Therefore, when the equation x = 72 - 3x, the value of 2 - 3x is -52.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. It typically contains one or more variables, which are symbols that can represent any number or value. The expressions on both sides of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation. Equations are used to describe relationships between quantities or to solve problems. They can be represented in various forms, including linear equations, quadratic equations, exponential equations, and trigonometric equations. Equations can be solved by performing operations on both sides of the equation to isolate the variable or variables.
Here,
When we are given that x = 72 - 3x, we can solve for x by first adding 3x to both sides of the equation:
x + 3x = 72
Combining like terms, we get:
4x = 72
Dividing both sides by 4, we get:
x = 18
Now that we know x = 18, we can substitute this value into the expression 2 - 3x:
2 - 3x = 2 - 3(18)
2 - 3x = 2 - 54
2 - 3x = -52
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Keenan scored 80 points on an exam that had a mean score of 77 points and a standard deviation of 4. 2 points. Rachel scored 78 points on an exam that had a mean score of 75 points and a standard deviation of 3. 7 points. Find Keenan's z-score, to the nearest hundredth
Keenan's z-score is 0.71, rounded to the nearest hundredth.
The z-score measures how many standard deviations an individual's score is from the mean, and can be calculated using the formula:
z = (x - μ) / σ
where x is the individual's score, μ is the mean score, and σ is the standard deviation.
For Keenan's exam:
z = (80 - 77) / 4.2
z = 0.71
Therefore, Keenan's z-score is 0.71, rounded to the nearest hundredth.
Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. In decimal, hundredth means 1/100 or 0.01. For example, the rounding of 2.167 to its nearest hundredth is 2.17.
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Solve each inequality (show work)
Answer:
5 less than or equal to x
Step-by-step explanation:
make x subject
You purchased 40 shares for $3.95/sh. If you sold the shares for a total of $200. Did you net a profit or a loss?
Answer: profit
Step-by-step explanation:
3.95 (price of one share) multiplied by 40 (the amount of shares bought) would have cost $158. so selling all for $200 would be a $42 profit
The length of a rectangular room is 9 feet longer than twice the width. If the room's perimeter is 150 feet, what are the room's dimensions?
Answer:
Length = 53 feet
Width = 22 feet
Step-by-step explanation:
Perimeter = 2(length + width)
Then:
a = 2w + 9 Ec. 1
150 = 2(a + w) Ec. 2
a = length
w = width
From Eq. 1:
a - 9 = 2w Eq. 3
From Eq. 2:
150 = 2*a + 2*w
150 = 2a + 2w
150 - 2a = 2w Eq. 4
Equalizing Eq. 3 and Eq. 4
a - 9 = 150 - 2a
a + 2a = 150 + 9
3a = 159
a = 159/3
a = 53
From Eq. 1:
a = 2w + 9
53 = 2w + 9
53 - 9 = 2w
44 = 2w
44/2 = w
w = 22
Check:
From Eq. 2
150 = 2(a+w)
150 = 2(53+22)
150 = 2*75
Gary's backpack weighs 1.2 pounds. His math textbook weighs 3.75 pounds, and his science textbook weighs 2.85 pounds. How much will his backpack weigh with the math and science textbooks in it?
Answer:
To find out how much Gary's backpack will weigh with the math and science textbooks in it, we need to add the weight of the textbooks to the weight of the backpack:
Total weight = backpack weight + math textbook weight + science textbook weight
Total weight = 1.2 + 3.75 + 2.85
Total weight = 7.8 pounds
Therefore, Gary's backpack will weigh 7.8 pounds with the math and science textbooks in it.
Answer: His backpack will weigh 7.8 pounds
Step-by-step explanation:
Gary's backpack already weights 1.2 pounds without the science and math textbook, now we add the weights of both the math and science textbook.
1.2 + 3.75 = 4.95
4.95 is the weight with only his math textbook in his bag
now we add the science textbooks weight to 4.95
4.95 + 2.85 = 7.8
7.8 is the weight of his backpack with both his science and math textbook in his bag
A production facility contains two machines that are used to rework items that are initially defective. Let X be the number of hours that the first machine is in use, and let Ybe the number of hours that the second machine is in use, on a randomly chosen day. Assume that X and Y have joint probability density function given by 3. f(x) = { 3/2(x^2 +y^2) 0
Answer:
Step-by-step explanation:
How to do matrix multiplication in MIPS?
