Answer:
The area of ∆DEF = 4.5in²
Step-by-step explanation:
From the above diagram,
∆BAC ~∆DEF
It is important to note that if two triangles are similar, the ratio of their areas is equal or equivalent to the ratio of the areas of their sides
This means for the above question, that
We have the bigger triangle = ∆BAC has a side of 4 in and Area = 8 in²
The small triangle has a side of 3in
Finding the scale factor k = ratio of the sides of both Triangles
k = 4/3
k² = (4/3)²
k² = 16/9
Hence,
Area of ∆BAC/ Area of ∆DEF = 16/9
8in²/Area of ∆DEF = 16/9
We cross Multiply
8 in² × 9 = Area of ∆DEF × 16
Divide both sides by 16
Area of ∆DEF = 72/16
= 4.5in²
Therefore, the Area of ∆DEF rounded to the nearest tenth = 4.5in²
Answer:
y = 0.265x - 494.7
Step-by-step explanation:
Let median age be represent by 'a' and time be represent by 't'
In 1980, median age is given 30
which means that
a₁ = 30
t₁ = 1980
In 2000, the median age is given 35.3
which means that.
a₂ = 35.3
t₂ = 2000
The slope 'm' of the linear equation can be found by:
m = (a₂ - a₁) /(t₂ - t₁)
m = (35.3 - 30)/(2000-1980)
m = 0.265
General form of linear equation is given by:
y = mx + c
y = 0.265x +c
Substitute point (1980,30) in the equation.
30 = 0.265(1980) + c
c = -494.7
Hence the the linear equation can be written as:
y = mx + c
y = 0.265x - 494.7
Answer:
Algebra book weighs 24 oz
Grammar book weighs 15 oz
Step-by-step explanation:
algebra = x and grammar = y
x = 2y-6
5x = 8y
5(2y-6) = 8y
10y - 30 = 8y
2y - 30 = 0
2y = 30
y = 15
x = 2(15)-6
x = 30-6
x = 24
Answer:
Thats smarttt
Step-by-step explanation:
You phrased it so it would get pass the brainly bots system, kudos to you!
Considering the situation described, we have that:
a) The critical value is of z = -1.645.
b) Since the test statistic is less than the critical value, we should reject the null hypothesis H0.
<h3>What is the critical value?</h3>
We have a left-tailed test, as we are testing if the proportion is less than a value. Hence the critical value is z with a p-value equals to the significance level, hence z with a p-value of 0.05, hence z = -1.645.
<h3>What is the decision?</h3>
Considering the test statistic, for a left-tailed test, we have that:
- Less than the critical value: Reject H0.
- Equal or greater: Do not reject.
In this problem, z = -2.39 is less than -1.645, hence we should reject the null hypothesis H0.
More can be learned about the test of an hypothesis at brainly.com/question/13873630
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