During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the machine recommends that the temperature of the machine part remain below 132 ° F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by T = -0.005x^2 + 0.45x + 125. Will the temperature of the part ever reach or exceed 132 ° F? Use the discriminant of a quadratic equation to decide.
A. no
B. yes
Answer: The answer saying YES, is WRONG, the CORRECT ANSWER IS NO.
Answer:
The answer is no
0.45^2-4(-.005)(125)=2.7025
so no it do not exceed
Step-by-step explanation:
What is the apparent solution to the system of equations graphed above?
(0,-1)
(0,3)
(1,2)
(2,1)
The equation below shows the relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F:
F = 9 over 5C + 32
Which of the following formulas correctly solves for C?
C = 5F − 32 over 9
C = 5 F over 9 − 32
C = 9 over 5(F − 32)
C = 5 over 9(F − 32)
Answer:
The correct option is 4.
Step-by-step explanation:
The relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F is defined by the given equation.
[tex]F=\frac{9}{5}C+32[/tex]
We need to find the formula for C.
Subtract 32 from both the sides.
[tex]F-32=\frac{9}{5}C+32-32[/tex]
[tex]F-32=\frac{9}{5}C[/tex]
Multiply both sides by 5.
[tex]5(F-32)=9C[/tex]
Divide both sides by 9.
[tex]\frac{5(F-32)}{9}=\frac{9C}{9}[/tex]
[tex]\frac{5}{9}(F-32)=C[/tex]
The formula for C is [tex]C=\frac{5}{9}(F-32)[/tex].
Therefore the correct option is 4.
If Zelda has a 300 inch roll of binding for a quilt and the quilt must be 84 inches long how wide can she make it
Let θ (in radians) be an acute angle in a right triangle, and let x and y, respectively, be the lengths of the sides adjacent and opposite θ. Suppose also that x and y vary with time.
a. How are dθ/dt, dx/dt and dy/dt related?
Please give steps and explain!
Answer:
dθ/dt = [(cos^2 θ)*(dy/dt * x - y * dx/dt)]/(x^2)
Step-by-step explanation:
Given that x and y are the lengths of the sides adjacent and opposite θ, then they are related by:
tan θ = y/x
Differentiating respect to t, we get:
sec^2 θ * dθ/dt = (dy/dt * x - y * dx/dt)/(x^2)
dθ/dt = [(cos^2 θ)*(dy/dt * x - y * dx/dt)]/(x^2)
Amounts of trade discounts are not fixed? True or False ...?
Trade discounts are not fixed; they are true to vary based on several factors including order volume, buyer-seller relationships, and industry norms. They are a dynamic component of economic transactions within the complex trade environment and are influenced by market interactions and broader economic principles.
The statement "Amounts of trade discounts are not fixed" is true. Trade discounts can vary greatly and are typically influenced by a variety of factors including the volume of the goods ordered, the relationship between the buyer and seller, and the industry standards.
For instance, when businesses deliver larger lots, volume discounts may be offered, which reflect the lower costs of providing goods in bulk rather than differences in willingness to pay. This variation in trade discounts ensures that each transaction is adjusted to meet the precise needs of both the buyer and seller, depending on the specific circumstances of the trade.
Moreover, the trade environment is complex and the interactions between buyers and sellers determine the gains from trade in an economy. These interactions depend on market structure, negotiation possibilities, and the mode of sale, such as retail or auction.
Consequently, trade discounts are part of a dynamic economic system where various elements such as free trade agreements, industry adjustments, transaction costs, and the unmeasured benefits of competition and product variety all play a role in shaping the final outcome.
Which of the following is the most profitable investment for a candy shop that earns $1 profit per pound of candy?
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Worker at $10 per hour, producing eight pounds of candy per hour
Worker at $12 per hour, producing 16 pounds of candy per hour
Machine with $5 per hour operating cost, producing 10 pounds of candy per hour
Machine with $8 per hour operating cost, producing 14 pounds of candy per hour
Answer:
Option 4). Machine with $8 per hour operating cost, producing 14 pounds of candy per hour.
