(a) The mold constant in Chvorinov's rule can be calculated using the formula t = C x V^n, where t is the solidification time, V is the volume of the casting, and n and C are constants. Given n=2, we can use the given solidification time of 4.6 min and the volume of the 2-in. cube (2x2x2) to calculate the mold constant C. Thus, C = t / V^n = 4.6 / 2^2 = 1.15. Therefore, the mold constant is 1.15.
(b) To calculate the solidification time for the 0.5 in. x 0.5 in. x 6 in. bar, we can use Chvorinov's rule again. The volume of the bar is (0.5 x 0.5 x 6) = 1.5 in^3. Thus, using the mold constant found in part (a), we can calculate the solidification time of the bar as t = C x V^n = 1.15 x 1.5^2 = 2.59 min. Therefore, the solidification time for the 0.5 in. x 0.5 in. x 6 in. bar is 2.59 min.
In casting, it is important to know the solidification time of the metal being poured to ensure that it cools and solidifies properly. Chvorinov's rule is a method used to estimate the solidification time of a casting. It assumes that the rate of solidification is proportional to the surface area of the casting and the temperature difference between the casting and the mold.
To calculate the mold constant in Chvorinov's rule, we can use the formula t = C x V^n, where t is the solidification time, V is the volume of the casting, and n and C are constants. Given the solidification time and the volume of the 2-in. cube, we can solve for C to find the mold constant.
To calculate the solidification time for the 0.5 in. x 0.5 in. x 6 in. bar, we can use the mold constant found in part (a) and the volume of the bar. Substituting these values in Chvorinov's rule formula, we can find the solidification time of the bar.
Chvorinov's rule is a useful method to estimate the solidification time of a casting. By calculating the mold constant and using the formula, we can determine the solidification time for different casting shapes and sizes. In this example, we calculated the mold constant and solidification time for a 2-in. cube and a 0.5 in. x 0.5 in. x 6 in. bar.
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This table shows values represented by an exponential function x= 0,1,2,3,4,5,6 y=1,3,9,27,64,125,216 what is the average rate of change for this function for the interval from x=2 to x=4?
27.5 is the answer
For this case we know that the average rate of change of a function is given by this general expression:
m = f(b) - f(a)/ b-a
For this special case from the info in the table we have:
a =2 , f(2) = 9
a =4 , f(4) = 64
And replacing the data with the average rate formula we got:
m = 64 - 9/4 - 2 = 27.5
And then the best answer for this case would be:
27.5
The exponential function is a mathematical function represented by f (x) = \ exp or e ^ {x}. Unless otherwise specified, the term generally refers to a function of a positive value of a real variable, but it can also be extended to complex numbers or generalized to other mathematical objects such as matrices and Lie algebras.
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not sure how to figure this out, help please
The second bus is traveling at a speed of 33.3 miles per hour.
Given that the speed of first bus is 60 miles per hour , distance between both the buses is 700 miles after 8 hour.
We are required to find the speed of second car which is heading towards south.
If first car is travelling at a speed of 60 miles per hour then the distance of first car after 8 hours is 60*8=480 miles.
We have been given that the distance between both the cars after 8 hours is 700 miles,So,
Distance of second car after 8 hours=700-480=220 miles.
We know that the speed is equal to distance divided by time.
We know that we have calculated distance after 8 hours so the speed of second car will be =20/6
=33.3 miles per hour
Hence the speed of second car which is heading towards south is 33.3 miles per hour.
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At the trial of a contract dispute, the plaintiff has offered to testify to what she heard the defendant say in a private conversation between the two of them, which the plaintiff secretly recorded on an audiotape that she did not offer in evidence. Is the plaintiff's testimony admissible
The plaintiff's testimony is admissible because plaintiff as personal knowledge of the statement of a party-opponent.
How to illustrate the information?The recording is coincidental with firsthand knowledge. The person could testify based upon firsthand knowledge and could also lay the foundation under Article 9 to authenticate the tape.
In this case, the tape is not required as a matter of the original writing rule, giving the proponent options to offer testimony from memory, and/or the opportunity to corroborate the in-court testimony by a demonstrative exhibit
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Jane takes out a loan for $100,000.00 over 10 years
and agrees to pay interest only at an annual rate of
8%. What will her monthly payment be?
$1799.10
Step-by-step explanation:Each year, the amount of money in the account is increased by 8%. This is the same as multiplying by 1.08 each year.
For 10 years, you multiply the original $100,000 by 1.08 a total of 10 times.
