Can y’all Plzs hep me I need this
Answer:
22.7 km
Step-by-step explanation:
The Pythagorean Theorem is:
a² + b² = c²
where a and b are legs and c is the hypotenuse.
The hypotenuse is the longest side of a right triangle and can be identified as being across from the right angle. The legs are interchangeable between the variables a and b.
Because it's clear that x is the hypotenuse:
15² + 17² = x²
225 + 289 = x²
514 = x²
√514 = √x²
x = √514
Because we can't simplify √514 anymore, we can keep it as radical 514 or round it:
22.6715681 ≈ 22.7
7th grade math!
Can somebody plz help answer these questions correctly (only if you remmeber how to do this) thx so much :3
WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DD
Answer:
I just learned about this, and if its wrong i am so so sorry
Step-by-step explanation:
a= 120
b= 60
w= 120
x= 120
r= 105
q= 105
p= 105
Answer:
a= 120
b= 60
w= 120
x= 120
r= 75
q= 105
p= 105
Step-by-step explanation:
|x+8|=x+8 what is x?
Answer:
x ≥ 0
Step-by-step explanation:
The absolute value of x+8 equals itself, thus x must be a real number (0 or any positive number).
The value of x in |x+8|=x+8 is -8.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that;
|x+8|=x+8
Now,
To solve this equation, we need to consider two cases:
Case 1: x+8 is positive or zero. Then |x+8|=x+8 and we can solve for x by subtracting 8 from both sides:
|x+8|=x+8
x+8=x+8
x=x
This means that any value of x is a solution in this case.
Case 2: x+8 is negative. Then |x+8|=-(x+8) and we can solve for x by adding 8 to both sides and dividing by -2:
|x+8|=-(x+8)
x+8=-(x+8)
2x=-16
x=-8
Therefore, by the given equation the answer will be -8.
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ2
6(y - 2) = -18
What is y?
Answer:
-1
Step-by-step explanation:
6 (y - 2) = -18
6y - 12 = -18
6y = -18 + 12
6y = -6
y = -1
If it takes Laine 4 hours to wash the windows, Leslie 5 hours to wash the same windows, and Lance 6 hours to wash the windows, how long would it take them all working together?
.8 hours
6 hours
1.6 hours
3.2 hours
1/4+1/5+1/6=1/x
LCM = 60
15/60+12/60+10/60=1/x
37/60=1/x
37x=60
x=60/37=1.62, round =1.6
1.6 HOURS
The number of hours they would take them all working together is around 1.6 hours.
What are ratios and proportions?A ratio is the divide of the two variables and the lower variable known as the denominator should not be zero.
Given that laine takes 4 hours to complete work
In 1 hour Laine will do 1/4 part of the work.
In 1 hour Leslie will do 1/5 part of the work.
In a 1-hour Lance will do 1/6 part of the work.
so let's suppose all done work by x hours then
1/4 + 1/5 + 1/6 = 1/x
x =1.6 so all together done the work by 1.6 hours.
For more information about ratio and proportion.
https://brainly.com/question/26974513
#SPJ5
A national health survey weighed a sample of 490 boys aged 6-11 and found that 67 of them were overweight. They weighed a sample of 530 girls aged 6-11 and found that 66 of them were overweight Conduct a hypothesis test to determine whether the proportion of overweight kids aged 6-11 among boys is greater than the proportion of overweight kids aged 6-11 among girls? Use level of significance 10%.
As the lower bound of the 90% confidence interval is below 0, there is not enough evidence to conclude that the proportion of overweight kids aged 6-11 among boys is greater than the proportion of overweight kids aged 6-11 among girls.
How to obtain the confidence interval?The sample proportions are given as follows:
Boys: 67/490 = 0.1367. Girls: 66/530 = 0.1245.The difference is then given as follows:
0.1367 - 0.1245 = 0.0122.
The standard error for each sample is given as follows:
[tex]s_B = \sqrt{\frac{0.1367(0.8633)}{490}} = 0.0153[/tex][tex]s_G = \sqrt{\frac{0.1285(0.8715)}{530}} = 0.0145[/tex]Then the standard error for the distribution of differences is given as follows:
[tex]s = \sqrt{0.0153^2 + 0.0145^2}[/tex]
s = 0.0211.
