The area of the poster is 28.75 feet square.
How to determine the areaNote that the area of a rectangle is given as;
Area = length × width
Length = 11. 5 feet
Width = 2. 5 feet
Area = 11. 5 × 2. 5
Area = 28. 75 feet square
Thus, the area of the poster is 28.75 feet square.
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A polynomial function g(x) has a positive leading coefficient. Certain values of g(x) are given in the following table. x –4 –1 0 1 5 8 12 g(x) 0 3 1 2 0 –3 0 If every x-intercept of g(x) is shown in the table and each has a multiplicity of one, what is the end behavior of g(x)?
Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
Considering the table, the roots are given as follows:
[tex]x_1 = -4, x_2 = 5, x_3 = 12[/tex]
Hence the function is:
f(x) = a(x + 4)(x - 5)(x - 12).
f(x) = a(x² - x - 20)(x - 12)
f(x) = a(x³ - 13x² - 32x + 240).
When x = 0, y = 1, hence the leading coefficient is found as follows:
240a = 1
a = 0.004167
Then:
f(x) = 0.004167(x³ - 13x² - 32x + 240).
The end behavior is given by the limits of f(x) as x goes to infinity, hence:
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 0.004167 x^3 = -\infty[/tex].[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 0.004167 x^3 = \infty[/tex].Hence the end behavior is that the function decreases to the left and increases to the right.
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Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589.
The value of x in the similar triangles is 18
How to solve similar triangles?Similar triangles have the same shapes but may have different sizes.
Corresponding side of similar triangles are a ratio of each other.
Therefore,
UV / BC = AU / AB
Hence,
UV = 444 units
BC = 703
AU = 20x + 108
AB = 20x + 108 + 273 = 20x + 381
Therefore,
444 / 703 = 20x + 108 / 20x + 381
cross multiply
444( 20x + 381) = 703(20x + 108)
8880x + 169164 = 14060x + 75924
8880x - 14060x = 75924 - 169164
-5180x = -93240
x = -93240 / -5180
x = 18
Therefore, the value of x in the similar triangles is 18
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Describe an algorithm for finding the smallest integer in a finite sequence of natural numbers.
Answer:
min = a_1
for i:= 2 to n:
if [tex]a_i[/tex] < min then min = [tex]a_i[/tex]
return min
Step-by-step explanation:
We call the algorithm "minimum" and a list of natural numbers [tex]a_1, a_2, \cdot\cdot\cdot, a_n.[/tex]
So lets first set the minimum to [tex]a_1[/tex]
min = a_1
now we want to check all the other numbers.
We can use a simple for loop, to find the minimum
min = a_1
for i:= 2 to n:
if [tex]a_i[/tex] < min then min = [tex]a_i[/tex]
return min
Answer:
The sequence of natural numbers is a_1, a_2, a_3, ..., a_n.
Use min as the variable that will contain the minimum value.
Set min = a_1
In a loop, compare min to each number from a_2 to an.
If min > a_i, then let min = a_i
min = a_1
for i = 2 to n
if min > a_i, then min = a_i
A study showed that low intenstisy vibration therapy reduce pain levels in patients with fibromyalgia. During each session in the study, vibration pads were placed on the pain site indicated by the patient. Pain reduction was measured through self-reporting after each session. Another study is being design to examine whether low intensity vibration therapy also reduces pain in patients suffering from ruptured disks at the lumbar region of the back. Three hundred male patients are subjects the new study. Part A: What is an appropriate design for the new study? Include treatments used, method of. treatment assignment, and variables that should be measure
Part b: if the study consists of 150 male and 150 female patients instead of 300 male patients would you change the study design if so, how would you modify your design? if not, why not?
Part c: could your design be double blind
Answer:
I didn't got the question well
Oliver and Layla each built a rectangular prism with centimeter cubes. Both prisms have a volume of 24 cubic centimeters but they do not look the same. Give possible dimensions for each prism.
Possible Dimensions of one prism are; 2cm, 3 cm and 4cm
Possible Dimensions of second prism are; 1 cm, 4 cm, 6 cm
How to find the dimensions of a rectangular Prism?We are told that volume of both rectangular prisms is; V = 24 cm³
Now, formula for Volume of a rectangular prism is;
V = lwh
where;
l is length
w is width
h is height
Thus, to solve this, we have to look for multiples of 24 which are;
1, 2, 3, 4, 6, 8, 12, 24.
