We need to know conversion of units to solve the given problem. The density of the material in grams per quart is 136.35 grams per quart.
We have been given the density of a certain material in pounds per cubic foot of volume. The density is 9 pounds per cubic foot of volume. We need to convert pounds per cubic foot to grams per quart, we need to separately convert pounds to grams and convert cubic foot to quart. Since it is density so we need to divide the value of pound in gram by the value of one cubic foot in quart and multiply the density to this value to get the desired result.
1 pound=453.592 grams
1 cubic foot= 29.94 quart
9 pounds per cubic foot= 9x 453.592/29.94=136.35 grams per quart
Therefore the density of the material in grams per quart is 136.35 grams per quart.
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help me please
thank you
Answer:
Domain: A, [tex](-\infty, \infty)[/tex]
Range: A, [tex][4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
{x+3y=7 -9x+2y=8 elimination or addition method
The solution to the system of equations is (-10/29, 71/29).
We are given a system of linear equations in two variables.We have two equations and two variables.The first equation is x+3y = 7.The second equation is -9x+2y = 8.We will use the elimination method to solve the equations.x + 3y = 7-9x + 2y = 8Multiply both sides of the first equation by -9.-9x -27y = -63Subtract this newly generated equation from the second equation.(-9x + 2y) - (-9x -27y) = 8 - (-63)-9x + 2y + 9x + 27y = 8 + 6329y = 71y = 71/29Use this value in the first equation to find the value of "x".x + 3y = 7x + 3(71/29) = 7x + 213/29 = 7x = 7 - (213/29)x = -10/29To learn more about equations, visit :
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A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solutioncontains 80% pure antifreeze. The company wants to obtain 320 gallons of a mixture that contains 15% pure antifreeze. How many gallons of water and howmany gallons of the premium antifreeze solution must be mixed?
Amount of water = 260 gallons
Amount of antifreeze = 60 gallons
Explanation:let the amount of water = w
amount of water + amount of antifreeze will give 320 gallons of mixture
w + amount of antifreeze = 320
amount of antifreeze = 320 - w ...(1)
The concentration for the antifreeze = 80% = 0.8
The concentration of the mixture = 15% = 0.15
From our question, we are mixing antifreeze with pure water (two different things). In our calculation, we can write the concentration in terms of water or in terms of antifreeze.
Writing the concentration in terms of amount of antifreeze
0.8(amount of antifreeze) + percent of antifreeze (amount of water) = concentraton of the mixture
The mixture contains 15% antifreeze
water contains no antifreeze, percent = 0
0.8(320 - w) + 0(w) = 0.15(amount of mixture)
0.8(320 - w) + 0 = 0.15(320)
256 - 0.8w + 0 = 48
256 - 0.8w = 48
collect like terms:
256 - 48 = 0.8w
208 = 0.8w
divide both sides by 0.8:
208/0.8 = w
w = 260
substitute for w in equation (1)
amount of antifreeze = 320 - 260 = 60
Amount of water = 260 gallons
Amount of antifreeze = 60 gallons
The length of a rectangle is 4ft less than 3 times width. Perimeter is 54 ft. What equation can be used to find the width of the rectangle
(3w-4)+2w=54
2(3w-4)+2w=54
w(3w-4)=54
2(4w-3)+2w=54
Answer:
b
Step-by-step explanation:
Here,
The length of a rectangle is 4ft less than 3 times the width
Then,
length=3w-4ft
Now,
2(l+w)=P
2(3w-4+w)=54
6w-8+2w=54
2(3w-4)+2w=54
Equation b can be used to find the width of the rectangle
The quotient of 4 times X and 2 more than Y
Answer:4x(y+2)
Step-by-step explanation:
A college student completed some courses worth 6 credits and some courses worth 4 credits. The student earned a total of 104 credits after completing 21 courses.How many courses worth 4 credits did the student complete?A. 11B. 26C. 13 D. 10
Let x be the number of four credit courses and let y be the number of six credit courses.
