In this type of problem. You need to determine first the unit dimension..
The dimension of the volume is in cubic so the unit dimension will be the cube root the volume:
Let u = unit dimension
[tex]u=\sqrt[3]{V}[/tex]So we now have the unit dimension, dilating it with a scale factor of k will give as a new volume. Since it is a unit dimension, you need to take the cube of it so you will arrive with the new volume.
So the new volume will be :
[tex]V_{\text{new}}=(uk)^3[/tex]or just simply :
[tex]V_{\text{new}}=(k\sqrt[^{}3]{V})^3[/tex][tex]k=\frac{\sqrt[3]{V_{\text{new}}}}{\sqrt[3]{V}}=\sqrt[3]{\frac{V_{new}}{V}}[/tex]Solving for the scale factor k :
[tex]k=\sqrt[3]{\frac{128}{2}}=\sqrt[3]{64}=4[/tex]So now we have the scale factor of k = 4
Now for the Surface Area , the dimension of it is in square units, so the unit dimension will be the square root of the surface area :
It has almost the same formula for k, but the difference is only the cube root or the square root.
So we can state that the New surface area will be :
[tex]SA_{\text{new}}=(k\sqrt[]{SA})^2[/tex]Solving for the New surface area :
[tex]SA_{\text{new}}=(4\sqrt[]{10})^2=160[/tex]So the answer is 160 square units.
Write the equation of the line, y = -2/3x + 4 y = 2/3x + 4 y = 3/2x + 4 y = -3/2% 4 4
Given data:
The given graph is shown.
The first point on the graph is (0, 4), and the second point on the graph is (2, 1).
The equation of the line passing through these points is,
[tex]\begin{gathered} y-4=\frac{1-4}{2-0}(x-0) \\ y-4=-\frac{3}{2}x \\ y=\text{ -}\frac{3}{2}x+4 \end{gathered}[/tex]Determine whether the following system of linear equations has no solution, only one solution, or infinitely many solutions. If the system has only one solution, find that solution.
You have the following system of equations:
3x - 3y + 3z = 0 (1)
2x - y - 3z = 2 (2)
-7x + 6y - 2z = -2 (3)
In order to determine if the previous system has solution or not, proceed as follow:
Add equation (1) and (2):
3x - 3y + 3z = 0
2x - y - 3z = 2
5x - 4y = 2 (5)
Multiply the equation (3) by -3 and the equation (2) by 2:
(-7x + 6y - 2z = -2)(-3)
21x - 18y + 6z = 6
(2x - y - 3z = 2)(2)
4x -2y - 6z = 4
Add the previous results:
21x - 18y + 6z = 6
4x -2y -6z = 4
25x - 20y = 10 (6)
You can notice that equation (6) is five times equation (5). It means that there is no way of getting a solution for x or y with equations (5) and (6).
the previous situation also means that there is no solution to the system of equations.
There is lightning rod on the top of a building. From a location 500 feet from the base of the building, the angle of elevation to the top of the building is measured to be 36°. From the same location, the angle of elevation to the top of the lightning rod is measured to be 38°. Find the height of the lightning rod. To earn full credit please share a diagram and include all your work and calculations
To better analyze the problem, let us draw an illustration:
To determine the height of the lightning rod, we have to determine the height of the building and the height of the building + lightning rod using the given angles and distance from the base.
Let's solve for the height of the building itself first. Use the 36-degree angle.
[tex]tan36=\frac{height\text{ }of\text{ }the\text{ }building}{distance\text{ }from\text{ }the\text{ }building}[/tex]Let's plug in the data to the function above and solve for the height of the building.
[tex]\begin{gathered} tan36=\frac{x}{500ft} \\ 500tan36=x \\ 363.2713ft=x \end{gathered}[/tex]Therefore, the height of the building itself is 363.2713 ft.
Moving on to the height of the building + lightning rod, use the tangent function still but this time, use the 38-degree angle.
[tex]\begin{gathered} 500tan38=x \\ 390.6428=x \end{gathered}[/tex]Therefore, the height of the building + lightning rod is 390.6428ft.
So, to determine the height of the lightning rod only, let's subtract the two calculated heights.
