For a linear equation the solutions are on the line, while for inequalities the solutions are above or below the line (sometimes the line is also included).
What are the differences?When we have a linear equation of the form:
y = line
The solutions on the graph of this equation are the points on the line.
Now, for inequalities like:
y > line
or
y < line.
The solutions are all the points above (or below) the line itself.
Finally, for inequalities like:
y ≥ line
y ≤ line
The solutions are above (below) the line and the line itself.
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Katie bought 4 sweaters that each cost the same amount and 1 skirt that cost 20$ . The items she bought cost a total of 160 before tax was added. What was the cost of each sweater?
A
$20\$ 20$20
Using simple linear equation we calculate the cost of a sweater as $35 .
A linear polynomial over a field, from which the coefficients are taken, can be equalised to zero to produce a linear equation.
The numbers that, when used to replace the unknowns in such an equation, result in the equality, are the solutions.There is just one possible answer when there is only one variable (providing that. The term "linear equation" frequently alludes indirectly to this specific situation, in which the variable is appropriately referred to as the "unknown."Let the cost of each sweater be x.
Cost of the skirt = $20
Let us form a linear equation to calculate the required cost
4x + 20 = 160
solving we get :
x = 35
Therefore the cost of a skirt is $35.
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the world population was 6.9 billion at the end of 2010 and is predicted to reach 9 billion by the end of 2050.1 (a) assuming the population is growing exponentially, what is the continuous growth rate per year? round your answer to three decimal places.
The continuous growth rate per year of the world population is 0.664%.
What is defined as Exponential Growth?Exponential growth occurs when the growth of a quantity at any point in time has been proportional towards its value at that point. If we have a few numbers, we could use simple exponential growth models to determine the population.We've been told to assume that population is growing at an exponential rate. As a result, we can employ the population model shown below.
N(t) = N₀ e∧(kt)
Here, N(t) represents the population after t years, N₀ represents the initial population, and k represents the continuous growth rate.
We've been told that initial population of 6.9 billion will increase to 9 billion in 40 years (2050-2010).
To use this information, we calculate the growth rate using the model described below.
N(40) = 6.9 e∧(40k)
N(40) = 9 (given)
9 = 6.9 e∧(40k)
Taking ㏑ both side
㏑ 9 = ㏑ 6.9 e∧(40k)
40k = ㏑(9/6.9)
k = 0.00664
k = 0.664%
Thus, the continuous growth rate per year of the world population is 0.664%.
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Select all of the values that have exactly 3 significant digits.
0.0807
O 005.5
13.41
0367.0
☐ 1,990
All the values with exactly three significant digits are: 0.0807, 1990
Significant digits of a number tell us what the actual meaningful representation of a number is. There are certain rules to figure out which digits in a number are significant such as
All non-zero digits in any number are significant. Ex: 33.4 has 3 significant digits; 19875 has 5 significant digits.All zeros between two non-zero digits are significant. Ex: 103.0078 has 7 significant digits. 700519 has 6 significant digits.Leading zeros that is all zeros to the left of the first non-zero digit and all zeros to the right of a decimal point are insignificant. 0.00081 has 2 significant digits; 0.547 has 3 significant digits.Zeros to the right of a decimal point are significant if and only if they are not followed by a non-zero digit. Ex; 92.00 and 20.00 both have 4 significant digits.After a decimal point, all zeros after the last non-zero digit are significant. Ex: 0.0079800 has 5 significant digitsTrailing zeros are significant in a whole number with a decimal point shown and insignificant if there is no decimal point shown. Ex: 540. has 3 significant digits while 540 has 2 significant digits.Thus the numbers with 3 significant digits are: 0.0807, 1990
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is m parallel to n. If so state the theorem you can use
Evaluate. Write your answer as a whole number or as a simplified fraction.
Submit
Answer: 1/121
Step-by-step explanation:
Any number raised to the power of 0 is 1
11^2 = 121
Point B' is the image of point B after a reflection in a line. Write the equation of the line.