To perform matrix multiplication in MIPS, we can use nested loops to iterate over the rows and columns of the matrices.
The outer loop iterates over the rows of the first matrix, while the inner loop iterates over the columns of the second matrix. We then perform the dot product of the corresponding row and column, which involves multiplying the elements and summing the products.
To perform multiplication efficiently, we can use MIPS registers to store intermediate values and avoid accessing memory unnecessarily. We can also use assembly instructions like "lw" and "sw" to load and store values from memory, and "add" and "mul" to perform arithmetic operations.
In summary, matrix multiplication in MIPS involves nested loops, efficient use of registers and assembly instructions, and arithmetic operations.
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Square ABCD is similar to square EFGH. The ratio of AB:EF is 1:4. The area of square EFGH is 14,400ft ft squared by 2. What is AB?
The Length of AB in square ABCD is 30 feet.
Since the squares ABCD and EFGH are similar, their corresponding sides are proportional, so we can set up the following relation:
AB/EF = 1/4
We can also use the fact that the ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding sides. Therefore,
AB²/EF² = (Area of square ABCD)/(Area of square EFGH)
Substituting the given values:
AB²/EF² = (Area of square ABCD)/(14400)
Since the areas of squares are proportional to the square of their sides, we can write,
Area of square ABCD/Area of square EFGH = (AB/EF)²
Substituting this into the above equation and solving for AB, we get,
AB²/EF² = (AB/EF)²
AB² = (AB/EF)² * EF²
AB² = (1/4)² * 14400
AB² = 900
AB = 30 feet
Therefore, the length of the side AB of square ABCD is 30 feet.
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We revisit a probabilistic model for a fault diagnosis problem from an earlier homework. The class variable C represents the health of a disk drive: C = 0 means it is operating normally; and C = 1 means it is in failed state. When the drive is running it continuously monitors itself using temperature and shock sensor, and records two binary features, X and Y. X =lif the drive has been subject to shock (e.g;, dropped) , and X = 0 otherwise Y =1if the drive temperature has ever been above 70*C, and Y = 0 otherwise. The following table defines the joint probability mass function of these three random variables: pxyc(r,y, c) 0.1 0.2 0.2 0 0 0 0 0 0 0.05 0.25
The probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.
The given table represents the joint probability mass function of the random variables, pxyc (r, y, c). r, y, and c denote the temperature, shock sensor, and health status of the disk drive. The values of r, y, and c are binary.The joint probability mass function of three random variables r, y, and c can be represented as follows:pxyc (r, y, c)= P(r, y, c)Here,P(r=0, y=0, c=0)= 0.1, P(r=0, y=1, c=0)= 0.2, P(r=1, y=0, c=0)= 0.2,P(r=0, y=0, c=1)= 0, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0,P(r=0, y=0, c=0)= 0, P(r=0, y=1, c=0)= 0, P(r=1, y=1, c=0)= 0.05,P(r=0, y=0, c=1)= 0.25, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0.From the given table, the probability of the disk drive being in a normal state, C=0, is P(C=0)=P(r=0, y=0, c=0)+P(r=0, y=1, c=0)+P(r=1, y=0, c=0)=0.1+0.2+0.2=0.5Hence, the probability of the disk drive being in a failed state, C=1, is:P(C=1)=P(r=0, y=0, c=1)+P(r=0, y=1, c=1)+P(r=1, y=0, c=1)+P(r=1, y=1, c=0)=0.25+0+0+0.05=0.3Therefore, the probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.