[tex]\begin{gathered} lightning\text{ }rod=390.6428ft-363.2713ft \\ lightning\text{ }rod=27.3715\approx27.37ft \end{gathered}[/tex]Answer:
The height of the lightning rod is approximately 27.37 ft.
The point A (-1,1) is reflected over the point (3,-1) and it's image is point B. What are the coordinates of point B?
B (7,-3)
1) Let's visualize this
Point A (-1,1) is reflected over the point (3,-1)
When point A(-1,1) is reflected over the point (-3,1) it goes 4 units to the right and 2 units down, so after the
2) So point B is (7,-3)
1 shown. If the diameter of a circle is of an inch, what 4 is its radius? 1 What is the radius r of a circle with a diameter of 4 a r in (Simplify your answer. Type an integer or a fraction.) Enter your answer in the answer box е e Save for ater
Given
d = 1/4 inch
d = diameter
Procedure
[tex]\begin{gathered} r=\frac{1}{2}d \\ r=\frac{1}{2}\cdot\frac{1}{4} \\ r=\frac{1}{8}\text{ inch} \end{gathered}[/tex]
Lex had b pounds of apples. She gave away 1/10 of the apples. Which of the following expressions represents the weight of apples she gave away?
A. B + 1/10
B. B x 1/10
C. B - 1/10
D. B divided by 1/10
PLS HELP
Answer:
B. B x 1/10
Step-by-step explanation:
Lex had b pounds of apples. She gave away 1/10 of the apples. Which of the following expressions represents the weight of apples she gave away?
A. B + 1/10 this would be giving away more than the apples she has
B. B x 1/10, correct
C. B - 1/10 this would be giving 9/10 lb apples away. This represents the apples she kept.
D. B divided by 1/10 Lex does not have this many to give away
Find the selling price of a $89.50 jacket with a 25% markup. Round to the nearest cent when necessary. $113.85 $111.22 $127.50 $111.88
$111.88 (option D)
Explanation:Selling price = ?
Cost price of jacket = $89.50
Markup % = 25% = 0.25
We'll apply markup formula:
[tex]markup\text{ \% = }\frac{selling\text{ price - cost price}}{\cos t\text{ price}}\text{ }\times\text{ 100}[/tex][tex]\begin{gathered} 0.25\text{ = }\frac{selling\text{ price - 89.50 }}{89.50} \\ \\ 0.25(89.50)\text{ = selling price - }89.50 \\ 22.375\text{ = selling price - 89.50} \\ 22.375\text{ + 89.50 = selling price} \end{gathered}[/tex][tex]\begin{gathered} \text{selling price = 111.875} \\ To\text{ the nearest cent,} \\ \text{Selling price = \$111.88 (option D)} \end{gathered}[/tex]Find the probability of winning a new tvFind the odds against the team winning its next match
a)
[tex]\frac{2}{7}[/tex]b)
[tex]\frac{12}{11}[/tex]ExplanationThe probability of an event occurring is intuitively understood to be the likelihood or chance of it occurring, the probability is givenby:
[tex]P(A)=\frac{favourable\text{ outcomes}}{total\text{ outcomes}}[/tex]so
Step 1
we can find the odds in favor by using the expression:
[tex]Odds\text{ in favor=}\frac{P(A)}{1-P(A)}[/tex]so
let
[tex]\begin{gathered} P(A)=unknown \\ odds\text{ in favor=}\frac{2}{5} \end{gathered}[/tex]now, replace and solve for P(A)
[tex]\begin{gathered} Odds\text{ in favor=}\frac{P(A)}{1-P(A)} \\ \frac{2}{5}=\frac{P(A)}{1-P(A)} \\ cross\text{ multiply } \\ 2(1-P(A))=5*P(A) \\ 2-2P(A)=5P(A) \\ add\text{ 2P\lparen A\rparen in both sides} \\ 2-2P(A)+2P(A)=5P(A)+2P(A) \\ 2=7P(A) \\ divide\text{ both sides by 7} \\ \frac{2}{7}=\frac{7P(A)}{7} \\ \frac{2}{7}=P(A) \end{gathered}[/tex]therefore, the probabilyt of winning a new TV is
[tex]\frac{2}{7}[/tex]Step 2
now, to find the odds against we need to use the formula:
[tex]odds\text{ agains=}\frac{1-P(A)}{P(A)}[/tex]so
let
[tex]P(B)=\frac{11}{23}[/tex]now, replace in the formula and calculate
[tex]\begin{gathered} odds\text{ against=}\frac{1-P(A)}{P(A)} \\ odds\text{ against=}\frac{1-\frac{11}{23}}{\frac{11}{23}} \\ odds\text{ against=}\frac{\frac{12}{23}}{\frac{11}{23}}=\frac{12*23}{11*23}=\frac{12}{11} \\ odds\text{ against=}\frac{12}{11} \end{gathered}[/tex]therefore, the odds against are
[tex]\frac{12}{11}[/tex]I hope this helps you
How many ways can 5 students be assigned a seat in a classroom if there are 9 seats in a row?
