To solve this problem, we must first set up an equation. We are told that the total number of seats in the auditorium is 1344. We are also told that the number of seats in each row exceeds the number of rows by 20.
Let's denote the number of rows as x. Therefore, the number of seats per row is x + 20 (as it exceeds the number of rows by 20). Setting up an equation would be as follows:
x * (x + 20) = 1344
This equation states that the number of rows times the number of seats per row equals the total number of seats.
Solving this equation requires finding the roots of a quadratic equation. We set it up as a quadratic equation ax² + bx + c = 0. Here, a = 1, b = 20, and c = -1344.
Solving a quadratic equation gives us two possible solutions, but in our case, we disregard the negative value, as the number of rows cannot be negative. So, we take the maximum of the two roots.
Solving this equation gives us x = 28.0, which represents the number of rows.
Finally, to find the number of seats in each row, we remember that it exceeds the number of rows by 20. So, we add 20 to the number of rows.
28.0 + 20 = 48.0
So, there are 48 seats in each row.
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Use the number line to find the ratio AC/CF simplify the ratio
A. 8/20
B 2/5
C 8/12
D 2/3
Answer:
The correct option is D.
Step-by-step explanation:
From the given number line it is clear that A=0, B=2, C=8, D=14, F=20 and G=22.
The length of line segment AC is
[tex]AC=C-A=8-0=8[/tex]
The length of line segment CF is
[tex]CF=F-C=20-8=12[/tex]
The ratio of line segment AC to CF is
[tex]\frac{AC}{CF}=\frac{8}{12}[/tex]
Cancel out the common factors.
[tex]\frac{AC}{CF}=\frac{2}{3}[/tex]
The simplified ratio of [tex]\frac{AC}{CF}[/tex] is 2/3.
Therefore the correct option is D.
The image of a figure is shown. What are the coordinates of X in the pre-image of the figure if the rule that created the image was T–5.2, 1.4(x, y)? PLEASE ANSWER
X =
a. (-7.2, 3.4)
b. (1.2, 6.6)
c. (3.2, 0.6)
b. (9.2,-0.4)
Which equation models the problem below if c represents the number of puppies whose eyes are closed?
There are 15 puppies in a photograph, and 11 of them have their eyes open.
How many puppies have their eyes closed?
c – 11 = 15
11 – c = 15
15 + c = 11
11 + c = 15
Answer:
11+c=15
Step-by-step explanation:
4 pups have their eyes closed
Which algebraic expression represent the phrase “ seven more than half of a number”?
Answer:
The given expression “ seven more than half of a number” can be written mathematically as [tex]7+\frac{1}{2}N[/tex]
Step-by-step explanation:
Given phrase “ seven more than half of a number”
We have to write the algebraic expression for the given phase.
Algebraic expression is the way of writing an expression in mathematical form using mathematical operations and variables.
Consider the given phrase “ seven more than half of a number”
Let the number be N,
Then half of number is [tex]\frac{1}{2}N[/tex]
and seven more means seven is added to this, the expresion becomes [tex]7+\frac{1}{2}N[/tex]
Thus, the given expression “ seven more than half of a number” can be written mathematically as [tex]7+\frac{1}{2}N[/tex]
Gustavo tested 1000 calculators to see if any were defective. The company claimed that the probability of a defective calculator was 1% per 1000 calculators. Gustavo found 15 defective calculators out of 1000.
What was the predicted frequency?
Predicted Frequency . . .
=(# of trials)(theoretical probability)
=(1000)(0.01)
The predicted frequency was ____
A: 1
B: 10
C: 100
D: 1000
What was the relative frequency?
Relative Frequency = Observed Frequency/Total Number of Trails
The relative frequency was _____
A: 0.15%
B: 1%
C: 1.5%
D: 15%
ITS 10
Then 1.5% thank this
2.1 + (–3.7h) + 1.9h – 1.4
What are the two equations created by the inequality |x–12| + 5 < 27? y1= and y2=
Answer:
y1= |x-12|
y2= 22
Which graph represents the two functions? Graph 3
Step-by-step explanation:
A town has a population of 2000 and grows at 4% every year what will be the population after 15 years to the nearest whole number
Answer:
3602
Step-by-step explanation:
The population of the town after 15 years will be approximately 3495.
Explanation:To find the population of the town after 15 years, we need to use the formula for compound interest: A = P(1 + r)^t, where A is the final amount, P is the initial amount, r is the growth rate expressed as a decimal, and t is the number of time periods. In this case, P = 2000, r = 0.04, and t = 15.
Using this formula, we can calculate the population after 15 years:
A = 2000(1 + 0.04)^15
A = 2000(1.04)^15
A ≈ 2000(1.747422)
A ≈ 3494.84
Rounding to the nearest whole number, the population after 15 years will be approximately 3495.
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PLEASE HELP ME!!!!!!!!!
Which set of points lies on the graph of x = -2?
A _____ is a type of variable that is not accounted for in a research experiment.
a. independent variable
b. dependent variable
c. confounding variable
Graph y= 1/3x+3 .I just need to know the plots
Answer:
The graph shows the given straight line.
