Final answer:
The algebraic equation that represents the relationship between the number of chairs, c, and the number of desks, d, in an office, where the number of chairs is five more than twice the number of desks, is c = 2d + 5.
Explanation:
The student's question pertains to creating an algebraic equation based on a given word problem describing the relationship between the number of chairs (c) and desks (d) in an office. The problem states that 'the number of chairs, c, is equal to five more than twice the number of desks, d'.
To formulate the equation that illustrates this relationship, we apply the information provided:
Identify the number of chairs as c.Determine that c is 'five more than' something, which suggests addition.Recognize that 'twice the number of desks' means 2 times d, or 2d.Combine the above to conclude that the 'five more than' is added to the 'twice the number of desks', which gives us the equation c = 2d + 5.Consider the system of equations. x – 3y = 9 1/5x - 2y = -1
Answer:
B
Step-by-step explanation:
Juan analyzes the amount of radioactive material remaining in a medical waste container over time. He writes the function f(x) = 10(0.98)x to represent the amount of radioactive material that will remain after x hours in the container. Rounded to the nearest tenth, how much radioactive material will remain after 10 hours?
Answer: There is approximately 8.2 amount of radioactive material that will remain after 10 hours.
Step-by-step explanation:
Since we have given that
[tex]f(x)=10(0.98)^x[/tex]
where, f(x) represents the amount of radioactive material that will remain after x hours in the container.
Since we have given that x = 10 hours.
So, our equation becomes,
[tex]f(10)=10\times (0.98)^{10}\\\\f(10)\approx 8.17\\\\f(10)\approx 8.2[/tex]
Hence, there is approximately 8.2 amount of radioactive material that will remain after 10 hours.
The center of a circle is (4, 6), and an endpoint of a diameter is (2, 5). What is the other endpoint of the diameter?
Answer:
(6,7)
Step-by-step explanation:
The center of a circle is (4, 6), and an endpoint of a diameter is (2, 5)
Since center is the mid point of two end points of diameter .
So, we will use mid point formula
[tex](x,y)=(4,6)[/tex]
[tex](x_1,y_1)=(2,5)[/tex]
Mid point formula : [tex]x =\frac{x_1+x_2}{2}[/tex] and [tex]y =\frac{y_1+y_2}{2}[/tex]
Substitute the values
[tex]4 =\frac{2+x_2}{2}[/tex] and [tex]6 =\frac{5+y_2}{2}[/tex]
[tex]8 =2+x_2[/tex] and [tex]12 =5+y_2[/tex]
[tex]6=x_2[/tex] and [tex]7=y_2[/tex]
Thus [tex](x_2,y_2)=(6,7)/tex]
Thus the other endpoint of the diameter is (6,7)
what is the simplified form of 3a4b-2c3?
The expression 3a4b-2c3 is already in its most simplified form because they are not like terms, thus cannot be combined.
Explanation:The given expression 3a4b-2c3 cannot be simplified further because it consists of variable components. Each of these components -- 3a, 4b, and 2c3 -- represent distinct and separate entities in the equation. Unlike in some mathematics problems, these components cannot be combined or simplified because they are not like terms. In algebra, like terms are terms that contain the same variables and powers. So only if the given equation was 3a + 2a or 4b - 3b, then they could be combined. But as it stands, 3a4b-2c3 is already in its most simplified form.
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The area of an artist's square canvas can hold 113 square inches of paint. What is the approximate length of one side of the canvas?
The expression below represents the number of bacteria in a petri dish after t hours. Interpret the meaning of the expression. A. The initial number of bacteria is 57, and the growth rate is 3.1% per hour. B. The initial number of bacteria is 57, and the growth rate is 31% per hour. C. The initial number of bacteria is 131, and the growth rate is 5.7% per hour. D. The initial number of bacteria is 131, and the growth rate is 57% per hour.
Answer:
The answer on edgenuity for dividing fractions is -3 on the assignment good luck!
Step-by-step explanation:
what is the value of x in the diagram
a.1/2
b.4/21
c.2
d.4
Answer:
2 so your answer would be C.
The base of a triangle is 12 in. The height is 7 in. What is the area of the triangle? A) 19 in2 B) 28 in2 C) 42 in2 D) 84 in2
Answer:
C. 42
Step-by-step explanation:
PLEASE HELP!!!!
Which equation matches the graph of the greatest integer function given below?
A. y=[x]-3
B. y=[x]-2
C. y=[x]+2
D. y=[x]+3
the correct answere is B
Frankie is practicing for a 5-kilometer race. His normal time is 31 minutes 21 seconds. Yesterday it took him only 29 minutes 38 seconds. How much faster was Frankie yesterday than his normal time?
