Given:
a.) The admission fee at a small fair is $2.50 for children and $4.00 for adults.
b.) On a certain day, 2400 people enter the fair and $7140 is collected.
Let,
x = total number of children
y = total number of adults
Let's generate two equations based on the given scenario:
EQUATION 1: Total number of children and adults entered the fair.
[tex]\text{ x + y = }2400[/tex]EQUATION 2: Total money collected from the admission.
[tex]\text{ 2.5x + 4y = }$7140$[/tex]We will be using the substitution method. We get,
[tex]\text{ x + y = }2400[/tex][tex]\text{ y = }2400\text{ - x}[/tex]Substitute to Equation 2:
[tex]\text{ 2.5x + 4y = }$7140$[/tex][tex]\text{ 2.5x + 4(}2400\text{ - x) = }$7140$[/tex][tex]\text{ 2.5x + 9600 - 4x = }$7140$[/tex][tex]\text{ 2.5x - 4x = }$7140$\text{ - 9600 }[/tex][tex]\text{ -1.5x }=\text{ }-2,460[/tex][tex]\text{ }\frac{\text{-1.5x}}{-1.5}\text{ }=\text{ }\frac{-2,460}{-1.5}[/tex][tex]\text{ x }=\text{ }1,640\text{ children}[/tex]Therefore, 1,640 children went to the fair.
For the adults,
x + y = 2400
1,640 + y = 2400
y = 2400 - 1,640
y = 760 adults
In summary: 1,640 children and 760 adults went to the fair.
The bank charged you an overdraft fee of $35 for not having enough money in your account.
What is the balance after the bank charged you the overdraft fee?
Which is true about the possible solutions of this function?
The possible solutions for the given function are as follows:
1 real root and 2 complex roots.What is a function?Each member of X receives exactly one element of Y in the case of a function from one set to the other.The sets X and Y collectively constitute the domain and codomain of the function.Any assertion, rule, or piece of legislation that proves the causal link between the independent and dependent variables (the dependent variable).In the graph, the real roots are the values when it crosses the x-axis.
The function has one real root because it crosses the x-axis just once in this instance.The function has two complex roots since both of its ends go to infinity.Therefore, the possible solutions for the given function are as follows:
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a delivery company requires that any box delivered must have a length plus girth (distance around) totaling no more than 120 inches. find the dimensions of the box with maximum volume that can be sent.
the dimensions of the box is length 20 and width 40inches with maximum volume that can be sent. is V = 16000 inches ^3
length + girth=116 inches
w + 4x= 120
volume=x^2*w
w=120-4x
V=x^2* (120-4x)
for max value, dv/dx=0
dv/dx= 240x-12x^2
240x-12x^2=0
20-x=0
x=20
w=120-4(20)
=40
V=20^2*40==16000inches^3
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X: 3 6 9 12 y: -22 -43 -64 -85 point-slope form:_ slope-intercept form:
point slope form = y-(-43)=[tex]-\frac{2}{21}[/tex](x-3)
slope intercept form = -[tex]\frac{152}{7}[/tex]=c
What is slope?Finding the ratio of "vertical change" to "horizontal change" between any two unique locations on a line yields the slope. Occasionally, the ratio is written as a quotient (also known as a "rise over run"), which produces the same number for every two unique points on the same line. Negative "rise" refers to a diminishing line. The line could be functional, established by a road surveyor, or depicted in a graphic that represents a road or a roof as a description or a design.
The absolute value of the slope is used to determine how steep, incline, or grade a line is. The steeper the line, the larger the absolute magnitude of the slope. A line's direction might be either horizontal, ascending, decreasing, or vertical
If a line is rising from left to right, it is increasing. Since m>0, the slope is positive.
If a line decreases from left to right, it is said to be diminishing. The slope is inverse, or m0.
A line has zero slope if it is horizontal. This function has a fixed value.
A line's slope is ambiguous if it is vertical.
Slope= [tex]\frac{x-x1}{y-y1}[/tex]= [tex]\frac{3-5}{-22+43}[/tex]=[tex]\frac{-2}{21}[/tex]
point slope form= y-(-43)=[tex]-\frac{2}{21}[/tex](x-3)
slope intercept formy=mx+c
-22=[tex]-\frac{2}{21}[/tex]*3+c
-22+[tex]\frac{2}{7}[/tex]=c
-[tex]\frac{152}{7}[/tex]=c
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Evaluate. Write your answer as a whole number or as a simplified fraction.
