Answer:
125000 square feet
Step-by-step explanation:
Since there are only three sides of the rectangle, the perimeter of the fence is:
Let x and y be the sides of the rectangle, we are left with:
2 * x + y = 1000
solving for and:
y = 1000 - 2 * x
The area of the corral is:
A = x * y
replacing
A = x * (1000 - 2*x)
A = 1000 * x - 2*x^2
to find the maximum for the parabolic function A = 1000 * x - 2*x^2
The function has a maximum since the quotient before x ^ 2 is negative: -2 <0
Amax = c - b^2 /4*a
where a = -2, b = 1000, c = 0
A max = 0 - 1000^2/(4 * (- 2))
A max = 125000 ft^2
The maximum possible area of the pen is 125000 square feet.
Final answer:
125,000 square feet,
Explanation:
Let us denote the length of the rectangular area parallel to the creek as L and the width of the area as W. Given that the total amount of fencing available is 1000 feet, we can express the perimeter that Jake can fence as 2W + L = 1000 feet, since the creek forms one of the longer sides of the rectangle, and no fencing is required there.
The area A of the rectangle is given by the product of its length and width, i.e., A = L × W. Our goal is to maximize A. From the perimeter equation 2W + L = 1000, we can express L as L = 1000 - 2W.
Substituting this into the area formula, we get A = W * (1000 - 2W). This is a quadratic function and can be written as
A = -2W^2 + 1000W, which is a parabola opening downwards. The maximum value of this function can be found by completing the square or by using the vertex form of a parabola.
The vertex of the parabola, which gives the maximum area, occurs at W = -b/(2a), with 'a' being the coefficient of
W^2 (-2 in this case) and 'b' the coefficient of W (1000 in this case). Plugging these values in, we find that
W = -1000 / (2 * -2) = 250.
Therefore, the width that gives the maximum area is 250 feet. Substituting W back into the perimeter formula, we get
L = 1000 - 2*250 = 500 feet.
So, the dimensions for the maximum area are 500 feet by 250 feet, and the maximum area is A = 500 * 250 = 125,000 square feet.
In a math class with 27 students, a test was given the same day that an assignment was due. There were 17 students who passed the test and 22 students who completed the assignment. There were 3 students who failed the test and also did not complete the assignment. What is the probability that a student passed the test given that they did not complete the homework
The probability that a student passed the test given that they did not complete the homework is [tex]\( \frac{3}{5} \)[/tex] or 60%.
To find the probability that a student passed the test given that they did not complete the homework, you can use conditional probability.
Let:
- [tex]\( A \)[/tex] be the event that a student passed the test.
- [tex]\( B \)[/tex] be the event that a student did not complete the homework.
You're asked to find [tex]\( P(A|B) \),[/tex] the probability of passing the test given not completing the homework.
From the given information:
- Total number of students [tex](\( N \)) = 27[/tex]
- Number of students who passed the test [tex](\( A \)) = 17[/tex]
- Number of students who did not complete the homework [tex](\( B \)) = \( N - 22 = 5 \)[/tex] (since 22 students completed the assignment)
Also, given that there were 3 students who failed the test and did not complete the assignment, we can infer that out of the 5 students who did not complete the homework, 3 of them failed the test.
So, [tex]\( P(A \cap B) = 3 \)[/tex] (the probability of a student both passing the test and not completing the homework).
Using the definition of conditional probability:
[tex]\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \][/tex]
We have:
- [tex]\( P(A \cap B) = 3 \)[/tex]
- [tex]\( P(B) = 5 \)[/tex]
Now we can calculate [tex]\( P(A|B) \)[/tex]:
[tex]\[ P(A|B) = \frac{3}{5} \][/tex]
So, the probability that a student passed the test given that they did not complete the homework is [tex]\( \frac{3}{5} \)[/tex] or 60%.
The probability that a student passed the test given they didn't complete the homework is 40%.
To solve this problem, we need to determine the probability that a student passed the test given they did not complete the homework. We'll use the given data:
27 total students17 students passed the test22 students completed the assignment3 students failed the test and did not complete the assignmentFirst, calculate the number of students who did not complete the homework:
5 because 27 total - 22 completed = 5 did not complete.
Next, find the number of students who passed the test and did not complete the homework.
Let’s define variables:
Passed test: ADidn't complete homework: BFailed test and didn't complete homework: AB'We're given that AB' = 3.
