The perimeter of a college athletic field is 104 meters and the length is 16m more than the width find the length and width
Answers
The length and width of the rectangle will be 19 meters.
What is the perimeter of the rectangle?The sum of all the sides of the rectangle will be known as the perimeter of the rectangle. Let L be the length and W be the width of the rectangle.
Then the perimeter of the rectangle will be
Perimeter of the rectangle = 2(L + W) units
The perimeter of a college athletic field is 104 meters and the length is 16 meters more than the width.
L = 14 + W
Then the length and width of the rectangle will be
P = 2(L + W)
104 = 2(14 + W + W)
52 = 14 + 2W
2W = 38
W = 19 meters
The length and width of the rectangle will be 19 meters.
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Related Questions
Selected from this population. find the probability that the sample mean is greater than 2.1 but less than 2.6.
Answers
Explain how to solve 2x + 7 = 15
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Which pair of measurements is not equivalent?
24 feet, 8 yards
24 inches, 2 feet
10 feet, 120 inches
3 miles, 15,480 feet
Answers
Hope This Helps
The pair of measurements that is not equivalent is 3 miles and 15,480 feet. All other pairs are equivalent when converted to the same units. This determines which measurements do not match in the same units.
To determine which pair of measurements is not equivalent, we need to convert them into the same units and compare them:
24 feet, 8 yards: 1 yard = 3 feet, so 8 yards = 8 * 3 = 24 feet. Therefore, 24 feet is equivalent to 8 yards.24 inches, 2 feet: 1 foot = 12 inches, so 2 feet = 2 * 12 = 24 inches. Therefore, 24 inches is equivalent to 2 feet.10 feet, 120 inches: 1 foot = 12 inches, so 120 inches = 120 / 12 = 10 feet. Therefore, 10 feet is equivalent to 120 inches.3 miles, 15,480 feet: 1 mile = 5280 feet, so 3 miles = 3 * 5280 = 15,840 feet. Therefore, 3 miles is not equivalent to 15,480 feet.Thus, the pair of measurements that is not equivalent is 3 miles, 15,480 feet.
Find the 75th derivative of y = cos(2x).
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Let y⁽ⁿ⁾ denote the n-th derivative of y wrt x.
The first few derivatives of y wrt x are the following:
n=1: y⁽¹⁾ = - 2¹ sin(2x)
n=2: y⁽²⁾ = - 2² cos(2x)
n=3: y⁽³⁾ = + 2³ sin(2x)
n=4: y⁽⁴⁾ = + 2⁴ cos(2x)
n=5: y⁽⁵⁾ = - 2⁵ sin(2x)
and so on
A pattern emerges
y⁽ⁿ⁾ = - 2ⁿ sin(2x) for n = 1, 5, 9, ...,
= - 2ⁿ cos(2x) for n = 2, 6, 10, ...,
= + 2ⁿ sin(2x) for n = 3, 7, 11, ...,
= + 2ⁿ cos(2x) for n = 4, 8, 12, ....
For n=75, we seek a constant, a, which begins with 1,2,3, or 4 such that
a + 4(n-1) = 75
That is,
n = (75-a)/4 is an integer.
Try a = 1: n = 18.5 (reject)
a = 2: n = 18.25 (reject)
a = 3: n = 18 (accept)
Therefore, y⁽⁷⁵⁾ = + 2⁷⁵ sin(2x).
Answer: 2⁷⁵ sin(2x)
The 75th derivative of y = cos(2x) can be found by dividing 75 by 4 to find the cycle it falls into due to the repeating pattern of cos and sin. Due to remainder 3 after division, the 75th derivative is equivalent to the 3rd derivative from the cycle, which is 8sin(2x), but scaled by 2 to the power of the number of completed cycles (18). This gives the final answer 2^18 * 8sin(2x).
Explanation:The process of finding the 75th derivative of a function can seem daunting or time-consuming, but with functions like cosines and sines, we can rely on the cycling pattern of these functions to simplify the task. This will significantly decrease the amount of computational effort needed.
