Inequality - Trevor needs to tutor more than 6 hours in order to make at least $180.
What is inequality?
inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. Either questions or theorems can be used to express inequality problems, and both can be solved using methods similar to those used to solve equations. The triangle inequality, for instance, states that the length of the remaining side of a triangle is greater than or equal to the sum of the lengths of any two of its sides. Many of these inequalities, including the Cauchy-Schwarz inequality, are used by mathematical analysis to prove some of its most significant theorems.
Total number of hours = 15
Let the hours spent tutoring French is x
Therefor, hours spent in scooping ice cream = (15-x)
Tutoring French is $15 an hour, total for x hours = 15x
Scooping ice cream is $10 an hour, 10×(15-x)= 150-10x
To make more than $180,
= 15x+ (150-10x)> 180
= 15x+150-10x>180
=15x-10x>180-150
=5x>30
=x>6
So, Trevor needs to tutor more than 6 hours.
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Is this statement true or false?
0 x 5 = 5 x 0
The statement is true. Multiplication is commutative, which means that the order of multiplication does not affect the result.
The statement "0 x 5 = 5 x 0" is true because of the commutative property of multiplication. In multiplication, the order of factors does not change the result.
When we multiply 0 by 5, it equals 0 since anything multiplied by 0 is 0. Similarly, when we multiply 5 by 0, the result is still 0. Both expressions are equal to 0, confirming the commutative property.
In summary, 0 x 5 and 5 x 0 are interchangeable and yield the same result, proving the truth of the statement based on the fundamental property of multiplication.
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Answer in graph form. Find <0 if sin0= 7/10 and cot0 is positive.
Sin(0)=-7/10
To get the right triangle's known sides, use the sine definition. Each value's sign is determined by the quadrant.
sin(0)=opposite/hypotenuse
Find the triangle formed by the unit circle's neighboring side. Use the Pythagorean theorem to determine the remaining side since the hypotenuse and opposite sides are known.
Adjacent=√hypotenuse²−opposite²
Change the equation's known values with new ones.
Adjacent=√(10)²−(7)²
Inside the radical, simplify.
Raise10the strength of2.
Adjacent=√100−(7)²
Raise−7the strength of2.
Adjacent=√100-49
Multiply −1 by 49.
Adjacent=√100−49
Subtract49 from 100.
Adjacent=√51
Find the cosine value.
Find the value of using the cosine definition.
cos(0).
cos(0)=adj/hyp
Replace with the known values.
cos(0)=√51/10.
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To get the right triangle's known sides, use the sine definition. The quadrant determines each value's sign.
The value of cos(0) exists √51/10.
What is meant by trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous unique trigonometric identities that relate a triangle's side length and angle.
To get the right triangle's known sides, use the sine definition. The quadrant determines each value's sign.
sin(0) = opposite/hypotenuse
To find the triangle formed by the unit circle's neighboring side. Use the Pythagorean theorem to determine the remaining side since the hypotenuse and opposite sides are known.
Adjacent = √hypotenuse² − opposite²
substitute the values in the above equation, we get
Adjacent = √(10)² − (7)²
Adjacent = √100 - 49
simplifying the above equation, we get
Adjacent = √51
To find the cosine value.
cos(0) = adjacent/hypotenuse
Replace with the known values.
cos(0) = √51/10.
Therefore, the value of cos(0) = √51/10.
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In the figure, AFGH~AKLM. Find LM.
32 cm
G
20 cm
F
H
24 cm
Det h
L
K
M
Answer:456
Step-by-step explanation:
First you grab the crabby patty formula and then you decide that by 3 multiply it by 6 then after all of that you do the equation 64%78+4637=456 so that’s how I got my answer.
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A new streaming service sent out a survey to 250 households to see who would be interested in its service. The company found that it could charge $45 per month, with a margin of error of ±1.5. If 1,000 people signed up for the service, what is the least amount of monthly revenue the company should expect?
