She will need 14feet rectangle wood for the frame. She will need 12 square feet rectangle tiles for the tabletop.
What is rectangle?
In the Euclidean plane, a rectangle is a trapezoid with four right angles. As an equiangular quadrilateral, which means that all of its angles are equal, it can also be referred to as a parallelogram with a right angle. A parallelogram with four evenly long sides is a square.
The distance (\(x_{1}\)\(y_{1}\)) and (\(x_{2}\),\(y_{2}\)) is
d= √(\(x_{1}\)-\(x_{2}\))^2+(\(y_{1}\)-\(y_{2}\))^2
The tabletop has consecutive vertices at (1, 5), (5, 5), (5, 2), and (1, 2)
Its length in distance of (1,5) and (5,5)
So, l= √(1-5)^2+(5-5)^2= √16=4 feet
Similarly the width in distance of (5,5) and (5,2)
So, w= √(5-5)^2+(5-2)^2=√9= 3 feet
The perimeter of the wood= 2(4+3)= 14 feet
The area of the rectangle tiles is = 4*3= 12 square feet.
Hence She will need 14feet rectangle wood for the frame. She will need12 square feet rectangle tiles for the tabletop.
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Kate opens a savings account with a deposit of $1250. After 2 years, she has
receives $112.50 in interest. What is the annual interest rate?
Answer:
4.5%
Step-by-step explanation:
Simple interest:
I = Prt
112.5 = 1250(r)(2)
1250r = 56.25
r = 0.045 = 4.5%
Answer: 4.5%
6. For the function f(x) = 3x4 – 24x?, = (a) [5] find all critical numbers. (b) [7] determine the intervals of increase or decrease. = (c) [6] find the absolute maximum and absolute minimum values on the interval [-3, 3]
A) The critical numbers of the function are x = 0, x = -2, and x = 2.
B) The function f(x) is decreasing on the intervals (-∞, -2) and (0, 2), and increasing on the intervals (-2, 0) and (2, ∞).
C) The absolute maximum value on the interval [-3, 3] is 96, which occurs at x = 2. The absolute minimum value is -48, which occurs at x = -2.
(a) To find the critical numbers of the function f(x) = 3x^4 - 24x^2, we need to determine where the derivative of the function is equal to zero or undefined. Let's find the derivative first: f'(x) = 12x^3 - 48x.
Setting f'(x) equal to zero and solving for x:
12x^3 - 48x = 0.
Factoring out the common factor of 12x:
12x(x^2 - 4) = 0.
This equation is satisfied when either 12x = 0 or x^2 - 4 = 0.
Solving 12x = 0, we find x = 0.
Solving x^2 - 4 = 0, we find x = ±2.
Therefore, the critical numbers of the function are x = 0, x = -2, and x = 2.
(b) To determine the intervals of increase or decrease, we need to examine the sign of the derivative in different intervals. We can create a sign chart:
x < -2 -2 < x < 0 0 < x < 2 x > 2
f'(x) | - + - + |
From the sign chart, we can see that f'(x) is negative on the interval (-∞, -2) and (0, 2), and positive on the interval (-2, 0) and (2, ∞).
Therefore, the function f(x) is decreasing on the intervals (-∞, -2) and (0, 2), and increasing on the intervals (-2, 0) and (2, ∞).
(c) To find the absolute maximum and absolute minimum values on the interval [-3, 3], we need to evaluate the function at the critical numbers and endpoints of the interval.
Evaluate f(x) at x = -3, -2, 0, 2, and 3:
f(-3) = 3(-3)^4 - 24(-3)^2 = 243 - 216 = 27,
f(-2) = 3(-2)^4 - 24(-2)^2 = 48 - 96 = -48,
f(0) = 3(0)^4 - 24(0)^2 = 0,
f(2) = 3(2)^4 - 24(2)^2 = 192 - 96 = 96,
f(3) = 3(3)^4 - 24(3)^2 = 243 - 216 = 27.
The absolute maximum value on the interval [-3, 3] is 96, which occurs at x = 2. The absolute minimum value is -48, which occurs at x = -2.
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distribute 6 balls into 3 boxes, one box can have at most one ball. The probability of putting balls in the boxes in equal number is?
