a) the constant of proportionality multiplies every actual linear dimension
b) height of a can of fruit juice is 3.85 inches high
What is Proportionality?
The term proportionality describes any relationship that is always in the same ratio.
Explanation for answer:
Since the desire is to have students look twice as tall, we expect the constant of proportionality to be [tex]\frac{1}{2}[/tex].
Instead, we're told that the stage manager is using a height of 44 inches to represent an 80-inch door.
This means their constant of proportionality is [tex]\frac{40}{80} = 0.55[/tex]
a) Any new props can be scaled by this factor (0.55) to find their height on set.
b) A 7-inch can would be scaled to [tex]7\times 0.55 = 3.85\ inches[/tex]
Question: The school's theater club is building sets that will make ordinary students look like giants. The actors need a door, a table, and a stool that will make them look almost twice as tall!
DOOR: actual height is 80 inches and Height on Set is 44 inches
TABLE: actual height is 28 inches
STOOL: actual height is 18 inches
How can the stage manager use the constant of proportionality to find the dimensions of any new props the director requires?
What should the height of a can of fruit juice used as a prop be if its actual height is 7 inches? Show your work.
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Let's multiply the top equation by -2. What would be our new equation?
2x + 3y = 12
4x - 7y = -54
New equation will be 4x + 6y = 24, if we multiply the equation 2x + 3y = 12 by -2.
Define multiplication.We can rapidly determine the total number of things by multiplying. When multiplying, we'll consider the number of groups with similar sizes and the number of items in each group. A fact involving multiplication is the result of two distinct integers. Additionally, the product is unaffected by the arrangement of the numbers. For instance, 32=6 and 23=6. The distributive, commutative, associative, removes a common factor, and neutral element characteristics of multiplication.
Given,
Equations:
2x + 3y = 12
4x - 7y = -54
Multiplying the top equation by -2:
-2(2x + 3y) = -2(12)
-2(2x) -2(3y) = -24
Product:
-4x - 6y = -24
Taking - common,
-(4x + 6y) = -24
4x + 6y = 24
New equation will be 4x + 6y = 24, if we multiply the equation 2x + 3y = 12 by -2.
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There are 121 boys and 116 girls signed up for a trip to an amusement park. The leader first makes groups of 9 students each and then assigns any remaining students to make some of the groups have 10 students. Part A How many groups of 10 students will there be? Explain. Part B How many groups of 9 students will there be? Explain.
The remainder is the amount "leftover" after performing some computation.
Hence,
(A) There are [tex]4[/tex] groups out of [tex]10[/tex] students.
(B) There are [tex]33[/tex] groups of [tex]9[/tex] students.
What is a remainder?
The remainder is the amount "leftover" after performing some computation. In arithmetic, the remainder is the integer "leftover" after dividing one integer by another to produce an integer quotient.
Here given that,
The strength of boys is [tex]121[/tex]
The strength of girls is [tex]116[/tex]
So, the total number of students are
[tex]121+116=337[/tex]
The leader first makes groups of [tex]9[/tex] students and then assigns any remaining students to make some of the groups have [tex]10[/tex] students.
So we divide by [tex]9[/tex] to find out the remainder and the total number of groups are:-
[tex]\frac{337}{9}=37[/tex]
and the remainder value is [tex]4[/tex].
Therefore, there are [tex]37[/tex] groups in the total out of which [tex]4[/tex] are out of [tex]10[/tex]students.
So,
[tex]\frac{37}{4}=33[/tex] groups are of [tex]9[/tex] students.
Hence,
(A) There are [tex]4[/tex] groups out of [tex]10[/tex] students.
(B) There are [tex]33[/tex] groups of [tex]9[/tex] students.
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Jan works from 30 to 40 hours per week during the summer. She earns $12.00 per hour. Her friend Rachel also has a job. Rachel's pay for t hours is given by the function r(t) = 11t, where 20 ≤ t ≤ 30. Find the domain and range of each function. Compare their hourly wages and the amount they earn per week.
j(t) domain:
≤ t ≤
j(t) range:
≤ j(t) ≤
r(t) domain:
≤ t ≤
r(t) range:
≤ r(t) ≤
select: Jan or Rachel
earns more per hour than
select: Jan or Rachel
. Jan earns from $ (blank)
to (blank) $
per week and Rachel earns from (Blank) $
to (Blank) $
per week.