B(2,-4), B'(6,-4)
Thanks! <3
The slope and intercept of the line are -2 and 0. The equation of the line is y = -2x
Equation of LineTo find the equation of line, we have to find the slope of the equation and its y-intercept.
The slope of a line can be calculated as
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\m = \frac{-4 - (-4)}{6 - 2}\\m = \frac{-8}{4} \\m = -2[/tex]
The slope of the line is equal to -2.
Lets find the intercept of the line;
The line of an equation is given as
[tex]y = mx + c[/tex]
We can pick point A and substitute its values to find c
[tex]y = mx + c\\- 4 = -2(2) + c\\-4 = -4 + c\\c = -4 + 4\\c = 0[/tex]
The equation of the line is y = -2x
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Luis wants to buy a skateboard that usually sells for $79.01. All merchandise is discounted by 12%. What is the total cost of the skateboard if Luis has to pay a state sales tax of 6.75%. Round your intermediate calculations and answer to the nearest cent. The total cost of the skateboard is?
The total cost of the skateboard after being discounted by 12% and then sales tax of 6.75% is$74.22.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
As per the given,
Usually, the price of the skateboard = $79.01
The 12% of 79.01 ⇒ (12/100)79.01 = $9.4812
The price after a 12% discount
79.01 - 9.4812 = $69.5288
The 6.75% of 69.5288 ⇒(6.75/100)69.5288 = $4.693194
The total price after applying the 6.75% tax,
$69.5288 + $4.693194 = $74.22
Hence "The total cost of the skateboard after being discounted by 12% and then sales tax of 6.75% is$74.22".
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Please help me with math
The set of numbers from least to greatest is-
5×10⁻², 6%, 2/5, 4/9, 2⁻¹, √3.
What is referred as the ascending order?The arrangement of numbers or even other items in order of increasing from smallest to largest is referred to as ascending order. Ascending order is represented by numbers that emerge on a number line from left to right. We generally represent it with commas or by using the 'less-than symbol (<)' between numbers.For the given numbers;
The given number are-
2/5, 5×10⁻², √3, 6%, 4/9, 2⁻¹.
These number can be written in the decimal form as;
2/5 = 0.405×10⁻² = 0.058√3 = 1.7326% = 0.064/9 = 0.442⁻¹ = 0.5Now arrange the number from least to greatest.
0.058, 0.06, 0.40, 0.44, 0.5, 1.73
Convert the number in given form.
5×10⁻², 6%, 2/5, 4/9, 2⁻¹, √3.
Thus, the number represented in the ascending order are-
5×10⁻², 6%, 2/5, 4/9, 2⁻¹, √3.
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i would really appreciate it, if I can get some help! Please look at both photos!
-
nbjhjkghjvhjvhjvhvjvhhklbjklbjblk
Subtract -1 3/5 - (-2 7/8)
Answer:
Answer down below!
Step-by-step explanation:
Your answer would be 1 11/40
For the steps, refer to the image below!
1.97 x 10 3 Standard Notation
The answer to the given notation is 1970
What is standard notation ?Any value between 1.0 and 10.0 that can be expressed as a decimal number and multiplied by a power of 10 is referred to as being in standard form. If you look closely, you will see that 1.23 is a decimal between 1.0 and 10.0, and as a result, we have the standard form of 123,000,000 as 1.23 108.
This is already an standard notation : 1.97 × 10³
10 raised to the power three means there are three zeroes.
thus if we were to solve this question it will be
1.97 × 1000
which is equal to 1970.00
= 1970 .
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Convert the angle \theta=310^\circθ=310
∘
theta, equals, 310, degrees to radians.
The degrees to radians conversion is given as 1° = π/180 radian thus the conversion of 310° is (31/18)π.
What is unit conversion?To convert any unit into another is called a unit conversion.
In order to convert units, we need to care about their dimensions their dimension should not be changed.
It is known that π radian = 180°.
1° = (π/180) radian.
Multiply both sides by 310
310° = (π/180)310
310° = (31/18)π
Hence "The degrees to radians conversion is given as 1° = π/180 radian thus the conversion of 310° is (31/18)π".
