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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Can someone please help me , thank you :)!
Answer:
a )
[tex]6 ( ? ) = 27[/tex]
b )
? = The amount of rice in each container.
So, 1 container = ( ? ) ounce.
6 containers have = 6 x ( ? ) ounces.
We know that 6 containers have 27 ounces so...
[tex]6 ( ? ) = 27[/tex]
[tex]? = \frac{27}{6}[/tex]
[tex]? = 4.5[/tex]
Final Answer: 4.5 ounces in each container
Hope this helps! :)
it costs a paper company 4x+185 dollars to produce x notebooks. how many notebooks can they produce for $285
The paper company can produce 25 notebooks for $285
How to determine the number of notebooks?From the question, the equation of the total cost is given as
Equation = 4x + 185
Rewrite as
Cost = 4x + 185
Express the equation as a cost function
So, we have the following representations
C(x) = 4x + 185
When the total cost is $285, we have
C(x) = 285
This gives
4x + 185 = 285
Subtract 185 from both sides
4x = 100
Divide by 4
x = 25
Hence, the number of notebooks is 25
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In 2016 the cdc estimated the mean weight of us women over the age of 20 years was 168.5 pounds with a standard deviation of 68 pounds. What is the expected mean for a sample of 150 women
The expected mean for a sample of 150 women is 168.5 pounds.
What is expected mean?Expected mean can be defined as the mean weight of a number . Based on the given data we were told that the mean weight of the us women was 168.5 pounds which implies that the expected mean is 168.5 pounds.
The formula for expected mean is :
E ( X ) = μ = ∑ x P ( x )
Where:
x = values of the random variable X
P(x) = Corresponding probability
∑ =Sum of all products xP(x)
μ = mean
Therefore the expected mean is 168.5 pounds.
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Question 5 (1 point), You are making your friend a triangular fabric decoration for their home. It has ripped so you need to go buy new fabric. The fabric you are buying is $3 per square foot. Using the dimensions below, how much money do you need to buy enough fabric?
Answer:
1). True
2). x = 16.4 m^2
3). A = 24, h = 4
4). A = 18.39
5). 162
Step-by-step explanation:
I took this quiz on K12 and got everything correct! Brainliest welcome! :)
if x represents the number of questions on test, analyze the meaning of each expression x+4
The meaning of the expression x + 4 as required in the task content is; "four more than the number of questions on test".
Determining word phrases from algebraic expressions.It follows from the task content that the word phrase which best represent the algebraic expression; x + 4 is to be determined.
Given; x = the number of questions on test.
It therefore follows that the algebraic expression x + 4 can be interpreted as; "four more than the number of questions on test".
Hence, the meaning of the expression is; "four more than the number of questions on test".
PS: Just like word phrases can be accurately represented by algebraic expressions, the latter can be represented by the former too.
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Write the equation of the line that passes through the points (5,—9) and (-7, 7).
Put your answer in fully simplified point-slope form, unless it is a vertical or
horizontal line.
Answer:
[tex]y-7=-\frac{4}{3}(x+7)[/tex]
Step-by-step explanation:
The slope of the line is [tex]\frac{-9-7}{5-(-7)}=-\frac{4}{3}[/tex].
The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex], so the equation is [tex]y-7=-\frac{4}{3}(x+7)[/tex].
Dr. Ortega gave Austin, one of her patients, 180 micrograms of medication. Based on Austin's height and weight, she expects that there will be about 162 micrograms remaining in his body after one hour. Dr. Ortega knows that the amount of medication remaining in Austin's body will continue to decrease each hour.
Write an exponential equation in the form y=a(b)x that can model the amount of medication in Austin's body, y, x hours after the medicine was administered.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
To the nearest microgram, how much of the medication can Dr. Ortega expect to remain in Austin's body after 6 hours?
micrograms
The exponential function that can model the amount of medication in Austin's body, y, x hours is of: [tex]y = 180(0.9)^x[/tex]
What is the exponential function?The definition of the exponential function is presented as follows:
[tex]y = a(b)^x[/tex]
The parameters a and b are listed as follows:
a is the amount when x = 0.
b is the rate of change.
Given that the initial dose was of 180 micrograms, hence the parameter a is;
a = 180.
After one hour, the concentration was of 162 micrograms, hence the parameter b is;
b = 162/180 = 0.9.
Hence the equation is:
[tex]y = 180(0.9)^x[/tex]
After six hours, the concentration is given as;
[tex]y = 180(0.9)^6[/tex]= 96 micrograms.
