Answer:
Width = 8 cm
Length = 48 cm
Step-by-step explanation:
Area of a Rectangle Formula: A = lw
Step 1: Write out expression:
l = 6w
w = w
Step 2: Plug in known variables
384 = 6w(w)
Step 3: Solve for w
385 = 6w²
w² = 64
w = 8
Step 4: Find l
l = 6(8)
l = 48
Find a tangent vector of unit length at the point with the given value of the parameter t. r(t) = 2 sin(t)i + 7 cos(t)j t = π/6
The tangent vector to r(t) at any t in the domain is
[tex]\mathbf T(t)=\dfrac{\mathrm d\mathbf r(t)}{\mathrm dt}=2\cos t\,\mathbf i-7\sin t\,\mathbf j[/tex]
At t = π/6, the tanget vector is
[tex]\mathbf T\left(\dfrac\pi6\right)=\sqrt3\,\mathbf i-\dfrac72\,\mathbf j[/tex]
To get the unit tangent, normalize this vector by dividing it by its magnitude:
[tex]\left\|\mathbf T\left(\dfrac\pi6\right)\right\|=\sqrt{(\sqrt3)^2+\left(-\dfrac72\right)^2}=\dfrac{\sqrt{61}}2[/tex]
So the unit tangent at the given point is
[tex]\dfrac{\mathbf T\left(\frac\pi6\right)}{\left\|\mathbf T\left(\frac\pi6\right)\right\|}=2\sqrt{\dfrac3{61}}\,\mathbf i-\dfrac7{\sqrt{61}}\,\mathbf j[/tex]
Applying derivatives, the tangent vector of unit length at the point given is:
[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{\sqrt{61}}i - \frac{7}{\sqrt{61}}j[/tex]
The vector function is:
[tex]r(t) = 2\sin{(t)}i + 7\cos{(t)}j[/tex]
The tangent vector is it's derivative, which is given by:
[tex]r^{\prime}(t) = 2\cos{(t)}i - 7\sin{(t)}j[/tex]
At point [tex]t = \frac{\pi}{6}[/tex], we have that:
[tex]r^{\prime}(\frac{\pi}{6}) = 2\cos{(\frac{\pi}{6})}i - 7\sin{(\frac{\pi}{6})}j[/tex]
[tex]r^{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{2}i - \frac{7}{2}[/tex]
[tex]r^{\prime}(\frac{\pi}{6}) = \sqrt{3}i - \frac{7}{2}[/tex]
The norm of the vector is:
[tex]|r^{\prime}(\frac{\pi}{6})| = \sqrt{\sqrt{3}^2 + (-\frac{7}{2})^2}[/tex]
[tex]|r^{\prime}(\frac{\pi}{6})| = \sqrt{\frac{61}{4}}[/tex]
[tex]|r^{\prime}(\frac{\pi}{6})| = \frac{\sqrt{61}}{2}[/tex]
The unit vector is given by each component divided by the norm, thus:
[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{\sqrt{3}}{\frac{\sqrt{61}}{2}}i - \frac{7}{2\frac{\sqrt{61}}{2}}j[/tex]
[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{\sqrt{61}}i - \frac{7}{\sqrt{61}}j[/tex]
A similar problem is given at https://brainly.com/question/20733439
The probability that a grader will make a marking error on any particular question of a multiple-choice exam is 0.10. If there are ten questions and questions are marked independently, what is the probability that no errors are made
Answer:
0.9^10
Step-by-step explanation:
The probability to make an error in 1 question =0.1 => The probability that this one particular question will be answered correctly is P=1-0.1=0.9
There are 10 questions that are independent from each other .
The probability to be answered correctly is 0.9 each. So the probability to answer correctly to all of them is
P(10quest=correct) =0.9*0.9*0.9*0.9*0.9*0.9*0.9*0.9*0.9*0.9=0.9^10
PLEASE ANSWER U NEED HELP!! determine which numbers The equations need to be multiplied by to form opposite terms of the y variable. 3x - 1/4y equals 15 2/3x - 1/6y equals 6 which number should be the first equation be multiplied by? which number should the second equation be multiplied by?
Answer:
4 -6
Step-by-step explanation:
have a great day!
Multiply the first equation by 2/3 and the second equation by -1.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
3x - (1/4)y = 15
(2/3)x - (1/6)y = 6
Multiply the equation 1 by 2/3, then we have
(2/3) · 3x - (2/3) · (1/4)y = (2/3) · 15
x - (1/6)y = 10
Multiply the equation 2 by -1, then we have
(-1) · (2/3)x - (-1) · (1/6)y = (-1) · 6
- (2/3) x + (1/6)y = - 6
Multiply the first equation by 2/3 and the second equation by -1.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ3
Which lines are parallel? Justify your answer.