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A square field has a side length of 6x10³ meters. Which of the following is its area in square meter
(1) 6x106
(3) 36x106
(2) 36×10⁹
(4) 6x10⁹
Answer:
36 × 10^6 m²
Step-by-step explanation:
Given the side length of a square = 6 × 10³m,
To solve for the area of a square, use the following formula:
A = S² where:
S = side of the square
Substitute the given value for the side into the formula:
A = S²
A = (6 × 10³)²
A = 36000000 or 36 × 10^6 m²
NOTE:
6 × 10³ is also the same as 6 × 1000 = 6000,
(6 × 10³)² is essentially 6,000² = 36,000,000
Therefore, its area in square meters is 36 × 10^6
Simplify 4 triangles to 16 squares
The expression 4 triangles to 16 squares when simplified is 1 triangle to 4 squares
How to simplify the expressionGiven that
4 triangles to 16 squares
When expressed as ratio, we have
Triangle : Square = 4 : 16
To simplify the ratio Triangle : Square = 4 : 16, we can divide both the numerator and denominator by their greatest common factor, which is 4.
So, we have
Triangle : Square = 4 : 16
Divide both sides by 4:
Triangle/4 : Square/4 = 1 : 4
So the simplified ratio is 1 : 4, which means for every one triangle, there are four squares.
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A barista mixes 12lb of his secret-formula coffee beans with 15lb of another bean that sells for $18 per lb. The resulting mix costs $20 per lb. How much do the barista's secret-formula beans cost per pound?
Answer: $22.50
Step-by-step explanation:
Let x be the cost per pound of the secret-formula coffee beans.
The total cost of the secret-formula beans is 12x dollars.
The total cost of the other beans is 15 × 18 = 270 dollars.
The total cost of the mix is (12 + 15) × 20 = 540 dollars.
Since the barista mixed 12 pounds of the secret-formula beans with 15 pounds of the other beans, the total weight of the mix is 12 + 15 = 27 pounds.
We can set up an equation based on the total cost of the mix:
12x + 270 = 540
Subtracting 270 from both sides:
12x = 270
Dividing both sides by 12:
x = 22.5
Therefore, the barista's secret-formula coffee beans cost $22.50 per pound.
g a second unit vector which is also orthogonal to both 8,-8,8 and 0,5,5 is the unit vector which points in the direction opposite to u1 -2/6.-1/6,1/6 this is the vector u2
The vector u2 is (0, √3/3, 2/3). It is a unit vector that is orthogonal to both 8,-8,8 and 0,5,5.
Given two vectors 8,-8,8 and 0,5,5, we need to find another unit vector that is orthogonal to both the given vectors. Let's call this vector u1.The vector u1 can be obtained by taking the cross product of the two given vectors:u1 = (8,-8,8) × (0,5,5)u1 = (-40,-40,40)
To get a unit vector, we need to normalize u1 by dividing it by its magnitude:|u1| = √((-40)² + (-40)² + 40²) = 60u1 = (-40/60, -40/60, 40/60) = (-2/3, -2/3, 1/3)Now we need to find another unit vector that is orthogonal to u1.
One way to do this is to take the cross product of u1 with another vector, and then normalize the result. We can choose any vector that is not parallel to u1. For example, we can choose the vector (1,0,0).u2 = u1 × (1,0,0)u2 = (-2/3, -2/3, 1/3) × (1,0,0)u2 = (0,1/3,2/3)
To get a unit vector, we need to normalize u2 by dividing it by its magnitude:|u2| = √(0² + (1/3)² + (2/3)²) = 1/√3u2 = (0, √3/3, 2/3)
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can anyone help me please???
thank you xxxx
Using the property of a kite: the angles formed by two unequal sides of a kite are equal. The value of ∠BCD∠BCD is
∠BCD = ∠BAD ⇒ ∠BCD = 106°
For triangles ABC and DEF, ∠A ≅ ∠D and B ≅ ∠E. Based on this information, which statement is a reasonable conclusion?
a. ∠C ≅ ∠D because they are corresponding angles of congruent triangles.
b. CA ≅ FD because they are corresponding parts of congruent triangles.
c. ∠C ≅ ∠F because they are corresponding angles of similar triangles.
d. AB ≅ DE because they are corresponding parts of similar triangles.
the triangles are similar, corresponding parts of the triangles are equal in measure. Thus, it is reasonable to conclude that [tex]AB ≅ DE.[/tex]
It is reasonable to conclude that [tex]AB ≅ DE[/tex]because triangles ABC and DEF are similar.
