The correct unit cost per car is $1.83.
To find the unit cost per car, we need to divide the total cost by the number of cars built. Since each student builds three mouse trap cars and spends an average of $5.50, the total cost for one student is $5.50.
Let's denote the unit cost per car as [tex]\( C \)[/tex]. The equation representing the total cost for one student is:
[tex]\[ 3C = \$5.50 \][/tex]
Now, we solve for [tex]\( C \)[/tex] to find the unit cost per car:
[tex]\[ C = \frac{$5.50}{3} \][/tex]
[tex]\[ C = $1.8333... \][/tex]
Rounding to two decimal places, the unit cost per car is approximately $1.83.
7/8,0.98,8/9 least to greatest
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.
The cost of 5 dresses and 2 belts is $48. The cost of 3 dresses and 2 belts is $32. Find the cost of a dress and a belt. Let x denote the cost of a dress and y denote the cost of a belt.
By setting up a system of linear equations and solving for x and y, we find that the cost of a dress is $8 and the cost of a belt is $4.
Explanation:To find the cost of a dress and a belt, we can set up a system of linear equations using the information given. Let x denote the cost of a dress and y denote the cost of a belt. We then have two equations:
5x + 2y = $48 (1)3x + 2y = $32 (2)Subtract equation (2) from equation (1) to eliminate y:
5x + 2y - (3x + 2y) = $48 - $32
2x = $16
Now we can solve for x:
x = $16 / 2
x = $8
Now that we know the cost of a dress (x), we can substitute this value into equation (2) to find the cost of a belt (y):
3(8) + 2y = $32
24 + 2y = $32
2y = $32 - $24
2y = $8
y = $8 / 2
y = $4
Therefore, the cost of a dress is $8 and the cost of a belt is $4.
What polynomial must be added to x^2-2x+6 so that the sun is 3x^2+7x?
The polynomial given below has _____ root(s).
3x2 - 8x + 4
A. two positive
B. two negative
C. two complex
D. one positive and one negative
The product of twenty-one negative integers is negative.
True
False
which is bigger 40% of 210 or 1/4 of 320
To find out which is bigger, we calculate 40% of 210 and 1/4 of 320. 40% of 210 is greater than 1/4 of 320.
Explanation:To find out which is bigger, 40% of 210 or 1/4 of 320, we need to calculate both values.
First, 40% of 210 can be calculated by multiplying 210 by 0.4. This gives us 84.
Next, 1/4 of 320 can be calculated by dividing 320 by 4. This gives us 80.
Therefore, 40% of 210 is greater than 1/4 of 320.
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.
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!
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.
A comic book costs $3.99, including tax. It is marked up 45%. What is the final price of the comic book after it is marked up? $1.80 $4.44 $5.79 $6.15
the real answer is 5.79, the other person had had miscalculation
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.
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
Find two consecutive whole numbers that /76 lies between.
Elsie pays $21.75 for 5 student tickets to the fair what is the cost of each student ticket
Use the stem and leaf plot shown to answer the following question.
WILL UPVOTE!
Factor the expression.
36c^2 −121
435 is 15% of what number?
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
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."
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
A similar question is solved here: https://brainly.com/question/17181309?referrer=searchResults
Find f if f"(theta)=sin (theta) + cos (theta), f(0)=3, and f'(0)=4
what is 14 9/100 as a decimal
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:
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.
Learn more about Sequence here:
https://brainly.com/question/2088649
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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.
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]
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
The vertices of ∆ABC are A(-2, 2), B(6, 2), and C(0, 8). What is the perimeter of ∆ABC in units?
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?