Answer:
Let the length of the rectangle be l and the width be w. Then, according to the problem statement, we have:
Perimeter of rectangle = 2(l + w) = 48 feet
Dividing both sides by 2, we get:
l + w = 24 feet
Now we can check the options:
A) 6 feet x 8 feet: l + w = 6 + 8 = 14 feet, which is not equal to 24 feet. Therefore, this option is not correct.
B) 12 feet x 12 feet: l + w = 12 + 12 = 24 feet, which is equal to the given perimeter. Therefore, this option is correct.
C) 16 feet x 8 feet: l + w = 16 + 8 = 24 feet, which is equal to the given perimeter. Therefore, this option is correct.
D) 12 feet x 4 feet: l + w = 12 + 4 = 16 feet, which is not equal to 24 feet. Therefore, this option is not correct.
So, the correct options are B) 12 feet x 12 feet and C) 16 feet x 8 feet.
Determine all solutions to the equation 2sin2x = 1 − cos x on the interval [0, 2π).
a: x equals pi over 2 comma 2 times pi over 3 comma 4 times pi over 3
b: x equals 0 comma pi over 3 comma 5 times pi over 3
c: x equals pi over 2 comma pi over 3 comma 5 times pi over 3
d: x equals 0 comma 2 times pi over 3 comma 4 times pi over 3
The solution to the given equation 2sin2x = 1 − cos x on the interval [0, 2π) as required is; Choice D; x equals 0 comma 2 times pi over 3 comma 4 times pi over 3.
What are the solutions to the given equations?It follows from the task content that the solutions to the given equation be determined.
On this note, since the give equation is;
2sin²x = 1 − cos x on the interval [0, 2π).
Recall sin²x = 1 − cos²x; therefore we have that;
2 - 2cos²x = 1 - cos x
2cos²x - cos x - 1 = 0.
let y = cos x so that we have;
2y² - y - 1 = 0
x = 1 or x = -1/2.
Therefore; cos x = 1 or cos x = -1/2.
Ultimately, the values of x in the given interval are; 0, 2π/3, 4π/3.
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Shouldn't be correct answer be option 2?
2+1=3 is the solution to the differentiation equation.
What does a calculus differential equation mean?A differential equation is an equation that explains a function's unknown derivative or derivatives. Take the equation, for example. The expression d y d x = x sin expresses the derivative of an unknown function.
Chain rule evaluation of the derivative on the left hand side yields the following results:
[tex]dxd {( dxdy ) 3 } =0. ⇒3( dxdy ) 2 dx 2 d 2 y =0[/tex]
Because the highest order derivative that appears in the equation is second order, the order of this differential equation is 2.
Its highest order derivative's power is the degree. Degree in this instance is 1.
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In the coordinate plane, the points X9, 5, Y−−3, 6, and Z−8, 4 are reflected over the x-axis to the points X′, Y′, and Z′, respectively. What are the coordinates of X′, Y′, and Z′?
Answer:
When a point is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate is multiplied by -1.
So, the coordinates of X' are (9, -5) since the x-coordinate remains the same and the y-coordinate is multiplied by -1.
Similarly, the coordinates of Y' are (-3, -6) and the coordinates of Z' are (-8, -4).
Therefore, X′ is (9,−5), Y′ is (−3,−6), and Z′ is (−8,−4).
use the slicing method to find the volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles.
the volume of the solid is [tex]V = π r2 (sqrt(3/4)r) / 3 = π r3 sqrt(3/4) / 3.[/tex]
Plugging in the given values, we get[tex]V = π (3)3 sqrt(3/4) / 3 = 27π/4.[/tex]
The volume of a solid with a circular base and cross sections taken parallel to one of the diameters that are equilateral triangles can be found using the slicing method. The formula for the volume of such a solid is:[tex]V = π r2 h/3,[/tex]where π is the constant pi, r is the radius of the circular base, and h is the height of the solid.
In this case, the radius of the circular base is 3 and the height is equal to the length of the sides of the
equilateral triangles. To find the height, we can use the Pythagorean Theorem. The hypotenuse of the triangle is 2r, so the length of the sides is sqrt(r2 - (r/2)2), which simplifies to sqrt(3/4)r.