Now, we must pick 3 numbers from the above in which their products will be equal to 24.
Thus;
Possible Dimensions of one prism are; 2cm, 3 cm and 4cm
Possible Dimensions of second prism are; 1 cm, 4 cm, 6 cm
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What is the completely factored form of f(x) = x3 – 2x2 – 5x + 6?
f(x) = (x + 2)(x – 3)(x + 6)
f(x) = (x + 2)(x – 3)(x – 6)
f(x) = (x – 2)(x + 3)(x – 1)
f(x) = (x + 2)(x – 3)(x – 1)
Answer:
The last option, (x+2)(x-3)(x-1)
Step-by-step explanation:
The completely factored form of f (x) = x³ - 2x² - 5x + 6 is,
⇒ f (x) = (x - 1) (x - 2) (x - 3)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
Function is,
⇒ f (x) = x³ - 2x² - 5x + 6
Now, We can factor the function as;
Since, 1 is a root of function as it satisfy the function.
So, One factor is,
⇒ (x - 1)
Find another roots as;
(x - 1) ) x³ - 2x² - 5x + 6 ( x² - x - 6
x³ - x²
----------
- x² - 5x
- x² + x
-------------
- 6x + 6
- 6x + 6
------------
0
Hence,
⇒ f (x) = x³ - 2x² - 5x + 6
⇒ f (x) = (x - 1) ( x² - x - 6 )
⇒ f (x) = (x - 1) ( x² - 3x - 2x - 6)
⇒ f (x) = (x - 1) ( x (x - 3) - 2 (x - 3))
⇒ f (x) = (x - 1) (x - 2) (x - 3)
Hence, The completely factored form of f (x) = x³ - 2x² - 5x + 6 is,
⇒ f (x) = (x - 1) (x - 2) (x - 3)
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A cash deposit box has five-dollar and ten-dollar bills in it totaling $450. There are eight times as many five-dollar bills as ten-dollar bills. How many bills are in the box?
Answer:
81
Step-by-step explanation:
The graph of y=x4 - 2x² + 1 is shown.
Which point is a relative maximum?
Answer: Point B
Reason:
This point is the highest point in the neighborhood or interval. Yes point D is higher up, but points immediately adjacent to point D are higher. This means D is not a relative max. We need a hill shape like where B is located. In contrast, point C is a relative minimum since it is at the bottom of the valley.
a group of students was randomly divided into two subgroups. one subgroup took a test in the morning, and the other took the same test in the afternoon. this table shows the results. compare the probability that a student will pass the test in the morning with the probability that a student will pass the test in the afternoon. draw a conclusion based on your results.
The conclusion is P(pass l morning) = 0.56
P(pass l afternoon) = 0.72
Conclusion: a student taking the test in the afternoon has a greater probability of passing than a student taking the test in the morning.
What are the probabilities?
Probability is the odds that a random event would happen. The odds that the event would happen lies between 0 and 1. The closer the probability is to one, the more likely it is for the event to happen.
P(pass l morning) = number of students who took the test in the morning and passed / total number of students that took the exam in the morning
28 / 50 = 0.56
P(pass l afternoon) = number of students who took the test in the afternoon and passed / total number of students that took the exam in the afternoon = 36 / 50 = 0.72
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Answer:
C
Step-by-step explanation:
Just took the quiz
HELP ASAPPPP PLEASE!!!!
Answer:
(c) 45°
Step-by-step explanation:
A protractor is used to measure angles by aligning one of the sides of the angle with the 0 mark on the protractor scale. Then the value of the angle is read from the same scale where it is crossed by the other side of the angle.
ApplicationHere, ray BA crosses the outer scale at 0. The other ray of the angle, BC, crosses the outer scale halfway between 40 and 50, obscuring the mark at 45°.
The measure of angle ABC is 45°.
C. 45°
Step-by-step explanation:When measuring with a protractor one of the rays should line up with the straight edge of the protractor, then match up the second ray to the tick marks. However, it can be confusing to tell how to read a protractor.
Clockwise
This angle moves clockwise. This means that the second ray is clockwise to the ray at the bottom. When using a protractor that opens up to the left like this, read the top row of the protractor. The second ray matches the 45-degree mark.