Calculate AB:
The total number of students who didn’t complete the homework is 5 (B + B'). Thus, AB (students who passed the test but did not complete the assignment) can be calculated as:
2 (because 5 - 3 = 2 for AB).
Then, the probability is:
P(A|B) = AB / B = 2 / 5. Therefore, the answer is 0.4 or 40%.
The Wilson family is planning an extended vacation in summer the map they are using has the scale 1 in. = 80 mi. How many inches represent 2,160 miles?
Answer:
27 inches
Step-by-step explanation:
you divide 2160 by 80 to get the number of inches
2160/80=27
Evaluate 8j - k + 14 when j = 0.25 and k = 1.
Steps to solve:
8j - k + 14; j = 0.25 and k = 1
~Substitute
8(0.25) - (1) + 14
~Simplify
2 - 1 + 14
~Subtract
1 + 14
~Add
15
Best of Luck!
Answer:
[tex]8j - k + 14 \\ 8 \times0 .25 - 1 + 14 \\ 2 - 1 + 14 \\ 1 + 14 = 15[/tex]
hope this helps you...
Point O is the center of the circle. Circle O is shown. Tangents D C and B C intersect at point C outside of the circle. Lines are drawn from points D and point B to center point O to form a quadrilateral. A line is drawn from point C to point A on the opposite side of the circle. The length of O D is 6, and the length of B C is 8. Angles D and B are right angles. What is the perimeter of quadrilateral DOBC?
Answer:
The perimeter is 28 (6 plus 8=14 14x2= 28)
Step-by-step explanation:
Plz mark brainliest!
The perimeter of quadrilateral DOBC that forms two right triangles is: 28 units.
What are Congruent Right Triangles?Based on the tangent theorem, triangles ODC and OBC are right triangles that are congruent. Therefore, their corresponding side lengths are equal.
Perimeter of quadrilateral DOBC = OB + DO + BC + CD = 6 + 6 + 8 + 8
Perimeter of quadrilateral DOBC = 28 units.
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The diameter of a circle is 7 inches. Find its area to the nearest tenth
Step-by-step explanation:
diameter=7 inches
Area of the circle= π(7/2)² inches²
=38.465
38.5 inches²
Answer:
38.5 inches
Step-by-step explanation:
r = 1/2d
r = 1/2 × 7
r = 3.5
[tex] \boxed{ \bold{formula = \pi \: {r}^{2} }}[/tex]
= 3.14 × 3.5 × 3.5
= 38.465 inches
Find its area to the nearest tenth
38.465 inches
= 38.5 inches
In your own words, what is relative frequency?
Answer:
A frequency is the number of times a given datum occurs in a data set.
Step-by-step explanation:
Before the coffee shop opens the employees bake 40 cookies which is 25 less than the number of donuts they make does the equation x+25=40 describe the situation if not write an equation that does and explain what the variable represents
Answer:
x-25 = 40
Step-by-step explanation:
Let the number of cookies made = x
The employees bake 40 cookies which is 25 less than the number of donuts they make
Number of Cookies is less than Number of Donuts by 25
Therefore the equation that describes the situation is given as:
x-25 = 40 where x is the number of cookies made.
Answer:
The equation is not correct
Step-by-step explanation:
Lets break it down
Cookies = 40
Donuts lets call it x since we dont have a figure
It is said that the 40 cookies is 25 less than the number of donuts
So therefore
x less than 25 = 40
x-25=40
To get x we add 25 to each side
x-25+25=40+25
x=65
Equation should be
x-25=40
That is 65-25 =40
rate of change in the equation y = 5 - 0.5x
A baseball fan is seated in the upper deck of a stadium 200 feet away from
homeplate. If the angle of depression to the field is 62 degrees, at what height is
the fan sitting? Hint: draw a picture and label the parts of the triangle and use
your trig ratio to find the height.*
Please find attached to this answer a well labelled diagram of the triangle
Answer:
Approximately 176.6 feet
Step-by-step explanation:
From the question, we are to find the height at which the baseball fan was sitting.
From the attached diagram the height at which the fan was sitting is equivalent to the opposite side of the triangle.
Hence , the appropriate trigonometric function to use to solve this question is the sine function.
