A surveyor stands 200ft from a building and looks up to the top of the building. Her eyes are 426ft away from the top. To the nearest degree, what is the angle of elevation from surveyor (her eyes) to the too of the building?

The angle of elevation is ____ degrees.

The value of x from the venn diagram if P(T | V) = 1/5 is 16

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

The venn diagram

From the venn diagram, we have the following probability values

P(T | V) = (x - 4)/(3x + x - 4)

Evaluate the like terms

So, we have

P(T | V) = (x - 4)/(4x - 4)

From the question, we have

P(T | V) = 1/5

This means that

(x - 4)/(4x - 4) = 1/5

When evaluated, we have

x = 16

Hence, the value of x is 16

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Answer:

huh very good answers to be honest i would go with B

Step-by-step explanation:

The perimeter of the polygon in this problem is given as follows:

20 units.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The side lengths for the polygon in this problem are given as follows:

Hence the perimeter of the polygon is given as follows:

2 x (3 + 7) = 20 units.

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After 17 months, there will be approximately $970.25 in Fred Flintstone's account.

To calculate the amount in Fred Flintstone's account after 17 months, we can use the formula for the future value of an ordinary annuity. The formula is:

[tex]A = P \times [(1 + r)^n - 1] / r[/tex]

Where:

A stands for the annuity's projected value.

P = the monthly deposit amount

r is the annual percentage rate of interest.

n is the number of compounding periods in total.

In this case, Fred Flintstone deposits $50 every month (P = $50), the interest rate is 12% per year compounded monthly, which means the monthly interest rate is 12% / 12 = 1% or 0.01 (r = 0.01), and the total number of compounding periods is 17 (n = 17).

Now that these numbers have been substituted, we can determine the future value using the formula:

A = $50 × [tex][(1 + 0.01)^{17}- 1] / 0.01[/tex]

A = $50 ×[tex][1.01^{17} - 1] / 0.01[/tex]

Using a calculator or spreadsheet, we can evaluate 1.01^17 to be approximately 1.194051.

A = $50 × [1.194051 - 1] / 0.01

A = $50 × 0.194051 / 0.01

A ≈ $970.25

Therefore, after 17 months, there will be approximately $970.25 in Fred Flintstone's account.

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The probability that a single randomly selected value is less than 83.6 is 55.966%.

The probability that a sample of size n = 173 is randomly selected with a mean less than 83.6 is 97.725%.

Given that,

A population of values has a normal distribution with μ= 78.5 and σ= 33.5.

z score = (x - μ) / σ

To find the probability of P(X < 83.6),

z = (83.6 - 78.5) / 33.5

  = 0.152

Corresponding p value = 0.55966

P(X < 83.6) = 55.966%

To find the probability of P(M < 83.6),

n = 173

s = 33.5 / √173 = 2.547

z = (83.6 - 78.5) / 2.547

  = 2.0024

Corresponding p value = 0.97725

P(M < 83.6) = 97.725%

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The table is completed thus;

1.Volume  = 1/10 ft³

2. Length = 0. 5m

3. Volume  = 1 in³

4.Length = 10km

We need to know that the formula for calculating the volume of a rectangular prism is expressed as;

Volume = Length × width × height

From the information given, we have that;

1. Volume = 1/4 × 2/3 × 3/5

Multiply the values, we get;

Volume = 6/60 = 1/10 ft³

2. Substitute the values, we have;

0. 0005 = 0.1 × 0. 01 × l

Multiply the values

Length = 0. 0005/0. 001 = 0. 5m

3. Substitute the values, we have;

Volume = 4/3 × 3/4 × 1

Multiply the values, we have;

Volume = 12/12 = 1 in³

4. Substitute the values, we have;

9. 9 = 1.1  × L × 0.9

multiply the values

Length = 9.9/0. 99

Divide the values

Length = 10km

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The exact length of the arc formed by a central angle measuring 120° in a circle with a radius of 12.3 cm is 8.2π cm.

To calculate the exact length of an arc formed by a central angle measuring 120° in a circle with a radius of 12.3 cm, we can use the formula:

Arc Length = (Central Angle / 360°) * Circumference

First, let's calculate the circumference of the circle:

Circumference = 2 * π * radius

Substituting the given radius value into the formula, we get:

Circumference = 2 * π * 12.3 cm

Circumference = 24.6π cm

Now, let's calculate the arc length using the central angle of 120°:

Arc Length = (120° / 360°) * 24.6π cm

Arc Length = (1/3) * 24.6π cm

Arc Length = 8.2π cm

Therefore, the exact length of the arc formed by a central angle measuring 120° in a circle with a radius of 12.3 cm is 8.2π cm.

