The difference between the price of an electric razor in 1983 and the cost of an electric razor when the cpi is 207, to the nearest cent is given by: Option D: $6.88
What is consumer price index?The consumer price index is the new cost of market basket in terms of percentage of old cost of market basket.
[tex]CPI_t[/tex] = consumer price index in current period[tex]C_t[/tex] = cost of market basket in current period[tex]C_0[/tex] = cost of market basket in base periodThen, we have:
[tex]CPI_t = \dfrac{C_t}{C_0} \times 100[/tex]
For this case, we're given that:
In 1983, CPI of considered razor = 185, and price = $57.81In some other year, the CPI of considered razor = 207, and price = $ ?? (to find).Let the base price of the razor in some base period be [tex]C_0[/tex]
Then, for year 1983, we get:
[tex]CPI_t = \dfrac{C_t}{C_0} \times 100\\\\185= \dfrac{57.81}{C_0} \times 100\\\\C_0 \approx 31.248 \: \text{(in dollars)}[/tex]
Now for the year when CPI is 207, let the price of th razor be $x, then we get:
[tex]CPI_t = \dfrac{C_t}{C_0} \times 100\\\\207 \approx \dfrac{x}{31.248} \times 100\\\\x \approx 64.683 \: \text{(in dollars)}[/tex]
The difference between the two prices is:
[tex]d \approx 64.683 - 57.81 = 6.87 \approx 6.88\: \text{(in dollars)}[/tex]
Thus, the difference between the price of an electric razor in 1983 and the cost of an electric razor when the cpi is 207, to the nearest cent is given by: Option D: $6.88
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Answer:
D
Step-by-step explanation:
Simplify −4(x+1)+6x . Write your answer in factored form.
Answer:
2(x - 2)
Step-by-step explanation:
- 4(x + 1) + 6x ← distribute parenthesis by - 4
= - 4x - 4 + 6x ← collect like terms
= 2x - 4 ← factor out 2 from each term
= 2(x - 2)
=================================================
Let's simplify this expression.
The first step is to use the distributive property, which states:-
[tex]\bigstar{\boxed{a(b+c)}[/tex]
Simplify:-
[tex]\bigstar{\boxed{-4(x+1)}[/tex]
[tex]\longmapsto\sf{-4x-4}[/tex]
Add 6x:-
[tex]\longmapsto\sf{-4x+6x-4}[/tex]
Combine Like Terms:-
[tex]\longmapsto\sf{2x-4}[/tex]
Now, we should write our answer in factored form, so we factor 2 out:-
[tex]\longmapsto\sf{2(x-2)}[/tex]
=============================================
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
Make x the subject a(x-a)=a^2
Answer:
x = 2a
Step-by-step explanation:
a(x - a) = a² ( divide both sides by a )
x - a = a ( add a to both sides )
x = 2a
Answer:
x = 2a
Step-by-step explanation:
Given equation
[tex]\sf a(x-a)=a^2[/tex]
Make x the subject
expand brackets:
[tex]\sf \implies ax-a^2=a^2[/tex]
Add [tex]\sf a^2[/tex] to both sides:
[tex]\sf \implies ax-a^2+a^2=a^2+a^2[/tex]
[tex]\sf \implies ax=2a^2[/tex]
Divide both sides by a:
[tex]\sf \implies \dfrac{ax}{a}=\dfrac{2a^2}{a}[/tex]
[tex]\sf \implies x=2a[/tex]
Final solution
[tex]\sf x=2a[/tex]
NOCTI MATH REVIEW
all
1) if the cost of one case of fresh pineapples is $14.95 for a case of 6, and the
calculated waste factor is 15 percent, what is the actual cost of each pineapple?
Using proportions, it is found that the actual cost of each pineapple is of $2.12
What is a proportion?A proportion is a fraction of a total amount.
In this problem, considering that the waste factor is of 15%, the total price should be of:
P = 0.85 x $14.95 = $12.7075.
For a case of 6 pineapples, hence the price of each is given by:
Pp = $12.7075/6 = $2.12.
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The actual cost of each pineapple with a waste factor of 15% is $12.71
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The cost of one case of fresh pineapples is $14.95 and the calculated waste factor is 15 percent. Hence:
Actual cost = 14.95 - 15% of 14.95 = $12.71
The actual cost of each pineapple with a waste factor of 15% is $12.71
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Brittany deposited $3,000 in a new account at her bank.