The critical value for a 90% confidence interval is given as follows:
z = 1.645.
The lower bound of the interval is:
0.0122 - 1.645 x 0.0211 = -0.0225.
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ4
Find all solutions of the equation in the interval [0°, 360°). cos(x) = -1
Answer:
180°
Step-by-step explanation:
cos(x) = - 1 has only 1 solution in the required interval , that is
x = [tex]cos^{-1}[/tex] (- 1) = 180°
Write an equation in point-slope form and slope-intercept form for each line
1. passes through (1, 9), slope = 2
2. passes through (4, -1), slope = -3
Answer:5.987
Step-by-step explanation:
An incoming college student took her college’s placement exams in French and mathematics. In French, she scored 85 and in math 80. The overall results for both exams are approximately normal. The French mean score was 72 with a standard deviation of 12, while the mean math score was 70, with a standard deviation of 7.8. On which exam did she do better compare with the other incoming college students? Compute the z-scores (round to 2 decimal places) and the percentiles (round to the nearest whole) for each exam to support your answer.
Answer:
Following are the responses to the given question:
Step-by-step explanation:
[tex]French \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Mathematics\\\\X= 85\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ X= 80\\\\\mu=72\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \mu =70\\\\\sigma=12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sigma= 7.8\\\\[/tex]
Formula:
[tex]\bold{Z-Score=\frac{x-\mu}{\sigma}}\\\\French \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Mathematics\\\\Z=\frac{85-72}{12} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Z=\frac{80-70}{7.8}\\\\=1.0833 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =1.2820\\\\[/tex]
In the french exam Z value is 1.0833 and in the maths exam Z value is 1.2820 that's why we can say that in maths exam, she does better than french exam.
if fis a differentiable function of rand g(x,y) = f(xy), show that x (dx)/(dg) - y (dg)/(dy) = 0
To prove that x(dx/dg) - y(dg/dy) = 0, we'll start by finding the derivatives of the functions involved.
Given that g(x, y) = f(xy), we can find the partial derivatives of g with respect to x and y using the chain rule:
∂g/∂x = ∂f/∂u * ∂(xy)/∂x = y * ∂f/∂u
∂g/∂y = ∂f/∂u * ∂(xy)/∂y = x * ∂f/∂u
Now, let's differentiate the equation x(dx/dg) - y(dg/dy) = 0:
d/dg (x(dx/dg) - y(dg/dy)) = d/dg (x(dx/dg)) - d/dg (y(dg/dy))
Using the chain rule, we can rewrite the derivatives:
d/dg (x(dx/dg)) = d/dx (x(dx/dg)) * dx/dg = x * d/dx (dx/dg)
d/dg (y(dg/dy)) = d/dy (y(dg/dy)) * dg/dy = y * d/dy (dg/dy)
Substituting these expressions back into the equation, we have:
x * d/dx (dx/dg) - y * d/dy (dg/dy) = 0
Now, let's simplify the equation further. Since dx/dg represents the derivative of x with respect to g, it is essentially the reciprocal of dg/dx, which represents the derivative of g with respect to x:
dx/dg = 1 / (dg/dx)
Similarly, dg/dy represents the derivative of g with respect to y. Therefore, we can rewrite the equation as:
x * d/dx (1/(dg/dx)) - y * d/dy (dg/dy) = 0
Taking the derivatives with respect to x and y, we have:
[tex]x * (-1/(dg/dx)^2) * (d^2g/dx^2) - y * (d^2g/dy^2) = 0[/tex]
Since dg/dx and dg/dy are partial derivatives of g, we can simplify further:
x * (-1/(∂g/∂x)^2) * (∂^2g/∂x^2) - y * (∂^2g/∂y^2) = 0
Finally, using the expressions we found for the partial derivatives of g earlier, we can substitute them into the equation:
x * (-1/(y * ∂f/∂u)^2) * (∂^2f/∂u^2 [tex]* y^2[/tex]) - y * (∂^2f/∂u^2 * [tex]x^2[/tex]) = 0
Canceling out the common factors, we are left with:
∂^2f/∂u^2 * x + ∂^2f/∂u^2 * y = 0
Since ∂^2f/∂u^2 is a constant (it does not depend on x or y), we can factor it out:
∂^2f/∂u^2 * (y - x) = 0
For the equation to hold, we must have either ∂^2f/∂u^2 = 0 or (y - x) = 0. However, the second condition (y - x) = 0 implies that y = x, which is not a necessary condition for the given equation to be true.
