Answer:
The null hypothesis is rejected.
There is enough evidence to support the claim that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm^2.
Test statistic t=-40.91
P-value = 0
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm^2.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=-10\\\\H_a:\mu_1-\mu_2< -10[/tex]
The significance level is 0.05.
The sample 1 (AISI 1064), of size n1=126 has a mean of 102.8 and a standard deviation of 1.2.
The sample 2 (AISI 1078), of size n2=126 has a mean of 121.3 and a standard deviation of 2.
The difference between sample means is Md=-18.5.
[tex]M_d=M_1-M_2=102.8-121.3=-18.5[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{1.2^2}{126}+\dfrac{2^2}{126}}\\\\\\s_{M_d}=\sqrt{0.011+0.032}=\sqrt{0.043}=0.2078[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-18.5-(-10)}{0.2078}=\dfrac{-8.5}{0.2078}=-40.91[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-2=126+126-2=250[/tex]
This test is a left-tailed test, with 250 degrees of freedom and t=-40.91, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-40.91)=0[/tex]
As the P-value (0) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm^2.
the polynomial p(x)=x^3-7x-6 has a known factor of (x+1) rewrite p(x) as a product of linear factors p(x)=
Answer:(x+1)(x+2)(x-3)
Because..
Find (f - g) (4)
f(x) = 4x - 3
g(x) = x^3+2x
a) 59
b) 85
c)-59
d) 285
The weights of steers in a herd are distributed normally. The standard deviation is 300lbs and the mean steer weight is 1100lbs. Find the probability that the weight of a randomly selected steer is between 920 and 1730lbs round to four decimal places.
Answer:
The probability that the weight of a randomly selected steer is between 920 and 1730 lbs
P(920≤ x≤1730) = 0.7078
Step-by-step explanation:
Step(i):-
Given mean of the Population = 1100 lbs
Standard deviation of the Population = 300 lbs
Let 'X' be the random variable in Normal distribution
Let x₁ = 920
[tex]Z = \frac{x-mean}{S.D} = \frac{920-1100}{300} = - 0.6[/tex]
Let x₂ = 1730
[tex]Z = \frac{x-mean}{S.D} = \frac{1730-1100}{300} = 2.1[/tex]
Step(ii)
The probability that the weight of a randomly selected steer is between 920 and 1730 lbs
P(x₁≤ x≤x₂) = P(Z₁≤ Z≤ Z₂)
= P(-0.6 ≤Z≤2.1)
= P(Z≤2.1) - P(Z≤-0.6)
= 0.5 + A(2.1) - (0.5 - A(-0.6)
= A(2.1) +A(0.6) (∵A(-0.6) = A(0.6)
= 0.4821 + 0.2257
= 0.7078
Conclusion:-
The probability that the weight of a randomly selected steer is between 920 and 1730 lbs
P(920≤ x≤1730) = 0.7078
Answer:
0.7975
Step-by-step explanation:
Which equation represents the line passing through points A and C on the graph below? On a coordinate plane, point A is at (2, 3), point B is at (negative 2, 1), point C is at (negative 4, negative 3), and point D is at (4, negative 5). y= negative x minus 1 y = negative x + 1 y = x minus 1 y = x + 1
The equation that represents the line that passes through the points A and C is y = x + 1
What is a linear equation?A linear equation is an equation that has a constant rate or slope, and is represented by a straight line
The points are given as:
(x,y) = (2,3) and (-4,-3)
Calculate the slope, m using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{-3 -3}{-4 - 2}[/tex]
Evaluate
m = 1
The equation is then calculated as:
y = m *(x - x1) + y1
So, we have:
y = 1 * (x - 2) + 3
Evaluate
y = x - 2 + 3
This gives
y = x + 1
Hence, the equation that represents the line that passes through the points A and C is y = x + 1
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Answer:
y = x + 1
Step-by-step explanation:
Edge2020
c. Find the price of 16 shirts if 5 costs GH¢80
Answer:
16 shirts = GH¢256
Step-by-step explanation:
If 5 shirts cost GH¢80
Let's determine the price of 16 shirts by cross multiplying the values
This method of evaluating answers is one of the essential methods .
