $\dfrac{(a +b)*h}{2} $}}\)

                               \(=\dfrac{(8+5)*3}{2}\\\\\\=\dfrac{13*3}{2}\\\\\\= \dfrac{39}{2}\\\\\\= 19.5 \ m^{2}\)

Triangle:

height = 4 m & base = 8 m

\(\boxed{\text{Area of triangle =$\dfrac{1}{2}*base*height$}}\)

                           \(=\dfrac{1}{2}*8*4\\\\\\= 4*4\\\\= 16 \ m^{2}\)

Base area = 19.5 + 16

                 = 35.5 m²

Volume of the figure = Base area * height

                                     = 35.5 * 14

                                      = 497 m³

The solution of system of equations is (6,-2) or (0,6)

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

(6,-2) and (0,6)

The given line graph has coordinates (6,-2) and (0,6)

The given table of values contain the same points (6,-2) and (0,6)

So, the solution of system of equations is (6,-2) or (0,6)

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Answer:

1. 13578 hours

2. 2.07264 m

3. 68038.856 grams

4. 129600 seconds

5. 46,300 Meters

Step-by-step explanation:

Don't forget me to mark me as brainliest ☺

Answer:

1. 13578 hours

2. 2.07264 m

3. 68038.856 grams

4. 129600 seconds

5. 46,300 Meters

Step-by-step explanation:

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Answer:

18.75 feet

Step-by-step explanation:

Answer:

it is .8333333333 and more 3's forever

Step-by-step explanation:

Answer:1/2

Step-by-step explanation:

Answer:

B.(x-3)(x+8)

Step-by-step explanation:

product of -3 and 8 is -24 and sum of -3+8 is +5

Answer:

(x+8) (x-3)

Step-by-step explanation:

x² + 5x – 24

What 2 numbers multiply to -24 and add to 5

8*-3 = -24

8+-3 = 5

(x+8) (x-3)

Taylor series is \(f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }\)

To find the Taylor series for f(x) = ln(x) centering at 9, we need to observe the pattern for the first four derivatives of f(x). From there, we can create a general equation for f(n). Starting with f(x), we have

f(x) = ln(x)

\(f^{1}(x)= \frac{1}{x} \\f^{2}(x)= -\frac{1}{x^{2} }\\f^{3}(x)= -\frac{2}{x^{3} }\\f^{4}(x)= \frac{-6}{x^{4} }\)

.

.

.

Since we need to have it centered at 9, we must take the value of f(9), and so on.

f(9) = ln(9)

\(f^{1}(9)= \frac{1}{9} \\f^{2}(9)= -\frac{1}{9^{2} }\\f^{3}(x)= -\frac{1(2)}{9^{3} }\\f^{4}(x)= \frac{-1(2)(3)}{9^{4} }\)

.

.

.

Following the pattern, we can see that for \(f^{n}(x)\),

\(f^{n}(x)=(-1)^{n-1}\frac{1.2.3.4.5...........(n-1)}{9^{n} } \\f^{n}(x)=(-1)^{n-1}\frac{(n-1)!}{9^{n}}\)

This applies for n ≥ 1, Expressing f(x) in summation, we have

\(\sum_{n=0}^{\infinite} \frac{f^{n}(9) }{n!} (x-9)^{2}\)

Combining ln2 with the rest of series, we have

\(f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }\)

Taylor series is \(f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }\)

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Answer: 29,692.5 gallons of water

Step-by-step explanation: first i multiplied 7.5 and 107 and got 802.5 and since it wanted to know about 37 days i multiplied 802.5 by 37 and got 29,692.5

The given statement is 1. Always true

2. Always true

3. Always true

4. Sometimes true

5. Never true

Statement 1: A line and a point are always coplanar.

Answer: Always true.

Reason: This statement is always true because a line and a point can always be found on the same plane. In Euclidean geometry, a plane is a flat surface that extends infinitely in all directions, and any two points on the plane can be connected by a straight line. Therefore, a line and a point will always lie on the same plane.

Statement 2: Congruent angles form vertical angles.

Answer: Always true.

Reason: Vertical angles are formed by the intersection of two lines. When two angles are congruent, it means they have the same measure. If two angles have the same measure and are formed by the intersection of two lines, then they are vertical angles. Therefore, congruent angles always form vertical angles.

Statement 3: Linear pairs that are congruent are right angles.

Answer: Always true.

Reason: A linear pair consists of two adjacent angles that share a common side and form a straight line. If the two angles of a linear pair are congruent, it means they have the same measure. In Euclidean geometry, a straight angle measures 180 degrees. If two angles in a linear pair are congruent and their measures add up to 180 degrees, then each angle must measure 90 degrees, which is the measure of a right angle. Therefore, linear pairs that are congruent are always right angles.