A. Lines a and b are pa because their corresponding angles are congruent.
B. Lines a and b are parallel because their same side exterior angles are congruent.
C. Lines e and f are parallel because their corresponding angles are congruent.
D. Lines e and f are parallel because their same side exterior angles are supplementary.
Answer:
A. Lines a and b are pa because their corresponding angles are congruent.
Step-by-step explanation:
The corresponding angles are both 110 degrees.
Pls help me I really need help
Answer:
26 - 7(n-1)
Step-by-step explanation:
subtract n times 7 from the start value.
But if we want to call the first term n=1, we have to subtract 1 from n.
which linear is represented by the graph?
What is the area , rounded to nearest hundredth?
Answer:
57
Step-by-step explanation:
Area of rectangle:
4 x 12
=48
Area of left triangle:
2 x 3 / 2
=3
Area of right triangle:
6 x 2 / 2
=6
Total Area:
48 + 3 + 6 = 57
Answer: 100
Step-by-step explanation: 4 * 12 = 48 6 * 2 / 0.5 = 24 3 * 2 / 0.5 = 12
48+24+12=84 84 to the nearest hundred is 100.
3/(2x-1)+4=6x/(2x-1)
X=?
Which of the following illustrates the truth value of the following mathematical statements?
6 + 3 = 9, and 5.5 = 20
Answer: 6 + 3 = 9
Step-by-step explanation:
5.5 does not equal to 20
Flying against the wind, a jet travels 3000 miles in 4 hours. Flying with the wind, the same jet travels 7500 miles in 6 hours. What is the rate of the jet in still air and what is the rate of the wind? g
Answer:
The rate of the jet in still air is 1125 miles per hour, and the rate of the wind is 375 miles per hour.
Step-by-step explanation:
Flying against the wind, the speed of the airplane is 750 miles per hour (3000/4), while flying with a downwind, its speed is 1500 miles per hour (7500/6). Therefore, the difference between the two speeds is 750 miles per hour, so since the distance traveled is the same, the midpoint between the two speeds is 375 miles per hour. Then, without wind, the plane would travel the same distances at a speed of 1125 miles per hour.
In conclusion, the rate of the jet in still air is 1125 miles per hour, and the rate of the wind is 375 miles per hour.
ok first person to answer my question will get marked as the brainliest answer and i will give you a thanks and a like. Each square below represents one whole. A square divided in 25 equal parts, all 25 of which are shaded Another square divided in 25 equal parts, 13 of which are shaded What percent is represented by the shaded area?
Answer:
76%
Step-by-step explanation:
First, we need to see how many total squares (parts) there are. There are 50.
Now, we need to see how many parts are shaded. So, 13 plus 25 will give us 38.
Our fraction is 38/50, which is 76%.
Hope this helped!
Answer: 76 percent
Step-by-step explanation:
We have two squares divided into exactly 25 indentical parts
In the first one 25 squares are shaded wich means 25/25
The second one we only 13 shaded square wich means 13/25
So in total we have 50 squares with 38 shaded ones
Wich means 38/50
38/50= 0.76
Multiply bu 100 to get the percentage wich 76 percent
Suppose Melissa borrows $3500 at an interest rate of 14% compounded each year,
Assume that no payments are made on the loan.
Do not do any rounding.
(a) Find the amount owed at the end of 1 year
(b) Find the amount owed at the end of 2 years.
PLEASE HELPPP!!!
The sum of an irrational number and a rational number is irrational. Sometimes True Always True Never True
Answer:
Always true
Step-by-step explanation:
Trust me
Answer:
true
Step-by-step explanation:
I need to find for both f(-1) and f(1) it’s
Answer:
f(-1) = -8
f(1) = -12
he data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted value?
Answer:
^Y= 26.72 + 0.0547Xi
^Y/[tex]_{X=3000}[/tex]= 190.82ºF
B. It is unrealistically high.
Step-by-step explanation:
Hello!
*Full text*
The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of .05. What is wrong with this predicted value?
Chirps in 1 min. 929 854 771 1004 1201 1027
Temperature (F) 81.3 77.3 64.8 80.3 92.2 80.9
What is the regression equation?
^y= _____ + _____
(Round the x-coefficient to four decimal places as needed. Round the constant to two decimals as needed)
What is the predicted value? ^y= _____ (Round to one decimal places as needed)
What is wrong with this predicted value?
A. The first variable should have been the dependent variable
B. It is unrealistically high.
C. It is only an approximation
D. Nothing is wrong with this value
To calculate the regression equation you have to estimate the slope and the y-intercept.
