Mr mole descend at the rate of 2.3 meters per minutes.
A rate in mathematics is the comparison of two related values expressed in dissimilar units.
The numerator of the ratio expresses the equivalent rate of change in the other (dependent) variable if the denominator of the ratio is presented as a single unit of one of these quantities and it is expected that this number may be altered systematically (i.e., is an independent variable).Examples of rates that are usually represented as "per unit of time" are speed, heart rate, and flux. An example of a ratio having a non-time denominator is the electric field ratio. Other examples include exchange rates and literacy rates (in volts per meter).The given equation to represent the position of Mr. Mole is
A = -2.3 t - 7
where A denotes the depth and t is the time.
Now the rate can be found out by dividing the change in depth by the change in time.
Differentiating we get
ΔA = -2.3 Δt
or, ΔA / Δt = -2.3
hence the rate of the mole is 2.3 meters per minutes.
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What should be done to both sides of the equation in order to solve 5 + x = -19?
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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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.
It takes 10 minutes to fry one steak - 5 minutes from each side. Two steaks can fit on a pan. What is the shortest possible time to fry 3 steaks
The shortest possible time is 15 minutes.
It takes 10 minutes to fry one steak - 5 minutes from each side. Two steaks can fit on a pan. What is the shortest possible time to fry 3 steaks?
If I go with the conventional way then I can fry two steaks together taking ten minutes and then I can fry the third one in another ten minutes. So total time 20 minutes.
Assuming that I have only one pan and three steaks to fry. We can even use unitary method .
I will put two steaks in the pan then after 5 minutes I will take out one steak and put the other steak while I will flip the steak which is still in the pan. So in first ten minutes I have only one steak ready. Then I will flip the newly added steak in the pan and put the half side fully cooked steak also in the pan. So in this way in the coming five minutes my other two steaks will also get cooked. Total time taken=5+5+5=15 minutes.
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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
Write the rational number as a decimal
1 5/6
The answer is 1.83
Step-by-step explanation:
Look it up
∠A and \angle B∠B are vertical angles. If m\angle A=(4x-4)^{\circ}∠A=(4x−4)
∘
and m\angle B=(5x-29)^{\circ}∠B=(5x−29)
∘
, then find the measure of \angle A∠A.
The value of angle A when A and B are vertical opposite angles is 96°.
How to illustrate the information?It should be noted that vertical angles are equal. Based on the information illustrated, it should be noted that angle A = 4x - 4 and angle B = 5x - 29.
Then, we will equate the equations and this will be:
Angle A = Angle B
4x - 4 = 5x - 29
Collect like terms
5x - 4x = -4 + 39
x = 25
Since angle A = 4x - 4 = 4(25) - 4 = 100 - 4 = 96°
Angle A is 96°.
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If ƒ(x) = x/2 −2 and g(x) = 2x² + x−3, find (ƒ +g)(x).
A. 2x² + 3x-6
B. 2x² - +1
C. ²-6
D. 2x²+2x+1
[tex](f+g)(x)=f(x)+g(x)\\\\=\frac{x}{2}-2+2x^2 +x-3\\\\=2x^2 +\frac{3}{2}x-5[/tex]
a healthy young student used an elliptical trainer for 40 minutes at the gym. although the workload remained constant, the student's heart rate rose to 150 beats per minute during the first 5 minutes, stayed at that level for the next 25 minutes, and then started to rise. it was 180 beats per minute at the end of the exercise period. what was the time interval between qrs complexes when the student's heart rate was 180 beats per minute?
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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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
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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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
Simplify the expression.
the quantity negative 1 over 8 times r minus 5 minus 1 over 6 times r end quantity minus the quantity negative 6 over 8 times r plus 3 end quantity
negative 8 over 14 times r minus 2
11 over 24 times r plus negative 2
negative 4 over 14 times r minus 8
11 over 24 times r plus negative 8
The correct answer is option D which is the expression is, 11 over 24 times r plus negative 8.
In mathematics, creating equations from word descriptions is referred to as a "word problem."
For example, in the question, equations are expressed in words and then rewritten in figures, which is the preferred way to write equations.
The equation is rewritten in words and solved as below.