Statement 4: The sum of angles that form a linear pair is less than 180 degrees.

Answer: Sometimes true.

Reason: The sum of angles that form a linear pair is always equal to 180 degrees, not less than 180 degrees. This is based on the definition of a linear pair, which states that the two angles in a linear pair are supplementary, meaning their measures add up to 180 degrees. However, if the statement said "less than or equal to 180 degrees," then it would be always true.

Statement 5: Vertical angles are complementary.

Answer: Never true.

Reason: Vertical angles are not complementary. Complementary angles are two angles that add up to 90 degrees. Vertical angles, on the other hand, are a pair of non-adjacent angles formed by the intersection of two lines. They do not necessarily have any specific relationship to each other in terms of their angle measures. Therefore, vertical angles are not complementary by definition.

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The truth of each statement depends on the properties of angles and theorems that support them. A line and a point are always coplanar, congruent angles can sometimes form vertical angles, congruent linear pairs are not always right angles, the sum of angles that form a linear pair is always 180 degrees, and vertical angles are never complementary.

To determine the truth of each statement, we need to consider the properties of angles and theorems that support them.

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The answers are a) H0: μ = 40, b) small sample size, c) t ≈ 2.402, d) the p-value for a two-tailed test with 12 degrees of freedom and a t-statistic of 2.402 is approximately 0.032 and e) we can conclude that the mean height of treated Begonias is significantly different from that reported in the journal.

(a) The null hypothesis states that the population mean height of treated Begonias, μ, is equal to the mean height reported in the journal, which is 40 centimeters.

H0: μ = 40

(b) Since the population standard deviation is unknown, we can use a t-test statistic for a small sample size.

(c) The test statistic for a two-sample t-test is calculated using the formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

In this case:

sample mean = 48

hypothesized mean = 40

sample standard deviation = 11

sample size = 13

t = (48 - 40) / (11 / √(13))

t ≈ 2.402

(d) To find the p-value, we need to compare the test statistic to the t-distribution with (n - 1) degrees of freedom, where n is the sample size.

In this case, we have 13 - 1 = 12 degrees of freedom.

Using a t-table, we find that the p-value for a two-tailed test with 12 degrees of freedom and a t-statistic of 2.402 is approximately 0.032.

(e) Since the p-value (0.032) is less than the significance level of 0.05, we reject the null hypothesis.

Therefore, we can conclude that the mean height of treated Begonias is significantly different from that reported in the journal.

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Based on Gru's schemes the probability that a. less than 101 schemes will succeed: 0.9983; b. more than 95 schemes will succeed: 0.0018; c. between 95 and 101 schemes will succeed: 0.9966.

Gru's schemes have a 7% chance of succeeding. Total number of Gru's schemes = 1100.

Using binomial distribution, we can find out the probability of number of successes in n number of trials.

Probability of success in each trial p = 0.07

Probability of failure in each trial q = 1 - 0.07 = 0.93

a) Probability that less than 101 schemes will succeed.

Total number of trials n = 1100

P(X < 101) = P(X ≤ 100)

P(X ≤ 100) = ∑P(X = x) for x = 0, 1, 2, ..., 100

Now we can use normal distribution to approximate this probability as the sample size is large enough to apply central limit theorem. So,

mean (μ) = np = 1100 × 0.07 = 77

standard deviation (σ) = √[npq] = √[1100 × 0.07 × 0.93] = 7.233

Using standard normal distribution,

Z = (X - μ) / σ

Z = (100 + 0.5 - 77) / 7.233 = 2.99

So, P(X ≤ 100) = P(Z ≤ 2.99)

From standard normal distribution table,

P(Z ≤ 2.99) = 0.9983

Therefore, P(X < 101) = P(X ≤ 100) = 0.9983

b) Probability that more than 95 schemes will succeed.

P(X > 95) = P(X ≥ 96)

P(X ≥ 96) = ∑P(X = x) for x = 96, 97, ..., 1100

Now we can use normal distribution to approximate this probability as the sample size is large enough to apply central limit theorem. So,

mean (μ) = np = 1100 × 0.07 = 77

standard deviation (σ) = √[npq] = √[1100 × 0.07 × 0.93] = 7.233

Using standard normal distribution,

Z = (X - μ) / σ

Z = (96 - 0.5 - 77) / 7.233 = 2.91

So,

P(X ≥ 96) = P(Z ≥ 2.91)

From standard normal distribution table,

P(Z ≥ 2.91) = 0.0018

Therefore, P(X > 95) = P(X ≥ 96) = 0.0018

c) Probability that between 95 and 101 schemes will succeed.

