Solving a system of equations we will see that the width is 40 feet.
What is the width of the floor?
We know that the floor has a rectangular shape, and the length is 20 feet longer than the width, so we can write the relation:
L = 20ft + W
Also, we know that a scale model of the floor has a length of 15 inches and a width of 10 inches, the same scale factor k is applied to the two of these, then we can write:
15 in = k*L
10in = k*W
So we have a system of equations:
L = 20ft + W
15 in = k*L
10in = k*W
Taking the quotient between the second and third equations we will get:
15in/10in = (k*L)/(k*W)
15/10 = L/W
1.5*W = L
Now we have two equations:
L = 20ft + W
1.5*W = L
We can substitute the second equation into the first one, so we will get:
1.5*W = 20ft+ W
1.5*W - W = 20ft
0.5*W =20ft
W = 20ft/0.5
W = 40ft
The width is 40 feet.
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(a) You have a 10 inch by 15 inch piece of tin which you plan to form into a box (without a top) by cutting a square from each corner and folding up the sides. How much should you cut from each corner so the resulting box has the greatest volume? (b) If the piece of tin is A inches by B inches, how much should you cut from each corner so the resulting box has the greatest volume?
Resulting box has the greatest volume for the values (25 ± 5√7)/6 .
This is a problem that can be solved using derivatives , maxima & minima and common logic.
Hence , going by logic :
Creating a flap of 'a' inches in width, the base of the box will be
(10 - 2a) by (15 - 2a)
and the depth of the box will be the width of the fold-up flap: a.
Then the volume of the box is
v = [tex]a(10 -2a)(15 -2a) = 150a -50a^2 +4a^3[/tex]
Using the derivative of the volume will be zero at the maximum volume.
0 = [tex]dv/da = 150 -100a +12a^2[/tex]
This has roots at
a = (100 ±√(100² - 4(12)(150)))/(2·12)
a = (100 ± √2800)/24 = (25 ± 5√7)/6
Only the smaller of these solutions gives a maximum volume.
You should cut (5/6)(5-√7) ≈ 1.962 inches to obtain the greatest volume.
Similarly , replacing the values of 10 by A and 15 by B , a generalized solution can be formed .
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find the probability of rolling a five or six on six sided number cube
Answer:
non-violence and kindness with animals
Step-by-step explanation:
and drop each item into the correct column. Order does not matter:
(1, 5); (4, 7) - corresponding, (3, 5) - Alternate Interior, (2, 7); (1, 8) - Exterior
(3, 6) are Consecutive Interior Angles.
Line of transversal:
Any line that crosses two straight lines at different locations is known as a transversal.
Corresponding Angles:
When two parallel lines cross the third one, the angles that are in the same relative position at each junction are referred to as corresponding angles to one another
Alternate Interior Angles:
The alternative interior angles are those that are on the inner side of the parallel lines but on the opposing sides of the transversal.
Alternate Exterior Angles:
Alternate external angles are positioned on the opposing sides of the transversal and are always outside the two lines where the transversal intersects.
Consecutive Interior Angles:
The pair of non-adjacent internal angles that are located on the same side of the transversal are referred to as consecutive interior angles.
Here we have
Two parallel lines intersected and formed the angles, ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8.
By the given information,
∠1 and ∠ 5 are corresponding angles
∠4 and ∠ 7 are corresponding angles
∠3 and ∠5 are Alternate Interior Angles
∠2, and ∠7 are Alternate Exterior angles
∠1 and ∠ 8 are Alternative Exterior angles
∠3 and ∠ 6 are Consecutive Interior Angles
Therefore,
(1, 5); (4, 7) - corresponding, (3, 5) - Alternate Interior, (2, 7); (1, 8) - Exterior
(3, 6) are Consecutive Interior Angles.
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Suppose that sin(0)=3/9. What cos(0)=____________. (round to 3 decimal
Using trigonometry identity the value of cosθ is 0.942.
What is round to 3 decimal?
Rounding to three decimal places is equivalent to rounding to the closest thousandth. Take 3.3685 as an example and round to the nearest thousandth. It is possible to round up to 3.369 or down to 3.368 because the third digit following the decimal point is 8 instead of 3.
