Can someone help me find X for number 4

A radio tower has a 64 ft Shadow cast by the sun. If the angle from the tip of the shadow to the top of the tower is 78.5°. what

Softa [21]

Step-by-step explanation:

right-angled triangle, and law of sine (for any type of triangles) :

a/sin(A) = b/sin(B) = c/sin(C)

where the sides and the correlated angles are always opposite from each other.

and we know that the sum of all angles in a triangle is always 180°.

so, the angle at the foot of the radio tower is 90°.

the angle from the top of the shadow to the top of the tower is 78.5°.

so, the third angle (at the top of the tower) is

180 - 90 - 78.5 = 11.5°

and with the law of sine we get

height/sin(78.5) = 64/sin(11.5)

height = 64×sin(78.5)/sin(11.5) = 314.57005... ft

6 0

2 years ago

Ben is making salsa.He needs 1/3 cups of chilies for each bach of salsa.Ben has 5/6 cup green chilies.How many baches of salsa c

FromTheMoon [43]

Answer:

The number of batches Ben can make with 5/6 cup of green chilies is $2\frac{1}{2}$ batches of salsa.

Step-by-step explanation:

From the question,

Ben needs 1/3 cups of chilies for a batch of salsa.

To determine how many batches of salsa he can make with 5/6 cup of green chilies,

Let the number of batches Ben can make with 5/6 cup of green chilies be x.

Now,

If 1/3 cups of green chilies is needed for 1 batch,

Then, 5/6 cups of green chilies will make x batches

1/3 × x = 5/6 × 1

x = 5/6 ÷ 1/3

x = $\frac{5}{6} \div \frac{1}{3}$

x = $\frac{5}{6} \times \frac{3}{1}$

x = $\frac{15}{6}$

x = $\frac{5}{2}$

x = $2\frac{1}{2}$

Hence, the number of batches Ben can make with 5/6 cup of green chilies is $2\frac{1}{2}$ batches of salsa.

5 0

3 years ago

Is 2.82842712475 a rational number

Galina-37 [17]

No---------------------------------

7 0

3 years ago

Let x represent the amount of frozen yogurt (in hundreds of gallons) sold by the G&T restaurant on any day during the summer

musickatia [10]

Answer:

a) The probability of selling less than 100 gallons (x≤1) is P=0.16.

b) The mean number of gallons is M=80 gallons.

Step-by-step explanation:

The probability of selling x, in hundred of gallons, on any day during the summer is y(x)=0.32x, in a range for x from [0;2.5].

The probability of selling less than 100 gallons (x≤1) is then:

$P(x\leq1)=\int_0^{100}0.32x\cdot dx\\\\P(x\leq1)=0.16(x_b^2-x_a^2)\\\\P(x\leq1)=0.16(1^2-0^2)=0.16$

The mean number of gallons can be calculated as:

$M=\int_0^{2.5}(y(x)/x)\cdot dx=\int_0^{2.5}(0.32)\cdot dx\\\\M=0.32(x_b-x_a)=0.32(2.5-0)=0.32*2.5=0.8$

3 0

3 years ago

An urn contains 3 red and 7 black balls. Players A and B take turns (A goes first) withdrawing balls from the urn consecutively.

andrey2020 [161]

Answer:

The probability that A selects the first red ball is 0.5833.

Step-by-step explanation:

Given : An urn contains 3 red and 7 black balls. Players A and B take turns (A goes first) withdrawing balls from the urn consecutively.

To find : What is the probability that A selects the first red ball?

Solution :

A wins if the first red ball is drawn 1st,3rd,5th or 7th.

A red ball drawn first, there are $E(1)= ^9C_2$ places in which the other 2 red balls can be placed.

A red ball drawn third, there are $E(3)= ^7C_2$ places in which the other 2 red balls can be placed.

A red ball drawn fifth, there are $E(5)= ^5C_2$ places in which the other 2 red balls can be placed.

A red ball drawn seventh, there are $E(7)= ^3C_2$ places in which the other 2 red balls can be placed.

The total number of total event is $S= ^{10}C_3$

The probability that A selects the first red ball is

$P(A \text{wins})=\frac{(^9C_2)+(^7C_2)+(^5C_2)+(^3C_2)}{^{10}C_3}$

$P(A \text{wins})=\frac{36+21+10+3}{120}$

$P(A \text{wins})=\frac{70}{120}$

$P(A \text{wins})=0.5833$

6 0

3 years ago