We know that the student have completed 21 courses, this means that:
[tex]x+y=21[/tex]We also know that he has 104 credits in total. This means that:
[tex]4x+6y=104[/tex]Then we have the system of equations:
[tex]\begin{gathered} x+y=21 \\ 4x+6y=104 \end{gathered}[/tex]To solve the system we solve the first equation for y and plug the value in the second one. That is:
[tex]y=21-x[/tex][tex]\begin{gathered} 4x+6(21-x)=104 \\ 4x+126-6x=104 \\ -2x=104-126 \\ -2x=-22 \\ x=\frac{-22}{-2} \\ x=11 \end{gathered}[/tex]Therefore, the student has taken 11 four credit courses.
Try this: Find "y." How does CPCTC help? A ABC EA ADC. Find y. A (3y) 21° D C С B. DO Pear Deck Interacti Do nove Students, enter a number!
AS ACD and ACBare congruent triangles, we have that
[tex]\begin{gathered} 3y=21\rightarrow \\ y=\frac{21}{3}=7 \end{gathered}[/tex]so the answer is y=7
Rewrite 0 = 1-2y+14x. As a linear equation
Answer:
y = 7x + 1/2
Step-by-step explanation:
0 = 1 - 2y + 14x
+2y +2y
2y = 1 + 14x
/2 /2 /2
y = 1/2 + 7x
y = 7x + 1/2
For right triangle find the missing quantity indicated below express the angle in degrees and minutes not just degrees please and round your answer
To find the angle we will use the sine theorem, but first we will find the measure of the missing side:
[tex]x^2=1325^2+2569^2[/tex][tex]x=\sqrt[]{1325^2+2569^2}[/tex][tex]x=\sqrt[]{8355386}^{\prime}\text{ }[/tex]measure of angle B must be:
[tex]\frac{sin\text{(B)}}{2569}=\frac{\sin (90^{\circ})}{\sqrt[]{8355386}}[/tex][tex]\sin (B)=\frac{2569}{\sqrt[]{8355386}}[/tex][tex]B=62.72^{\circ}[/tex]Finally convert B to degrees and minutes:
[tex]\frac{1^{\circ}}{60^{\prime}}=\frac{0.72^{\circ}}{m^{\prime}}[/tex][tex]m^{\prime}=0.72\cdot60=43.2^{\prime}[/tex][tex]B=62^{\circ}43.2^{\prime}\text{ }[/tex]Find the volume of the figure. Round your answers to the nearest tenth. It is recommended you use the button on your calculator to solve. 8 mi. 5 mi. Volume of the cylinder = mi3
Write out the volume of a cylinder shown below
Formula
[tex]\begin{gathered} \text{Volume of a cylinder = }\Pi r^2\text{ h} \\ where\text{ radius = 5mi , height = 8mi , }\Pi\text{ = 3.142} \\ \text{Volume of a cylinder = }3.142x(5)^2x8 \\ V=628.4mi^3 \\ ThereforeVolumeofthecylinder=628.4mi^3\text{ (nearest tenth)} \end{gathered}[/tex]Hence the volume of the figure = 628.4mi³
Due to an economic downturn, a company had to decrease its staff from 48 employees to 24 employees. What was the percentage decrease in staff?
we get that the decrease percentage is
[tex]\frac{48-24}{48}\cdot100=\frac{24}{48}\cdot100=50\text{ \%}[/tex]so the percentage of decrease is 50%
help;aaefefdsfsd fnujyhvbnmhgf rfdgtrbtg get it?
The value of the expression [tex]\frac{-4[5(7-13)-19]}{2(-1)}[/tex] is - 98.
The abbreviation BODMAS rule is used to assist kids to recall the proper order of operations when performing mathematics. Operations are essentially the various mathematic operations we can do on numbers. "Brackets, Order, Division, Multiplication, Addition, Subtraction" is what it stands for.
A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Consider the expression,
[tex]\frac{-4[5(7-13)-19]}{2(-1)}[/tex]
Using the BODMAS rule,
We will first solve the parenthesis.
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=\frac{-4[35-65-19]}{-2}[/tex]
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=\frac{-140+260+76}{-2}[/tex]
Now, the next step is to divide the expression.
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=\frac{-140}{-2}+\frac{260}{-2}+\frac{76}{-2}[/tex]
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=70-130-38[/tex]
Subtracting the expression,
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=-98[/tex]
Hence, the value of the expression is - 98.