Step-by-step explanation:
We have to find the most profitable investment for a candy shop that earns $1 per pound of candy.
We will take up each option one by one.
Option 1).
Producing eight pounds of candy per hours means profit = $1×8 = $8
But workers take $10 per hours so expenditure = $8 - $10 = -$2
There is a loss of $2 in this investment.
Option 2).
Production of 16 pounds candy per hour will make the profit = $1 × 16 = $16
But workers take $12 per hour so profit earned = 16 - 12 = $4
Option 3).
Machine produces 10 pound of candy per hour so profit will be = $1 ×10 = $10
Operating cost of the machine = $5 per hour
So profit generated = profit - Operating cost of machine
= 10 - 5 = $5
Option 4).
Profit earned by production of 14 pounds of candy per hour = $1 × 14 = $14
Operating cost of the machine = $8 per hour
Therefore, Total profit per hour = 14 - 8 = $6
Finally we can say that the maximum profit will be generated in option 4.
Therefore, Option 4) will be the best option to invest.
Final answer:
The most profitable investment for a candy shop is the machine with an $8 per hour operating cost, producing 14 pounds of candy per hour, yielding a net profit of $6 per hour.
Explanation:
The task is to determine the most profitable investment for a candy shop that makes $1 profit per pound of candy. To calculate the profitability of each option, we need to figure out the net profit per hour for each.
Worker at $10 per hour, producing eight pounds of candy per hour:
Profit = 8 pounds * $1 profit per pound - $10 wage per hour = $8 - $10 = -$2 per hour.
Worker at $12 per hour, producing 16 pounds of candy per hour:
Profit = 16 pounds * $1 profit per pound - $12 wage per hour = $16 - $12 = $4 per hour.
Machine with $5 per hour operating cost, producing 10 pounds of candy per hour:
Profit = 10 pounds * $1 profit per pound - $5 operating cost per hour = $10 - $5 = $5 per hour.
Machine with $8 per hour operating cost, producing 14 pounds of candy per hour:
Profit = 14 pounds * $1 profit per pound - $8 operating cost per hour = $14 - $8 = $6 per hour.
Comparing the net profit per hour for each option, the Machine with $8 per hour operating cost, producing 14 pounds of candy per hour, is the most profitable investment.
how to solve a quadratic equation by using the quadratic formula?
Final answer:
To solve a quadratic equation using the quadratic formula, put the equation in ax² + bx + c = 0 form, identify a, b, and c, plug them into the formula x = (-b ± √(b² - 4ac)) / (2a), calculate the discriminant, and find the two possible values for x.
Explanation:
To solve a quadratic equation by using the quadratic formula, you should follow these steps:
First, make sure that the equation is in the standard quadratic form, which is ax² + bx + c = 0.Identify the coefficients a, b, and c from the equation.Plug these values into the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a).Calculate the discriminant D, which is the part under the square root: b² - 4ac.The discriminant tells you the nature of the roots:For example, if we have the equation t² + 10t - 200 = 0, by identifying a=1, b=10, and c=-200, and plugging them into the quadratic formula, we can solve for t.
2 times the sum of a number and 4 is no more than three times the sum of a number and 7 decreased by 4
7/8,0.98,8/9 least to greatest
Select all situations that could be represented by a constant rate.
A) the number of cars manufactured per day at a factory
B) the speed of a toy rocket as it is launched straight into the air the number of
C) rotations per minute made by a fan
D) the population increase of a bacteria colony in a petri dish
Choose the method of pay that would result in the most earnings for one month on sales of $73,620. a. Straight commission of 6% on all sales. b. Monthly salary of $3,000 plus 2% commission on all sales. c. Graduated commission of 4% on the first $50,000 in sales and 9% on anything over that. d. Graduated commission of 5% on the first $35,000 in sales and 7% on anything over that.