Therefore, the only possibility is ∂^2f/∂u^2 = 0, which implies that the equation x(dx/dg) - y(dg/dy) = 0 holds.
In conclusion, we have shown that x(dx/dg) - y(dg/dy) = 0 under the assumption that f is a differentiable function of r and g(x, y) = f(xy).
Learn more about differnetiation here:
https://brainly.com/question/28099315
#SPJ11
Cranor and Christensen study diabetics insured by two employers. Group 1 subjects were employed by the City of Asheville, North Carolina, and group 2 subjects were employed by Mission-St. Joseph’s Health System. The data are displayed in the following table.
Weight (Pounds) Group 1 Group 2 252 215 240 185 195 240 190 302 310 210 205 270 312 212 190 200 159 126 238 172 170 204 268 184 190 170 215 215 136 140 320 254 183 200 280 148 164 287 270 264 214 288 210 200 270 270 138 225 212 210 265 240 258 182 192 203 217 221 225 126 Source: Data provided courtesy of Carole W. Carnor, Ph.D. 220 295 202 268 220 311 164 206 170 190
ANSWER SHOULD BE BASE ON THE FF:
State the null and alternative hypothesis
Level of significance
Test statistics
Decision Rule
Stata Output
Statistical Decision
Conclusion
Linear Regression Model and Interpretation (if necessary)
Null and alternative hypothesis: The null hypothesis is that the mean weight of the diabetics insured by two employers is similar.
In contrast, the alternative hypothesis is that the mean weight of the diabetics insured by two employers is not equal. Level of significance: The level of significance
(α) is the probability of rejecting the null hypothesis when it is valid. The commonly used level of significance is 0.05.
Test statistic: Assuming the population variances are equal, the test statistic is the t-distribution.
Decision Rule: Reject H0 if the t-value is greater than 2.060 or less than -2.060 and accept H0 if the t-value is between 2.060 and -2.060.
State Output: Assuming equal variances, the p-value associated with a two-tailed t-test for equality of means is 0.2682.Statistical decision: Since the p-value is greater than 0.05, we accept the null hypothesis and conclude that the mean weight of diabetics insured by the two employers is equal.
Conclusion: Therefore, there is no considerable difference in the mean weight of diabetics insured by two employers in the City of Asheville and Mission-St. Joseph’s Health System. Linear regression model and interpretation (if necessary): A linear regression model was not necessary in this study.
To know more about probability refer to:
https://brainly.com/question/27342429
#SPJ11
A bag contains three different balls, one red (r), one blue(b), one white(w). TWO balls are drawn from the bag without replacement one after the other (at random without looking) and the colors recorded. This means once the first color is drawn, the first ball is kept out of the bag and only 2 colors remain when the second ball is drawn. List the sample space. [Use lower case letters for the colors, preserve the given order, commas separating pairs, no spaces.]
Answer:
The total sample list is 6
Step-by-step explanation:
The bag has following balls
Red - 1
Blue -1
White -1
Two balls are drawn from the bag without replacing the other -
The probability of drawing 1st ball of any color - 1/3
The probability of drawing 2nd ball of any color - 1/2
These two events are independent of each other
Hence, the probability of deriving two balls without replacement is 1/3*1/2 = 1/6
Hence, the total sample list is 6
The sample space is the list of possible outcomes of an experiment
The sample space is {rb, rw, br, bw, wr, wb}
The color of the three balls is represented as:
Red = r
Blue = b
White = w
Given that the selection is without replacement, the sample space would be:
rb, rw, br, bw, wr, wb
The count of the sample space represents the sample size.
Hence, the sample size of the experiment is 6, and the sample space is {rb, rw, br, bw, wr, wb}
Read more about sample space at:
https://brainly.com/question/16347135
what is the best approximation for the area of this circle? use 3.14 to approximate pi. responses
a.12.6 m²
b.25.1 m²
c.50.2 m²
d.158.0 m²
The best approximation for the area of this circle is approximately 50.2 m².Option (c) is the correct answer.
To determine the best approximation for the area of this circle, we need to use the formula for the area of a circle, which is given by A = πr².
