Answer:
42 square units
Step-by-step explanation:
The area of the rectangle is the product of its length and width:
area = 6(x -8)
The area of the triangle is half the product of its base and height:
area = (1/2)(x-3)·7
These two areas are equal, so we have ...
6(x -8) = (1/2)(x -3)(7)
6x -48 = 3.5x -10.5 . . . . eliminate parentheses
2.5x = 37.5 . . . . . . . . . . . add 48 -3.5x
x = 15 . . . . . . . . . . . . . . . divide by 2.5
The area of the rectangle is ...
area = 6(15 -8) = 42 . . . . square units.
Answer:
For the exponential distribution:
We know that the exponential distribution is skewed but the sample mean for this case using a sample size of 60 would be approximately normal, so then we can conclude that if we have a sample size like this one and an exponential distribution we can approximate the sample mean to the noemal distribution and indeed use the Central Limit theorem.
Step-by-step explanation:
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
For this case we have a large sample size n =60 >30
The exponential distribution is the probability distribution that describes the time between events in a Poisson process.
For the exponential distribution:
We know that the exponential distribution is skewed but the sample mean for this case using a sample size of 60 would be approximately normal, so then we can conclude that if we have a sample size like this one and an exponential distribution we can approximate the sample mean to the noemal distribution and indeed use the Central Limit theorem.
A. The area of a square is given as:
<span>A = s^2 </span>
Where s is a measure of a side of a square. s = (2 x – 5)
therefore,
<span>A =
(2 x – 5)^2 </span>
Expanding,
A =
4 x^2 – 20 x + 25
<span>B.
The degree of a polynomial is the highest exponent of the variable x, in this case
2. Therefore the expression obtained in part A is of 2nd degree.</span>
Furthermore,
polynomials are classified according to the number of terms in the expression.
There are 3 terms in the expression therefore it is classified as a trinomial.
<span>C.
The closure property demonstrates that during multiplication or division, the
coefficients and power of the variables are affected while during
multiplication or division, only the coefficients are affected while the power
remain the same.</span>
Step-by-step explanation:
x + y = 16 (*)
x^2 + y^2 = 146 (**)
(*) <=> x= 16-y
substitute x = 16 - y
(**) <=> (16-y)^2 + y^2 = 146
<=> y^2 - 2.16.y + 16^2 + y^2 = 146
<=> 2y^2 - 32y + 110 = 0
<=> y^2 - 16y + 55 = 0
<=> (y-11)(y-5) = 0
<=> y=11 or y= 5
For y = 11, we have x= 16-11=5
For y=5, we have x= 16-5=11
Answer: (x,y) = (11,5) ; (5,11)
Answer:
Hiya there!
Step-by-step explanation:
The two numbers are 9 and 3.
<em><u>Hope this helped!</u></em> :D
