Answer:
The width is:
[tex]-2+\sqrt{26}\text{ meters}\text{ }(\text{or approximately 3.0990 meters})[/tex]
And the length is:
[tex]2+\sqrt{26}\text{ meters}\text{ } (\text{or approximately 7.0990 meters})[/tex]
Step-by-step explanation:
Recall that the area of a rectangle is given by:
[tex]\displaystyle A = w\ell[/tex]
Where w is the width and l is the length.
We are given that the length of a rectangle is four meters longer than the width. Thus:
[tex]\ell = w + 4[/tex]
And we also know that the area of the rectangle is 22 square meteres.
Substitute:
[tex](22)=w(w+4)[/tex]
Distribute and isolate the equation:
[tex]w^2+4w-22=0[/tex]
The equation isn't factorable, so we can instead use the quadratic formula:
[tex]\displaystyle w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = 4, and c = -22. Substitute:
[tex]\displaystyle w = \frac{-(4)\pm\sqrt{(4)^2-4(1)(-22)}}{2(1)}[/tex]
Evaluate:
[tex]\displaystyle\begin{aligned} w &= \frac{-4\pm\sqrt{104}}{2}\\ \\ &=\frac{-4\pm\sqrt{4\cdot 26}}{2} \\ \\ &=\frac{-4\pm2\sqrt{26}}{2} \\ \\ & = -2\pm \sqrt{26} \end{aligned}[/tex]
Thus, our two solutions are:
[tex]w_1=-2+\sqrt{26}\approx 3.0990\text{ or } w_2=-2-\sqrt{26}\approx-7.0990[/tex]
Since the width cannot be negative, we can ignore the second solution.
Since the length is four meters longer than the width:
[tex]\ell = (-2+\sqrt{26})+4=2+\sqrt{26}\text{ meters}[/tex]
Thus, the dimensions of the rectangle are:
[tex]\displaystyle (2+\sqrt{26}) \text{ meters by } (-2+\sqrt{26})\text{ meters}[/tex]
Or, approximately 3.0990 by 7.0990.
Find the length of the other two side of the isosceles right triangle
Answer:
The other two sides are 7 units each.
Step-by-step explanation:
The triangle is isosceles.
The sides are in the ratio of
[tex]x : x : x \sqrt{2}[/tex]
The hypotenuse is
[tex]7\sqrt{2}=x \sqrt{2}\\\\x = 7[/tex]
So, the other two sides are 7 units each.
A study was done to determine the average number of homes that a homeowner owns in his or her lifetime. For the 50 homeowners surveyed, the sample average was 5.1 and the sample standard deviation was 3.8. Calculate the 95% confidence interval for the true average number of homes that a person owns in his or her lifetime.
Answer:
The 95% confidence interval for the true average number of homes that a person owns in his or her lifetime is (4,6.2).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 50 - 1 = 49
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0096
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0096\frac{3.8}{\sqrt{50}} = 1.1[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 5.1 - 1.1 = 4
The upper end of the interval is the sample mean added to M. So it is 5.1 + 1.1 = 6.2.
The 95% confidence interval for the true average number of homes that a person owns in his or her lifetime is (4,6.2).
For the following relation, find the: a) Reflexive closure b) Symmetric closure c) Transitive closure 2 You may include explanation if you like but no explanation is required. Your solution may be a graphical representation.v g
Answer:
Following are the complete solution in the attached file.
Step-by-step explanation:
The object of a popular carnival game is to roll a ball up an incline into regions with different
values. The probability that Angus will get 100 points in a roll is 40%, 200 points is 35%, and
300 points is 25%. Find the expected value, E(X), of a roll.
O 185
O 200
O 400
O 150
The expected value, E(x) of the given observation is 185
The expected value is the mean of the overall observed value or random value. In other words, it is the average of the observed values.
The given parameters can be represented as:
[tex]\begin{array}{cccc}x & {100} & {200} & {300} \ \\ P(x) & {40\%} & {35\%} & {25\%} \ \end{array}[/tex]
The following formula calculates the expected value:
[tex]E(x) =\sum x * P(x)[/tex]
So, we have:
[tex]E(x) = 100 * 40\% + 200 * 35\% + 300 * 25\%[/tex]
[tex]E(x) = 40 + 70 + 75[/tex]
[tex]E(x) = 185[/tex]
Learn more about expected values at:
https://brainly.com/question/16726343
if 12 +2 =2 orderly what is 6 +3 orderly
Answer:
3
Step-by-step explanation:
Please Mark me brainliest
Answer:
aren't one of the numbers in the equations supposed to be negative?