This means that corresponding parts of the two triangles are equal in measure. Specifically, ∠A and ∠D are equal in measure, as are ∠B and ∠E.
Therefore, the corresponding sides AB and DE are equal in measure.
A way to show that the two triangles are similar is by using the AA Similarity Postulate.
This postulate states that if two angles of one triangle are equal in measure to two angles of a second triangle, then the two triangles are similar. In this case, [tex]∠A ≅ ∠D and B ≅ ∠E[/tex], which means the two triangles are similar.
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please help i have been trying to get an answer for 5+ hours
How is the quotient of 556 and 16 determined using an area model?
Enter your answers in the boxes to complete the equations. Your final answer should be a mixed number in simplest form.
Answer:
To use an area model to determine the quotient of 556 and 16, we can divide a rectangle of area 556 into 16 equal parts. Each part will have an area of 556/16.
We can start by dividing 556 into 16 groups of 10 (160), and then into 16 groups of 3 (48). That leaves us with a remainder of 4.
So we have:
556 = 16 x 34 + 48 + 4
This shows that 556 can be written as 16 times some whole number (34) plus a remainder of 48 + 4/16.
Simplifying the remainder, we have:
48 + 4/16 = 48 + 1/4 = 48.25
Therefore, the quotient of 556 and 16 is:
556/16 = 34 1/4
The quotient of 556 and 16 using an area model can be determined by producing a rectangle with the total area of 556 and one side of 16. The length of the other side will be the quotient. In this case, the quotient is 34 3/4.
Explanation:When asked to determine the quotient of 556 and 16 using the area model, one way to think of this is making a rectangle. The total area is 556 and one side is 16. The length of the other side will be the quotient.
Start by first estimating how many times 16 could fit into 556. Let's take 30 as an estimate, because 30*16 = 480, which is relatively close to 556. Draw a rectangle with the width of 16 and the length of 30.
Find the difference between the rectangle's area and 556. So, 556 - 480 = 76. Now, 76 is our remaining area to fill. 16 goes into 76 four more times, adding up to 64.
There is still a leftover area, which is 76-64 = 12. This is smaller than our width of 16. So, your final answer is 34 12/16 or 34 3/4 in simplest form.
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A price was first decreased by 12%, then it was decreased again by an additional 5%. What is the percent of the total decrease?
The answer is not 17%.
Please help!!!!
10 PTS
Answer:
83.6%
Step-by-step explanation:
Let's say the original price is x
x decreased by 12% means 88% of x is left.
0.88x decreased by 5% means 95% of 0.88x is left.
This means the answer is: 0.88x * 0.95 = 0.836
The percent of the total decrease is 83.6%
Hope this helps :)
Have a great day!
Estimating the within-group variance. Refer to the previous exercise. Here are the cell standard deviations and sample sizes for cooking enjoyment: Find the pooled estimate of the standard deviation for these data. Use the rule for examining standard deviations in ANOVA from Chapter 12 (page 560) to determine if it is reasonable to use a pooled standard deviation for the analysis of these data.
In the following question, among the given options, the statement is said to be, The pooled estimate of the standard deviation for the data given is √(54.14^2/10 + 24.26^2/10) = 22.74.
According to the rule for examining standard deviations in ANOVA from Chapter 12 (page 560), the within-group standard deviation should be no more than twice the size of the between-group standard deviation. In this case, the between-group standard deviation is 44.85 and the within-group standard deviation (22.74) is less than twice the size of the between-group standard deviation, so it is reasonable to use a pooled standard deviation for the analysis of these data.
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60 identical machines in a factory pack 150 crates of limes per day
between them.
a) Write the ratio of the number of machines to the number of crates
packed per day in the form 1: n.
b) How many crates of limes would 70 of these machines pack per day?