When you find the derivative of y = cos(2x), the function cycles in a pattern every four times. The first derivative of y = cos(2x) is -2sin(2x), the second derivative is -4cos(2x), the third derivative is 8sin(2x), and the fourth derivative is 16cos(2x). As you can see, we've returned to the original function (scaled by a factor of 16).
So to find the 75th derivative, divide 75 by 4 to get remainder of 3. This means the 75th derivative is the same as the 3rd derivative, but scaled by 2 to the power of the number of full cycles (which is 18). Hence, the 75th derivative of y = cos(2x) is 2^18 * 8sin(2x).
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I an a factor of 28. the other factor is 4. what number am i
Answers
The correct answer is 7
Because 7 * 4 = 28
I hope this helps!
Hope this helps have a nice nite
5x-3 (2x-4)=7x+16. solve for x
Answers
1st step: Distributive Property
5x-6x+12=7x+16
2nd step: Combine Like Terms
-x+12=7x+16
-12 . -12
-x=7x+4
-7x -7x
-8x=4
/-8 . /-8
x=-1/2
Bryson hopes to win a three-day vacation in a drawing that is being held at his office. He purchased 40 raffle tickets. There were 500 raffle tickets sold. What is the theoretical probability of Bryson winning the trip?
A-2/25
B-1/5
C-4/5
D-500/40
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In a 4 x 3 factorial design, there are how many levels of the first grouping factor?
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A flag in the shape of a right triangle is hung over the side of a building as shown below. The total weight of the flag is 250 pounds and it has uniform density. a = 15 and b = 39.
Answers
Answer:
(a) The density of flag is [tex]\dfrac{25}{27}[/tex] Pounds per square foot
(b) The weight of strip is [tex]\dfrac{20}{9}(15-h)\Delta h[/tex] Pounds
(c) The work is [tex]\dfrac{20}{9}(15-h)h\Delta h[/tex] foot-pounds
(d) The exact work by roof is 1250 foot-pounds
Step-by-step explanation:
(a) We are given a flag in the shape of a right triangle.
The total weight of flag is 250 pounds and Uniform density.
Base of the flag [tex]=\sqrt{b^2-a^2}[/tex]
[tex]=\sqrt{39^2-15^2}=36[/tex]
Area of the flag [tex]=\dfrac{1}{2}\times 36\times 15 = 270[/tex]
Weight of flag = 250 pounds
[tex]Density =\dfrac{Weight}{Area}=\dfrac{250}{270}=\dfrac{25}{27}[/tex]
Hence, The density of flag is [tex]\dfrac{25}{27}[/tex]
(b) Weight of strip which is h feet below the roof.
Length of strip [tex]=\dfrac{36}{15}(15-h)[/tex]
Width of strip [tex]\Delta h[/tex]
Weight = Density x area
[tex]=\dfrac{25}{27}\times \dfrac{36}{15}(15-h)[/tex]
[tex]=\dfrac{20}{9}(15-h)\Delta h[/tex]
Hence, The weight of strip is [tex]\dfrac{20}{9}(15-h)\Delta h[/tex]
(c) Work slice to move h feet above to the roof
work[tex]=Weight\times displacement[/tex]
[tex]=\dfrac{20}{9}(15-h)\Delta h\times h[/tex]
[tex]=\dfrac{20}{9}(15-h)h\Delta h[/tex]
Hence, The work is [tex]\dfrac{20}{9}(15-h)h\Delta h[/tex] foot-pounds
(d) Exact work on the roof by hanging flag
[tex]W=\int_0^{15}\dfrac{20}{9}(15-h)hd h[/tex]
[tex]W=\dfrac{20}{9}(\dfrac{15h^2}{2}-\dfrac{h^3}{3})|_0^{15}[/tex]
[tex]W=1250-0[/tex]
[tex]W=1250[/tex]
Hence, The exact work by roof is 1250 foot-pounds
Final answer:
The weight of the flag is distributed uniformly across its area, with the entire 250 pounds concentrated at the centroid point.
Explanation:
To find the centroid of a right triangle, we can use the following formulas:
[tex]\[ x_c = \frac{b}{3} \][/tex]
[tex]\[ y_c = \frac{a}{3} \][/tex]
Where:
[tex]- \( x_c \)[/tex] is the x-coordinate of the centroid.