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Hey can you pleas help me on this math problem thank you
Given:
Nolan wraps 36 presents in 12 hours on Saturday
And wraps 42 presents in 14 hours on Friday
If y = number of gifts, and x = number of hours
So, the proportional equation will be as follows:
[tex]y=kx[/tex]Where k is the constant of proportionality
Total gifts = y = 36 + 42 = 78
Total hours = x = 12 + 14 = 26
So, subtitute into the euation to find k
[tex]\begin{gathered} 78=k\cdot26 \\ k=\frac{78}{26}=3 \end{gathered}[/tex]So, the answer will be the constant = 3
For a particular nature trail, the amounts of time that hikers take to walk the trail are normally distributed.The mean of the times is 30.1 minutes,and the standard deviation is 3.6 minutes.For a sample of 4 hikers,what is the probability that the mean time for the sample is less than 28 minutes?
Let X be the normally distributed random variable representing the time hiker takes to walk the trail.
Given that mean and standard deviation are 30.1 and 3.6 minutes, respectively,
[tex]\begin{gathered} \mu=30.1 \\ \sigma=3.6 \end{gathered}[/tex]The sample size is 4,
[tex]n=4[/tex]The z-score corresponding to any value of 'x' is given by,
[tex]z=\frac{x-\mu}{\sigma}[/tex]So the probability that the mean time for the sample is less than 28 minutes is calculated as,
[tex]\begin{gathered} P(X<28)=P(z<\frac{28-30.1}{3.6}) \\ P(X<28)=P(z<-0.58) \\ P(X<28)=P(z>0.58) \\ P(X<28)=P(z>0)-P(0From the Standard Normal Distribution Table,[tex]\varnothing(0.58)=0.2190[/tex]Substitute the value,
[tex]\begin{gathered} P(X<28)=0.5-0.2190 \\ P(X<28)=0.281 \\ P(X<28)=28.1\text{ percent} \end{gathered}[/tex]Thus, there is approximately 28.1% probability that the mean time for the sample is less than 28 minutes.
What is the degree of a polynomial?
Answer:
A polynomial's degree is the greatest power of a variable in a polynomial equation. The degree indicates the highest exponential power in the polynomial (ignoring the coefficients)
Step-by-step explanation:
The degree of a polynomial is the exponent of the leading term. For example, (x + 1) is a first-degree polynomial because x has an exponent of 1. (x^5 + 2y^4 - 3y^3 + y^2 - x + 3) is a fifth-degree polynomial because x has an exponent of 5.
2 - 2f(x)X + 1g(x) = 18 - 3.2Escreva (fog)(2) como uma expressão em função de 2.(fog)(x) =
Answer
[tex](f\text{ o g)(x) = }\frac{3x-16}{17-3x}[/tex]Explanation
We are given that
f(x) = (2 - x)/(x + 1)
g(x) = 18 - 3x
We are then asked to find (f o g)(x)
(f o g) (x) is the same as writing the expression for f(x) but instead of x, we will write g(x) in the expression.
[tex]\begin{gathered} f(x)=\frac{2-x}{x+1} \\ (\text{fog)(x) = }\frac{2-g(x)}{g(x)+1} \end{gathered}[/tex]Recall that
g(x) = 18 - 3x
So,
[tex]\begin{gathered} (\text{fog)(x) = }\frac{2-g(x)}{g(x)+1} \\ (\text{f o g)(x) = }\frac{2-(18-3x)}{18-3x+1} \\ (f\text{ o g)(x) = }\frac{2-18+3x}{17-3x} \\ (f\text{ o g)(x) = }\frac{-16+3x}{17-3x} \\ (f\text{ o g)(x) = }\frac{3x-16}{17-3x} \end{gathered}[/tex]Hope this Helps!!!
help me pleasee!!
thank you
Answer:
f(x) = -9 * (x - 2) + 7
f(x) = -9x + 18 + 7
f(x) = -9x + 25
I need some help with this problem. Thanks.
Answer:
Natural:G
Whole number: B
Integer: H,D,J
Rational: A,F,E,I
Irrational: C,K
Step-by-step explanation:
The triangle ABC pictured below is a right, isosceles triangle. If the length of side AC is 3, give the lengths of the other two sides and the measures of angle A and angle B.
From the statement, we know that we have a right triangle that:
0. has an angle ∠C = 90°,
,1. is also an isosceles triangle,
,2. has a side AC = 3.