It's important to note that in this case, since the central angle is given in degrees, the result is expressed in terms of π. If you need a decimal approximation, you can calculate the numerical value using an appropriate approximation for π.

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Answer:

D. [tex]-sin^2x[/tex]

The length of YZ to the nearest tenth is 12.1.

We are given that;

(x1, y1) = (0, 5) (x2, y2) = (12, 3)

we need to use the distance formula, which is:

d = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging these values into the distance formula, we get

d = √((12 - 0)^2 + (3 - 5)^2)

d = √(144 + 4)

d = √(148) d ≈ 12.17

Therefore, by the distance the answer will be 12.1.

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Jorge would earn $1,800 in interest over the course of one year.

We can determine the interest generated in a year if Jorge deposits $30,000 in an account that offers 6% yearly interest.

Interest = Principal * Rate

Principal = $30,000

Rate = 6% (which can be expressed as 0.06)

Interest = $30,000 * 0.06

Interest = $1,800

Therefore, Jorge would earn $1,800 in interest over the course of one year.

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Answer:

the second option

Step-by-step explanation:

Answer:

DC = 53

Step-by-step explanation:

the midsegment EF is half the sum of the bases , that is

[tex]\frac{AB+DC}{2}[/tex] = EF

[tex]\frac{41+DC}{2}[/tex] = 47 ( multiply both sides by 2 to clear the fraction )

41 + DC = 94 ( subtract 41 from both sides )

DC = 53

Answer:

slope = - [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given the equation of the line is

y = - [tex]\frac{1}{3}[/tex] x + 3 ← in slope- intercept form

with slope m = - [tex]\frac{1}{3}[/tex]

If the value of sin x = 0.2, then the values for sin(π - x) is 0.2.

Given that,

the value of sin x = 0.2

We have to find the value of sin(π - x).

We know the trigonometric rule that,

sin(π - x) = sin (x)

for any value of x.

So here whatever the value of x, the value of  sin(π - x) is sin (x) itself.

So here sin x = 0.2.

So, by the rule,

sin(π - x) = sin (x) = 0.2

Hence the value is 0.2.

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Answer:

x is -1/b yw

Step-by-step explanation:

Answer:

105.5mm²

Step-by-step explanation:

There are a rectangle and two triangles.

Rectangle

6x13=78

Big Triangle

1/2x4x10.75=21.5

Small Triangle

1/2x3x4=6

78+21.5+6=105.5

Answer:

30

Step-by-step explanation:

To find the least common denominator (LCD) of 2/3 and 2/10, determine the smallest common multiple of the denominators.

The prime factorization of 3 is 3, and the prime factorization of 10 is 2 * 5.

To find the LCD, we take the highest power of each prime factor that appears in either denominator:

Therefore, the LCD is  2 * 3 * 5 = 30.

The expression "Twenty-two increased by the square of a number" in algebraic notation is 22 + x²

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

Twenty-two increased by the square of a number

Represent the number with x

So the statement can be rewritten as follows:

The square of a number means x²

So, we have the following

Twenty-two increased by x²

Twenty-two increased by 22 +

So, we have the following

22 + x²

Hence, the expression "Twenty-two increased by the square of a number" in algebraic notation is 22 + x²

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Answer:

17 + 19i

Step-by-step explanation:

i = √-1

(3 - 2i) (1 + 7i)

= 3(1) + 3(7i) - 1(2i) - (2X7)(i²)

= 3 + 21i - 2i - 14(√-1)²

= 3 + 19i - 14 (-1)

= 3 + 19i + 14

= 17 + 19i

Answer:

2(xy-7)=20

Step-by-step explanation:

looked it up ejejej

Answer:

x = -5

Step-by-step explanation:

Answer:

  x = -5

Step-by-step explanation:

You want the solution to the equation 2x -10 = 4x.

Subtracting 2x from both sides gives ...

  -10 = 2x

Dividing both sides by 2 gives ...

  -5 = x

The solution is x = -5.

