You are standing 190 meters away from the base of a building. The angle of elevation to the top of the
building is 25°. What is the height of the building?

Answer:

P(A and B) = P(A)P(B)

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

= about .17 = about 17%

Investment B is an ordinary  subvention with$ 3,906.64 in the account after one time. The correct answer is option d.    

To determine which investment is an ordinary  subvention and the  unborn value after one time, we first need to understand that an ordinary  subvention is a series of equal payments made at the end of each period.

Given the table, we can see that Investment A has payments starting in January and ends in November( missing December), while Investment B starts in February and ends in December.

thus, Investment B is the ordinary  subvention since the payments are made at the end of each month.  Now let's calculate the  unborn value of Investment B after one time  

1. Convert the periodic interest rate to a yearly rate( 10.035)(1/12)- 1 ≈0.002867

2. Determine the number of payments made 11 months  3. Use the  unborn value of  subvention formula FV =  P *(( 1 r) n- 1)/ r  

Where P =  yearly payment($ 350),

r =  yearly interest rate(0.002867), and n =  number of payments( 11) . Plug in the values

FV =  350 *(( 10.002867) 11- 1)/0.002867 ≈3906.64  

So, Investment B is an ordinary  subvention with$ 3,906.64 in the account after one time. The correct answer is optiond.

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Step 1: Add Equation 2 and Equation 3 to eliminate z.

(-x + y - z) + (x - 3y) = -1 + 3

y - 4y = 2

-3y = 2

y = -2/3

Step 2: Substitute the value of y (-2/3) into Equation 3 to find the value of x.

x - 3(-2/3) = 3

x + 2 = 3

x = 1

Step 3: Substitute the values of x and y into Equation 1 to find the value of z.

3(1) - 8(-2/3) + z = 8

3 + 16/3 + z = 8

9/3 + 16/3 + z = 8

25/3 + z = 8

z = 8 - 25/3

z = 24/3 - 25/3

z = -1/3

Therefore, the solution to the system of equations is:

x = 1

y = -2/3

z = -1/3

The x intercepts of the parabola with  vertex (-1,2) and y intercept (0,3) does not exist

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

vertex (-1,2) and y intercept (0,3).

A parabola is represented as

y = a(x - h)² + k

Where

Vertex = (h, k)

Using the above as a guide, we have the following:

y = a(x + 1)² + 2

Also, we have

a(0 + 1)² + 2 = 3

So, we have

a = 1

This means that

y = (x + 1)² + 2

Set to 0 to calculate the x-intercepts

(x + 1)² + 2 = 0

This gives

(x + 1)² = -2

Take the square root

(x + 1) = comple numbers

Hence, the x intercepts of the parabola does not exist

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The equation of the line with yellow point in slope intercept form is y = 7 / 6 x + 2.

The equation of a straight line can be represented in different form such as slope intercept form, point slope form, etc.

Therefore, let's represent the line with yellow point in slope intercept form.

Hence,

y = mx + b

where

Therefore, using (0, 2) and (6, 9).

m = 9 - 2 / 6 - 0

m = 7 / 6

Hence, let's find the y-intercept

y = 7 / 6 x + b

2 = 7 / 6(0) + b

b = 2

Therefore,

y = 7 / 6 x + 2.

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The height of the skyscraper is D. 156.26 ft

To determine the height of the skyscraper,  we need to consider the following trigonometric identities listed thus;

From the information given, we have that;

Angle, θ = 38 degrees

The shadow casted is the adjacent side of the angle and is 200 ft

The height off the skyscraper is the opposite side

Now, using the tangent identity, we have that;

tan θ = opposite/adjacent

tan 38 = h/200

cross multiply the values, we get;

h = 200(0.7812)

Multiply the values

h = 156. 26 ft

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Answer:

side AC

Step-by-step explanation:

is the opposite angle B because it is the furthest you can get on the triangle to be away from point B.