Acute vs Obtuse
There is another way to tell which row of numbers to read. By looking at the drawn angle we can tell the angle is acute (smaller than a right angle). So, the measurement must be less than 90. Therefore, the top row must apply in this situation, meaning the angle is 45°.
Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least 100 pieces of sushi in total.
Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains 12 pieces and costs \$8 dollar sign, 8.
Let R represent the number of additional rolls that Sofia orders.
Sofia will order 7 more rolls of sushi (84 pieces) and pay $56St
Step-by-step explanation: im right
Find the value of t for which (4,6,3, t) is a linear combination of (1,3,-4,1), (2,8,-5,-1) and (-1,-5,0,2)
The value of t for which (4, 6, 3, t) is a linear combination of (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2) is equal to 13.
How to find a vector as a linear combination of other vectors
In this question we must solve for t such that (4, 6, 3, t) is a linear combination of vectors (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2), which means that non-zero coefficients have to be found by algebraic handling:
(4, 6, 3, t) = α₁ · (1, 3, - 4, 1) + α₂ · (2, 8, - 5, - 1) + α₃ · (- 1, - 5, 0, 2)
Which is equivalent to this system of linear equations:
α₁ + 2 · α₂ - α₃ = 4
3 · α₁ + 8 · α₂ - 5 · α₃ = 6
- 4 · α₁ - 5 · α₂ = 3
α₁ - α₂ + 2 · α₃ - t = 0
Whose solution is (α₁, α₂, α₃, t) = (38, - 31, - 28, 13). The value of t for which (4, 6, 3, t) is a linear combination of (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2) is equal to 13.
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PLS HELPPPPP ASAPPP OR IMAAA FAIL HELPPPPPPPPPPPPPPPPPPPPPPPPPPPp
Answer:
Step-by-step explanation:
(a). A = 5x( 7x - 2 ) - 3x( 2x + 4 )
(b). A = 35x² - 10x - 6x² - 12x = 29x² - 22x
A = 29x² - 22x
Find the zeros of polynomial function
X³-4x²-7x+5
The zeros of the polynomial function are -1.728, 0.56 and 5.167
How to solve the zeros?The polynomial function is given as:
x^3 - 4x^2 - 7x + 5
Next, we plot the graph of the polynomial
From the graph, the polynomial cross the x-axis when
x = -1.728, 0.56 and 5.167
Hence, the zeros of the polynomial function are -1.728, 0.56 and 5.167
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select all the statements that are true
Answer:
C & D
Step-by-step explanation:
A. 4 is greater than 0, so use the third equation to find f(x). 4*4 - 1 = 15, so A is wrong.
B. -2 is less than 0, so use the first equation to find f(x). -(-2) + 1 = 3, so B is also wrong.
C. -1 is less than 0, so use the first equation to find f(x). -(-1) + 1 = 2, so C is correct.
D. 1 is greater than 0, so use the third equation to find f(x). 1*1 - 1 = 0, so D is also correct.
Question
n⃗ =⟨−2, −1⟩ and D=[−4423].
What is D⋅n⃗ ?
Enter your answer as a vector by filling in the boxes.
The dot product of the D⋅n is 32.
According to the statement
We have given the value of n vector and d matrix and we have to find the dot product of these.
So, For this purpose,
The given values:
n = {-2,-1} and D = [−4423].
The dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers, and returns a single number.
So, The d matrix become
[tex]D = \left[\begin{array}{cc}-4&4&\\2&3&\\\end{array}\right][/tex]
Now solve it with the help of multiplication then the matrix become
D = (-12, -8)
and n = {-2,-1}
Now multiply both terms with the dot product.
So, the dot product of the both terms will become
D.n = 24 +8
Then
The output of the dot product of both terms is 32.
So, The dot product of the D⋅n is 32.