Sine = Opposite / Hypotenuse
Opposite is unknown so we refer to it as Y
Hypotenuse = 200feet
While the Angle of depression = 62°
Therefore,
Sine 62° = Y/ 200 feet
Cross multiply
Sine 62° × 200 feet = Y
Y = 176.58951857 feet
Approximately 176.6 feet
Therefore , the height at which the fan is sitting is 176.6 feet
Mr.Estevez got a new post mounted mail box. He dug out the old one and left a square hole and only measured one side. Mr.Estevez measured a side of 9.75cm's. What is the square area of dirt Mr. Estevez needs to fill up the hole for his new mailbox. (Round to the nearest tenth)* 0 95.1cm2 0 95.06cm2 0 95.1cm O 95.06cm
Answer:
[tex]95.1\ cm^2[/tex]
Step-by-step explanation:
we know that
A square is a quadrilateral that has four equal sides and four equal interior right angles.
The area of the square is given by the formula
[tex]A=b^2[/tex]
where
b is the length side of the square
In this problem we have
[tex]b=9.75\ cm[/tex]
substitute in the formula
[tex]A=(9.75)^2=95.06\ cm^2[/tex]
Round to the nearest tenth
[tex]A=95.1\ cm^2[/tex]
Answer:
95.06cm
Step-by-step explanation:
Hope this helps
Sum of the odd integers between 30 & 54
Answer:
504
Step-by-step explanation:
The sum of the odd numbers between 30 and 54 will be 504.
What are the numbers?A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols. In several numeral systems, the same set of symbols may represent various numbers.
Given numbers are 30 and 54. The sum of the odd integers will be calculated by using the formula below:-
Sn = ( n / 2 ) [ a1 + a2 ]
The total numbers between 30 and 54 will be 12.
Sn = ( 12 / 2 ) [ 31 + 53 )
Sn = 6 x ( 84 )
Sn = 504
Therefore, the sum of the odd numbers between 30 and 54 will be 504.
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There are 14 girls and 2 boys taking karate lessons. Write the ratio that compares the number of girls taking karate lessons to the total number of students taking karate lessons
Answer:
The correct answer is 7 : 8.
Step-by-step explanation:
There are 14 girls and 2 boys taking karate lessons.
Total number of students taking the karate class is 16.
The ratio that compares the number of girls taking karate lessons to the total number of students taking karate lessons is given by 14 : 16 = 7 : 8.
This can be interpreted as for every 8 students in the karate lesson, 7 of them are girls.
A water bottle has a label that is 3.5 inches high. If the bottle has a radius of 2 inches, how much paper would be needed to put labels on one dozen water bottles?
Answer:
527.52 in2 of paper.
Step-by-step explanation:
The area of the water bottle label can be calculated by the product of its circunference length and its height.
The length of its circunference is calculated as:
C = 2 * pi * r
C = 2 * 3.14 * 2 = 12.56 inches
Now, to find the area of the label, we just multiply the length by the height:
Area = C * h = 12.56 * 3.5 = 43.96 in2
As we want to know the amount of paper for 12 water bottles, we multiply the area of one label by 12:
Total Paper = 12 * 43.96 = 527.52 in2
It will be needed 527.52 in2 of paper.
-
Which of the following are alternate exterior angles?
Answer:
Are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.
write an equation for the function that includes the following points (2, 32) and (3, 64)
Answer:
y=32x-32
Step-by-step explanation:
this time no algorithm or equation was needed i saw that if the equation was y=32x there would be ordered pairs (1,32) and (2,64) so to delay it by 1 on the x side just subtract the slope from the y - intercept sorry if that doesn't make sense
A car travels 218.5 miles on 9.5 gallons of gas what is the gas mileage
Answer:
23 miles per gallon
Step-by-step explanation:
Take the miles and divide by the gallons
218.5 miles/ 9.5 gallon
23 miles per gallon
Answer:
23m/g
Step-by-step explanation:
If a car travels 218.5 miles on 9.5 gallons, you can find how many miles can be traveled on one gallon.
You can make the equation 9.5g=218.5, let g be gallons of gas.
Divide by 9.5 on both sides.
g= 23
The gas mileage is 23 miles for one gallon of gas.
Martin has a shoe box with the dimensions 4 inches, by 6 inches, by 10 inches. He wants to determine if a relay baton inches will fit in the box. What is the longest length that the relay baton can be and still fit in the box? (Round to the nearest tenth if needed.) Your answer: 10 inches 12.3 inches 10.8 inches 7.2 inches
Answer:
10 inches.
Step-by-step explanation:
First we need to find what is the bigger dimension of the box, because the relay baton will occupy the box, and the larger dimension of the relay baton (that is, it's length) need to be less or equal than the larger dimension of the box.
The dimensions of the box are: 4 inches, 6 inches and 10 inches.
