As a percentage, a card at random 5, 6, 7, 8 9, 7.5, 6.42, 5.62. Per cent is derived from the Latin adverbial phrase per centum, which means "by the hundred." The Latin phrase made its way into English in the 16th century.
What is meant by percentage?A percentage is a number or ratio that is expressed as a fraction of one hundred. The percent sign, "%," is commonly used, but the abbreviations "pct.", "pct.," and sometimes "pc" are also used. A percentage is a number with no dimensions; it has no unit of measurement. Percentage = (Original number/Another number) x 100 is the formula for calculating the percentage of one number from another. A percentage is a value or ratio that represents a fraction of 100 in mathematics. Percentage means one hundred percent. There are no units in it. A percentage is a number that tells us how much out of 100 we are talking about, and it can also be written as a decimal or a fraction - three for the price of one.Therefore,
45/5 = 9
45/6 = 7.5
45/7 = 6.42
45/8 = 5.62
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Ken spends $344.76 before tax at a hardware store. If the sales tax rate in his city is 7.5%, what is the total cost of his purchase? Round to the nearest cent if necessary.
Answer:
$370.62
Step-by-step explanation:
Ken spends $344.76 before tax at a hardware store. If the sales tax rate in his city is 7.5%, what is the total cost of his purchase? Round to the nearest cent if necessary.
7.5% = 0.075
0.075 * $344.76 = $25.857 in tax so:
cost + tax
$344.76 + $25.857 = $370.617
rounded: $370.62
Last year, Leila opened an investment account with $8800. At the end of the year, the amount in the account had decreased by 6%.
Answer:
The new value is $8,272
Step-by-step explanation:
8800 x (1 - 0.06) = 8272
kayla used her cell phone for four days . her average calling time was 130 minutes each day .suppose that kayla used the phone for m minutes on fifth day . write an algebraic expression for the average number of minutes she spent on the phone over five days.
Answer:
130-60m
Step-by-step explanation:
The values of x and y vary directly
and one pair of values are given.
Write an equation that relates x
and y.
x = 2, y = 5
[?]
y =
X
The equation that relates x and y is given as y = 2.5x
What is direct variation in mathematics?The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a.
The formula for direct variation is in the form of
y = kx
where we have the value of y = 5, the value of x = 2
we have to put this in the formula above
5 = 2k
to get the value of k we would have to divide through by 2
k = 5 / 2
k = 2.5
Hence we would have y = 2.5x
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Determine the length of the line segment shown. graph of line segment from negative 6 comma negative 5 to 0 comma 3 100 units 25 units 10 units 8 units
The length of the line segment will be 10 units.
What is Distance?
The distance between two points (x₁ , y₁) and (x₂, y₂) is defined as;
D = √( y₂ - y₁)² + (x₂ - x₁)²
Given that;
Two endpoints of the line segment are (6, -5) and (0, 3).
Now,
The length of the line segment is distance between two endpoints (6, -5) and (0, 3).
So, The distance between two endpoints (6, -5) and (0, 3) is calculated as;
D = √(0 - 6)² + (3 - (-5))²
D = √36 + 64
D = √100
D = 10 units
Thus, The length of the line segment will be 10 units.
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2. Sketch a list or tree diagram to represent
the sample space of flipping a penny, a nickel,
and a dime one time each.
There are total 8 possible outcomes if we flip penny , nickel , dime together. We can show these outcomes by the Tree diagram or by listing each outcome separately.
The one way to create an organized list to represent the sample space
Penny NICKEL DIME
H H H
H H T
H T H
H T T
T H H
T H T
T T H
T T T
The another way to create an organized list to represent the sample space is to make a tree diagram .