Help me please with this question
9514 1404 393
Answer:
21
Step-by-step explanation:
Let c represent the number of child tickets sold. Then 2c is the number of adult tickets sold. The total revenue is ...
5.80c +9.50(2c) = 520.80
24.80c = 520.80 . . . . . . . . . simplify
c = 21 . . . . . . . . . . . . . . divide by 24.80
21 child tickets were sold that day.
Melinda takes out a loan to purchase a car. The balance on her loan after x months is represented by the equation y = 10,000 – 250x and the value of the car after x months is represented by y = 8,000 – 50x. Which statement describes when Melinda’s loan will be equal to the value of the car?
After 10 months, the loan and value of the car will both be equal to $7,500.
After 12 months, the loan and value of the car will both be equal to $7,000.
After 14 months, the loan and value of the car will both be equal to $6,500.
After 16 months, the loan and value of the car will both be equal to $6,000.
Answer:
Step-by-step explanation:
12 months
Answer:
12 months b on edg
Step-by-step explanation:
edg 2022
create a graph of 4.95 + 3.99
Answer:
????
Step-by-step explanation:
as in y = 4.95 + 3.99 or points? if so just draw a horizontal line at 8.94
A small boat can travel at 28 per hour how many hours will it take to go across the bay that is 56 miles wide
Answer:
2 hours
Remember that time = distance/rate
The distance you need to cover is 56 miles, while you go 28 miles per hour. Using these, we get this:
time=56/28
time=2
So it will take two hours to go across a 56 mile wide bay at 28 mph.
Step-by-step explanation:
At a local company, 15% of the employees are women. every day, 9% of them bring their lunch to work, while only 3% of the men bring lunch. Find the probability that a randomly selected employee
a. is a woman goven that the person brings their lunch to work.
b. brings their lunch to work given that person is a woman.
c. is a woman given that the person brings their lunch to work.
Answer:
a) 0.3462 = 34.62% that a randomly selected employee is a woman given that the person brings their lunch to work.
b) 0.09 = 9% probability that a randomly selected employee brings their lunch to work given that person is a woman.
c) 0.3462 = 34.62% that a randomly selected employee is a woman given that the person brings their lunch to work.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Questions a/c:
Questions a and c are the same, so:
Event A: Brings lunch to work.
Event B: Is a woman.
Probability of a person bringing lunch to work:
9% of 15%(woman)
3% of 100 - 15 = 85%(man). So
[tex]P(A) = 0.09*0.15 + 0.03*0.85 = 0.039[/tex]
Probability of a person bringing lunch to work and being a woman:
9% of 15%, so:
[tex]P(A \cap B) = 0.09*0.15[/tex]
Desired probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.09*0.15}{0.039} = 0.3462[/tex]
0.3462 = 34.62% that a randomly selected employee is a woman given that the person brings their lunch to work.
Question b:
Event A: Woman
Event B: Brings lunch
15% of the employees are women.
This means that [tex]P(A) = 0.15[/tex]
Probability of a person bringing lunch to work and being a woman:
9% of 15%, so:
[tex]P(A \cap B) = 0.09*0.15[/tex]
Desired probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.09*0.15}{0.15} = 0.09[/tex]
0.09 = 9% probability that a randomly selected employee brings their lunch to work given that person is a woman.
the perimeter of a square is less than or equal to 50 find the range of the value of the length of the square
Answer:
12.5 ≥ s >0
Step-by-step explanation:
The perimeter of a square is given by
P = 4s where s is the side length
50 ≥ 4s
Divide each side by 4
50/4 ≥ 4s/4
25/2 ≥ s
12.5 ≥ s
A study was done to determine the proportion of voters that feel that their local government is doing an adequate job. Of the 220 voters surveyed, 175 feel that their local government is doing an adequate job. Calculate the 95% confidence interval for the true proportion of voters that feel that their government is doing an adequate job.
Answer:
( 0.742, 0.849 )
Step-by-step explanation:
sample size = 220
number of voters with positive response ( i.e. number of voters who believe the government is doing right ) = 175
Calculate the 95% confidence interval
P = 175 / 220 = 0.796
the 95% confidence interval = ( 0.796 ± 0.054 )
attached below is the detailed solution
The picture shows the graphs of the movement of a pedestrian (B) and a bicyclist (A) . Using the graphs, answer the following questions:
How many times is the distance covered by the bicyclist for 1 hour greater than the distance covered by the pedestrian for the same amount of time?
Answer:
15km
Step-by-step explanation:
hope it is well understood?
