Answer:
3, 12
Step-by-step explanation:
Et x and y be the required integers.
Case 1: x = 5y - 3...(1)
Case 2: xy = 36
Hence, (5y - 3)*y = 36
[tex]5 {y}^{2} - 3y = 36 \\ 5 {y}^{2} - 3y - 36 = 0 \\ 5 {y}^{2} - 15y + 12y - 36 = 0 \\ 5y(y - 3) + 12(y - 3) = 0 \\ (y - 3)(5y + 12) = 0 \\ y - 3 = 0 \: or \: 5y + 12 = 0 \\ y = 3 \: \: or \: \: y = - \frac{12}{5} \\ \because \: y \in \: I \implies \: y \neq - \frac{12}{5} \\ \huge \purple{ \boxed{ \therefore \: y = 3}} \\ \because \: x = 5y - 3..(equation \: 1) \\ \therefore \: x = 5 \times 3 - 3 = 15 - 3 = 12 \\ \huge \red{ \boxed{ x = 12}}[/tex]
Hence, the required integers are 3 and 12.
let
x = one integer
y = another integer
x = 5y - 3
If the product of the two integers is 36, then find the integers.
x * y = 36
(5y - 3) * y = 36
5y² - 3y = 36
5y² - 3y - 36 = 0
Solve the quadratic equation using factorization method
That is, find two numbers whose product will give -180 and sum will give -3
Note: coefficient of y² multiplied by -36 = -180
5y² - 3y - 36 = 0
The numbers are -15 and +12
5y² - 15y + 12y - 36 = 0
5y(y - 3) + 12 (y - 3) = 0
(5y + 12) (y - 3) = 0
5y + 12 = 0 y - 3 = 0
5y = - 12 y = 3
y = -12/5
The value of y can not be negative
Therefore,
y = 3
Substitute y = 3 into x = 5y - 3
x = 5y - 3
x = 5(3) - 3
= 15 - 3
= 12
x = 12
Therefore,
(x, y) = (12, 3)
Read more:
https://brainly.com/question/20411172
Pls help me help me
Answer:
C.
Step-by-step explanation:
When two lines are parallel, their slopes are the same.
Since the slope of line l is 2/7, the slope of its parallel line m must also be 2/7.
The answer is C.
Answer:
C. 2/7
Step-by-step explanation:
Parallel lines are lines that have the same slopes.
We know that line l is parallel to line m.
Therefore, the slope of line l is equal to the slope of line m.
[tex]m_{l} =m_{m}[/tex]
We know that line l has a slope of 2/7.
[tex]\frac{2}{7} =m_{m}[/tex]
So, line m also has a slope of 2/7. The answer is C. 2/7
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!
pls help me pls pls
Answer:
B
Step-by-step explanation:
the slope of parallel lines are equal
The surface area of an open-top box with length L, width W, and height H can be found using the
formula:
A = 2LH + 2WH + LW
Find the surface area of an open-top box with length 9 cm, width 6 cm, and height 4 cm.
Answer:
174 square cm
Step-by-step explanation:
2(9×4) + 2(6×4)+ 9×6
2(36) + 2(24) + 54
72 + 48 + 54
120 + 54
174
Someone pls help me
The slope greater than one would be the last image, because for every step in x, you get more than one y step.
The slope between 1 and 0 would be the second image
And the slope less than 0 would be the third image
A square with side lengths of 3 cm is reflected vertically over a horizontal line of reflection that is 2 cm below the bottom edge of the square. What is the distance between the points C and C’? cm What is the perpendicular distance between the point B and the line of reflection? cm What is the distance between the points A and A’? cm
Answer:
a) 4 cm
b) 5 cm
c) 10 cm
Step-by-step explanation:
The side lengths of the reflected square are equal to the original, and the distance from the axis(2) also remains the same. From there, it is just addition.
Hope it helps <3
Answer:
A) 4
B) 5
C) 10
Step-by-step explanation:
edge2020
If Brooklyn College students have an IQ of 100, on average, with a standard deviation of 16 points, and I collect 48 BC Psychology students to see how Psych majors compare to all of BC, find the following:_______.