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The distribution of the salaries at a small business is strongly skewed with many people making very modest salaries and a few making very large salaries. Which measure of center, mean or median, is a better indication of a "typical” salary at this business?
The mean is better because it is not affected by the high salaries.
The median is better because it is not affected by the high salaries.
It cannot be determined without knowing the actual salaries.
Either one would be a good measure of a typical salary because they are the same value.
(Plss someone help, this is my last try... ima cry if I fail this sh again)
The measure of center that is a better indication of a "typical” salary at this business is A. The mean is better because it is not affected by the high salaries.
How to illustrate the information?When the majority of the data are gathered on the left of the distribution curve or the histogram, the distribution is said to be positively skewed, or skewed to the right.
If the majority of the data are gathered on the right side of the distribution curve or the histogram, the distribution is said to be negatively skewed, or to the left. It is assumed that many employees at tiny businesses earn extremely low pay while a select few earn very high salaries. In this case, the mean gives between information about the data.
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HELP ME PLEASE!!! THANK U SO MUCH IF U HELP ME, UR HELP WILL BE APPRECIATED <3
Answer:
1b) in first image
1c) in second image
customers send emails to a help desk of an online retailer every 2 minutes, on average, and the standard deviation of the inter-arrival time is also 2 minutes. the online retailer has three employees answering emails. it takes 4 minutes to write a response email, on average. the standard deviation of the service times is 2 minutes. this is a g/g/k queue. what is the arrival rate? what is the service rate?
The arrival rate is found to be 30 emails per hour and the service rate is calculated to be 45 emails per hour.
It has been mentioned in the question that in every 2 minutes, customers send emails to a help desk of an online retailer, on an average, and the standard deviation of the inter-arrival time is also given to be 2 minutes. The online retailer has three employees for answering those emails.
It takes almost 4 minutes to write a response email to the customer, on average. The standard deviation (SD) of the service times is 2 minutes. This is a g/g/k type queue.
Therefore the arrival rate per hour is given by the following relation:
Arrival rate in 1 hr = No. of minutes in an hr / inter arrival time of email taken in minutes
Given here,
No. of minutes in an hour = 60 minutes
Inter arrival time of the email taken in minutes = 2 minutes
∴ Arrival rate in 1 hr = 60 / 2
= 30 emails / hr
Hence the arrival rate is 30 emails per hour.
Now for finding out the service rate we have the following formula:
Service rate = No. of minutes in an hr x No. of employes answering/ average time that is required to write response email
Given here,
No. of minutes in an hr = 60 minutes
No. of employes answering = 3
Average time that for writing response email = 2 minutes
∴ Service rate = 60 * 3 / 4
= 45 emails / hr
Hence the service rate is 45 emails per hour.
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Pancakes are made with 1½ cups water and 1/2
What is the ratio of water to milk?
cup milk.
1 1/2 : 1/2 is the rario of wayer to milk
The ratio of water to milk is 3:1.
What are ratios ?The quantitative relation between two amounts showing the number of times one value contains or is contained within the other is called ratio.
Water = 1½ cups
= 3/2 cups
Milk = 1/2 cup
Ratio of Water to milk
= 3/2 : 1/2
= 3/2 ÷ 1/2
= 3/2 x 2/1
= 3/1
so, the ratio of water to milk is 3:1.
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write an equation for each line
FIRST GETS BRAINLIEST PLS HURRY
Reasoning 5 Jack calculates 6 x 102 + 3 x 10³ = 9 × 105 Explain Jack's mistake, and write in the correct answer in standard index form.
Answer:
3.6*10³
Step-by-step explanation:
Jack cannot add the powers of 10 because they are in addition. We can apply the exponent rule only when they are in multiplication.