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Find sin 2x, cos 2x, and tan 2x from the given information.
tan x=-1/5
sin 2x =
cos 2x =
tan 2x =
The values of the different trigonometric functions are as follows:
2x = -5/13Cos 2x = 12/13Tan 2x = -5/12.What is trigonometry?The study of relationships between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations.Now, solve using trigonometry as follows:
tan x=-1/5Now, we have:
sin 2x= (2tan x)/(1 + tan²x)=2*-1/5/(1+(-1/5)²)=-2/5(1+1/25)=-2/5/(26/25)=-2/5*25/26=-10/26=-5/13Then, calculate as follows:
cos 2x= (1 - tan²x)/(1 + tan²x)=(1-(-1/5)²)/(1+(-1/5)²)=(1-1/25)/(1+1/25)=24/25/26/25=24/25*25/26=24/26=12/13Now, we obtain:
tan 2x= 2tan x/(1-tan² x)=2*-1/5/(1-(-1/5)²)=-2/5/(1-1/25)=-2/5/24/25=-2/5*25/24=-10/24=-5/12Therefore, the values of the different trigonometric functions are as follows:
2x = -5/13Cos 2x = 12/13Tan 2x = -5/12.Know more about trigonometry here:
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PLS HELP ME ASAP IM SO CONFUSED?
Basically, Least Common Multiple(LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers. GCF/HCF ( Greatest/Highest Common Factor) is the highest number that divides exactly into two or more numbers.
Answers:
9) LCM of 36, 3, 12 = 36
GCF of 36, 3, 12 = 3
10) LCM of 6, 54, 12 = 108
GCF of 6, 54, 12 = 6
11) LCM of 16, 8, 12 = 48
GCF of 16, 8, 12 = 4
A street light is mounted at the top of a 15-ft-tall pole. a man 6 ft tall walks away from the pole with a speed of 6 ft/s along a straight path. How fast is the tip of his shadow moving when he is 50 ft from the pole?
The tip of his shadow moving when he is 50 ft from the pole is 10ft/s
What is meant by differentiation?The practical approach of differentiation may be performed utilizing just algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.
The theory offers the following fundamental guidelines for differentiating the sum, product, or quotient of any two functions f(x) and g(x) whose derivatives are known (where a and b are constants) for functions constructed of combinations of these types of functions
I assume the man and pole are standing straight up, which means the 2 triangles are similar to each other.
(y-x)/y =6/15
15(y-x)=6y
9y=15x
y=(5/3)x
Differentiating both sides with respect to t,
dy/dt=(5/3)dx/dt
We know that, dx/dt= 6 ft/s
((5/3)*6=10 ft/s
Therefore, the tip of his shadow moving when he is 50 ft from the pole is 10ft/s
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A boat sails 285 miles south and then 132 miles west. What is the magnitude of the boats resultant vector?
The magnitude of the boats resultant vector is 314.1 mi
What is a vector?A vector is a physical quantity that has both magnitude and direction.
What is a resultant vector?A resultant vector is the sum of two or more vectors.
How to find the boats resultant vector?Since the boat sails 285 miles south and then 132 miles west, we have that its first direction vector is r = (285 mi)j. Also, its direction vector west is r' = -(132 mi)i
So, the resultant vector R = r + r'
= (285 mi)j + (132 mi)i
= (132 mi)i + (285 mi)j
So, the magnitude of the resultant vector is R = √(r² + r'²)
So, substituting thevalues of the variables into the equation, we have
R = √(r² + r'²)
R = √((285 mi)² + (132 mi)²)
R = √(81225 mi² + 17424 mi²)
R = √(98649 mi²)
R = 314.08 mi
R ≅ 314.1 mi
So, the resultant vector is 314.1 mi
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Alton estimated that 230 people attended the band concert. The actual count for attendance was 200 people. Find the percent of error. 13% 15% 30% 86%
The percent of error is 15%. The correct option is B.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Alton estimated that 230 people attended the band concert.
The actual count for attendance was 200 people.
To find the percent of error:
230 - 200 / 200
= 30 / 200
= 0.15
0.15 decimal to the percentage is 15%.
Therefore, the error is 15%
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4y=16x-4 in standard form?
The standard form of linear equation is 4x - y = 1.
What is the standard form of a linear equation?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).
The slope intercepts form a linear equation is y = mx + c, where m is the slope and c is y-intercept of the line.