The bank pays 6% interest compounded annually.
Brittany makes no additional deposits or withdraws.
What will be the balance of the account at the end of 3 years? (Include Decimal with the cents; No Commas)
The total amount accrued, principal plus interest, with compound interest on a principal of $3,000.00 at a rate of 6% per year compounded 1 times per year over 3 years is $3,573.05.
Compound InterestGiven Data
Principal = $3000Rate = 6%Time = 3 yearsA = P + I where
P (principal) = $3,000.00
I (interest) = $573.05
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 6/100
r = 0.06 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 3,000.00(1 + 0.06/1)^(1)(3)
A = 3,000.00(1 + 0.06)^(3)
A = $3,573.05
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- 13/14 divided -26/4 im soo confujsed with this lesson btw this is for math review just
so u know
A fair coin is tossed 3 consecutive times. What is the probability that the result of the first toss is heads and the results of the next two are tails?
A: 1/8
B: 1/6
C: 1/2
D: 1/4
Answer: a). 1/8
Step-by-step explanation:
If the coin is fair, then the odds of getting heads or tails should be equal, 12.
Then 3 tosses of tails will have a chance of 12⋅12⋅12=18.
Let m and n be two positive integers greater than 1 . If
[tex] \displaystyle\sf \lim_{a\to 0 }\bigg\lgroup \dfrac{e^{\cos(a^n)}-e}{a^m}\bigg\rgroup =-\bigg\lgroup \dfrac{e}{2}\bigg\rgroup [/tex]
Then the value of [tex]\dfrac{m}{n}[/tex] is ?
A mirror is in the shape of an isosceles right triangle and has a hypotenuse length of seven times the square root of two. What is the length of one of the legs?
square root of two.
3.5
seven times the square root of two.
7
The length of one of the legs of an isosceles right triangle and has a hypotenuse length of seven times the square root of two is 7 units.
What is an Isosceles triangle?Isosceles triangles are triangles that has two of it sides equal to each other. The base angles of an isosceles triangle are equal.
The isosceles triangle is also a right angle triangle. The hypotenuse is the longest side of a right angle triangle.
Therefore,
hypotenuse = 7(√2)
let the length of the other legs = x
Therefore, using Pythagoras theorem
c² = a² + b²
(7(√2))² = x² + x²
49 × 2 = 2x²
98 = 2x²
x² = 98 / 2
x = √49
x = 7 units
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Pls help me thank you God bless
Answer:
8
Step-by-step explanation:
10/3 divided by 5/12
10/3 multiple 12/5
So the 3 and 12 will cross out same as 10 and 5 then we will get 8 as an answer
A composite figure is comprised of a semicircle, trapezoid, and 2 rectangles. How can you decompose the composite figure to determine its area? as a circle, three rectangles, and a triangle as a circle, a trapezoid, and four triangles as a semicircle, three rectangles, and a square as a semicircle, a trapezoid, and two rectangles.
The way we can decompose the composite figure to determine its area is given by: Option D: as a semicircle, a trapezoid, and two rectangles.
How to calculate the surface area of a composite figure?Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc.
When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.
Thus, we have:
[tex]\text{Area of composite figure} = \sum (\text{Area of composing figures})[/tex]
That ∑ sign shows "sum"
Since the considered composite figure consists of a semicircle, trapezoid, and 2 rectangles, so we can find its area by their use.
Thus, the way we can decompose the composite figure to determine its area is given by: Option D: as a semicircle, a trapezoid, and two rectangles.
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Answer:
d
Step-by-step explanation:
i just finished the test
STOP WITH THE LINKS! please? Help? NO LINKS!?????
Answer:
The answer is 24
just multiply 6 and 4 together
The surface areas of two similar figures are given. The volume of the larger figure is given. Find the volume of the smaller figure.
SA= 576 in^2
SA= 1024 in^2
V= 2240 in^3
Answer:
945 in²
Step-by-step explanation:
The scale factor of two figures is k.
The scale factor of their surface areas is k².
The scale factor of their volumes is k³.