Here, we are given the value of π to be approximately equal to 3.14.
Now, we need to determine the radius of the circle.
From the diagram, we can see that the diameter of the circle is 8 meters.
Therefore, the radius is half of this, which is 4 meters.
Substituting the values of π and r into the formula, we get: A = πr²= 3.14 × 4²= 3.14 × 16= 50.24 (to two decimal places)
Therefore, the best approximation for the area of this circle is approximately 50.2 m².Option (c) is the correct answer.
know more about area of this circle
https://brainly.com/question/28642423
#SPJ11
A sample of 92 one-year-old spotted flounder had a mean length of 123.47 millimeters with a sample standard deviation of 18.72 millimeters, and a sample of 138 two-year-old spotted flounder had a mean length of 129.96 millimeters with a sample standard deviation of 31.60 millimeters. Construct an 80% confidence interval for the mean length difference between two-year-old founder and one-year-old flounder. Let µ_1, denote the mean tength of two-year-old flounder and round the answers to at least two decimal places.
An 80% confidence interval for the mean length difference, in millimeters, between two-year-old founder and one-year old flounder is___<µ_1-µ_2<_____
The 80% confidence interval for the mean length difference between two-year-old and one-year-old spotted flounder is [5.15, 7.83] millimeters.
How to calculate the valueFor an 80% confidence interval, we need to find the critical value associated with a two-tailed test. Since the sample sizes are large, we can use the z-distribution. The critical value for an 80% confidence interval is approximately 1.282.
ME = 1.282 * 1.0466 ≈ 1.3426
Confidence interval = Point estimate ± Margin of error
Confidence interval = 6.49 ± 1.3426
Finally, rounding to at least two decimal places:
Confidence interval = [5.15, 7.83]
Therefore, the 80% confidence interval for the mean length difference between two-year-old and one-year-old spotted flounder is [5.15, 7.83] millimeters.
Learn more about confidence interval on
https://brainly.com/question/15712887
#SPJ4
If we were to make a poset of the form (A, |), where is the symbol for divisibility, which of the following sets A would yield a poset that is a total ordering? O A- (1, 4, 16, 64) O A- (1.2,3, 4, 6, 12) O A 1,2,3, 4, 6, 12, 18, 24) OA+{1 , 2, 3, 6, 12)
The sets A {1.2,3,4,6,12}, A{1,2,3,4,6,12,18,24}, and A{1,2,3,6,12} all yield a poset that is a total ordering.
In order for a partially ordered set (poset) to be a total order, every pair of elements must be comparable, i.e., for every pair of elements x, y in A, either x | y or y | x must be true.
Therefore, we should choose a set A that satisfies this condition.Let us consider each set in turn:(1, 4, 16, 64)This set contains powers of 4, which are not all divisible by each other.
For example, 16 | 64, but 16 does not divide 4.
Hence, this set is not a total order.{1.2,3, 4, 6, 12}In this set, 1 divides every other element, so it satisfies the condition for being a total order. Therefore, this set yields a poset that is a total order.
(1, 2, 3, 4, 6, 12, 18, 24)This set has the same elements as the previous set, plus some more. Hence, it also satisfies the condition for being a total order.
Therefore, this set yields a poset that is a total order.{1 , 2, 3, 6, 12}In this set, 1 divides every other element, 2 divides 6 and 12, and 3 divides 6 and 12.
Therefore, it satisfies the condition for being a total order.
Hence, this set yields a poset that is a total order.In conclusion, the sets A {1.2,3,4,6,12}, A{1,2,3,4,6,12,18,24}, and A{1,2,3,6,12} all yield a poset that is a total ordering.
Know more about poset here,
https://brainly.com/question/31920203
#SPJ11
The expression 2 3 4 2 is equivalent to A. 2 7 B. 2 12 C. 8 5 D. 8 6
Answer:
B. 2 12
Step-by-step explanation:
maaf kalo salah ituh jawabbanya menurut guwah
PLEASEEEEEEEEEEEEEEE HELPPPPPPPPPPPPPPPPPPPPPPP
Express 2^6 x (1/4)^5 / (16)^3 as a power with a base of 4
the expression 2⁶ × (1/4)⁵ / (16)³ can be written as 4⁻⁸.
