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2 years ago

Find the area of the shape shown below.

Mathematics

2 answers:

Elena-2011 [213]2 years ago

8 0

Answer:

31 1/2

Step-by-step explanation:

You find the area for the triangle on top and the rectangle on the bottom. In order to find the area of the triangle, multiply 7 and 3. Then divide the product which is 21 by 2. So the area of the triangle is 21/2 which could also be written as 10 1/2. Next, you find the area of the rectangle which is 7x3. You get 21. Finally, you add the two areas to get 31 1/2. It could also be written as 63/2 or 31.5

Liula [17]2 years ago

3 0

Answer:

31.5

Step-by-step explanation:

We can add the areas together

We have a rectangle and a triangle

The area of the rectangle is

A = lw

= 7*3

= 21

The area of the triangle is

A = 1/2 bh

= 1/2 (7)*3

= 21/2

= 10.5

Add them together

A = 21 + 10.5

=31.5

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A probability calculator is required on this problem; answer to six decimal places. Suppose we will spin the wheel pictured 400

KiRa [710]

Answer:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=400, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We need to check the conditions in order to use the normal approximation.

$np=400*0.2=80 \geq 10$

$n(1-p)=400*(1-0.2)=320 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=400*0.2=80$

$\sigma=\sqrt{np(1-p)}=\sqrt{400*0.2(1-0.2)}=8$

So then we can approximate the random variable as $X \sim N(\mu = 80, \sigma = 8)$

And we want this probability:

$P(90< X< 110)$

We can use the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

And replacing we got:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

8 0

2 years ago

What is the math paper lesson 68

lapo4ka [179]

Do u mean from the book or something?

3 0

1 year ago

Which ordered pairs in the form (x, y) are solutions to the equation 3x – 4y = 21? Choose all answers that are correct.

bekas [8.4K]

A. (−3, 3)
3x – 4y = 21
3(-3) - 4(3) = 21
-21 = 21 >>>>> not equal

B. (−1, −6)
3(-1) - 4(-6) = 21
21 = 21 >>>>>>>>>>Equal

C. (7, 0)
3(7) - 4(0) = 21
21 = 21>>>>>>>>>>equal

D. (11, 3)
3(11) - 4(3) = 21
21 = 21 >>>>>>>>>equal

5 0

1 year ago

Read 2 more answers

A triangle ABC is inscribed in a circle, such that AB is a diameter. What are the measures of angles of this triangle if: measur

shutvik [7]

Answer:

The measures of angles of this Δ are 23° , 67° , 90°

Step-by-step explanation:

* Lets talk about some facts in the circle

- An inscribed angle is an angle made from points sitting on the

circle's circumference

- A central angle is the angle formed when the vertex is at the center

of the circle

- The measure of an arc of a circle is equal to the measure of the

central angle that intercepts the arc.

- The measure of an inscribed angle is equal to 1/2 the measure of

its intercepted arc

- An angle inscribed across a circle's diameter is always a right angle

- The triangle is inscribed in a circle if their vertices lie on the

circumference of the circle, and their angles will be inscribed

angles in the circle

* Now lets solve the problem

- Δ ABC is inscribed in a circle

∵ its side AB is a diameter of the circle

∵ Its vertex C is on the circle

∴ ∠C is inscribed and across the circle's diameter

∴ ∠C is a right angle

∴ m∠C = 90°

∵ The measure of arc BC = 134°

∵ ∠A is inscribed angle subtended by arc BC

∵ The measure of an inscribed angle is equal to 1/2 the measure

of its intercepted arc

∴ m∠A = 1/2 × 134° = 67°

∵ The sum of the measures of the interior angles of a triangle is 180°

∵ m∠A = 67°

∵ m∠C = 67°

∵ m∠A + m∠B + m∠C = 180°

∴ 67° + m∠B + 90° = 180°

∴ 157° + m∠B = 180° ⇒ subtract 157 from both sides

∴ m∠B = 23°

* The measures of angles of this Δ are 23° , 67° , 90°

4 0

1 year ago

Leena walked 2/3 of a mile What is 2/3 written as a sum of unit fractions with the denominator of nine

aliya0001 [1]

Bear in mind that multiplying anything, and anything whatsoever by 1, has a product of the anything itself.

so, let's multiply 2/3 by 1 then and check about,

$\bf \cfrac{same}{same}=1\qquad thus\cfrac{2}{3}\cdot 1\implies \cfrac{2}{3}\cdot \cfrac{3}{3}\implies \cfrac{6}{9}
\\\\\\
\textit{now, we can split that and write it as a sum}\implies \cfrac{1+5}{9}\implies \cfrac{1}{9}+\cfrac{5}{9}$

3 0

2 years ago