__

Additional comment

When all of the coefficients have a common factor, sometimes we like to divide the equation by that factor. Here, all of the coefficients are even, so we can start by dividing the equation by 2:

  x -5 =2x

Now subtracting x gives the solution:

  -5 = x

It still takes 2 steps, so the approach you take will be the one you're most comfortable with.

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Answer:

To find the horizontal distance between Luke and the kite, we can use trigonometry. The horizontal distance is equal to the length of the string multiplied by the cosine of the angle. Let's calculate it:

Horizontal distance = 400 feet * cos(50°)

Using a calculator, we can find the cosine of 50 degrees to be approximately 0.6428. Multiplying this by 400 feet, we get:

Horizontal distance = 400 feet * 0.6428 ≈ 257.12 feet

Therefore, the horizontal distance between Luke and the kite is approximately 257.12 feet when rounded to the nearest hundredth.

Step-by-step explanation:

The normal distribution is solved and the retirement ages are normally distributed

P(x ≤ 62) ≈ 22.7%

P(x ≥ 70) ≈ 10.6%

P(55 ≤ x ≤ 60) ≈ 14.5%

P(60 ≤ x ≤ 70) ≈ 78.9%

Given data ,

To solve these probability questions, we can use the properties of the normal distribution. Let's calculate each probability:

a)

P(x ≤ 62):

To find this probability, we need to calculate the z-score corresponding to x = 62 and then find the area under the standard normal distribution curve to the left of that z-score. The formula to calculate the z-score is:

z = (x - mean) / standard deviation

In this case:

z = (62 - 65) / 4 = -0.75

Using a standard normal distribution table or a calculator, we can find that the area to the left of z = -0.75 is approximately 0.2266 or 22.7%

b)

P(x ≥ 70):

To find this probability, we need to calculate the z-score corresponding to x = 70 and then find the area under the standard normal distribution curve to the right of that z-score. Again, we use the z-score formula:

z = (x - mean) / standard deviation

In this case:

z = (70 - 65) / 4 = 1.25

Using a standard normal distribution table or a calculator, we can find that the area to the right of z = 1.25 is approximately 0.1056 or 10.6%

c)

P(55 ≤ x ≤ 60):

To find this probability, we need to calculate the z-scores corresponding to x = 55 and x = 60, and then find the area between those two z-scores under the standard normal distribution curve. Again, we use the z-score formula:

z = (x - mean) / standard deviation

For x = 55:

z1 = (55 - 65) / 4 = -2.5

For x = 60:

z2 = (60 - 65) / 4 = -1.25

Using a standard normal distribution table or a calculator, we can find that the area between z = -2.5 and z = -1.25 is approximately 0.1446 or 14.5%

d)

P(60 ≤ x ≤ 70):

To find this probability, we need to calculate the z-scores corresponding to x = 60 and x = 70, and then find the area between those two z-scores under the standard normal distribution curve.

Using the same z-score formula as above:

For x = 60:

z1 = (60 - 65) / 4 = -1.25

For x = 70:

z2 = (70 - 65) / 4 = 1.25

Using a standard normal distribution table or a calculator, we can find that the area between z = -1.25 and z = 1.25 is approximately 0.7887 or 78.9%

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The values for each probability are:

P(x ≤ 62) is approximately 22.7%.

P(x ≥ 70) is approximately 10.6%.

P(55 ≤ x ≤ 60) is approximately 9.9%.

P(60 ≤ x ≤ 70) is approximately 89.4%.

We have,

To solve these probability problems, we can use the standard normal distribution and Z-scores.

First, we need to convert the given values to Z-scores using the formula: Z = (X - μ) / σ, where X is the given value, μ is the mean, and σ is the standard deviation.

a)

P(x ≤ 62):

Z = (62 - 65) / 4 = -0.75

Using a standard normal distribution table or a calculator, we can find the corresponding area under the curve for a Z-score of -0.75.

This gives us a probability of approximately 0.2266.

To convert this probability to a percentage, we multiply by 100: 0.2266 * 100 ≈ 22.7%

b)

P(x ≥ 70):

To find the probability of x being greater than or equal to 70, we can use the complement rule: P(x ≥ 70) = 1 - P(x < 70)

Z = (70 - 65) / 4 = 1.25

Using a standard normal distribution table or a calculator, we can find the probability of a Z-score being less than 1.25, which is approximately 0.8944.

Now,

We can calculate P(x ≥ 70) = 1 - P(x < 70) = 1 - 0.8944 = 0.1056.