Little's prediction for the second tests median score  is 84

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

The dot plot

The median is the middle number on the dot plot

From the dot plot, the middle number is

Middle = 70

This means that

Median = 70

For the new prediction, we have

New median = 70 * (1 + 20%)

Evaluate

New median = 84

Hence, Little's prediction for the second tests median score  is 84

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Answer:

Solving the system of equations.

Point form: (3+√25,−3+√2),(3−√25,−3−√2)

Equation form:

x=3+√25,y=−3+√2x=3−√25,y=−3−√2

Step-by-step explanation:

Answer:

7/2

Step-by-step explanation:

7 x 4 / 8

= 7 x 1/2

= (7 x 1)/2

= 7/2

Note

1. When you see a fraction, first simplify the numerator and denominator.

That is,

In 4/8,

4 is the numerator

8 is the denominator

4/8 = 1/2

2. Multiply number with numerator, then divide it with the denominator

7 x 1/2

7 x 1 = 7

(7 x 1)/2 = 7/2

The required answer is mAD = 126°

Step 1: Recall Inscribed Angles of a Circle Theorem.

Step 2: It means m∠ABD ≡ m∠ACD. So, it can be written:

(11x - 3)° (8x + 15)°

Step 3: Evaluate for x:

11x - 3 = 8x + 15

X = 6

Step 4: Substitute x = 6 in 11x - 3 as:

11(6) - 3

Step 5: Evaluate for answer:

11 × 6 - 3

= 63

Step 6: Now recall Measure of an Inscribed Angle:

m∠ABD = ¹/₂ MAD

Step 7: Substitute m∠ABD = 63 in above equation:

63 = ½ mAD

Step 8: Evaluate for answer:

63 = ¹/₂ AD

AD = 126

Step 9

Thus, the required answer is:

MAD = 126°

Solution

The required answer is:

mAD = 126°

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The entries of the first row is 3,6. Option B

To add the entries of the first row in the two matrices, we need to first identify the first row of each matrix and then add the corresponding entries together.

Matrix A:

[1  4]

[7  1]

Matrix B:

[2  2]

[4  3]

To add the first rows of these matrices, we simply add the corresponding entries:

1+2      4+2

2          6

Hence, the entries of the first of the two matrices is 2,6

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The measure of angle BC is 27 degrees.

To find the measure of angle BC, we need to use the angle sum property of triangles. In triangle ABC, the sum of all angles is equal to 180 degrees. We know that angle ACD is a straight angle and therefore measures 180 - 45 = 135 degrees.

Additionally, we know that angle ADB is also a straight angle and therefore measures 180 - 18 = 162 degrees.

To find angle BCD, we subtract the measure of angle ACD from the measure of angle ADB, which gives us:

m BCD = m ADB - m ACD
m BCD = 162 - 135
m BCD = 27 degrees

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The 6 drawings are grouped to one another

Given data ,

Let the 6 drawings into be divided into two groups of 3 drawings each

And , drawings of each group is similar to one another in some way

where Group 1: ABD

On simplifying the equation , we get

Their curves and the points are in a same order

Group 2: CEF

On simplifying the equation , we get

Their curves and points are oppositely drawn

Hence , the drawings are solved

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The complete question is attached below :

Group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together.

(a) The probability that exactly 4 orders will arrive in 30 minutes is 0.1127

(b) The probability that at least 2 orders will arrive in an hour is 0.7586.

(a)  We need to adjust λ to reflect the 30-minute time interval:

λ = 5 orders per hour * 0.5 hours = 2.5 orders in 30 minutes

Now we can plug in the numbers and calculate the probability:

P(X = 4) = ([tex]e^{2.5}[/tex]) *) [tex]2.5^{4}[/tex]/ 4! = 0.1127

(b) We can use the Poisson probability formula again, with λ = 5 orders per hour and x = 0 or 1:

P(X < 2) = P(X = 0) + P(X = 1) = 0.0404 + 0.2010 = 0.2414

Then we can subtract this from 1 to get the probability that at least 2 orders will arrive in an hour:

P(X ≥ 2) = 1 - P(X < 2) = 1 - 0.2414 = 0.7586

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The value of the expression is determined as 14.

