Answer:
a) 9 days
b) 47 days
Step-by-step explanation:
Given information:
Distance worm climbs each day = 5 ftDistance worm falls back each night = 3 ftPart (a)[tex]\begin{array}{|c|r|c|r|}\cline{1-4} \sf Day & \sf Height\:{(ft) & \sf Night & \sf Height\:(ft) \\\cline{1-4} 1 & 5 & 1 & 5 - 3 = 2\\\cline{1-4} 2 & 2 + 5 = 7 & 2 & 7 - 3 = 4 \\\cline{1-4} 3 & 4 + 5 = 9 & 3 & 9 - 3 = 6 \\\cline{1-4} 4 & 6 + 5 = 11 & 4 & 11 - 3 = 8 \\\cline{1-4} 5 & 8 + 5 = 13 & 5 & 13 - 3 = 10 \\\cline{1-4} 6 & 10 + 5 = 15 & 6 & 15-3=12\\\cline{1-4} 7 & 12 + 5 = 17 & 7 & 17 - 3 = 14 \\\cline{1-4} 8 & 14 + 5 = 19 & 8 & 19-3=16\\\cline{1-4} 9 & 16 + 5 = 21 &&\\\cline{1-4}\end{array}[/tex]
On the first day the worm climbs 5 ft, but slips back 3 ft during the first night.
On the second day the worm climbs a further 5 ft, so is now at 7 ft, but slips back 3 ft during the second night. Therefore, it starts the third day at a height of 4 ft.
The progression continues this way so that the worm starts the 9th day at a height of 16 ft. As it climbs 5 feet during the day, it will reach the height of 20 ft during the 9th day, and so will climb out of the ravine before it sleeps for the night.
Therefore, it will take 9 days for the worm to crawl up a 20 ft ravine.
This can be modeled as an arithmetic sequence:
[tex]y=a+(x-1)d[/tex]
where:
y = height of ravinex = number of daysa = initial height after the first dayd = common difference = 2Therefore:
[tex]\implies y=5+(x-1)2[/tex]
[tex]\implies y=5+2x-2[/tex]
[tex]\implies y=3+2x[/tex]
Part (b)To calculate how long it will take the worm to crawl up the ravine if it is 97 ft high, substitute y = 97 into the equation and solve for x:
[tex]\implies 3+2x=97[/tex]
[tex]\implies 3+2x-3=97-3[/tex]
[tex]\implies2x=94[/tex]
[tex]\implies \dfrac{2x}{2}=\dfrac{94}{2}[/tex]
[tex]\implies x=47[/tex]
Therefore, it will take 47 days for the worm to crawl up a 97 ft ravine.
The area of the walkway and garden is represented by the expression
2x2 + 12x + 16. Write an expression in factored form that represents
the area of the walkway. Then find the area of the walkway if x is
3 meters. (Hint: Subtract the expression that represents the area of the
garden from the expression that represents the area of both before
factoring.)
The factorized form of the quadratic is 2*(x + 2)*(x + 4), and when x = 3m, the walkway area is 52 square meters.
How to factorize the area equation?
Here we know that the area is given by the expression:
2x^2 + 12x + 16
To factorize this, we need to find the roots of the quadratic equation, these are the solutions of:
2*x^2 + 12x + 16 = 0
The solutions are given by:
x = (-12 ± √(12^2 - 4*2*16))/(2*2)
x = (-12 ± 4)/4
The two solutions are:
x = (-12 + 4)/4 = -2
x = (-12 - 4)/4 = -4
Then the factored form is:
y = 2x^2 + 12x + 16 = 2*(x^2 + 6x + 8) = 2*(x + 2)*(x + 4)
Now we want to get the area if the walkway if x = 3, the total area of the walkway and the garden will be:
y = 2*(3 + 2)*(3 + 4) = 70
And the garden measures x by 2x, then if x = 3, the area of the garden is:
a = x*2x = 3*(2*3) = 18
Then the area of the walkway alone is:
70 - 18 = 52
The area of the walkway is 52 square meters.