The larger dimension of the box is 10 inches. So, If we want the relay baton to fit in the box, the maximum length it can have is 10 inches.
Tom and Martha are making punch for a party. The proportions given in the recipe are 2 parts of lemonade to 1 part each of pineapple juice and ginger ale. If they need 6 liters of punch, how many liters of each of the ingredients should they buy?
Answer:
They need to buy 3 litters of lemonade, 1.5 litters of pineaple juice and 1.5 litters of ginger ale.
Step-by-step explanation:
In order to calculate the amount of each ingredient they need for 6 liters of punch we can first create fractions for each ingredient based on the proportions we were given. This is shown bellow:
2 litters lemonade + 1 litter pineapple juice + 1 litter ginger ale = 4 litters punch
Then we have:
lemonade = 2/4
pineaple juice = 1/4
ginger ale = 1/4
If we want to make 6 liters of punch we can just apply this fractions to know how much of each we need:
lemonade = 6*(2/4) = 12/4 = 3 litters
pineaple juice = 6*(1/4) = 1.5 litters
ginger ale = 6*(1/4) = 1.5 litters
They need to buy 3 litters of lemonade, 1.5 litters of pineaple juice and 1.5 litters of ginger ale.
Jenna has 30 buttons. She is organizing her buttons into 6 boxes. She puts the same number of buttons in each box. Write an expression that you use to find the number of buttons in each box.
Answer:
The expression will be x = 30/6 and she'll have 5 buttons in each box.
Step-by-step explanation:
In order to write the expression for the number of buttons in each box we first need to attribute a variable to that value, in this case we will use "x". The number x will be given by the division of all the buttons she has by the number of boxes she wants to organize them in. We have:
x = (number of buttons)/(number of boxes)
x = 30/6 = 5 buttons per box
The expression will be x = 30/6 and she'll have 5 buttons in each box.
3x ^ 3 - x ^ 2 Determine if the expression is polynomial or not . If it is a polynomial , state the type and degree of the polynomimal . The given expression a polynomial
The expression
[tex]3x^{3} -x^{2}[/tex]is a polynomial. Its type is cubic and the degree is 3.
Explanation:The given mathematical expression
[tex]3x^{3} -x^{2}[/tex]is a polynomial. A polynomial is an expression that is made up of variables and coefficients, using only the operations of addition, subtraction, and multiplication and non-negative integer exponents. The type of this polynomial is cubic, because the highest power of the variable (the degree) is 3. In this case, the highest degree is the highest exponent of the variable 'x', which is 3. Hence the given polynomial is cubic, with degree of 3.
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Solve 2x^2+5x +5=0 round solutions to the nearest hundredth
Answer: i3
Step-by-step explanation:
Answer:13
Step-by-step explanation:
A rectangle has a length of 6 feet and a width of 4 feet. The perimeter of the rectangle can be found using the equation =2×6+2×4. Which equation can also be used to find the perimeter of the rectangle?
Answer:
The correct answer is perimeter is given by 2 × ( l + w), where l is the length and w is the width of the rectangle.
Step-by-step explanation:
A rectangle has a length of 6 feet and a width of 4 feet. The perimeter of the rectangle can be found using the equation =2×6+2×4.
Let l be the length and w be the width of a rectangle.
Since there four sides of a rectangle, the perimeter is given by adding all the sides.
Therefore perimeter of the rectangle is given by l + l + b + b = 2×l +2×w = 2 × ( l + w).
The equation given by 2 × ( l + w) can also be used to find the perimeter of any given rectangle.
The perimeter of a rectangle is found by using the formula P = 2l + 2w, where P is the perimeter, l is the length and w is the width. Use the formula and operations of equations to fill in the missing information on the table below. Complete your work in the space provided. Include the entire process for completing the table.
Answer:
#1: 11 cm
#2: 16.5 in
#3: 2.5 feet
Step-by-step explanation:
#1
[tex]P=2l+2w[/tex] Solve for width by substracting 2l on both sides to isolate 2w
[tex]P-2l=2w[/tex]
or
[tex]2w=P-2l[/tex]
Replace.
