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2 years ago

Why is ac smaller than ad if they both look very close

Mathematics

1 answer:

kakasveta [241]2 years ago

8 0

Let's begin by listing out the information given to us:

We start out by observing that Triangles MKR & ACD are similar or proportional

$\begin{gathered} MK=21;AC=\text{?} \\ MR=24;AD=28\frac{4}{5} \\ KR=CD=\text{?} \end{gathered}$

We will solve for the missing side by using the similar triangle theorem. This is shown below:~

$\begin{gathered} \Delta MKR\approx\Delta ACD \\ \frac{MK}{AC}=\frac{MR}{AD} \\ \frac{21}{AC}=\frac{24}{28\frac{4}{5}} \\ \text{Cross multiply, we have:} \\ 24\cdot AC=28\frac{4}{5}\cdot21 \\ AC=\frac{28\frac{4}{5}\cdot21}{24}=25\frac{1}{5} \\ AC=25\frac{1}{5} \end{gathered}$

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From a point on the ground 12 ft. from the base of a flagpole, the angle of elevation of the top of the pole measures 53°. How t

torisob [31]

Answer:

4.75 feet

Step-by-step explanation:

Let the height of the flagpole be x

Sin 53 = x/12

x = 12 × Sin 53

x = 12 × 0.3959

x = 4.75 feet

5 0

3 years ago

If a pair of regular dice are tossed once, use the expectation formula to determine the expected sum of the numbers on the upwar

Darya [45]

Answer:

The expected sum of the numbers on the upward faces of the two dice is 7.

Step-by-step explanation:

Consider the provided information.

If two pair of dice tossed the possible out comes are:

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6,6)

Now we need to find the expected sum of the numbers on the upward faces of the two dice.

The expected sums can be:

Sum: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Prob: 1/36, 2/36, 3/36, 4/36, 5/36, 6/36, 5/36, 4/36, 3/36, 2/36, 1/36

As we know that the expectation of experiment can be calculated as:

$P(S_1)\cdot S_1+P(S_2)\cdot S_2+........+P(S_n)\cdot S_n$

Here S represents the numerical outcomes and P(S) is the respective probability.

Substitute the respective values in the above formula.

$=2\times\frac{1}{36}+3\times\frac{2}{36}+4\times\frac{3}{36}+5\times\frac{4}{36}+6\times\frac{5}{36}+7\times\frac{6}{36}+8\times\frac{5}{36}+9\times\frac{4}{36}+10\times\frac{3}{36}+11\times\frac{2}{36}+12\times\frac{1}{36}\\=\frac{252}{36}\\=7$

Hence, the expected sum of the numbers on the upward faces of the two dice is 7.

8 0

4 years ago

I need help with number 9.<br> simple algebra.

Veseljchak [2.6K]

Answer:

C 1099

Step-by-step explanation:

The volume of a cylinder is given by

V = pi * r^2 *h

We know the radius is 5 and the height is 14

Substitute in what we know

V = 3.14 * 5^2 *14

V = 3.14 *25*14

V =1099 in^3

4 0

4 years ago

To ride an amusement park ride, your height must be at or above the line on the sign. For each set of information, write an inte

Rainbow [258]

Answer:

3ft tall yes 2ft and 12inches no

Step-by-step explanation:

hope this helps

7 0

3 years ago

The cost of renting a table at the flea market is based on a fixed price per day plus an initial registration fee. If it costs $

Simora [160]

Answer:

c = 15d + 30

Step-by-step explanation:

Hey there!

This can be represented by an equation of a line, where the number of days is our x-values(d), and the price is our y-values(c).

The price for one day ($45) and the price for 4 days($90) are specific points on that line.

The points are (1, 45) and (4, 90).

We can first find the slope of the line:

As the price rises 45, the days increase by 3
Slope = rise/run
Slope = 45/3
Slope = 15

Now we can find the base price, by plugging the slope and a point into the equation y = mx + b.

Solve for b:

y = mx + b
45 = 15(1) + b
45 = 15 + b
30 = b

The base price (b) is 30.

The equation is $\text{\boxed{c = 15d + 30}}$

6 0

2 years ago