Its Simple! 1 minute and 47 seconds! You gotta do 31 mins and 21 seconds - 29 mins and 38 seconds! Which give you a whooping 1 minute and 47 seconds! I hope i helped you!
$10.00 divided by $1.49
Evaluate the expression when y=-5
Y^2-8Y+4
Mora ate 8.5 Containers of Yogurt one week. Each Container Held 5.4 Ounces Of Yogurt . HOW Many Ounces Of Yogurt Did she eat in all
Final answer:
Mora ate a total of 45.9 ounces of yogurt after consuming 8.5 containers, with each container holding 5.4 ounces.
Explanation:
The student asked how many ounces of yogurt Mora ate after consuming 8.5 containers, with each container holding 5.4 ounces. Mora ate 8.5 containers of yogurt, with each container holding 5.4 ounces of yogurt. To calculate the total amount of yogurt consumed, we multiply the number of containers by the amount of yogurt each container holds.
To solve this, simply calculate 8.5 containers × 5.4 ounces/container = 45.9 ounces of yogurt in total. This is the total amount of yogurt Mora ate during that week.
If y varies inversely as x and y is 6 when x is 12 what is x when y is 14.4
the answer is option A. 5
What is the solution to this equation?
3(4x + 3) = 2x - 5(3 - x) + 2
Each statement describes a transformation of the graph of y = log2x.
Which statement correctly describes the graph of y = log2(x + 3) - 9?
It is the graph of y = log2x translated 3 units down and 9 units to the left.
It is the graph of y = log2x translated 9 units down and 3 units to the right.
It is the graph of y = log2x translated 9 units down and 3 units to the left.
It is the graph of y = log2x translated 3 units up and 9 units to the left.
it's C: It is the graph of y = log2x translated 9 units down and 3 units to the left.
A polygon that has all sides the same measure and all angles the same measure is called what? A. Convex polygon B. Concave polygon C. Irregular polygon D. Regular polygon
The circle has a diameter of 16 inches. What is the area of the circle?
In triangle NOP, Np is extended through Point P to Point Q, m < NOP =(x+17) degrees, m< PNO =(2x-4) degrees, and m< OPQ=(5x-17) degrees. Find m< OPQ
To find the measure of angle OPQ, set up an equation using the given angles in triangle NOP. Simplify the equation and solve for x. Substitute the value of x back into the expression for angle OPQ to find the measure of the angle.
Explanation:To find the measure of angle OPQ, we can set up an equation using the given angles in triangle NOP:
(x+17) + (2x-4) + (5x-17) = 180
Simplifying the equation, we get: 8x - 4 = 180
From this, we can solve for x: 8x = 184, x = 23.
Now that we have the value of x, we can substitute it back into the expression for angle OPQ: 5(23) - 17 = 108 degrees.
Thus, the measure of angle OPQ is 108 degrees.
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A slice is made parallel to the base of a right rectangular pyramid, as shown.
What is the area of the resulting two-dimensional cross-section?
Enter your answer in the box.
in²
In the Chang family's budget, 0.6% of the expenses are for internet service. What is the fraction of the family's expenses is for internet service? Write the fraction in the simplest form.
What are the lower, middle, and upper quartiles of this data? 122, 164, 71, 98, 84, 147, 114, 111, 98, 85, 104, 71, 77
Answer:
The lower, middle, and upper quartiles of this data are 80.5, 98 and 118 respectively.
Step-by-step explanation:
The given data set is
122, 164, 71, 98, 84, 147, 114, 111, 98, 85, 104, 71, 77
Arrange the data set in ascending order.
71, 71, 77, 84, 85, 98, 98, 104, 111, 114, 122, 147, 164
Divide the data set in equal parts.
(71, 71, 77, 84, 85, 98), 98, (104, 111, 114, 122, 147, 164)
Now divide each parenthesis in two equal parts.
(71, 71, 77), (84, 85, 98), 98, (104, 111, 114), (122, 147, 164)
Lower quartile is
[tex]Q_1=\frac{77+84}{2}=80.5[/tex]
Middle quartile is
[tex]Median=Q_2=98[/tex]
Upper quartile is
[tex]Q_3=\frac{114+122}{2}=118[/tex]
Therefore, the lower, middle, and upper quartiles of this data are 80.5, 98 and 118 respectively.
what is the maximum number of possible extreme values for the function f(x)=x^4+x^3-7x^2-x+6
A. 3
B. 4
C. 5
D. 2
A 4th degree polynomial will have at most 3 extreme values. Since the degree is even, there will be one global extreme, with possible multiplicity. The remainder, if any, will be local extremes that may be coincident with each other and/or the global extreme.
(The number of extremes corresponds to the degree of the derivative, which is 1 less than the degree of the polynomial.)