$43,500
$45,250
$46,500
$47,000
Based on the amount that the streaming service could charge per month and the margin of error, the least amount of monthly revenue that would be reasonably expected is $43,500
How to find the least revenue expected?First, find the revenue of the new streaming service at its least amount:
= Charge for the month - margin of error
= 45 - 1.5
= $43.50
The least revenue the company can expected then is:
= Least revenue from streaming service x number who signed up for ther service
= 43.50 x 1,000
= $43,500
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A rectangular sheet of paper is 12 and 1/2 cm long and 10and 2/3 cm wide
Find the perimeter
There is a sales tax of $6 on an item that costs $80 before tax,the sales tax of the second item is $21 how much does the second item cost before sales tax
Answer:
39$
Step-by-step explanation:
if the tax is 6 dollars 6 goes into 21 3 times making 18 add 18 to 21 and that is your answer.
please help me with both of these questions! need them asap!!! thanks!!
Answers- D) 4.4π & Area-44
1. To solve the first equation we must use the equation for find Circumfrence C=2πr. Our r is 2.2 so our equation would look as C= 2π2.2. Since 2 and 2.2 are whole numbers we can multiply them by one another and that gives us 4.4. So our final answer would be C= 4.4π or D)
2. The best way to solve for our area would be to cut the shapes straight down the middle. Now the two shapes will be 7x4 and 4x4. 7x4 is 28 and 4x4 is 16. To get our final answer we would add 28 and 16, which is 44. To show this one your work draw a line going straight down to cut the shapes into a square and a rectangle. (view source)
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A high-interest savings account pays 5.5% interest compounded annually. If $300 is deposited initially and again atthe first of each year, which summation represents the money in the account 10 years after the initial deposit?10Ο Σ300(0.055) 2-1n=110Ο Σ305.5(1.055) 2-1n=110316.5(0.055)-1カ%3D110Σ316.5(1.055) 2-1n=1Save and ExitNextSubmitMark this and return
For this problem we use the formula for compund interest and substitute the 5.5% of interest annually and the initial deposit of $300:
[tex]\Sigma^{n=10}_{n=1}300(0.055)^{n-1}_{}[/tex]Answer: first option.
Write an equation for the following math sentence.
One half times the difference of twenty and a variable is two thirds
one half times the quantity y minus 20 equals two thirds
one half times the quantity 20 minus y equals two thirds
one half times y minus 20 equals two thirds
one half times 20 minus y equals two thirds
Answer:
One half times the difference of twenty and a variable is two thirds
one half times the quantity y minus 20 equals two thirds
one half times the quantity 20 minus y equals two thirds
one half times y minus 20 equals two thirds
one half times 20 minus y equals two thirds
0.5(20 - y) = 2/3
One half times the difference of twenty and a variable is two thirds :
1/2(20 - y) = 2/3
[this one im not too sure, please confirm it cause i don't think it is clear enough]
One half times the quantity y minus 20 equals two thirds :
1/2(y - 20) = 2/3
One half times the quantity 20 minus y equals two thirds :
1/2(20 - y) = 2/3
One half times y minus 20 equals two thirds :
1/2 x y - 20 = 2/3
One half times 20 minus y equals two thirds :
1/2 x 20 - y = 2/3
Round the number shown on the calculator to 1 decimal place (1 d.p.).
Answer:
Step-by-step explanation:
As you see the picture the number is 1.249
step 1
As you know before decimal the digits are said to be ones,tens, hundred so on and starts from left to right.
But after decimal it goes right to left and they are said ones,tenth,hundredth
step 2
so here it says 1 decimal place means ones means one digit after dot or point so its 2
The number rounded off to 1 decimal place is 1.2
what is rounding off a decimal number?Rounding is a process to estimate a particular number in a context. To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, round up. Rounding decimals refer to the rounding of decimal numbers to a certain degree of accuracy.
Given here, the number is 1.249 and thus the number rounded upto 2 decimal place is 1.25 and further rounding up the number to one decimal place we get 1.2
Hence, the number rounded upto one decimal place is 1.2
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20 is 80% of what number?