Given linear equation is:
4y=16x-4
Subtract 16x from both sides:
4y - 16x = -4
Divide both sides by -4
-y + 4x = 1
4x - y = 1
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i’m stuck on c and e
Evaluate y(x ÷ 2) if x is 20 and y is 10
Answer:
100
Step-by-step explanation:
x = 20
x ÷ 2
= 20 ÷ 2
= 10
y = 10
y ( x ÷ 2 )
= 10 x 10
= 100
Mr. Dunston and Mr. Dolland spent $45 all
together. Mr. Dunston and Ms. Campbell
spent $65 all together. If Ms. Campbell spent
3 times as much as Mr. Dolland, how much
did Mr. Dunston spend?
Mr. Dunston spend is $35.
Given:
Mr. Dunston and Mr. Dolland spent $45 all together.
Mr. Dunston and Ms. Campbell spent $65 all together.
If Ms. Campbell spent 3 times as much as Mr. Dolland.
Let x , y , z be spend of dunston ,dolland and campbell.
x + y = 45
x + z = 65
z = 3*y
x + 3y = 65
on substracting x + y = 45 and x + 3y = 65 we get,
x + y - x - 3y = 45 - 65
-2y = -20
2y = 20
y = $10.
substitute y value,
x + 10 = 45
x = 45 - 10
x = $35
Therefore Mr.Dunston spend $35.
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Which expression is equivalent to the expression below?
2.1 + (–3.7h) + 1.9h – 1.4
3.5 – 5.6h
−1.1h
0.7 + 1.8h
0.7 – 1.8h
Using the simplification, the equivalent expression of 2.1+(–3.7h)+1.9h–1.4 is 0.7–1.8h.
In the given question we have to find the equivalent expression of the given expression.
The given expression is 2.1+(–3.7h)+1.9h–1.4
Now solving the given expression to find the equivalent expression.
Now solving the expression
=2.1 + (–3.7h) + 1.9h – 1.4
Firstly simplifying the bracket
=2.1–3.7h+ 1.9h – 1.4
=(–3.7h+ 1.9h)+(– 1.4+2.1)
= –1.8h + 0.7
We can write it as
=0.7–1.8h
Hence, the equivalent expression of 2.1+(–3.7h)+1.9h–1.4 is 0.7–1.8h.
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Please help me I need help
Answer:
p = 20
Step-by-step explanation:
[tex]\rm \implies \dfrac{p}{2} - 9 = 1 \\ \\ \rm \implies \dfrac{p}{2} - 9 + 9 = 1 + 9 \\ \\ \rm \implies \dfrac{p}{2 } = 10 \\ \\ \rm \implies \dfrac{p}{ \cancel{2}} \times \cancel{2} = 10 \times 2 \\ \\ \rm \implies p = 20[/tex]
In a raffle, 100 tickets are sold. George buys 10 tickets Julia by 5 tickets. There is one winning ticket. Find a probability that
a. George will win
b. jullia will win
Probability of (a) George winning is 0.1
(b) Julia winning is 0.05
Given in question,
Total ticket sold = 100
George bought tickets = 10
Julia bought tickets = 5
Winning ticket = 1
Selecting 1 ticket from 100 = [tex]\left[\begin{array}{ccc}100\\1\\\end{array}\right][/tex]
= 100
Selecting 1 ticket from 10 = [tex]\left[\begin{array}{ccc}10\\1\\\end{array}\right][/tex]
= 10
Selecting 1 ticket from 5 = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]
= 5
Probability = favorable outcome/total outcome
Probability of George winning = [tex]\frac{10}{100}[/tex]
= 0.1
Probability of Julia winning = [tex]\frac{5}{100}[/tex]
= 0.05
Hence, probabilities are 0.1 and 0.05 respectively.
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What is the probability of rolling a number less than or equal to 3 on a standard six-sided die
The probability of rolling a number that is less than 3 is P = 1/2.
How to find the probability?
A standard six-sided die has the following outcomes:
{1, 2, 3, 4, 5, 6}
The outcomes that are less than or equal to 3 are:
{1, 2, 3}
Assuming all the outcomes have the same probability, the probability of rolling a number less than or equal to 3 on a standard six-sided die will be equal to the quotient between the number of outcomes that meet the condition and the total number of outcomes.
