Answer:
The volume of the prism is 54 in³.
This can be calculated by multiplying the length by the width by the height.
Which comes out to 9 in x 1 ¹⁄ ³ in x 4 ²⁄ ³ in = 54 in³.
A rancher has 600
feet of fencing to put around a rectangular field and then subdivide the field into 3
identical smaller rectangular plots by placing two fences parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.
The dimensions of the rectangular field that maximize the enclosed area are 150 feet by 75 feet.
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
Let's call the length of the rectangle "l" and the width "w".
We can write two equations based on the given information -
Perimeter equation: 2l + 4w = 600 (since there are two sets of parallel sides, we have to add an extra "w" to the perimeter equation)
Area equation: A = 3lw (since the field is divided into 3 equal parts)
We want to maximize the enclosed area, which means we want to find the values of "l" and "w" that make the area as large as possible.
We can use the perimeter equation to solve for one of the variables in terms of the other -
2l + 4w = 600
2l = 600 - 4w
l = 300 - 2w
Now we can substitute this expression for "l" into the area equation -
A = 3lw
A = 3(300 - 2w)w
A = 900w - 6w²
To find the maximum area, we can take the derivative of this equation with respect to "w" and set it equal to zero -
dA/dw = 900 - 12w = 0
12w = 900
w = 75
So the width of each of the smaller rectangular plots is 75 feet.
We can use the perimeter equation to find the length -
2l + 4w = 600
2l + 4(75) = 600
2l = 300
l = 150
Therefore, the dimensions value are obtained as 150 feet by 75 feet.
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Jillian measures two line segments. Segment A is 12.4 centimeters long and segment B is
4 centimeters in length. Which best represents the ratio of the length of segment A to the length
of segment B?
4
1
3.1
3.1
3.1 best represents the ratio of the length of segment A to segment B.
What is ratio?
By comparing two amounts of the same unit and finding the ratio, one can determine how much of one quantity is included in the other.
We are given that Jillian measures two line segments.
The length of Segment A is measured as 12.4 centimeters and the length of Segment B is measured as 4 centimeters.
So, on comparing both the lengths, we get
⇒12.4 : 4
⇒124 : 40
⇒3.1
Hence, 3.1 best represents the ratio of the length of segment A to segment B.
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NEED HELP WILL GIVE BRAINLIEST IF I GET FULL HELP ON BOTH QUESTIONS
The inverse of the function is y = (-3x + 50)/4.
The domain of the inverse function are {4, 5, 6, 10}.
The range of the inverse function are {5, 8, 9, 13}.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At point (5, 10), an equation of the line f(x) can be calculated by using the point-slope form:
y - 10 = (6 - 10)/(8 - 5)(x - 5)
y - 10 = -4/3(x - 5)
y = -4x/3 + 20/3 + 10
y = -4x/3 + 50/3
y = (-4x + 50)/3
In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;
x = (-4y + 50)/3
3x = -4y + 50
4y = -3x + 50
y = (-3x + 50)/4
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Point G' has coordinates (-5, 2). If it was reflected across the y-axis, what were the coordinates of its pre-image?
(-5, -2)
(5, 2)
(2, -5)
(5, -2)
Answer: Second answer, (5,2)
Step-by-step explanation:
To reflect across the y axis, it would be: (x,y) -> (-x,y)
So, (-5,2) reflected across the y axis would be (5,2)
Prove the following: In a semigroup (written multiplicatively) multiplication of subsets is associative?
Therefore , the solution of the given problem of unitary method comes out to be x = (ab)c = a(bc) .
An unitary method is what?The job can be finished by multiplying the variable information obtained using this kind of nanosection alongside the results of the two people who used the unilateral approach. In essence, this mean that whenever a desired item happens, either the chosen entity is described or the tone of both commercial manufacturing is skipped. A varying fee of Inr ($1.01) might have been necessary for forty pens.
