We have a problem that can be solved with a system of equations.
First we need to identify the equations of the system.
We have two unknown variables, the number of adult's tickets sold and the number of children's tickets sold. Let's call them:
- number of adult's tickets sold: x
- number of children's tickets sold: y.
The total number of tickets sold, 5600, is the sum of these:
[tex]x+y=5600_{}[/tex]And since the prices are 27.25 (adult) and 12.00 (children), the total revenue (117311.50) will be the sum of these prices multiplyied by the number of tickets of each of them:
[tex]27.25x+12.00y=117311.50[/tex]So, the system of equations is:
[tex]\begin{gathered} _{}x+y=5600_{} \\ 27.25x+12.00y=117311.50 \end{gathered}[/tex]Since we want y the number of children's tickets sold, we can solve for the other varible, x, in one equation, and substitute into the other.
Solving in the first equation, we have:
[tex]\begin{gathered} x+y=5600 \\ x=5600-y \end{gathered}[/tex]And substituting into the other:
[tex]\begin{gathered} 27.25x+12.00y=117311.50 \\ 27.25(5600-y)+12.00y=117311.50 \\ 27.25\cdot5600-27.25y+12.00y=117311.50 \\ 152600-15.25y=117311.50 \\ -15.25y=117311.50-152600 \\ -15.25y=-35288.50 \\ y=\frac{-35288.50}{-15.25} \\ y=2314 \end{gathered}[/tex]Since y is the number of children's tickets sold, then the number of children's tickets sold is 2314.
Edmond divided 8 3/4 gallons of ketchup equally into 2 smaller bottles to put on the tables in his hamburger restaurant. How much ketchup did he put in each bottle?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
total ketchup = 8 3/4 gallons
bottles = 2
ketchup in each bottle = ?
Step 02:
[tex]8\text{ + }\frac{3}{4}=\frac{32+3}{4}=\frac{35}{4}[/tex][tex]\frac{\frac{35}{4}}{\frac{2}{1}}=\frac{35\cdot1}{4\cdot2}=\frac{35}{8}[/tex]The answer is:
Edmond put 35/8 gallons of ketchup in each bottle.
Kerala is a marine biologist studying the breeding habits of an exotic species of sea turtlesLast year she observed the number of pregnant mother titles at each beach on an isolated island in the pacific. The histogram below summarizes the data. Use the histogram to answer each question
a) The number of beaches in each class is represented by the height of the class. The class that has the least frequency is the one with 5-7.
We can see that the height is 2, thus the number of beaches in this class is 2.
b) We can see that each class has width 3:
2 to 4: 2, 3, 4
5 to 7: 5, 6, 7
and so on
The width of each class is 3.
c) The classes with 11 or more are the last two, from 11 to 13 and from 14 to 16.
The height of the class 11 to 13 is 4
The height of the class 14 to 16 is 7
The total beaches with 11 or more pregnant turtles is the sum: 4 + 7 = 11
Graph y=3/4x+2. i got the y intercept but i don’t know how to do the other point
ANSWER
EXPLANATION
Once we have the y-intercept we have to find another point - since two points are enough to draw a line. To find this other point we can use the slope of the line. We can write the slope of a line as:
[tex]m=\frac{\text{rise}}{\text{run}}[/tex]In this line rise = 3 and run = 4. This means that the other point is 4 units to the right of the y-intercept and 3 units up:
Mark this new point and draw a line through both points.
do the data in the table Represent a linear function?
Answer:
The correct option is the last one "no"
Explanation:
To see if the table represents a linear function, we can mark each point in the cartesian plane and connect them with a line. If all of the points lie in the line, then the table represents a linea
(-79.2x + 80) +(74.5x -89y) in standard form
Ok, so:
We want to write (-79.2x + 80) +(74.5x -89y) in standard form:
So, -79.2x + 80 + 74.5x - 89y is equal to:
-4.7x - 89y + 80.