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The new town jewelry company purchased 501 carat diamond rings for $125,000 based on the following information find the selling price purring to the nearest cent
The selling price of the 501 carat diamond rings is approximately $168,750.00, rounded to the nearest cent.
To find the selling price of the 501-carat diamond rings, we need to use the information given about the cost of the purchase and the markup percentage.
Let's assume the markup percentage is m. Then, the selling price S can be calculated as:
S = C * (1 + m/100)
where C is the cost of the purchase ($125,000 in this case).
If the markup percentage is not given, we can use another piece of information to calculate it. For example, if we know that the company wants to earn a profit of P dollars on the sale, we can set the equation:
S - C = P
and solve for the markup percentage:
m = (P/C) * 100
Assuming a markup percentage of 35%, we can calculate the selling price as:
S = 125,000 * (1 + 35/100)
S ≈ $168,750.00
Therefore, the selling price of the 501 carat diamond rings is approximately $168,750.00, rounded to the nearest cent.
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Can someone help me out with these indices?
Using the law of indices, the values of the unknown are 1/2, -2/3, -3, 1, 10, 0, 7/12, and -4/17
What is the result of the indicesTo solve these problems, we need to apply the laws of indices to the question as required.
11. 10⁻³ˣ * 10ˣ = 1/10
using multiplication law of indices;
x = 1/2
12. 3⁻²ˣ ⁺¹ * 3⁻²ˣ ⁻³ = 3⁻ˣ
x = -2/3
13. 4⁻²ˣ * 4ˣ = 64
x = -3
14. 6⁻²ˣ * 6⁻ˣ = 1/216
x = 1
15. 2ˣ * 1/32 = 32
x = 10
16. 2^(-3p) * 2^(2p) = 2^(2p)
p = 0
17. 64 * 16⁻³ˣ = 16³ˣ⁻²
x = 7/12
18. 81^(3n + 2) / 243^(-n) = 3^4
n = -4/17
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Your science teacher bought 6 posters for the classroom that cost $30. The rainforest posters cost $5.50 each and the ocean posters cost $4 each. How many of each did your teacher buy?
Answer: The science teacher bought 4 rainforest posters and 2 ocean posters.
Step-by-step explanation: Let x be the number of rainforest posters and y be the number of ocean posters that the science teacher bought.
We know that the teacher bought 6 posters in total, so we have:
x + y = 6 (equation 1)
We also know that the cost of the 6 posters was $30, so we have:
5.5x + 4y = 30 (equation 2)
To solve for x and y, we can use either substitution or elimination method. Let's use the elimination method by multiplying equation 1 by 4 and subtracting it from equation 2:
5.5x + 4y = 30
-4x - 4y = -24
Simplifying, we get:
1.5x = 6
x = 4
Substituting x = 4 into equation 1, we get:
4 + y = 6
y = 2
Therefore, the science teacher bought 4 rainforest posters and 2 ocean posters.
The volume of a solid hemisphere of radius 2 cm
Answer:
The volume of a solid hemisphere with radius r is given by the formula:
V = (2/3)πr^3
In this case, the radius of the hemisphere is 2 cm. Substituting this value into the formula, we get:
V = (2/3)π(2 cm)^3
V = (2/3)π(8 cm^3)
V = (16/3)π cm^3
Therefore, the volume of the solid hemisphere is (16/3)π cubic centimeters.
Answer:
(16/3)π cm³ ≈ 16.76 cm³ (nearest hundredth)
Step-by-step explanation:
The volume of a solid hemisphere is given by the formula:
[tex]\boxed{V = \dfrac{2}{3}\pi r^3}[/tex]
where r is the radius of the hemisphere.