Here,
We must demonstrate that the following formula holds for any subsets A, B, and C of S in order to demonstrate that multiplication of subsets is associative:
=> (AB)C = A(BC)
where AB and BC stand for the sets created by increasing all of the elements in A by all of the elements in B, and vice versa.
We must demonstrate that every element on the left-hand side is also an element on the right-hand side and vice versa in order to demonstrate that (AB)C = A(BC).
Let x represent any one of the (A*B)C elements. If a, b, and c are all in A, then x can be expressed as
=> x = (ab)*c by definition. * being associated with S gives us:
=> x = (ab)c = a(bc)
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HELLLPPPPP me please
The length and the width of the model are Length = 2 and Width = 3x² + 5x + 6
Why 6x cant be the lengthThe expression 6x cant be the length because 12 cannot divide 6x without becoming a radical expression
Calculating the length and the widthWe have
Area = 6x² + 10x + 12
Factor out 2
Area = 2(3x² + 5x + 6)
This means that
Length = 2 and Width = 3x² + 5x + 6
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How long would it take for a ball dropped from the top of a 81ft building to hit the ground round your answer to two decimal places
Answer:
Set the height equal to (1/2)gt^2 and solve for t.
h = (1/2)gt^2
t = (2h/g)^1/2
Plug in the numbers and get your answer in seconds:
h = 81 ft
g = 32 ft/s^2
Step-by-step explanation:
There are rectangular cards divided into 4 equal cells with different shapes
, , , drawn in each cell. Cards can be placed side by side only if the
same shapes appear in adjacent cells on their common side. 9 cards are used
to form a rectangle as shown in the figure. Which of the following cards was
definitely NOT used to form this rectangle
The sοlutiοn οf the given prοblem οf rectangle cοmes οut tο be E is the answer.
A rectangle is what?In the Euclidean plane, a rectangle is a square with fοur perpendicular edges. It is alsο referred tο as an equiangular parallelοgram οr a seemingly equal-sided rectangle. The trapezοid can alsο have a straight edge. Fοur οf the sides οf a square are equal in length. Rectangular quadrilaterals have fοur equal sides and fοur 90° edges. Its name is sοmetimes "rectangular trapezοid" as a cοnsequence.
Here,
Due tο the shared suits οf the adjacent sectiοns.
Therefοre,
Case 1: Triangles and circles must be arranged in a series fοr hοrizοntal fitting.
Therefοre,
A, C, and D are excellent οptiοns. Sο they can't be the sοlutiοns.
Again,
Case 2.
Tο accοmmοdate vertically,
Rectangle and Triangle need tο be in the same cοlumn. And B is where that is happening.
sο that,
The οnly exceptiοn is:
"E" is the answer.
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Complete question:
A rectangular corral of 117 square meters is to be fenced off and then divided by a fence into two sections, as shown in the figure to the right. If the cost of fencing for the boundary is $10 per meter and the dividing fence costs $6 per meter, find the dimensions of the corral that minimize the cost of the fencing.
Answer:
the dimensions of the corral that minimize the cost of the fencing are approximately 17.91 meters by 6.54 meters.
Step-by-step explanation:
Let the length of the corral be x, and the width be y. We know that the area of the corral is 117, so:
xy = 117
We also know that the corral is divided by a fence into two sections. Let the length of one section be L, and the width be y. Then, the length of the other section will be x - L, and the width will still be y. The total fencing cost will be:
10(2x + 2y) + 6(L + 2y)
Simplifying this expression, we get:
20x + 32y + 6L
Using the area equation, we can rewrite this as:
20x + 32(117/x) + 6L
To minimize the cost, we need to take the derivative of this expression with respect to L, and set it equal to zero:
d/dL [20x + 32(117/x) + 6L] = 6 = 0
Solving for L, we get:
L = x/2
Therefore, the two sections of the corral will have equal length. Substituting this value of L into the expression for total fencing cost, we get:
20x + 32y + 3x
Simplifying this, we get:
23x + 32y
Using the area equation to substitute for y, we get:
23x + 32(117/x)
Taking the derivative of this expression with respect to x, and setting it equal to zero, we get:
23 - 3744/x^2 = 0
Solving for x, we get:
x = sqrt(3744/23) ≈ 17.91
Substituting this value of x into the area equation, we get:
y = 117/x ≈ 6.54
Therefore, the dimensions of the corral that minimize the cost of the fencing are approximately 17.91 meters by 6.54 meters.