Jan earns more than Rachel. The range of what Jan earns is 360 dollars to 480 dollars per week. The range of what Rachel earns is 220 dollars to 330 dollars per week.
How to solve for the Range and the domain of the functionsJan's pay function is given as /(t) = 12 dollars this is the same as 12 dollars in one hour
the time that she has to work is given a 30 hours to 40 hours.
Hence the domain would be written as
domain : 30 ≤ t ≤ 40
we have to make use of the values of t
f(t) = 12 * 30 = 360
f(t) = 12 * 40 = 480
The range of Jan is going to be
range : 360 ≤ t ≤ 480
b. For Rachel, t is going to vary between 20 ≤ t ≤ 30
domain : 20 ≤ t ≤ 30
r*t = 11t
= 11 x 20 = 220
= 11 x 30 = 330
The range is given as
range: 220 ≤ t ≤ 330
Jan earns more per hour than Rachel
The amount earned is, Jan earns from 360 dollars to 480 dollars per week.
Rachel earns from 220 dollars to 330 dollars per week.
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Simplify the fraction
Answer:
Step-by-step explanation:
Solve the inequality and enter your solution as an inequality comparing the
variable to the solution.
-18+x< 16
Answer here
Solution of the given inequality -18 + x < 16 is equal to x < 34.
As given in the question,
Given inequality is equal to :
-18 + x < 16
Get the value of the variable x by adding 18 both the side of the inequality we get,
-18 + x + 18 < 16 + 18
Collect all like terms together we get,
⇒ x + (-18 + 18 ) < 34
⇒ x + 0 < 34
Solution of the inequality -18 + x < 16 is given by
⇒ x < 34
For the given inequality -18 + x < 16 the value of variable x is less than 34.
Therefore, solution of the given inequality -18 + x < 16 is x < 34.
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quotient of 2÷ 3/7 iready
Answer:
6/7
Step-by-step explanation:
2÷3/7=2*3/7
6/7
Fill in the missing term on each line. Simplify any fractions.
3(9w+ 2) = 19w + 6
_+ 6 = 19w + 6 Apply the distributive property
_+6=6
8w =_
W =_
Subtract 19w from both sides
Subtract 6 from both sides
Divide both sides by 8
Answer:
27w+2=19w+6
27w+19w=6+2
w(27+19)=8
w(27+19)/27+19=8/27+19
w=8/(27+19)
Find the area of the shaded region. Round your answer to two decimal places.
The area of the shaded region is x=245 feet for both rectangle and circle.
What is meant by area?The quantity area expresses the extent of a region on a plane or a curved surface. The area of a plane region or plane area refers to the area of a form or planar lamina, whereas surface area refers to the area of an open surface or the boundary of a three-dimensional object. Area can be defined as the amount of material of a given thickness required to make a model of the shape, or the amount of paint required to cover the surface with a single coat. It is the two-dimensional equivalent of the length of a curve or the volume of a solid.
The area of a shape can be calculated.
Area of shaded region=Area of rectangle-1/2(Area of circle)
=L×B-1/2(πr²)
=23×14-1/2((22/7)×7×7)
=322-77
=245 feet
Therefore, the area of the shaded region=245 feet
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Can anyone help me with this, I need an accurate answer also if possible. -thanks
Answer:
y=x-7
Step-by-step explanation:
we know the y intercept is -7 since when x was 0 g(x) is -7
We write it in slope intercept form which is y=mx+b
m- slope
b- y- intercept
To find slope we do y2-y1/x2-x1
-5+7/2-0
2/2
1
1 is the slope so we just keep it X on the equation and the equation will be
y=x-7
Hopes this helps please mark brainliest
Solve. 4h+8=9h-7 step by step
Answer:
h=3
Step-by-step explanation:
4h+8=9h-7
subtract 4h
8=5h-7
add 7
15=5h
divide 3
h=3
Translate each phrase into a variable expression. Use n for the variable.
Nine increased by twice a number
The expression of the phrase " Nine increased by twice a number " is 2n + 9
The given phrase is
Nine increased by twice a number
We have to convert the the phrase to the expression
The expression is the mathematical statement that consist of different variables, numbers and mathematical operators. The mathematical operators are addition, subtraction, division and multiplication. The equal sign and inequality will not be the part of expression.