Answer: 25?
Step-by-step explanation:
which, if any, of the following are antiderivatives of the function e x 2 ? circle all that apply, or ‘none’ as appropriate. z x 2 1 e t 2t dt z x √ 2 e t 2 dt e x 2 2x z x 2 0 e t dt n
The anti derivative of the function eˣ² is eˣ²/2x.
What is defined as the anti derivative?Derivatives are the inverse of antiderivatives. An antiderivative is a function that does the opposite of what a derivative does. There are many antiderivatives of one function, but they all take the shape of a function + an arbitrary constant. Indefinite integrals rely heavily on antiderivatives.An antiderivative, F, of the a function, f, is a function that may be differentiated to get the original function, f. In other words, an antiderivative is defined mathematically as follows: ∫ f(x) dx = F(x) + C, where C is the integration constant.The given function is; eˣ².
To find the anti derivative of the function, integrate the function with respect to x.
Let y = eˣ²
Integration of exponential function remains same but applying the chain rule, the derivative of the power of exponent comes at the denominator.
∫y. dx = ∫eˣ² .dx.
∫eˣ² .dx. = eˣ²/(d/dx)x²
∫eˣ² .dx. = eˣ²/2x
Thus, the anti derivative of the function is found as eˣ²/2x.
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help I have an exam coming up and I need to understand how to answer this problem
The surface area of the given pyramid is equivalent to 108 square inches.
Surface area of a pyramidThe surface area of a figure is the sum of the area of the surfaces of such figure.
The given pyramid is made up of 4 triangles and a square base.
Surface area = Area of square + 4(area of triangle)
Surface area = (6 * 6) + 4(1/2 * 6 * 6)
Surface area = 36 + 4(18)
Surface area = 36 + 72
Surface area = 108 square inches
Hence the surface area of the square based pyramid is 108 square inches
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Jayden had pizza delivered. Jayden tips $5 for deliveries or 10% of the purchase, whichever is higher. The pizza delivered cost $29.50.
How much will Jayden tip?
Answer:
Five dollars?
Step-by-step explanation:
I don’t fully understand the question, so apologies if I am incorrect!
Please help me with this ASAP!
Answer:
[tex] \frac{ {a}^{3} }{14 {b}^{2} {c}^{4} } [/tex]
Step-by-step explanation:
[tex] {14}^{ - 1} = \frac{1}{14} [/tex]
[tex] {b}^{ - 2} = \frac{1}{ {b}^{2} } [/tex]
[tex] \frac{ {14}^{ - 1} {a}^{3} {b}^{ - 2} }{ {c}^{4} } = \frac{ {a}^{3} }{14 {b}^{2} {c}^{4} } [/tex]
19238 divide by 15 write answer to 1decimal place
why do we draw a median
What is the unknown angle measure in the given triangle?
A. 58
B. 122
C. 148
D. 180
58
Step-by-step explanation:
sum of angle inside a triangle is equal to 180
plus 90 and 32 you get 122 now subtract 180 and 122 the answer will be 58
Please help me with this question
Distributive property, Subtraction property of equality, and Division property of equality had been used respectively according to the blanks provided.
First is distributive property, which states that if the equation is complex it needs to be simplified. The distributive property uses the PEMDAS rule which is the priority sequence in which the equation needs to be solved.
P stands for Parentheses, E stands for Exponents, M stands for Multiplication, D stands for Division, A stands for Addition, and S stands for Subtraction.
Second is the subtraction property of equality, which states the same number could be subtracted from both the side which is left-hand side and the right-hand side to solve an equation.
And the last is the division property of equality, which states the same number could be divided from both the side which is left-hand side and the right-hand side to solve an equation.
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PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!
At a lacrosse tournament, students are charged $7 per ticket and adults are charged $10 per ticket. If 450 people attended the tournament, and a total of $3,600 was collected in ticket fees, how many students attended the tournament?