I’s it yes or no because you have to justify the answer
Yes, both triangles are similar.
What is similar triangle?Similar triangles are two triangles that have the same shape, but may differ in size. In other words, their corresponding angles are congruent and their corresponding sides are proportional. This means that if you were to scale one triangle up or down, it would still maintain the same shape as the other triangle.
In ΔABC,
AC² = 36² +15²
AC² = 1521 = 39²
AC = 39
In ΔXYZ,
XY² = 24² +10²
XY² = 676 = 26²
XY = 26
If the ratio of the sides of both triangles are similar So we can say that the both triangles are similar.
AB/XZ = BC/YZ = AC/XY
15/10 = 36/24 = 39/26
3/2 = 3/2 = 3/2
Here we can see that the ratio of the sides of both triangles are similar So we can say that the both triangles are similar.
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How does the slope of the red triangle compare to the slope of the blue triangle 
A: the slope of the blue triangle is twice the slope of the red triangle
B: the slope of the red triangle steeper than the slope of the blue triangle
C: the slopes of the two triangles are the same
D: the slope of the red triangles have the slope of the blue triangle
Hence, in answering the stated question, we may say that C: the two graphs triangles' slopes are the same.
What is graphs?Mathematicians use graphs to visually explain or chart events or variables. A graph point often indicates a connection between one thing and another. A graph, a non-linear data structure, is constituted of nodes (vertices) and edges. Glue the nodes, which are also called as vertices. This graph has E=1, 2, 1, 3, 2, 4, and (2.5) edges and V=1, 2, 3, 5. (3.5). (4.5). Graphical representations of exponential growth in analytical charts (bar charts, pie charts, line charts, and so on). a graph of a logarithmic triangle.
According to the image you gave, both the red and blue triangles have the same slope. As a result, the solution is:
C: the two triangles' slopes are the same.
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what is the measure of MN
Answer:
45 degrees I think
Step-by-step explanation:
sorry if wrong
12 1/2 4 7/10 = ? Select one answer. show your work A 7 6/8 B 7 8/10 C 8 6/8 D 8 8/10
According to the question the option C is the correct answer that is 8 6/8 or 8 ¾ calculated by simplifying the fraction.
what is fraction?To represent a whole, every number of equal parts or fractions can be utilised. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio of a numerator to the denominator. They can all be expressed as simple fractions as integers. A fraction appears in a complex fraction's numerator or denominator. The numerators of true fractions are smaller than the denominators. A sum that is a fraction of a total is called a fraction. You can analyse something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolise half of a whole number or object.
To add mixed numbers, we need to first convert any fractions to a common denominator. In this case, we can use 10 as the common denominator.
12 1/2 = 12 + 1/2 = 12 + 5/10 = 12 5/10
4 7/10 = 4 + 7/10
Now we can add the two mixed numbers:
12 5/10 + 4 7/10 = 16 12/10
Simplifying the fraction by dividing the numerator and denominator by their greatest common factor of 2, we get:
16 12/10 = 16 6/5
Therefore, the answer is C) 8 6/8 or 8 3/4.
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Simplify: 5/6-17/12-5/3 A. -19/12 B.-17/12 C.1/4 D.23/12
HELP ASAP pls!!!
Answer:
The simplified expression is -13/12. (are you sure you don't have a typo somewhere), double checked.
Step-by-step explanation:
First, let's simplify the expression inside the absolute value bars:
5/6 - 17/12 = 10/12 - 17/12 = -7/12
Next, we can simplify the expression outside the absolute value bars:
| -7/12 | - | 5/3 |
= 7/12 - 5/3 (since the absolute value of -7/12 is 7/12)
= 7/12 - 20/12
= -13/12
The simplified expression is -13/12.