It's just Making sure that the values within each side of the wall to symbol crosses each other.
But one shirt = GH¢80/5
one shirt = GH¢16
So
5 shirts= GH¢80
16 shirts = (16 shirts * GH¢80)/5 shirts
16 shirts = GH¢1280/5
16 shirts = GGH256
evaluate -x+4 when x = -2
Answer:
6
Step-by-step explanation:
=> -x+4
Given that x = -2
=> -(-2)+4
=> 2+4
=> 6
Answer:
6
Step-by-step explanation:
You just have to input -2 into the statement and then solve
= -(-2) + 4
= 2+ 4
= 6
Explain how you found the volume of the rectangular prism with a hole through it. Explain how you found the volume of the rectangular prism with a hole through it.
Answer:
Step-by-step explanation:
We khow that the volume of a prism the product of the base and the height
We have a hole inside it so we must khow what is the geometrical form of this whole to calculate its volum then substract from the total volume
Sample Answer:
I found the volume of the large rectangular prism. Then I found the volume of the small rectangular prism. I subtracted the volume of the smaller prism from the volume of the larger prism.
Let f(x) = −4(0.25)^x. The graph of g(x) = f(x)+k is shown below. Identify the value of k. k=
A heavy rope, 30 ft long, weighs 0.4 lb/ft and hangs over the edge of a building 80 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it.How much work W is done in pulling half the rope to the top of the building
Answer:
180 fb*lb
45 ft*lb
Step-by-step explanation:
We have that the work is equal to:
W = F * d
but when the force is constant and in this case, it is changing.
therefore it would be:
[tex]W = \int\limits^b_ a {F(x)} \, dx[/tex]
Where a = 0 and b = 30.
F (x) = 0.4 * x
Therefore, we replace and we would be left with:
[tex]W = \int\limits^b_a {0.4*x} \, dx[/tex]
We integrate and we have:
W = 0.4 / 2 * x ^ 2
W = 0.2 * (x ^ 2) from 0 to 30, we replace:
W = 0.2 * (30 ^ 2) - 0.2 * (0 ^ 2)
W = 180 ft * lb
Now in the second part it is the same, but the integral would be from 0 to 15.
we replace:
W = 0.2 * (15 ^ 2) - 0.2 * (0 ^ 2)
W = 45 ft * lb
Following are the calculation to the given value:
Given:
[tex]length= 30 \ ft\\\\mass= 0.4 \ \frac{lb}{ft}\\\\edge= 80 \ ft \\\\[/tex]
To find:
work=?
Solution:
Using formula:
[tex]\to W=fd[/tex]
[tex]\to W=\int^{30}_{0} 0.4 \ x\ dx\\\\[/tex]
[tex]= [0.4 \ \frac{x^2}{2}]^{30}_{0} \\\\= [\frac{4}{10} \times \frac{x^2}{2}]^{30}_{0} \\\\= [\frac{2}{10} \times x^2]^{30}_{0} \\\\= [\frac{1}{5} \times x^2]^{30}_{0} \\\\= [\frac{x^2}{5}]^{30}_{0} \\\\= [\frac{30^2}{5}- 0] \\\\= [\frac{900}{5}] \\\\=180[/tex]
Therefore, the final answer is "[tex]180\ \frac{ lb}{ft}[/tex]".
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Nika baked three loaves of zucchini bread. Each cake needed StartFraction 17 over 4 EndFraction cups of flour. Which expression shows the best estimate of the number of cups of flour that Nika used? 4 + 4 + 4 = 12 5 + 5 + 5 = 15 4 + 4 + 4 = 16 17 + 17 + 17 = 51
Answer:
(A)4 + 4 + 4 = 12
Step-by-step explanation:
Each of Nika's cake needed 17/4 cups of flour. Now, we know that:
[tex]\dfrac{17}{4}=4.25 \approx 4[/tex]
Therefore, for three loaves of bread, the best estimate of the number of cups of flour Nika used is:
4 + 4 + 4 = 12
The correct option is A.
Answer:
The correct answer is A.)4 + 4 + 4 = 12
Please someone help!!!