To express the given expression 2⁶ × (1/4)⁵ / (16)³ as a power with a base of 4, we can simplify the expression using the properties of exponents:
2⁶ × (1/4)⁵ / (16)³
First, we simplify the exponents:
2⁶ = 64 = 4³
(1/4)⁵ = 4⁻⁵
(16)³ = 4⁶
Now, we substitute these simplified values back into the expression:
4³ × 4⁻⁵/4⁶ = 4³ × 4⁻⁵ × 4⁻⁶
= 4³⁻⁵⁻⁶
= 4⁻⁸
Finally, we express the simplified expression as a power with a base of 4: 4⁻⁸
Therefore, the expression 2⁶ × (1/4)⁵ / (16)³ can be written as 4⁻⁸.
Learn more about expression here
https://brainly.com/question/20511436
#SPJ4
I’m begging you please please ASAP ASAP please ASAP thank you please please ASAP
Answer:
The ratio is [tex]\frac{2}{3}[/tex].
Step-by-step explanation:
The ratio of the perimeters of Quad ABCD to Quad WXYZ = [tex]\frac{perimeter of ABCD}{perimeter of WXYZ}[/tex]
But considering sides AB and WX,
representative factor for both figures = [tex]\frac{12}{8}[/tex]
So that;
WX = 12
XY = 1.5 x 6 = 9
YZ = 1.5 x 7 = 10.5
WZ = 1.5 x 7 = 10.5
Thus,
perimeter of Quad ABCD = 6 + 7 + 7 + 8
= 28
perimeter of Quad WXYZ = 9 + 10.5 + 10.5 + 12
= 42
The ratio of the perimeters of Quad ABCD to Quad WXYZ = [tex]\frac{28}{42}[/tex]
= [tex]\frac{2}{3}[/tex]
Zc and Zx are supplementary angles. Zy measures 49º.
What is the measure of Zx?
Answer:
Zx = 131
Step-by-step explanation:
The angles will equal to 180, so therefore you will do 180-49=Zx
What is the surface area of the rectangular prism below
7 7 14
A.496 B.490 C.980 D.248
Answer:
B.490
Step-by-step explanation:
Correct me if im wrong
Answer: 490
Step-by-step explanation:
Use the Division Algorithm to show that the cube of any integer is of the form 9k, 9k + 1 or 9k + 8. (Hint: By the Division Algorithm, the integer a is of one of the forms 9q, 9q + 1, ..., 9q + 8; establish the result for 9q + 3 and 9q + 7 only.)
Using the Division Algorithm we have shown that the cube of any integer is of the form 9k, 9k + 1 or 9k + 8
To show that the cube of any integer is of the form 9k, 9k + 1, or 9k + 8, we will use the Division Algorithm. We will establish the result for the cases of 9q + 3 and 9q + 7.
Let's consider the case of 9q + 3, where q is an integer. We want to show that the cube of any integer of the form 9q + 3 is also of the form 9k, 9k + 1, or 9k + 8.
Let's choose an arbitrary integer, let's say n, such that n = 9q + 3.
Taking the cube of n:
n³ = (9q + 3)³
= 729q³ + 243q² + 27q + 27
Now, let's express this in terms of 9k, 9k + 1, or 9k + 8:
n³ = 729q³ + 243q² + 27q + 27
= 9(81q³ + 27q² + 3q + 3) + 18 + 9
= 9(81q³ + 27q² + 3q + 3 + 2) + 7
We can see that n³ can be expressed in the form 9k + 7, where k = 81q³ + 27q² + 3q + 3 + 2.
Therefore, we have shown that for the case of 9q + 3, the cube of any integer of that form is of the form 9k + 7.
Now, let's consider the case of 9q + 7, where q is an integer. We want to show that the cube of any integer of the form 9q + 7 is also of the form 9k, 9k + 1, or 9k + 8.
Similar to the previous case, let's choose an arbitrary integer, let's say n, such that n = 9q + 7.
Taking the cube of n:
n³ = (9q + 7)³
= 729q³ + 441q² + 147q + 49
Now, let's express this in terms of 9k, 9k + 1, or 9k + 8:
n³ = 729q³ + 441q² + 147q + 49
= 9(81q³ + 49q² + 16q + 5) + 4
We can see that n³ can be expressed in the form 9k + 4, where k = 81q³ + 49q² + 16q + 5.