_______________________
Simplify the following:
abs(5/6 - 17/12) - abs(5/3)
Put 5/6 - 17/12 over the common denominator 12. 5/6 - 17/12 = (2×5)/12 - 17/12:
abs(((2×5)/12 - 17/12)) - abs(5/3)
2×5 = 10:
abs(10/12 - 17/12) - abs(5/3)
10/12 - 17/12 = (10 - 17)/12:
abs(((10 - 17)/12)) - abs(5/3)
10 - 17 = -7:
abs((-7)/12) - abs(5/3)
Since 5/3 is a non-negative constant, abs(5/3) = 5/3:
abs(-7/12) - 5/3
Since -7/12 is a negative constant, abs(-7/12) = 7/12:
7/12 - 5/3
Put 7/12 - 5/3 over the common denominator 12. 7/12 - 5/3 = 7/12 + (4 (-5))/12:
7/12 - (5×4)/12
4 (-5) = -20:
7/12 + (-20)/12
7/12 - 20/12 = (7 - 20)/12:
(7 - 20)/12
7 - 20 = -13:
Answer: (-13)/12
A customer purchased 10 items at a rummage sale. The prices paid are given in the table. What amount of change should the customer have received given that the customer paid with a $20 bill?
The amount of change that the customer will be given when payment is made with a $20 bill would be = $7.15. That is option G.
How to calculate the cost balance of the customer?The total number of items purchased by the customer = 10
The cost for 5 items = $1.60× 5 = $8
The cost of 3 items = $1.25×3 = $3.75
The cost of 2 items = $0.55×2 = $1.1
The total cost = 8+3.75+1.1 = $12.85
Therefore, the change of the customer when $20 bill is used = 20-12.85
= $7.15.
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On a menu, there are 5 beef options, 3 pork options, 6 chicken options, and 4 vegetarian options. One of the options is selected at random. Determine the theoretical probability of selecting a meat option. Express your answer as a fraction in simplest form. HELP!
Answer: The theoretical probability of selecting a meat option is 7/9.
Step-by-step explanation:
5 beef + 3 pork + 6 chicken + 4 veggie = 18 options total
meat options = 18 (total) - 4 veggie = 14 meat options
14/18 = 7/9
construct a quadratic equation of -2 +3
[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +2 )( x -3 ) = \stackrel{0}{y}}\hspace{4em}\stackrel{\textit{now, assuming that}}{a=1}\hspace{5em}1( x +2 )( x -3 ) =y \\\\\\ ~\hfill {\Large \begin{array}{llll} x^2-x-6=y \end{array}}~\hfill[/tex]
A flower bed is in the shape of a triangle, with a base of 15 feet and a height of 9 feet. What is the area of the flower bed? (4 points)
The area of the flower bed is 67.5 square feet.
An area in mathematics is what?The area of an object is the space that is enclosed by its boundaries. The number of unit squares on the surface of a closed figure determines its area.
The following formula provides the area of a triangle:
(1/2) * Base * Height = Area
Inputting the values provided yields:
Area equals (1/2) * 15 * 9
Dimensions: 67.5 square feet
The flower bed therefore has a 67.5 square foot space.
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Please help . A burglar alarm system has six fail-safe components. The probability of each failing is 0.05. Find the probability that fewer than three will fail. Round to the nearest thousandth.
Answer:
Answer:
0.050
Rounded to the nearest 0.001 or
the Thousandths Place.
Step-by-step explanation:
Explanation
0.05__
You rounded to the nearest thousandths place. The _ in the thousandths place rounds down to 0 because the digit to the right in the ten thousandths place is _.
0.050
When the digit to the right is less than 5 we round toward 0.
0.05 was rounded down toward zero to 0.050
85 POINTS!!! With brainiest 5th grade please complete this page below you can print it or do it online please just do it
Answer:
1. 8
2. 24
3. 15
4. 135
b. 135 x 1/9
5. the answer is 24
Find the area of the triangle.