To distribute 6 balls into 3 boxes such that each box can have at most one ball, we can consider the following possibilities:
Case 1: Each box contains one ball.
In this case, we have only one possible arrangement: putting one ball in each box. The probability of this case is 1.
Case 2: Two boxes contain one ball each, and one box remains empty.
To calculate the probability of this case, we need to determine the number of ways we can select two boxes to contain one ball each. There are three ways to choose two boxes out of three. Once the boxes are selected, we can distribute the balls in 2! (2 factorial) ways (since the order of the balls within the selected boxes matters). The remaining box remains empty. Therefore, the probability of this case is (3 * 2!) / 3^6.
Case 3: One box contains two balls, and two boxes remain empty.
Similar to Case 2, we need to determine the number of ways to select one box to contain two balls. There are three ways to choose one box out of three. Once the box is selected, we can distribute the balls in 6!/2! (6 factorial divided by 2 factorial) ways (since the order of the balls within the selected box matters). The remaining two boxes remain empty. Therefore, the probability of this case is (3 * 6!/2!) / 3^6.
Now, we can calculate the total probability by adding the probabilities of each case:
Total Probability = Probability of Case 1 + Probability of Case 2 + Probability of Case 3
= 1 + (3 * 2!) / 3^6 + (3 * 6!/2!) / 3^6
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can someone please help PLEASE
Aaron travels 125 miles in 2.5 hours. At this rate, how far will he be able to travel in 6 hours?
Answer:
I believe it is 687.5 miles
Step-by-step explanation:
Answer:
750
Step-by-step explanation:
Three friends map their houses on a coordinate grid. Alex's house is located at point (7, 18). Jimmy's house is at point (-9, 7). Jimmy's house is located halfway between Alex's house and Kara's house. Which ordered pair represents Kara's house?
A (1, 12.5)
B. (24,-4)
C. (-25,-4)
D. (2,25)
Tamir buys tickets to two concerts this season. One has a face value of $32.50, and one has a face value of $26.50. He uses a coupon and gets both tickets at One-fourth off. If he pays with a $50 bill, how much change should Tamir receive?
$5.75
$7.63
$30.13
$44.25
Answer:
Its A)
Step-by-step explanation:
I took the test and got it right
Answer:
A
Step-by-step explanation:
ik i am in the future
Hello!
The question i need help with is attached... the deadline is Wednesday however I would really appreciate if you could please send the answer by today to make it easier for me
Thank you !
The box plot shows the algebra scores of students in class A and class B.
The median score of class A is _____.
The interquartile range of class B is ____.
The difference of the medians of class A and class B is
the interquartile range of either data set.
Answer:
\(Mid(A) = 73\)
\(IQR(B) = 8\)
The difference of the medians of class A and class B is between the interquartile range of either data set.
Step-by-step explanation:
Given
The attached box plots
To answer this, see attached image for how to read a box plot
With reference to the attached image of how to read the box plot;
Solving (a): The median of class A
\(Mid(A) = 73\)
Solving (b): IQR of class B
IQR is calculated as:
\(IQR =Q_3 - Q_1\)
From the box plot of class B, we have:
\(Q_3 = 87\)
\(Q_1 = 79\)
So, we have:
\(IQR(B) = 87 - 79\)
\(IQR(B) = 8\)
Solving (c):
\(Mid(A) = 73\)
\(Mid(B) = 82\)
\(IQR(B) = 8\)
IQR of class A is calculated as:
\(IQR =Q_3 - Q_1\)
From the box plot of class A, we have:
\(Q_3 = 76\)
\(Q_1 = 68\)
So, we have:
\(IQR(A) = 78 - 68\)
\(IQR(A) = 10\)
The difference (d) between the medians is:
\(d =Mid(B) - Mid(A)\)
\(d = 82 - 73\)
\(d = 9\)
From \(smallest\) to \(largest\), we have: 8, 9, 10
i.e. IQR(B), d, IQR(A)
Answer:
73
8
about half.
Step-by-step explanation:
Solve for x: -3x-5=16
The value of x is -7
What are algebraic expressions?These are expressions that are made up of terms, variables, constants, factors and coefficients.