[tex]- \( y_c \)[/tex] is the y-coordinate of the centroid.
[tex]- \( a \)[/tex] is the length of the side perpendicular to the base (height).
[tex]- \( b \)[/tex] is the length of the base.
Given \( a = 15 \) and \( b = 39 \), we can calculate the centroid as follows:
[tex]\[ x_c = \frac{39}{3} = 13 \][/tex]
[tex]\[ y_c = \frac{15}{3} = 5 \][/tex]
So, the centroid of the triangle is located at the point (13, 5).
Now, regarding the weight distribution, if the flag has uniform density, the center of mass (or centroid) would be the point where the total weight is concentrated. Since the total weight of the flag is 250 pounds, and the centroid is the point of concentration of mass, the entire weight of the flag, 250 pounds, can be considered to act at the centroid.
Therefore, the weight of the flag is distributed uniformly across its area, with the entire 250 pounds concentrated at the centroid point.
Consider the equation y = 14 – 2x. with y on the vertical axis and x on the horizontal axis, the horizontal intercept of this line is
Answers
2x = 14
x = 7
The horizontal intercept is (7,0)
Lenny uses two pieces of yarn for a craft project. The first piece is 5.89 meters long. The second piece is 2.147 meters long. What is the total length of the two pieces of yarn? Enter your answer in the box. M__
Answers
The total length of the two pieces is 8.037 meters
Answer: 8.04 meters
Step-by-step explanation:
length of first piece of yarn = 5.89 meters
length of second piece of yarn = 2.147 meters
Total length of of the two pieces of yarn = length of first piece of yarn + length of second piece of yarn = 5.89 meters + 2.147 meters = 8.037 meters
The rule apply for the addition and subtraction is :
The least precise number present after the decimal point determines the number of significant figures in the answer.
Thus the answer will be 8.04 meters as least precise number 5.89 contains two decimal places.
Suppose in a market for iTune cards demand is Qd = 1500 - 250P, and supply is Qs = 850P. Find the equilibrium P* and Q*.
Answers
Given that the demand is Qd = 1500 - 250P, and supply is Qs = 850P, at equilibrium,
1500 - 250P = 850P
850P + 250P = 1500
1,100P = 1,500
P = $1.36
and the equilibruim Q is 1500 - 250(1.36) = 1,159
Therefore, the equilibruim P* is $1.36 and the equilibruim Q* is 1,159.
A backpack that normally sells for 39 is on sale for 34% off. Find the amount of the discount and the sale price.
Answers
34% of 39 is 13.26 ( 34% = .34 × 39 = 13.26)
Subtract that from 39 to find the amount of the discount:
39 - 13.26 = 25.74
So, the amount of discount on the backback is 25.74%.
^ And that's your answer! I hope this was helpful! :)
True or false, the decimal form of 3 3/8 is 3.38
Answers
Hope this helps!
Something greater tha 1/2 yard but less than 5/8 yard??
Answers
Hope this helps!
find the product. List the units. 8 h $9/h
Answers
answer
$72
The product is equivalent to $72.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a rate of $9 per hour for 8 hours.
Now, for 1 hour, the cost is $9. Therefore, for 8 hours, we can write -
x = 9 x 8
x = $72
Therefore, the product is equivalent to $72.
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If one score is randomly selected from a normal distribution with m = 100 and s = 20, the probability of obtaining a score between x = 90 and x = 100 is p = 0.3085.
a. True
b. False
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Find the specified element in the inverse of the given matrix
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you didn't show a matrix.
the components of the matrix are the elements.