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Find A u B. (Use the roster method to write the set.)
A = {1, 0, 1}, B = {0, 1, 7}
Answer:
{ 0, 1 , 7}
Step-by-step explanation:
A U B= {1,0,1}. {0,1,7}
={0,1,7}
x
12
20
48
y
9
15
24
The table gives values from a linear relationship.
• Complete the table
• Write an equation that represents the relationship shown in the
table.
Find the measure of indicated angle or solve variable if necessary
Value for the 3 straight lines are 180,28 , 152.
What is a straight line, exactly?
Simply put, a straight line is a line devoid of bends. A straight line is one that does not curve and reaches to infinity on both sides.
CBE = 28 + 90 = so the angle is 118 degrees
ABF = you already got the answer written down, 28
CBA = this is not 180 like you wrote, CBA = ABD - CBD
Straight lines = 180, so ABD = 180
You already found out that CBD = 28
so CBA = 180 - 28 so the answer CBA = 152
So, answers for the 3 lines are 180,28 , 152
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Write an equation of the line with the given slope and the given y-intercept. Express the answer in standard form.
[tex]slope \frac{5}{8} , y-intercept (0,\frac{1}{4} )[/tex]
Answer:
5x - 8y = -2
Step-by-step explanation:
m = 5/8, x = 0, y = 1/4
so y = mx + b
1/4 = 5/8(0) + b
b = 1/4
so y = 5/8x + 1/4
8y = 5x + 2
5x - 8y = -2
Two factory plants are making TV panels. Yesterday, Plant A produced 10,000 panels. Three percent of the panels from Plant A and 10% of the panels from Plant B were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 5%
If the overall percentage of the defective panels from the two plants is 5% then plant B produced 4000 panels in total.
This question can be solved by formulating the problem into the form of a linear equation having two variables. Linear equation in two variables can be represented in the form of ax+by+c=0 where a, b and c are real numbers and x, y are variables or the coefficients, and a, b ≠ 0.
Let the production from plant A be x, and according to the question x=10000.
Also, let the production from plant B be y.
Now, as 3% of products are found defective from plant A and 10% of products are found defective from plant B and overall defective products is 5%.
Thus, 0.03x+0.1y=0.05(x+y)
As x=10000 then
0.03×10000+0.1y=0.05(10000+y)
300+0.1y=500+0.05y
0.05y=200
=>y=4000
Thus, the total number of panels produced by plant B is equal to 4000.
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es
Angela Simpson is considering the purchase of a home entertainment center. The product attributes she plans to consider and the
weights assigned to each attribute are listed in the table below.
Product Attributes
Portability
Sound projection
Warranty
Angela rated the brands as follows.
Brand A
Brand B
Brand C
0.2
0.5
0.3
Brand A
Brand B
Brand C
Sound
Portability Projection Warranty
7
8
10
5
Product
Evaluation Rating
87100
Using the consumer buying matrix, conduct a quantitative product evaluation rating for each brand. What other factors is Tammy likely
to consider when making her purchase? (Do not round intermediate calculations. Round your answers to 1 decimal place.)
9
7
Product Evaluation Rating for Brand A = 7.5
Product Evaluation Rating for Brand B = 7.4
Product Evaluation Rating for Brand C = 8.3
A product's acceptability for customers or a specific group is determined through the methodical process of product evaluation.
A visual representation of consumer behavior in terms of purchasing choices is a consumer buyer matrix. It also serves as a marketing tool for strengthening and expanding brands.