Substitute the given radius, r = 2 cm, into the formula, and solve for V:
[tex]\begin{aligned}\implies V &= \dfrac{2}{3}\pi(2)^3\\\\&= \dfrac{2}{3}\pi \cdot 8\\\\&= \dfrac{16}{3}\pi\; \sf cm^3\end{aligned}[/tex]
Therefore, the volume of the solid hemisphere of radius 2 cm is (16/3)π cm³ or approximately 16.76 cm³ (nearest hundredth).
find the circumference of each circle
Answer:
[tex]\large\boxed{\mathtt{C=100 \pi \ in.}}[/tex]
[tex]\large\boxed{\mathtt{C \approx314.16 \ in.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked for the circumference of this circle.}[/tex]
[tex]\textsf{Let's review what the Circumference of a circle actually is.}[/tex]
[tex]\large\underline{\textsf{What is the Circumference?}}[/tex]
[tex]\textsf{The Circumference is is the length 'on' the circle.}[/tex]
[tex]\textsf{Circumference is the Perimeter of the Circle; The sum of all the curved edges.}[/tex]
[tex]\large\underline{\textsf{How do we find the Circumference?}}[/tex]
[tex]\textsf{To find the Circumference, we should use a common, and simple formula.}[/tex]
[tex]\mathtt{Circumference=(Diameter) \pi}[/tex]
[tex]\textsf{Pi will be multiplied by the Diameter of the Circle.}[/tex]
[tex]\textsf{Because we are given the Diameter, we can start solving for x.}[/tex]
[tex]\large\underline{\textsf{Substitute;}}[/tex]
[tex]\mathtt{Circumference \ (C)=(100 \ in.) \pi}[/tex]
[tex]\large\boxed{\mathtt{C=100 \pi \ in.}}[/tex]
[tex]\large\boxed{\mathtt{C \approx314.16 \ in.}}[/tex]
Which state is located at point C?
a map of the United States. New York, Indiana, and Kansas are labeled. There is an A marking the state south of New York along the Atlantic coast. There is a B marking the state east of Indiana. There is a C marking the state north of Indiana. There is a D marking the state northeast of Kansas. There is an E marking the state south of Kansas.
New Jersey
Ohio
Michigan
Iowa
According to the information provided, the state is at point C, Michigan.
Based on the information provided, the state located at point C is Michigan.
What is logical thinking?Logical reasoning consists of aptitude questions that require logical analysis to arrive at a suitable solution. Most of the questions are conceptual, the rest are unconventional.
Logical thinking follows he is divided into two types.
Oral reasoning:
It is the ability to logically understand concepts expressed in words and solve problems. Oral reasoning tests your ability to extract information and meaning from sentences. Non-verbal thinking:
It is the ability to logically understand concepts represented by numbers, letters, and combinations of numbers and words and solve problems. Nonverbal reasoning tests your ability to reason and guide the logic and implications of information in a problem.
Much of the logic curriculum can be classified into his two types above.
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Given a list (0, 1, 1, 2, 3, 5, 8, 13, 17), the binary search algorithm calls BinarySearch(list, 0, 8, 3). What is the index of the middle element?
The index of the middle element is 4.
The list (0, 1, 1, 2, 3, 5, 8, 13, 17), the binary search algorithm calls Binary Search (list, 0, 8, 3). The index of the middle element is 4. The binary search algorithm works by dividing a list into halves and looking at the value in the middle of the list. This is compared with the target value, and based on the comparison, one-half of the list is discarded as the search is continued in the other half. This is continued until the target value is found or it is clear that it is not on the list. In the given case, the list is (0, 1, 1, 2, 3, 5, 8, 13, 17), and the algorithm calls Binary Search(list, 0, 8, 3).
Here, the first parameter of the Binary Search function is the list, the second parameter is the lower index of the part of the list being searched, the third parameter is the upper index, and the fourth parameter is the value being searched. In the given case, the lower index is 0, the upper index is 8, and the value being searched is 3. The index of the middle element in the list is calculated as (0 + 8) / 2 = 4.
Therefore, the index of the middle element is 4.
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If you have the following data about
a box of bouncy balls, about how
many bouncy balls are estimated to
be in the box?
Mass of Bouncy Balls + Box = 17,342
grams
Mass of 45 Balls = 505 grams
Mass of Box ONLY = 429 grams
Approximately, how many bouncy
balls are in the box?
Bouncy Balls in Box
Enter
there are approximately 1506 bouncy balls in the box.
What is mass ?
Mass is a physical property of matter, which refers to the amount of substance present in an object. It is typically measured in units of grams or kilograms, and can be thought of as a measure of the object's inertia or resistance to acceleration. Mass is often used interchangeably with weight in everyday language, but they are technically different concepts. Weight is a measure of the force of gravity acting on an object, and varies depending on the object's location in the gravitational field.