This tends to be simplified to:
[tex]100,000 * 1.08^{10}[/tex]
This gives $215892.4997.
This is paid back over 10 years, which is 10 x 12 months, or 120 months.
Divide the $215892.4997 by 120 to get the monthly payment of:
$1799.10 (round to 2 decimal places as it is a currency)
When rolling a single number cube, what are the odds, in simplest form, in favor of rolling a 2 or a 3?
A. 1:1
B. 1:2
C. 1:3
D. 1:5
Answer:
C
Step-by-step explanation:
There are 6 outcomes and you are seeking 2 of them.
2/6 or 1/3 1:3
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
8x +12y = -108
Answer:
y=-(2/3)x -9
Step-by-step explanation:
shuffle the equation so that y is alone in left hand side
The coefficient of x in the right hand side is the slope of line and the other term in right hand side is constant term
The slope-intercept form of the given equation will be y = -2x/3 - 9.
What is slope-intercept form?The meaning of slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
Given an equation, 8x +12y = -108
Converting in slope-intercept form,
12y = -108 - 8x
y = -2x/3 - 9
Hence, the slope-intercept form of the given equation will be
y = -2x/3 - 9.
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Which of the following systems of equations has the solution (1, 6)?
y = –5x – 1
y = –x + 7
y = 5x + 1
y = x – 7
y = 5x + 1
y = –x – 7
y = 5x + 1
y = –x + 7
Answer:
Step-by-step explanation:
hello :
the system is : y = 5x + 1
y = –x + 7
put : x=1 you have y = 6
Find the dependent value
for the graph
y = 5x + 30
when the independent value is - 5.
y = [?]
Given that B is the midpoint of the arc AC, find
(i) the length of BD,
(ii) the perimeter of the shaded region
(iii) the area of the shaded region.
Ans:
8.49
21.4
20.5
i. Line BD = 6√2 cm
ii. Perimeter = 3 (π + 4) cm
iii. Area = 18 ( π - 2) cm
How to determine the parametersLet the length of BD = x
Since B is the midpoint of the arc AC, then ∠BOC = 15°
In ΔBDB
Let's use the trigonometric ration, tan
[tex]Tan 45 = \frac{BD}{CD}[/tex]
CD = x
Then, using the Pythagorean theorem
[tex]x^2 + x^2 = 12^2[/tex]
[tex]2x^2 = 144[/tex]
[tex]x^2 = \frac{144}{2}[/tex]
[tex]x = \sqrt{72}[/tex]
[tex]x = \sqrt{36 *2}[/tex]
[tex]x = 6\sqrt{2}[/tex]
Thus, line BD is [tex]6\sqrt{2}[/tex] cm
ii. Perimeter = BC + BD + CD
= 2πr/8 + x + r - x
= π(12)/4 + r
= 3π + 12
= 3 ( π + 4) cm
iii. Area of shaded area = Area of BOC + Area of BOD
⇒ πr^2/8 × 1/2x^2
= π144/8 × 1/2(72)
= 18π - 36
= 18 ( π - 2) cm²
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Solve the rational equation by multiplying both sides by the lcd. check your results for extraneous solutions. 3 x2 5x 6 x − 1 x 2 = 7 x 3 x = is a solution. x = is an extraneous solution.
The solution and extraneous solution of the equation as given are; x=7 and x=-2 respectively.
What is the solution of the equation?It follows that the equation given is;
(3/(x²+5x+6)) + ((x-1)/(x+2)) = 7/(x+3)
Hence, by multiplying both sides by (x²+5x+6); we have;
3 + x² +2x -3 = 7x + 14.
x²-5x -14 = 0
On this note, the solutions of the quadratic equation are; x =7 and x=-2.
It therefore follows that x= 7 is a solution while x=-2 is an extraneous solution because it renders (x-1)/(x+2) undefined.
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Answer:
x=7
x=-2
Step-by-step explanation:
Which expression is equivalent to startroot 8 x superscript 7 baseline y superscript 8 baseline endroot? assume x greater-than-or-equal-to 0.
Expression which is equivalent to [tex]$\sqrt{8 x^{7} y^{8}}[/tex] is [tex]$=2 \sqrt{2} x^{3} y^{4} \sqrt{x}$[/tex].
What are equivalent expressions?
Expressions that function identically despite having distinct appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).
Solution of the given equation [tex]$\sqrt{8 x^{7} y^{8}}[/tex].