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A rotating light is located 17 feet from a wall. The light completes one rotation every 2 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 20 degrees from perpendicular to the wall.
When the the light's angle is 20° from perpendicular to the wall, and the light is rotating at an angular speed of one rotation in 2 seconds the rate the light projected onto the wall is moving is approximately 60.48 feet/s
What is angular speed?Angular speed, ω, is the angle, θ, in radians rotated by a rotating object per second. The unit of angular speed is radians per second, rad/s.
Mathematically;
[tex]\omega = \dfrac{\Delta \theta}{\Delta t}[/tex]
Where;
Δt = The time the object rotates through an angle of Δθ
The distance of the light from the wall, x = 17 feet
Time it takes the light to complete one rotation = 2 seconds
Angle the light makes with the perpendicular wall = 20°
[tex]tan(\theta) = \dfrac{y}{x}[/tex]
The distance the light has moved along the wall, y = x × tan(θ)
Therefore;
The y = 17 × tan(θ)
The angular velocity of the light, ω = θ/t
Therefore, θ = ω × t = ω·t
Which gives; y = 17 × tan(ω·t)
[tex]\omega = \dfrac{2\cdot \pi}{2}\ rad/s = \pi \ rad/s[/tex]
Therefore; x = 17 × tan(·t)
[tex]\dfrac{dy}{dt} = \dfrac{d}{dt} \left(17\times tan(\omega\cdot t)\right) = 17\cdot \omega\cdot sec^2(\omega \cdot t)[/tex]
ω = π rad/s (constant)
ω·t = θ
Therefore;
[tex]\dfrac{dy}{dt}= 17\cdot \omega\cdot sec^2(\theta)[/tex]
Rate the light is moving along the wall, dy/dt when θ = 20°, is therefore;
[tex]\dfrac{dy}{dt}= 17\times \pi\cdot sec^2(20^{\circ}) \approx 60.48[/tex]
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Find P(AUB) of P(A)=2/5,P(B)=2/7 and A and B are Independent
P(A∪B)=24/35 when A and B are independent and P(A)=2/5,P(B)=2/7
What is meant by probability?Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 signifying impossibility and 1 expressing certainty. The greater the likelihood of an occurrence, the more likely it will occur.
Probability theory, which is widely used in domains such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy, has given these concepts axiomatic mathematical formalization.
Given,
P(A)=2/5
P(A)=2/7
P(A∪B)=?
And also given that A and B are independent then,
P(A∩B)=0
P(A∪B)=P(A)+P(B)-P(A∩B)
P(A∪B)=(2/5)+(2/7)-0
P(A∪B)=(14+10)/35
P(A∪B)=24/35
Therefore, P(A∪B)=24/35 when A and B are independent.
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If A and B are independent events, P(A)=0.15, and P(B)=0.77, what is P(B|A)?
The Probability of P(B│A) is 0.77
What are independent events?Independent events are those events whose occurrence is independent on any other event. For example, if we flip a coin in the air and get the outcome as tail, then again if we flip the coin but this time we get the outcome as Head, In both cases, the occurrence of both events is independent of each other. It is a type of events in probability.
If A is the event that even number will appear when a die is rolled and B is when 4 or 6 appears
P(A)= 3/6 = 1/2 and P(B) = 2/6 = 1/3
Also A and B is the event ‘the number appearing is even and a multiple of 4 or 6 so that
P(A ∩ B) = 1/6
P(B│A) = P(A ∩ B)/ P(A)
= 1/6 /1/2= 1/3 = P(B)
Therefore P(B│A) = P(B)
if A= 0.15 and P(B)= 0.77
P(B│A) = 0.77
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Pedro and Rebecca were trying to solve the equation:
0.1x^2 - 0.7x + 1.2 = 0
Pedro said, “I can multiply the entire equation by 10 and then factor. Then I can solve using the zero product property.”
Rebecca said, “I'll solve using the quadratic formula with a = 0.1 1, b = -0.7 and c = 1.2"
WHOs Strategy works?