According to the question:
First, we need to find the mass of the bouncy balls in the box by subtracting the mass of the box only from the mass of the box and bouncy balls.
Mass of bouncy balls in box = Mass of box and bouncy balls - Mass of box only
Mass of bouncy balls in box = 17,342 - 429
Mass of bouncy balls in box = 16,913 grams
Next, we need to find the mass of one bouncy ball by dividing the mass of 45 balls by 45.
Mass of one bouncy ball = Mass of 45 balls / 45
Mass of one bouncy ball = 505 / 45
Mass of one bouncy ball = 11.222 grams
Finally, we can estimate the number of bouncy balls in the box by dividing the mass of the bouncy balls in the box by the mass of one bouncy ball.
Number of bouncy balls in box = Mass of bouncy balls in box / Mass of one bouncy ball
Number of bouncy balls in box = 16,913 / 11.222
Number of bouncy balls in box ≈ 1506
Therefore, there are approximately 1506 bouncy balls in the box.
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Find the derivative of the function h(w), below. It may be to your advantage to simplify before differentiating: h(w) = 7w arcsin w h' (w)=
Therefore, the derivative of the function h(w) is h'(w) = [tex]7*arcsin(w) + w*cos(w)*7.[/tex]
The derivative of the function h(w) is h'(w) = [tex]7*arcsin(w) + w*cos(w)*7[/tex]. To find this, first simplify the original function using the identity arcsin(w) = sin-1(w), then use the chain rule. We get:
h'(w) = 7*sin-1(w) + w*cos(sin-1(w))*7
Since sin-1(w) is the inverse of sin(w), we can substitute w for sin(w). This gives us:
h'(w) = 7*sin-1(w) + w*cos(w)*7[tex]7*sin-1(w) + w*cos(w)*7[/tex]
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Miguel bought 22 pounds of flour for $12. How many dollars did he pay per pound of flour?
Rewrite the following in the form log(c).
log(15) -log(3)
The logarithmic expression given as log(15) -log(3) when simplified is log(5).
How to rewrite the logarithmic expressionGiven that
log(15) -log(3)
The form is
log(c)
Using the logarithmic identity that states log(a) - log(b) = log(a/b), we can rewrite the given expression as:
log(15) - log(3) = log(15/3)
And simplifying the expression inside the logarithm, we get:
log(15) - log(3) = log(5)
So the given expression, log(15) - log(3), can be written in the form log(c) as log(5).
This means that the logarithm of 5 is equivalent to the difference between the logarithms of 15 and 3.
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I NEED HELP ON THIS ASAP, IT'S DUE TODAY!
The inequalities which the number lines represent are as follows;
x > 3
x <= 2.
What are inequalities ?A mathematical comparison and expression of the relationship between two expressions is known as an inequality.
It can be seen as a generalization of an equation and is denoted by a symbol like ">", "", "", or "".
In contrast to an equation, which only has one solution, an inequality may have several answers or none at all.
The values that give rise to an inequity are its remedies.
The range of potential values for a variable is one example of how inequality models limits or limitations in the real world.
They can also be used to describe how two variables relate to one another, such as when one is more than or less than the other.
According to our question-
the inequality is; x <= 2
the inequality is; x > 3
x > 3
x <= 2
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the picture pls answer my picture.
Answer:
$63 more in tax
Step-by-step explanation:
Takis is 5.25 in tax
PlayStation is 68.25
well, we know the tax is 10.5% so let's get them for both.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10.5\% of 49.99}}{\left( \cfrac{10.5}{100} \right)49.99} ~~ \approx ~~ 5.25[/tex]
[tex]\stackrel{\textit{10.5\% of 649.99}}{\left( \cfrac{10.5}{100} \right)649.99} ~~ \approx ~~ 68.25\hspace{9em}\underset{ \textit{taxes' difference} }{\stackrel{ 68.25~~ - ~~5.25 }{\approx\text{\LARGE 63}}}[/tex]
find a basis for the vector space of polynomials of degree at most two which satisfy the constraint . how to enter your basis: if your basis is then enter .