Give any decimals in your answers to 1 d.p.
a) To write the ratio of the number of machines to the number of crates packed per day in the form 1: n, we need to find the number of crates packed per day per machine. We can do this by dividing the total number of crates packed per day by the number of machines:
Number of crates packed per day per machine = 150 crates/day ÷ 60 machines = 2.5 crates/machine/day
Therefore, the ratio of the number of machines to the number of crates packed per day in the form 1: n is 1:2.5 or 2:5.
b) To find out how many crates of limes 70 of these machines would pack per day, we can use the ratio from part (a) to set up a proportion:
1 machine : 2.5 crates/day = 70 machines : x crates/day
Solving for x, we get:
x = (70 machines × 2.5 crates/day) / 1 machine = 175 crates/day
Therefore, 70 of these machines would pack 175 crates of limes per day.
Step-by-step explanation:
a) The ratio of the number of machines to the number of crates packed per day can be written as:
60 : 150
To simplify this ratio, we can divide both sides by 10:
6 : 15
Finally, we can divide both sides by 3 to get the ratio in the form 1 : n:
1 : 2.5
Therefore, the ratio of the number of machines to the number of crates packed per day is 1 : 2.5.
b) If 60 machines can pack 150 crates per day, then one machine can pack:
150/60 = 2.5 crates per day
So, 70 machines can pack:
70 × 2.5 = 175 crates per day
Therefore, 70 machines can pack 175 crates of limes per day.
suppose the minimum volume of a clown is 60,000 cm3 and the volume of my car is 3 million cm3. 55 is______ the maximum number of clowns that can fit in my car.
a. An upper bound on
b. Not a bound
c. A lower bound on
d. exactly
When the minimum volume of a clown is 60,000 cm³ and the volume of a car is 3 million cm³, 55 is an upper bound on the maximum number of clowns that can fit in a car. The correct answer is Option A.
What are bounds?Bounds are the maximum and minimum limits that are permitted, within which something can or must be performed. Bounds are used to refer to an acceptable range of values that provide safe operation or performance. In mathematics, a set of bounds can define the limits of the amount of things or objects.
The minimum volume of a clown is 60,000 cm³, so to fit 55 clowns in a car we need:
55 clowns × 60,000 cm³/clown = 3,300,000 cm³
This is lower than the volume of the car. Therefore, 55 is an upper bound on the maximum number of clowns that can fit in the car.
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What is an abiotic factor that can prevent the organism from becoming preserved, AFTER it has been buried?
Answer options:
1. Groundwater
2. Predators & animals that eat bones.
3. Scavengers & plants that use the nutrients of fossils.
4. Other animals of the same species as the organism that died.
The abiotic factor that can prevent the organism from becoming preserved, AFTER it has been buried is groundwater.
What is an abiotic factor that can prevent the organism from becoming preserved, AFTER it has been buried?An abiotic factor refers to a non-living component of an ecosystem that influences the survival and growth of living organisms.
Groundwater can cause the dissolution of minerals present in the sediment that encases the buried organism.
This process can lead to the destruction of the fossilized remains, as the minerals provide the framework for the preservation of the organism's hard parts (such as bones or shells).
Groundwater can also cause the erosion of the sediment, which can expose the buried remains and make them vulnerable to biotic factors such as scavengers, predators, and decomposers.
Predators and animals that eat bones, scavengers and plants that use the nutrients of fossils, and other animals of the same species as the organism that died are all biotic factors that can affect the preservation of the organism, but they do so before or during the burial process.
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Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 15 people took the trip. She was able to purchase coach tickets for $220 and first class tickets for $910. She used her total budget for airfare for the trip, which was $8130. How many first class tickets did she buy? How many coach tickets did she buy?
You put $200 at the end of each month in an investment plan that pays an APR of 4. 5%. How much will you have after 18 years? Compare this amount to the total deposits made over the time period.
a.
$66,370. 35; $43,200
c.
$66,380. 12; $43,000
b.
$66,295. 23; $43,000
d.
$66,373. 60; $43,200
As per the given APR, the sum of amount after 18 years is $66,373. 60, and the total deposits made over the time period is $43,200. (option d).
To calculate this, we can use the formula for future value of an annuity:
FV = PMT x (((1 + r)⁻¹) / r)
where FV is the future value, PMT is the monthly payment, r is the monthly interest rate (which is calculated by dividing the APR by 12), and n is the number of payments (which is 18 x 12 = 216 in this case).