[tex]$\sqrt{8 x^{7} y^{8}}=\sqrt{8} \sqrt{x^{7}} \sqrt{y^{8}}$[/tex]
[tex]$=\sqrt{8} \sqrt{x^{7}} \sqrt{y^{8}}$[/tex]
Simplify [tex]$\sqrt{x^{7}}: x^{3} \sqrt{x}$[/tex]
[tex]$=\sqrt{8} x^{3} \sqrt{x} \sqrt{y^{8}}$[/tex]
Simplify [tex]$\sqrt{y^{8}}: y^{4}$[/tex]
[tex]$=\sqrt{8} x^{3} \sqrt{x} y^{4}$[/tex]
[tex]$\sqrt{8}=2 \sqrt{2}$[/tex]
[tex]$=2 \sqrt{2} x^{3} \sqrt{x} y^{4}$[/tex]
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The complete question is :
Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0. x y squared StartRoot 8 x cubed EndRoot 2 x cubed y cubed StartRoot x y squared EndRoot 2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot 4 x cubed y Superscript 4 Baseline StartRoot x EndRoot
The nth term of a sequence is 2n2² - 4n+4 Work out the 8th term of the sequence. 8th term= Submit Answer Skip for Now
The nth term of a sequence exists 2n2² - 4n+4 is 36.
What is PEMDAS' order of operations?The order of operations exists as a rule that describes the right sequence of measures for estimating a math expression. We can recognize the order utilizing PEMDAS: Parentheses, Exponents, Multiplication, and Division (from left to right), Addition, and Subtraction (from left to right).
[tex]$2*8*2^{2} - 4*8+4[/tex]
Follow the PEMDAS order of operations
Calculating the exponents, we get 2² = 4
[tex]= 2*8*4 - 4*8+4[/tex]
= 64-32 +4
= 36
Therefore, the nth term of a sequence that exists 2n2² - 4n+4 is 36.
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The two-way table represents data from a survey asking teachers whether they teach English, math, or both.
The joint relative frequency is 21%.
What is the joint relative frequency?Joint relative frequency can be described as the ratio of the frequency of data in a certain category to the total number of data points in that category.
The joint relative frequency for teachers who teach math and not English = number of teachers who teach maths and not English / total number of teachers
(22 / 104) x 100 = 21%
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Pack of 100 index cards , 15 cmx 10 cm paper density 200 gsm what is the area of the cards on the table
a)15000 square cm or 1.5 square meter
b)32
c)80 GSM
d)0.405 gram
refer to the following images for solutions :
Index cards are used for a wide range of applications and environments: in the home to record and store recipes, shopping lists, contact information, and other organizational data; in business to record presentation notes, project research and notes, and contact information; in schools as flashcards or other visual.
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HELP?? A lunch combo has the following options: Entree: Hamburger, Hotdog, Chicken sandwich Side: Apples, Salad Drink: Milk, Water What is the sample size of these outcomes?
Using the Fundamental Counting Theorem, the sample size of these outcomes is of 12.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Considering the number of options for Entree, Side and Drink, the parameters are:
n1 = 3, n2 = 2, n3 = 2.
Hence the sample size of outcomes is:
N = 3 x 2 x 2 = 12.
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bridget went fishing with her dad. Bridget caught the first fish of the day and it weighed f ounces. that day she caught four more fish one was 2 times the weight of the first fish another was 2 more than 3 times the weight of the first fish. next was 1/2 the weight of the first fish and the last was 3/5 the weight of the first fish. bridgets dad caught four fish. the first fish he caught weighed 2 more than 3 times the weight of the first fish that day one fish weighed 4/5 the weight of the first fish caught that day one weighed 4 more than 2 times the weight of the first fish cought that day and the last weighed 1/2 the weight of the first fish caught.
Assuming all the fishes caught by Bridget and her dad have the same total weight, then the first fish Bridget caught would weigh 5 ounces while the first fish caught by her dad weighed 17 ounces.
What is weight?Weight can be defined as the force acting on an object or a physical body due to the effect of gravity. Also, the weight of a physical object (body) is typically measured in Newton or ounces.
How to calculate the weight of the first fish?First of all, we would determine the weight of all of the fishes caught by both Bridget and her father (dad) while translating the word problem into an algebraic equation as follows:
For Bridget, we have:
Bridget's fish = f + 2f + 3f + 2 + ½f + ⅗f
Bridget's fish = 7 f/10 + 2 ......equation 1.
For her dad, we have:
Dad's fish = 3f + 2 + ⅘f + 2f + 4 + ½f
Dad's fish = 6 3f/10 + 6 ......equation 2.