Therefore, we have shown that for the case of 9q + 7, the cube of any integer of that form is of the form 9k + 4.
By using the Division Algorithm and establishing the results for the cases of 9q + 3 and 9q + 7, we have shown that the cube of any integer is of the form 9k, 9k + 1, or 9k + 8.
Learn more about Division Algorithm here
https://brainly.com/question/14542601
#SPJ4
Of the 1500 students at Marshall
Junior High, 38% are 7 graders.
What is the total number of 7
graders at Marshall Junior High?
Write a proportion and solve.
Answer:
36+25= 61
61/600 x 100 = 10.1 %
Step-by-step explanation: Hope This helped!!!!
Help ASAP! Will name brainliest!
I need help with my homework
Answer:
Step-by-step explanation:
1. b. Alt. Exterior angles
a. 7x + 8 = 6x + 18
c. x + 8 = 18
x = 10
d. 6(10) + 18 = 60 + 18 = 78
7(10) + 8 = 70 + 8 = 78
2. 15x + 10 + 12x + 8 = 180
same side angles
27x + 18 = 180
27x = 162
x = 6
15(6) + 10 = 90 + 10 = 100 degrees
12(6) + 8 = 72 + 8 = 80 degrees
3. 12x + 2 = 11x + 6
x + 2 = 6
x = 4
12(4) + 2 = 48 + 2 = 50 degrees
11(4) + 6 = 44 + 6 = 50 degrees
corresponding angles
Can someone help me pls
Answer:
The answer would be C
Step-by-step explanation:
This is because 3/4 times two is 6/4 simplified is 1 1/2
1. This Question Is Compulsory (a) Find the following Laplace transform and verse Laplace transform (1) Llet+')} (1) L- [8 marks) (b) 18 = 1+k8-2+ 3+ 3k and 7 - 1 - 2k, obtain the following (1) ä. ax, (1) 6x5)-(ä xk), (iv) 2:a)3 +34 (12 marks) () Find the point at which the plane 22 - 5y + z = 5 and the line Ft) - (+1) + (24+ 1)3+ (t+1)! (where t is a real number) intersect. [3 marks) (d) Compute the curvature and principal unit normal vector for the curve rt) 2 sin(t)+ 2 con(e) { for t > 0. [6 marks] 2t? (e) For the two matrices A= 12 0 0-7 5 3 B= B=(- :) 0 Find (1) AT, (1) BT, (ii) B(AT) and (iv) (AB)". [8 marks) (t) Find the determinant and trace of the matrix 5-13 10 0 - 2 1 0 3 [6 marks) Solve the following system of simultaneous equations using Gauss-Jordan elimination: 2.11 + 12 = -2, -92+372 = 4. [7 marks] Page 2 of 4
Part a. Find the Laplace transform and inverse Laplace transform of Let+')} and L- [8 marks]Laplace transform of Let+')} is given as: L(et+')} = 1/s-(1/ s+2)Let's try to this.1/s-(1/ s+2) = (s+2-s)/s(s+2) = 2/s(s+2)L-1{2/s(s+2)}= L-1{(1/s)-(1/s+2)} = e^(-2t) - 1
Part b. 18 = 1+k8-2+ 3+ 3k and 7 - 1 - 2k, obtain the following: i) ä. ax, ii) (ä xk), iii) 2:a)3 +34 i) 18 = 1+k8-2+ 3+ 3k
Let's simplify this as follows.18 = 12 + k + 3k - 2k + 3k-1 - 4k+1/218 = 12 - k + 2k + 2k + 3(1/k) - 4k+1/2a=12, b=-1, c=2 and d=2Therefore,ä. ax = ad-bc = 24 + 2 = 26ii) (ä xk) = (cd - bc)i + (ab - ad)j + (ad - bc)k = 1i - 2j + 24kiii) 2:a)3 +34 = 2(ad-bc) + 3(ab-ad) + 4(cd-bc) + 3(bd - ac) = 52
Part c. Find the point at which the plane 22 - 5y + z = 5 and the line Ft) - (+1) + (24+ 1)3+ (t+1)! (where t is a real number) intersect. [3 marks]. Let's substitute the given line in the plane equation. 2(1+4t) - 5(3+1t) + z = 5 solving for z, we get
z = 12t - 13
Substitute this z in line equation to get the point of intersection.(1+t, 4+2t, 12t-13)
Part d. Compute the curvature and principal unit normal vector for the curve rt) 2 sin(t)+ 2 con(e) { for t > 0. [6 marks]. Given curve r(t) = 2 sin(t) + 2 cos(t).