[tex]2w=26-2(2)\\2w=26-4\\2w=22\\w=\frac{22}{2}\\ w=11cm[/tex]
----------------------------------------------------------------------------
#2
[tex]P=2l+2w[/tex]
[tex]P=2(3.5)+2(4.75)\\P =7+9.5\\P=16.5in[/tex]
----------------------------------------------------------------------------
#3
[tex]P=2l+2w[/tex]
Solve for l
[tex]2l=P-2w\\2l=7-2(1)\\2l=7-2\\2l=5\\l=\frac{5}{2}\\ l=2.5feet[/tex]
Fiona must find the length indicated by the dotted line for the tiles she is installing. She knows that each polygon is a regular hexagon with a perimeter of 7.5 in. What is the length of the dotted line? Round to the nearest hundredth.
Answer: The length of the dotted line is 3.75 inches.
Please refer to the picture attached for the missing part of the question
Step-by-step explanation: From the information given we have a regular hexagon, that is a six-sided polygon (all sides equal) with the perimeter given as 7.5 inches. The perimeter is the distance all around the figure, hence to determine the length of one side,
Length = 7.5/6
Length = 1.25
Also, the interior angles of a hexagon can be derived with the formula;
Angles = 180 (n - 2)
Where n is the number of sides of the polygon
Interior Angles = 180 (6 - 2)
Interior Angles = 180 x 4
Interior Angles = 720
If the total of the interior angles equals 720, then each angle can be calculated as;
Each Angle = 720/6
Each Angle = 120
Please refer to attached picture tagged SOLUTION Diagram)
Taking triangle GED as shown in the picture, angle E and angle D measure 60 degrees each. This is because angle E in the entire hexagon ABCDEF measures 120 degrees. The line from point G in the center of the hexagon divides the angle into two equal halves. Same applies to all other five angles in the hexagon. Having angle E and D equal to 120 (that is 60 + 60) angle G would be equal to 180 - 120 {sum of angles in a triangle equals 180) which gives us 60. In effect we have an equilateral triangle, with all angles equal. This also means all sides are equal, hence if line ED equals 1.25, it simply means line GE and line GD equals 1.25 as well.
From this result we can now conclude that the line that runs across the hexagon from point F to point C is 1.25 plus 1.25 which equals 2.50.
The dotted line as indicated in the question runs across one side of the hexagon and all through another hexagon, hence the total length of the dotted line equals;
Dotted line = 1.25 + 2.50
Dotted line = 3.75
Therefore the length of the dotted line is 3.75 inches
Which function shows a fabric with a price of $1.25 per square yard?
Answer:
x(1.25)
Step-by-step explanation:
x is the yards.
so for example if you need 2 yards of fabric replace x with 2.
Answer:
x=1.25
Step-by-step explanation:
edgu
What is the value of the expression below?
√16 + 5 *1
Answer:
9
Step-by-step explanation:
√16=4
5*1=5
4+5=9
hope this helps
You own 4 different shorts, 5 different t-shirts and 5 different caps. If
you want to wear one of each,
How many different combinations of clothing do you have?
combinations
Answer:
5
xD
Step-by-step explanation:
Answer:
100
Step-by-step explanation:
Multiply 4, 5 and 5 which gives 100.
If you were to flip a coin 140 times, how many times would you expect the coin to land on tails?
Answer: 70 times
Step-by-step explanation:
If you were to flip a coin 140 times you would expect it to land on tails 70 since 140 divided by 2 is 70 although coins are normally not evenly weighed meaning that it most likely not going to land evenly on both sides.
i really struggle with these kinda of questions oops
SOLVE
4(5x-2)=2(9x+3)
thanks
Step-by-step explanation:
4(5x-2) = 2(9x+3)
20x-8 = 18x+6
20x-18x = 6+8
2x=14
x= 14/2
∴ x= 7 [ANS]
Bella manages a volunteer group. The time (T) that it takes a group of volunteers to construct a house varies inversely as the number of volunteers (V). It takes 20 volunteers to build a house in 63 hours. Write an equation to model this situation. Next, find how many volunteers it would take to build a house in 30 hours.
Answer:
42 Volunteers
Step-by-step explanation:
The time (T) that it takes a group of volunteers to construct a house varies inversely as the number of volunteers (V).
This is written as:
[tex]V \propto \frac{1}{T} \\$Introducing the variation constant k\\V = \frac{k}{T}\\$It takes 20 volunteers to build a house in 63 hours.$\\When V=20, T=63\\V = \frac{k}{T}\\20 = \frac{k}{63}\\k=20*63=1260\\$Therefore, the equation connecting V and T is:$\\V = \frac{1260}{T}\\$When T=30 hours, we want to determine the number of volunteers needed V$\\V = \frac{1260}{30}=42\\$42 Volunteers will be needed.$[/tex]