Equating eqn. 1 and eqn. 2, we have:
7 f/10 + 2 = 6 3f/10 + 6
7 f/10 - 6 3f/10 = 6 - 2
8f/10 = 4
8f = 40
f = 40/8
Bridget, f = 5 fishes.
Since her dad's fish weighed 2 more than 3 times, we have:
Dad = 3f + 2
Dad = 3(5) + 2
Dad = 15 +2
Dad = 17 ounces.
In conclusion, the first fish Bridget caught would weigh 5 ounces while the first fish caught by her dad weighed 17 ounces assuming all the fishes caught by Bridget and her dad have the same total weight.
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Complete Question:
Bridget went fishing with her dad. Bridget caught the first fish of the day, and it weighed f ounces. That day, she caught four more fish. One was 2 times the weight of the first fish, another was 2 more than 3 times the weight of the first fish, the next was 1/2 the weight of the first fish, and the last was 3/5 the weight of the first fish. Bridget’s dad caught four fish. The first fish he caught weighed 2 more than 3 times the weight of the first fish caught that day. One fish weighed 4/5 the weight of the first fish caught that day, one weighed 4 more than 2 times the weight of the first fish caught that day, and the last weighed 1/2 the weight of the first fish caught that day.
If all the fish Bridget caught have the same total weight as all the fish her dad caught, then the first fish Bridget caught weighed___ ounces and the first fish her dad caught___ weighed ounces.
Complete the following tasks for this equation: b/7.8= -2.15.
1. give an estimate for the solution. be sure to explain how you arrived at the estimate, either by showing an equation or in words.
2. solve the equation. show or explain your work.
3. compared to your estimate, is your answer reasonable? explain your answer in complete sentences.
Answer:
Step-by-step explanation:
Factors
A term in multiplication for an entire variety by which a bigger complete quantity may be dividedA divisor is an integer that evenly divides a range without leaving the restFactorization is the decomposition of an item right into a product of other objectsInteger factorization, the manner of breaking down a composite quantity into smaller non-trivial divisorsA coefficient, a multiplicative thing in an expression, usually more than a fewThe act of forming a component institution or quotient ring in summary algebraA von Neumann algebra, with a trivial centerFactor (graph principle), a spanning subgraphAny finite contiguous sub-sequence of a word in a group concept(b)/(7.8)=-2.15
Multiply each term in the equation by 7.8.
(b)/(7.8)*7.8=-2.15*7.8
Cancel the common factor of (1)/(7.8).
1b=-2.15*7.8
Multiply -2.15 by 7.8 to get -16.77.
1b=-16.77
Divide each term in the equation by 1.
(1b)/(1)=-(16.77)/(1)
Cancel the common factor of 1.
b=-(16.77)/(1)
Divide -16.77 by 1 to get -16.77.
b=-16.77
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Which of the following statements accurately describes the demographics of Arab and Muslim Americans
One accurate statement amount Arab Americans is that b. Arab Americans include both Muslims and Christians.
What is a fact about Arab Muslims?Arab Muslims are known to include both Muslims and Christians and indeed it is estimated that more Arab Americans are Christians as opposed to Muslims.
They are also quite urbanized and have very high rates of education which has given then access to more income.
Options for this question include:
a. Arab Americans are not urbanized.
b. Arab Americans include both Muslims and Christians.
c. Arab Americans rank relatively low in terms of income and occupation
d. Arab Americans tend to have low levels of education and skills.
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Find 8. Round to the nearest degree.
OA. 68°
OB. 69°
OC. 22°
OD. 21°
Answer:
A
Step-by-step explanation:
[tex]\cos \theta=\frac{3}{8} \\ \\ \theta=\cos^{-1} \left(\frac{3}{8} \right) \\ \\ \theta \approx 68^{\circ}[/tex]
if a =76 and b=287
what is( a+b/2)/a-bx2
The value of the given expression (a + b/2)/a - bx² = 219.5/(76 - 287x²).
What is an expression?An expression is the combination of variables, coefficients, and constants that are separated by an arithmetic operator(+, -, ...).
Calculation:The given expression is
(a + b/2)/a - bx²
It is given that a = 76 and b = 287
On substituting,
(a + b/2)/a - bx² = (76 + 287/2)/76 - 287x²
⇒ (76 + 143.5)/76 - 287x²
⇒ 219.5/(76 - 287x²)
Therefore, the given expression for the values a = 76 and b = 287 is 219.5/(76 - 287x²).