Given that :
Product Attributes -
Probability = 0.2
Sound projection = 0.5
Warranty = 0.3
Probability of Brand A = 7
Probability of Brand B = 10
Probability of Brand C = 6
Sound projection of Brand A = 8
Sound projection of Brand B = 6
Sound projection of Brand C = 10
Warranty of Brand A = 7
Warranty of Brand B = 8
Warranty of Brand C = 7
Calculation of Product Evaluation Rating :
Brand A = (7 x 0.2) + (8 x 0.5) + (7 x 0.3) = 1.4 + 4 + 2.1 = 7.5
Brand B = (10 x 0.2) + (6 x 0.5) + (8 x 0.3) = 2 + 3 + 2.4 = 7.4
Brand C = (6 x 0.2) + (10 x 0.5) + (7 x 0.3) = 1.2 + 5 + 2.1 = 8.3
Therefore,
Product Evaluation Rating for Brand A = 7.5
Product Evaluation Rating for Brand B = 7.4
Product Evaluation Rating for Brand C = 8.3
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Which expression are equivalent to 13^6 divide by (13^8)(13^-4)/13^-2
The figure below shows parallel lines cut by a transversal:
A pair of parallel lines is shown, cut by a transversal.
Which statement is true about ∠7 and ∠8?
For the given parallel ines cut by a transversal line the correct statement is (4). ∠7 and ∠8 are supplementary because they are a pair of adjacent angles that form a straight line.
What types of angles are formed when a transversal cuts paralle lines?The intersections of two parallel lines formed by a transversal form several angles. These are referred to as transversal angles. Here are some examples of transversal angles:
Corresponding anglesAlternate Interior AnglesAlternate Exterior AnglesCo-interior AnglesAngles are said to be supplementary to each other when two adjacent angles are formed at a point on a line so that the sum of their measures is 180°.
∠7 and ∠8 are supplementary in the attached figure since they represent a pair of adjacent angles which constitute a straight line.
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The correct question:
Please Help! The figure below shows parallel lines cut by a transversal:
Which statement is true about ∠7 and ∠8?
1. ∠7 and ∠8 are supplementary because they are a pair of corresponding angles.
2. ∠7 and ∠8 are complementary because they are a pair of adjacent angles on a straight line.
3. ∠7 and ∠8 are congruent because they are a pair of adjacent angles on a straight line.
4. ∠7 and ∠8 are supplementary because they are a pair of adjacent angles that form a straight line.
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to this system of inequalities in the coordinate plane.
3y > 2x + 12
2x + y ≤ -5
Plotting the inequalities using online graphing calculator. The graph is attached.
What is the example of inequality?
A disparity in size, quantity, quality, social standing, or another aspect is what is meant by the term "inequality." When you have ten of something and someone else has none, that is an instance of inequality.Given the system of inequalities:
3y > 2x + 12
3y - 2x > 12 (1)
2x + y < -5 (2)
Plotting the inequalities using online graphing calculator. The graph is attached.
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Pls solve a question on my hw (1/5)p=15
What is 48 = 3x - 15
Answer: x=21
Step-by-step explanation:
PLEASE HELP. STEP BY STEP NEEDED
So solutions of the linear quadratic systems are (-5,-3) and (1,3)
Given,
y = x²+5x -3 . . . . . . . . . .. ..1
y-x= 2 . . . . . .. . . . . . . . . . . 2\
From 1 and 2
y=x+2
substitute y=x+2 in 1
x+2= x²+5x -3
x²+5x -x-3-2 = 0
x²+4x -5=0
x²+5x-x -5=0
x(x+5) -1(x+5) = 0
(x+5)(x-1)=0
x= -5 and x=1
at x=-5
y=x+2=-5+2=-3
at x=1
y=x+2=1+2=3
So solutions of the linear quadratic systems are (-5,-3) and (1,3)
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5(2y-3)=40y what is the answer to this question
Answer:
y=-2
Step-by-step explanation:
5(2y-3)=40y
10y-15=40y
-15=30y
-2 = y
y = -2
Ben bought a house for $78,850 and received a rebate of 15% off. He paid 6% in sales tax. How much did he save?
$525
Step-by-step explanation:
Ben bought the house for $78,850 so 78,850 divided by 0.15 equals 525. So the answer is $525.