1. mu =
2. sigma =
3. mu _x bar =
4. sigma _x bar =
Answer:
1 [tex]\mu = 100[/tex]
2 [tex]\sigma = 16[/tex]
3 [tex]\mu_x = 100[/tex]
4 [tex]\sigma _{\= x } = 2.309[/tex]
Step-by-step explanation:
From the question
The population mean is [tex]\mu = 100[/tex]
The standard deviation is [tex]\sigma = 16[/tex]
The sample mean is [tex]\mu_x = 100[/tex]
The sample size is [tex]n = 48[/tex]
The mean standard deviation is [tex]\sigma _{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x } = \frac{16 }{\sqrt{48} }[/tex]
[tex]\sigma _{\= x } = 2.309[/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...
The left and right page numbers of an open book are two consecutive integers whose sum is 389. Find these page numbers
Step-by-step explanation:
Maybe the page numbers can be 143 and 246
143 + 246 = 389
Answer:
194 and 195
Step-by-step explanation:
x = 1st page
x + 1 = 2nd page
x + x + 1 = 389
2x + 1 = 389
2x = 388
x = 194
x + 1 = 195
What is the equation of the line that is parallel to the given line and passes through the point (12, -2)? A) y = -6/5x + 10 B) y= -6/5x + 12 C) y = -5/6x -10 D) y = 5/6x - 12
Answer:
D
Step-by-step explanation:
Parallel lines are those that have the same slope, or coefficient of x.
Here, let's calculate the slope of the given line. Slope is the difference in the y-coordinates divided by the difference in the x-coordinates, so given the two coordinates (12, 6) and (0, -4):
slope = m = (-4 - 6) / (0 - 12) = -10 / (-12) = 10/12 = 5/6
So the slope is 5/6. That means the equation we want should also have a slope of 5/6. Already, we can eliminate A, B, and C, leaving D as our answer. But, let's check.
The equation of a line can be written as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is the coordinates of a given point.
Here, our slope is 5/6 and our given point is (12, -2). So plug these in:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-2)=(5/6)(x-12)[/tex]
[tex]y+2=\frac{5}{6} x-10[/tex]
[tex]y=\frac{5}{6} x-12[/tex]
This matches D, so we know that it's the correct answer.
~ an aesthetics lover
The answer is D I just took the test
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
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:
g red bell pepper seeds germinates 85% of the time. planted 25 seeds. What is the probability that 20 or more germinate
Answer:
[tex] P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)[/tex]
And replacing using the mass function we got:
[tex]P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156[/tex]
[tex]P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211[/tex]
[tex]P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217[/tex]
[tex]P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161[/tex]
[tex]P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759[/tex]
[tex]P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172[/tex]
And adding the values we got:
[tex] P(X\geq 20) = 0.8381[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=25, p=0.85)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
We want to find the following probability:
[tex] P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)[/tex]
And replacing using the mass function we got:
[tex]P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156[/tex]
[tex]P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211[/tex]
[tex]P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217[/tex]
[tex]P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161[/tex]
[tex]P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759[/tex]
[tex]P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172[/tex]
And adding the values we got:
[tex] P(X\geq 20) = 0.8381[/tex]
What is the distance between (−11, −20) and (−11, 5)?
−25 units
−15 units
15 units
25 units
Answer:
IT'S NOT -15 FOR SUREEE
Step-by-step explanation:
I Believe it's 15
pls help me hepl me
Answer:
b at most 199
Step-by-step explanation:so the total was 121 and there is a flat fee of 21.50 so you subtract that out and gat 99.5 since its .5 per mile its going to be divided giving 199 and that is the most she could have driven.
A school is 16km due west of a school q.
What is the bearing of q from p?
Answer:
16 km due west
Step-by-step explanation:
The bearing of the school p from school q is 16 km due west.
To find the bearing of school q from school p, we have to find the direction that the school q is with respect to school p.
Since p is directly west of q, then it implies that q must be directly east of p.
We now know the direction.
Since the distance from q to p is exactly the same as the distance from p to q, then, the distance from p to q is 16 km.
Hence, the bearing of q from p is 16 km due west.