1024 in² / 576 in² = 16/9 = k²
k = √(16/9) = 4/3
k³ = (4/3)³
k³ = 64/27
2240 in³ × 27/64 = 945 in²
The school cafeteria sells two kinds of wraps: vegetarian and chicken. The vegetarian wrap costs $1.00 and the chicken wrap costs $1.90. Today they made $78.60 from the 57 wraps sold. How many of the wraps so ld were vegetarian?
PointM is the midpoint of AB. if the coordinates of A are (6,-4) and the coordinates of M are (4,2), what are the coordinates of B?
Ok here is the fastest way to do this:
Since M is the midpoint of AB, and the x-value of M is smaller than A, this means that M is to the left of A.
Subtract x-value of M from x-value of A: 6 - 4 = 2
We know that B is also to the left of M. So you subtract 2 from the x-value of M: 4 - 2 = 2
Notice that of the choices below, only one answer has the x-value of 2.
B
Candice is putting together a business outfit. There are 6 pairs of pants and 2 dress shirts to choose from. How many different outfits can Candice put together?
Do u guys have apps for solving geometry/ triangle problems????
This is the best I could find
Some recommended apps for solving geometry and triangle problems are "Ge oGebra," "De smos Geometry," and "Ma thway."
Ge oGebra: Ge oGebra is a versatile mathematics app that covers various topics, including geometry and triangles. It provides interactive tools for constructing and analyzing geometric shapes, making it a valuable resource for visualizing and understanding different properties and theorems related to triangles.
De smos Geometry: While De smos is primarily known for its graphing capabilities, the De smos Geometry app also offers tools for creating and manipulating geometric shapes, including triangles. It can help users explore and solve various triangle-related problems.
M athway: M athway is a comprehensive math problem-solving app that covers a wide range of topics, including geometry and triangles. Users can input specific problems, and the app provides step-by-step solutions, making it a helpful tool for both learning and verifying answers to geometry and triangle problems.
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------------The given question is incomplete, the complete question is:
"What are some recommended apps for solving geometry and triangle problems?"-------------
Find the unknown coordinate for each reflection.
Figure ABCDE is reflected across the y-axis to
form figure A'B'C'D’E
Answer:
A'=(-3,6)
B'=(-5,5)
C'=(-4,2)
D'=(-2,2)
E'=(-1,4)
Step-by-step explanation:
Simply keep the y coordinate the same on all of the points on the preimage and make the x coordinates negative.
Hope this helps!!!
Find the missing side of a right triangle if side a=7 and side b=11.
Step-by-step explanation:
c² = a² + b²
c² = 7² + 11²
c² = 49 + 121
c² = 170
now u have to square root it
c² = 170
c = 13
A survey of 600 people was conducted to find thier favorite book genre. The survey results are shown in the table o the right. Adventure:102, Comedy: 114, Mystery:84, Romance:132
Part A: How many people responed with a genre other than one of the genres listed?
Part B: Develop a complete probabiliy model to describe all possible reasons, including 'other' as one response.
PLEASE HELP ASAP
The probability shows that the number of people who responed with a genre other than one of the genres listed is 168.
How to calculate the probability?The number of people who responded with a genre other than one of the genres listed will be:
= 600 - (102 + 114 + 84 + 132)
= 600 - 332
= 168
The probability for adventure = 102/600 = 0.17
The probability for comedy = 114/600 = 0.19.
The probability for mystery = 84/600 = 014
The probability for romance = 132/600 = 0.22
The probability for others = 168/600 = 0.28
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Write an equivalent expression to
(x+7)+3y
Answer:
2x+14+6y
Step-by-step explanation:
What is the difference between a metric and a norm?
Answer:
A norm and a metric are two different things. .
Step-by-step explanation:
The norm is measuring the size of something, and the metric is measuring the distance between two things. A metric can be defined on any set . It is simply a function which assigns a distance (i.e. a non-negative real number) to any two elements .
The major difference between the matric and norms is that metric is a unit of measurement that measures the distance between two objects. The size of a single thing is measured by a norm.
What is measurement?It is defined as the numerical quantity that gives an idea about an object's size, length, width, and many more. It can be used to compare two objects.
The major difference between metrics and norms is as follows:
A metric is a unit of measurement that measures the distance between two objects. The size of a single thing is measured by a norm.Metrics may be expressed on almost anything, however, a norm can only be defined on vector spaces but since the definition of a norm requires that the things measured by the norm be added and scaled.Thus, the major difference between the matric and norms is that metric is a unit of measurement that measures the distance between two objects. The size of a single thing is measured by a norm.