The method of pay that results in the most earnings is the second method of pay
In order to determine which method of pay would result in the most earnings , the value of each method would be determined
Value of the first option
6% commission on all sales = 6% x $73,620.
0.06 x $73,620. = $4,417.20
Value of the second option
Monthly salary of $3,000 plus 2% commission on all sales = $3,000 + (2% x $73,620)
$3,000 + (0.02% x $73,620)
= $3000 + $1472.40
= $4472.40
Value of the third option
Graduated commission of 4% on the first $50,000 in sales and 9% on anything over that.
= (4% x $50,000) + (9% x $23,620)
= $2000 + $2125.80
= $4125.80
Value of the fourth option
Graduated commission of 5% on the first $35,000 in sales and 7% on anything over that.
= (5% x$35,000) + (7% x $38,620)
= $1750 + $2703.40
= $4,453.40
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Elsie pays $21.75 for 5 student tickets to the fair what is the cost of each student ticket
Which of these statements is punctuated properly?
"You're kidding she said". You are not going in there.
"You're kidding" she said "You are not going in there."
"You're kidding," she said. "You are not going in there."
"You're kidding, she said. You are not going in there."
What is the equation of the line that passes through (4, -1) and (-2, 3)?
2x - 3y - 5 = 0
2x + 3y - 5 = 0
-2x + 3y - 5 = 0
I know for sure that the answer is 2x + 3y - 5 = 0 I just need somone to explain it!
Find the missing length indicated.
The vertices of ∆ABC are A(-2, 2), B(6, 2), and C(0, 8). What is the perimeter of ∆ABC in units?
What polynomial must be added to x^2-2x+6 so that the sun is 3x^2+7x?
435 is 15% of what number?
[6.01] Systems of equations with different slopes and different y-intercepts have more than one solution.
Always
Sometimes
Never
what is 1626 divided by 12 as a mixed number
Answer:
1626 divided by 12 is written as [tex]\frac{271}{2}=135\frac{1}{2}[/tex]
Step-by-step explanation:
To find : What is 1626 divided by 12 as a mixed number ?
Solution :
Writing 1626 divided by 12 in a fraction from,
[tex]\frac{1626}{12}[/tex]
Writing fraction in simpler form by reducing with common factors,
[tex]\frac{1626}{12}=\frac{2\times 3\times 271}{2\times 2\times 3}[/tex]
[tex]\frac{1626}{12}=\frac{271}{2}[/tex]
Writing [tex]\frac{271}{2}[/tex] in mixed fraction by dividing 271 by 2,
[tex]271=135\times 2+1[/tex]
i.e. [tex]\frac{271}{2}=135\frac{1}{2}[/tex]
Therefore, 1626 divided by 12 is written as [tex]\frac{271}{2}=135\frac{1}{2}[/tex]
Find f if f"(theta)=sin (theta) + cos (theta), f(0)=3, and f'(0)=4
write the statement using absolute value notation:
the distance between x and 4 is 3
Write a function Rule that represents the situation: A workers earnings e are a function of the number of hours n worked at a rate of $8.75 per hour
The function rule representing a worker's earnings e as a function of hours n worked at a rate of $8.75 per hour is e(n) = 8.75 × n. This formula is used to calculate the worker's pay based on their hours worked.
Explanation:To represent a worker's earnings e as a function of the number of hours n worked at a rate of $8.75 per hour, you would write the function rule as:
e(n) = 8.75 × n
Here, n represents the number of hours worked and e(n) represents the earnings for those hours.
For example, if a worker puts in 8 hours of work, their earnings would be calculated as:
e(8) = 8.75 × 8
= $70
This means the worker would earn $70 for an 8-hour workday.
Express the function \[\frac{n^3}{1000} - 100n^2 - 100n + 3\]in terms of \(\huge{\Theta}\)notation ...?
What is the determinant of an identity matrix?