Then, -89y = 4.7x - 80
And finally, y = ((-4.7)/(89))x + 80/89
Write in standard form the equation of a line passing through the point (-3, 4) and having the slope m = 2.
then the equation in standard form:
[tex]\begin{gathered} y=mx+b \\ y=2x+10 \end{gathered}[/tex]You deposit 500$ in a savings account that earns 2.5 interest compounded yearly. Find the balance in the account after the given amount of time A. 1 yearB. 5 years C. 20 years
In order to find the balance after the given time, use the following formula:
I = P(1 + r/n)^(t·n)
where
r: interes rate = 2.5% = 0.025
n: frequency = 1
t: time = 1, 5, 20
P: principal investment = 500
replace the previous values of the parameters into the formula for I:
A. 1 year:
I = $500(1 + 0.025/1)^(1·1) = $512.5
B. 5 years:
I = $500(1 + 0.025)^(5·1) = $565.7
C. 20 years
I = $500(1 + 0.025)^(20·1) = $819.3
43)Solve the system 4x+2y=-3 4x-3y=22A. (7, –5)B. (7/4, –5)C. (7/4, 5)D. (4, –5)
Given,
The linear pair of equations are:
[tex]\begin{gathered} 4x+2y=-3 \\ 4x-3y=22 \end{gathered}[/tex]Required
The solution of the pairs of equations.
Taking the first equation as,
[tex]\begin{gathered} 4x+2y=-3 \\ 2y=-4x-3 \\ y=-2x-1.5 \end{gathered}[/tex]Substituting the value of y in second equation then,
[tex]\begin{gathered} 4x-3y=22 \\ 4x-3(-2x-1.5)=22 \\ 4x+6x+4.5=22 \\ 10x=17.5 \\ x=1.75 \\ x=\frac{7}{4} \end{gathered}[/tex]Substituting the value of x in first equation,
[tex]\begin{gathered} y=-2x-1.5 \\ y=-2(1.75)-1.5 \\ y=-3.5-1.5 \\ y=-5 \end{gathered}[/tex]Hence, the solution of the system is(7/4, -5).
Please help me solve this math question. Please explain each step clearly
a) Since the relation is proportional, the graph is a line.
In order to graph a line we only need two points and connecting them we get the line.
In this case, we know that at 4h the pool has 5200 gallons. The point woud be (4, 5200)
Now we need another point. The simplest one is the origin. When the time is zero, the amount of water in the pool is also 0, then we have another point (0, 0)
Now with the points (0, 0) and (4, 5200) we can graph the relationship.
b) We need to compair the filling rates. In the graph provided we can see that in 3 hours, there is 10,800 gallons. Since the other pool had 5,200 gallons in 4 hours, is clear that the second pool fills much more quicker.
Which graph shows the solution to this system of linear inequalities?y2 2x+3ys-2x-4
To solve this problem, we will graph the solution set of each inequality and the solution to the system will be the intersection of the solution sets.
Graph of the solution set of the first inequality:
Graph of the solution set of the second inequality:
The graph of the overlap of the solution sets is:
Answer: Option B.For the following pair of variables state the units that might be used to measure each variable. then state whether you believe that the two variables are correlated .if you believe they are correlated, state whether the correlation is positive or negative. explain your reasoningTo measure fertility rate for women the unit _ might be used. to measure life expectancy the unit _ might be used. what correlation if any is there between the variables?
Problem
For the following pair of variables state the units that might be used to measure each variable. then state whether you believe that the two variables are correlated .if you believe they are correlated, state whether the correlation is positive or negative. explain your reasoningTo measure fertility rate for women the unit _ might be used. to measure life expectancy the unit _ might be used. what correlation if any is there between the variables?
Solution
To measure fertility rate for women the number of births per 1000 women might be used.
To measure life expectancy the years might be used.
what correlation if any is there between the variables?
For this case we would expect that the correlation would be positive. With higher number of life expectancy years we would expect a higher number of births
the sum of pi and 3/4 is a (n)_________ numberA. RationalB. NaturalC. WholeD. Irrational
Remember that pi is an irrational number which means it has infinite decimal without a pattern.
