The system of equations is [tex]\[ \begin{cases} x + y = 45 \\ 12x + 8y = 456 \end{cases} \][/tex]
How did we arrive at this equation?
Let's denote the number of 12-person tables as [tex]\( x \)[/tex] and the number of 8-person tables as [tex]\( y \)[/tex]. Since there are 45 tables in total, we can express the first equation as:
[tex]\[ x + y = 45 \][/tex]
Now, considering the total number of people seated, we know that each person at a 12-person table occupies one seat, and each person at an 8-person table occupies one seat as well. The total number of people is 456. Therefore, the second equation is:
[tex]\[ 12x + 8y = 456 \][/tex]
So, the system of equations is:
[tex]\[ \begin{cases} x + y = 45 \\ 12x + 8y = 456 \end{cases} \][/tex]
These equations represent the conditions that the total number of tables is 45 and the total number of people seated is 456, with no empty seats.
) find the function satisfying the y′−3y=9e6t y′−3y=9e6t and y(0)=3.y(0)=3.
A circle has radius of 119.3 mm. What is the circumstance of the circle
The hypotenuse of a right triangle measures 10 inches, and the side opposite to ∠θ, one of the non-right angles, is 5 inches long. The measure of ∠θ is
Explain how you can use a model to find 4X 3/8. Include a drawing and a solution
in 2012 the population of a city was 6.25 million the exponential growth rate was 3.22% per year
find the exponential growth function estimate the population of the city in 2018
One focus of a hyperbola is located at (−1, 7). One vertex of the hyperbola is located at (−1, 5). The center is (−1, −3). What is the equation of the hyperbola?
Answer:
C) (y+3)^2/64-(x+1)^2/36=1
Step-by-step explanation:
Just took the review in edg
To solve this problem, we just need to substitute the values into the equation and solve. the equation of hyperbola and solve. This will give
[tex]\frac{(y+ 3)^2}{64} - \frac{(x+1)^2}{36} =1[/tex]
Equation of a HyperbolaThe standard equation of a hyperbola is given as
[tex]\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1\\[/tex]
The data given are;
focus = (-1, 7)vertex = (-1, 5)center = (-1, -3)Let's substitute the values into the equation of hyperbola and solve. This will give
[tex]\frac{(y+ 3)^2}{64} - \frac{(x+1)^2}{36} =1[/tex]
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10 POINTS!!!
Premier Tire sells three categories of tires: good, better, and best. The good tires cost $106, the better tires cost $156, and the best tires cost $190. The good tires sell 3 times as fast as the best tires and the better tires sell 2.5 times as fast as the best tires. If the total amount of tire sales in January was $233,480, how many of each category of tire was sold? (Round your answer to the nearest whole number.)
which equation is equivalent to log3(x+5)=2
What is the sum of the polynomials? (8x2-9y2-4x)+(x2-3y2-7x)
Answer:
D
Step-by-step explanation:
To the nearest tenth, find the perimeter of ∆ABC with vertices A(-1,4), B(-2,1) and C(2,1). Show your work
ANSWER
The perimeter is 11.4 units
EXPLANATION
Perimeter is the distance around the figure.
We use the distance formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
to determine the length of all the sides and add them.
[tex]|AB|=\sqrt{(-2--1)^2+(1-4)^2}[/tex]
[tex]|AB|=\sqrt{(-1)^2+(-3)^2}[/tex]
[tex]|AB|=\sqrt{1+9}[/tex]
[tex]|AB|=\sqrt{10} \approx 3.162[/tex]
[tex]|AC|=\sqrt{(2--1)^2+(1-4)^2}[/tex]
[tex]|AC|=\sqrt{(2+1)^2+(1-4)^2}[/tex]
[tex]|AC|=\sqrt{(3)^2+(-3)^2}[/tex]
[tex]|AC|=\sqrt{9+9}[/tex]
[tex]|AC|=\sqrt{18} \approx 4.24[/tex]
[tex]|BC|=\sqrt{(2--2)^2+(1-1)^2}[/tex]
[tex]|BC|=\sqrt{(2+2)^2+(1-1)^2}[/tex]
[tex]|BC|=\sqrt{(4)^2+(0)^2}[/tex]
[tex]|BC|=\sqrt{14}=4[/tex]
Therefore perimeter=[tex]|AB|+|BC|+|AC|[/tex]
=[tex]4.00+3.16+4.24[/tex]
=[tex]11.40[/tex] units
given than segment FE is parallel to segment DG, which of the following statements is no true
A spherical helium balloon has a diameter of 30 cm. How much helium is needed to fill the balloon, in cubic centimeters? Round your answer to the nearest centimeter
Sal can mop a certain floor in 8 minutes by himself.If Sal and ben can mop the floor together in 6 minutes,how long does it take Ben to mop the floor alone?
