The sum of two consecutive integers is 99. Find the value of the smaller integer. (Show work)

A small theater sold 72 tickets for a play. The ratio of adult tickets to child tickets was 4:1. The ratio of adult tickets to s

Y_Kistochka [10]

Answer:

Adult 36

Children 9

senior 27

Step-by-step explanation:

We have 3 types of tickets as seen from the question;

Adult, children and seniors tickets.

Now, looking at the question critically,

Since the ratio of adults to children and senior citizens stands at 4: a specific value, we can then conclude that the ratio of tickets sold is 4:1:3

where 1 and 3 represents the ratio for the children and seniors respectively

So let’s calculate the individual ratio now.

For the total, we have 4 + 1 + 3 = 8

Thus, for the adults, we have 4/8 * 72 = 36

For the children, we have 1/8 * 72 = 9

For the seniors, we have 3/8 * 72 = 27

3 0

3 years ago

Mark rolls 2 fair dice and adds the results from each.

Natali5045456 [20]

Answer:

P ( X > 5 ) = 72,2 %

Step-by-step explanation:

The probability of success ( outcomes bigger than 5 )

If dice 1 outcome is 6 no matter wich outcome we get from dice 2 all events are successful, the we have 6 outcomes

If dice 1 outcome is 5 we also have 6 outcomes

If dice 1 outcomes is 4 we have 5 positive outcomes

If dice 1 outcome is 3 we have 4 positive outcomes

If dice 1 outcome is 2 we have 3 positive outcomes

if dice 1 outcome is 1 we have 2 positive outcomes

Total evaluating dice 1: positive outcomes 26

We will get the sames results analysing dice 2 then we have a total of

52 successful events

And total numbers of outcomes is 36 + 36 = 72

Then

P ( X > 5 ) = 52/72

P ( X > 5 ) = 0,722

P ( X > 5 ) = 72,2 %

7 0

3 years ago

Use distance formula d=√(X2 – X1 )2 + (X2 – X1 )2, calculate the distance r from the origin to the point r (-2, √5).

lesya692 [45]

$d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} \\d = \sqrt{(\sqrt{5} - (-2))^{2} + (\sqrt{5} - (-2))^{2}} \\d = \sqrt{(\sqrt{5} + 2)^{2} + (\sqrt{5} + 2)^{2}} \\d = \sqrt{(4 + 4\sqrt{5} + 5) + (4v + 4\sqrt{5} + 5)} \\d = \sqrt{0 + 0} \\d = \sqrt{0} \\d = 0$

7 0

3 years ago

Emir is standing in a treehouse and looking down at a swingset in the yard next door. The angle of depression from Emir's eyelin

boyakko [2]

<h3>Answer: 24 feet (Choice D)</h3>

=============================================

Explanation:

Refer to the diagram below. The goal is to find x, which is the horizontal distance from the base of the tree to the swing set.

Focus on triangle BCD.

The angle B is roughly 30.26 degrees, and this is the angle of depression. This is the amount of degrees Emir must look down (when starting at the horizontal) to spot the swing set.

We know that he's 14 ft off the ground, which explains why AB = CD = 14.

The goal is to find BC = AD = x.

---------------------------

Again, keep your focus on triangle BCD.

We'll use the tangent ratio to say

tan(angle) = opposite/adjacent

tan(B) = CD/BC

tan(30.26) = 14/x

x*tan(30.26) = 14

x = 14/tan(30.26)

x = 23.9965714046732

That value is approximate. Make sure your calculator is in degree mode.

That value rounds to 24 feet when rounding to the nearest whole foot.

6 0

3 years ago

Mrs. Larnell is making snacks for a class picnic. She puts 1/4 pounds of apples,1/8 pound of nut mix,and 1/16 pound of chocolate

Tasya [4]

$\frac{1}{4}:\frac{1}{8}:\frac{1}{16}\\\frac{1}{4}*24:\frac{1}{8}*24:\frac{1}{16}*24\\\frac{24}{4}:\frac{24}{8}:\frac{3}{2}\\6:3:1.5\\6+3+1.5=9.5$

9 pounds 8 ounces

6 0

3 years ago

The sum of two consecutive integers is 99. Find the value of the smaller integer. (Show work)​

The sum of two consecutive integers is 99. Find the value of the smaller integer. (Show work)