100
150
200
300
The line parallel to y=-4x-1 that passes through the point (3,-2)
Answer:
y=-4x+10
Step-by-step explanation:
-2= -4(3)+b
-2=-12+b
-10=b
the overall change in temperature when the temperature is 10 degrees fahrenheit at 9:00 am and 10 degrees fahrenheit at 6:00 pm.
The change in temperature based on the time and the temperature given is 0.
What is temperature?It should be noted that temperature simply means the degree of coldness and hotness of a particular body.
In this case, we want to calculate the overall change in temperature when the temperature is 10 degrees fahrenheit at 9:00 am and 10 degrees fahrenheit at 6:00 pm.
Therefore, the change will be the subtraction of the values given. This will be:
= 10°F - 10°F
= 0
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Given that log 2 = 0.3010 and log 3 = 0.4771, find log √30 without using a calculator.
Answer:
0.73855.
Step-by-step explanation:
log √30
log 30^1/2
= 1/2 log 30
30 = 2 * 3 * 5
= 3 * 10
So, log 30
= log (3*10) = log 3 + log 10
= 0.4771 + 1
= 1.4771
and log √30
= 1/2 log 30
= 1/2 * 1.4771
= 0.73855
the volume of a spherical balloon expands as air is pumped into it. assume air is being pumped at a constant rate of 400π in³/sec.what is the radius of the balloon when its volume is 972π in³?use the formula:v=46πr3v = \frac{4}{6} \pi r ^{3} v=64πr3
The radius of the given sphere will be 9/π.
What is a sphere?A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is denoted by the letter r, and the given point is its center. The sphere is a three-dimensional shape that is sometimes referred to as a circle's second cousin. A sphere is a solid shape that is round, without edges. Balloons, playing balls, and even light bulbs are examples of objects with sphere shapes.So, the formula for the volume of a sphere: V = 4/3πr³
Volume is 972, then the radius will be:
972 = 4/3πr³3(972) = 4πr³2,916 = 4πr³πr³ = 2916/4πr³ = 729r³ = 729/πr = ∛729/πr = 9/πTherefore, the radius of the given sphere will be 9/π.
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Can someone help me understand the following because I’m confused?
Given:
a.) Each small box of paper weighs 50 pounds.
b.) Each large box of paper weighs 80 pounds.
c.) There were 4 more large boxes shipped than small boxes.
d.) The total weight was 1750 pounds.
Since the scenario is involving two types of boxes, we will be using two variables to represent each of them.
Let,
x = the total number of the small box of paper
y = the total number of the large box of paper
Let's now generate the system of equations that we will be using to able to solve the problem.
1st relationship: There were 4 more large boxes shipped than small boxes.
Putting this into equation, we get:
[tex]\text{ y = x + 4}[/tex]2nd relationship: The total weight was 1750 pounds.
For us to get the total weight, we will be adding the sum of the number of each box by the weight each box has.
We get,
[tex]\text{ 50x + 80y = 1750}[/tex]In summary:
Let x = the total number of the small box of paper
Let y = the total number of the large box of paper
System of equations:
a.) y = x + 4
b.) 50x + 80y = 1750
Pastels weekly salary includes base pay plus commission of his sales. the equation s=700+0.07c models between his weekly sales in dollars and the amount of his sales in dollars. find pastels salary in dollars for a week when his sales were 0$
the equation s=700+0.07c models between his weekly sales in dollars and the amount of his sales in dollars. pastels salary in dollars for a week when his sales were 0$ is $700.
Pastels weekly salary includes base pay plus commission of his sales.
the equation s=700+0.07c models between his weekly sales in dollars and the amount of his sales in dollars.
find pastels salary in dollars for a week when his sales were 0$
the model is given as
s=700+0.07c
let us solve for c, the sales made
s =700 +0.07c given sales is 0$
then s=700
Hence , the equation s=700+0.07c models between his weekly sales in dollars and the amount of his sales in dollars. pastels salary in dollars for a week when his sales were 0$ is $700.
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If TU= 16, UV = x + 4, and TV = 8x - 15, what is IV?