It will give:
P = 3/6 = 1/2 = 0.5
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factor and graph the equation -0.01x² +0.5x
The graph and factor to the given equation are x= 50 or x=0.
What is equation?
An equation may be a formula in arithmetic that expresses the equality of 2 expressions by connecting them with the sign =.
Main body:
I am assuming the equation as : -0.01[tex]x^{2}[/tex] + 0.5x =0
Now first removing the decimal from the equation ,
-[tex]x^{2}[/tex]/100 + 5x/10 = 0
-[tex]x^{2}[/tex] + 50 x = 0
switching signs , we get
[tex]x^{2}[/tex] - 50x= 0
taking x as common
x(x-50) =0
so either x = 0
or
x- 50 = 0
x =50
Hence the value of x are 0 or 50.
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A local grocery store offers 3 brands of laundry detergent. Brand A costs $14.99 and contains 40 fluid ounces of detergent. Brand B costs $19.99 and contains 50 fluid ounces of detergent. Brand C costs $21.99 and contains a half-gallon of detergent. Which of the detergents has the best value?
Answer:
$ 52.63
Step-by-step explanation:
The brand C detergent has the best value.
What is Arithmetic?The mathematical branch known as arithmetic deals with the study and application of numbers, their relationships, and mathematical observations.
As per the given data in the question:
The information regarding the quantity and cost of 3 detergents is given in the question.
We have to find out which detergent is the most economical.
The detergent with the lowest cost/quantity will be the most economical.
For Brand A
Cost = $14.99
Quantity = 40 ounces
cost/quantity = 14.99/40 = 0.374 dollar/ounce
For Brand B
Cost = $19.99
Quantity = 50 ounces
cost/quantity = 19.99/50 = 0.399 dollar/ounce
For Brand C
Cost = $21.99
Quantity = 1/2 gallon = 64 ounces
cost/quantity = 21.99/64 = 0.343 dollar/ounce
The brand C detergent has the best value.
Hence, The brand C detergent has the best value.
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The area of a rectangular garden is 224 square meters. The width is 6 meters longer than one-half of the length. Find
the length and the width of the garden. Use the formula, area = length • width.
Pls help
[tex]\textit{area of a rectangle}\\\\ A=Lw ~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ A=224\\ w=\stackrel{\textit{half-length plus 6}}{\frac{L}{2}+6~\hfill } \end{cases}\implies 224=L\left( \cfrac{L}{2}+6 \right)\implies 224=\cfrac{L^2}{2}+6L[/tex]
[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2(224)=2\left( \cfrac{L^2}{2}+6L \right)}\implies 448=L^2+12L \\\\\\ 0=L^2+12L-448\implies 0=(L-16)(L+28)\implies \boxed{L= \begin{cases} -28\\\\ 16 ~~ \textit{\LARGE \checkmark} \end{cases}} \\\\\\ \stackrel{\textit{since we know that}}{w=\cfrac{L}{2}+6}\implies w=\cfrac{16}{2}+6\implies \boxed{w=14}[/tex]
now, let's notice, "L" has two valid values but for this case "L" cannot be negative.
estimate each sum or difference.
74/10+42/5
The sum of the fraction 74/10 + 42/5 is 15 4/5.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, the fraction will be illustrated as:
= 74/10 + 42/5
Change to mixed numbers
= 7 4/10 + 8 2/5
= 7 4/10 + 8 4/10
= 15 8/10
= 15 4/5
The value is 15 4/5.
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Simplify (5-3)2+8\2x3-7+1
Answer: 12/0
Step-by-step explanation: (5−3)(2)+8
(2)(3)−7+1
=
(2)(2)+8
(2)(3)−7+1
=
4+8
(2)(3)−7+1
=
12
(2)(3)−7+1
=
12
6−7+1
=
12
−1+1
=
12
0
=
1
0
;)
A movie producer wants to cast a dog and a cat in her next film, and the talent agency
has 18 dogs and 24 cats to choose from.