The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 3639 3639 miles, with a variance of 145,161 145,161 . If he is correct, what is the probability that the mean of a sample of 41 41 cars would differ from the population mean by less than 126 126 miles
Answer:
96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
A reminder is that the standard deviation is the square root of the variance.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 3639, \sigma = \sqrt{145161} = 381, n = 41, s = \frac{381}{\sqrt{41}} = 59.5[/tex]
Probability that the mean of the sample would differ from the population mean by less than 126 miles
This is the pvalue of Z when X = 3639 + 126 = 3765 subtracted by the pvalue of Z when X = 3639 - 126 = 3513. So
X = 3765
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3765 - 3639}{59.5}[/tex]
[tex]Z = 2.12[/tex]
[tex]Z = 2.12[/tex] has a pvalue of 0.983
X = 3513
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3513 - 3639}{59.5}[/tex]
[tex]Z = -2.12[/tex]
[tex]Z = -2.12[/tex] has a pvalue of 0.017
0.983 - 0.017 = 0.966
96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles
Which equation should be used to find the volume of the figure?
V=1/3(10)(6)(12)
V=1/2(10)(6)(12)
V=1/3(10)(6)(13)
V=1/2(10)(6)(13)
Answer:
The answer is option 1.
Step-by-step explanation:
Given that the volume of pyramid formula is:
[tex]v = \frac{1}{3} \times base \: area \times height[/tex]
The base area for this pyramid:
[tex]base \: area = area \: of \: rectangle[/tex]
[tex]base \: area = 10 \times 6[/tex]
Then you have to substitute the following values into the formula:
[tex]let \: base \: area = 10 \times 6 \\ let \: height = 12[/tex]
[tex]v = \frac{1}{3} \times 10 \times 6 \times 12[/tex]
Answer:
A. V = 1/3 (10)(6)(12)
Step-by-step explanation:
Just took the test and got it right
Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. They are considering a promotion that involves mailing discount coupons to all their credit card customers. This promotion will be considered a success if more than 10% of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of 100 credit card customers.
a. Develop hypotheses that can be used to test whether the population proportion of those
who will use the coupons is sufficient to go national.
b. The file Eagle contains the sample data. Develop a point estimate of the population
proportion.
c. Use αα= .05 to conduct your hypothesis test. Should Eagle go national with the
promotion?
Answer:
a) Alternative hypothesis: the use of the coupons is isgnificantly higher than 10%.
Null hypothesis: the use of the coupons is not significantly higher than 10%.
The null and alternative hypothesis can be written as:
[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]
b) Point estimate p=0.13
c) At a significance level of 0.05, there is not enough evidence to support the claim that the proportion of coupons use is significantly higher than 10%.
Eagle should not go national with the promotion as there is no evidence it has been succesful.
Step-by-step explanation:
The question is incomplete.
The sample data shows that x=13 out of n=100 use the coupons.
This is a hypothesis test for a proportion.
The claim is that the proportion of coupons use is significantly higher than 10%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]
The significance level is 0.05.
The sample has a size n=100.
The point estimate for the population proportion is the sample proportion and has a value of p=0.13.
[tex]p=X/n=13/100=0.13[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.1*0.9}{100}}\\\\\\ \sigma_p=\sqrt{0.0009}=0.03[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.13-0.1-0.5/100}{0.03}=\dfrac{0.025}{0.03}=0.833[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>0.833)=0.202[/tex]
As the P-value (0.202) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the proportion of coupons use is significantly higher than 10%.
Find a parabola with equation y = ax2 + bx + c that has slope 5 at x = 1, slope −11 at x = −1, and passes through the point (2, 18).
By "slope" I assume you mean slope of the tangent line to the parabola.
For any given value of x, the slope of the tangent to the parabola is equal to the derivative of y :
[tex]y=ax^2+bx+c\implies y'=2ax+b[/tex]
The slope at x = 1 is 5:
[tex]2a+b=5[/tex]
The slope at x = -1 is -11:
[tex]-2a+b=-11[/tex]
We can already solve for a and b :
[tex]\begin{cases}2a+b=5\\-2a+b=-11\end{cases}\implies 2b=-6\implies b=-3[/tex]
[tex]2a-3=5\implies 2a=8\implies a=4[/tex]
Finally, the parabola passes through the point (2, 18); that is, the quadratic takes on a value of 18 when x = 2:
[tex]4a+2b+c=18\implies2(2a+b)+c=10+c=18\implies c=8[/tex]
So the parabola has equation
[tex]\boxed{y=4x^2-3x+8}[/tex]
Using function concepts, it is found that the parabola is: [tex]y = 4x^2 - 3x + 14[/tex]
----------------------------
The parabola is given by:
[tex]y = ax^2 + bx + c[/tex]
----------------------------
Slope 5 at x = 1 means that [tex]y^{\prime}(1) = 5[/tex], thus:
[tex]y^{\prime}(x) = 2ax + b[/tex]
[tex]y^{\prime}(1) = 2a + b[/tex]
[tex]2a + b = 5[/tex]
----------------------------
Slope -11 at x = -1 means that [tex]y^{\prime}(-1) = -11[/tex], thus:
[tex]-2a + b = -11[/tex]
Adding the two equations:
[tex]2a - 2a + b + b = 5 - 11[/tex]
[tex]2b = -6[/tex]
[tex]b = -\frac{6}{2}[/tex]
[tex]b = -3[/tex]
And
[tex]2a - 3 = 5[/tex]
[tex]2a = 8[/tex]
[tex]a = \frac{8}{2}[/tex]
[tex]a = 4[/tex]
Thus, the parabola is:
[tex]y = 4x^2 - 3x + c[/tex]
----------------------------
It passes through the point (2, 18), which meas that when [tex]x = 2, y = 18[/tex], and we use it to find c.
