Triangle RST is the pre-image of triangle UVW with a scale factor of 3. Find the area of triangle UVW if the area of triangle RST is 9 cm2. a.) Set up an equation on how to solve for the missing area using the Area Ratios for Similar Figures.

b.) What is the area of triangle UVW?

Answers

Answer 1

Answer: A. (Area of triangle UVW)/(Area of triangle RST)=3^2=9
B. Substitute Area of triangle RST=9 into the equation above.

(Area of triangle UVW)/9=9
Area of triangle UVW =9x9=81 cm^2

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If two lines are parallel, which statement must be true?A.The two lines have undefined slopes.
B.The two lines have opposite slopes.
C.The two lines have zero slopes.
D.The two lines have the same slope.

Answers

Answer:

Option (d) is correct.

The two lines have the same slope.

Step-by-step explanation:

Given : two parallel lines

We have to choose one statement that is true regarding Parallel lines.

Parallel lines are those lines that do not intersect each other and distance between them remains same throughout the plane.

Also , parallel lines have same slope.

From the graph attached below both lines have parallel and have same slope.

equation of line :

2x + 3y = 10 and 6x + 3y = 10

Both are parallel and have slope -2

Thus, Option (d) is correct.

The two lines have the same slope.

Answer: Option D. The two lines have the same slope.

When two lines are parallels, they must have the same slope and they never intersect, then answer is:
Option D. The two lines have the same slope.

A person 100 meters from the base of a tree, observes that the angle between the ground and the top of the tree is 18 degrees. Estimate the height h of the tree to the nearest tenth of a meter.

Answers

The required height of the tree is 32.5 meters.

Given that,
A person 100 meters from the base of a tree, observes that the angle between the ground and the top of the tree is 18 degrees. To estimate the height h of the tree to the nearest tenth of a meter.

What are trigonometric equations?

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,
let the height of the tree be x, and the slant height from the foot of the person to the top of the tree be h,
according to the question,
base length = 100
cos 18 = 100 / h
h = 105.14
Now,
sin 18 = x / h
sin 18 = x / 105.14
x = 32.5 meters

Thus, the required height of the tree is 32.5 meters.

Learn more about trigonometry equations here:

brainly.com/question/22624805

#SPJ2

This is right angle trig. We know that...

cos(18°) x hypotenuse = 100

hypotenuse = 100/cos(18°)

hypotenuse = 105.15 meters approx.

Because they want the height of the tree we want "sin(18°) x hypotenuse".

sin(18°) x 105.15 = 32.5 meters approx.

answer: 32.5 meters approx.

In Juneau, Alaska, the 30-year annual snowfall average is 86.7 inches with a standard deviation of 40.4 inches. The last four years saw an average annual snowfall of 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 inches. Hia performs a hypothesis test on this data to determine if the next 30-year norm will have a different average if the trend from the last four years continues. She uses a significance level of 5%. Which of the following is a conclusion that she may make?a) The z-statistic is 1.44, so the null hypothesis cannot be rejected.
b) he z-statistic is 1.68, so the null hypothesis cannot be rejected.
c) The z-statistic is 1.85, so the null hypothesis should be rejected.
d) The z-statistic is 4.6, so the null hypothesis should be rejected.

Answers

The expected value of the amount of average snowfall for over 30 years is 86.7 inches with a standard deviation of 40.4 inches. To verify if this particular trend continues, we must check the significance value of the amount snowfall for the past four years. Given that the snowfall for past years are as follows: 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 inches. Thus the mean of the sample would be: (115.7 + 62.9 + 168.5 + 135.7)/4 = 120.7 inches. To compute for the z-score, we have z-score = (x – μ) / (σ / √n) where x is the computed/measured value, μ is the expected mean, σ is the standard deviation, and n is the number of samples. Using the information we have, z-score (z) = (120.7 - 86.7) / (40.4/ √4) = 1.68 In order to reject the null hyptohesis our probability value must be less than the significance level of 5%. For our case, since z = 1.68, P-value = 0.093 > 0.05. Therefore, the answer is B.

Answer:

its B

Step-by-step explanation:

While scuba diving, Alex counted the number of sea turtles and jellyfish he saw. After a few minutes, he counted 4 seaturtles and 12 jellyfish. This ratio remained consistent during the remainder of his dive.
Part A
Using the given ratio, complete the table.
Number of
Number of
Sea Turtles
Jellyfish
1
4
24
14
60

Answers

Answer:

The values which are added to the table are;

Sea turtles = 1, Jellyfish = 3

Sea turtles = 4, Jellyfish = 12

Jellyfish = 24, Sea turtles= 8

Sea turtles = 14, Jellyfish = 42

Jellyfish = 60, Sea turtles= 20

Step-by-step explanation:

The given parameters are;

The ratio of sea turtles to jellyfish = 4:12

Therefore, the ratio of sea turtles to jellyfish = 1:3

Which gives;

When the number of sea turtles = 1, the jellyfish = 1 × 3 = 3 Jellyfishes

When the number of sea turtles = 4, the jellyfish = 4 × 3 = 12 Jellyfishes

When the number of sea jellyfishes = 24, the number of sea turtles = 24/3 = 8 sea turtles

When the number of sea turtles = 14, the jellyfish = 14 × 3 = 42 Jellyfishes

When the number of sea jellyfishes = 60, the number of sea turtles = 60/3 = 20 sea turtles

The values given in the table can be presented as follows;

Number of Sea Turtles ${}$ Number of Jellyfish

1 ${}$ 3

4 ${}$ 12

8 ${}$ 24

14 ${}$ 42

20 ${}$ 60

Event B is dependent on event A, and event A occurs before event B. Which expression is equal to the probability of event A?

Answers

An event is the result of a random experiment or a group of shared results.
It could be defined as every subset of a sample space because the sample space is a collection of all possible results of a random experiment.

When the event B is dependenting on event A,

$\to \bold{P(B \cap A) \neq P(B)* P(A)}\n\n$