Given that sinθ=3/9
Divide the denominator and numerator by 3:
sinθ=1/3
To find the value of cosθ, use trigonometry identity.
The trigonometry identity is sin²θ + cos²θ = 1
Solve the identity for cosθ:
Subtract both side by sin²θ:
cos²θ = 1 - sin²θ
Take square root on both sides:
cos θ = √(1 - sin²θ)
Putting sinθ = 1/3 in the above equation:
cos θ = √(1 - (1/3)²)
cos θ = √(1 - 1/9)
cos θ = √((9 - 1)/9)
cos θ = √(8/9)
cos θ = 0.9428
cos θ = 0.943 (round to 3 decimal places)
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Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) C 540 a 3.0, 4.0, LA = C = Solve triangle ABC. (If an answer does not exist,, enter DNE. Round your answers to one decimal place.) b 69 35, LA 72° C = C = a = Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a 28, b = 39, c 29 LA = Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) = 17, 13, c 22 a = LA= o Sketch the triangle 500 LA B 770 C = 270 c 270 50° 77 50° 770 270 A A A 770 50° 270 270 50° 77 C A Solve the triangle using the Law of Sines. (Round side lengths to the nearest integer.) a = b Sketch the triangle. 100° LA = 270, C=60 C 100° 60 100° 27 27° C 60 C C 270 60 100° 27 100° A 60 A Solve the triangle using the Law of Sines. (Round side lengths to one decimal place.) a = b =
The measures of the lengths of the sides and angles of the triangles found using the law of cosines and the law of sines are presented as follows;
Question 1
∠A = 47.35°
∠B = 78.65°
c = 3.3
Question 2
∠B = 78.24°
∠C = 29.76°
a = 67.03
Question 3
∠A = 45.77°
∠B = 86.417°
∠C = 47.813°
Question 4
∠A = 36.15°
∠B = 60.48°
∠C = 93.37°
Question 5
a = 258.98
b = 327.41
∠C = 53°
Question 6
a = 34.11
b = 73.987
∠C = 53°
What is the law of cosines?The law of cosines is a relationship between two sides (b and c) and the included angle, (∠A) and the third side (a) of the triangle.
Mathematically; a² = b² + c² - 2·b·c·cos(A)
Question 1
The dimensions of the triangle ΔABC are;
a = 3.0, b = 4.0, ∠C = 54°
The law of cosines indicates that we get;
c² = b² + a² - 2·b·a·cos(∠C)
Therefore;
c² = 3.0² + 4.0² - 2 × 3.0 × 4.0 × cos(54°) ≈ 10.893
c ≈ √(10.893) ≈ 3.3The law of sines indicates that we get;
sin(54°)/3.3 = sin(∠A)/3.0
∠A = arcsine(3 × sin(54°)/3.3) ≈ 47.35°∠B = 180° - 54° - 47.35° ≈ 78.65°Question 2
b = 69, c = 35, ∠A = 72°
a² = 69² + 35² - 2 × 69 × 35 × cos(72°) ≈ 4493.45
a ≈ √(4493.45) ≈ 67.03The law of sines indicates that we get;
sin(72°)/67.03 = sin(∠B)/69
∠B = arcsine(69 × sin(72°)/67.03) ≈ 78·24°
∠B ≈ 78.24°∠C = 180° - 72° - 78.24° ≈ 29.76°
∠C ≈ 29.76°Question 3
a = 28, b = 39, c = 29
a² = b² + c² - 2·b·c·cos(A)
cos(A) = (a² - (b² + c²)) ÷ (2·b·c)
Therefore; cos(A) = (28² - (39² + 29²)) ÷ (-2 × 39 × 29) ≈ 0.6976
∠A = arccos(0.6976) ≈ 45.77°sin(45.77)/28 = sin(B)/39
sin(B) = 39 × sin(45.77)/28 ≈ 0.998
∠B = arcsine(0.998) ≈ 86.417°∠C = 180° - 45.77° - 86.417° = 47.813°Question 4
a = 13, b = 17, c = 22
cos(A) = (13² - (17² + 22²)) ÷ (-2 × 17 × 22) ≈ 0.807
∠A ≈ arccos(0.807) ≈ 36.15°sin(36.15)°/13 = sin(∠B)/17
sin(∠B) = 17 × sin(36.15)°/13
∠B =50.48° ∠C = 180° - 36.15° - 50.48° ≈ 93.37°Question 5
The parameters of the triangle are; ∠A = 50°, ∠B = 77°, c = 270
Please find attached the sketch of the triangle in the correct option created with MS Word