and the elements of the inverse matrix are the elements of the inverse matrix
1)
so if matrix A is 1 4 1
2 5 2
3 6 3
2)
14114
25225
36336
3)
15 24 12
15 12 24
4)
[A]=(15+24+12=51)-(15+12+24=51)
[A]=0
5)
52 23 25
63 23 36
41 11 14
63 33 36
41 12 14
52 12 25
6)
15-12 6-6 12-15
12-6 3-3 6-12
8-5 2-2 5-8
7)
3 0 -3
6 0 -6
3 0 -3
8)
(+)3 (-)0 (+)-3
(-)6 (+)0 (-)-6
(+)3 (-)0 (+)-3
=
3 0 -3
-6 0 6
3 0 -3
9)
3 -6 3
N= 0 0 0
-3 6 -3
10) the inverse of [A]= 1/|A|*[N]
which is in this case ⁻A= 0
because |A|=0
Its number 15. Thank you
Answers
Factoring like this is simply the distributive property in reverse. We can check if we did the factoring right by distributing the outer term x back into the inner terms
Let's multiply the outer x by each of the inner terms (a, b and d)
x times a = ax
x times b = bx
x times d = dx <--- the result should be d and not dx
-----------------------------------------------------------------------------
Here is the proper way to solve for x. We first need to move the d over, which is done by subtracting d from both sides. Once all of the x terms are on one side, we can finally factor out the x. Then after that we divide both sides by the quantity (a+b)
k = ax + bx + d
k - d = ax + bx + d - d
k - d = ax + bx
k - d = x(a + b)
(k - d)/(a + b) = x(a + b)/(a + b)
(k - d)/(a + b) = x
x = (k - d)/(a + b)
The final answer is
x = (k - d)/(a + b)
which can be written as
[tex]x=\frac{k-d}{a+b}[/tex]
If you choose to use the first option, then make sure you use parenthesis as shown. The parenthesis are important to make sure that you divide all of "k-d" over all of "a+b" as one big fraction.
Why do you round 117290 up to 120000
Answers
Please help badly I cannot answer
Answers
now, if we take 356 as the 100%, what is 89 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 356&100\\ 89&x \end{array}\implies \cfrac{356}{89}=\cfrac{100}{x}\implies x=\cfrac{89\cdot 100}{356}[/tex]
The temperature in Fairbanks, Alaska, fell 10 degrees in 2 hours.
Explain why the average temperature change was –5ºF per hour.
Answers
I hope this helped ya :)
The temperature fall can be represented by −10. To find the average change per hour, divide −10 by 2. −10 divided by 2 is −5.
James covers a distance of 8 meters in the first second of a 100 meter race. Then, he sprints at a speed of 9 meters per second. How far is James from the finish line 9 seconds after the race has started? a. 11 c. 28 b. 20 d. 80
Answers
9 seconds after the race....so there are 8 seconds that he is sprinting 9 meters per second.....(8 * 9) = 72 meters....plus the 8 meters for the 1st second = (72 + 8) = 80 meters....
and if it is 100 meter race, and he has ran 80 meters, then that leaves 20 meters from the finish line....answer is D
Answer:
Option b. 20 meters
Step-by-step explanation:
James covers a distance of 8 meters in the first second of 100 meter race.
Then, he sprints at a speed of 9 meters per second.
We have to find how far is James from the finish line 9 seconds after the start of the race.
James covers distance in first second = 8 meters.
Time remaining in 9 seconds after running 8 meter = 9 - 1 = 8 seconds.
In another 8 seconds James covers the distance = speed × time
= 9 × 8 = 72 meters
Total distance covered in 9 seconds = 8 + 72 = 80 meters
Distance remaining in 100 meter race after 9 seconds = 100 - 80 = 20 meters.
James is 20 meters far from the finish line 9 seconds after the race has started.
Option b. 20 meters is the answer.
124,248-55,679 show me how you get this answer
Answers
- 55,679
68,569
List any restrictions on the domain for the equation [tex] \frac{x+9}{x+2} [/tex]
Answers
now, what values of "x" makes the denominator 0? let's check,
x+2 = 0
x = -2
so, if "x" ever becomes -2, then you'd get
[tex]\bf \cfrac{x+9}{x+2}\implies \cfrac{x+9}{-2+2}\implies \implies \cfrac{-2+9}{-2+2}\implies \stackrel{und efined}{\cfrac{7}{0}}[/tex]
so, the domain, or values "x" can take on safely, are any real numbers EXCEPT -2.
Part a determine the correct sketches for v=100cos(ωt+ϕ) versus ωt for ϕ=90∘, 45∘, 0∘, −45∘, and −90∘.
Answers
Ф = π/2, π/4, 0, -π/4, -π/2 rad.
The given function is
v = 100 cos(ωt + Ф)
Create the following tables.