Answer:
Step-by-step explanation:
A, B and C must be real numbers, and A and B are not both zero (which would cause division by zero in the calculation of the slope).
Which graph represents an exponential function?
Answer:
Presumably the first graph solely based on its shape.
Graph A is showing the exponential function. Then the correct option is A.
What is an exponential function?The mathematical expression f(x)= [tex]e^x[/tex] denotes the exponential function. The term typically refers to the positive-valued function of a real variable, unless otherwise specified.
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data. In graph A we can see that the values are varying exponentially from the second quadrant to the first quadrant.
Hence, the correct option is A.
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The number of large cracks in a length of pavement along a certain street has a Poisson distribution with a mean of 1 crack per 100 ft. a. What is the probability that there will be exactly 8 cracks in a 500 ft length of pavement
Answer:
6.53% probability that there will be exactly 8 cracks in a 500 ft length of pavement
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Poisson distribution with a mean of 1 crack per 100 ft.
So [tex]\mu = \frac{ft}{100}[/tex], in which ft is the length of the pavement.
What is the probability that there will be exactly 8 cracks in a 500 ft length of pavement
500ft, so [tex]\mu = \frac{500}{100} = 5[/tex]
This is P(X = 8).
[tex]P(X = 8) = \frac{e^{-5}*5^{8}}{(8)!} = 0.0653[/tex]
6.53% probability that there will be exactly 8 cracks in a 500 ft length of pavement
Which of the following relations is a function?
A{(1, 3), (2, 3), (4,3), (9. 3)}
B{(1, 2), (1, 3), (1.4), (1,5)}
C{(5, 4), (-6, 5), (4, 5), (4, 0)}
D{(6,-1), (1, 4), (2, 3), (6, 1)}
Consider the following set of sample data: (34, 32, 34, 32, 40, 37, 31, 31, 29, 27). We're interested in using this data to test a null hypothesis about the population mean. Which of the following statements are true?
I. Assuming this represents a random sample from the population, the sample mean is an unbiased estimator of the population mean.
II. Because they're robust, t procedures are justified in this case.
III. We'd use zprocedures here, since we're interested in the population mean.
a. I only
b. II only
c. III only
d. I and II only
e. I and III only
Answer:
Option I and II
Step-by-step explanation:
I. Assuming this represents a random sample from the population, the sample mean is an unbiased estimator of the population mean.
II. Because they're robust, t procedures are justified in this case.
The t procedures are utilized because they are used as a hypothesis testing tool, which allows for testing of an hypothesis applicable to a population where in this case we are testing the null hypothesis about the population mean.
Suppose that you collect data for 15 samples of 30 units each, and find that on average, 2.5 percent of the products are defective. What are the UCL and LCL for this process? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Round up negative LCL values to zero. Round your answers to 3 decimal places.)
Answer:
The UCL is [tex]UCL = 0.054[/tex]
The LCL is [tex]LCL \approx 0[/tex]
Step-by-step explanation:
From the question we are told that
The quantity of each sample is n = 30
The average of defective products is [tex]p = 0.025[/tex]
Now the upper control limit [UCL] is mathematically represented as
[tex]UCL = p + 3 \sqrt{\frac{p(1-p)}{n} }[/tex]
substituting values
[tex]UCL = 0.025 + 3 \sqrt{\frac{0.025 (1-0.025)}{30} }[/tex]
[tex]UCL = 0.054[/tex]
The upper control limit (LCL) is mathematically represented as
[tex]LCL = p - 3 \sqrt{\frac{p(1-p)}{n} }[/tex]
substituting values
[tex]LCL = 0.025 - 3 \sqrt{\frac{0.025 (1-0.025)}{30} }[/tex]
[tex]LCL = -0.004[/tex]
[tex]LCL \approx 0[/tex]
Find all solutions to the equation.
7 sin2x - 14 sin x + 2 = -5
If yall can help me for Pre-Calc, that would be great.
-Thanks.