Answer:
5 times.
Step-by-step explanation:
First, look at the values of each line at the 1-hour mark.
For line A (the bicyclist), the distance is about 25 km.
For line B (the pedestrian), the distance is about 5 km.
To determine how many times greater the bicyclist distance is than the pedestrian, divide the values:
[tex]\frac{25\text{km}}{5\text{km}}=5[/tex]
Therefore, the distance covered by the bicyclist for 1 hour is 5 times greater than the distance covered by the pedestrian for the same amount of time.
write your answer in simplest radical form
Answer:
x = 2 yd
Step-by-step explanation:
Angles of 45 degreees = two congruent legs
for the Pythagorean theorem
2x^2 = 8
x^2 = 4
x = 2
U looking for BRAINLIEST? I'll give it to the first person to get it right
What is the shape of the distribution shown below?
A: The distribution is skewed to the left.
B: The distribution is approximately symmetrical.
C: The distribution is skewed to the right.
Answer:
A: The distribution is skewed to the left.
Step-by-step explanation:
Skewness:
If the distribution has a long left tail, it is skewed to the left.
If it has a long right tail, it is skewed to the right.
Otherwise, it is approximately symmetrical.
In this question:
Lots of values on the start(left), few on the end(right), so it is skewed to the left, and the correct answer is given by option a.
Find the missing side of the right triangle.
Answer:
√202
Step-by-step explanation:
since it's the hypotenuse you are required to find
x²=11²+9²
x²=121+81
√x²=√202
x=√202
I hope this helps
Write a linear equation representing the information shown in the table.
A) y = –2∕5x – 5
B) y = –5∕2x – 5
C) y = 5∕2x – 5
D) y = 2∕5x – 5
Answer:
C. y = ⁵/2x - 5
Step-by-step explanation:
The linear equation representing the information on the table can be expressed in the slope-intercept form as y = mx + b, where,
m = slope = change in y/change in x
b = y-intercept/initial value = the value of y when x is zero
✔️Find m using two pairs given, say (0, -5) and (2, 0):
slope (m) = (0 - (-5))/(2 - 0) = 5/2
m = ⁵/2
✔️Find b:
when x = 0, y = -5. Therefore, y-intercept, b, is -5
b = -5
✔️To write the equation, substitute m = ⁵/2 and b = -5 into y = mx + b
Thus:
y = ⁵/2x + (-5)
y = ⁵/2x - 5
Emma went out shopping with her father and bought a dress that cost $40.00. In class, she
learned to find the sales tax by multiplying by .08 (the sales tax in her state is 8%). Emma
found the tax, and then added the tax to the original amount. Emma's mother suggested that
she should just multiply the cost of the dress by 1.08 and that this method would give her the
final answer with the tax included. Emma was confused. Who is right? Work it out both ways
and explain your thinking.
Answer:
Both ways are correct
If you multiply the cost by 8% and add, you will still get 108% as your total.
Answer:
Both ways are correct
Step-by-step explanation:
Father's way is ( 40 × 0.08 ) + 40 = $43.2
Mothers way is 40 × 1.08 = $43.2
If the area A of a triangle is 60 m- (square meters) and the base b is 20 m, what is the altitude h?
Answer:
not sure
Step-by-step explanation:
a+B+C+=d
What is the midpoint of the line segment AB?
Answer:
(5.5,0)
Step-by-step explanation:
Mid point is ((3+8)/2,(4-4)/0)=(5.5,0)
Given the mean for six numbers is 24. If three numbers which are x, (x + 2) and (x - 2) are added into the data set, the value of mean changed to 30. Calculate the value of x.
Answer:
42
Step-by-step explanation:
We know that the mean of 6 numbers is 24. This means that
[tex] \frac{x}{6} = 24[/tex]
Solve for x.
[tex]x = 144[/tex]
If we add, x, (x+2), and (x-2). We will have 9 terms. The value of mean will change to 30. This also means that
[tex] \frac{270}{9} = 30[/tex]
[tex]144 + x + (x + 2) + (x - 2) = 270[/tex]
[tex]3x + 144 = 270[/tex]
[tex]3x = 126[/tex]
[tex]x = 42[/tex]
g A manufacturer of nickel-hydrogen batteries randomly selects 100 nickel plates for test cells, cycles them a specified number of times, and determines that 11 of the plates have blistered. Does this provide compelling evidence for concluding that more than 10% of all plates blister under such circumstances
Complete Question
A manufacturer of nickel-hydrogen batteries randomly selects 100 nickel plates for test cells, cycles them a specified number of times, and determines that 11 of the plates have blistered. Does this provide compelling evidence for concluding that more than 10% of plates blister under such circumstances?