UV = 11 and TV = 41
What is ruler postulateA line segment has two fixed end points in a line. The length of the line segment is the distance between two fixed points. The length can be measured by units such as centimeters, millimeters, feet or inches
The points on a line are matched one to one with the real numbers in ruler postulate. Coordinate of the point is the real number that corresponds to a point. The distance between points A and B (AB) is equal to the difference of the coordinates of A and B.
As given,
TU = 16, UV = x+4 and TV = 8x -15
TU + UV = TV
16 + x+4 = 8x -15
16 + 4 +1 5 = 8x - x
35 = 7x
x = 35/5
x= 7
We can find UV = x + 4 by substituting the value of x
= 7 +4
= 11
and TV = 8x - 15
= (8*7) - 15
=56 - 15
=41
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Which of the following statements is not
true about the linear equation, y + 3 = -2(x-7)?
O The line has a slope of -2
O The linear equation can also be written as y=-2x +11
O The line contains the point (7,-3)
O The line contains the point (-7, 3)
Answer: Option 4
Step-by-step explanation:
This is true because the coefficient of x is -2.[tex]y+3=-2x+14 \implies y=-2x+11[/tex], so this is true.Substituting [tex]x=-7[/tex], [tex]y=(-2)(7)+11 =-3[/tex], so this is true.Substituting [tex]x=7[/tex], [tex]y=-2(-7)+11=3[/tex]. so this is false.A metal bat is dropped from a hot air balloon and strikes the ground 6 seconds later. How high was the hot air balloon?
The balloon was flying at a height of 176.58 m .
The fundamentals of an object's motion, such as its position, velocity, or acceleration over time, are defined by kinematics equations of motion. An object's motion in one, two, and three dimensions is determined by these three equations of motion. One of three equations of motion can be used to calculate components like displacement (s), velocity (initial and final), time (t), and acceleration (a). The following are the three motion equations:
Initial formula: v = u + at
The second formula is s = ut + 0.5at2.
The third formula is v2 = u2 + 2as.
Let t stand for the duration of the metal bat's flight, s for the height at which the hot air balloon was traveling, and u for the metal bat's initial vertical velocity since it is simply dropped.
Given: The metal bat took 6 seconds to reach the ground.
With t = 12 and u = 0, the second equation of motion gives us s = 0*t + 0.5*9.81*162 = 176.58 m.
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1. The following data give the lengths of time (in weeks) taken to find a full-time job 18 civil engineering majors who graduated in 2005 from a small college. 6 12 21 15 8 4 6 13 16 30 7 24 11 48 15 10 14 14 25 a) Find the average length of time taken to find a full-time job The average length in time is b) Find the standard deviation
The average length of time taken to find a full-time job is 16 and the standard deviation is 10.51.
Total Population = N = 18
Data is given below
[tex]x_{i}[/tex] 6 12 21 15 8 4 6 13 16 30 7 24 10 48 15 14 14 25
Mean = μ = ( ∑ [tex]x_{i}[/tex] ) / N
μ = ( 6 + 12 + 21 + 15 + 8 + 4 + 6 + 13 + 16 + 30 + 7 + 24 + 10 + 48 + 15 + 14 + 14 + 25 )/18
μ = 288/18 = 16
Mean = μ = 16
[tex]x_{i}[/tex] 6 12 21 15 8 4 6 13 16 30 7 24 10 48 15 14 14 25
([tex]x_{i}[/tex] - μ)^2 100 16 25 1 64 144 100 9 0 196 121 64 36 1024 1 4 4 81
∑([tex]x_{i}[/tex] - μ)^2 = 100 + 16 + 25 + 1 + 64 + 144 + 100 + 9 + 0 + 196 + 121 + 64 + 36 + 1024 + 1 + 4 + 4 + 81 = 1990
Standard Deviation =√ (∑([tex]x_{i}[/tex] - μ)^2 / N )
Standard Deviation =[tex]\sqrt{1990/18}[/tex] = 10.5145 = 10.51
Thus, the standard deviation is 10.51 and the average length of time taken to find a full-time job is 16 .
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