We need to find the first and second derivatives. r'(t) = 2 cos(t) - 2 sin(t)r''(t) = -2cos(t) - 2sin(t)
From these values, we get |r'(t)| = sqrt(8)K(t) = |r'(t)|/|r"(t)|^3/2K(t) = 2^(3/2)/8^(3/2)K(t) = 1/4^(1/2)K(t) = 1/2
Therefore the curvature is 1/2Now, let's find the principal unit normal vector. N(t) = r''(t)/|r"(t)|N(t) = <-1/sqrt(2),1/sqrt(2)>
Part e. For the two matrices A= 12 0 0-7 5 3 B= B=(- :) 0
Find i) AT, ii) BT, iii) B(AT) and iv) (AB)" [8 marks]
i) AT =Transpose of A = 1 -7 0 2 5 3
ii) BT =Transpose of B = 1 0 -3 0 2 1
iii) B(AT) =B(Transpose of A) = 1 -7 0 2 5 3(-1) 0 0 7 -5 -3= -1 7 0 -2 -5 -3
iv) (AB)" =(AB)^-1=Inverse of AB Let's calculate AB first. AB =12 0 0-7 5 3(-1) 0 0-5 2 -1= -1 0 0 1
Therefore, the inverse of AB is1 0 0-1
To know more about Laplace transform refer to:
https://brainly.com/question/31583797
#SPJ11
Assume that 7 people, including the husband and wife pair, apply for 6 sales positions. People are hired at random. What is the probability that one is hired and one is not?
The probability that one is hired and one is not is 5/7.
Given that there are 7 people, including the husband and wife pair, apply for 6 sales positions. People are hired at random.The probability that one is hired and one is not is obtained as follows:
Total number of ways to choose 6 people out of 7 is given by, `n(S) = 7C6 = 7`
The number of ways in which the husband and wife pair will be selected and 4 other people will be selected out of remaining 5 is given by, `n(E) = 5C4 = 5`
Therefore, the probability that one is hired and one is not can be expressed as:
Probability = n(E) / n(S)
Probability = 5/7
To know more about probability:
https://brainly.com/question/31828911
#SPJ11
There are 7 people for 6 positions. We know that the husband and wife pair both want a job, so we can count them as a single "unit" for this calculation. So there are effectively 6 people for 6 positions.
The required probability is 2/3.
There are two possible outcomes for the husband-wife pair:
Either both are hired or both are not hired. For the probability that one is hired and one is not:
Find the probability that the husband-wife pair are hired and subtract that from 1 (to get the probability that one is hired and one is not). The probability that the husband-wife pair are hired is:
[tex]\frac {\binom{5}{4}}{\binom{6}{4}} = \frac{5}{15}[/tex]
[tex]= \frac{1}{3}[/tex]
So the probability that one is hired and one is not is:
[tex]1 - \frac{1}{3} = \frac{2}{3}[/tex]
The required probability is 2/3.
To know more about probability visit
https://brainly.com/question/32004014
#SPJ11
Boilermaker House Painting Company incurs the following transactions for September.
1. September 3 Paint houses in the current month for $16,000 on account.
2. September 8 Purchase painting equipment for $17,000 cash.
3. September 12 Purchase office supplies on account for $2,700.
4. September 15 Pay employee salaries of $3,400 for the current month.
5. September 19 Purchase advertising to appear in the current month for $1,100 cash.
6. September 22 Pay office rent of $4,600 for the current month.
7. September 26 Receive $11,000 from customers in (1) above.
8. September 30 Receive cash of $5,200 in advance from a customer who plans to have his house painted in the following month.