Easy points!
Answer:
53.06 ft^2
Step-by-step explanation:
Calculate semi perimeter and use Scalence triangle area formula
Semi perimeter: a+b+c/2
Area of Scalence triangle: √s(s-a)(s-b)(s-c). {where s=semi perimeter}
Answer: I don't know
What is the common difference in the arithmetic sequence 10, 8, 6, 4, ...?
1/2
-1/2
-2
2
Answer:
The common difference in an arithmetic sequence is the constant difference between any two consecutive terms. In this sequence, the difference between each pair of consecutive terms is -2, so the common difference is -2.
Therefore, the answer is -2.
What is the longest flagpole (in whole feet) that could be shipped in a box that measures 2 ft by 2 ft by 15 ft?
The longest flagopole that could fit in the box is 15.26 feet
What is the longest flagopole that could fit in the box?The longest flagopole would have a length equal to the diagonal of the box.
It goes, lengthwise, from one vertex to the opposite vertex, and if the dimensions of the box are x, y, z, then the diagonal is:
d = √(x² + y² + z²)
In this case the box is 2ft by 2 ft by 15ft, then the diagonal is:
d = √(2² + 2² + 15²) = 15.26
That is the maximum length that can fit in the box, 15.26ft
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(b). A competitive market has the demand schedule p=420-2q and the supply schedule p= 60+ 4q where p is measured in naira. (i) Find the equilibrium values of p and q. (ii) What will happen to these values if the government imposes a tax of N24 per unit on q?
1. The equilibrium quantity = 60, the equilibrium price = 300
2. If the government imposes the tax of 24, the quantity supplies would fall to 56, and the price would rise to 308
How to solve for equilibriumAt equilibrium we have P = Q
that is price is equal to quantity. Such that we would have:
420-2q = 60+ 4q
take the like terms
420 - 60 = 4q + 2q
360 = 6q
q = 360 / 6
q = 60
The equilibrium quantity = 60 then equilibrium price =
420-2q
420 - 2 * 60
300
The equilibrium price is 300
2. If the government imposes 24 dollar per unit
420-2q = 60+ 4q + 24
420 - 2q = 84 + 4q
420 - 84 = 4q + 2q
336 = 6q
56 = q
420-2 * 56
p = 308
If the government imposes the tax of 24, the quantity supplies would fall to 56, and the price would rise to 308
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Calculate the size of one exterior angle and one exterior angle of a regular ten-sided shape (decagon)
Answer:
36∘
Step-by-step explanation:
Decagon has ten sides and ten angles. All these sides and angles are equal to each other. Therefore, the measure of each exterior angle of a regular decagon is 36∘
The total cost of producing a type of boat is given by C(x)=21000−40x+0.1x^2
, where x is the number of boats produced. How many boats should be produced to incur minimum cost?
Using differentiation, 200 boats should be produced to incur minimum cost
What is meant by differntiation?A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable in mathematics. A crucial calculus technique is the derivative.
Differentiation is a technique for determining a function's derivative. In mathematics, the technique of differentiation is used to determine the instantaneous rate of change in a function dependent on one of its variables. The most typical illustration is the velocity, or rate of change of displacement with respect to time.
Minimum boats can be found by differentiating the given function,
[tex]C(x)=21000 - 40x+0.1x^2[/tex]
Differentiating with respect to x,
0 = 0.2x - 40
0.2x = 40
x = 200
∴ 200 boats should be produced to incur minimum cost.
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You have four fun things in a bag (scorpion, tarantula, centipede, and wasp). You reach into the bag and randomly grab two fun things, one after the other, keeping both. Create a tree diagram, table, or list that models the sample space for this event.
Answer: Here is a table that models the sample space for this event:
Scorpion Tarantula Centipede Wasp
First S1 T1 C1 W1
Second S2 T2 C2 W2
Each combination of two fun things is represented by a two-letter code. For example, "S1T2" represents grabbing the scorpion first and the tarantula second.