∠C = 180° - 50° - 77° = 53°a/sin(50°) = 270/sin(53°)
a = sin(50°) × 270/sin(53°) ≈ 258.98
a = 258.98b = sin(77°) × 270/sin(53°) ≈ 329.41
b ≈ 329.41Question 6
The parameters of the triangle are;
∠A = 27°, ∠B = 100°, c = 60
Please find attached the drawing of the correct triangle
∠C = 180° - 27° - 100° = 53°
∠C = 53°
60/sin(53°) = a/sin(27°)
a = sin(27°) × 60/sin(53°) ≈ 34.11
b = sin(100°) × 60/sin(53°) ≈ 73.987
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What is the rate of return when 12 shares of Stock
A, purchased for $22/share, are sold for $465? The
commission on the sale is $9.
Rate of Return
Enter the appropriate value into the
formula to calculate the rate of return.
F
profit or loss
total cost
Total Cost = $273
Profit = $192
Rate of Return = [? ]
Answer:
The Rate of return would then be 192 / 273 ≈ 70.32%
A function is shown in the table below:
What is the average rate of change of the function from X equals -7 to X equals 2?
A. -90/101
B. 101/90
C. -101/90
D. 90/101
The average rate of change of the given function from x equals -7 to x equals 2 is calculated as: B. 101/90.
How to Find the Average Rate of a Function for a Given Interval?If we are given a function, f(x), to find the average rate of change of the function within the interval from a to b, the formula to use is:
Average rate of change = f(b) - f(a) / b - a.
Given the table that represents function, we have the following:
a = -7
b = 2
f(a) = f(-7) = -2.7
f(b) = f(2) = 7.4
Plug in the values into the formula:
Average rate of change = (7.4 - (-2.7)) / (2 - (-7))
= (7.4 + 2.7) / 2 + 7)
= 10.1 / 9
= 101/90
Therefore, the average rate of change is: B. 101/90.
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Find X, 50 points if you answer
Answer:
x=38
Step-by-step explanation:
linear par
180-134=46
180-84=96
sum of a triangle is 180
96+46+x=180
142+x=180
x=180-142
x=38
t²-8t+16 can be factorized to give an expression of the form (t + a)², where a is an integer.
Work out the value of a.
Answer:
a = 4
Step-by-step explanation:
Step 1: Find two numbers that multiply to give 16 and add to give -8.
t²-8t+16 = 0
t² -4t -4t + 16 = 0
The two numbers are 4 and -4.
Step 2: Rewrite the equation in the form (t + 4)(t - 4).
t² - 8t + 16 = (t + 4)(t - 4)
Step 3: Factor the equation to get (t + 4)².
(t + 4)² = (t + 4)(t + 4)
Therefore, a = 4.
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let $f(x)$ be a polynomial with integer coefficients. suppose there are four distinct integers $p,q,r,s$ such that $$f(p)
The smallest possible value of f ( t ) = 9 based on the values of p , q , r , s.
Given :
Let f ( x ) be a polynomial with integer coefficients. Suppose there are four distinct integers p , q , r , s such that f ( p ) = f ( q ) = f ( r ) =f ( s ) = 5. If t is an integer and f ( t ) > 5,
Let g(x) = f(x) − 5.
g(x) = (x−p)(x−q)(x−r)(x−s)h(x)
The condition f(t) > 5 translates to g(t) > 0.
Since p,q,r,s,t are distinct integers, the smallest possible positive value of (t−p)(t−q)(t−r)(t−s) is 4 :
the four numbers in the parentheses are all distinct integers ≠ 0, so the smallest value we can get from the product (−2)⋅(−1)⋅1⋅2. }
The smallest possible positive value of h(t) is 1, since we must have g(t)≠0.