BOILERMAKER HOUSE PAINTING COMPANY
Trial Balance
Accounts Debit Credit
Cash $11,300selected answer incorrect not attempted
Accounts Receivable 6,200selected answer incorrect not attempted
Supplies 2,900selected answer incorrect not attempted
Equipment 22,400selected answer incorrect not attempted
Accounts Payable not attempted 3,600selected answer incorrect
Deferred Revenue not attempted 5,000selected answer incorrect
Common Stock not attempted 20,000selected answer incorrect
Retained Earnings not attempted 8,000selected answer incorrect
Service Revenue not attempted 15,000selected answer incorrect
Salaries Expense 3,200selected answer incorrect not attempted
Advertising Expense 1,200selected answer incorrect not attempted
Rent Expense 4,400selected answer incorrect not attempted
Totals $51,600 $51,600
The trial balance provides a summary of Boilermaker House Painting Company's financial transactions for the month of September. The company engaged in several activities during the month, including providing painting services, purchasing equipment and office supplies, paying salaries, renting office space, and receiving cash from customers.
In the first transaction, the company painted houses for customers in the current month, generating service revenue of $16,000 on account. This resulted in an increase in the Accounts Receivable balance, representing the amount owed by customers.
The second transaction involved the purchase of painting equipment for $17,000 in cash. This expenditure was recorded as an increase in the Equipment account, which reflects the company's tangible assets.
Next, the company purchased office supplies on account for $2,700. This transaction increased the Supplies account and created an obligation in the form of an Accounts Payable.
The fourth transaction involved paying employee salaries of $3,400 for the current month. This expense was recorded in the Salaries Expense account, which represents the cost of labor incurred by the company.
In the fifth transaction, the company spent $1,100 in cash to purchase advertising, which was intended to appear in the current month. This expense was recorded in the Advertising Expense account.
The sixth transaction involved paying office rent of $4,600 for the current month. This expense was recorded in the Rent Expense account, representing the cost of utilizing office space.
In the seventh transaction, the company received $11,000 in cash from customers who had previously been billed for the painting services provided. This increased the Cash balance, reflecting the inflow of funds.
Lastly, the company received $5,200 in advance cash from a customer who planned to have their house painted in the following month. This created a liability in the form of Deferred Revenue, as the company had not yet provided the corresponding service.
Learn more about the Accounts:
brainly.com/question/14138124
#SPJ11
Consider the hypotheses shown below. Given that xˉ=49,σ=11,n=32,α=0.10, complete parts a and b. H0:μ≤47H1:μ>47 a. What conclusion should be drawn? b. Determine the p-value for this test. a. The z-test statistic is (Round to two decimal places as needed.) a. The z-test statistic is (Round to two decimal places as needed.) The critical z-score(s) is(are) (Round to two decimal places as needed. Use a comma to separate answers as needed.) Because the test statistic the null hypothesis. b. The p-value is (Round to three decimal places as needed.)
The conclusions are as follows:
a. We reject the null hypothesis.
b. The p-value for this test is approximately 0.001.
To complete parts a and b, we can follow the steps for hypothesis testing.
a. The z-test statistic can be calculated using the formula:
z = ([tex]\bar{X}[/tex] - μ) / (σ / √n)
Given:
[tex]\bar{X}[/tex] = 49
σ = 11
n = 32
Substituting these values into the formula, we get:
z = (49 - 47) / (11 / √32) ≈ 2.90
The z-test statistic is approximately 2.90 (rounded to two decimal places).
To determine the critical z-score(s), we need to find the z-value that corresponds to the significance level α = 0.10. Since the alternative hypothesis is one-sided (μ > 47), we are performing a right-tailed test.
Using a standard normal distribution table or a calculator, the critical z-score for a right-tailed test at α = 0.10 is approximately 1.28 (rounded to two decimal places).
Because the test statistic z = 2.90 is greater than the critical z-score of 1.28, we reject the null hypothesis.
b. The p-value represents the probability of obtaining a test statistic as extreme as the observed value (or more extreme) assuming the null hypothesis is true. Since the alternative hypothesis is μ > 47, we are looking for the probability in the right tail of the distribution.
Using a standard normal distribution table or a calculator, we can find the p-value corresponding to the z-test statistic z = 2.90. The p-value is the area under the curve to the right of 2.90.
The p-value is approximately 0.001 (rounded to three decimal places).
Therefore, the conclusions are as follows:
a. We reject the null hypothesis.
b. The p-value for this test is approximately 0.001.
Learn more about Z-score here
https://brainly.com/question/31871890
#SPJ4