[tex]\sf 6 *10^2 + 3*10^3= 6*100 + 3*1000\\[/tex]
= 600 + 3000
= 3600
[tex]\sf = 3.6 * 10^3[/tex]
What must be the units of R, the gas constant, in this formula? A. Newton • meter per kelvin B. mole • kelvin per Newton • meter C. Newton • meter per mole • kelvin D. Newton • meter • kelvin per mole
Solve R:
Multiply both sides of the equation by V:
[tex]\begin{gathered} PV=V\cdot\frac{\text{nRT}}{V} \\ \\ PV=nRT \end{gathered}[/tex]Divide both sides of the equation by nT:
[tex]\begin{gathered} \frac{PV}{nT}=\frac{\text{nRT}}{nT} \\ \\ \frac{PV}{nT}=R \end{gathered}[/tex]Then, R is:
[tex]R=\frac{PV}{nT}[/tex]Use the given units in the equation above:
[tex]R=\frac{N\cdot m^3}{mol\cdot K}[/tex]Then, the units of R are: Newton*cubic meter per mol*KelvinDeshaun invested in a savings bond for 4 years and was paid simple interest at an annual rate of 2%. The total interest that he earned was $160. How much did he invest?
For a Simple Interest of $160, the amount that he invested is $2000.
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Given:
Simple Interest (S.I.) = $160
Rate of Interest (R) = 2%
Time Period (T) = 4 Years
Let the Principal Amount be $P
We know,
[tex]S.I. =\frac{P*R*T}{100}[/tex]
Putting the given values in the formula, we get:
[tex]S.I. =\frac{P*R*T}{100}\\S.I. =\frac{P*2*4}{100} =\frac{P*8}{100}\\ 160 =\frac{P*8}{100} \\P = \frac{160*100}{8} =\frac{16000}{8} = 2000[/tex]
Hence, He Invested $2000
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Answer:
$2,000
Step-by-step explanation:
Simple Interest Formula
[tex]\large\boxed{\sf I = Prt}[/tex]
where:
I = Total interest accrued.P = Principal.r = Interest rate (in decimal form).t = Time (in years).Given values:
I = $160r = 2% = 0.02t = 4 yearsSubstitute the given values into the formula and solve for P:
[tex]\implies \sf 160=P \cdot 4 \cdot 0.02[/tex]
[tex]\implies \sf 160=0.08P[/tex]
[tex]\implies \sf P=\dfrac{160}{0.08}[/tex]
[tex]\implies \sf P=2000[/tex]
Therefore, the amount Deshaun invested was $2,000.
The measures of the exterior angles of a quadrilateral are 2x°, 3x°, 9x°, and 10x°. Find the measure of the largest exterior angle.
An isosceles triangle has a perimeter of 46 inches. The base is 6 less than twice each of the congruent legs. What is the sum of the lengths of the two congruent legs?
Answer: 26 inches
Step-by-step explanation:
An isosceles triangle has two congruent legs.
1) Set up the equations
P = b + 2L
b = 2L-6
2) Substitute for variables
46 = (2L - 6) + 2L
3) Solve the equation
46 = 4L - 6
52 = 4L
13 = L
4) Solve the problem
It asks for what is the sum of the two congruent legs
13 + 13 = Ans
26 = Ans
1.75 x 1.25 estimate
Answer:
2.1875
(in nearest hundredths it would be 2.19(rounded)
49 = 7/6u solve for u simplify your answer as much as possible
Answer:
Step-by-step explanation:
49 = 7/6u
49 * 6/7 = 7/6u * 6/7
42 = u
simplify a5/a2. can someone help fast
Answer:
⇔[tex]a^{3}[/tex]
Step-by-step explanation:
Law of Indices
Division law: [tex]\frac{a^{5} }{a^{2} }[/tex] =[tex]a^{5-2} =a^{3}[/tex]
g + 3 < 6
please help me
The solution to the given inequality expression is g <3
Linear inequalityInequality are expressions not separated by an equal sign. They are separated by a less than, greater than, less than or equal to and greater than or equal to.