The value of the expression is calculated as follows;

We will apply the principle known as BODMAS;

B - bracket

O - Off

D - division

M - multiplication

A - addition

S - subtraction

The given expression; = (27 · 3  -  1719 ÷ 1719) ÷ 8 + 5² - 3³  + (8 · 4  -  2·13)

We will simplify the expression as follows;

(27 · 3  -  1719 ÷ 1719) = (81  -  1719/1719) = (81 - 1) = 80

(8 · 4  -  2·13) = (32  -  26) = 6

= 80 ÷ 8 + 5² - 3³  + 6

= (80/8) +  5² - 3³  + 6

= 10 +  5² - 3³  + 6

= (10 + 5² + 6) - 3³

= 41 - 27

= 14

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Answer:

5.52 million people with blood group O in KwaZulu-Natal.

Step-by-step explanation:

Multiple alleles refer to the existence of more than two possible alleles (or variations) of a gene within a population. In the case of blood groups, there are multiple alleles for the gene that controls blood type, resulting in the four possible blood groups: A, AB, B, and O.

The blood group AB is the least common in the human population, with only 3% of people having this blood type.

To calculate the number of people who will have blood group O in KwaZulu-Natal, we need to multiply the total population by the percentage of people with blood group O.

9.2 million x (60/100) = 5.52 million people with blood group O in KwaZulu-Natal.

Answer:

----------------------

AB and AC are perpendicular since AB is tangent to circle at point A.

BC is the hypotenuse of ΔABC and it length is:

Find the length of AB using Pythagorean theorem:

The right Riemann sum is an overestimate.

The left Riemann sum is an underestimate.

For n=2, the interval [0,1] is divided into 2 subintervals of equal width, so Δx = (1-0)/2 = 1/2.

Left Riemann Sum with n=2:

The left endpoints of the subintervals are x=0 and x=1/2.

f(0) = e⁰ = 1

f(1/2) = [tex]e^1^/^2[/tex]

So, the left Riemann sum is:

Δx[f(0) + f(1/2)] = (1/2)[1 +[tex]e^1^/^2[/tex]] = (1/2) + (1/2)[tex]e^1^/^2[/tex]

sum = (1/2) + (1/2)[tex]e^1^/^2[/tex]

Right Riemann Sum with n=2:

The right endpoints of the subintervals are x=1/2 and x=1.

f(1/2) = [tex]e^1^/^2[/tex]

f(1) = e¹ = e

So, the right Riemann sum is:

Δx[f(1/2) + f(1)] = (1/2)[[tex]e^1^/^2[/tex] + e] = (1/2)[tex]e^1^/^2[/tex] + (1/2)e

sum = (1/2)[tex]e^1^/^2[/tex]+ (1/2)e

Since [tex]e^1^/^2[/tex] > 1, the right Riemann sum is an overestimate, and the left Riemann sum is an underestimate.

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Answer:

6 cm³

Step-by-step explanation:

The figure is a triangular prism with a triangular base with side lengths 3 cm, 4 cm, 5 cm. The height of the prism is 1 cm.

The sides measuring 3 cm and 4 cm form a right angle.

V = BH

where B = area of the base, and

H = height of the prism.

The base is a triangle, so B = (1/2)bh,

where b = base of the triangle, and

h = height of the triangle

V = (1/2)bhH

V = (1/2)(3 cm)(4 cm)(1 cm)

V = 6 cm³

The SinL as a fraction in the simplest form is 12/13.