Step-by-step explanation:
We are given an equation:
[tex]y = \displaystyle\frac{1}{3}x + 3[/tex]
The attached image shows the graphical plot for the given equation.
If we compare the given equation to the
[tex]y = mx+c[/tex]
where m is the slope and c is the y-intercept of the straight line.
Comparing, we get:
[tex]m = \displaystyle\frac{1}{3}\\\\c = 3[/tex]
The line will pass by the points (-3, 2), (0, 3), and (3, 4)
Given is an equation y = x/3+3 we need to graph it,
Let's pick a few x-values and determine the y-values that go with them:
Y equals (1/3) when x = -3(-3) + 3 = -1 + 3 = 2
Y = (1/3)(0) + 3 = 0 + 3 = 3 when x = 0.
Y = (1/3)(3) + 3 = 1 + 3 = 4 for x = 3.
The points (-3, 2), (0, 3), and (3, 4) can now be plotted on the coordinate plane.
A straight line running across these locations will form the graph.
The line will have a positive slope because the value of x is positive (1/3).
Given that the y-intercept is 3, the line will cross the y-axis at (0, 3).
The plotted points (-3, 2), (0, 3), and (3, 4) lie on the line, and the line continues indefinitely in both directions.
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Need help I dont know how to do this please help!
2. Graph the number on a number line.
10/7
The school cafeteria has two meal options in the main line today: a grilled chicken sandwich or a spicy fried chicken sandwich one lunch period, 60 people order the grilled chicken sandwich, and 90 people order the spicy fried chicken sandwich. 40 of the eople who ordered the grilled chicken sandwich got a chocolate mitk to drink. If the sandwich choice and the drink choice are independent, how many of the people who ordered the spicy fried chicken sandwich got a chocolate milk?
Answer:
60 of the people who ordered the spicy fried chicken sandwich got a chocolate milk.
Step-by-step explanation:
Consider the provided information.
60 people order the grilled chicken sandwich, and 90 people order the spicy fried chicken sandwich.
40 Out of 60 people who order grilled chicken sandwich got a chocolate milk to drink.
Let say x number of people out of 90 got chocolate milk drink.
Now we need to find the people who ordered the spicy fried chicken sandwich got a chocolate milk.
The above information can be written as:
[tex]\frac{40}{60}=\frac{x}{90}[/tex]
[tex]\frac{40}{60}\times 90=x[/tex]
[tex]x=20\times 3[/tex]
[tex]x=60[/tex]
Hence, 60 of the people who ordered the spicy fried chicken sandwich got a chocolate milk.
The number of people who ordered the spicy fried chicken sandwich and got a chocolate milk is calculated as 50.
The number of people who ordered the spicy fried chicken sandwich and got a chocolate milk is to be determined.
Step-by-step explanation:
Calculate the total number of people who ordered the spicy fried chicken sandwich minus the number who got a chocolate milk with the grilled chicken (90 - 40 = 50).Therefore, 50 people who ordered the spicy fried chicken sandwich got a chocolate milk.Jeannette earns $3.50 per hour and 4% commission on the gross amount of
her sales. How much did she earn the week she worked 35 hours and sold
$4,550 worth of merchandise?
a. $304.50
b. $182
c. $186.90
d. $122.50
HELP ASAPPP
an angle bisector of a triangle divides the opposite side of the triangles into segments 6cm and 4cm long. A second side of triangle is 7.4 cm long. Find the longest and shortest possible lengths of the thrid side of the triangle
Why would someone choose to use a graphing calculator to solve a system of linear equations instead of graphing by hand? Explain your reasoning.
Sample Response: A graphing calculator is more accurate than graphing by hand. If the slope and/or y-intercept is a fraction or decimal, it is more difficult to accurately graph by hand. Using a calculator might also be more time efficient because it might accept a line in any form. A calculator’s window can be adjusted quickly instead of having to redraw a graph by hand when adjusting the scale.
The volume of a sphere is 3,000π m3. What is the surface area of the sphere to the nearest square meter? 165 m2 2,158 m2 1,079 m2 37,699 m2
Please help me solve for r
Hannah completed 3/4 of her homework on Saturday morning and 1/8 ofit on Saturday night. How much more homework does she need to complete?
WILL GIVE BRAINLIEST, 5 STARS, AND THANK YOU
The Polygons are similar, but not necessarily drawn to scale. Find the value of x.
You are preparing to tile the floor of a rectangular room that is 15.5 feet by 18 feet in size. The tiles you plan to use are squares, measure 12 inches on each side, and are sold in boxes that contain enough tiles to cover 25 square feet. Each box costs $30.
To determine the cost of materials you multiply 15.5 by 18, divide by 25, round up to the next whole number, and multiply by 30. Is this correct?
A) Yes.
B) No, you need to round down and then multiply by 30.
C) No, you need to round down and then multiply by 144.
D) No, you need to divide by 144, round up, and then multiply by 30.