Given the linear equation below:
g + 3 < 6
We are determine the unknown variable "g"
First, we need to subtract 3 from both sides to have;
g + 3 - 3 < 6-3
g < 6 - 3
g < 3
Hence the solution to the given inequality expression is g < 3
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George is building a fence. It takes him 1/2 an hour to build 1/3 of a section of a fence. At this rate, what fraction represents the section of fence George can build per hour? Express your answer as a fraction.
Answer:
2/3
Step-by-step explanation:
If 1/3 rd of the fence can be built in 1/2 hr then in 1 hour which is 1/2 x 2 the fraction of the fence that can be built is 1/3 x 2 = 2/3
a box is to be constructed from a sheet of cardboard that is 10 cm by 60 cm by cutting out squares of length x by x from each corner and bending up the sides. what is the maximum volume this box could have? (round your answer to two decimal places.)
The maximum volume of the box is 54 cm³ .
To obtain the largest volume feasible, multiply each measurement by the largest possible error. To find the least volume that may be created, multiply after subtracting the biggest possible error from each measurement.
Given :
a box is to be constructed from a sheet of cardboard that is 10 cm by 60 cm
cutting out squares of length x by x from each corner and bending up the sides
⇒ (50-2x)(10-2x)(x)
⇒ 500-100x-20x+4x^2) (x)
⇒ 4x^3-120x^2+500x
⇒ dv/dx 12x^2-240x+500=0
⇒ 3x^2-60x+125=0
⇒ Quadratic formula x=[60 ± √2100]/6
⇒ x= 2.36 or 17.64
volume max: 45.28 x 5.28 x 2.36= 564 cm^3
Hence The maximum volume of the box is 54 cm³
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All men are mortal. Joe is a man. Therefore Joe is mortal. If the first two statementsare true, then the conclusion must be true.
Answer:
Step-by-step explanation:
Yes
Which expression is equivalent to (1)/(2^(-2)*3^(-2)) ?
Answer:
B Description is in the picture
Answer:
[tex]2^2*3^2[/tex]
Step-by-step explanation:
By definition of a negative exponent: [tex](\frac{a}{b})^{-x}=(\frac{b}{a})^x=\frac{b^x}{a^x}[/tex]
In the last step I simply distributed the exponent, but this actually goes both ways! So we can do: [tex]\frac{b^x}{a^x}\implies(\frac{b}{a})^x[/tex]
The next thing you need to know is that: [tex](ab)^x=a^x*b^x[/tex]
and like the previous statement, it works both ways! So this means: [tex]a^x*b^x\implies (ab)^x[/tex]
So the denominator of the expression given can be expressed as:
[tex](2^{-2}*3^{-2})\implies (2*3)^{-2}[/tex]
Lastly you need to understand: [tex]1^x[/tex] just simplifies to one, because [tex]1*1*1*1...\text{ x amount of times}[/tex] will stay equal to one. So we can thing of 1 as being raised to some number, even if not explicitly stated.
This helps because we can write one as: [tex]1^{-2}[/tex]
so now we have the expression:
[tex]\frac{1^{-2}}{(3*2)^{-2}}[/tex]
Well this can because now we can "factor" out this exponent just like how it was demonstrated in the beginning
We get the expression: [tex](\frac{1}{3*2})^{-2}[/tex]
Now we use the definition of a negative exponent, to get the reciprocal giving us the expression
[tex](\frac{3*2}{1})^{2}[/tex]
We can now "distribute" this exponent across the division to get
[tex]\frac{(3*2)^2}{1^2}[/tex]
Well 1 squared just simplifies to 1, so it's redundant to write.
This gives us the expression:
[tex](3*2)^2[/tex]
and as stated before we can distribute this across multiplication, and another way to think of it is:
[tex](3*2)^2\implies (3^2*2^2)\\\\\\text{because } (3*2)^2\implies (3*2)*(3*2)\implies(3*3)*(2*2)[/tex]
we're just grouping the like terms, so we can write them as an exponent.
So this gives us our final expression:
[tex]3^2*2^2[/tex]
or
[tex]2^2*3^2[/tex]
which is the option B, since the order in which we multiply does not matter.