A) State H_0 and H_a, (5 pts)
B) Test the hypothesis using the P-Value approach at a significance level of 4%: (15 pts)
Expert Answer
Answer:
a)[tex]H_0:p=0.10[/tex]
[tex]H_a:p>0.10[/tex]
b) We fail to reject Null hypothesis
Step-by-step explanation:
From the question we are told that:
Sample size n=100
No. with blistered x=11
a)
Generally the Hypothesis given as
[tex]H_0:p=0.10[/tex]
[tex]H_a:p>0.10[/tex]
b)
Since p=0.10
Therefore
[tex]p'=\frac{11}{100}[/tex]
[tex]p'=0.11[/tex]
Test statistics
[tex]Z=\frac{p'-p}{\sqrt{p(1-p)}}[/tex]
[tex]Z=\frac{0.11-0.10}{\sqrt{0.10*0.90/100}}[/tex]
[tex]Z=1.33[/tex]
From table
[tex]P-Value =0.092[/tex]
Therefore
P-value >0.04 significance level
Hence,We cannot conclude that at [tex]4\%[/tex] significance level the proportion is greater than [tex]10\%[/tex]
We fail to reject Null hypothesis
[tex] - x ^{2} + 2x - 6 = 0[/tex]
how to do,I don't know the step
answer is
[tex]x = 1 - \sqrt{5} i \: \: \: \: \: or \: \: 1 + \sqrt{5} i[/tex]
Answer:
there are several methods to "solve a quadratic"
you can look them all up...
Graphing, factoring, completing the square, taking roots, quadratic formula are the common methods....
given the way you are asking the question I think that you are supposed to use the quadratic formula ..
please look at the image of the formula and
realize that you problem has
a=-1
b=2
c=6
just plug in those numbers into the formula and you will get the results in the "answer"
NOTE [tex]\sqrt{-x}[/tex] is written as ix ( [tex]\sqrt{-25} = 5i[/tex] )
Step-by-step explanation:
x= -2+√ (2)²- (4)(-1)(-6)
(2)(-1)
and
x= -2-√ (2)²- (4)(-1)(-6)
(2)(-1)
Find the measure of the incanted angle to the nearest degree
Answer:
15.5⁰ or approximately 16⁰
Step-by-step explanation:
let unknown side be x
cos x= 53/55
cos x= 0.9636
x=cos inverse of 0.9636
x=15.5⁰
Answer:
[tex]cosx = \frac{53}{55} \\ x = {cos}^{ - 1} ( \frac{53}{55} ) \\ x = 15.4987[/tex]
I thought of a number. I added 15, tripled it and then subtracted 3 from the result. I got 42. What was my number?
Answer:
45
Step-by-step explanation:
15 x 3 = 45 - 3 = 42
What is 4x-3(x-2y)+1/2(6x-8y) in fraction form
Answer:
Hola
Step-by-step explanation:I need points
Answer:
4x+2y
Step-by-step explanation:
Cho hệ vectơ:
X1=(2;1;0;1); X2=(1;1;0;-1); X3=(0;-1;2;2); X4=(1;0;2;1)
a) Xét xem hệ vectơ trên độc lập tuyến tính hay phụ thuộc tuyến tính.
b) Biểu diễn vectơ X 4 qua các vectơ còn lại.
Answer:
i dont no the ans
Step-by-step explanation:
What is the conjugate of
square root 8 - square root 9
Answer:
[tex]\sqrt{8}+\sqrt{9}[/tex]
Step-by-step explanation:
By definition, the conjugate of a binomial is when you switch the operator (either + or -) in between the terms. For example, the conjugate of [tex]a+b\sqrt{c}=a-b\sqrt{c}[/tex] as we are just changing the addition symbol (+) to a subtraction symbol (-).
Therefore, the conjugate of [tex]\sqrt{8}-\sqrt{9}[/tex] occurs when we change the subtraction symbol to an additional symbol, hence the answer is [tex]\boxed{\sqrt{8}+\sqrt{9}}[/tex]
HELP WITH 16 What is the value of X
Answer:
C - 136
(115+157)/2
Step-by-step explanation:
Find the equation of the circle, if (4, -2)
and (2, 1) are the extremities of the
diameter.
Answer:
(x-3)^2+(y+1/2)^2=3.25
Step-by-step explanation:
The radius of the circle would be the midpoint of diameter. Radius is (3,-1/2) and the length would be 1.8.