If the equation is
[tex]7\sin^2x-14\sin x+2=-5[/tex]
then rewrite the equation as
[tex]7\sin^2x-14\sin x+7=0[/tex]
Divide boths sides by 7:
[tex]\sin^2x-2\sin x+1=0[/tex]
Since [tex]x^2-2x+1=(x-1)^2[/tex], we can factorize this as
[tex](\sin x-1)^2=0[/tex]
Now solve for x :
[tex]\sin x-1=0[/tex]
[tex]\sin x=1[/tex]
[tex]\implies\boxed{x=\dfrac\pi2+2n\pi}[/tex]
where n is any integer.
If you meant sin(2x) instead, I'm not sure there's a simple way to get a solution...
Suppose A is a 5times7 matrix. How many pivot columns must A have if its columns span set of real numbers RSuperscript 5? Why?
Answer:
Five
Step-by-step explanation:
Pivot columns are said to be columns where pivot exist and a pivot exist in the first nonzero entry of each row in a matrix that is in a shape resulting from a Gaussian elimination.
Suppose A = 5 × 7 matrix
So; if A columns span set of real numbers R⁵
The number of pivot columns that A must have must be present in each row. In a 5 × 7 matrix ; we have 5 rows and 7 columns . So , since A must be present in each row, then :
The matrix must have five pivot columns and we can infer that about the statements that "A has a pivot position in every row" and "the columns of A spans R⁵" are logically equivalent.
pls help me help me help me
Answer:
C. -3/2
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes.
We know that line m is perpendicular to line l.
Line l has a slope of 2/3. To find the slope of line m, find the negative reciprocal of 2/3.
Negative: switch the sign
2/3 --> -2/3
Reciprocal: switch the numerator (top number) and denominator (bottom number)
-2/3 --> -3/2
Line m has a slope of -3/2 and C is correct.
Answer:
C
Step-by-step explanation:
perpendicular lines have negative reciprocal slope
Find the length of a side of a square whose diago- nal is 16 cm long. Round your answer to the nearest tenth.
Answer:
11.3 cm
Step-by-step explanation:
(see attached for reference)
using the Pythagorean theorem
hypotenuse ² = length ² + length ²
16² = L² + L²
16² = 2L² (express 2 = (√2)²
16² = (√2)²L²
16² = (√2L)²
16 = √2L
L = 16 /√2
L = 11.3 cm
11.3
use Pythagoras theorem give each side is "a"
a^2+a^2=16^2
2*a^2=256
a^2=256/2=128
a=sqrt(128)=11.3 sqrt=square root
Given
f(x) = 2x2 + 1
and
g(x) = 3x - 5
find the following.
f-g
Answer:
The answer is
2x² - 3x + 6Step-by-step explanation:
f(x) = 2x² + 1
g(x) = 3x - 5
To find f - g(x) subtract g(x) from f(x)
That's
f-g(x) = 2x² + 1 - (3x - 5)
= 2x² + 1 - 3x + 5
= 2x² - 3x + 6
Hope this helps you
Suppose the displayed ask is $20.05 for 100 shares and the displayed bid is $20 for 150 shares. What happens if another dealer places a limit order to buy 50 shares for $20.02?
Answer:
There will be no transaction
Step-by-step explanation:
Given:
Displayed ask price = $20.05 for 100 shares
Displayed bid price = $20 for 150 shares
Explain:
If a limit order to buy = 50 shares for $20.02
Computation:
Displayed bid will be not accepted because, displayed bid price is for 150 shares not 100 shares
Limited order will be also not accepted.
So, there will be no transaction.
What is the approximate length of minor arc LM? Round
to the nearest tenth of a centimeter.
12.4 centimeters
15.7 centimeters
31.4 centimeters
36.7 centimeters
Answer:
Length of the arc LM = 15.7 cm
Step-by-step explanation:
To determine the length of the arc LM we have to find the circumference of the the big circle then divide by the ratio of the angle or go straight to use the radians as the angle and look for the length.