^Y= a + bX
Estimate of the slope:
[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }[/tex]
n= 6
∑X= 5786 ∑X²= 5691944 [tex]\frac{}{X}[/tex]= 964.33
∑Y= 476.80 ∑Y²= 38277.76 [tex]\frac{}{Y}[/tex]= 79.47
∑XY= 465940.4
[tex]b= \frac{465940.4-\frac{5786*476.80}{6} }{5691944-\frac{(5786)^2}{6} }= 0.0547[/tex]
Estimate of the Y-intercept:
[tex]a= \frac{}{Y} -b*\frac{}{X}[/tex]
[tex]a= 79.47 -0.0547*964.33= 26.696= 26.72[/tex]
The estimated regression equation is:
^Y= 26.72 + 0.0547Xi
^Y/[tex]_{X=3000}[/tex]= 26.72 + 0.0547*3000= 190.82ºF
At the rate of 3000 chirps per minute it is expected a temperature of 190.82ºF
As you can see it is unrealistic to think that the chirping rate of bugs will have any effect over the temperature. For what is known about bugs, they tend to be more active to higher temperatures.
Considering the value obtained, as it is incredible high, if this regression was correct, every time the chirping rate of bugs increases, the ambient temperature would rise to levels incompatible with life.
I hope this helps!
Find the inverse of the following function: f(x) = 8√x for x ≥ 0
Answer:
Step-by-step explanation:
Rewrite the function f(x) = 8√x as y = 8√x.
To find the inverse function, do the following:
1) Interchange x and y. We get x = 8√y
x x^2
2) Solve this result for y: (x/8) = √y => y = ( -------- )^2, or y = ---------
8 64
which of the following is the correct factorization of the trinomial below?
-7x^2 + 5x + 12
a. 7(x+1) (-x + 12)
b. -1 (7x - 12) (x+1)
c. (-7x + 12) (x - 1)
d. -7 (x - 6) (x+1)
Answer:
The answer is option B.
Hope this helps you
Answer:
The answer is B
Step-by-step explanation:
A baseball card collector buys and opens 360 packs of 1989 Fleer baseball cards. He is told that there is a 2.3% chance of anyone pack containing the coveted Billy Ripken error card. Find the mean and standard deviation of the random variable "number of Billy Ripken error cards ound", where n-360
Answer:
Mean: 8.28
Standard deviation: 2.84
Step-by-step explanation:
This random variable "number of Billy Ripken error cards found" can be described by the binomial distribution, with sample size n=360 (number of packs) and probability of success p=0.023 (probabillity of a pack containing the coveted Billy Ripken error card).
Then, the mean and standard deviation are calculate as for the binomial distribution:
[tex]\mu=np=360\cdot 0.023=8.28\\\\\sigma=\sqrt{np(1-p)}=\sqrt{360\cdot 0.023\cdot 0.977}=\sqrt{8.08956}\approx2.84[/tex]
Write and solve the equation and then check your answer. A number increased by twenty-six is forty-two. Which statements are correct? Check all that apply. This is an addition problem. This is a subtraction problem The correct equation is s + 26 = 42. The correct equation is s – 26 = 42. To solve the equation, add 26 to both sides. To solve the equation, subtract 26 from both sides.
Answer:
equation= s+26=42
to solve,subtract 26 from both sides
Step-by-step explanation:
lets say the number is S
to increase is to add
S+26=42
solution
S+26(-26)=42-26
S=16
Answer:
A: This is an addition problem.C: The correct equation is s + 26 = 42. F: To solve the equation, subtract 26 from both sides.Explanation: Correct on Edg 2020.
What is the equation of a line that goes through the point (0, 2) and has a slope of 1?
Answer: y=x+2
Step-by-step explanation:
The slope-intercept equation is y=mx+b. The m is slope, and the b is the y-intercept. Since we are given the slope, we can fill it into m. We also know that the y-intercept is on the y-axis, meaning the x-coordinate is 0. The point we were given is (0,2). This means the y-intercept is 2. Our equation is y=x+2.
Answer:
y=x+2
Step-by-step explanation:
Slope intercept form is:
y=mx+b
where m is the slope and b is the y-intercept.
We know that this line has a slope of 1. Therefore, we can substitute 1 in for m.
y=1x+b
1x is equal to just x, so change 1x to x.
y=x+b
Now we must find the y-intercept, or b.
Y-intercepts are where the line crosses the y axis. The x-coordinate is always a 0.
Therefore, (0,y) is the coordinates of a y-intercept, and the "y" is the y-intercept.