We shall use
ωt : 0 π/2 π (3/2)π 2π
Ф = π/2
ωt+Ф : π/2 π (3π)/2 2π (5π)/2
v : 0 -100 0 100 0
Ф = π/4
ωt+Ф : π/4 (3/4)π (5/4)π (7/4)π (9/4)π
v : 70.7 -70.7 -70.7 70.7 70.7
Ф = 0
ωt+Ф : 0 π/2 π (3/2)π 2π
v : 100 0 -100 0 100
Ф = -π/4
ωt+Ф : -π/4 π/4 (3/4)π (5/4)π (7/4)π
v : 70.7 70.7 -70.7 -70.7 70.7
Ф = -π/2
ωt+Ф: -π/2 0 π/2 π (3/2)π
v : 0 100 0 -100 0
Sketches of graphs for the different cases are shown below.
Unfortunately, arsenic occurs naturally in some ground water†. a mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. a well in texas is used to water cotton crops. this well is tested on a regular basis for arsenic. a random sample of 36 tests gave a sample mean of x = 6.8 ppb arsenic, with s = 2.9 ppb. does this information indicate that the mean level of arsenic in this well is less than 8 ppb? use α = 0.01. (a) what is the level of significance? 0.01 state the null and alternate hypotheses. h0: μ = 8 ppb; h1: μ > 8 ppb h0: μ = 8 ppb; h1: μ < 8 ppb h0: μ > 8 ppb; h1: μ = 8 ppb h0: μ < 8 ppb; h1: μ = 8 ppb h0: μ = 8 ppb; h1: μ ≠ 8 ppb (b) what sampling distribution will you use? explain the rationale for your choice of sampling distribution. the standard normal, since the sample size is large and σ is known. the student's t, since the sample size is large and σ is unknown. the student's t, since the sample size is large and σ is known. the standard normal, since the sample size is large and σ is unknown. what is the value of the sample test statistic? (round your answer to three decimal places.) -2.483 (c) estimate the p-value. p-value > 0.250 0.125 < p-value < 0.250 0.050 < p-value < 0.125 0.025 < p-value < 0.050 0.005 < p-value < 0.025 p-value < 0.005 sketch the sampling distribution and show the area corresponding to the p-value. webassign plot webassign plot webassign plot webassign plot (d) based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? are the data statistically significant at level α? at the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. at the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. at the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. at the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) interpret your conclusion in the context of the application. there is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb. there is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb.
Answers
For a hypothesis test, the significant level is given by α. From the question, we were told that α = 0.01.
Therefore, the significant level is 0.01.
Our previous knowledge is that a mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use, we know want to know from a sample of 36 tests whether the mean level of arsenic in a particular well is less than 8 ppb.
Therefore, the null and the alternative hypothesis are:
[tex]H_0:\mu=8\ pbb \\ \\ H_a:\mu\ \textless \ 8\ pbb[/tex]
Part B:
The sampling distribution to be used is the student's t, since the sample size is large and σ is unknown.
The test statistics is given by:
[tex]t= \frac{\bar{x}-\mu}{s/\sqrt{n}} \\ \\ = \frac{6.8-8}{2.9/\sqrt{36}} \\ \\ = \frac{-1.2}{2.9/6} = \frac{-1.2}{0.4833} \\ \\ =-2.483[/tex]
Part C:
The p-value for a t-distribution test statistics of -2.483 with a degree of freedom of 35 is given by 0.0090
Thus 0.005 < p-value < 0.025
Part D:
Since the p-value is less that the significant level, we reject the null hypothesis and conclude the data are statistically significant.
i.e.
at the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
Part E:
Therefore, we conclude that there is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb.
Write an equation of the line in the figure.
Answers
Slope intercept y = 6/5x -1
Point slope form (y - 5) = 6/5 (x - 5)
Nancy withdrew $19 from her bank account to pay for markers write in integer to represent this situation
Answers
Withdrawing is like taking out money from her account.
So, the integer that represents this situation is -$19.
I hope that was helpful! c:
Then, subtract 29- 24.65
Final answer: $4.35
For the box shown, the total area is 94 cm2. determine the value of x