Order the numbers 0.64, 2/3 , 65%, and 7/10 from least to greatest.
Answer:
0.64, 65%, 2/3, 7/10
Step-by-step explanation:
The first step to solve this problem is writing all numbers on the same format:
I am going to write as percentages in the decimal format. So
0.64 = 0.64
2/3 = 0.667
65% = 65/100 = 0.65
7/10 = 0.7
So the correct answer is:
0.64, 65%, 2/3, 7/10
Ari thinks the perfect milkshake has 3 ounces of caramel for every 5 scoops of ice cream. Freeze Zone makes batches of milkshakes with 6 ounces of caramel and 8 scoops of ice cream. What will Ari think about Freeze Zone's milkshakes?
Answer: Ari thinks amount of caramel is more for perfect milkshake as there is only need for 4.8 ounces of caramel but Freeze Zone is using 6 ounces of caramel.
Step-by-step explanation:
Since we have given that
Ari has 3 ounces of caramel for every 5 scoops of ice-cream .
Freeze Zone makes batches of milkshakes with 6 ounces of caramel and 8 scoops of ice-cream.
According to Ari,
For every 5 scoops of ice-cream, he needs 3 ounces of caramel
For every 1 scoop of ice-cream, he needs
[tex]\frac{3}{5}\text{ ounces of caramel}[/tex]
For every 8 scoops of ice-cream, he needs
[tex]\frac{3}{5}\times 8=\frac{24}{5}=4.8\text{ ounces of caramel}[/tex]
So, Ari thinks amount of caramel is more for perfect milkshake as there is only need for 4.8 ounces of caramel but Freeze Zone is using 6 ounces of caramel.
Ari will think Freeze Zone's milkshakes have the perfect amount of caramel.
Explanation:To determine what Ari will think about Freeze Zone's milkshakes, we need to compare the ratio of caramel to ice cream in Ari's perfect milkshake to the ratio in Freeze Zone's milkshakes.
Ari's perfect milkshake has 3 ounces of caramel for every 5 scoops of ice cream, so the ratio is 3:5.
Freeze Zone's milkshakes have 6 ounces of caramel for every 8 scoops of ice cream, so the ratio is 6:8.
To simplify both ratios, we can divide the numbers by their greatest common divisor. The GCD of 3 and 5 is 1, so the simplified ratio for Ari's perfect milkshake is 3:5. The GCD of 6 and 8 is 2, so the simplified ratio for Freeze Zone's milkshakes is 3:4.
Since both ratios are the same, we can conclude that Ari will think Freeze Zone's milkshakes have the perfect amount of caramel.
Rewrite the standard equation in slope-intercept form: 3x-8y=24
The equation 3x - 8y = 24 can be written in slope intercept form as y = [tex]\frac{3}{8}[/tex] x - 3.
What is Slope?Slope of a line is defined as the value of the change in the values of the y coordinates with respect to the change in the values of the x coordinate.
It can also be defined as the tangent of the angle that the line makes with the X axis.
The standard equation of a line in slope intercept form is, y = mx + c, where m is the slope and c is the y intercept.
y intercept is the y coordinate when the line touches with the Y axis. The x coordinate of that point will be zero.
The given equation is,
3x - 8y = 24
Subtracting both sides of the equation with -3x,
3x - 8y - 3x = 24 - 3x
-8y = 24 - 3x
Dividing both sides by -8, we get,
y = -3 + [tex]\frac{3}{8}[/tex] x
y = [tex]\frac{3}{8}[/tex] x - 3
Hence the standard equation in slope intercept form for 3x - 8y = 24 is y = [tex]\frac{3}{8}[/tex] x - 3.
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Rewrite 17/20 and 21/25, so that they have a common denominator then use <,>or = to order 17/20 and 21/25
a sticker price on a new vehicle is $33985 , but the dealer cost is $27700 and you want to offer 4% over the dealer cost. what would be the offered amount?
Compounding with different interest rates a deposit of $750 earns interest rates of 10.5 percent in the first year and 7.5 percent in the second year. what would be the second year future value? $890.91 $885.00 $829.43 $1,635.00
Beethoven wrote 9 symphonies and mozart wrote 27 piano concertos. if a university radio station announcer wishes to play first a beethoven symphony and then a mozart concerto, in how many ways can this be done?
There are 243 different ways the university radio station announcer can play a Beethoven symphony followed by a Mozart concerto, calculated by multiplying the number of Beethoven symphonies (9) by the number of Mozart concertos (27).