1) From points 2 and 3, we know that:
[tex]AC=BC=3.[/tex]Because we have a right triangle, we can use Pitagoras Theorem, which states that:
[tex]c^2=a^2+b^2.[/tex]Where:
• c = AB = hypotenuse,
,• a = BC = 3,
,• b = AC = 3.
Replacing these data in the equation above, we get:
[tex]c^2=3^2+3^2=9+9=18\Rightarrow AB=c=\sqrt{18}.[/tex]2) From point 2 we know that angles A and B must be equal:
[tex]\angle A=\angle B.[/tex]From geometry, we know that the inner angles of a triangle sum up to 180°, so we have:
[tex]\angle A+\angle B+\angle C=180\degree\Rightarrow2\angle A+\angle C=180\degree\Rightarrow\angle A=\frac{180\degree-\angle C}{2}=\frac{180\degree-90\degree}{2}=45\degree.[/tex]Where we have used point 1.
AnswerThe sides of the triangle are:
• AB = √18,,
,• AC = 3,
,• BC = 3.
The angles of the triangle are:
• ∠A = 45°,,
,• ∠B = 45°,,
,• ∠C = 90°.
Consider a trebuchet launching a flaming stone over a castle wall. It is mounted on a small hill and has a parabolic trajectory (neglecting air resistance). Once it crashes into the ground on the other side of the castle wall, it comes to rest. This motion is described by the function below, where x, measured in meters, represents horizontal displacement from the launch position and y = f(x) represents vertical distance from the ground, measured in meters.
f(x) = -0.25x2 + 3.15x + 5
Determine the contextual domain and range and justify your answers. What is the peak height of the flaming stone?
The domain of function f(x) is the set of all real numbers.
the range of function f(x) is, f ≤ 14.9225
And the peak height of the flaming stone would be, 14.9 meters
In this question, we have been given a trebuchet launching a flaming stone over a castle wall. It is mounted on a small hill and has a parabolic trajectory. Once it crashes into the ground on the other side of the castle wall, it comes to rest. This motion is described by the function f(x) = -0.25x² + 3.15x + 5, where x, measured in meters, represents horizontal displacement from the launch position and y = f(x) represents vertical distance from the ground, measured in meters.
We need to determine the contextual domain and range and justify your answers.
The domain of function f(x) is the set of all real numbers.
The range of function f(x) is, f ≤ 14.9225
From the range of the function, the peak height of the flaming stone would be, 14.9 meters
Therefore, the domain of function f(x) is the set of all real numbers.
the range of function f(x) is, f ≤ 14.9225
And the peak height of the flaming stone would be, 14.9 meters
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The figure below is the graph of the dimensions of a rectangle whoseadjacent side lengths exhibit direct variation.
Concept
What is a direct variation? A direct variation is a direct relationship between two variables in which increase in one variable lead to increase in the other variable and decrease in one variable lead to decrease in the other variable.
Hence, the relationship fron the graph between Height and Width of the rectangle is not a direct variation.
Therefore,
The relationship is not a direct variation.
Final answer
Option B = False
hello would you mind checking if this is correct ?
we will use here pythagoras theorem here,
5^2 + 12^2 = C^2
25 + 144 = C^2
C = root 169
c = 13
3. A data set has six numbers. Four of the numbers are: 4, 3, 8, 12. If the mode is 3, find at least three possibilities for the other two numbers.
The possibility of the other two numbers in the given data set is 3.
What do we mean by a number?An object that can be counted, measured, and given a name is a number. The initial examples are the natural numbers 1, 2, 3, 4, and so forth. In language, numbers can be expressed using number words. The symbols referred to as numerals can be used to represent specific numbers in a more general way; for instance, the numeral "5" stands for the number five. Due to the limited amount of symbols that can be learned, fundamental numbers are typically arranged in a numeral system, which is a systematic manner of representing any number. The Hindu-Arabic numeral system, which enables any number to be expressed using a combination of 10 fundamental numeric symbols known as digits, is the most widely used numeral system.So, by observing the data, we can simply conclude that:
As the mode is 3, the remaining two numbers are 3.Therefore, the possibility of the other two numbers in the given data set is 3.
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Ally bought 4 liters of lemonade, 3,000 milliliters of iced tea, and 2,500 milliliters of fruit punch. How many liters of drinks in total did she buy?