Consider the number as n
Twice the number = 2n
nine increased by twice a number = 2n + 9
Hence, the expression of the phrase " Nine increased by twice a number " is 2n + 9
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Find the area of the following figure:
(Use π=3.14 when finding your final answer. Do not round and Do not enter units!)
Area = _______ mm²
Answer:
521 mm2
Step-by-step explanation:
Formulas:
area of circle= 3.14 x radius x radius
area of semicircle = 0.5 x 3.14 x radius x radius
diameter of circle= 20mm
radius=0.5x20mm=10mm
area of trapezium= 0.5 x (base+base) x height
Working:
area of semicircle= 0.5 x 3.14 x 10mm x 10mm = 157mm2
area of trapezium = 0.5 x (20mm+32mm) x 14mm = 364mm2
total area of figure= 157mm2 + 364mm2 =521mm2
6 x (2/3 divided by 2) + 0.5
The given expression has a value of 2.5.
The BODMAS rule is named after the letters in the acronym: B - Brackets, O - Order of powers or roots, D - Division, M - Multiplication. A stands for addition, and S stands for subtraction. According to the BODMAS rule, mathematical statements having several operations must be solved from left to right in the BODMAS order.
Given expression 6 x (2/3 divided by 2) + 0.5
To solve this expression, we must employ the BODMAS rule.
First 2/3 divided by 2
(2/3)/2
= 1/3
Now multiply 1/3 with 6
= 1/3 x 6
= 2
Now add both 2 and 0.5
= 2 + 0.5
= 2.5
Therefore the value of the given expression is 2.5
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Factor 18p-3618p−3618, p, minus, 36 to identify the equivalent expressions.
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
3(9p-12)3(9p−12)3, left parenthesis, 9, p, minus, 12, right parenthesis
(Choice B)
B
9(2p-4p)9(2p−4p)9, left parenthesis, 2, p, minus, 4, p, right parenthesis
(Choice C)
C
2(9p-18)2(9p−18)2, left parenthesis, 9, p, minus, 18, right parenthesis
(Choice D)
D
18(p-2)18(p−2)
After simplification, the equivalent expression is 18(p-2). So the option D is correct.
In the given question,
We have to find factor 18p-36 equivalent expressions.
The given option is
A. 3(9p-12)
B. 9(2p-4p)
C. 2(9p-18)
D. 18(p-2)
The given expression is 18p-36.
We simplify the given expression to find their equivalent expression.
To simplify the expression we take out the common term from both terms.
We can see that 18 is a common multiply of both number 18 and 36. SO we take out 18 from both terms.
Taking common 18
18p-36 = 18(p-2)
Hence, the equivalent expression is 18(p-2). SO the option D is correct.
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An earthworm accelerates from a speed of 0.01 m/s to 0.02 m/s over a distance of 0.9 m. How long did it take?
By using the formula of acceleration, it can be calculated that
Time taken by an earthworm to accelerate from a speed of 0.01 m/s to 0.02 m/s over a distance of 0.9 m is 59.88 s
What is acceleration?
At first, it is important to know about velocity
Distance travelled by a body per unit interval of time in a particular direction is called Velocity
The rate of change of velocity is called acceleration.
Acceleration is a vector quantity as the direction is taken into account.
Initial velocity of earthworm (u)= 0.01 m/s
Final velocity of earthworm (v) = 0.02 m/s
Distance (s) = 0.9 m
We know,
[tex]v^2 = u^2 + 2as\\0.02^2 = 0.01^2 + 2 \times a \times 0.9\\0.02^2 - 0.01^2 = 1.8a\\(0.02 + 0.01)(0.02 - 0.01) = 1.8a\\a = \frac{0.03 \times 0.01}{1.8}\\a = 0.000167 \ ms^{-2}[/tex]
Again,
v = u + at
0.02 = 0.01 + 0.000167[tex]\times[/tex] t
t = [tex]\frac{0.02 - 0.01}{0.000167}[/tex]
t = 59.88 s
Time taken by an earthworm to accelerate from a speed of 0.01 m/s to 0.02 m/s over a distance of 0.9 m is 59.88 s
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Visit each of the three credit reporting agencies and find an example of a credit report. For each, describe a different portion of the credit report
and how it is evaluated for credit worthiness.
Answer:
Doesn't make a lot of sense. Can you be more specific.