Thus the smallest possible value of g(t) is 4, and therefore the smallest possible value of f(t) is 9, and it is achieved for t=2 if we have
f(x)=x(x−1)(x−3)(x−4)+5
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Full question ;
Let f(x) be a polynomial with integer coefficients. Suppose there are four distinct integers p,q,r,s such that f(p)=f(q)=f(r)=f(s)=5. If t is an integer and f(t)>5, what is the smallest possible value of f(t)?
A side of the triangle below has been extended to form an exterior angle of
132°. Find the value of x
Answer:
x = 15°
Step-by-step explanation:
⭐the exterior angle of a triangle is equal to the sum of the angles that is opposite of said exterior angle
Thus, to solve for x, we have to make an equation in regards of the exterior angle.
132° = x° + 117°
∴ 15 = x° . . . . subtract 117 from LHS and RHS
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Write a polynomial function in standard form of 3rd degree with zeros
polynomial function for x = 4, - 1 & 2. are
[tex]x^{3}[/tex] - [tex]x^{2}[/tex] - 10x - 8
What is polynomial function?In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.f(x) = anxn + anxn+1 +... + a2x2 + a1x + a0 is the formula for a polynomial. The greatest power of x in an expression is the polynomial's degree. Polynomials of degree 0, 1, 2, 3, and 4 are constant (non-zero) polynomials, linear polynomials, quadratics, cubics, and quartics, respectively.Zero polynomial function, linear polynomial function, quadratic polynomial function, and cubic polynomial function are the four most prevalent forms of polynomials used in precalculus and algebra.Given data :
Given the zeroes (roots) of a polynomial are: 4, - 1 & 2.
Here, we are given three roots of the polynomial. That means, the polynomial must be of third degree.
Also, (x - a) is a factor of the polynomial if and only if x = a is a root of the polynomial.
Here, 4, - 1 & 2. are roots. So, the factors are: ( x - 4 ) ( x + 1 ) ( x - 2 )
Multiplying them will result in the polynomial.
= ( x - 4 ) ( x + 1 ) ( x - 2 )
= ( [tex]x^{2}[/tex] - 3x - 4 ) ( x + 2 )
= Distribute parentheses : [tex]x^{2}[/tex] . x + [tex]x^{2}[/tex] . 2 - 3xx - 3x . 2 - 4x - 4 . 2
= Simplify [tex]x^{2}[/tex] .x - [tex]x^{2}[/tex] . 2 - 3xx - 3x . 2 - 4x - 4 . 2
= [tex]x^{3}[/tex] - [tex]x^{2}[/tex] - 10x - 8
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Which polynomial represents the difference below?
8x³ + 5x+6-(2x² + 3x)
OA. 10x¹0 + 8x² +6
OB. -2x7 + 8x³ + 8x+6
O C. 6x¹0+2x+6
OD. -2x7 + 8x³ + 2x+6
The difference of the given polynomials 8x³+5x+6 and 2x²+3x is 8x³-2x²+2x+6. So, the correct answer is D.
What is the subtraction of polynomials?To subtract polynomials from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.
Given that, 8x³+5x+6-(2x²+3x)
Group the like terms are perform the addition or subtraction
= 8x³+5x+6-2x²-3x
= 8x³+(5x-3x)-2x²+6 (Here, like terms are 5x and 3x)
= 8x³+2x-2x²+6
= 8x³-2x²+2x+6
So, the standard form of obtained polynomial is 8x³-2x²+2x+6.
The polynomials difference is 8x³-2x²+2x+6. Therefore, option D is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Which polynomial represents the difference below?
8x³ + 5x+6-(2x² + 3x)
A. 10x+ 8x² +6
B. -2x² + 8x³ + 8x+6
C. 6x¹⁰+2x+6
D. -2x²+ 8x³+2x+6
Mark is cutting 5.3125 inches from a 13.375-inch plank in order to fit it for a dog house he is building.
long will the new board be when he finishes?
