G(x)=23x+1; find g (-3), g (0),and f (9x+6)
1 answer:
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Answer:
statistic value t= 5.43
p-value: < 0.00001.
Step-by-step explanation:
Hello!
To obtain information over the corrosion-resistance properties of a certain type of steel conduit a random sample of 45 specimens was taken and buried for two years.
The study variable is:
X: Max. penetration of a steel conduit.
The data of the sample
n= 45
sample mean X[bar]= 53.4
sample standard deviation S= 4.2
The conduits are manufactured to have a true average penetration of at most 50 mills, symbolically: μ ≤ 50
The hypothesis is:
H₀: μ ≤ 50
H₁: μ > 50
α: 0.05
To choose the corresponding statistic to use to study the population mean, the variable must have a normal distribution. There is no available information to check this, so I'll just assume that the variable has a normal distribution and, since the population variance is unknown and the sample is small, the statistic to use is a Student t.
Under the null hypothesis, the critical region and the p-value are one-tailed.
Critical value:
Rejection rule:
Reject the null hypothesis when t ≥ 1.68
t=
t= 5.43
The calculated value is greater than the critical value, thedecision is to rject the null hypothesis.
p-value:
P(t ≥ 5.43) = 1 - P(t < 5.43) = < 0.00001.
The p-value is less than α so the decision is to reject the null hypothesis.
Since the null hypothesis was rejected, then the population average of the penetration of the conduits specimens is greater than 50 mils. It is not recommendable to use these conduits.
I hope it helps!
QUESTION 1
The figure is a tra-pezoid.
The area of a trapezoid is given by the formula;
We substitute the values to obtain;
QUESTION 2
The approximate length of the ribbon is equal to the circumference of the circular table cloth.
We can find this by using the formula for calculating the circumference of a circle.
where is the radius of the circular table cloth.
We substitute this value and into the formula to get;
The approximate length of the ribbon is 22.0ft to the nearest tenth.
QUESTION 3
Type of quadrilateral:Rectangle
Explanation: A rectangle has 4 angles that are right angles.
The two pairs of opposite sides of a rectangle are also congruent.
QUESTION 4.
The circumference of a semi circle is calculated using the formula;
where is the radius of the semicircle.
QUESTION 5
The area of the entire figure is the area of the semicircle plus the area of the isosceles triangle.
QUESTION 6
The area of the parallelogram is given by the formula;
From the diagram, .
Given, A=23.7 inches squared.
We substitute the values to obtain;
QUESTION 7
The area of a rectangle is given by the formula;
The area of the bigger rectangle
The area of the smaller rectangle
The area of the shaded region