Step-by-step explanation:
The Creditworthiness is how a lender determines that you will default on your debt obligations, or how worthy you are to receive new credit
What are credit reporting agencies?Credit reporting companies, also known as credit bureaus or consumer reporting agencies, are companies that compile and sell credit reports.
Given are three credit reporting agencies.
Creditworthiness is how a lender determines that you will default on your debt obligations, or how worthy you are to receive new credit. Your creditworthiness is what creditors look at before they approve any new credit to you. The 3 C's of credit worthiness are Character, Capacity and Capital. Creditworthiness is determined by several factors including your repayment history and credit score.
Therefore, the Creditworthiness is how a lender determines that you will default on your debt obligations, or how worthy you are to receive new credit.
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How is Addy 4+ -4 similar to adding 4+4 how is it different use the words and models to explain
4- (+) (-4) is similar to 4+4 by the rule of addition in integers that is if Negative + Negative then Add the number and put the sign of greater number.
What is integer?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples. Three categories of integers exist: Zero (0) (0) Good integers (Natural numbers) Integer Negatives (Additive inverse of Natural Numbers).
The rules of addition in integers says,
- + - = +
by this,
4-(-4)=8
by concept of addition,
4+4=8
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if a volume of an object varies directly with its width and if the volume is 16, while the with is 4 what is k?
The value of k is 4.
What is Proportion ?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
Volume= 16
Width = 4
So, we can write the relation as
Volume= k (width)
k = Volume/ width
k= 16/4
k = 4
Hence, the value of k is 4.
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Please help with answers
The value of x is 11° and measure of other two angles are 80° and 117°
What is triangle?A triangle can be defined as a polygon which has three angles and three sides. The interior angles of a triangle sum up to 180°, and the exterior angles sum up to 360°.
Given that, the interior angles of the triangle are 37° and (3x+47)° and an exterior angle measures (5x+ 62)°
We know that the sum of two interior angles equals to the measure of an exterior angle,
Therefore, 37° + (3x+47)° = (5x+ 62)°
x = 11°
Hence, The value of x is 11° and measure of other two angles are 80° and 117°
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Find the first term and the common difference of the arithmetic sequence described. Give a recursive formula for the sequence. Find a formula for the nth term. 5 th term is 0; 45 th term is -120
The first term of the sequence is 12 and the common difference is -3.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.
Given that a formula for the nth term. 5th term is 0; 45th term is -120. The common difference is calculated as,
a₁ + d(5-1) = 0
a₁ + d(45 - 1) = -120
Solve the above equation,
a₁ + 4d = 0
-a₁ - 44d= +120
___________
-40d = 120
d = -3
The value of the first term is,
a₁ + 4d = 0
a₁ + 4 x -3 = 0
a₁ = 12
Therefore, the first term of the sequence is 12 and the common difference is -3.
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can anyone help with this
Answer:
bla blablablablabla
Step-by-step explanation:
blablablablablabla
marie bought 1/2 gallon of milk which she finished after 6 days if she drank the same amounteach day how many gallons a day did she drink
She drinks 1/12 gallons of milk each day
How to determine how many gallons a day did she drink?From the question, we have the following parameters that can be used in our computation:
Size of milk = 1/2 gallons
Number of days = 6 days
These parameters can be represented as
(x, y) = (6, 1/2)
The number of gallons a day she drinks can then be represented as the slope/unit rate and the unit rate is then calculated as
unit rate = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 0) and (6, 1/2)
Substitute the known values in the above equation
So, we have the following equation
Slope = (1/2 - 0)/(6 - 0)
Evaluate the quotient
Slope = 1/12
Hence, the number of gallons she drinks a day is 1/12
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Note one gallon of water equals 231 cubic inches. If Anna is going to clean the fish tank which measures 48 inches long by 11 inches wide by 35 inches high, how many gallons of water will it take to fill the fish tank?
If any one sees this question please help me answer it because I am having a lot of trouble.
It will take 80 gallons of water to fill the fish tank.
What is volume?The amount of space occupied by a three-dimensional object or region of space.