Radius= 30cm
π= 3.142
Value of the angle is in radians
360° = 2π
π = 180
π/6 = 180/6
π/6= 30
Value of the angle is 30°
Length of the arc = 2πr * 30/360
Length of the arc = 2πr/12
Length of the arc = πr/6
Length of the arc = 30π/6
Length of the arc =5π
Length of the arc = 5*3.142
Length of the arc = 15.71
Approximately Length of the arc
= 15.7cm
Answer:
B. 15.7cm
Step-by-step explanation:
What is the slope of the function, represented by the table of values below?
Answer:
C. -2
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Simply use 2 xy values and plug them into the formula:
m = (-4 - 0)/(5 - 3)
m = -4/2
m = -2
Answer:
-2
Step-by-step explanation:
Since we have two points we can use the slope formula
m = (y2-y1)/(x2-x1)
= (10-6)/(-2-0)
=4/-2
-2
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 117.7-cm and a standard deviation of 2.2-cm. For shipment, 29 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is greater than 118.5-cm.
Answer:
Required probability is 0.9748
Step-by-step explanation:
given data
mean [tex]\mu[/tex] = 117.7-cm
standard deviation [tex]\sigma[/tex] = 2.2-cm
sample size n = 29
solution
we consider here random variable which represents here length of rod= x
so get here first z that is express as
[tex]Z = \dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
put here value with x value 118.5-cm
[tex]Z = \dfrac{118.5-117.7}{\dfrac{2.2}{\sqrt{29}}}[/tex]
Z = 1.9582
p value is 0.9748
so required probability is 0.9748
evaluate -x+4 when x = -2
Answer:
6Step-by-step explanation:
f(x)=-x+4
f(-2)=-(-2)+4
f(-2)=+2+4
f(-2)=6
Answer:
6
Step-by-step explanation:
-(-2)+4=___
+(+2)+4=6
Find the area of the parallelogram with vertices A(−1,3,3), B(0,5,7), C(1,2,6), and D(2,4,10).
Answer:
Step-by-step explanation:
The diagonal of the parallelogram ABCD divides it into 2 equal triangles. Considering triangle ABC, it means that the area of the parallelogram would be
2 × area of triangle ABC
Writing the vertices of triangle ABC,
A(−1,3,3), B(0,5,7), C(1,2,6)
We would determine the length of each side of the triangle.
AB = √(0 - - 1)² + (5 - 3)² + (7 - 3)^2
AB = √(1 + 4 + 16) = √21
BC = √(1 - 0)² + (2 - 5)² + (6 - 7)²
BC = √(1 + 9 + 1) = √11
AC = √(1 - - 1)² + (2 - 3)² + (6 - 3)²)
AC = √(4 + 1 + 9) = √14
We would apply the heron's formula for determining the area of a triangle
Area = √s(s - a)(s - b)(s - c)
Where
s = (a + b + c)/2
a = AB, b = BC, c = AC
s = (√21 + √11 + √14)/2 = 5.82
s - a = 5.82 - √21 = 1.24
s - b = 5.82 - √11 = 2.5
s - c = 5.82 - √14 = 2.08
Area = √(5.82 × 1.24 × 2.5 × 2.08) = 6.126
Therefore, area of parallelogram ABCD is
6.126 × 2 = 12.252
Stuck Right now, Help would be appreciated :)
Answer:
C. c = (xv - x) / (v - 1).
Step-by-step explanation:
v = (x + c) / (x - c)
(x - c) * v = x + c
vx - vc = x + c
-vc - c = x - vx
vc + c = -x + vx
c(v + 1) = -x + vx
c = (-x + vx) / (v + 1)
c = (-x + xv) / (v + 1)
c = (xv - x) / (v + 1)
So, the answer should be C. c = (xv - x) / (v + 1).
Hope this helps!
6th grade math help me please :))
Answer:
The answer is option D.
3u + 1 + 7y
All the terms here are different and cannot be combined
Hope this helps you
Find the sum. A. 4x2 – x – 5 B. 10x2 + 7x – 5 C. –10x2 + 7x + 11 D. 4x2 + x – 11
Answer:
A
Step-by-step explanation:
7x² - 4x - 8 - [ -3x² - 3x - 3]
In subtraction, flip the sign of all terms in the minuend
7x² - 4x - 8
3x² + 3x + 3
4x² - x - 5