Find the difference: −14 −(−12)
Answer:
=-2
________________________________________________________
[tex]a-\left(-b\right)=a+b[/tex] <- Apply this rule too -14-(-12)
[tex]-14-\left(-12\right)=-14+12[/tex]
[tex]=-14+12[/tex]
[tex]-14+12=-2[/tex] <- Add the numbers
[tex]=-2[/tex]
________________________________________________________
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what is the domain of h
h: The domain
-5 ≤ x ≤ 5
if m ∟n, solve for x. (x + 21) (3x + 9) giving brainliest
Answer:
[tex](x + 21)(3x + 9) \\ x(3x + 9) + 21(3x + 9) \\ 3 {x}^{2} + 9x + 63x + 189 \\ 3 {x}^{2} + 72x + 189[/tex]
Desmos how would you explain the difference between volume and surface area?
Answer:
Volume is when you are finding the space inside of a 3D figure, and surface area is when you are finding the area of the surface(s) of a figure.
Hope this helps :)
I’m doing linear equations please help !! 1+6x=19
A square acre of land is 5,280 square yards.
Between which two integers is the length of one side?
Between 17 and 18 yards
Between 72 and 73 yards
Between 24 and 243 yards
Between 1,320 and 1,321 yards
The two integers which the length of one side is in between are 72 yards and 73 yards
How to determine between which two integers is the length of one side?The given parameters are
Area = 5280 square yards
Shape = Square
The area of a shape is calculated using
Area = Length^2
So, we have
Length^2 = 5280 square yards
Take the square root of both sides
Length = 72.66 yards
72.66 yards is between 72 yards and 73 yards
Hence, the two integers which the length of one side is in between are 72 yards and 73 yards
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Select the correct answer. Julie ran a race 2 minutes faster than Teri did. If Julie ran the race in 28 minutes, which equation can be used to find the number of minutes, m, it took Teri to run the race? A.m+2=28 B.m-2=28 C.2m=28 D.1/2m=28
Answer:
Step-by-step explanation:
its A. If julie ran 2 minutes more, then your simply adding 2 minutes to whatever teri got to get 28 (what julie got).
Jemuel and Lemuel are asked to paint a house.Jemuel can paint the house by himself 16hrs and Lemuel can paint by himself in 12hrs .How long would it take to paint the house if they work together?
Answer:
9 and 3/5 hours or 9 hours and 36 minutes
Step-by-step explanation:
Rate x times = number of jobs
Jemuel's rate is 1 job/ 16 hours.
Lemuels's rate is 1 job/12 hours.
1/16T + 1/14T = 1 Get a common denominator of 48
3/48T + 2/48 t = 1
5/48T = 1 Multiply both sides by 48/5
(45/5)(5/48)T = 1(48/5)
t = 48/5 = 9 3/5 hours.
Describe the transformation from the graph off to the graph of g. PLEASE HELP!
Answer:
translation 3 units up: g(x) = f(x)+3
Step-by-step explanation:
You are given graphs of f(x) and g(x) and want to know the transformation that gives g(x) from f(x).
Transformations of graphsThe sorts of transformations of graphs that we study are translation, scaling (horizontally or vertically), and reflection about an axis.
Here, both graphs have the same shape, but one is in a different place than the other. The applicable transformation is one of translation.
TranslationThe vertex of f(x) is at (0, -1). The vertex of g(x) is at (0, 2). We note the x-value has not changed, but the y-value has had 3 added to it. (-1 +3 = 2)
g(x) = f(x) +3 . . . . . . the function f is translated 3 units upward.
Keilantra has $660 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $488.20.
She buys 2 bicycle reflectors for $11.17 each and a pair of bike gloves for $19.05.
She plans to spend some or all of the money she has left to buy new biking outfits for $37.26 each.
Write and solve an inequality which can be used to determine xx, the number of outfits Keilantra can purchase while staying within her budget.
The number of outfits she can buy is 3.