We are given

The side NM = 5,

The side LM = 12,

By using Pythagoras' theorem, we can say that;

NL² = NM² + LM²

Substitute the values of NM and LM;

NL² = 12² + 5²

NL = 13,

For Sin L = perpendicular side/hypotenuse side

Sin L = NM / NL,

Sin L = 12/13

Therefore, the SinL as a fraction in the simplest form is 12/13

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Answer: 30,620 people

Step-by-step explanation:

We will use the given formula for exponential growth.

➜ 1.55% / 100 = 0.0155

➜ 2022 - 2017 = 5 years

          [tex]A=Pe^{rt}[/tex]

          [tex]A=(28,337\;people)e^{(0.0155)(5\;years)}[/tex]

          [tex]A=(28,337\;people)e^{0.0775}[/tex]

          [tex]A=(28,337\;people)e^{0.0775}[/tex]

          [tex]A=30,620.4587 \approx 30,620\;people[/tex]

Answer:

23/100 equals 23%.

Answer: 23%

Step-by-step explanation: When doing these problems, remember, 100 and a 100% are the same thing, so when you have a problem like this, divide 25 by 100, then multiply by a 100.

The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.

Let x be the hotel charge before tax in the first city, and y be the hotel charge before tax in the second city. Then we have:
y = x + 1500   (the hotel charge before tax in the second city was $1500 higher than in the first)
0.075x + 0.05y = 825   (the total hotel tax paid for the two cities was $825)
We can use the first equation to solve for y in terms of x:
y = x + 1500
Then we can substitute this expression for y into the second equation:
0.075x + 0.05(x + 1500) = 825
Simplifying this equation, we get:
0.075x + 0.05x + 75 = 825
0.125x = 750
x = 6000
So the hotel charge before tax in the first city was $6000. Using the first equation, we can find the hotel charge before tax in the second city:
y = x + 1500
y = 6000 + 1500
y = 7500
So the hotel charge before tax in the second city was $7500.
Therefore, the answer is: The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.

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The distance from point B to point A is given as follows:

15,893 ft

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For each angle, we have that:

Hence the position A is obtained as follows:

tan(16º) = 7200/a

a = 7200/tangent of 16 degrees

a = 25109 ft.

The position B is obtained as follows:

tan(38º) = 7200/b

b = 7200/tangent of 38 degrees

b = 9216 ft.

Hence the distance is of:

25109 - 9216 = 15,893 ft.

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Answer:

To express the expression 2/5 - 4/y + 3 as a single fraction, we need to find a common denominator for the fractions involved.

The common denominator for 5 and y is 5y.

First, we'll rewrite 2/5 as an equivalent fraction with the denominator 5y:

2/5 = (2 * y)/(5 * y) = 2y/5y

Next, we'll rewrite 4/y as an equivalent fraction with the denominator 5y:

4/y = (4 * 5)/(y * 5) = 20/5y

Now, we can rewrite the expression with the common denominator 5y:

2y/5y - 20/5y + 3

Since the denominators are now the same, we can combine the numerators:

(2y - 20 + 3 * 5y)/(5y)

Simplifying further:

(2y - 20 + 15y)/(5y) = (17y - 20)/(5y)

The function equation for the graph above include the following: B. f(x) = -[x] + 3.

In Mathematics and Geometry, a greatest integer function can be defined as a type of function which returns the greatest integer that is less than or equal (≤) to the number.

Mathematically, the greatest integer that is less than or equal (≤) to a number (x) is represented as follows:

y = [x].

By critically observing the given graph, we can logically deduce that the parent function was reflected over the y-axis (negative slope) and it was vertically translated from the origin by 3 units up;

y = [x]

f(x) = -[x] + 3.

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Answer:131

Step-by-step explanation:

Use BEDMAS

9x(7+7)+5

=9 x 14 + 5

= 126 + 5

= 131

Answer:

400π m3

Step-by-step explanation:

V = πr^2h

V = π(5^2)(16)

V = π(25)(16)

V = 400π