Let the new board after final cutting is x. So the new board that is fit for the house will be x= 8.0625
What is subtraction method?A method for calculating the length of a psychological process that involves timing the reactions to two different tasks—one that involves the psychological process in issue and the other—and then subtracting the second reaction time from the first.
What are three types of subtraction?Taking away, part whole and comparison are three types of subtraction.
Let the old house =y= 13.375 inches
Cutting from old house=z= 5.3125 inches
New board=x= y-z
= 13.375-5.3125
= 8.0625
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Let the new board after final cutting is x. So the new board that is fit for the house will be x= 8.0625
What is subtraction method?
A method for calculating the length of a psychological process that involves timing the reactions to two different tasks—one that involves the psychological process in issue and the other—and then subtracting the second reaction time from the first.
What are three types of subtraction?
Taking away, part whole and comparison are three types of subtraction.
Let the old house =y= 13.375 inches
Cutting from old house=z= 5.3125 inches
New board=x= y-z
= 13.375-5.3125
= 8.0625
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What is it? I swear I have no idea
By using matrix, it can be calculated that:
[tex]\frac{1}{4}C = \begin{bmatrix}3 & 4 & -5 \\ 1 & -6 & 7\end{bmatrix}[/tex]
What is a matrix?The term "matrix" refers to any configuration of numbers in the form of rows and columns. a collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers.
In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. Solving linear equations is made easier by it. Matrices are incredibly priceless items that are used in a variety of contexts. In addition to mathematical applications, matrices are employed in a wide range of scientific disciplines. Nearly every element of our life uses engineering mathematics.
Here,
[tex]C = \begin{bmatrix} 12 & 16 & -20 \\ 4 & -24 & 28 \end{bmatrix}[/tex]
[tex]\frac{1}{4}C = \begin{bmatrix} 12\times \frac{1}{4} & 16 \times \frac{1}{4} & -20 \times \frac{1}{4} \\ 4 \times \frac{1}{4} & -24 \times \frac{1}{4}& 28 \times \frac{1}{4}\end{bmatrix}\\\\\frac{1}{4}C = \begin{bmatrix}3 & 4 & -5 \\ 1 & -6 & 7\end{bmatrix}[/tex]
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A group consisting of 28 aggressive zombies triples in size every hour. Which
equation matches the number of zombies after 7 hours?
Answer:196
Step-by-step explanation:
Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by
C(p) =
8100p
100 − p
(a) Is C(p) undefined at any p-value? If so, what value? (If an answer does not exist, enter DNE.)
p =
(b) What is the domain of C(p) as given by the equation? (Enter your answer using interval notation.)
(c) What is the domain of C(p) in the context of the application? (Enter your answer using interval notation.)
(d) What happens to the cost as the percent of pollution removed approaches 100%?
The cost increases (bounded by 8100) as p increases.
The cost decreases (bounded by 0) as p increases.
The cost decreases without bound as p increases.
The cost increases without bound as p increases.
The cost remains constant a
(a) C(p) is not defined since we can't divide by 0.
(b) The domain of C(p) as given by the equation is (-∞, 100) ∪ (100, ∞)
(c) The domain of C(p) in the context of the application is [0, 100)
(d) The percentage of particulate pollution removed from an industrial plant can't be negative or higher or equal than 100
Here we have given that Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by
C(p) = 8100p / (100 − p)
And we need to find the following.
(a) In general ma the we know that dividing by zero is not possible one.
Therefore, C(p) is undefined when we try to divide it by 0.
(b) The domain of C(p) is the function is not defined at p =100 the domain would be written as,
=> D = (-∞, 100) ∪ (100, ∞)
(c) The domain of C(p) in the context of the application is calculated as,
=> D = [0, 100)
Therefore, the percentage of particulate pollution removed from an industrial plant can't be negative or higher or equal than 100.
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One hundred elk, each 1 year old, are introduced into a game preserve. The number N(t) alive after t years is predicted to be N(t)=100(0.9)^t
(a) Estimate the number alive after 7 years. (Round your answer to the nearest whole number.)