Here is the list of all possible outcomes:
S1S2
S1T2
S1C2
S1W2
T1S2
T1T2
T1C2
T1W2
C1S2
C1T2
C1C2
C1W2
W1S2
W1T2
W1C2
W1W2
And here is a tree diagram that shows the same information:
|----S2
|----T2
First --|----C2
|----W2
|
|----S2
|----T2
Second--|----C2
|----W2
The branches on the left represent the first fun thing that is grabbed, and the branches on the right represent the second fun thing that is grabbed.
Step-by-step explanation:
The equivalent expression
The equivalent expression is (x -2)/(x+4)(x + 6)
How to determine the equivalent expressionIt is important to note that algebraic expressions are defined as expressions composed of coefficients, terms, variables, constants and factors.
They are also made up of arithmetic operations.
Also, equivalent expressions are defined as expressions that have the same solution but differs in the arrangement of the terms.
From the information given, we have the expression;
(x - 2)/x² + 10x + 24
Now, let's factorize the denominator, we have;
x² + 10x + 24. Find the pair factors of 24 that add up to 10, we get;
x² + 4x + 6x + 24
Factorize in pairs
x(x + 4) + 6(x + 4)
Then, substitute the expressions;
(x -2)/(x+4)(x + 6)
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Suppose I am rolling a standard 6-sided dice. Let A be the event I roll a prime number, Let B be the event I roll a number less than or equal to 4. I ran a trial 10 times and got the results 2, 4, 3, 1, 5, 6, 1, 3, 2, 1
What is the experimental P(B)
The experimental probability of rolling a number less than or equal to 4 is 0.7.
How is conditional probability calculated? What does it mean?The likelihood that an event (A) will occur given the occurrence of another event (B) is known as conditional probability. P(A|B), which stands for "the probability of A given B," is used to express it. You must first determine P(A and B) by multiplying the odds of A and B happening together. Next, you may compute P(A|B). The conditional probability of A given B is then obtained by dividing the result by P(B).
Several situations in everyday life, including medical diagnosis, industrial quality control, and risk assessment in insurance, call for the usage of conditional probability.
Given that, the trial was run 10 times.
Thus,
P(B) = (number of times B occurred) / (total number of trials)
= 7 / 10
= 0.7
Therefore, the experimental probability of rolling a number less than or equal to 4 is 0.7.
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Indicate whether the two functions are equal. If the two functions are not equal, then give an element of the domain on which the two functions have different values.
(a). f: Z → Z, where f(x) = x^2.
g: Z → Z, where g(x) = |x|^2.
(b). f: Z × Z → Z, where f(x,y) = |x + y|.
g: Z × Z → Z, where g(x,y) = |x| +| y|.
(c). B = {0, 1}
f: B × B → B × B, where f(x,y) = (1-y, 1-x)
g: B × B → B × B, where g(x,y) = (x,y)
The functions are equal in option A, and aren't equal in B (try input x =1 and y = -1) and in C (try input x = 0 and y = 0).
Are the functions equal in the domains?The first one is:
(a). f: Z → Z, where f(x) = x^2.
g: Z → Z, where g(x) = |x|^2.
Yes, these functions are equal, this happens because both outcomes will always be positive, indifeterent of the absolute value part.
b) f: Z × Z → Z, where f(x,y) = |x + y|.
g: Z × Z → Z, where g(x,y) = |x| +| y|.
These are different, if x = 1 and y = -1
f(1, - 1) = |1 - 1| = 0
g(1, -1) = |1| + |-1| = 2
c) B = {0, 1}
f: B × B → B × B, where f(x,y) = (1-y, 1-x)
g: B × B → B × B, where g(x,y) = (x,y)
This is clearly false, when x and y are 0 and 0 we have:
f(0, 0) = (1 - 0, 1 - 0) = (1, 1)
While g gives:
g(0, 0) = (0, 0)
These functions are different.
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