If we add a number to pi we would still get an irrational number because the sum of a rational and an irrational won't give another type of number than an irrational.
Therefore, the right answer is D.Master Level2. Brandon is wrapping the present shown below. How many square centimeters ofwrapping paper will he need?Height: 7 cmWidth:10 cmLength: 22 cm
Given the following:
Height = 7cm
Width = 10cm
length = 22cm
We were asked to find the number of square centimeters of wrapping paper Brandon will be needing.
To solve for this, we will be using the total surface formula.
Total surface formula (SA) = 2lw + 2lh + 2hw)
factoring out 2
SA = 2(lw + lh + hw)
lw = 22 x 10 = 220cm²
lh = 22 x 7 = 154cm²
hw = 7 x 10 = 70cm²
So,
SA =2(220 + 154 + 70)
SA = 2(644)
SA = 1288cm²
A small office supply store sells paper clipsin packs of 100 and packs of 250. If thestore has 84 packs of paper clips in stocktotaling 12,300 paper clips, how manypaper clips would a customer buy if he buyshalf of the packs of 250 that the store hasin stock?
The first equation should represent the total number of packs, each with 100 or 250 paper clips
i,e. x + y = 84 (1)
The second equation should represent the total number of paper clips. Because x represents packs with 100 paper clips and y represents packs with 250 paper clips, the second equation is
100x + 250y = 12,300 (2)
Simplify the linear equation;
x + y = 84
x = 84 - y
Substitute the value of x = 84 - y in the equation (2);
100x + 250y = 12300
100(84 - y) + 250y = 12300
8400 - 100y + 250y = 12300
8400 + 150y = 12300
150y = 12300 - 8400
150y = 3900
y = 3900/150
y = 26
Substitute the value of y = 26 in the equation x = 84 - y
x = 84 - y
x = 84 - 26
x = 58
The store has 26 packs of 250 paper clips in stock.
The customer would buy 13 × 250 = 3,250 paper clips,
Answer : 3250
What is the relative value of F(x) when the value of x is close to 2 for the function F(x) = 1/x+2, whose graph is shown below?A. A very large numberB. ZeroC. A very small numberD. Either a very large number or a very small number
Answer:
D. Either a very large number or a very small number
Explanation:
Given the function:
[tex]F(x)=\frac{1}{x+2}[/tex]As can be seen from the graph, the point x=2 is an asymptote of the function.
Thus, the relative value of F(x) when the value of x is close to 2 is either a very large number or a very small number.
Option D is correct.
Henry runs up 10 flights of stairs.Then, he runs down 10 flights of stairs.Does this situation represent additiveinverses? Explain.
Problem
Henry runs up 10 flights of stairs. Then, he runs down 10 flights of stairs. Does this situation represent additive inverses? Explain.
solution
For this case we know that Henry runs up 10 stairs and thenhe goes down 10 stairs so for this case yes that represent additive inverses because the net operation is:
10 +(-10)=0
And he back againt to 0
What are the new vertices of quadrilateral KLMN if the quadrilateral is translated two units to the right and four units upward?
The given transformation is
[tex](x,y)\rightarrow(x+2,y+4)[/tex]We have to apply this translation to each vertex.
[tex]\begin{gathered} K(-4,-2)\rightarrow K^{\prime}(-2,2) \\ L(-1,-2)\rightarrow L^{\prime}(1,2) \\ M(-1,-5)\rightarrow M^{\prime}(1,-1) \\ N(-4,-5)\rightarrow N^{\prime}(-2,-1) \\ \end{gathered}[/tex]According to this result, the right answer is C.6,9x,y3,3I need to find a equation relating to x and y
Answer:
[tex]y=2x-3\rightarrow Slope-intercept\text{ form}[/tex]Step by step explanation:
As a first step to find the equation of the line, we need to calculate the slope.