How many different dog-cat options are possible for the producer? (please explain)
Step-by-step explanation:
there are 18 dogs to choose 1 dog.
therefore, these are 18 options.
for each of these 18 options there are 24 cats to choose from.
so, altogether, there are
18×24 = 432
dog-cat options.
There are are 432 ways to choose dog-cat options are possible for the producer.
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.
Total Number of Dogs= 18
Total Number of cats= 24
so, the number easy to select
= 18 x 24
= 432
Hence, there are 432 ways to choose dog-cat options are possible for the producer.
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The midpoint of AB is M (5, 1). If the coordinates of A are (3,6), what are
the coordinates of B?
After raining for 3/4 of an hour, a rain gauge 2/5 of the way full if it continued to rain at the same rate for 15 more minutes what fraction of the rain gauge will be filled
When it rains at the same rate for 15 more minutes, the fraction of the rain gauge that will be filled is 2/15.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.
From the information, after raining for 3/4 of an hour, a rain gauge 2/5 of the way full. It's important to note that 3/4 is (3 × 1/4).
Therefore, we will divide 2/5 by 3 and this will be:
= 2/5 ÷ 3
= 2/5 × 1/3
= 2/15
This is the value of the rain gauge.
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Divide the monomial denominator by writing the fraction as the sun or difference of fractions.
Division of the monomial denominator by writing the fraction as the sum or difference of fractions is [tex]8x+8 - \frac{1}{x^{3}}[/tex].
What is a polynomial equation?
Polynomial long division is a generalized variant of the well-known arithmetic operation known as long division. It is an algorithm for dividing a polynomial by another polynomial of the same or lower degree.
We have,
[tex]\frac{8x^{4} + 8x^{2} - 1}{x^{3}}[/tex]
Break down the polynomial and divide:
[tex]= \frac{8x^{4} }{x^{3} } + \frac{8x^{2}}{x^{3}} + \frac{-1}{x^{3}}[/tex]
Calculating each division we get
[tex]=8x+ 8x - \frac{1}{x^{3} }[/tex]
Therefore the final answer is
[tex]\frac{8x^{4} +8x^{3} −1}{x^{3}} = 8x+8 - \frac{1}{x^{3}}[/tex]
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8) I bought 4 baseball cards for y dollars each and 3 card holders for $2.50
each. I paid a total of $19.50. What is the cost per baseball card?
PROVE IT!! SHOW YOUR WORK!!!!!
A) $3 B) $4 C) $5.50 D) $6
Answer:
$3
Step-by-step explanation:
Total of all = $19.50
3 Card holders total = $7.50
4 Baseball card total = ?
We know that 19.50 is the sum of the holders and cards together so we subtract $7.50 from $ 19.50.
$19.50-$7.50=$12 for ALL four baseball cards
We know that 4 baseball cards are $12, but if we DIVIDE 12 by four, we get the individual price per card.
12/4 = $3
Complete (assume $60,000 of overhead to be distributed): (Enter amount of overhead allocated as whole dollar amounts. Round your ratio answers to the nearest hundredth.) Sq. Ft. Ratio Amount of Overhead Allocated Dept. A 10,000 A B Dept. B 30,000 C D
The calculation of the ratios, resulting from the square feet occupied by Departments A and B, and the amounts of allocated overhead costs to the two departments are as follows:
Ratio Amount
Department A 1/5 $10,000
Department B 4/5 $40,000
What is the ratio?The ratio is the relative value relationship shared by two or more numbers.
Ratios are fractional values depicted in fractions, decimals, and percentages.
Like proportions, ratios show how much a value or variable is contained in another.
Total overhead = $60,000
Overhead Allocation:Department Square Feet Ratio Amount of Overhead Allocated
Dept. A 10,000 A = 1 B = $15,000 ($60,000 x 1/4)
Dept. B 30,000 = 3 D = $45,000 ($60,000 x 3/4)
Ratios = 10,000:30,000
= 1:3
Sum of Ratios = 4
Thus, based on the ratios, Department A is allocated $15,000, while Department B will be allocated $45,000 of the distributable overhead costs.
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