How many outfits can she buy?The The first step is to determine the total cost of all the items already bought.
Total cost = cost of new bicycle + (cost of one reflector x number of reflectors) + cost of the gloves
$488.20 + (2 x $11.17) + 19.05
$488.20 + 19.05 + $22.34 = $529.59
Now, determine the amount that is left to buy the outfits :
$660 - $529.59 = $130.41
Here are inequality signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The inequality sign that would be used is ≤
(cost of one outfit x number of outfits) ≤ amount left
$37.26x ≤ $130.41
x ≤ 130.41 / 37.26
x ≤ 3.5
x = 3
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Identify the terms, coefficients, and the constants in the expression. 11q + 2
The term, coefficient and constant in the expression are 11q, 11 and 2 respectively.
What are the parts of an algebraic expression?The parts of an algebraic expression are;
TermsCoefficientsConstantsTerms: A term can be defined as a number, a variable, or the product of two or more variables or that of a product of a number and a variable.
The term is 11q
Coefficients: A coefficient is defined as an integer multiplied by the variable.
The coefficient is 11
Constants: A constant is a number that do not change.
The constant is 2
Thus, the term, coefficient and constant in the expression are 11q, 11 and 2 respectively.
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7 x 7 - 2 ( 11/8 - 3/8 ) pls help me
It's 47. I used a calculator.
Julian saved between $30 and $52
over the summer. His friend Daniela
saved twice as much. Let n represent
the amount of money Daniela saved.
What is the compound inequality?
The compound inequality is 60 < n < 104.
Let 'x' denote the amount of money saved by Julian.
Then x is between $30 and $52.
I.e., x>30 and x<52.
This can be written as a single inequality by combining the both.
i.e., 30 < x < 52
His friend Daniela saved twice as much as Julian.
Let 'n' denotes the amount of money Daniela saved.
Then n = 2x
We need to write the compound inequality for the money saved by Daniela.
As Daniela saved twice as much as Julian, it will be between 2 x 30 = $60 and 2 x 52 = $104
So the compound inequality is 60 < n < 104.
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4. A rocking horse has a weight limit of 60 pounds.
a. What percentage of the weight limit is 33 pounds?
b. What percentage of the weight limit is 114 pounds?
c. What weight is 95% of the limit?
Show your work
a. 55% of the maximum weight is 33 pounds.
b. 114 pounds is 190% of the weight limit.
c. 57 pounds is 95% of the maximum.
Answer to Part a:
Let c be the weight limit percentage for 33 pounds.
Then we have (60 x c)/100 = 33 pounds
This implies 3c/5 = 33
This means that 3c = 33 x 5 = 165.
This means that c = 165 / 3 = 55.
Therefore 55% of the weight limit is 33 pounds.
Answer to Part b:
Let d be the weight limit percentage for 114 pounds.
Then we have (60 x d)/100 = 114 pounds
This implies 3d/5 = 114
This means that 3d = 114 x 5 = 570.
This means that d = 570 / 3 = 190.
Therefore 190% of the weight limit is 114 pounds.
Answer to Part c:
95% of the weight limit is
= 95 x 60 /100
= 95 x 3/5
= 19 x 3
= 57
Therefore, 95% of the weight limit is 57 pounds.
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36. THOUGHT PROVOKING
Draw a different figure that
has the same perimeter as
the triangle shown. Explain
why your figure has the
same perimeter.
x+3
3x
2x + 1
A figure with the same perimeter as the one shown is a rectangle of base 3x and height 2, as given in the end of the question.
What is the perimeter of a figure?The perimeter of a figure is given by the sum of all the outer sides of the figure.
Hence, for this problem, the perimeter is given by:
P = x + 3 + 2x + 1 + 3
P = 6x + 4.
A figure with the same perimeter as the one shown is a rectangle of base 3x and height 2, as given in the end of the question, as:
3x + 3x + 2 + 2 = 6x + 4.
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