The vector space of polynomials of degree at most two that satisfies the constraint is given by the span
{1 + x + x², 1 - x + x²}.
To find a basis for the given vector space, we first determine the dimensions of the space.
The vector space of polynomials of degree at most two is of the form:
p(x) = a + bx + cx²
This vector space contains infinitely many vectors because it is a function space.
The constraint p(1) = 1 + 2a + b + c = 0 means that the dimension of the subspace is two rather than three.
Next, we will obtain a basis for the vector space of polynomials of degree at most two that satisfy the constraint:
span{1, x - 1, x(x - 1)} is a basis for the subspace of the vector space that satisfies the constraint.
To find the basis for the subspace, we can use the definition of a basis.
A basis is a set of vectors that spans the subspace, and that are linearly independent.
We must demonstrate that this basis spans the subspace and that it is linearly independent.
If p(x) = a + bx + cx² satisfies the constraint p(1) = 0, then we have
1 + 2a + b + c = 0, which means a = (-b - c + 1)/2.
Then p(x) = (-b - c + 1)/2 + bx + cx².
Now, we find a basis for the subspace that satisfies the constraint by selecting vectors and demonstrating that they are linearly independent.
span{1, x - 1, x(x - 1)} is a basis for the subspace because they are linearly independent and span the subspace.
Span{1, x - 1, x(x - 1)} spans the subspace because any polynomial in the subspace can be expressed as a linear combination of the elements of the basis.
1 = (1/2) (1 + x - x(x - 1) - x + x(x - 1)) = (1/2)(1 - x²)x - 1 = x - 1x(x - 1) = x² - x
Since the coefficients of 1, x - 1, and x² - x are unique, the three polynomials are linearly independent, so they form a basis.
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Mr. Smith earns $23.20 per hour for the first 40
hours he works in a week. He earns 1.5 times that
amount per hour for each hour beyond 40 hours in
a week. Last week Mr. Smith worked 51.5 hours.
How much money did he earn last week?
A) $400.20
B) $1,328.20
C) $928.00
D) $1,194.80
Answer:For the first 40 hours, Mr. Smith earned:
$23.20/hour × 40 hours = $928.00
For the additional 11.5 hours, he earned:
$23.20/hour × 1.5 = $34.80/hour
So, for these hours, he earned:
$34.80/hour × 11.5 hours = $400.20
Adding these amounts together, we get:
$928.00 + $400.20 = $1,328.20
Therefore, Mr. Smith earned $1,328.20 last week.
Step-by-step explanation:
Verify that W is a subspace of V. Assume that V has the standard operations.
W is the set of all 3x2 matrices of the form [a,b;(a+b),0;0,c] and V=M[-subscript-(3,2)]
The zero vector: The zero vector 0 = [0,0;0,0;0,0] is also a member of W. Thus, the third criterion is satisfied.
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FACTOR 6x²- 18x - 60
Answer: 6(x+2)(x-5)
Step-by-step explanation:
1: Factor by grouping- A 6 can be distributed in all 3 terms, when we do this we get 6(x²-3x-10).
2: This is in the form 6(x²+bx+c). So, to continue factoring, just forget about the six for a while and find two factors of c that add up to b. These two factors are -5 and 2.
3: Fill in the blanks with either factor. (x+?)(x+?) We get (x+2)(x-5).
4: Bring back the 6 to the beginning of the equation to get a final answer of 6(x+2)(x-5).
during the computer daze special promotion, a customer purchasing a computer and printer is given a choice of three free software packages. there are 8 different software packages from which to select. how many different groups of software packages can be selected?
Therefore, there are 336 different groups of software packages that can be selected from the 8 different software packages offered during the Computer Daze special promotion.
There are 8 different software packages to choose from during the Computer Daze special promotion. Since the customer purchasing a computer and printer is given a choice of 3 free software packages, this means that there are 336 different groups of software packages that can be selected.
To calculate this, the total number of possibilities can be found by using the formula nPr,
where n is the total number of choices, and r is the number of items chosen. This can be written as 8P3. 8P3 is equal to[tex]8x7x6 = 336.[/tex]
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Make a number line and mark the points that represent the following values of x. x²=16
please show with numberline for brainliest :) please help my class is tomorrow and im finishing homework
Answer:
See below.