Algebraic expressions are expressions made up of arithmetic operations, such as;
AdditionMultiplicationDivisionBracketParenthesesFrom the information given, we have that;
-3x-5=16
collect the like terms
-3x = 16 + 5
-3x = 21
Divide by the coefficient of x
x = -7
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Which equation could represent a linear combination of the system?
The equation that could represent a linear combination of the system 2/3x + 5/2y = 15 and 4x + 15y = 12 is 0 = 26
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the linear combination to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2/3x + 5/2y = 15
4x + 15y = 12
Multiply the first equation by 6, to eliminate the fractions.
6 * (2/3x + 5/2y = 15)
This gives
4x + 15y = 90
Subtract the equation 4x + 15y = 90 from 4x + 15y = 12
4x - 4x + 15y - 15y = 12 - 90
Evaluate the difference
0 + 0 = -78
Evaluate the sum
0 = -78
The above equation is the same equation as option (b) 0 = 26
This is so because they both represent that the system of equations have no solution
Hence, the equation that could represent a linear combination of the system is 0 = 26
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Complete question
The system of equations below has no solution.
2/3x + 5/2y = 15
4x + 15y = 12
Which equation could represent a linear combination of the system?
-7 x - 2y = -13
x - 2y = 11
Rectangle A B C D is transformed by a combination of two transformations so that all points on AB are invariant and there are no other invariant points.
The first transformation is
a reflection in the line with equation y = k, where ‘k’
is an integer and k ≠1
Describe fully the second transformation.
(2 marks)
It is a translation by vector
(?)
The second transformation that is applied to rectangle A B C D is a translation.
Explain about fully the second transformation:A translation is a transformation that moves an object a certain distance in a certain direction without changing its size or orientation. In this case, the translation is represented by a vector, which is a mathematical object that has both magnitude and direction. The vector for this translation would have the form (x, y), where x and y are the horizontal and vertical distances that the object is moved.In the case of rectangle A B C D, since all points on AB are invariant, it means that the translation vector has the same magnitude in the horizontal direction as it does in the vertical direction. This is why the vector for the translation is represented by (?), as the values of x and y are not given. The only thing that is specified in the problem is that the translation vector moves the rectangle in a direction that is different from the reflection line y = k, as there are no other invariant points.To learn more about second transformation refer to;
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3) Suppose u(x) = 5x³x²-3x+9, v(x) = 3x²-x-7, w(x) = 3x³ + x² -4,and f(x) = u(x) +v(x) - w (x). Select from the available choices to make the following sentence true. f is a polynomial function with a degree of (A) -4 B 1 2 3 E 6 a constant term of (A -4 (B 1 2 3 E 6 and a leading coefficient of -4 B 1 C 2 D 3 E) 6 https://web algebranation.com/#/assessment ist
The degree of a polynomial function is the highest degree of its terms. To find the degree of f(x), we need to first find the degree of each of its component functions.
u(x) = 5x³x²-3x+9 has a degree of 6 (sum of the exponents of the highest degree term)
v(x) = 3x²-x-7 has a degree of 2
w(x) = 3x³ + x² -4 has a degree of 3
Therefore, f(x) = u(x) + v(x) - w(x) has a degree of 6 (highest degree of the terms) and a leading coefficient of 5 (leading coefficient of u(x)).
To find the constant term of f(x), we need to evaluate f(x) when x = 0:
f(0) = u(0) + v(0) - w(0) = 9 + (-7) - 4 = -2
Therefore, the correct choices are:
A) Degree of 6
B) Constant term of -2
E) Leading coefficient of 5
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Choose the correct answer. Find the unknown, k, by solving the following proportion: (k)/(1.2)=(4)/(3) 1.7 1.6 1.4 1.3
The correct answer is 1.6. By solving the proportion, we determined that the value of k that satisfies the given equation is approximately 1.6.
To find the unknown value, k, in the proportion (k)/(1.2) = (4)/(3), we can cross-multiply and solve for k.
cross-multiplying the proportion, we have:
3k = 4 * 1.2
Multiplying the numbers:
3k = 4.8
To isolate k, we divide both sides of the equation by 3:
k = 4.8 / 3
Evaluating the division, we find:
k ≈ 1.6
Therefore, the correct answer is 1.6. By solving the proportion, we determined that the value of k that satisfies the given equation is approximately 1.6.