We are given the point:
(0,2)
Since the x-coordinate is a 0, the y-intercept is 2. Substitute 2 in for b.
y=x+b
y=x+2
The equation of the line is y=x+2
A ball is thrown vertically upward from the ground. Its distance in feet from the ground in t seconds is s equals negative 16 t squared plus 256 t. After how many seconds will the ball be 1008 feet from the ground?
Answer:
7 seconds
Step-by-step explanation:
Given the height equation of the motion;
s = -16t^2 + 256t
At s = 1008 ft
The equation becomes;
1008 = -16t^2 + 256t
16t^2 - 256t + 1008 = 0
Solving the quadratic equation for t;
Factorising, we have;
16(t-7)(t-9) = 0
t = 7 or t = 9
When the ball is going up it would reach the given height at time t = 7 seconds.
When it is coming down it would reach the given height at time t = 9 seconds.
how do you graph y=–7/3x+2. PLEASE HELP ME
Graph the line using the slope and y-intercept, or two points.
Slope: -7/3
y-intercept: 2
Please mark me as brainliest if possible. Stay safe and God bless you!!
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- Eli
the sum of the first 20 terms of an A.P is identical to the sum of the first 22 term.If the common difference is -2; find the first terms
Answer:
First term a = 41
Step-by-step explanation:
Arithmetic Progression:
Common differences d = -2
[tex]S_{n}=\frac{n}{2}(2a+[n-1]d)\\\\S_{20}=\frac{20}{2}(2a+19*[-2])\\\\[/tex]
= 10*(2a - 38)
= 10*2a - 10*38
=20a - 380
[tex]S_{22}=\frac{22}{2}(2a+21*[-2])\\\\[/tex]
= 11 (2a -42)
=11*2a - 11*42
= 22a - 462
[tex]S_{22}=S_{20}\\\\[/tex]
22a - 462 = 20a - 380
22a = 20a - 380 + 462
22a = 20a + 82
22a - 20a = 82
2a = 82
a = 82/2
a = 41
First term a = 41
Use the Pythagorean theorem to calculate the diagonal of a TV is it's length is 36 inches and its width is 15 inches. Round your final answer to one decimal place.
Answer:
39 inches
Step-by-step explanation:
sqrt(15^2 + 36^2) = 39
If $\sqrt{5+n}=7$, then what is the value of $n$?
Answer:
44
Step-by-step explanation:
We can solve the equation by simplifying it.
[tex]$\sqrt{5+n}=7$[/tex], let's square both sides.
[tex]5+n = 49[/tex]. Now lets subtract 5 from both sides.
[tex]n = 44[/tex].
Hope this helped!
Answer:
44
Step-by-step explanation:
[tex]\sqrt{5+n}=7\\\\5+n=7^2=49\\\\n=49-5\\\\\boxed{n=44}[/tex]
What is the solution to the inequality below?
x < 5
A. x< 25 or x>-25
B. x < 25 or x>0
O C. x< 25 and x > 0
O D. x < 25 and x>-25
Answer:
C. x < 25 and x ≥ 0
Step-by-step explanation:
Fastest and easiest way to do this is to graph the inequality and find out the lines.
Tagall
er travels at an average speed of 64 miles per hour. How many miles does it travel in 4 hours and 45 minutes?
Answer:
304 miles
Step-by-step explanation:
Distance = rate times time
changing 4 hours 45 minutes to decimal form
4 45/60 = 4.75
D = 64 mph * 4.75
=304 miles
What is the solution to the following equation?
X/3 - 14 = -2
Answer:
x = 36
Step-by-step explanation:
x/3 - 14 = -2
x - 42 = -6
x = -6 + 42
x = 36
Hope this helps! :)
Answer:
x= 36
Step-by-step explanation:
X/3 - 14 = -2
Add 14 to each side
X/3 - 14+14 = -2+14
x/3 = 12
Multiply each side by 3
x/3 * 3 = 12*3
x = 36
A grocery store estimates that customers arrive at the rate of 15 per hour. The cashier can serve customers at a rate 20 per hour. Calculate the average number of customers in a line. Group of answer choices
Answer:
The average number of customers in a line = 2.25
Step-by-step explanation:
We are given;
Mean arrival rate;a = 15 customers per hour
Mean service rate;s = 20 customers per hour
Now, we want to find the average number of customers in the line. It is given by the formula;
N_q = a(W_q) = a²/(s(s - a)
Plugging in relevant values, we have;
N_q = 15²/(20(20 - 15))
N_q = 225/100
N_q = 2.25
toilet rolls come in packs of 4 and 9
the 4 packed price $2.04
and the 9 packed is priced at $4.68
Answer: 2.04÷ 4= 0.51
4.68÷9= 0.52
4 pack is better value by 0.01