Explanation:To determine how many different ways the university radio station announcer can play a Beethoven symphony followed by a Mozart concerto, we use the fundamental principle of counting. Since there are 9 Beethoven symphonies and 27 Mozart piano concertos, we multiply the two numbers together.
The calculation is as follows:
Beethoven symphonies: 9 optionsMozart concertos: 27 optionsTherefore, the total number of combinations for playing one Beethoven symphony followed by one Mozart concerto is:
9 symphonies × 27 concertos = 243 possible combinations
This shows there are 243 different ways the radio station announcer can choose a pairing of a Beethoven symphony and a Mozart concerto to play back-to-back.
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Describe two different methods to find the elapsed time from 2:30 PM to 2:58 P. M.
Each blade on a windmill is in the shape of a triangle with a base of 7 ft and height of 4 ft if there are four blades on the windmill, what is the total area of the blades.
Solution :
As per the problem we have
Each blade on a windmill is in the shape of a triangle with a base of 7 ft and height of 4 ft.
There are four blades on the windmill.
we have been asked to find the total area of the blades.
Area of one blade[tex] =\frac{1}{2}*base*height=\frac{1}{2}*7*4 =14 \ ft^2\\ [/tex]
Total are of blades[tex] =4*\text{Area of one blade}\\ [/tex]
Total are of blades[tex] =4*14=56 \ ft^2\\ [/tex]
If rectangle ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A' lie?
Answer:
A' would be return to its original position .
Step-by-step explanation:
Given : If rectangle ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°.
To find : where would point A' lie.
Solution : We have given that ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°
By the reflection rule over y axis .( x ,y) →→ ( -x ,y)
Suppose A ( x ,y) if we reflect it over y axis then
A( x ,y) →→ A'( -x ,y)
Now reflect it over x axis (-x ,y) →→( -x ,-y)
Now rotate by 180° it become ( -x, -y) →→( x ,y)
Hence , it return to its original position .
Therefore, A' would be return to its original position .
Help please ...........MATH
If $200 is put in the bank and each year the account earns 5% simple interest, then how much interest will be earned in two years?
An artist wants to reduce the size of a drawing using a scale factor of 3:13:1 . The original drawing has an area of 720 square inches. What is area of the new drawing? Enter your answer in the box.
Answer: 80
MsEHolt is correct, the answer is 80[tex]in^2[/tex]
John ran the 100-m dash with a time of 9.96 sec. If this pace could be maintained for an entire 26-mi marathon, what would his time be?
By calculating the average speed of a 100-meter dash and then applying it to the marathon distance, it would take approximately 1.16 hours, or 1 hour, 9 minutes, and 28 seconds to complete a 26-mile marathon at that pace.
Explanation:The student is asking how long it would take for someone to run a 26-mile marathon if they maintained the same speed as a 100-meter dash completed in 9.96 seconds. To calculate this, we first need to find the runner's average speed during the 100-meter dash. The speed (v) is distance (d) divided by time (t), so:
v = d / t = 100 meters / 9.96 seconds = 10.04 meters/second
Next, we convert the marathon distance from miles to meters. There are 1,609.34 meters in a mile, so:
26 miles * 1,609.34 meters/mile = 41,842.84 meters
To find the time (t) to run the marathon, we divide the total distance by the average speed:
t = 41,842.84 meters / 10.04 meters/second = 4,167.49 seconds
Finally, we convert seconds to a more understandable unit of time, hours and minutes:
4,167.49 seconds / 60 seconds/minute = 69.46 minutes
69.46 minutes / 60 minutes/hour ≈ 1.16 hours
So, John would complete the marathon in approximately 1.16 hours, or 1 hour, 9 minutes, and 28 seconds if he could maintain his 100-meter dash pace for the entire marathon.
Leroy's total employee compensation was $50,150 last year. His total job expenses for traveling and for professional developement for the year were $3,500. Which of the following represents his total job benefits?
a.
$53,650
b.
$50,150
c.
$46,650
d.
$47,650
Answer is :
a.
$53,650
100% correct
Answer:
Correct answer is a.$53,650
Step-by-step explanation:
Total job benefits includes both employee compensation and the expenses for traveling and for professional development for the year.
So we need to add those together to fond the total job benefits.
Total job benefits = employee compensation + expenses for traveling and for professional development
Total job benefits = $[tex]50,150+3500[/tex]
=$[tex]53,650[/tex]
Therefore correct answer is a.$53,650
Answer:
a. $53,650
Step-by-step explanation:
Is the given sequence arithmetic? If so, identify the common difference. 3.2, 3.5, 3.8, 4.1, . . .
Texas has 254 counties, California has 58 counties, Florida has 67 counties,how many more counties does texas have than the number of counties in California and Florida combined