A - Only Pedro's
B - Only Rebecca's
C - Both
D - Neither
The correct strategy between Pedro and Rebecca trying to solve the quadratic equation: 0.1x^2 - 0.7x + 1.2 = 0 is A - Only Pedro's
How to determine the correct strategyThe given function is a quadratic function which is solved by several method including the method both Pedro and Rebecca are trying to use
Pedro's method is the factorization method and the steps mentioned are correct
However Rebecca's method has some error
The equation is: 0.1x^2 - 0.7x + 1.2 = 0
factor of the leading coefficient a is 0.1, Rebecca is using 0.11
The error of using 0.11 instead of 0.1 will make the method ineffective
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Which describes the graph of y=-(x - 3)² + 2?
O A. Vertex at (-3,2)
OB. Vertex at (3,-2)
OC. Vertex at (-3, -2)
OD. Vertex at (3, 2)
x-3=0
so x = 3
-(y-2)=0
so y = 2
vertex = (3,2)
earns $14.50 per hour. His regular hours
are 40 hours per week, and he receives
time-and-a-half overtime. Find his total pay
for a week in which he works 46 hours.
Answer: 667
Step-by-step explanation:
14.50 x 46
Differentiate the function with respect to x.
Differentiation of f(x) is [tex]-8x^{3} sinx^{4}[/tex].
Given,
f(x) = [tex]cos2x^{4}[/tex]
Now, we will differentiate f(x) with respect to x,
[tex]\frac{d}{dx}cos2x^{4} = (\frac{d}{dx}cos2x^{4})(\frac{d}{dx}2x^{4} )[/tex]
[tex]= (-sin2x^{4})(2*4x^{3})[/tex]
[tex]= -8x^{3}sin2x^{4}[/tex]
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. You get an auto loan at 3.5% interest for 5 years; please answer the following.
A. You can afford a $250 per month car payment; how expensive a car can you afford?
B. You purchase a car for $8000 with a $2000 down payment, what are your monthly payments?
Using the monthly payment formula, it is found that:
A. You can afford a car at a price of $13,742.36.
B. The monthly payments are of $109.15.
What is the monthly payment formula?The monthly payments are given by the equation presented as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
The variables involved in the equation are listed and explained as follows:
P is the initial amount.r is the interest rate.n is the number of payments.For item a, the parameters are given as follows:
A = 250, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60
Hence the maximum value of the car is obtained as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]250 = P\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]
0.0181919241P = 250
P = 250/0.0181919241
P = $13,742.36
For item b, the parameters are given as follows:
P = 6000, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60
(P = 6000 as the 2000 of the down payment are already paid, hence not subjected to interest).
Hence the monthly payments are given as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 6000\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]
A = 6000 x 0.0181919241
A = $109.15.
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Hi can someone please help me? Thank you!
There are 3 trees in your neighbor's yard. Each tree in the yard has 2 birdhouses and each birdhouse has 4 birds. How many birds are
there in all?
In a photo contest, two judges are giving scores to each photo. Each judge gives a score for impact (worth 40%), composition (worth 30%), lighting (worth 20%), and color balance (worth 10%). Lester entered a photo in the contest and received the following scores: Impact: 8 and 9 Composition: 7 and 7 Lighting: 8 and 7 Color balance: 5 and 7 Enter a number in each box to create an expression that represents Lester's final score.
Lester's final score from the two Judges is 7.6
How to calculate Lester's final scoreThe scores of the judges are in percentage and this will be converted to decimal by dividing by 100
impact (worth 40%) = 0.4
composition (worth 30%) = 0.3
lighting (worth 20%) = 0.2
color balance (worth 10%) = 0.1
Average score from the Judges will be used to multiply the percentages
Impact: 8 and 9
= 8.5 * 0.4 = 3.4
Composition: 7 and 7
= 7 * 0.3 = 2.1
Lighting: 8 and 7
= 7.5 * 0.2 = 1.5
Color balance: 5 and 7
= 6 * 0.1 = 0.6
sum of the scores gives Lester's final score as 7.6
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Describe a real life siuation for each problem
1. -3 + (-4)
2. -3 (+2)
Answer:
1. I'm $3 in debt, and I spend 4 more dollars. I am now 4 dollars more in debt than I was before.
2. I'm $3 in debt, and I pay back $2 of debt. I am now $1 in debt.
Step-by-step explanation:
-Hope this helped
Last year, Dan had $ 10,000 into invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 7% simple interest per year. After one year, he received a total of $730 in interest. How much did he invest in each account?
The amount invested in the account that yields 10% simple interest is $1,000.
The amount invested in the account that yields 7% simple interest is $9,000.