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What’s is the answer for
5x + 15=
What is x equivalent to?
A single card is drawn at random from a standard 52 card deck.Work out the following probabilities in their simplest form
Answer:
A
Step-by-step explanation:
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
.Specifications for a piece of material used in the manufacture of a bed mattress require that the piece be between 63.76 and 64.24 inches. The process that produces the piece yields a mean of 64 and a standard deviation of 0.1 inches. The distribution of output is normal. What percentage of the pieces will meet the length specs?
The correctanswer is-the percentage of the pieces that will meet the length specs is 98.78%.
The given data may be a random variable that takes after the normal distribution with mean μ=64 and standard deviation σ=0.1
The required value is to discover the rate of the pieces that will meet the length specs which is between 63.76 and 64.24 inches.
To find the required percentage, standardize the given limits as follows: Lower Limit: (63.76 - μ) / σ= (63.76 - 64) / 0.1 = -2.4
Upper Limit: (64.24 - μ) / σ= (64.24 - 64) / 0.1 = 2.4
Using the Standard Normal Distribution Table, the probability that the value will fall between -2.4 and 2.4 is found to be 0.9878.
The required percentage is then found by multiplying the probability by 100, which is: Percentage = 0.9878 x 100% = 98.78%
Therefore, the percentage of the pieces that will meet the length specs is 98.78%.
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Put the following numbers in order:
3.28, -4/5, -7.1, 0, 11/12, π, .889753, -4 1/3 help please!
In order of smallest to largest.
1) -7.1
2) -4 1/3
3) -4/5
4) .889753
5) 11/12
6) 0
7) π
8) 3.28
Sides or angles with the same measure are congruent. True or false
Answer:
True
Step-by-step explanation:
Use implicit differentiation to find an equation of the tangent line x+y-1=ln(x^6+y^6), (1,0)
The equation of the tangent line to the curve x+y-1=ln(x^6+y^6) at the point (1,0) is x - 1 = 0
The equation of the tangent line to the curve given by the equation x+y-1=ln(x^6+y^6) at the point (1,0) can be found using implicit differentiation.
Step 1: Differentiate both sides of the equation with respect to x:
d/dx (x+y-1) = d/dx (ln(x^6+y^6))
Step 2: Apply the chain rule to the right side of the equation:
1 + dy/dx = (1/(x^6+y^6)) * (6x^5 + 6y^5 * dy/dx)
Step 3: Rearrange the equation to isolate dy/dx:
dy/dx = (6x^5 + 6y^5)/(x^6 + y^6 - 1)
Step 4: Substitute the coordinates of the point (1,0) into the equation to find the slope of the tangent line at that point:
dy/dx = (6(1)^5 + 6(0)^5)/(1^6 + 0^6 - 1) = 6/0
Note: The slope of the tangent line is undefined, indicating that the tangent line is vertical.
Step 5: Using the point-slope form of a line, we can write the equation of the tangent line:
y - 0 = (6/0)(x - 1)
The equation of the tangent line to the curve x+y-1=ln(x^6+y^6) at the point (1,0) is x - 1 = 0. However, it's important to note that the slope of the tangent line is undefined, indicating that the line is vertical.
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is the area of the rectangle 40 or 96 square feet? explain
Answer: 96ft
Step-by-step explanation:
Width times hight equals area. So 12x8=96ft
Answer:
the answer 96 feet
Step-by-step explanation:
how do we determine the significance of the slope in regression?
The significance of the slope in regression can be determined by conducting a hypothesis test
The slope of the regression line in a regression analysis shows how dependent variable changes as the independent variable increases by a unit. A hypothesis test on a slope coefficient, commonly referred to as the beta coefficient or the regression coefficient, can be used to ascertain the significance of the slope. The slope coefficient is compared to a null hypothesis value of zero in the hypothesis test.
The null hypothesis is rejected and it is determined that there is a significant association between the independent and dependent variables if the p-value for the slope coefficient is less than the significance threshold. Therefore, slope is not equal to zero and there is an association amongst changes in the independent variable and those in the dependent variable.