(b) What percentage of the herd dies each year?
a) The number alive after 7 years is given as follows: 48.
b) The percentage of herd that dies each year is of 10%.
What is the exponential function?The exponential function in the context of this problem is defined as follows:
N(t)=100(0.9)^t.
The parameters of the function are defined as follows:
The amount of herd alive after 7 years is found with the numeric value at t = 7, replacing the lone instance of t in the function by 7, hence:
N(7) = 100 x (0.9)^7 = 48.
(rounding to the nearest whole number).
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Which of the following gives the correct matrix for this system of equations in reduced row echelon form? x1-3x2-x3 + 3x4 = 2 -xi-2x2-x3 +4x4 = 2 -2x1+4x2 +4x3 +4x4 =-3 12 5 14 100 17 5 18 001 14 1 -3 -1 32 0 -5 -2 74 00ー36-3 b) 1 0 0 -36 9 1 22 010 001_ -_ 1 22 -1 -3 1 3 2 d 0 1 0 0 0 22 -12 -7 1 0 0 0 e) 25 010 -5 0 0 6 -16 f O None of the above
The correct matrix for this system of equations in row reduced echelon form amongst the given options is none of the above.
The given system of equations to get the reduced row echelon form is:
x1 - 3x2 - x3 +3x4 = 2
-x1 - 2x2 - x3 +4x4 = 2
-2x1 + 4x2 + 4x3 +4x4 = -3
To get the reduced row echelon form we need to form the matrix:
[tex]\left[\begin{array}{ccccc}1&-3&-1&3&2\\-1&-2&-1&4&2\\-2&4&4&4&-3\end{array}\right][/tex]
Row reduced echelon form of a matrix is one in which the pivot points equal 1, go from top left to bottom right, there are 0's above and below each pivot point.
R2-R1:
[tex]\left[\begin{array}{ccccc}1&-3&-1&3&2\\-2&1&0&1&0\\-2&4&4&4&-3\end{array}\right][/tex]
R3-R2 then R2+2R1 then R1+R3 then R2+2R3 then R3-3R2
[tex]\left[\begin{array}{ccccc}1&0&3&6&-1\\0&1&6&13&-2\\0&0&-14&-36&3\\\end{array}\right]\\[/tex]
(-1/14)R3 then R2-6R3 then R1-3R3
[tex]\left[\begin{array}{ccccc}1&0&0&-12/7&-5/14\\0&1&0&-17/7&-5/7\\0&0&1&18/7&-3/14\\\end{array}\right]\\[/tex]
which is the reduced row echelon form of the given system of equations.
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Select all of the lines of reflection that will carry the rectangle back onto itself.
The lines that carry the rectangle onto itself are x = 0 and y = 1
How to determine the lines that carry the rectangle onto itself?The graph that completes the question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The rectangular graph
The coordinates of one end of the graph are
(-3, 3) and (-3, -1)
Next, we calculate the midpoint of these ends
So, we have
Midpoint = 1/2(x₁ + x₂, y₁ + y₂)
Substitute the known values in the above equation, so, we have the following representation
Midpoint = 1/2(-3 + 3, -1 + 3)
Evaluate the like terms
Midpoint = 1/2(0, 2)
So, we have
Midpoint = (0, 1)
So, we have
x = 0 and y = 1
Hence, the reflection lines are x = 0 and y = 1
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Can anyone solve I need help urgent thank you
Answer:
Step-by-step explanation:
3.14 x 3=9.42
ANSWER THIS ASAP! FIRST PERSON TO ANSWER GETS EXTRA 50 POINTS. I KNOW ITS ALOT. BUT I REALLY NEED THIS ANSWER. I WILL ALSO MARK BRAINIEST. ANSWER FAST! DEADLINE IS 11:20.
A student is painting a brick for his teacher to use as a doorstop in the classroom. He is only painting the front of the brick. The vertices of the face are (−4, 2), (−4, −11), (4, 2), and (4, −11). What is the area, in square inches, of the painted face of the brick?