How much was invested in each account?The first step is to form a system of equations using the information provided in the question:
a + b = $10,000 equation 1
0.1a + 0.07b = 730 equation 2
Where:
a = amount invested in the account that yields 10% simple interest
b = amount invested in the account that yields 7% simple interest
The elimination method would be used to solve the equations
Multiply equation 1 by 0.1
0.1a + 0.1b = 1000 equation 3
Subtract equation 2 from equation 3
0.03b = $270
Divide both sides of the equation by 0.03
b = $270 / 0.03
b = 9,000
Substitute for b in equation 1
a + 9,000 = 10,000
a = 10,000 - 9,000
a = 1000
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Help Geometry (ASAP!!)
Answer:
yes if b is odd then b+6 is odd
Step-by-step explanation:
example
consider a odd number 1,3,5,7,and 9
1+6=7
3+6=9
5+6=11
7+6=13
9+6=15
all answers are odd number
A car dealership decreased the price of a certain car by 5%. The original price was $47,200.
What is the new value and the original value?
Answer:
New: $44,840 Original: 47,200
Step-by-step explanation:
You have to multiply 47,200 by 95% or 0.95
Translate the sentence into an equation.
The square of a number is equal to the square root of that number.
The equation of the sentence, the square of a number is equal to the square root of that number, is [tex]x^{2} =\sqrt{x}[/tex].
According to the question,
We have the following information:
The square of a number is equal to the square root of that number.
Now, let's take this number to be x.
Now, square of this number will be [tex]x^{2}[/tex] and the square root of this number will be [tex]\sqrt{x}[/tex].
Now, according to the sentence, we will have the following expression:
[tex]x^{2} =\sqrt{x}[/tex]
Hence, the equation of the sentence, the square of a number is equal to the square root of that number, is [tex]x^{2} =\sqrt{x}[/tex].
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What is the value of x?
The required value of x is 3 in the given equilateral triangle.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
The triangle given in the figure is an equilateral triangle.
We know that all sides are equal in the equilateral triangle.
As per the given figure,
side AB = side AC
6x - 3 = 3x + 6
6x - 3x = 6 + 3
Apply the arithmetic operation,
3x = 9
x = 9/3
x = 3
Therefore, the required value of x is 3 in the given equilateral triangle.
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Find the sum: (2x² + x + 3) + (3x² + 2x + 1)
A. 3x² + 5x+4
B. 5x²+3x+4
OC. 6x + 2x + 3
OD. 5x²+2x+4
Answer:
B
Step-by-step explanation:
Combine 2x^2 and 3x^2 to get 5x^2.
5x²+x+3+2x+1Combine x and 2x to get 3x.
5x²+3x+3+1Add 3 and 1 to get 4.
5x²+3x+4The correct option is B.Please help with this table. Not sure why this is difficult
An auto insurance company charges males 16-18 years old a base price of $1100 for insurance in a given year. Their accuracies have determined that there is a 8.5% a claim will be made against such a policy and an average claim of $4900. What does the insurance company expect to make on average off of each policy holder?
If a claim will be made against such a policy and an average claim of $4900. the insurance company should make on average off of each policy holder is $683.5.
How to find the amount the company should make?Using this formula to find the amount
Amount = [Percentage claim × ( Base price - Average claim)] + [(1 - percentage claim) × Base price]
Let plug in the formula
Amount = [0.085 × ($1,100 - $4,900)] + [(1-0.085) × $1,100]
Amount = [0.085 × (- $3,800)] + [(0.915 × $1,100]
Amount = -$325+ $1,006.5
Amount = $683.5
Therefore the insurance company will make the amount of $683.5.
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Can anyone help me in this question? pls.........
Answer: A
Step-by-step explanation :
HE ASKED YOU ABOUT AN EQUALTULAR ( TO EQUALED AND OPPSITE ANGLE )
What is 4/5 ÷ 1/3? The quotient is 2 and
Answer:4/5 : 1/3=4/5 x 3/1=12/5
Step-by-step explanation:
Answer:
12/5
Step-by-step explanation:
If you set it in the calculator 4/5 ÷ 1/3 you get = 12/5
was it helpful?
589 in base five is
589 in base five is [tex]4324_{5}[/tex].
Given number:
589
converting to [tex]589_{5}[/tex].
⇒ 5|589
⇒ 5|117|4
⇒ 5|23|2
⇒ 5|4|3
⇒ 5|4|4
Now we write the last digit from last number to first that is,
= [tex]4324_{5}[/tex].
Hence 589 in base five is [tex]4324_{5}[/tex].
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