Plugging in the numbers, we get:
FV = $200 x (((1 + 0.045/12)²¹⁶ - 1) / (0.045/12)) = $66,373.60
Therefore, you would have approximately $66,373.60 in your investment plan after 18 years.
Now let's compare this amount to the total deposits made over the time period. In this case, the total deposits would be:
$200 x 12 x 18 = $43,200
Hence the correct option is (d).
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A cat gave birth to 333 kittens who each had a different mass between 147147147 and 159\,\text{g}159g159, start text, g, end text. Then, the cat gave birth to a 4^{\text{th}}4 th 4, start superscript, start text, t, h, end text, end superscript kitten with a mass of 57\,\text{g}57g57, start text, g, end text.
The answer to the question is 334 kittens.
Given that a cat gave birth to 333 kittens who each had a different mass between 147 g and 159 g. Then the cat gave birth to a 4th kitten with a mass of 57 g.
First of all, we will find out the range of the mass of kittens. The range is given as follows;Range = Maximum Value - Minimum Value Range = 159 g - 147 g Range = 12 g
Now, the cat gave birth to a 4th kitten with a mass of 57 g, we can say that the minimum value of kitten's mass is 57 g.So, the maximum value of kitten's mass can be calculated as follows;Maximum Value = 57 g + Range Maximum Value = 57 g + 12 g Maximum Value = 69 g Now, we can say that all kittens with a mass of 69 g or less would be born because the minimum value of kitten's mass is 57 g and the range of mass is 12 g.
Therefore, the answer to the question is 334 kittens.
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A system of equations is graphed on the coordinate plane.
A student concludes that the solution of the system is (-0.5, 1.5).
Is this correct? Justify your response.
The correctness of the student's solution, we need to have the equations of the system.
A system of equations is graphed on the coordinate plane. A student concludes that the solution of the system is (-0.5, 1.5). Is this correct? Justify your response.To conclude that a system of equations has a solution in the coordinate plane, a set of ordered pairs (x, y) should satisfy both equations in the system of equations. That is, the system of equations should have a point (x, y) that is a solution of both equations.Only by testing the solution in the given system of equations can we know if the student's conclusion is correct. If the solution is satisfied by the system of equations, then the answer is true. Otherwise, it is false. However, since no system of equations is provided in the question, we cannot test the student's solution.To justify the correctness of the student's solution, we need to have the equations of the system.
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Write
a real-world situation that can be
represented by 15 + c = 17.50. Tell what
the variable represents. Then solve the
equation and describe what your answer
represents for the problem situation. Can you also please try to make it something a little original I need help with this ASAP pls.
The given expression is
[tex]15 + c = 17.50[/tex]
We can use this expression to model the cost for a service.
Let's say that your gardener charges an initial amount of $15, and an additional per hour. If the gardener worked only for one hour, and the total cost charged was $17.50, how much was the additional cost?
So, the given expression models this real life situation, we can answer the problem by just solving the equation for [tex]c[/tex]
[tex]15 + c = 17.50[/tex]
[tex]c=17.50-15[/tex]
[tex]c=2.50[/tex]
Answer: Well C equals 2.5. You could use...
You have 3 sticks. one stick is 15 inches long and the other is 17.50. You want to get a small stick to add to the first one so that the first and last stick is equal to the 2nd stick. C is the third stick. 15+C = 17.50. What is the length of C?
Step-by-step explanation:
EASY
Move all terms not containing C to the right side of the equation. C = 2.5
calculator may be used to determine the final numeric value, but show all steps in solving without a calculator up to the final calculation. the surface area a and volume v of a spherical balloon are related by the equationA³ - 36πV² where A is in square inches and Vis in cubic inches. If a balloon is being inflated with gas at the rate of 18 cubic inches per second, find the rate at which the surface area of the balloon is increasing at the instant the area is 153.24 square inches and the volume is 178.37 cubic inches.
Answer:
10.309 in²/s
Step-by-step explanation:
Given A³ = 36πV² and V' = 18 in³/s, you want to know A' when A=153.24 in² and V=178.37 in³.