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Not entirely sure….some help please?
Answer:
55°
Step-by-step explanation:
The definition of an isosceles triangle is that there are two sides of equal length and one side of a different length. Because two sides have the same length, their respective angles have the same measure. For example, side BC goes with angle A; because it is the same length as side AB which goes with angle C, angles A and C are the same. Just set the angles equal to each other and begin solving an algebraic expression as shown here:
[tex]3x+40=x+50\\3x-x+40 = x-x+50\\2x+40=50\\2x+40-40=50-40\\2x=10\\\frac{2x}{2} =\frac{10}{2} \\x=5[/tex]
Now that you know what x is equal to, plug it into angle A's equation.
[tex]3(5)+40\\15+40\\55[/tex]
Angle A is equal to 55°
If the radius of a circle is x cm. what is the length of it's circumferences?
Answer:
44/7x
Step-by-step explanation:
circumference of circle= 2πr
=2×22/7×x
=44/7x
Identify the area of the rhombus.
Answer:
A=130cm2
Step-by-step explanation:
13x10=130
Linear relationships are important to understand because they are common in the world around you. For example, all rates and ratios are linear relationships. Miles per gallon is a common rate used to describe the number of miles a car can travel on one gallon of gasoline. Dollars per gallon, or the price of gas, is a linear relationship as well. What other relationships can you think of that are linear? How do they affect your everyday life?
Two other examples of linear relationships are changes of units and finding the total cost for buying a given item x times.
Other examples of linear relationships?
Two examples of linear relationships that are useful are:
Changes of units:
These ones are used to change between units that measure the same thing. For example, between kilometers and meters.
We know that:
1km = 1000m
So if we have a distance in kilometers x, the distance in meters y is given by:
y = 1000*x
This is a linear relationship.
Another example can be for costs, if we know that a single item costs a given quantity, let's say "a", then if we buy x of these items the total cost will be:
y = a*x
This is a linear relationship.
So linear relationships appear a lot in our life, and is really important to learn how to work with them.
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In the figure shown, MR←→− is parallel to ST←→. If m∠SPR = 126°, what is m∠PST?
Answer:
its 54
Step-by-step explanation:
i got it right on time4learning
Jessica is going to paint her
patio. It is made up
of two
rectangles. One measures
7ft. x 4 ft. x 5ft. and the other
measures 10ft. x 8ft. x 6ft.
What is the total area of her
patio?
Answer:
514 square feet
Step-by-step explanation:
2(7×4+4×5+5×7)+2(10×8+8×6+10×6)
=2*83 +2*188
=166+376
=542 square feet
7*4=28
542-28=514 square feet
Answer:
640ft
Step-by-step explanation:
7ft×4ft×5ft = 160
10ft×8ft×6ft=480
Add them together
480+160=640 so the answer is 640ft
10. Which expression is equivalent to 4
(4-3)*(4042)* ?
பமccee
A.
4-4
В.
4 3
C
413
D.
4 14
Answer:
C Because the evolution of wasted numbers is incorrect
PLEASE HELP AS SOON AS EVER I NOYL HAVE 5 MINS WILL GIVE BRAINLY!
Answer: E
Step-by-step explanation:
Side triangles; 6.
(3x4/2=6)
There are 2 triangles.
Back of triangle thing is 24.
Top area is 40.
Bottom area is 32.
12+24+40+32
Answer is 108.
I THINK that is the correct answer. I am so so sorry if it isn't.
Answer:
E- 108 in squared. Hope this helps!
Step-by-step explanation:
Ash company reported sales of $580,000 for year 1, $630,000 for year 2, and $680,000 for year 3. Using year 1 as the base year, what is the revenue trend percent for years 2 and 3??
Answer:
Year 2: 109.4%
Year 3: 118.9%
Step-by-step explanation:
Given;Ash company reported sales of $580,000 for year 1$630,000 for year 2, $680,000 for year 3.Now,
For the revenue trend percent for year 2
Year 2: $580,000 / $530,000 × 100 = 109.4%
For the revenue trend percent for year 3
Year 3: $630,000 / $530,000 × 100 = 118.9%
Thus, The answer is 109.4% and 118.9%.
-TheUnknownScientist 72