P(95 ≤ X ≤ 101) = P(X ≤ 101) - P(X < 95)

P(X < 95) is already calculated in (a).

P(X ≤ 101) = 0.9983

Therefore,

P(95 ≤ X ≤ 101) = P(X ≤ 101) - P(X < 95) = 0.9983 - 0.0017 = 0.9966

Hence, the probability that less than 101 schemes will succeed is 0.9983. The probability that more than 95 schemes will succeed is 0.0018. The probability that between 95 and 101 schemes will succeed is 0.9966.

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Answer:

equation: y = 24x

Step-by-step explanation:

if y and x is proportional,

y = kx

72 = k * 3

k = 24

→ Here the constant if 24

so the equation that relates x and y :

y = 24x

i attached a pdf, hopefully it helps you understand!

Answer:

x=13/33 and y=12/33

Step-by-step explanation:

x=13/33 and y=12/33

Answer:

Com o aumento da população no início da Baixa Idade Média, muitas pessoas saíram do campo para viver nas cidades. Quais trabalhos eles passaram desempenhar?

Step-by-step explanation:

The probability that the next chew Henry removes will be cherry or watermelon, expressed as a fraction in simplest form, is 8/11.

The number of times a cherry chew was selected is 20, and the number of times a watermelon chew was selected is also 20. Therefore, the total number of times either cherry or watermelon chew was selected is 20 + 20 = 40.

Thus, the probability that the next chew Henry removes will be cherry or watermelon can be expressed as a fraction: 40/55.

However, we can simplify this fraction. Both 40 and 55 are divisible by 5, so we can divide both the numerator and denominator by 5:

= 40 / 55

= 8 / 11

Therefore, the probability that the next chew Henry removes will be cherry or watermelon, expressed as a fraction in simplest form, is 8/11.

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Answer:

48 centimeters

Step-by-step explanation:

This deals with the midline theorem.

The midline is defined by a seg that is joined by the midpoints of 2 sides.

The midline is half of the base, so if it is 10, the base is 20 cm.

You see that 26 cm is 1/2 of the hypotenuse because it is bisected, sot he whole thing is 26(2) or 52.

Now you have to solve for x using the Pythagorean theorem.

20^2 (400) + x^2  = 52^2 (2704)

Subtracted 400 from both sides to get x^2 by itself.

x^2 = 2304

Take the square root of both sides to isolate x (take the principle root)

x= 48 centimeters.

Hope this helps!

Answer:

translation

Step-by-step explanation:

because a reflection across the x-axis is not right, and neither is across the y-axis. The triangle was also not rotated 90 degrees. It was translated 8 units to the right and 4 units up.

the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done.

A force applied across a distance is what is referred to as work.

In this problem,

the force applied is the weight of the cable (5 lb/ft) multiplied by the length of the cable (100 ft).

Therefore, the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done.Work is a force applied across a distance, and it is measured in a unit of energy called foot-pounds. In this problem, the force applied is the weight of the cable (5 lb/ft) multiplied by the length of the cable (100 ft). Therefore, the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done. This means that 500 ft-lb of energy must be expended in order to move the cable 100 ft. This energy can be provided by a variety of sources, such as human labor, a motor, or some other mechanism.

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Answer:

don't understand....................

Answer:

A

Step-by-step explanation:

Answer:johns my fraind

Step-by-step explanation:

Answer:

C. 3×(h-6)

Step-by-step explanation:

Sana makatulong

Answer:

Stanley needs 31 feet and 2 inches of fencing.

Step-by-step explanation:

In order to answer this problem, you need to find the perimeter of the dog run.

Since: \(P=2(l+w)\)

and \(l=149\) inches & \(w=56\) inches

Plug in what we know :

\(P=2(149+56)\)

and solve:

\(P=410\) inches

The dog run has a perimeter of 410 inches.

However, now we need to subtract 36 inches since the gate doesn't need fencing.

\(410-36=374\) inches.

The dog run needs 374 inches of fencing.

In order to find out how many feet of fencing that is, divide it by 12.

\(\frac{374}{12}\) = 31.16666667 OR \(31\frac{2}{12}\), meaning 31 feet and 2 inches.

Answer:

31 feet and 2 inches of fencing :))<3

Step-by-step explanation:

Number of hours does it take for the temperature to change by -4. 4°C is 5.5 hours

To solve this problem, we can use the formula for finding the change in temperature

Change in temperature = rate of change × time

where the rate of change is -0.8°C per hour and the change in temperature we want to find is -4.4°C. So, we can plug in these values and solve for time

-4.4°C = (-0.8°C / hour) × time

Dividing both sides by -0.8°C / hour, we get

time = 5.5 hours

Therefore, it will take 5.5 hours for the temperature to change by -4.4°C.

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