One side of a square flower bed is 22 feet long. How many plants are needed if they are to be spaced 22 inches apart around the outside of the bed?
To find out how many plants are needed, we calculate the perimeter of the square flower bed, convert that to inches, and then divide by the spacing of the plants. In this case, about 48 plants would be needed.
Explanation:This problem can be solved using the properties of a square and unit conversion. Since a square has four equal sides and each side of the square flower bed is 22 feet long, the total perimeter of the flower bed would be calculated as 22 feet * 4, which is 88 feet. Next we need to convert these feet to inches since the plants are spaced 22 inches apart. There are 12 inches within a foot, so 88 feet equals 1,056 inches (88*12).
Once you have the total length in inches, you can determine the number of plants by dividing the total length in inches by the distance each plant is to be spaced. Thus, 1,056 inches divided by 22 inches gives us approximately 48 plants.
So, if you want to space your plants 22 inches apart around a square flower bed where each side is 22 feet, you will need 48 plants.
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Three consecutive even integers add to −6. What are these integers?
A cruise boat travels 48 miles Downstream in 2 hours and returns Upstream in 3 hours. Find the speed of the boat in still water and the rate of the Stream.
Final answer:
The speed of the cruise boat in still water is 20 mph and the rate of the stream is 4 mph.
Explanation:
The student is asking about a problem related to the rate of the boat in still water and the rate of the stream, given the times it takes to travel downstream and upstream. To solve this, we can use the following steps:
Let the speed of the boat in still water be b mph and the rate of the stream be s mph.Downstream, the effective speed is b + s and upstream it's b - s.Using the formula distance = speed imes time, we have two equations based on the given information: 48 miles = (b + s) imes 2 hours for downstream and 48 miles = (b - s) imes 3 hours for upstream.Solve the two equations simultaneously to find the values of b and s.Let's solve the equations:
48 = 2(b + s) => 24 = b + s48 = 3(b - s) => 16 = b - sAdding both equations:
24 + 16 = (b + s) + (b - s) => 40 = 2b => b = 20 mph (boat speed in still water)Subtracting the upstream equation from the downstream equation:24 - 16 = (b + s) - (b - s) => 8 = 2s => s = 4 mph (rate of the stream)Therefore, the speed of the boat in still water is 20 mph and the rate of the stream is 4 mph.
The graph of f(x) = 2x3 – 19x2 + 57x – 54 is shown below. mc018-1.jpg How many roots of f(x) are rational numbers?
Answer: there are 3 root of f(x) which are rational numbers (2,0), (3,0) and (4.5,0)
Explanation:
Rational numbers are those that can be written in the form of p/q: q should not be equal to zero
since, the graph cuts x-axis at three points but rational are two
all integers are rational numbers
attached is the graph please have a look at it
There are 3 grams of sodium in 1/2 of a liter of soda.how much is in 2/3 of a liter
2 cards are drawn from a standard deck of 52 playing cards. how many different 2-card hands are possible if the drawing is done without replacement?
Final answer:
There are 1326 different 2-card hands possible when drawing without replacement from a standard deck of 52 playing cards, using combinations to calculate it.
Explanation:
To determine how many different 2-card hands are possible from a standard deck of 52 playing cards when drawing without replacement, we need to consider combinations since the order of the cards does not matter. Using the combination formula C(n, r) = n! / (r!(n - r)!), where n is the total number of items and r is the number of items to choose, we calculate C(52, 2).
We have:
n = 52 (total number of cards)
r = 2 (number of cards to choose)
Therefore, the calculation is as follows:
C(52, 2) = 52! / (2!(52 - 2)!) = 52! / (2! * 50!) = (52 * 51) / (2 * 1) = 1326.
So, there are 1326 different 2-card hands possible when drawing without replacement from a standard deck of cards.
A radio station sent a letter in the mail to 1000 randomly chosen residents within its broadcast area. The letter contained one dollar and a survey. The survey asked recipients to track their radio habits over a week. The survey was to be filled out and sent back in to the radio station. Identify a problem with the study.
A) Some of the sample data are missing
C) The data are based on reported results
D) The correlation between the variables implies causality
The correct answer is D) The correlation between the variables implies causality.
What is a survey?A survey is a research method used for collecting data from a predefined group of respondents to gain information and insights into various topics of interest.
Now it is said that, A radio station sent a letter in the mail to 1000 randomly chosen residents within its broadcast area. The letter contained one dollar and a survey. The survey asked recipients to track their radio habits over a week. The survey was to be filled out and sent back in to the radio station.
So, here the problem with the survey that the survey is the self filled thus there is a possibility that the people may not be honest while filling the survey.Hence causing casualities.
Thus the correct answer is D) The correlation between the variables implies causality
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