Answer:
<em>The calculated value z = 1.3145 < 2.326 at 0.02 level of significance</em>
<em>The null hypothesis is accepted </em>
<em>Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.</em>
Step-by-step explanation:
<em><u>Step(i)</u></em>:-
An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.
<em>The mean of the Population 'μ' = 28.0miles/gallon</em>
Given data after testing 270 cars, they found a mean MPG of 27.8. Assume the variance is known to be 6.25.
<em>The sample size 'n' = 270 </em>
<em>Mean of the sample 'x⁻' = 27.8</em>
<em>Given Population variance 'σ² = 6.25</em>
<em>The standard deviation of Population 'σ' = √6.25 = 2.5</em>
<u><em>Step(ii):-</em></u>
<em>Null hypothesis :H₀: 'μ' = 28.</em>
<em>Alternative hypothesis :H₁: 'μ' ≠28.</em>
<em>The test statistic </em>
<em></em><em></em>
<em></em><em></em>
<em>Z = -1.3145</em>
|Z| = |<em>-1.3145|= 1.3145</em>
<u><em>Step(iii)</em></u><em>:-</em>
<em>The tabulated value of z-score at 0.02 level of significance = 2.326</em>
The calculated value z = 1.3145 < 2.326 at a t 0.02 level of significance
<em>The null hypothesis is accepted </em>
<em>Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.</em>
<em></em>
<em></em>
The area of the parallelogram of height 9 in and base 13 in will be 117in².
<h3>What is the area of a parallelogram?</h3>The area of a parallelogram is the product of the base and the height of the figure.
The area of a parallelogram = Base x Height
WE have given a parallelogram of height 9 in and base 13 in.
So,
The area of a parallelogram = Base x Height
A = Base x Height
A = 13 × 9
A = 117in²
Hence, the area of the parallelogram will be 117in².
Learn more about the area;
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Answer:
Step-by-step explanation:
1. Let the number be x
x^2 + 4x = 21
x^2 + 4x - 21 = 0
Solve the quadratic equation using factorization method
x^2 - 3x + 7x - 21 = 0
x(x - 3) + 7(x - 3) = 0
(x - 3)(x+7) = 0
x - 3 = 0 x + 7 = 0
x = 3 x = -7
The number is either 3 or -7
2. Same solution as number 1
3. Let
Width = x
Length = 2x - 3
Area of the rectangle = 9 square ft
Area of a rectangle = length × width
9 = (2x - 3) (x)
9 = 2x^2 - 3x
2x^2 - 3x - 9 = 0
Solve using quadratic formula
a = 2
b = -3
c = -9
x = -b +or- √b^2 - 4ac / 2a
= -(-3) +or- √(-3)^2 - 4(2)(-9) / 2(2)
= 3 +or- √ 9 - (-72) / 4
= 3 +or- √9 + 72 / 4
= 3 +or- √81 / 4
= 3 +or- 9 / 4
x = (3 + 9)/4 or (3 - 9) / 4
= 12 / 4 or -6 / 4
x = 3 or -3/2
Width can not be a negative value
So,
Width = x = 3 ft
Length = 2x - 3
= 2(3) - 3
= 6 - 3
= 3ft
2.if the sum of the square of the number and 4 time that number is 21 the what is the number?
3. the length of the rectangle is 3 less than twice the width. if the area is 9 square ft, the length and width of the rectangle.
4.given the figure below. find the area of the shaded part of the rectangle if the area of the big but angle is 6 times the area of the unshaded rectangle
Unshaded area
Length = 2x
Width = x
Shaded area
Length = (2x+3)
Width = (x+3)
Area of the shaded area = 6 × the unshaded area
(2x) (x) = 6(2x + 3)(x+3)
2x^2 = 6(2x^2 + 6x + 3x + 9)
2x^2 = 12x^2 + 36x + 9x + 54
2x^2 = 12x^2 + 45x + 54
12x^2 + 45x + 54 - 2x^2 = 0
10x^2 + 45x + 54 = 0
Answer:
The approximate probability that 10 squared centimeters of dust contains more than 10110 particles is 0.1357
Step-by-step explanation:
For a sample of 10 sqaured centimeters of dust, the total amount of asbestos particles has a Poisson distribution with a mean of 1000/1 * 10 = 10000.
We will approximate this probability to a normal distribution. The variance is also 10000 (because it is poisson), therefore the standard deviation is √10000 = 100. Lets call X the distribution, and W its standarization, given by
We have
Where is the cummulative distribution function of a standard normal distribution. The values of
are well known and they can be found in the attached file.
We conclude that the approximate probability that 10 squared centimeters of dust contains more than 10110 particles is 0.1357.