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I need help on this question please help me
The expression that shows the best use of the associative and commutative properties is [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]. The correct option is C. [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]
Associative and Commutative propertiesFrom the question, we are to determine the expression that shows the best use of the associative and commutative properties
The given expression is
[tex]\frac{3}{4}-5+9 -\frac{2}{4}+2[/tex]
To easier simplify the expression, we can group the fractions together and group the whole numbers together
That is,
[tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]
Hence, the expression that shows the best use of the associative and commutative properties is [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]. The correct option is C. [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]
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solve the system of equations. y=3x+2 y=x^2-4+2
The solutions to the system of equations are (4, 15) and (-1,-1)
How to solve the system of equations?The system of equations is given as:
y=3x+2
y=x^2-4+2
Substitute y=3x+2 in y=x^2-4+2
3x + 2=x^2-4+2
Simplify
x^2 - 3x - 4 = 0
Expand
x^2 + x - 4x - 4x = 0
Factorize
x(x + 1) - 4(x + 1) = 0
This gives
(x - 4)(x + 1) = 0
Solve for x
x = 4 and x = -1
Substitute these values in y=3x+2
y = 3(4)+2 = 15
y = 3(-1)+2 = -1
Hence, the solutions to the system of equations are (4, 15) and (-1,-1)
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ienes una cuerda que mide 90 cm. Hay que partir la cuerda en 2 segmentos (A y B). La cuerda B debe ser 5 veces más grande que la cuerda A. ¿Cuánto mide la cuerda B?
Basada en el concepto de relación, tenemos que la cuerda B tiene una longitud de 75 centímetros y la cuerda A es de 15 centímetros.
¿Cuánto mide cada segmento de cuerda?
En este problema debemos hallar dos segmentos de cuerda que cumple la siguiente relación, basada en el enunciado citado:
5 = (90 cm - x)/x (1)
5 · x = 90 cm - x
6 · x = 90 cm
x = 15 cm
Basada en el concepto de relación, tenemos que la cuerda B tiene una longitud de 75 centímetros y la cuerda A es de 15 centímetros.
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Linear functions f(x) and g(x) have been combined by addition and multiplication. The table shows values for the sum, s(x), and product, p(x).
Which statements correctly compare the sum and product? Check all that apply.
Both functions have a constant rate of change.
The sum is linear and the product is quadratic.
The x-intercepts are the same.
The sum has one y-intercept and the product has two x-intercepts.
Both functions decrease for x ≥ 2.
The statements that correctly compare the sum and product of the function are:
The sum is linear and the product is quadratic.The sum has one y-intercept and the product has two x-intercepts.What is a linear function?A linear function simply means a function that represents a straight line on the coordinate plane.
In this case, the sum is linear and the product is quadratic while the sum has one y-intercept and the product has two x-intercepts.
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Please help
The mean length of 7 childrens' index finger is 7.8cm.
The mean length of 7 adults' index finger is 17.7cm.
What is the mean length (rounded to 2 DP) of these 14 people's index finger?
The combined mean of the 14 people's index finger is: 12.75 cm.
How to Find the Combined Mean?Combined mean = [(mean of first group × number of data of the first group) + (mean of second group × number of data of the second group)] ÷ (number of data of the first group + number of data of the second group).
Given the following:
Mean of first group = 7.8
Number of data of the first group = 7
Mean of second group = 17.7
Number of data of the second group = 7
Combined mean = [(7.8 × 7) + (17.7 × 7)] / (7 + 7)
Combined mean = 178.5 / 14
Combined mean = 12.75 cm.
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how do I type in greater than in my computer
Answer:
hold shift then press the lil right arrow next to the question mark
Step-by-step explanation:
Answer:
shift + >
Step-by-step explanation:
Hope this helps
A store is selling two mixtures of nuts in 20-ounce bags. The first mixture has 15 ounces of peanuts combined with five ounces of cashews, and costs $4.75. The second mixture has five ounces of peanuts and 15 ounces of cashews, and costs $6.25. How much does one ounce of peanuts and one ounce of cashews cost?
The cost of one ounce of peanuts is $0.20
The cost of one ounce of cashew is $0.35
What are the linear equations that represent the question?15p + 5c = 4.75 equation 1
5p + 15c = 6.25 equation 2
Where:
p = cost of one ounce of peanutsc = cost of one ounce of cashewWhat is the cost of one ounce of peanut and cashew?Multiply equation 2 by 3
15p + 45c = 18.75 equation 3
Subtract equation 1 from equation 3
40c = 14
c = 14/40
c = $0.35
Substitute for c in equation 1
15p + (5 x 0.35) = $4.75
15p + 1.75 = 4.75
15p = 4.75 - 1.75
15p = 3
p = 3/15
p = $0.20
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The rectangular part of the field shown below is 160 yd long and the diameter of each semicircle 12 yd. How much will it cost to fertilize the field at 0.25 per square yard? Use π = 3.14 and round to the nearest cent.