DifferentiationUsing implicit differentiation, we have ...
3A²·A' = 36π·2V·V'
A' = (36π·2)/3·V/A²·V' = 24πV/A²·V'
A' = 24π·(178.37 in²/(153.24 in²)²·18 in³/s
A' ≈ 10.309 in²/s
The surface area is increasing at about 10.309 square inches per second.
__
Additional comment
There are at least a couple of ways a calculator can be used to find the rate of change. The first attachment shows evaluation of the expression we derived above. The second attachment shows the rate of change when the area is expressed as a function of the volume.
The result rounded to 5 significant figures is the same for both approaches.
Which of the following represents vector vector t equals vector PQ in trigonometric form, where P (–13, 11) and Q (–18, 2)?
t = 10.296 sin 60.945°i + 10.296 cos 60.945°j
t = 10.296 sin 240.945°i + 10.296 cos 240.945°j
t = 10.296 cos 60.945°i + 10.296 sin 60.945°j
t = 10.296 cos 240.945°i + 10.296 sin 240.945°j
The correct answer is option (C).
What are the fundamental forms of trigonometry?Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent are the six functions (cot).
The equation t = Q - P, where Q and P are the specified locations, can be used to determine the components of the vector t. Therefore:
t = (–18, 2) – (–13, 11) = (–18 + 13, 2 – 11) = (–5, –9) (–5, –9)
The vector's magnitude is given by:
|t| = √(–5)^2 + (–9)^2 = √106 ≈ 10.296
The formula = tan1 (y/x), where x and y are the vector's components, can be used to determine the direction of the vector t. The direction must be expressed in terms of sine and cosine functions because we are required to represent the vector in trigonometric form.
θ = tan⁻¹ (–9/–5) ≈ 60.945°
In trigonometric form, the vector t is thus represented as follows:
t = [t|cos|i] + [t|sin|j]
We get the following by altering the values of |t| and:
t = 10.296 cos I + 10.296 sin j of angle 60.945
As a result, the following is the proper trigonometric representation of the vector t:
t = 10.296 cos I + 10.296 sin j of angle 60.945
Thus, alternative is the right response (C).
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1. The line segment AB has endpoints A(-5, 3) and B(-1,-5). Find the point that partitions the line segment in
a ratio of 1:3
Answer:
To find the point that partitions the line segment AB in a ratio of 1:3, we can use the following formula:
P = (3B + 1A) / 4
where P is the point that partitions the line segment in a ratio of 1:3, A and B are the endpoints of the line segment, and the coefficients 3 and 1 represent the ratio of the segment we are dividing.
Substituting the values, we get:
P = (3*(-1, -5) + 1*(-5, 3)) / 4
P = (-3, -7)
Therefore, the point that partitions the line segment AB in a ratio of 1:3 is (-3, -7).
Step-by-step explanation:
give three examples of contracts you are currently a part of or have been a part of in the past. identify whether they are unilateral or bilateral; express or implied; executed or executory.
The three examples of contracts are:
Employment ContractRental AgreementPurchase AgreementContracts are legal agreements between two or more parties that involve the exchange of goods, services, or money. They can be classified as unilateral or bilateral, express or implied, executed or executory.
Here are three examples of contracts that a person can be a part of:
Employment Contract: An employment contract is a bilateral, express contract between an employer and an employee. It defines the terms and conditions of employment, including salary, benefits, and job responsibilities. An employment contract is executed when both parties have agreed to the terms of the agreement and have signed the contract.Rental Agreement: A rental agreement is a unilateral or bilateral, express or implied, executory contract between a landlord and a tenant. It outlines the terms of the lease, such as the duration of the tenancy, rent, security deposit, and maintenance responsibilities. A rental agreement can be either oral or written. It is considered executed when the tenant moves in and starts paying rent.Purchase Agreement: A purchase agreement is a bilateral, express contract between a buyer and a seller. It outlines the terms of the sale, including the price, payment terms, delivery method, and warranty. A purchase agreement is executed when the buyer pays the agreed-upon amount and the seller delivers the product or service.To know more about the "contracts":https://brainly.com/question/5746834
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