[tex]y = 4x^2 - 3x + c[/tex]
[tex]18 = 4(2)^2 - 3(4) + c[/tex]
[tex]c + 4 = 18[/tex]
[tex]c = 14[/tex]
Thus:
[tex]y = 4x^2 - 3x + 14[/tex]
A similar problem is given at https://brainly.com/question/22426360
The area of this parallelogram is 120 ft2 find the value of h
Answer: 6
Step-by-step explanation:
A=bh plus 120 for A and 20 for B
120=20b
/20 divide by 20 each side
H=6
15 3/4 is what decimal
━━━━━━━☆☆━━━━━━━
▹ Answer
15.75
▹ Step-by-Step Explanation
3 ÷ 4 = .75
15 + .75 = 15.75
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
The function f(x) = -x2 + 40x - 336 models the daily profit, in dollars, a shop makes for selling donut
combos, where x is the number of combos sold and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? Show
the work that leads to the answer. (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? Show
the work that leads to the answer. (5 points)
(10 points)
Answer:
This question should be worth atleast 20 points
Step-by-step explanation:
a. For the vertex, input the funtion into the calculator, and see where the turning piont is, that is the vertex.
b. Solve using this vormula.
x= (-b ±[tex]\sqrt{b^2 - 4ac}[/tex])/2a
you will get two asnwrs, both are correct.
A car is traveling on Michigan Street towards Ward Street. The car planes to turn right into Ward Street. what is the angle measure of the turn.
Pls help ASAP
There is a set of 100 obserations with a mean of 46 and a standard deviation of 0. What is the value of smallest obserstion in a set?
Answer:
Solution = 46
Step-by-step explanation:
I believe you meant standard deviation. Standard deviation is defined as the variation of the data set, or the differences between the values in this set. In order for the standard deviation to be 0, all values should be the same.
Now if the mean is 46, the smallest possible number of each value in the data set should be 46 as well. This is considering the mean is the average of the values, and hence any number of values in the data set being 46 will always have a mean of 46. Let me give you a demonstration -
[tex]Ex. [ 46, 46, 46 ], and, [46, 46, 46, 46, 46]\\Average = 46 + 46 + 46 / 3 = 46,\\Average = 46 + 46 + 46 + 46 + 46 / 5 = 46[/tex]
As you can see, the average is 46 in each case. This proves that a data set consisting of n number of values in it, each value being 46, or any constant value for that matter, always has a mean similar to the value inside the set, in this case 46. And, that the value of the smallest standard deviation is 46.
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]
I NEED HELP PLEASE THANKS!
Jenny is sitting on a sled on the side of a hill inclined at 15°. What force is required to keep the sled from sliding down the hill if the combined weight of Jenny and the sled is 90 pounds? (Show work)
Answer:
23.29 lbs
Step-by-step explanation:
The force on Jenny due to gravity can be resolved into components perpendicular to the hillside and down the slope. The down-slope force is ...
(90 lbs)sin(15°) ≈ 23.29 lbs
In order to keep Jenny in position, that force must be balanced by an up-slope force of the same magnitude.
Compute the critical value z Subscript alpha divided by 2 that corresponds to a 86% level of confidence.
Answer:
z = 1.476
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.86}{2} = 0.07[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.07 = 0.93[/tex], so [tex]z = 1.476[/tex]
The answer is z = 1.476
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
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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