The slope is represented by the following equation:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{where,} \\ \text{ (x}_1,y_1)and(x_2,y_2)_{}_{} \\ \text{are the points given} \end{gathered}[/tex]Then, the slope of the line would be:
[tex]\begin{gathered} m=\frac{9-3}{6-3} \\ m=\frac{6}{3} \\ m=2 \end{gathered}[/tex]Then, by the slope-point form of the line we can get slope-intercept form:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=2(x-3) \\ y=2x-6+3 \\ y=2x-3\rightarrow Slope-intercept\text{ form} \end{gathered}[/tex]What is the length of the hypotensis?If necessary round to the nearest 10th
We need to use the pythagorean theorem:
In a right triangle we have:
hyppootenuse
leg1
leg2
And the theorem says:
[tex]\text{hyppotenuse}^2=\text{leg}1^2+\text{leg}2^2[/tex]In this case:
leg1 = 9cm
leg2 = 3cm
[tex]c^2=(9cm)^2+(3cm)^2[/tex]And solve for c:
[tex]\begin{gathered} c=\sqrt[]{81cm^2+9cm^2} \\ c=\sqrt[]{90cm^2} \\ c\approx9.486832\ldots \end{gathered}[/tex]To the nearest tenth:
c = 9.5cm
A pyramid has a square base of 120ft. On a side. The four slant faces are all congruent isosceles triangles with base angles 55 degrees. Find the height of the pyramid?
Our first approach will be to get the slant height, i.e. the sides of the triangle. We can get this via the sine rule as:
We can get the side of the isosceles to be:
[tex]\begin{gathered} \frac{120}{\sin70}=\frac{x}{\sin 55} \\ x=\frac{120\sin 55}{\sin 70}=104.6ft \end{gathered}[/tex]Now we need to find the perpendicular height.
To do that, we need to find the length of the diagonal of the base. We will apply the Pythagoras theorem.
This is given as:
[tex]\begin{gathered} d=\sqrt[]{o^2+a^2} \\ \text{ Where:} \\ o=\text{opposite = length of base} \\ a=\text{adjacent = length of base} \end{gathered}[/tex][tex]\begin{gathered} d=\sqrt[]{120^2+120^2} \\ d=170\text{ ft} \end{gathered}[/tex]Next, we plot the triangle that will help us get our perpendicular height.
We now find h.
[tex]\begin{gathered} h=\sqrt[]{104.6^2-85^2} \\ h=60.96\text{ ft} \end{gathered}[/tex]The perpendicular height is 60.96 ft
What survey contains the best example of a sampling error
Answer:
The correct option is the second one: "a survey of high school students to determine the favorite type of doll"
This is a sampling error, because it's very unlikely that high school students have a favorite doll, and the results won't be very use
A-Lab assistant need to create a 900 ml mixture that is 4.5% hydroelectric acid. The assistant has solutions of 3% and 5.5% in supply at the lab. Using the variables x and y to represent the number of milliliters of 3% solution and the number of milliliters of the 5.5% solution respectively, determine a system of equation that describes the situation.Enter the equations below separated by a comma.How many milliliters of the 3% solution should be used?How many milliliters of the 5.5% solution should be used?
Let x and y to represent the number of milliliters of 3% solution and the number of milliliters of the 5.5% solution respectively. Given that the volume of the mixture is 900 ml, we have
x + y = 900
The mixture should contain 4.5% hydroelectric acid. Recall, percentage is expressed in terms of 100. The concentration of the mixture is
4.5/100 * 900 = 40.5
x should contain 3% of hydroelectric acid. The concentration of x is
3/100 * x = 0.03x
y should contain 5.5% of hydroelectric acid. The concentration of y is
5.5/100 * y = 0.055y
The equation representing the concentration would be
0.03x + 0.055y = 40.5
Thus, the required system of equations is
x + y = 900
0.03x + 0.055y = 40.5
From the first equation,
x = 900 - y
Substituting x = 900 - y into the second equation, we have
0.03(900 - y) + 0.055y = 40.5
27 - 0.03y + 0.055y = 40.5
- 0.03y + 0.055y = 40.5 - 27
0.025y = 13.5
y = 13.5/0.025
y = 540
x = 900 - y = 900 - 540
x = 360
360 ml of 3% solution and 540 ml of 5.5% solution should be used.