Step-by-step explanation:
Here's a number line showing the points that represent the values of x that satisfy the equation x² = 16
|---------------------------|---------------------------|
-4 0 4
On this number line, I have marked the points -4, 4, which are the two solutions to the equation x² = 16. These values of x make the left-hand side of the equation equal to 16.
what are the dimensions of the soup can of greatest volume that can be made with a 150 square inches of tin
The dimensions of the can of greatest volume that can be made with 150 square inches of tin are a radius of approximately 5.78 inches and a height of approximately 3.85 inches.
What are the dimensions?The dimensions of the soup can of greatest volume that can be made with 150 square inches of tin are given by the formula [tex]V = \pi r^2h[/tex], where V is the volume of the can, r is the radius of the base, and h is the height of the can. We can solve for the radius and height of the can using the given information.
Let the radius of the base be r and the height of the can be h. Then, the surface area of the can is given by the formula [tex]A = 2\pi rh + 2 \pi r^2[/tex]. We are given that the surface area of the can is 150 square inches, so we can write the equation [tex]2 \pi rh + 2 \pi r^2 = 150[/tex]. We need to find the dimensions of the can that maximize its volume, V. To do this, we can use the formula for the derivative of V with respect to r, which is [tex]dV/dr = 2 \pi rh + \pi r^2 dh/dr[/tex].
Setting this equal to zero and solving for h, we get [tex]h = -2r/3[/tex]. Substituting this into the equation for A, we get the equation [tex]2 \pi r(-2r/3) + 2 \pi r^2 = 150[/tex], which simplifies to [tex]-4 \pi r^2/3 + 2 \pi r^2 = 150[/tex]. Solving for r, we get [tex]r = 5.78[/tex] inches. Substituting this into the equation for h, we get [tex]h = -3.85[/tex] inches.
Since we cannot have a negative height, we must discard this value and take the positive value of h, which is approximately 3.85 inches. Therefore, the dimensions of the can of greatest volume that can be made with 150 square inches of tin are a radius of approximately 5.78 inches and a height of approximately 3.85 inches.
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Solve for x, using the tangent lines.
X
46°
× = [ ? ]°
Please answer ASAP, if you could include an explanation that would also help!
Considering the tangent-secant theorem, the value of x is given as follows:
x = 55º.
What is the secant-tangent theorem?The secant-tangent theorem states that when a tangent and a secant line intersect at a point outside a circle, the measure of the angle of intersection is given by half the difference between the arc length of the far arc by the arc length of the near arc.
Hence the equation is given as follows:
y = (far arc - near arc)/2.
The parameters for this problem are given as follows:
far arc = 145º.near arc = 35º.Angle = x.Then, applying the theorem, the value of x is given as follows:
x = (145 - 35)/2
x = 55º.
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(a) describe the relationship between distance and travel time. (select all that apply.) positive negative moderate weak linear nonlinear
The relationship between distance and travel time. It is not excessively strong or weak. In other words, the rate of change in journey time is moderate and constant with respect to distance.
positive negative moderate weak linear nonlinear relationship between distance and travel time can be described as follows:•
Positive• Linear• Moderate
Explain as we move from point A to point B, the distance covered and the travel time it takes to get there are positively correlated. As the distance increases, the travel time required to reach the destination also increases, resulting in a positive correlation.
The relationship between distance and travel time is linear because the rate at which distance is covered remains constant, resulting in a straight-line relationship on a graph. It means that if distance doubles, the travel time will also double, indicating a linear relationship.
Hence, the linear relationship is also referred to as a direct relationship. On a graph, the line that represents the relationship between distance and travel time is moderate. This implies that the slope of the line is neither too steep nor too gentle.
Thus, it is neither too strong nor too weak. In other words, the rate of change in travel time is consistent as distance changes, making it moderate.
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It takes 5 people 4 hours to clean a hall. How long will it take 8 people to clean the same hall at the same rate?
We can use the formula:
Work = Rate x Time
Let's assume that the amount of work involved in cleaning the hall is the same regardless of the number of people doing the job. Therefore, the amount of work done by 5 people in 4 hours is the same as the amount of work done by 8 people in t hours, where t is the time taken by 8 people to clean the hall.