The area of the painted face with vertices at (-4, 2), (-4, -11), (4, 2), and (4, -11) which represents a rectangle is 104 square inches
What is a rectangle?A rectangle is a quadrilateral with the four interior angles that are each right angles, and opposite sides that are congruent and parallel.
The specified vertices of the face of the brick are;
(-4, 2), (-4, -11), (4, 2), and (4, -11)
The graph of the above point used to draw the quadrilateral representing the shape of the face in the question, created with MS Word, is attached
From the attached graph and drawing, we get;
Shape of the face of the doorstop = A rectangle
Length of the sides of the quadrilateral (rectangle)
Length = 2 - (-11) = 13
Width = 4 - (-4) = 8
Area of a rectangle Length × Width
Area of the painted face of the brick, A = 13 × 8 = 104
The area of the rectangular painted face of the brick = 104 square inches
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A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 414 gram setting. Based on a 8 bag sample where the mean is 407 grams and the standard deviation is 18, is there sufficient evidence at the 0.025 level that the bags are underfilled? Assume the population distribution is approximately normal.
Step 1 of 5:
State the null and alternative hypotheses.
Step 2 of 5:
Find the value of the test statistic. Round your answer to three decimal places.
Step 3 of 5:
Specify if the test is one-tailed or two-tailed.
Step 4 of 5:
Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Step 5 of 5:
Make the decision to reject or fail to reject the null hypothesis.
Question #2:
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.8 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 26 samples is 4.6 ppm with a standard deviation of 1.2. Does the data support the claim at the 0.025 level? Assume the population distribution is approximately normal.
Step 1 of 5:
State the null and alternative hypotheses.
Step 2 of 5:
Find the value of the test statistic. Round your answer to three decimal places.
Step 3 of 5:
Specify if the test is one-tailed or two-tailed.
Step 4 of 5:
Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Step 5 of 5:
Make the decision to reject or fail to reject the null hypothesis.
A)
A manufacturer of banana chips would like to know whether its bag-filling machine works correctly at the 414-gram setting.
So, Null hypothesis: [tex]H_{0}[/tex] : μ < 414
It is believed that the machine is underfilling the bags.
So, Alternate hypothesis: [tex]H_{1}[/tex] : μ < 414
Given,
n= 8
Population standard deviation (б) = 18
x= 407
We will use the t-test since n > 8 and we are given the population standard deviation.
t=x-μ / (б/[tex]\sqrt{n-1}[/tex])
t= [tex]\frac{407-414}{\frac{18}{\sqrt{7} } }[/tex]
t= -1.028
Use the t table to find p value
p-value = 12.706
Level of significance α = 0.025
p-value>α
It is a two-tailed test.
So, we fail to reject the null hypothesis.
So, its bag-filling machine works correctly at the 414-gram setting.
B)
Let μ be the population mean amount of ozone in the upper atmosphere.
As per the given, we have
[tex]H_{0}[/tex] : μ = 4.8
[tex]H_{1}[/tex] : μ ≠ 4.8
Sample size: n= 26
Sample mean = 4.6
Standard deviation = 1.2
Since population standard deviation is now given, so we use a t-test.
t= [tex]\frac{4.6-4.8}{\frac{1.2}{\sqrt{25} } }[/tex]
t= -0.2/0.24
t= -0.833
It is a two-tailed test.
We are accepting the null hypothesis.
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Find the volume of a cone with a radius of 3 feet and a height of 7 feet. Enter
the answer in terms of pie
The volume of a rectangular prism is 6,618.375 cm3. If the height is 13.25 cm and the length is 27 cm, what is the value of the width?
A: 18.125 cm
B: 18.5 cm
C: 18.75 cm
D: 18.86 cm
The value of width will be;
⇒ 18.5 cm
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The volume of a rectangular prism = 6,618.375 cm³
The height is 13.25 cm and the length is 27 cm.
Now,
We know that,
The volume of rectangular prism = Length x Width x Height
Substitute all the values, we get;
⇒ 6,618.375 = 27 × x × 13.25
⇒ 6,618.375 / 357.75 = x
⇒ x = 18.5 cm
Thus, The value of width = 18.5 cm
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Sydney went to the store and bought candy that was priced according to the weight in pounds. She purchased 2 1/4 pounds of black licorice, 1 7/8 pounds of red licorice, and 1 1/2 pounds of butterscotch candy. if the candy costs $ 4.00 per pound, how much did Sydney spend on candy?