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some one help me please
Answer:
(0,3)
Step-by-step explanation:
The y-intercept is the point where the line touches the y-axis and x is 0.
Answer:
(0,3)
Step-by-step explanation:
The y-intercept is when the line crosses the y-axis, in this case the point is at (0,3)
Which of these shapes are congruent
Answer:
Option A is probably the answer
If you have any question please contact me
Answer: A is the answer, should be right
This question is worth 15 points.
A bedding set that regularly sells for $86
is on sale with a 20% discount. How
much will the total sale be including a 5%
sales tax?
The total sale of the bedding set including 5% sale tax is $69.66
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Discount = 20% of 86 = 0.2 * 86 = 17.2
Selling price of bed = 5% of 17.2 = 0.05 * 17.2 = 0.86
Total sale = 86 - 17.2 + 0.86 = 69.66
The total sale of the bedding set including 5% sale tax is $69.66
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Ruby buys 24 books and 5 pens.she pays with a 500 rupee note and get rs90 as change.shania bought 12 books and 10 pens for rs280.find the cost of 1 pen.
The cost of one pen is Rs 15.
How to find the cost of one pen?It is given that Ruby paid with a 500 rupee note and got Rs 90 back.
This means that she spent 410 rupees.
Therefore the cost of 24 books and 5 pens is Rs 410.
Let the cost of books be x and the cost of pens be y.
Therefore, we can form the following equations:
24x + 5y = 410 (1)
12x + 10y = 280 (2)
We have to find the value of y.
Multiply the second equation by 2:
24x + 20y = 560 (3)
Now subtract the first equation from the third equation:
24x + 20y - 24x - 5y = 560 - 410
15y = 150
y = 15.
The variable y represents the cost of one pen.
This means that the cost of one pen is Rs 15.
Therefore, we have found that the cost of one pen is Rs 15.
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Rationalize the denominator:
GRADE 9
CBSE
Answer:
1. a)
[tex] \begin{gathered} \frac{2}{ \sqrt{3} - 1 } = \frac{2}{ \sqrt{3} - 1} \times \ \frac{ \sqrt{3} + 1}{ \sqrt{3} + 1 } \\ = \frac{2 \sqrt{3} + 2 } {( \sqrt{3} ) {}^{2} - 1 {}^{2} } = \frac{2 \sqrt{} 3}{3 - 1} = \frac{2 \sqrt{3} }{2} \\ = \sqrt{3} \end{gathered}[/tex]
[tex]\\[/tex]
b)
[tex]\begin{gathered} = > \: \: \frac{7}{ \sqrt{12} - \sqrt{5} } \\ \\ = > \: \: \frac{7}{ \sqrt{12} - \sqrt{5} } \times \frac{ \sqrt{12} + \sqrt{5} }{ \sqrt{12} + \sqrt{5} } \\ \\ = > \: \: \frac{7( \sqrt{12} + \sqrt{5} ) }{ {( \sqrt{12}) }^{2} - {( \sqrt{5}) }^{2} } \\ \\ = > \: \: \frac{7( \sqrt{12} + \sqrt{5}) }{12 - 5} \\ \\ => \: \: \frac{ \cancel{7}( \sqrt{12} + \sqrt{5} ) }{ \cancel{7}} \\ \\ => \: \: \sqrt{12} + \sqrt{5} \end{gathered}[/tex]
1-:
[tex] \displaystyle \frac{2}{ \sqrt{3} - 1 } [/tex]
[tex] \displaystyle = \frac{2}{( \sqrt{3} - 1)( \sqrt{3} + 1 } \\ [/tex]
[tex] \displaystyle2 \frac{ \sqrt{3} + 1 }{ \sqrt{3 {}^{2} - 1 {}^{2} } } [/tex]
by( a-b×a+b=a²b²)[tex] \displaystyle2 \frac{ \sqrt{3} + 1}{3 - 1} [/tex]
[tex] \displaystyle \: \sqrt{3} + 1[/tex]
[tex] \displaystyle2 - ) \frac{7}{ \sqrt{12} - \sqrt{5} } [/tex]
[tex] \displaystyle\frac{ \sqrt{12} \sqrt{5} }{ \sqrt{12 {}^{2} } \times \sqrt{5 {}^{2} } } [/tex]
[tex] \displaystyle7\frac{ \sqrt{12} + \sqrt{5} }{7} = \sqrt{12} + \sqrt{5} [/tex]
[tex] \displaystyle3) = \frac{8 + 3 \sqrt{5} }{64 - 45} \\ = \frac{8 - 3 \sqrt{5} }{19} [/tex]
which of the following rational functions is graphed below?