We can set up an equation based on this:
5 people x 4 hours = 8 people x t hours
Simplifying this equation, we get:
20 = 8t/5
which implies, t = 25/8
Therefore, it will take 25/8 hours or 3 hours and 7.5 minutes for 8 people to clean the hall at the same rate as 5 people.
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A tank is full of water when a valve at the bottom of the tank is opened. The equation V = 62(151 - t) gives the volume of water in the tank, in cubic meters, after t hours.What is the volume of water in the tank before the valve is opened?__ cubic metersHow long does it take the tank to fully empty?___ hoursFind an equation for DV/dtdV/dt = __ PreviewWhat is the flow rate after 23 hours? ____ Select an answerWhen is the water flowing out of the tank the fastest?t= ____ hours
1. The volume of water in the tank before the valve is opened is 9362 cubic meters. 2. It takes 151 hours for the tank to fully empty.
What is modelling in math?Modeling is the process of representing and analyzing real-world events using mathematical ideas and methods. It is a crucial component of mathematics because it enables systematic, quantitative prediction, problem-solving, and understanding of complicated processes.
We may learn about the behavior of systems, test hypotheses, and arrive at wise conclusions by using mathematical models. We may use models to enhance processes, forecast results, and discover key factors.
The equation of the volume is given as V = 62(151 - t).
At t= 0 we have the volume as:
V = 62(151 - 0) = 9362 cubic meters
To empty the tank we take V = 0:
0 = 62(151 - t)
151 - t = 0
t = 151
Hence, the volume of water in the tank before the valve is opened is 9362 cubic meters and it takes 151 hours for the tank to fully empty.
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A team of 3 identical robotic lawn mowers can cut 15.6 acres of grass in a garden for
a single battery charge. How many acres can cut a team of 5 identical robotic lawn
mowers for a single battery charge?
Answer:
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Step-by-step explanation:
Midsize robot lawnmowers cut up to half an acre or about 22,000 square feet. Large robot lawnmowers can cut up to 1 acre, or 43,560 square feet, or more
Answer: 26 acres
Step-by-step explanation:
26 acres
Divided 15.6/3 to get unit rate, then multiply by 5 to get answer.
The inside diameters of bearings used in an aircraft landing gear assembly are known to have a standard deviation of A random sample of 15 bearings has an average inside diameter of 8. 2535 cm. (a) Test the hypothesis that the mean inside bearing diameter is 8. 25 cm. Use a two-sided alternative and (b) Find the P-value for this test. (c) Construct a 95% two-sided confidence interval on the mean bearing diameter
(a) The hypothesis that the mean inside bearing diameter is 8. 25 cm is 6.78.
(b) The p value is zero because if we observe a sample that is unlikely to fall below zero (if the statistician can detect it, we can get a p-value of exactly zero.
(c) At 95% two-sided confidence interval on the mean bearing diameter is 8.2527 or 8.2543.
Hypothesis:
Hypotheses (plural hypotheses) are proposed explanations for phenomena. For a hypothesis to be a scientific hypothesis, the scientific method requires that it can be tested. Scientists often base scientific hypotheses on past observations that cannot be satisfactorily explained by existing scientific theories. Although the words "hypothesis" and "theory" are often used interchangeably, a scientific hypothesis is not the same as a scientific theory. A working hypothesis is a tentatively accepted hypothesis that is proposed for further research in a process that begins with an educated guess or idea.
(a) The hypothesis that the mean inside bearing diameter is 8. 25 cm. By Using the two sided alternative:
H₀= 8.25
H₁ ≠ 8.25
Z = X - 8.25÷ sd/√π
= x - 8.25÷ 0.002/3.14
= 6.78 > 1.96 (CV)
(b) the P-value for this test is:
p( value) = 0
because if we observe a sample that is unlikely to fall below zero (if the statistician can detect it, we can get a p-value of exactly zero.
(c) X ± Zᵃ ÷ sd/√π
= 8.2527 or 8.2543
At 95% two sided confidence interval on the mean bearing diameter is 8.2527 or 8.2543.
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