It will cost $508.26 to fertilize the field having the length 160 yards and the diameter of the semicircles is 12 yards.
Given that the field is 160 yards long and the diameter is 12 yards and charge of 1 square yard of fertilizing is $0.25.
We are required to find the total cost of fertilizing the field.
The total cost of fertilizing the field will be the product of the cost of 1 square yards and the area of the field.
When we will observe the field carefully then we will say that the diameter of the semi circle is equal to the breadth of the rectangle. There are two semicircles so we have to just find the area of 1 circle and the area of 1 rectangle.
Area of the field=Area of rectangle+Area of circle
=length* breadth+π[tex]r^{2}[/tex]
=160*12+3.14*[tex]6^{2}[/tex]
=1920+3.14*36
=1920+113.04
=2033.04 [tex]yards^{2}[/tex]
Cost of fertilzing the field=2033.04*0.25
=$508.26
Hence It will cost $508.26 to fertilize the field having the length 160 yards and the diameter of the semicircles is 12 yards.
Question is incomplete as the figure which is attached should be included.
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Decide whether the conditions create a unique triangle, multiple triangles, or no triangle m∠A=65∘ m∠B=75∘ m∠C=40∘
Answer:
multiple triangles
Step-by-step explanation:
add the numbers up it adds to 180 which is the sum of a triangle and could create other triangles
Use the information provided to write the general conic form equation of the circle: Ends of a diameter: (11, -2) and (9, 4)
The equation for a circle is:
[tex](x-a)^{2} + (y-b)^{2} + = r^{2}[/tex]
Where (a,b) is the circle's center and r is the circle's radius.
First, we can find the center point of the circle. Because the two points from the problem are the endpoints of a diameter, the midpoint of the line segment is the center point of the circle.
The formula to find the mid-point of a line segment giving the two endpoints is:
M = [tex](\frac{x_{1} + x_{2} }{2}[/tex], [tex]\frac{y_{1} + y_{2} }{y} )[/tex]
Where M is the midpoint and the given points are:
[tex](x_{1}, y_{1} )[/tex] and [tex](x_{2} , y_{2})[/tex]
Substituting the values from the two points in the problem gives:
[tex]M = (\frac{11+9}{2}[/tex],[tex]\frac{-2+4}{2} )[/tex]
[tex]M = (\frac{11+9}{2}[/tex],[tex]\frac{2-4}{2})[/tex]
[tex]M = (\frac{20}{2} , \frac{2}{2})[/tex]
[tex]M = (10,1)[/tex]
$274 for 40 hours of work as a unit rate
Answer:
6.85 units per hourStep-by-step explanation:
$274 for 40 hours of work as a unit rate
in practice you look for the hourly wage, you find it by dividing the wages divided by the working hours
274 : 40 = 6.85 units per hour
Factor:
y(a−b)-(a−b)
Answer: [tex](a-b)(y-1)[/tex]
Step-by-step explanation:
Factoring out (a-b) gives [tex](a-b)(y-1)[/tex].
Select the story problem that this division problem represent 1/2 2/5 (Repost)
The story problem that aligns with the division problem is A. A whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the whiteboard?
How to illustrate the division problem?From the information given, it can be seen that 1/2 is divided by 2/5.
In this case, the story that aligns with it is that a whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the whiteboard?
In this case, the length is multiplied by width to get the area.
Therefore, the correct option is A.
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Factories completely 2x * (2x + 1) ^ 2 + (2x + 1)(4x ^ 2 - 3)
The factored form of the polynomial is (x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242).
How to factor an algebraic equation
In this question we have an algebraic expression to be expanded by means of algebraic properties, the purpose of this handling is to modify the polynomial until its standard form is finally obtained and later we find its factor form by Cardano's method. Now we proceed to show the procedure in detail:
2 · x · (2 · x + 1)² + (2 · x + 1) · (4 · x² - 3) Given
2 · x · (4 · x² + 4 · x + 1) + (2 · x + 1) · (4 · x²) + (2 · x + 1) · (- 3) Perfect square trinomial/Distributive property
8 · x³ + 4 · x² + 2 · x + 8 · x³ + 4 · x² - 6 · x - 3 Distributive property/(- 1) · a = - a
16 · x³ + 8 · x² - 4 · x - 3 Distributive property/Definitions of addition and subtraction
(x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242) Cardano's method/Result
The factored form of the polynomial is (x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242).
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