Answer:
The determinant of an identity matrix is always 1.
Step-by-step explanation:
Given : An identity matrix.
We have to find the determinant of an identity matrix.
Consider an identity matrix,
Identity matrix is a matrix having entry one in its diagonal and rest all entries are zero.
Let us consider a 2 × 2 identity matrix,
[tex]I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]
We know determinant of a 2 × 2 matrix
[tex]I=\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]
is given by
D = ad - bc
Thus, here a = 1 , b = 0 , c= 0 d= 1
Thus, D = 1 - 0 = 1
Thus, The determinant of an identity matrix is always 1.
Find the product.
(-2x ^2) ^3 -3x
Final answer:
To find the product of (-2x^2)^3 and -3x, first calculate the cube of -2x^2 (-8x^6), then multiply it by -3x to obtain 24x^7.
Explanation:
The student has asked to find the product of two expressions, (-2x^2)^3 and -3x. To solve this, we first calculate the cube of -2x^2, which is -8x^6, then we multiply this result by -3x to find the final product.
So, let's perform these two steps:
Cube of -2x^2: (-2x^2)^3 = (-2)^3 × (x^2)^3 = -8 × x^6 = -8x^6
Multiplication by -3x: -8x^6 × -3x = 24x^7
Therefore, the product is 24x^7.
generate the first five terms in the sequence using the explicit formula. yn=-5n-5
The first five terms in the sequence generated by the explicit formula [tex]y_n[/tex] = -5n - 5 are: -10, -15, -20, -25, -30.
To generate the first five terms in the sequence using the explicit formula [tex]y_n[/tex] = -5n - 5,
we substitute the values of n from 1 to 5 into the formula.
For n = 1:
[tex]y_1[/tex]= -5(1) - 5 = -10
For n = 2:
[tex]y_2[/tex] = -5(2) - 5 = -15
For n = 3:
[tex]y_3[/tex] = -5(3) - 5 = -20
For n = 4:
[tex]y_4[/tex] = -5(4) - 5 = -25
For n = 5:
[tex]y_5[/tex] = -5(5) - 5 = -30
Therefore, the first five terms in the sequence generated by the explicit formula [tex]y_n[/tex] = -5n - 5 are:
-10, -15, -20, -25, -30.
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what is another way to express 48 + 32?
Answer:16( 3+2)
Step-by-step explanation:
Another way of expressing 48 + 32 are:
32 + 48 and 80.
Addition is a basic mathematical operation that combines two numbers to give a total or sum.
The given expression is:
48 + 32
The commutative property is:
A+B = B+A
Since Addition always holds the commutative property
Therefore, we can write the given expression as,
32 + 48
We can also express it by direct sum,
3 2
+ 4 8
_______
8 0
_______
So, the sum of 32 and 48 is 80.
Hence,
We can express the given expression as 32 + 48 and 80.
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An object with a mass of 6.3 kg has a mass of 7.1newtons applied to it, what is the resulting acceleration of the object
The resulting acceleration of the object is approximately [tex]\( 1.127 \, \text{m/s}^2 \).[/tex]
To find the resulting acceleration of an object when a force is applied to it, you can use Newton's second law of motion, which states:
F = ma
Given that the force F = 7.1 Newtons and the mass m = 6.3 kg, we can rearrange the formula to solve for acceleration:
[tex]\[ a = \frac{F}{m} \]Substitute the given values:\[ a = \frac{7.1 \, \text{N}}{6.3 \, \text{kg}} \]Now, divide to find the acceleration:\[ a = \frac{7.1}{6.3} \, \text{m/s}^2 \]\[ a = 1.127 \, \text{m/s}^2 \][/tex]
So, the resulting acceleration of the object is approximately [tex]\( 1.127 \, \text{m/s}^2 \).[/tex]
Complete question:
An object with a mass of 6.3 kg has a force of 7.1 Newtons applied to it. What is the resulting acceleration of the object?