How to write and solve the equation
Given expression is,
[tex](\frac{-1}{8}*r-5-\frac{1}{6} *r)-(\frac{-6}{8} *r+3)[/tex]
solving the equation:
= [tex](\frac{-1}{8} *r-5-\frac{1}{6} *r)-(\frac{-6}{8} *r+3)[/tex]
= [tex](\frac{-r}{8} -5-\frac{r}{6} )-(\frac{-6r}{8} +3)[/tex]
opening the parenthesis leads to change of signs as follows
= [tex]\frac{-r}{8} -5-\frac{r}{6} +\frac{6r}{8} -3[/tex]
= [tex]\frac{-r}{8} -\frac{r}{6} +\frac{6r}{8} -5-3[/tex]
= [tex]\frac{-3r-4r}{24}+\frac{6r}{8} -8[/tex]
= [tex]\frac{-7r}{24} +\frac{6r}{8} -8\\[/tex]
= [tex]\frac{-7r+18r}{24} -8[/tex]
= [tex]\frac{11r}{24} -8[/tex]
= [tex]\frac{11}{24} *r+(-8)[/tex]
Therefore the correct answer is option D which is 11 over 24 times r plus negative 8.
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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.
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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I need it solved in steps that I can write down please
The values of indicated function are-
f(-4) = 6f (0) = -6f(1) = -4What exactly is the function?A function is described as the interaction of a set of inputs with one output each.A function is a relationship between inputs in which each input is precisely related to one output.Also every function has a domain, a codomain, and a range. A function is generally denoted by f(x), where x is the input.The general representation of a function is y = f. (x).A function in mathematics is a special correlations among inputs (the domain) as well as outputs (the codomain), in which each input has exactly each output as well as the output can be directly linked to its input.For the given question;
For finding the values of the function, see the values for y axis with respect to the given values of x from the graph.
a: f(-4), input value is (-4), output on y axis is 6.
f(-4) = 6.
b: f(0), input value is (0), output on y axis is -6.
f(0) = -6.
c: f(1), input value is (1), output on y axis is -4.
f(1) = -4.
Thus, the range for the state functions are obtained.
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Rewrite 140 + 200 using the GCF and factoring.
Answer:
20(7 + 10)
Step-by-step explanation:
The GCF of 200 and 140 are 20
.: by GCF and factoring we have:
20(7 + 10)
Opening the bracket still gives the initial expression.
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
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.
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)
HOPE THIS HELPS GOOD LUCK!!
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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In complete sentences, explain the following:
What could happen if you don't stick to a budget?
20 is 80% of what number?
Answer: 25?
Step-by-step explanation:
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 $300:
[tex]\Sigma^{n=10}_{n=1}300(0.055)^{n-1}_{}[/tex]Answer: first option.
Money in Brazil is called a Real (abbreviated R$). Davi starts a coffee business. He makes 3.82 R$ for every cup of coffee sold. How many cups would he need to sell to make at least 500 R$ profit?
What's the inequality for this story?
Write the steps to solve it
What is the solution
When this inequality is graphed will the limit be an open or closed circle?
When this inequality is graphed will the line have an arrow pointing to the right or to the left?
Davi needs to sell 131 cups to make at least R$500 profit , the inequality for this story is 3.82x ≥ 500 ,
In the question ,
it is given that
Davi makes R$3.82 per cup of coffee sold .
he needs to make at least R$500 profit
let the number of cups of coffee sold = x ,
the term "at least" means " ≥ " ,
So , According to the question , the inequality becomes
3.82x ≥ 500
x ≥ 130.89
x ≥ 131 .....as number of cups cannot be in decimal .
so the minimum number of cups to be sold is 131 cups.
When the inequality x ≥ 131 , will be graphed then the limit will be an closed circle as equal to sign is included in the inequality .
as when the numbers increases , it move towards right side
So, When the inequality is graphed, the line will have an arrow pointing towards the right .
Therefore , Davi needs to sell 131 cups to make at least R$500 profit ,
the inequality for this story is 3.82x ≥ 500 ,
the limit of graph will be closed circle and arrow will be pointing towards right .
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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
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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what is the answer to: 4y+8x=4 with solution
Find the measure of w
Answer:
56
Step-by-step explanation:
Because w and 124 make a straight line. So you would need to subtract 180 from 124
Answer:
A )56
Step-by-step explanation: