Answer:
Step-by-step explanation:
The formula for determining the distance between two points on a straight line is expressed as
Distance = √(x2 - x1)² + (y2 - y1)²
Where
x2 represents final value of x on the horizontal axis
x1 represents initial value of x on the horizontal axis.
y2 represents final value of y on the vertical axis.
y1 represents initial value of y on the vertical axis.
From the given information,
x2 = - 1
x1 = 4
y2 = 6
y1 = 3
Therefore,
Distance = √(- 1 - 4)² + (6 - 3)²
Distance = √(- 5² + 3²) = √(25 + 9) = √34
Distance = 5.83
Answer:
(u - 1)(4u + 3)
Step-by-step explanation:
Given
4u² - u - 3
Consider the factors of the product of the coefficient of the u² term and the constant term which sum to give the coefficient of the u- term.
product = 4 × - 3 = - 12 and sum = - 1
The factors are - 4 and + 3
Use these factors to split the u- term
4u² - 4u + 3u - 3 ( factor the first/second and third/fourth terms )
= 4u(u - 1) + 3(u - 1) ← factor out (u - 1) from each term
= (u - 1)(4u + 3)
Thus
4u² - u - 3 = (u - 1)(4u + 3) ← in factored form
Answer:
Step-by-step explanation:
Hello!
The researchers want to compare the weight of the basset hounds in 1915 with the weight of the basset hound in 2015.
Using a sample of 36 male basset hounds taken in 1915 and a sample of 36 male basset hounds taken in 2015 a 90% CI for the difference of mean weights of the basset hounds (2015-1915) was constructed:
Group 1
X₁: Weight of a basset hound measured in 1915
n₁= 36
Group 2
X₂: Weight of a basset hound measured in 2015
n₂= 36
Difference X₂ - X₁
X[bar]₂ - X[bar]₁= -2.8cm
margin of error d= 1.3cm
90% CI: [-1.4; -1.5]cm
The calculated CI is two-tailed, you can use it to decide over a two-tailed hypothesis test for the same parameter of interest over the same level. If the hypothesis is:
H₀: μ₂ - μ₁=0
H₁: μ₂ - μ₁≠0
α: 0.10
The CI doesn't contain the zero, so you could reject the null hypothesis. With this, you can conclude that the difference between the average weight of the basset hounds in 2015 and the average weight of the basset hounds in 1915.
Judging by the fact that both limits of the confidence interval are negative, as well as the difference between point estimators, it seems that the weight of the basset hounds in 2015 is less than their weight in 1915. Of course, you are not valid to make that kind of conclusion without a proper hypothesis test.
Answer:
<h2>9</h2>
Step-by-step explanation:
Step one:
given
Let the number of tests graded be g = 27
time taken t = 3 hours
Required
The constant relating the time and the number of tests
Step two:
<em>"The constant of variation is the number that relates two variables that are directly proportional or inversely proportional to one another."</em>
so that the direct variation is
g∝kt
g=t/k
k= g/t
k=27/3
k=9
Answer:
f(-2) = 1
Step-by-step explanation:
f(x) = x^2 + 2x + 1
To find the value f(-2), replace x with -2 and evaluate the expression.
f(-2) = (-2)^2 + 2(-2) + 1
f(-2) = 4 - 4 + 1
f(-2) = 1