To convert this probability to a percentage, we multiply by 100: 0.1056 * 100 ≈ 10.6%

c)

P(55 ≤ x ≤ 60):

Z1 = (55 - 65) / 4 = -2.5

Z2 = (60 - 65) / 4 = -1.25

Using a standard normal distribution table or a calculator, we can find the probability of a Z-score being less than -1.25, which is approximately 0.1056.

Using the same method, we can find the probability of a Z-score being less than -2.5, which is approximately 0.0062.

Now, we can calculate the probability between -2.5 and -1.25 by subtracting the two probabilities:

P(-2.5 ≤ Z ≤ -1.25) = P(Z ≤ -1.25) - P(Z ≤ -2.5) = 0.1056 - 0.0062 = 0.0994.

To convert this probability to a percentage, we multiply by 100: 0.0994 x 100 ≈ 9.9%

d)

P(60 ≤ x ≤ 70):

Using the same Z-scores as in part c), we can find the probability of a Z-score being less than -1.25, which is approximately 0.1056.

Using the complement rule, we can find P(60 ≤ x ≤ 70) = 1 - P(x < 60) = 1 - 0.1056 = 0.8944.

To convert this probability to a percentage, we multiply by 100: 0.8944 * 100 ≈ 89.4%

Therefore,

P(x ≤ 62) is approximately 22.7%.

P(x ≥ 70) is approximately 10.6%.

P(55 ≤ x ≤ 60) is approximately 9.9%.

P(60 ≤ x ≤ 70) is approximately 89.4%.

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Answer:

solutions at first 1/2+2/3 take common of 2 and 3 and the common is 6 so 1×3+2×2÷6 ,=7/6 answer

Answer:

Eve is 46 and her son is 23

Step-by-step explanation:

let x be the son's age then Eve is 2x. the difference in their ages is 23 , so

2x - x = 23 , that is

x = 23

then

Eve = 2 × 23 = 46 years

son = 23 years

The interval width is 6, while the interval with the most values is 12 -18. There are 30 values in the dataset and the number of values that are 18 or greater is 12. The interval that the number 12 falls into is 12 - 18.

The interval width is gotten by dividing the range of values by the number of intervals.

This gives us: 30 - 0/5  = 6

So, the interval width is 6.

The interval that has the most values is 12 - 18. This is the point where we have the bars with the longest range.

The number of values in the dataset is 30 and this is the maximum number.

The interval where the number 12 will be included is 12 to 18.

The values that are 18 or higher are 12.

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A bond will pay income based on an interest rate while stock may give dividends to investors. Both interest income and dividends contribute to the return on an investment.

The return encompasses both interest income and dividends received by the investor. When investing in bonds, the income generated is in the form of interest payments which are typically fixed and predetermined based on the bond's coupon rate. The stocks provide the potential for dividends which are a portion of the company's profits distributed to shareholders.

Both interest income from bonds and dividends from stocks contribute to the overall return on the investment. We must note that the return on an investment can also be influenced by other factors such as capital gains or losses when buying or selling the asset.

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Rounding to the nearest tenth, the probability of selecting a divisor of 18 from the given cards is approximately 33.3%.

To find the probability of selecting a divisor of 18 from the given cards (2, 3, 4), we need to determine how many of those cards are divisors of 18 and divide it by the total number of cards.

Divisors of 18 are numbers that evenly divide 18 without leaving a remainder. The divisors of 18 are 1, 2, 3, 6, 9, and 18.

Out of the given cards (2, 3, 4), only the number 2 is a divisor of 18.

Since there is only 1 card out of the total 3 cards that is a divisor of 18, the probability (P) of selecting a divisor of 18 can be calculated as:

P = Number of favorable outcomes / Total number of possible outcomes

P = 1 / 3

To express the probability as a percentage, we multiply the probability by 100:

P = (1 / 3) * 100 = 33.3%

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The option that is equivalent to x is given as follows:

The number of ways to choose 5 letters from S without replacement.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

As the order is not important, the combination formula is used in this problem.

Hence the number of ways to choose 3 letters from a set of 8 is given as follows:

C(8,3) = 8!/(3! x (8-3)!) = 56.

The number of ways to choose 5 letters from the same equivalent is the same, as:

C(8,5) = 8!/(5! x (8 - 5)!) = 56.

Which gives the option equivalent to x.

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