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Which graph shows a system of equations with the solution (5, -3)?
Right-hand bottom graph shows a system of equations with the solution (5, -3).
What is Graph?A diagram that depicts the connection between two values, measures, or other objects as a line or curve.
According to the inquiry,
Due to the fact that the two lines meet at the position where they do, the graph on the bottom right depicts a system of equations with the answers (5, -3) (5, -3).
Therefore, the proper answers to the problem are represented by the bottom right.
Right-hand bottom graph has the proper equations and their answers (5,-3).
Right-hand bottom graph shows a system of equations with the solution (5, -3).
The complete question is
Which graph shows a system of equations with the solution (5, -3)?
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Did I do this right?
Adrian bought a car worth $12000 on 36 easy installments of $375. Answer the following questions. (1) How much total amount did Adrian pay in 36 months? Answer: Total payment A = $ (2) Identify the letters used in the simple interest formula I = Prt. I= $ P= $ and t years. (3) Find the rate of interest in percentage. Answer: r %. ASK YOUR TEACHER
3) since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.
(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:
Total payment A = Monthly installment * Number of installments
= $375 * 36
= $13,500
Therefore, Adrian paid a total of $13,500 over the course of 36 months.
(2) In the simple interest formula I = Prt, the letters used represent the following variables:
I: Interest (the amount of interest paid)
P: Principal (the initial amount, or in this case, the car worth)
r: Rate of interest (expressed as a decimal)
t: Time (in years)
(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:
r = (I / Pt) * 100
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en una tienda de ropa, la semana pasada, 3 pantalones y 2 abrigos costaban 245€. Esta semana estos artículos tienen un descuento del 20% y 5% respectivamente. Si ahora un pantalón y un abrigo cuestan 100,75€, ¿qué costaba cada artículo antes de la rebaja?
Solving a system of equations we can see that each pair of pants costs €82.94 and each coat costs €26.37
How to find the original cost?
Let's define the variables:
x = cost of a pant
y = cost of a coat.
First, we know that:
3x + 2y = 245
And then there are discounts of 20% and 5%, and the cost of one of each is 100.75, then:
0.8x + 0.95y = 100.75
Then we have a system of equations:
3x + 2y = 245
0.8x + 0.95y = 100.75
We can isolate x on the second equation to get:
x = (100.75 - 0.96y)/0.8
x = 125.9 - 1.2y
Replace that in the other equation:
3*(125.9 - 1.2y) + 2y = 245
Solving for y:
3*125.9 - 3*1.2y + 2y = 245
y*(2 - 3*1.2) = 245 - 3*125.9
y = (245 - 3*125.9)/(2 - 3*1.2)
y = 82.94
Then the value of x is:
x = 125.9 - 1.2*82.94
x = 26.37
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Who knows how to do this I TRULY NEED HELP
Answer:
is the answer 7ft?
Step-by-step explanation:
i am not completely sure
Set up a ratio of the height over the distance to the mirror/
X/5 = 28/7
Cross multiply:
7x = 140
7? = 140
Divide both sides by 7
? = 140/7
? = 20
The answer is 20 feet
Use the data in the table to complete the sentence. x y –2 7 –1 6 0 5 1 4 The function has an average rate of change of __________.
Answer: To find the average rate of change, evaluate the function at the given points.
Evaluate the difference of the function at the given points.
Divide the difference of the function at the given points with the difference of the given points.
Step-by-step explanation:
The Average of rate is -1.
Everytime it goes up by one the y goes down by 1 so it would be -1.
The average rate of change of the function in the table given is: -1.
What is Average Rate of Chnge of a Function?Average rate of change of a function = change in y / change in x = rise/run.
Given the table representing a function, and using two set of ordered pairs, (-2, 7) and (0, 5):
Average rate of change of the function = (7 - 5)/(-2 - 0)
Average rate of change of the function = 2/-2
Average rate of change of the function = -1.
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(this is all the points I'm able to give) Find the surface area of the composite figure.
SA = [ ? ] cm^2
Answer:
{x}^{2}+5x+6
x
2
+5x+6
Step-by-step explanation: