30 1/2 cups soup divided by 3: 10 1/6 cups or 10 1/2 cups per container.
What is interpretation ?
Interpretation is the process of understanding and explaining the meaning of something, such as a text, a piece of artwork, or a scientific data. In the context of mathematics and problem solving, interpretation refers to understanding the meaning of a mathematical expression or equation in the context of the problem or situation being described.
In this context, "30 and 1 half cups of oup" refers to the amount of soup that Avery has in the large pot, and "divided by 3" refers to the number of smaller containers Avery plans to divide the soup into. There are two different ways to interpret 30 and 1 half divided by 3 in this context ,
Avery will divide the 30 and 1 half cups of soup equally among 3 smaller containers. This means that each container will hold (30 + 1/2) / 3 = 10 and 1/6 cups of soup.
Avery will pour out 10 and 1/2 cups of soup from the large pot into each of the 3 smaller containers. This means that after Avery has poured out all the soup, the large pot will be empty and the 3 smaller containers will each contain 10 and 1/2 cups of soup.
30 1/2 cups soup divided by 3: 10 1/6 cups or 10 1/2 cups per container.
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Avery will divide the 30 and 1 half cups of soup equally among 3 smaller containers. This means that each container will hold (30 + 1/2) / 3 = 10 and 1/6 cups of soup.
Avery will pour out 10 and 1/2 cups of soup from the large pot into each of the 3 smaller containers. This means that after Avery has poured out all the soup, the large pot will be empty and the 3 smaller containers will each contain 10 and 1/2 cups of soup.
What is the angle between lines 2x 3y =- Z?.
The angle between lines 2x 3y =- Z is 90°
We will simplify the given equation of lines in the standard form of x/a=y/b=z/c
where a, b and c are the direction ratios of the line.
We will calculate the angle between these lines using the formula:
[tex]cos\alpha =\frac{a_{1}a_2 +b_1b_2+c_1c_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2} }[/tex]
we are given two lines as 2x = 3y = – z and 6x = -y = -4z
We can write them in standard form xa=yb=zc
as:
For 2x = 3y = – z ⇒x/1/2=y/1/3=z/−1/4
Comparing this equation with the standard equation, we get the direction ratios of this line:
a₁= 1/2
b₁=1/3
c₁ = -1
For 6x = -y = -4z ⇒x/1/6=y−1=z/−1/4
Comparing this equation with the standard equation, we get the direction ratios of this line:
a₂= 1/6, b₂= -1, c₂= −1/4
Now, putting these values of a₁, a₂, b₁, b₂, c₁, and c₂
in the equation of cosα, we get
[tex]cos\alpha =\frac{a_{1}a_2 +b_1b_2+c_1c_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2} }[/tex]
[tex]cos\alpha =\frac{\frac{1}{2} *\frac{1}{6} +\frac{1}{3} *(-1)+(-1)\frac{(-1)}{4} }{\sqrt{(\frac{1}{2})^2 +(\frac{1}{3})^2 +(-1)^2}\sqrt{(\frac{1}{6} )^2+(-1)^2+(\frac{-1}{4})^2 } }[/tex]
[tex]cos\alpha =\frac{\frac{1}{12} -\frac{1}{3} +\frac{1}{4} }{{\sqrt{(\frac{1}{2})^2 +(\frac{1}{3})^2 +(-1)^2}\sqrt{(\frac{1}{6} )^2+(-1)^2+(\frac{-1}{4})^2 } } }[/tex]
[tex]cos\alpha =\frac{\frac{1}{12} -\frac{1}{12} }{{\sqrt{(\frac{1}{2})^2 +(\frac{1}{3})^2 +(-1)^2}\sqrt{(\frac{1}{6} )^2+(-1)^2+(\frac{-1}{4})^2 } } }[/tex]
cosα=0°
cos⁻¹(cosα)=cos⁻¹(0)
α=90°
Therefore, the angle between the lines 2x = 3y = – z and 6x = -y = -4z is 90°
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three consicutive integers add up to 57 ? what are these integers?
Answer:
18, 19, 20
Step-by-step explanation:
Let the integers be x - 1, x, x + 1.
x - 1 + x + x + 1 = 57
3x = 57
x = 19
x - 1 = 18
x = 19
x + 1 = 20
Answer: 18 , 19 , 20
Step-by-step explanation:
18+19+20=57
How to write a system of linear inequalities represented by the graph?.
To write a system of linear inequalities represented by the graph solution boundary line dashed for > and < and solid for ≤ and ≥ is used.
These steps will be used to graphically solve a set of linear inequalities:
1. Find y's inequality solution.
2. Represent the inequality as a linear equation and, depending on the inequality sign, graph the line as either a solid line or a dashed line.
a. Draw the line as a dashed line if the inequality symbol is missing an equals sign ( or >).
b. Draw the line as a solid line if the inequality sign contains an equals sign (or ).
3. Darken the area when the inequality is satisfied.
4. For every disparity, repeat steps 1 through -3.
5. The region where all of the inequalities intersect will be the solution set.
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Which statement about this figure is true?
has no rotational symmetry.
It has rotational symmetry with an angle of rotation of 120°.
It has reflectional symmetry with five lines of symmetry.
The line of reflection is also known as the axis of symmetry. Then the correct option is C.
What is the axis of symmetry?Axial symmetrical is similarity around an axis; an item is internally symmetric if it retains its appearance when turned around an axis.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
The reflection does not change the shape and size of the geometry. But flipped the image.
From the graph, if it is rotated by 72°. Then the figure will remain the same. And the line of reflection is also known as the axis of symmetry.
Thus, the correct option is C.
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The marked price of a drawing table is $12,90 if a discount going to be 18%is offered on the table what is the sale price?
Answer:
$10.57
Step-by-step explanation:
$12.90
- 18%
----------
$10.57
-12 + 3m=m - 2
Thank u
Answer:
m = 5
Step-by-step explanation:
-12 + 3m=m - 2
3m = m + 10
2m = 10
m = 5
Let's check
-12 + 3(5) = 5 - 2
-12 + 15 = 3
3 = 3
So, m = 5 is the correct answer.
Each lap around a school's track ismi. Noriko wants to run 1 mi. She wants to know how many
laps she needs to run around the track.
Complete the model to show how many laps Noriko needs to run.
0
B
1
1-2
2
The number of laps that Noriko needs to run is given as follows:
6 laps.
How to obtain the number of laps that Noriko needs to run?The number of laps that Noriko needs to run is obtained applying the proportions in the context of this problem.
The length of one lap is given as follows:
1/6 miles.
Hence the number of laps that Noriko needs to run for a total of one mile is obtained dividing one mile by the length of a single lap, as follows:
1/(1/6) = 6 x 1 = 6 laps.
Missing InformationEach lap around the school's track is of 1/6 mi.
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Marco forgot to label the volume for 3 ice core samples. The mass of 1 full box is 18.6 g; the other 2 boxes are 9.1 g each. What is the volume, in cubic centimeters, of the 3 samples? (Hint: Use the formula Volume = Mass Density to solve the problem.)
The volume of each of the 3 samples is given as follows:
Sample of 18.6 g: 20.67 cm³.Each of the two samples of 9.1 g: 10.11 cm³.How to obtain the volume of each sample?The density is given by the division of the mass by the volume, hence:
Density = Mass/Volume
The equation can be solved for the volume as follows:
Volume = Mass/Density.
The density of ice is given as follows:
0.9 g/ cm³.
Hence the volume of each sample is given as follows:
Sample of 18.6 g: 18.6/0.9 = 20.67 cm³.Each of the two samples of 9.1 g: 9.1/0.9 = 10.11 cm³.More can be learned about density, mass and volume at https://brainly.com/question/1354972
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A carpenter ha a board that i three and one fourth inche long. He join a econd board to the end that i five and three fourth inche long. What i the total length? implify if poible
The total length of the two boards is 9 inches.
An inch can be defined as a unit of length in the customary system of measurement. Length in inches is either represented by in or ''. For instance, 5 inches can be written as 16 in or 16''. of a foot.
as given, a carpenter has a board that is three and one fourth inches long
i.e. the carpenter has a board that is 3.25 inches long.
and a second board to the end that is five and three fourth inches long
i.e. another board that is 5.75 inches long.
When joined together, the total length of the two boards is 3.25 inches + 5.75 inches = 9 inches.
Therefore, the total length of the two boards is 9 inches.
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How do you write a solution set of a system?.
A solution set in of a linear equation system mathematics to the set of values correctly solve such system which inputted into a system of equations correctly .
The main steps to follow calculating solution sets for a linear equations of system
first step is to Convert the system into a matrix equation
secondly Rewrite matrix equation into an augmented matrix
next step is Computing the reduced echelon form of the augmented matrix by use of Gaussian elimination processes
after that The reduced echelon form of the matrix will provide the values for the unknown variables,
using these solutions to writing down the parametric vector equation form that contain the complete set of solutions for the system.
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2. Match each pair of points to the slope of the line that joins them. A. (9, 10) and (7.2) B. (-8,-11) and (-1,-5) C. (5,-6) and (2,3) D. (6.3) and (5.-1) E. (4,7) and (6.2) 1.4 2.-3 3.-2/20 m 67 4.9
The rise and run of the line may be determined using two of its points, and the slope can be calculated.
Given two points, how do you calculate a line's slope?Given two line-side coordinates, use the slope formula to determine the slope of the line. Slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations.The rise and run of the line may be determined using two of its points, and the slope can be calculated. The rise and run are terms for the vertical and horizontal changes between two places, respectively. In order to calculate the slope, multiply the rise by the run. Rise + run = a slope.To learn more about slope refer to:
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The correct matches are: A. Slope = 1.56, B. Slope = 0.86, C. Slope = 3
D. Slope = -5.61, E. Slope = -0.44
Given two points, how do you calculate a line's slope?Given two line-side coordinates, use the slope formula to determine the slope of the line. Slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations.
Here are the correct matches of each pair of points to the slope of the line that joins them:
A. (9, 10) and (7.2) - Slope = (10 - 7.2)/(9 - 7.2) = 2.8/1.8 = 1.56
B. (-8,-11) and (-1,-5) - Slope = (-5 - (-11))/(-1 - (-8)) = 6/7 = 0.86
C. (5,-6) and (2,3) - Slope = (3 - (-6))/(2 - 5) = 9/3 = 3
D. (6.3) and (5,-1) - Slope = (-1 - 6.3)/(5 - 6.3) = -7.3/1.3 = -5.61
E. (4,7) and (6.2) - Slope = (6.2 - 7)/(4 - 6.2) = -0.8/1.8 = -0.44
So, the correct matches are:
A. Slope = 1.56
B. Slope = 0.86
C. Slope = 3
D. Slope = -5.61
E. Slope = -0.44
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In the payments, credits, and tax section of the 1040EZ form shown below, which of these dollar amounts could be on line 10 if $4184 is on line 11 and the taxpayer will neither receive a refund nor owe the IRS ?
The amount on line 10 (total payments and credits) must be equal to the amount on line 11 (amount you owe) which is C: $4184.
How to calculate difference?
The difference is a mathematical operation used to find the amount by which one number is greater or smaller than another number. It is calculated by subtracting the smaller number from the larger number. The difference can be represented by the symbol "-" or the word "minus"
The dollar amount that could be on line 10 if $4184 is on line 11 and the taxpayer will neither receive a refund nor owe the IRS is $4184.
Line 10 on the 1040EZ form is for the "Total payments and credits" which is the sum of all payments made throughout the year, including any tax payments, estimated tax payments, and any credits the taxpayer is entitled to.
Line 11 is for the "Amount you owe" which is the difference between the total tax liability (calculated on the form) and the total payments and credits.
If the taxpayer will neither receive a refund nor owe the IRS, it means that the total payments and credits are equal to the total tax liability.
Hence, the amount on line 10 (total payments and credits) must be equal to the amount on line 11 (amount you owe) which is $4184.
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The dimensions of a cylinder are shown in the diagram. Which measurement is closest to the lateral surface area in square centimeters of the cylinder
The lateral surface area of a cylinder is 1110.8 cm².
Derive the formula for the volume of cylinder.Consider a very thin cross section of a cylinder whose thickness is [dh] {differential or very small value}. The volume of this cross section would be -
dV = πr² dh
For complete cylinder -
∫dV = πr² ∫dh
[V - 0] = πr² [h - 0]
V = πr²h
Given are the dimensions of a cylinder are shown in the diagram.
We can write the lateral surface area as -
LSA = 2πrh
LSA = 2 x 3.14 x 8.8 x 20.1
LSA = 1110.8 square centimeters.
Therefore, the lateral surface area of a cylinder is 1110.8 cm².
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Tell whether b=11 is a solution of -3=8-b .
Answer:
Yes. Since 8 - 11 is -3, -3= -3
Step-by-step explanation:
-3=8-b
-3=8-11
-3=-3
Answer:
Look Below ↓↓↓
Step-by-step explanation:
Let's solve it and see if it is:-
[tex]\bf -3=8-b[/tex]
Simplify both sides of the equation:-
[tex]\bf -3=8-b[/tex]
[tex]\bf -3=8+-b[/tex]
[tex]\bf -3=-b+8[/tex]
Flip the equation:-
[tex]\bf -b+8=-3[/tex]
Subtract 8 from both sides:-
[tex]\bf -b+8-8=-3-8[/tex]
[tex]\bf -b=-11[/tex]
Divide both sides by -1:-
[tex]\bf \cfrac{-b}{-1}=\cfrac{-11}{-1}[/tex]
[tex]\bf b=11[/tex]
Therefore, yes b = 11!!
_____________________
Hope this helps!
Have a great day!
Eiko is wearing a magic ring that increases the power of her healing spell by 30 % 30%30, percent. Without the ring, her healing spell restores � HH health points. Which of the following expressions could represent how many health points the spell restores when Eiko is wearing the magic ring?
The expression 1.3H represents the relationship between the number of health points restored by Eiko's healing spell with and without the magic ring.
H represents the number of health points restored by the spell without the ring. The expression 0.3H represents the additional 30% increase in the power of the spell due to the magic ring, as the ring increases the spell's power by 30%.
Adding the two, H + 0.3H, gives us the total number of health points restored by the spell with the magic ring, which is equal to 1.3 times the number of health points restored by the spell without the ring.
So, when Eiko is wearing the magic ring, her healing spell restores 1.3 times as many health points as without the ring, represented by the expression 1.3H.
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Need help please……..
According to the solving the probability of the spinner and the dice
A. = 1 / 2.
B. = 1/6.
What is probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Why does probability matter?Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures as well as the risk of health impacts are related.
According to the given information:for the spinner
total number of division = 4
the pink colored sections = 2
Number of Favorable Outcomes / Total Number of Outcomes is the formula for probability.
Probability = 2 / 4.
Probability = 1 / 2.
for the Dice
total number of division = 6
the pink colored sections = 1
Number of Favorable Outcomes / Total Number of Outcomes is the formula for probability.
Probability = 1/6.
Probability = 1/6.
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help meeeeee pls!!!!
Step-by-step explanation:
domain : the interval or set of all valid x-values.
range : the interval or set of all valid y-values (function result values).
A is correct
theoretically all real numbers are valid as x. but for this application of the function only non-negative integer values make sense (e.g. half a cycle does not make any sense).
C is correct
via A we are allowing all real numbers to be valid input values, so, we have to allow also all real numbers to be valid output (function result) values.
D is correct
the y-intercept means the y-value, when the function curve intersects the y-axis.
this is only possible, when x = 0.
5⁰ = 1
as any x⁰ = 1
F is correct
the bigger x, the bigger 5^x.
and the smaller x, the closer y, the function result, gets to 0. particularly, when we allow negative input values (as we said in A).
Is A ={ x x² 4 and 3x 9 an empty set justify your answer?.
Yes, the given set A={x:x²=4 and 3x=9(0)} is an empty set.
Given the set:
A={x:x²=4 and 3x=9(0)}
Consider the equation:
x²=4
Solve for x:
x²=4⇒x=±2
Consider the other equation:
3x = 9
Solve for x:
3x = 9⇒x = 3
Because the square of the set element should be 4, the element should be 2 or -2, but 2 or -2 multiplied by 3 gets 6 or -6, which is not equal to 9. As a result, no element exists that can meet both conditions.
The value of ‘x’ is not same in both cases, so this is a null set.
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please help me i swear i’ll give u crown. INTEGRALS INTEGRALS
the other part is uploaded in my profile INTEGRALS PLEASE HELP ME
Answer:
[tex]\textsf{1)} \quad 4.1875[/tex]
[tex]\textsf{2)} \quad \dfrac{1}{2}x^{4}-x^{3}+x^{2}-3x+\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration:
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
The area between a curve and the x-axis can be found using definite integration. The definite integral of f(x) with respect to x between the limits x = a and x = b:
[tex]\displaystyle \int^b_a \text{f}(x)\; \text{d}x=\left[\text{g}(x)\right]^b_a=\text{g}(b)-\text{g}(a)[/tex]
where a is the lower limit and b is the upper limit.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}\left(+\text{C}\right)$\end{minipage}}[/tex]
Question 1Given function:
[tex]\text{f}(x)=\dfrac{1}{4}x^3+\dfrac{1}{6}x+1[/tex]
From inspection of the given graph:
Lower limit a = -1Upper limit b = 2Therefore:
[tex]\begin{aligned}\displaystyle\int^2_{-1}\left(\dfrac{1}{4}x^3+\dfrac{1}{6}x+1\right)\;\text{d}x&=\left[\dfrac{1}{4\cdot4}x^{3+1}+\dfrac{1}{6\cdot 2}x^{1+1}+x\right]^2_{-1}\\\\&=\left[\dfrac{1}{16}x^4+\dfrac{1}{12}x^2+x\right]^2_{-1}\\\\&=\left(\dfrac{1}{16}(2)^{4}+\dfrac{1}{12}(2)^2+(2) \right)-\left(\dfrac{1}{16}(-1)^4+\dfrac{1}{12}(-1)^2+(-1)\right)\\\\&=\left(1+\dfrac{1}{3}+2\right)-\left(\dfrac{1}{16}+\dfrac{1}{12}-1\right)\\\\&=\dfrac{10}{3}+\dfrac{41}{48}\\\\&=\dfrac{67}{16}\\\\&=4.1875\end{aligned}[/tex]
Question 2[tex]\begin{aligned}\displaystyle \displaystyle \int (x^2+1)(2x-3)\; \text{d}x&=\displaystyle \int \left(2x^3-3x^2+2x-3\right)\; \text{d}x\\\\&=\dfrac{2}{4}x^{3+1}-\dfrac{3}{3}x^{2+1}+\dfrac{2}{2}x^{1+1}-3x+\text{C}\\\\&=\dfrac{1}{2}x^{4}-x^{3}+x^{2}-3x+\text{C}\end{aligned}[/tex]
Find the maximum and minimum values for 4x + y if -2 <= y <= 2, y <= -3x + 5 and y <= 3x + 5
Answer:
max : 2, min : -2
Step-by-step explanation:
this question is kinda hard and brain-intensive but i think i am right
Answer:
max : 2, min : -2
Step-by-step explanation:
max : 2, min : -2
Select all of the following algebraic rules that represent a dilation that is an enlargement?.
First and fourth options are in dilation that is an enlargement as k>1 for enlargement in the expression (kx, ky).
Dilation is the enlarging or shrinking of a fine element( a point on a match grid, polygon, line member) using a specific scale factor. Dilation is one of the five major metamorphoses ingeometry.When a dilation in the match aeroplane has the origin as the center of dilation, you can find points on the dilated image by multiplying the x- and y- equals of the original figure by the scale factor. For scale factor k, the algebraic representation of the dilation is( x, y) →( kx, ky)
The introductory formula to find the scale factor of a ballooned figure is Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
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The complete question is :
Which of the following algebraic rules that represent a dilation that is an enlargement?
1 (1 1/3 x, 1 1/3y)
2 - (1/2 x, 1/2y)
3 - ( 0.1 x, 0.1 y)
4 (3 1/10 x, 3 1/10y)
What is a degree polynomial called?.
Answer:
Step-by-step explanation:
the degree of a polynomial is determined by the biggest exponent. For example, in this equation: 6x^4+3x^3+3x^2+2x+1, you can see that the biggest exponent is the 4, so it would be a polynomial of the 4th degree.
help me pls, thanks!
Use this equation for the questions below: y=log(5x+10)+8
Create a real-life application problem involving your chosen function type
Explain how to determine all of the key properties of your specific function and how to sketch the graph
Ask two interesting, realistic questions about the situation in context.
Question 1: Determine the value of the dependent variable given a value of the independent
Question 2: Determine the value of the independent variable given a value of the dependent
Show how you would solve both problems using only algebra. Show all of the steps.
Question 1: The value of the dependent variable given a value of the independent is 11.54 (thousands of people)
Question 2: The value of the independent variable given a value of the dependent is 1998 (5 years after 2000)
How do we get the values?Real-life application problem: The population of a city is growing at a rate modeled by the equation y = log(5x + 10) + 8, where y is the population in thousands and x is the number of years since the year 2000.
To determine the key properties of the function and sketch its graph:
The function is a combination of a logarithmic and an exponential function.
The domain of the function is all real numbers (since the logarithm function is defined for all positive numbers)
The range of the function is all real numbers greater than or equal to 8 (since the minimum value of the function is 8)
The graph of the function will be a smooth, continuous curve that starts at the point (0,8) and increases without bound as x increases.
Question 1: Determine the value of the population (y) given a value of x = 5 (number of years since 2000)
Solution:
y = log(5x + 10) + 8
y = log(5(5) + 10) + 8
y = log(25 + 10) + 8
y = log(35) + 8
y = 3.54 + 8
y = 11.54 (thousands of people)
Question 2: Determine the value of x (number of years since 2000) given a population of y = 12 (thousands of people)
Solution:
y = log(5x + 10) + 8
12 = log(5x + 10) + 8
4 = log(5x + 10)
5x + 10 = 10^4
5x = 9990
x = 1998 (5 years after 2000)
Note that this is not a realistic scenario, as the population of a city cannot be negative except in the case of extinction.
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Eva is deciding between two landscaping companies for her place of business.
Company A charges $35 per hour and a $300 equipment fee. Company B charges $45
per hour and a $100 equipment fee. Let A represent the amount Company A would
charge for t hours of landscaping, and let B represent the amount Company B would
charge for t hours of landscaping. Write an equation for each situation, in terms of t,
and determine the number hours, t, that would make the cost of each company the same.
For seven hours of landscaping, Company B would be less expensive than Company A.
What is an equation?An equation is defined as any pair of expressions that both contain the equal sign.
Because of this, Company charges $35 per hour and a $250 equipment fee, compared to Company B's $25 per hour and $300 equipment fee.
For t hours of landscaping, Company A will bill the following:
A = 35t + 250 (1) (1)
In a similar vein, Company B bills the following sum for t hours of landscaping:
B = 25t + 300 (2) (2)
Solve equation (1) now with t = 7:
A = 35 (7) + 250
A = 245 + 250
A = 495
So, for 7 hours of landscaping, business A would bill $495.
Similarly, when equation (2) is resolved for t = 7,
B = 25(7) + 300
B = 175 + 30
B = 475
So, for 7 hours of gardening, business B would bill $475.
Therefore, for seven hours of landscaping, Company B would be less expensive than Company A.
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Lisa accidentally spilled a quart of water into her swimming pool. The pool is rectangular and measures 12 ft by 20 ft. By how much did the water level in the pool increase?
(nearest hundred thousandth)
(A) 0.00167 in
(B) 0.00334 in
(C) 0.00668 in
(D) 0.0134 in
(E) 0.0267 in
The water level will increase by 0.00167 inches, so the correct option is A.
By how much did the water level in the pool increase?
We know that Lisa spilled a volume of 1 quart of water on its pool, and the dimensions of the pool are:
12ft = 12*(12 inches) = 144 inches
20ft = 20*(12 inches) = 240 inches.
And we know that:
1 quart = 57.75 in³
Then if the level change is H, then then we can write the equation for the volumes:
1 quart = volume of increase in the pool
1 quart = (144 in)*(240 in)*H
57.75 in³ = (144 in)*(240 in)*H
H = (57.75 in³)/( (144 in)*(240 in))
H = 0.00167 in
So the correct option is A.
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How do you graph y 2x 4 on a graph?.
The curve's y-intercept is 4, and its slope is 2.
To depict the curve, we will make use of the idea of slope and intercept in linear equations.
A line's slope and y-intercept are represented by the equation y = mx + c, where m represents the slope and c represents the y-intercept.
When y = 2x - 4 is put into comparison with the generic form, we get
The curve has a slope of 2 and a y-intercept of -4.
Picking two points on the line y = 2x – 4 will make it easier for us to plot the graph.
Since the supplied line's y-intercept is 4, the line y = 2x - 4 must pass through (0, -4).
Put y = 0
0 = 2x - 4
x = 2
Line passes through (2,0).
Draw a line passing through (0,4) and (2,0) and we get the graph.
Correct question :
How do you graph y = 2x - 4 on a graph?
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I don’t know the answer to this question
The required arcs that are shorter than the semi circle are DA,DB,DC,AC,AB .
What is an arc of a circle that is smaller than a semicircle?Minor arc: an arc that is less than a semicircle. A minor arc is named by using only the two endpoints of the arc.
Given here: Arcs of a circle.
An arc whose measure is less than 180 degrees is called a minor arc. An arc whose measure is greater than 180 degrees is called a major arc. An arc whose measure equals 180 degrees is called a semicircle, since it divides the circle in two. And a semicircle subtends and angle of 180 at the center of the circle.
Thus all the arcs that measure less than 180 are shorter than the semi circle
∴DA,DB,DC,AC,AB are the arcs that measure less than 180 at the center of the circle.
Hence, The required arcs are DA,DB,DC,AC,AB .
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The expression is
equivalent to
Answer:
option 3 = 20w^5
Step-by-step explanation:
attached the solution, hope that helps ....
In the Mississippi River Delta, fresh water (0% salinity) mixes with salt water from the Gulf of Mexico (3.5% salinity). If 1,000 gallons of river water mixes with 3,000 gallons from the Gulf, how many gallons result, and what is its percent salinity? (Estimate a reasonable percent range for your answer before you solve.)
The percent salinity of the resulting mixture is given as follows:
2.63%.
How to obtain the percent salinity?The percent salinity of the resulting mixture is obtained applying the proportions in the context of the problem.
The proportions are obtained applying the weighed mean, as follows:
0 x 1000 + 0.035 x 3000 = 105 gallons of salt.
Considering that the total mixture is of 1000 + 3000 = 4000 gallons, the percentage of salt in the resulting mixture is given as follows:
105/4000 x 100% = 2.63%.
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