1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sonbull [250]
3 years ago
15

The figure below shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced:

Mathematics
1 answer:
rodikova [14]3 years ago
6 0

Answer:

The question has missing figure, the figure is in the attachment.

The length of wood needed to replace AD is 5.01\ in.

Step-by-step explanation:

Given;

ABC is a triangle in which AB is of 12 inches in length.

∠DCB = 30°        ∠ACD = 15°

Solution,

In ΔABC,  BC=12 in

∠ACB = ∠DCB +  ∠ACD = 30\°+15\°=45\°

tan∠ACB =\frac{AB}{BC}

tan45\°=\frac{AB}{BC}\\ 1=\frac{AB}{12} \\AB=12\ in

Now in ΔDCB,

∠DCB = 30° and  BC=12 in

tan∠DCB =\frac{DB}{BC}

tan30\°=\frac{DB}{12}\\\frac{1}{\sqrt{3} } =\frac{DB}{12} \\DB=\frac{12}{\sqrt{3} } =\frac{12\times\sqrt{3} }{3}=4\sqrt{3}

DB = 4\times1.732=6.928\ in

Length of AD = Length of AB - Length of DB

Length of AD= 12-6.928=5.072\approx5.01\ in

Thus  the length of wood needed to replace AD is 5.01\ in.

You might be interested in
Suppose that a large number of samples are taken from a population. Which of the following sample sizes will be most likely to r
Montano1993 [528]

If you use a large enough statistical sample size, you can apply the Central Limit Theorem (CLT) to a sample proportion for categorical data to find its sampling distribution. The population proportion, p, is the proportion of individuals in the population who have a certain characteristic of interest (for example, the proportion of all Americans who are registered voters, or the proportion of all teenagers who own cellphones). The sample proportion, denoted

6 0
3 years ago
Read 2 more answers
Consider a discrete random variable x with pmf px (1) = c 3 ; px (2) = c 6 ; px (5) = c 3 and 0 otherwise, where c is a positive
PtichkaEL [24]
Looks like the PMF is supposed to be

\mathbb P(X=x)=\begin{cases}\dfrac c3&\text{for }x\in\{1,5\}\\\\\dfrac c6&\text{for }x=2\\\\0&\text{otherwise}\end{cases}

which is kinda weird, but it's not entirely clear what you meant...

Anyway, assuming the PMF above, for this to be a valid PMF, we need the probabilities of all events to sum to 1:

\displaystyle\sum_{x\in\{1,2,5\}}\mathbb P(X=x)=\dfrac c3+\dfrac c6+\dfrac c3=\dfrac{5c}6=1\implies c=\dfrac65

Next,

\mathbb P(X>2)=\mathbb P(X=5)=\dfrac c3=\dfrac25

\mathbb E(X)=\displaystyle\sum_{x\in\{1,2,5\}}x\,\mathbb P(X=x)=\dfrac c3+\dfrac{2c}6+\dfrac{5c}3=\dfrac{7c}3=\dfrac{14}5

\mathbb V(X)=\mathbb E\bigg((X-\mathbb E(X))^2\bigg)=\mathbb E(X^2)-\mathbb E(X)^2
\mathbb E(X^2)=\displaystyle\sum_{x\in\{1,2,5\}}x^2\,\mathbb P(X=x)=\dfrac c3+\dfrac{4c}6+\dfrac{25c}3=\dfrac{28c}3=\dfrac{56}5
\implies\mathbb V(X)=\dfrac{56}5-\left(\dfrac{14}5\right)^2=\dfrac{84}{25}

If Y=X^2+1, then X^2=Y-1\implies X=\sqrt{Y-1}, where we take the positive root because we know X can only take on positive values, namely 1, 2, and 5. Correspondingly, we know that Y can take on the values 1^2+1=2, 2^2+1=5, and 5^2+1=26. At these values of Y, we would have the same probability as we did for the respective value of X. That is,

\mathbb P(Y=y)=\begin{cases}\dfrac c3&\text{for }y=2\\\\\dfrac c6&\text{for }y=5\\\\\dfrac c3&\text{for }y=26\\\\0&\text{otherwise}\end{cases}

Part (5) is incomplete, so I'll stop here.
8 0
3 years ago
What is the distance between -10 and 5 on the number line?
stiks02 [169]

Answer:

the distance is 15

Step-by-step explanation:

because if we take away the negative on the -10 and make it positive 10 and add 5 it would be 15 spaces

8 0
3 years ago
= 1/2 (u+v)t
RoseWind [281]

The distance travelled by an object is 50 m.

<h3>What is Distance?</h3>

The distance between two points is the length of the path connecting them.

Here, given equation of distance

         S = 1/2 (u + v)t

Where s is the distance traveled by an object (in meters)

initial velocity u (in m/s)

final velocity v (in m/s).

t in seconds.

Now, given values are;

u = 8 m/s ;  v = 12 m/s ;   t = 5 sec.

    S = 1/2 (8 + 12)5

    S = 1/2 (20)5

    S = 100/2

    S = 50 m.

Thus, the distance travelled by an object is 50 m.

Learn more about Distance from:

brainly.com/question/15172156

#SPJ1

5 0
2 years ago
Solve −4(x + 10) − 6 = −3(x − 2).<br> a −40<br> b −46<br> c −52<br> d 52
12345 [234]
The answer is C. -52.
6 0
3 years ago
Read 2 more answers
Other questions:
  • Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel.
    12·2 answers
  • Josephine has a rectangular garden with an area of 2x2 + x – 6 square feet
    5·2 answers
  • | k-9 | &gt; -4 <br><br><br> just need help.
    8·2 answers
  • boxes of sticky finger popsicles are 4.50 . The supermarket is offering 30% coupon off coupon . what is the price with the coupo
    14·2 answers
  • There are 25 students acting in a high school play. They make up 2% of the high school students. Hoy many students attend at the
    15·2 answers
  • All I need is the answer if right will be marked THE BRAINLIEST
    14·1 answer
  • one room length 12.8 and breadth equals to 850 CM inside that room there is a bad length is 300 cm and breadth is 400 cm find th
    5·1 answer
  • The triangular face of the given prism has an interior angle with a measure of 55° and an exterior angle with a measure of 95°.
    7·2 answers
  • What value of x makes this equation true?<br><br> 6x - 3 = 5x - 5
    13·1 answer
  • If you use mobile payment and lose your phone, you should NOT:
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!