The rational function represented in the given graph is; f(x) = 1/(x - 4)
How to Interpret Graph of Asymptotes Functions?From the given graph , the vertical asymptote is at x = 4
Let's find out the vertical asymptote of each function
To find out vertical asymptote we set the denominator = 0
A) x + 4 = 0
x = -4
This is not correct
B) 4x = 0
x = 0
Not correct
C) Denominator does not have a variable and so is also incorrect
D) x - 4 = 0
x = 4
Thus, this is correct
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I AM ASKING AGAIN HELP GUYZ
Answer:
[tex]\huge\boxed{\sf C, \ D \ and \ E}[/tex]
Step-by-step explanation:
Given expression:
= 2(4f + 2g)Distribute 2 to both terms.
= 8f + 4gWe can also split 8f into 4f and 4f.
= 4f + 4f + 4gIf we take 4 common
= 4(f + f + g)
= 4(2f + g)[tex]\rule[225]{225}{2}[/tex]
Answer: Heya! ~
8f + 4g also 4(2f + g) and 4f + 4f+ 4gStep-by-step explanation:
Given: Expression 2(4f + 2g)
We have to choose an equivalent expression to the given expression 2(4f + 2g)
Consider the given expression 2(4f + 2g)
Apply Distributive property, a( b + c) =ab + ac
We have,
a = 2, b = 4f and c = 2g
2(4f + 2g) = 8f + 4g
Now, take 4 common from each term, we have,
8f + 4f = 4 (2f + g)
Now, We have,
a = 2, b = 4f and c = 2g
2(4f + 2g) = 8f + 4g
Now, take 4 common from each term, we have,
8f + 4f = 4 (2f + g)
Now, an equivalent expression to the given expression 2(4f + 2g) is 8f + 4g and 4 (2f + g)
- Keira
Aaron is designing a party game in which he needs exactly 24 possible outcomes. which sets of actions can he use to have a statistically fair game?
If Aaron is designing a party game in which he needs exactly 24 possible outcomes, then he can use the following sets of actions to have a statistically fair game from the Statistics point of view,
Toss a coin twice, and then then roll a 6-sided number cube.
How can he play a statistically fair game to get exactly 24 outcomes?
The game has 24 alternative outcomes, as far as we know. The next step is to identify a series of activities that produces 24 distinct outcomes with equal probabilities.
The first of the alternatives is the only one with a sample space of 24 elements.
Flip two coins, then roll a D6.
The results of each coin toss are 2: (tails and heads).
There are 6 outcomes for the D6: (1, 2, 3, 4, 5, 6)
The combined outcomes of the two throws and rolling the number are then given by the product between the numbers of outcomes for each individual part, as solved below:
C = 2 × 2 × 6
C = 24
Thus, by tossing a coin twice, and then then rolling a 6-sided number cube, Aron can play a statistically fair game if h needs exactly 24 outcomes.
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Equal amounts of peanuts, cashews, and almonds are packed separately in bags. If 3 bags, one of each kind, cost a total of $3.00 and 2 bags of peanuts and 2 bags of cashews cost a total of $3.50, how much does 1 bag of almond cost
The cost of 1 bag of almond is $1.25
What is linear equation?
An equation in which the highest power of the variable is one is known as linear equation.
We can find the cost of 1 bag of almond as shown below:
Let the cost of 1 bag of peanut be $x
Let the cost of 1 bag of cashews be $y
Let the cost of 1 bag of almonds be $z
x + y + z=3 (1)
2x+2y=3.50
Dividing by 2
x + y=1.75
Putting in equation (1)
1.75+z=3
z=3-1.75
z=1.25
Hence, the cost of 1 bag of almond is $1.25
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Ammonia (NH3) can be made using the reversible reaction shown. Which change would keep this reaction from shifting to form more of the produce Decreasing the pressure in the reaction ? 3H2 + N2 ⇄ 2NH3 + energy A. Decreasing the pressure in the reaction vessel
Decreasing the pressure in the reaction vessel will keep this reaction from shifting to form more of the produce(ammonia).
What is Pressure?This is defined as the force per unit area of a body and the S. I unit is in Pascal.
Ammonia production involves reaction between hydrogen and nitrogen gas in which pressure has an effect on the reaction rate unlike in solids and liquids. An increase in pressure will result in more products being formed and vice versa.
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