Given that, Anna is going to clean the fish tank, which measures 48 inches long by 11 inches wide by 35 inches high
The fish tank is cuboidal,
Volume of cuboid = length*width*height
Therefore, volume of fish tank = 48*11*35 = 18,480 in³
1 gallon = 231 in³
So, 18,480 in³ = 18,480/231 gallons = 80 gallons
Hence, Volume of tank = 80 gallons
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Find which are the errors and solve correctly the problem:
Answer:
[tex]f^{-1}(y) = \sqrt{x-5}[/tex]
Step-by-step explanation:
You have to switch the f(x) to x and the x's to y's
[tex]x = y^2 + 5[/tex]
[tex]\sqrt{x-5} = \sqrt{y^2}[/tex]
[tex]y = \sqrt{x - 5}[/tex]
Let f(x) = 4 + 2x and g(x) = 1/2x + 2 . Find f(g(x)) . Simplify the expression.
f(g(x)) = ___
Answer: x + 8
Step-by-step explanation:
[tex]f(g(x))=f(\frac{1}{2}x+2) = 4+2(\frac{1}{2}x+2) = 4+x+4 =x +8[/tex]
Simplify the expressions
a) (30+10 ÷ 2)-5-10
b) (30 + 10) = 2.5-10
c) 30 + 10 = 2(5-10)
(d) 30+ (10 ÷ 2·5)-10
The solution of the expressions are
(a) (30+10 ÷ 2)-5-10 = 20
(d) 30+ (10 ÷ 2·5)-10 = 24
What is meaning of expressions?
An expression is a combination of operations, variables, and numbers.
What is BODMAS rule?
According to the BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by 'order' (that means powers and roots, etc.), then division, multiplication, addition and subtraction from left to right.
Given expression is
(30+10 ÷ 2)-5-10
Applying BODMAS rule:
= (30 + 5) - 5 - 10
= 35 - 5 - 10
= 30 - 10
=40
Second expression is:
30+ (10 ÷ 2·5)-10
= 30 + (10 ÷ 10) - 10
= 30 + 1 - 10
= 31 -10
= 21
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please help write the reasons that are needed to complete the proof in the picture
Answer:
a. Given
b. thru any 2 points there exists a line (you can draw a line)
c. Definition of Regular Polygon
d. Definition of Regular Polygon
e. Given
f. Def of Midpoint
g. SAS: Side-Angle-Side congruence
h. CPCTC - Corresponding Parts of Congruent Triangles are Congruent
i. Definition of Regular Polygon
j. Reflexive
k. SSS: Side-Side-Side congruence
l. CPCTC
Step-by-step explanation:
I encourage you to look up all of the above reasons to get a better understanding of what they are!!
Willy is an avid fisherman of the world. As he travels, he goes fishing 2 times on every mainland Country he visits and goes fishing 5 times on every Island he visits.
As far as he remembers, Willy went fishing 65 times in the total of the 25 unique Countries and Islands he visited.
How many Countries and Islands did Willy visit? (Where and represent the countries and islands)
The number of mainland countries is 20 and the number of island countries is 5 countries that Willy visited.
How to calculate the value?Let the number of mainland be represented by m
Let the number of island be represented by x.
This will be illustrated as:.
m + x = 25 .... i
2m + 5x = 65 .... ii
From equation i, m = 25 - x.
Put this into equation ii
2m + 5x = 65
2(25 - x) + 5x = 65
50 - 2x + 5x = 65
3x = 65 - 50
3x = 15
Divide
x = 15 / 3
x = 5
Island countries = 5
Since m + x = 25
m = 25 - 5 = 20
Mainland countries = 20
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Convert the expression (10) 1/3 to radical form.
Answer:
cubic root 10 power 1
Step-by-step explanation:
Apply the rule
x
m
n
=
n
√
x
m
to rewrite the exponentiation as a radical.
3
√
10
1
Anything raised to
1
is the base itself.
3
√
10
The result can be shown in multiple forms.
Exact Form:
3
√
10
Decimal Form:
2.15443469
…
Donna used a total of 2 1/6 gallons of gas while driving her car. Each hour she was driving, she used 7/10 gallons of gas. What was the total number of hours she was driving?
The total number of hours Donna used driving is 3 2/21 hours
What is rate?A rate is a special ratio in which the two terms are in different units. For example, For 1 hour Donna is using 7/10 gallons of fuel while driving.
The two quantities there are time in hours and the quantity of fuel used in gallons.
If Donna used 7/10 gallon for 1 hour
then 1 gallon will last for 1÷7/10= 1× 10/7= 10/7
Therefore for 2 1/6 gallon = 10/7×2 1/6= 10/7×13/6
= 3 2/21 hours
Therefore the total number of hours used driving with 2 1/6 gallons is 3 2/21
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