A plane is 110 mi north and 189 mi east
ANSWER:
30.2°
STEP-BY-STEP EXPLANATION:
The angle x can be calculated by means of the tangent trigonometric ratio, which relates the opposite leg to the adjacent leg, just like this:
[tex]\begin{gathered} \tan x=\frac{\text{ opposite}}{\text{ adjacent }} \\ \text{ opposite = 110} \\ \text{ adjacent = 189} \end{gathered}[/tex]We substitute and calculate for x just like this:
[tex]\begin{gathered} \tan\:x\:=\:\frac{110}{189} \\ x=\tan^{-1}\left(\frac{110}{189}\right) \\ x=30.2\degree \end{gathered}[/tex]Therefore, the angle is 30.2°
Students in Introductory Chemistry are recording the masses of samples as part of a lab experiment. for 5 samples, Sidney has recorded these masses: 4 grams 6 grams 4 grams 8 grams 2 grams What is the mode of the masses?
Solution
For this case we have the following data given:
4, 6, 4, 8, 2
We need to remember that the mode is the most repeated value so then the answer would be:
Mode= 4
which situation could be written mathematically as 10÷1/2A) The amount of time it would take to watch ten 1/2 hour videos.B) The amount of time it would take to watch half of a ten minute video.C) The number of 1/2 hour videos in ten hours.D) The number of minutes in one tenth of a 1/2 hour video.I also need to show my work :)
Which situation could be written mathematically as 10÷1/2?
10 ÷ 1/2 = 10 x 2/ 1 = 20
If there are 1/2 hour videos in ten hours, then there are also 20 videos
The correct answer is Option C - The number of 1/2 hour videos in ten hours.
I have a practice problem that I need answered, thank you
Given inequality:
[tex]6x^2-x\text{ }<\text{ 2}[/tex]Re-arranging:
[tex]6x^2-x\text{ - 2 }<\text{ 0}[/tex]Factorizing the expression to the left:
[tex]\begin{gathered} 6x^2-2x\text{ + x -2 }<\text{ 0} \\ 6x^2\text{ -4x +3x -2 }<\text{ 0} \\ (3x-2)(2x+1)\text{ }<\text{ 0} \end{gathered}[/tex]Hence:
[tex]\begin{gathered} 3x-2\text{ }<\text{ 0} \\ 3x\text{ }<\text{ 2} \\ x\text{ }<\text{ }\frac{2}{3} \end{gathered}[/tex]Since their product is negative. one of the factors would be positive.
[tex]\begin{gathered} 2x\text{ + 1 > 0} \\ 2x\text{ > -1} \\ \frac{2x}{2}\text{ >}-\text{ }\frac{1}{2} \\ x\text{ > -}\frac{1}{2} \end{gathered}[/tex]The solution on a number line:
The solution on interval notation:
[tex]\mleft(-\frac{1}{2},\: \frac{2}{3}\mright)[/tex]How to solve for area of number 6 to the nearest square unit
132 square meters
Explanations:6) The given composite function is made up of a large rectangle and a small rectangle as shown:
The area of the composite figure = Area of the rectangle A + area of rectangle B
Since area of the rectangle = Length * width, hence;
[tex]\begin{gathered} \text{Area of the figure=}LW+lw \\ \text{Area of the figure=(9m}\times12m\text{)+(}4m\times6m\text{)} \\ \text{Area of the figure=}108m^2+24m^2 \\ \text{Area of the figure=}132m^2 \end{gathered}[/tex]Hence the area of the composite figure is 132 square meters
Use the number line to determine if each number is a solution . And don't worry this is just a practice :)
C. How long until there are only 20 mg remaining.
Therefore, it will take 12.52 hours
given the function given the function f of x equals 5 (x + 4) ^ 3/2 which of the following represent its y-intercept