a) 45
b) 14
c) 362,880
d) 15,120
e) 126
f) None of the above.
Answer: I believe it is D! hope this helps
Step-by-step explanation:
find the equation of the line when 6 is the y intercept
...........................................
Jamie runs a math-tutoring program. For each student, she charges an enrollment fee of $63.00 plus $18.00 per hour of tutoring. If h representsthe number of hours a student participates in tutoring, which inequality symbolizes when a student's average cost per hour of tutoring is nomore than $22.207
Hence, the inequality which symbolizes when a student's average cost of tutoring is no more than $22.207 is:
[tex]\frac{63}{h}+18\leq22.207[/tex]9
You're applying for a job that has a skills test requirement. In order
to pass you need to get 48 of the 55 questions correct. What
percent of the questions do you need to answer correctly?
O
55%
Using the given percentages we can calculate that the 87.27 percent of questions needed to be answered correctly .
The word "percent" comes from the Latin phrase per centum, which meaning "hundred" or "by the hundred."
Per was regularly abbreviated to "p" and eventually disappeared entirely. The Italian term per cento, which means "for a hundred," progressively reduced to become the symbol for "percent." The current "%" symbol is derived from the "cento," which was composed of two circles and a horizontal line. Due to inconsistent usage, it is not always clear from the context what a% is in reference to. The usual interpretation of a quantity's "10% rise" or "10% drop" is that it refers to the quantity's initial value.The number of questions that are required to pass = 48
total number of questions = 55
Percentage of questions = 48/55 × 100 = 87.27 %
Therefore he will need to answer 87.27 % question correctly to pass.
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Density is a unit rate measured in units of mass per unit of volume. The mass of a garnet is 5.7 grams. The volume is 1.5 cubic centimeters (cm3). What is the density of the garnet?
The density of the garnet is 3.8
Mass of the garnet = 5.7 grams
Volume = 1.5 cm^3
Since each element and compound has a distinct density, DENSITY is a physical attribute of matter. In a qualitative sense, density is the quantification of the relative "heaviness" of things with a constant volume.
A crumpled piece of paper of the same size is visibly less dense than a rock. A ceramic cup is denser than a styrofoam cup. Use the styrofoam vs. ceramic cup comparison to illustrate how closely "packed" or "busy" the material appears to be.
The density of the garnet =. Mass/Volume
= 5.7/1.5
= 3.8
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Jessica was 44 inches at the beginning of 6th grade. At the end of 8th grade she was 62 inches. What was her
percent increase?
Answer:
40.91%
Step-by-step explanation:
62 - 44 = 18
18/44 = 0.4091
0.4091*100 = 40.91%
Then the increase percent is:
40.91%
find the standard deviation for the following set of numbers 29,31,37,42
I’m
not too sure on the next steps and very confused
The standard deviation for the following set of numbers 29,31,37,42 is 34.75.
Why is there a standard deviation?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Standard deviation:
= (29 + 31 +37 + 42 )/ 4
= 34.75
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.Which expression is equivalent to 45 ÷ (2 - x)?
A
45
2-X
B (2-x) = 45
C 45+ (x - 2)
D
2-x
45
The equivalent expression to 45÷(2-x) is 45/(2-x).
According to the question,
We have the following expression:
45÷(2-x)
Or in other words, it can be said that 45 is divided by (2-x).
Now, when we are finding the equivalent expression of any expression for that matter then the final expression after solving any expression should be equal to the original one.
For example, the equivalent expression for 3/5 is 6/10 because when we divide the second fraction by we will get 3/5.