Answer:
9.5 liters
Explanation:
The volume of each drink that Ally bought is:
• Lemonade: 4 liters
,• Iced tea: 3,000 milliliters
,• Fruit Punch: 2,500 milliliters
Since we are required to find the total in liters, convert the volumes given in milliliters to liters.
[tex]\begin{gathered} 1000\text{ milliliters}=1\text{ liters} \\ \implies1\text{ milliliter}=\frac{1}{1000}\text{ liter} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 3000\text{ milliliter}=\frac{3000}{1000}=3\text{ liter} \\ 2500\text{ m}\imaginaryI\text{ll}\imaginaryI\text{l}\imaginaryI\text{ter}=\frac{2500}{1,000}=2.5\text{ l}\imaginaryI\text{ter} \end{gathered}[/tex]Therefore, the total volume in liters will be:
[tex]4+3+2.5=9.5\text{ liters}[/tex]Ally bought 9.5 liters of drinks in total.
Find C.Round to the nearest tenth.20 ft\22 ftAB18 ftC = [? ]°Law of Cosines: c2 = a2 + b2 - 2ab cos C=Enter
The given triangle is shown below
From the triangle
[tex]a=22ft,b=20ft,c=18ft,C=\text{?}[/tex]Using the law of Cosines
[tex]c^2=a^2+b^2-2ab\cos C[/tex]Substitute the values of a, b, c into the formula
This gives
[tex]18^2=22^2+20^2-2(22)(20)\cos C[/tex]Simplifying the expression
[tex]\begin{gathered} 324=484+400-880\cos C \\ 324=884-880\cos C \end{gathered}[/tex]Collect like terms
[tex]\begin{gathered} 324-884=-880\cos C \\ -560=-880\cos C \end{gathered}[/tex]Divide both sides by -880
[tex]\begin{gathered} \frac{-560}{-880}=\cos C \\ \cos C=0.6364 \end{gathered}[/tex]Find the value of C
[tex]\begin{gathered} C=\cos ^{-1}(0.6364) \\ C=50.5^{\circ} \end{gathered}[/tex]What function translates the function f(x) = to the right 2 units and up 10 units?
g(x)= |
Answer:
g(x) = | x - 2 | + 10
Step-by-step explanation:
given g(x) then g(x± h ) is a horizontal translation of g(x)
• if h > 0 then a move to the left of h units
• if h < 0 then a move to the right of h units
here the move is 2 units to the right, then
g(x) = | x - 2 |
given g(x) then g(x) + c is a vertical translation of g(x)
• if c > 0 then a move up
• if c < 0 then a move down
here the move is 10 units up , then
g(x) = | x - 2 | + 10
What is the image point of (-2,-3) after a translation right 2 units and up 4 units?
Helps ASAP just 6 and 7 please and thank you
Using a calculator, we calculate the following
[tex]\begin{gathered} 1.41^2=1.9881 \\ 1.42^2=2.0164 \end{gathered}[/tex]Based on these calculations, the square root of 2 is between 1 and 2.
A hexagonal prism whose base has area 25.6 square centimeters and who’s height is 8.9 centimeters
We are given the following information about a hexagonal prism.
Base area = 25.6 cm²
Height = 8.9 cm
Recall that the volume is given by
[tex]V=B\cdot h[/tex]Where B is the area of the base and h is the height of the hexagonal prism.
Let us substitute the given values into the above formula
[tex]\begin{gathered} V=B\cdot h \\ V=25.6\cdot8.9 \\ V=227.84\: cm^3 \end{gathered}[/tex]Therefore, the volume of the given hexagonal prism is 227.84 cubic centimeters.
Instruction: State whether the data are symmetrical, skewed to the left, or skewed to the right:a.1; 1; 1; 2; 2; 2; 2; 3; 3; 3; 3; 3; 3; 3; 3; 4; 4; 4; 5; 5b.16; 17; 19; 22; 22; 22; 22; 22; 23c.87; 87; 87; 87; 87; 88; 89; 89; 90; 91
Based on the data in question a, the graph for the data is skewed to the left. This can be graphed and seen visually but also by calculating the mean and the median of the data set. The mean of the data is 2.85 and the median is 3. Since the mean is less than the median, we can see that the data is negatively skewed, or skewed to the left.
