In ΔXYZ, y = 53 inches, z = 55 inches and ∠X=120°. Find the length of x, to the nearest inch.

aivan3 [116]

Okay so uh i think it’s this: 15% of 60=0.15* 60=9
9 is what percent of 180 i think..?
9/180=1/20=5/100=5%

7 0

3 years ago

After an extensive advertising campaign, the manager of a company expects the proportion of potential customers that recognize a

lina2011 [118]

Answer:

Step-by-step explanation:

Hello!

The study variable is:

X: number of customers that recognize a new product out of 120.

There are two possible recordable outcomes for this variable, the customer can either "recognize the new product" or " don't recognize the new product". The number of trials is fixed, assuming that each customer is independent of the others and the probability of success is the same for all customers, p= 0.6, then we can say this variable has a binomial distribution.

The sample proportion obtained is:

p'= 54/120= 0.45

Considering that the sample size is large enough (n≥30) you can apply the Central Limit Theorem and approximate the distribution of the sample proportion to normal: p' ≈ N(p; $\sqrt{\frac{p(1-p)}{n} }$ )

The other conditions for this approximation are also met: (n*p)≥5 and (n*q)≥5

The probability of getting the calculated sample proportion, or lower is:

P(X≤0.45)= P(Z≤ $\frac{0.45-0.6}{\sqrt{\frac{0.6*0.4}{120} } }$ )= P(Z≤-3.35)= 0.000

This type of problem is for the sample proportion.

I hope this helps!

5 0

3 years ago

A rope of length 18 feet is arranged in the shape of a sector of a circle with central angle O radians, as shown in the

creativ13 [48]

Answer:

$A(\theta)=\frac{162 \theta}{(\theta+2)^2}$

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Let

r ---> the radius of the sector

s ---> the arc length of sector

Find the radius r

we know that

$2r+s=18$

$s=r \theta$

$2r+r \theta=18$

solve for r

$r=\frac{18}{2+\theta}$

step 2

Find the value of s

$s=r \theta$

substitute the value of r

$s=\frac{18}{2+\theta}\theta$

step 3

we know that

The area of complete circle is equal to

$A=\pi r^{2}$

The complete circle subtends a central angle of 2π radians

so

using proportion find the area of the sector by a central angle of angle theta

Let

A ---> the area of sector with central angle theta

$\frac{\pi r^{2} }{2\pi}=\frac{A}{\theta} \\\\A=\frac{r^2\theta}{2}$

substitute the value of r

$A=\frac{(\frac{18}{2+\theta})^2\theta}{2}$

$A=\frac{162 \theta}{(\theta+2)^2}$

Convert to function notation

$A(\theta)=\frac{162 \theta}{(\theta+2)^2}$

6 0

4 years ago

Factor 5v^2 - 23v - 10

AfilCa [17]

Answer:

$(5v + 2)(v - 5)$

Step-by-step explanation:

Hello!

The expression is written in the form of $ax^2 + bx + c$

Let's factor by grouping:

$ac = -50$

The sum of the factors of -50 should add up to -23.

-25 and 2 work for this.

Expand and factor:

$5v^2 - 23v - 10$
$5v^2 - 25v + 2v - 10$
$5v(v - 5) +2(v -5 )$
$(5v + 2)(v - 5)$

The factored expression is $(5v + 2)(v - 5)$

7 0

2 years ago

A triangle with the coordinates (6,4), (2,-1), and (-3,5) is translated 4 Units left and rotate 180 degrees about the origin. Wh

ankoles [38]

Answer:

(-2,-4),(2,1), and (7,-5)

Step-by-step explanation:

The given triangle has coordinates (6,4), (2,-1), and (-3,5).

When we translate 4 units left, the we obtain:

(6,4)------>(6-4,4)=(2,4)

(2,-1)----->(2-4,-1)=(-2,-1)

(-3,5)----->(-3-4,5)=(-7,5)

When the resulting figure is rotated 180° about the origin, the coordinates of the final figure becomes

(2,4)------>(-2,-4)

(-2,-1)----->(2,1)

(-7,5)------->(7,-5)

NB: The mapping for 180° rotation is:

(x,y)----->(-x,-y)

8 0

3 years ago