Now, in this case, the equivalent expression will be:
45/(2-x)
Because the fraction also means division.
Hence, the correct option is A.
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Frazer is buying paint to paint one of his walls. The wall measures 3 feet bu 5 feet. A por of paint will cover 20 square feet. Will it be enoigh to cover his wall?
Yes, It will be enough to cover the wall.
What is the perimeter?A perimeter is the length of a two-dimensional shape's boundary. It is sometimes described as the total length of the object's sides. The perimeter of that shape is equal to the algebraic sum of the lengths of its sides. For the various geometric shapes, we have formulas.
Area: 3×5=15 square feet [s=length-width]
Perimeter: (3+5) × 2 = 16 feet
∵ 15 square feet <20 square feet
∴ It will be enough
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A party rental company has chairs and tables for rent. The total cost to rent 12 chairs and 2 tables is $39. The total cost to rent 3chairs and 5 tables is $57. What is the cost to rent each chair and each table?00Х$?Cost to rent each chair: slCost to rent each table: s]
let
x = cost of single chair
y = cost of single table
[tex]\begin{gathered} 12x+2y=39 \\ 3x+5y=57 \\ 2y=39-12x \\ y=\frac{39}{2}-6x \\ \\ 3x+5(\frac{39}{2}-6x)=57 \\ 3x+\frac{195}{2}-30x=57 \\ -27x=57-\frac{195}{2} \\ -27x=97.5 \\ x=\frac{-40.5}{-27} \\ x=\text{ 1.5} \\ \\ 12x+2y=39 \\ 12(1.5)+2y=39 \\ 18+2y=39 \\ 2y=39-18 \\ y=\frac{21}{2} \\ y=10.5 \end{gathered}[/tex]cost of rent of each chair = $1.5
cost of rent of each table = $10.5
if a population of a town decreases by 5% every 3 years would it be exponential ?
Yes, the population would be exponential.
What are exponents?
Exponentiation is a numerical technique denoted by the symbol bn that involves two integers, the base b and the exponent or power n, and is spoken as "b (raised) to the (power of) n." Exponentiation corresponds to repeated multiplication of the base when n is a positive integer: bn is the product of multiplying n bases. Typically, the exponent is displayed as a superscript to the right of the base. In such scenario, bn is referred to as "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or simply "b to the nth."
Yes, the population would be exponential.
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Evaluate the expression uv^2 + 5uv + u^2 for u = 3 and v = 4.1171128496
Answer:
117 (1st option)
Explanation:
Given:
[tex]uv^2+5uv+u^2[/tex]To find:
the value of the expression when u = 3 and v = 4
To determine the value, we will substitute for u and v in the expression
[tex]\begin{gathered} uv^2+5uv+u^2\text{ = 3\lparen4}^2)\text{ + 5\lparen3\rparen\lparen4\rparen + 3}^2 \\ \\ =\text{ 3\lparen16\rparen + 60 + 9} \\ \\ =\text{ 48 + 69} \\ \\ =\text{ 117 \lparen1st option\rparen} \end{gathered}[/tex]Consider the quadratic equation y = ×^2 + 4x + 7 Complete the square to express the quadratic in standard form y = a(x - h)^2+ k a= h = k = [tex]y = {x}^{2} + 4x + 7[/tex]complete the square
To write the equation;
[tex]y=x^2+4x+7[/tex]in standard form, we will follow the steps below:
From the above
a=1
b=4
c=7
So find (b/2a)²
=[4/2(1)]²
=(4/2)²
=2²
=4
We will now have;
y = (x²+4x+4) + 7-4
y=(x+2)² +3
comparing with;
y=a(x-h)² + k
a=1
h=-2
k=3
ХBased on the table, which best predicts the end behaviorof the graph of f(x)?f(x)-6-20-5-4-3-2-101As xoo, fx) - 00, and as x, f(x) – 00.As X-oo, f(x) - oo, and as X - -co, f(x) – 4.O As X - co, f(x) – oo, and as X - oo, f(x) - 09.As x - 00, f(x) ---, and as Xoo, f(x) = -0.440-2.-6-1023
Given the table:
x f(x)
-5 -6
-4 -2
-3 0
-2 4
-1 4
0 0
1 -2
2 -6
3 -10
Let's find the best behaviour if the graph.