E) No, you need to divide by 144, round down, and then multiply by 30.
To find the cost of tiling the room, you have to calculate the area in square feet, convert tile size to the same units, calculate how many boxes needed and round up, then multiply by the cost per box. The correct answer is D).
Explanation:The correct answer is D). The process to determine the cost of the tiles needed to cover the room starts with calculating the area of the room in square feet. This is done by multiplying the room's length and width, so 15.5 feet * 18 feet which equals 279 square feet.
The tiles are 12 inches in size on each side, but the dimensions of the room are in feet. Therefore, we need to convert the tile size to square feet. Since 1 foot = 12 inches, 1 square foot = 144 square inches. Our tile is 12 inches * 12 inches = 144 square inches, which equals 1 square foot.
However, the tiles are sold in boxes that cover 25 square feet. So, we will divide the total room area by the area covered by one box of tiles. 279 square feet / 25 = 11.16 boxes needed, approximately.
It's important to round up at this stage, as you can't buy a fraction of a box. So, you'd need 12 boxes.
The last step is to calculate the total cost, which is done by multiplying the number of boxes by the cost of each box. So, 12 * $30 equals $360.
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1. Sarah bought a mango tree that grows 4 cm each day. It was 10 cm tall when she bought it and now it is 82 cm. Write an equation to express the growth of this tree. Let "x" represent the number of days Sarah has owned the tree.
2. How many days has Sarah owned the tree?
Use the quadratic formula to solve for the roots of the following equation. x 2 – 4x + 13 = 0
By using the quadratic formula, the roots of the equation are,
⇒ x = 2 ± (√3/2) i
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The quadratic equation is,
⇒ x² - 4x + 13 = 0
Now, By using the quadratic formula, the roots of the equation are,
⇒ x² - 4x + 13 = 0
⇒ x = - (- 4) ± √ (- 4)² - 4×1×13 / 2
⇒ x = 4 ± √16 - 52 / 2
⇒ x = 4 ± √- 36 / 2
⇒ x = 4 ± √6 i / 2
⇒ x = 2 ± (√3/2) i
Thus, We get;
⇒ x = 2 ± (√3/2) i
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Final answer:
The roots of the quadratic equation x² - 4x + 13 = 0 are complex numbers, specifically 2 + 3i and 2 - 3i, obtained through applying the quadratic formula.
Explanation:
To solve the quadratic equation x² – 4x + 13 = 0 using the quadratic formula, we first identify a, b, and c from the equation. Here, a=1, b=-4, and c=13. The quadratic formula is ‘x' equals minus ‘b’, plus-or-minus the square root of ‘b’ squared minus four ‘a’ ‘c', all over two 'a'. Applying these values, we get:
x = – (-4) ± √((-4)² – 4(1)(13)) / (2)(1)
This simplifies to:
x = 4 ± √(16 – 52) / 2
x = 4 ± √(-36) / 2
Since the square root of -36 is 6i (where i is the imaginary unit √(-1)), the solutions are:
x = (4 ± 6i) / 2
x = 2 ± 3i
Therefore, the roots of the equation are 2 + 3i and 2 - 3i, which are complex numbers.
kelly ran 2 miles and burned 240 calories. the next day she ran 3 miles and burned 360 calories. the next day4 miles and 480 miles. if this pattern continues, how
many calories will she burn if she runs 8 miles?
Answer:
She will burn 960 calories if she runs 8 miles
Jeremiah scored 28 points in yesterday's basketball game. He made a total of 17 baskets. Some of the baskets were field goals (worth two points) and the rest were free throws (worth one point). How many field goals did Jeremiah make? How many free throws did he make?
Answer:
6 and 11
Step-by-step explanation:
What is value of x?
https://static.k12.com/nextgen_media/assets/8093716-NG_GMT_SemB_08_UT_12.png
The calculated measure of the angle x is 76 degrees
How to determine the measure of the angle xFrom the question, we have the following parameters that can be used in our computation:
The figure
Also, we have
Angle with a measure of 76 degrees
By the theorem of corresponding angles, we have
x = 76
Hence, the measure of the angle x is 76 degrees
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Find the smallest possible set (i.e., the set with the least number of elements) that contains the given sets as subsets. {jill, john, jack}, {susan, sharon}
The smallest possible set that contains the given sets as subsets is,
⇒ {jill, john, jack, Susan, sharon}
What is mean by Subsets?
A set 'A' is a subset of another set 'B' , if all the element of the set A are element of set of 'B'.
Given that;
The subsets are;
⇒ {jill, john, jack} , {Susan, sharon}
Now,
Clearly, A subsets of a set is contain all the elements of subsets.
So, We get the set;
Set = {jill, john, jack, Susan, sharon}
Thus, The smallest possible set that contains the given sets as subsets is,
⇒ {jill, john, jack, Susan, sharon}
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Please help with 2 questions.
Mr Savage used 3 gallons of paint to cover 1,350 square feet of wall space. At this rate, how much paint will be needed to cover 1,800 square feet