Answer:
$22.50
Step-by-step explanation:
10 -8 -6 -4
| 10+
8
67
-2
4.2
-2
-4-
-6
-8
-10
2
4 6 8 10
Write an equation for the graph, where y depends on x.
The equation of given graph is y = 2x + 6.
What is equation of line?
The formula for a straight line is y = mx + c where c is the height at which the line intersects the y-axis, also known as the y-intercept, and m is the gradient.
Given:
The graph of the line is given.
From graph we have to find the equation of line.
Let the graph passes through the points (0, 6) and (2, 10).
From these two points to find the slope.
Slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here, [tex](x_1, y_1) = (0, 6), (x_2, y_2) = (2, 10)[/tex]
⇒ Slope = m = [tex]\frac{10-6}{2-0}= \frac{4}{2} = 2[/tex]
So, the slope is 2.
Now to find the equation of line.
Consider, the point - slope form of the line,
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex]m = 2, (x_1, y_1) = (0, 6)[/tex]
⇒
[tex]y-6=2(x-0)\\y-6=2x\\y=2x+6[/tex]
Hence, the equation of given graph is y = 2x + 6.
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The vertices of quadrilateral PQRS are listed.
P(3,7). Q(6,-2), R(0,-4), S(-3,5)
Which of the following is the strongest classification that identifies quadrilateral PQRS?
O A.
Quadrilateral PQRS IS a parallelogram.
O B.
Quadrilateral PQRS is a rectangle.
• c.
Quadrilateral PQRS is a square.
• D.
Quadrilateral PQRS is a trapezoid.
Answer: O B. Quadrilateral PQRS is a rectangle.
Step-by-step explanation: The image should help you picture my answer. Good luck with your end of semester test!
Have a great day! :)
NO LINKS!! Please help me with this problem. Part 8ff
Answer:
[tex]\dfrac{1}{36n^2+6n}[/tex]
Step-by-step explanation:
Given factorial expression:
[tex]\dfrac{(6n-1)!}{(6n+1)!}[/tex]
[tex]\boxed{\begin{minipage}{6cm}\underline{Factorial Rule}\\\\$n!=\:n\cdot \left(n-1\right) \cdot \left(n-2\right) \cdot ... \cdot 3 \cdot 2\cdot 1$\\ \end{minipage}}[/tex]
Apply the factorial rule to the numerator and denominator of the given rational factorial expression:
[tex](6n-1)!=\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1[/tex]
[tex]\left(6n+1\right)!=\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{(6n-1)!}{(6n+1)!}&=\dfrac{\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1}{\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1}\\\\&=\dfrac{1}{(6n+1) \cdot 6n}\\\\&=\dfrac{1}{6n(6n+1)}\\\\&=\dfrac{1}{36n^2+6n}\end{aligned}[/tex]
Answer:
[tex]\cfrac{1}{6n(6n+1)}[/tex]--------------------------------
We know that:
n! = 1·2·3·4·...·nTherefore:
(6n + 1)! = (6n - 1)!·6n·(6n + 1)Therefore:
[tex]\cfrac{(6n-1)!}{(6n+1)!} =\cfrac{(6n-1)!}{(6n-1)!(6n)(6n+1)} =\cfrac{1}{6n(6n+1)}[/tex]Karla is saving money to visit her relatives in Florida. It costs $1,000 for the plane ticket and $250 per night for the hotel. Using the function that represents the cost c based on the number of nights n Karla spends in Florida, how many nights can Karla stay in Florida if she saves $3,000?
Answer: 8 Nights
Step-by-step explanation:
Cost of a plane ticket to Florida(c) = $1000
cost at the hotel per night (n)
Amount left with Karla after spending on the flight ticket =
$3000-$1000= $2000
To find out how many nights she can stay we should divide the remaining amount she has with (n) = $2000/$250 = 8
Hence Karla can stay for 8 nights