From the table, as the values of x increases, the values of f(x) decreases and as the values of y decreases, the values of f(x) decreases.
From the table of values, we can see that as x approaches negative infinity, f(x) approaches negative infinity.
Also, as x approaches infinity, f(x) approaches negative infinity.
Thus, we have the statement that best predicts the behaiour of the graph f(x):
As x ==> ∞, f(x) ==> -∞, and as x ==> -∞, f(x) ==> -∞
ANSWER:
A concession stands sells drinks and hotdogs the number of drinks sold is five more than four times the number of hotdogs sold the stands sells 500 items how many hotdogs were sold
Answer:120
Step-by-step explanation:
Marissa is selling paintings for $15 each and bracelets for $7 each. Her goal is to sell at least $800 in products, and she must sell at least 60 bracelets. Which of the following combinations will satisfy these constraints?
20 paintings and 65 bracelets
25 paintings and 60 bracelets
26 paintings and 61 bracelets
14 paintings and 45 bracelets
If Marissa is selling paintings for $15 each and bracelets for $7 each. Her goal is to sell at least $800 in products, and she must sell at least 60 bracelets. Then 20 paintings and 65 bracelets will satisfy the given constraints.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Marissa is selling paintings for $15 each and bracelets for $7 each.
Let x represents paintings and y represents bracelets
7x+15y≥800...(1)
Marissa must sell at least 60 bracelets.
y ≥ 60..... (2)
Now substitute 60 in 1
7x+15(60)≥800
7x+900≥800
7x≥-100
x≤20
Hence of the following combinations 20 paintings and 65 bracelets will satisfy these constraints
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Answer:
26 paintings and 61 bracelets
Step-by-step explanation:
if you do 26x15=390 and 61x7=427 390+427=817
so the answer is 26 paintings and 61 bracelets
also i took the test so i know this is right
Factor 2x2 + 8x − 90 completely.
we have the expression
[tex]2x^2+8x-90[/tex]step 1
Factor 2
[tex]2(x^2+4x-45)[/tex]step 2
Simplify
[tex]2(x^2+4x-45)=2(x+9)(x-5)[/tex]Karen's furniture store advertised a table at 23% discount. The original selling price was $123, and the sale price was $100. What is the sales price?
Using the original selling price calculate the real sales price that it should be if there is a discount of 23%
[tex]\begin{gathered} SalesPrice=OrigalPrice\cdot(1-0.23) \\ SalesPrice=123\cdot(0.77) \\ SalesPrice=94.71 \end{gathered}[/tex]The sales price is higher than it should be.
Sue learned to sing a total of 10 pieces over the course of 5 weeks of voice lessons. After 8
weeks of voice lessons, how many pieces will Sue be able To sing total?
Answer:
2 pieces per week. 10 pieces/ 5 weeks. 16 pieces for 8 weeks. ? 16 pieces total.
Step-by-step explanation:
For jewelry prices in a jewelry store, state whether you would expect a histogram of the data to be bell-shaped, uniform, skewed left, or skewed rightChoose the correct answer below."O UniformO Skewed rightSkewed leftO Bell shaped+
For jewelry prices in a jewelry store, histogram of the data will be bell-shaped .
The graph of a function is shown in the figure.30110X-101What is the value of the function for =2?
The function's value for x = 2 is the point (y-coordinate) on the graph corresponding to x = 2.
If you go to x = 2, then go to the function, it is located at y = -2.
Hence, the value of the function for x = 2, is:
-2Mr. Perkins has \$ 120$120 in a savings account. The interest rate is 5 \%5% per year and is simple interest. How much will he have in 2 years?
Answer:
$12
Step-by-step explanation:
Simple interest calculation is
I = Prt
where P is the principal, r is the rate of interest as a decimal and t the number of years
Given
P = 120, r = 5% = 5/100 = 0.05 and t = 2 years
the simple interest
= 120 x 0.05 x 2 = $12
==============================================
Work Shown:
i = P*r*t
i = 120*0.05*2
i = 12
Mr. Perkins earns $12 in simple interest over the two year period. His account balance will be 120+12 = 132 dollars
------------
Slight shortcut:
A = P*(1+r*t)
A = 120*(1+0.05*2)
A = 132