Answer:
1 / 121
Step-by-step explanation:
4^0 = 1
11^2 = 121
4^0 / 11^2 = 1 / 121
Hi I need help with this question, please and thank you
We have the following number, we need to simplify:
[tex]6\cdot\sqrt[]{-2401}[/tex]we can also express this as:
[tex]\begin{gathered} 6\cdot\sqrt[]{(-1)\cdot(2401)} \\ 6\sqrt[]{(-1)\cdot(49)\cdot(49)} \end{gathered}[/tex][tex]\begin{gathered} =6\sqrt[]{-1\cdot49^2} \\ =6\cdot\sqrt[]{-1}\cdot\sqrt[]{49^2} \\ =6\cdot\sqrt[]{-1}\cdot49 \\ =6\cdot49\cdot\sqrt[]{-1} \end{gathered}[/tex]since:
[tex]\sqrt[]{-1}=i[/tex]which represents the imaginary number,
then, we get:
[tex]6\sqrt[]{-2401}=6\cdot49\cdot i=294i[/tex]find the measures for angles one and two
The measure of the angles x and y are 71 degrees and 109 degrees after applying the concept of vertically opposite angles.
What are vertically opposite angles?
It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
From the figure:
The value of y can be found by applying the concept of vertically opposite angles:
y = 109 degrees
x = [360 - 2(109)]/2
x = (360 - 218)/2
x = 71 degrees
Thus, the measure of the angles x and y are 71 degrees and 109 degrees after applying the concept of vertically opposite angles.
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Translate the following phrase into a math expression whichever is appropriate use x to represent the unknown number Six less than the quotient of nine and a number
Given,
The phrase is,
Six less than the quotient of nine and a number
Consider, the number is x.
The mathematicsl expression of quotient of nine and a number is,
[tex]\frac{9}{x}[/tex]The mathematical expression of six less than is,
[tex]-6[/tex]Combining both statements then,
[tex]\frac{9}{x}-6[/tex]Hence, the mathematical expession is 9/x -6.
Answer:
9/x -6
Step-by-step explanation:
if x= 10.069 what does x + 420=?
Answer:
10.069 +420 =430.069
Step-by-step explanation:
first step is to add the number 420 to the number before the decimal so 420+10 which equals to 430
Then
u add the number that comes after the decinal together or if only one of them has a number after the decimal place back that number after youre given answer....
How do I find a function from a graph? please I need help, I do not understand how this works. The picture below is my homework I am not asking for the answer I would just like someone to explain how this works please.
Answer:
F(x)=-(x+4)(x-1)
Step-by-step explanation:
the thing hit both -4 and 1 but in the function -4 become 4 and 1 become-1 so (x+4)(x-1) but we need to make it negative so -(x+4)(x-1)
Destiny wants to compare interest rates quoted by four local banks for a deposit that she wants to make in an IRA account for a period of 4 years. Which bank pays the highest interest for this 4-year IRA account?
Chase Bank: 2 1/2%, Jefferson City Trust: 1.7%, Bank of America: 2.12%, First State Bank: 1 3/4%
Responses
Bank of America
First State Bank
Jefferson City Trust
The bank that pays the highest interest for this 4-year IRA account is Chase Bank.
What are interest rates?It should be noted that interest rates simply means the cost of borrowing or the gain from savings.
In this case, Destiny wants to compare interest rates quoted by four local banks for a deposit.
Chase Bank: = 2 1/2% = 2.5%
Jefferson City Trust:l = 1.7%,
Bank of America = 2.12%
First State Bank = 1 3/4% = 1.75%
Therefore, the highest is Chase Bank as it gives 2.5%.
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Express 0.000301 in scientific notation
Step-by-step explanation:
hola nose inglés q te valla bien
Answer:
you can start out by writing the number in standard form, which means that it shouldn't exceed to 10 . So in this case, we are writing it as 3.01⋅10−4 instead of 30.1⋅10−3 , hope it helpeful
Write a quadratic function in standard form whose graph has the given characteristics.
passes through (-8, 0), (-6. - 16), and (2, 0)
y =
Answer:
Step-by-step explanation:
Kaltlin has a patio that is in the shape of a rectangle with an area of 1500 ft?. She has decided to expand the patio so that it can hold mpatio will be a larger rectangle. The current patio has a length of 50 ft and a width of 30 ft. She plans on making the new length 2 timesthe new width 2 times the current width.
It is given that area of rectangle of Kaitlin is 1500 sq.ft. with length 50 ft and a width of 30 ft.
The new area when new length 2 times the current length and the new width 2 times the current width.
[tex]A=(50\times2)\times(30\times2)=100\times60=6000ft^2[/tex]a. The size of Kaitlin new patio is
[tex]100\times60=6000ft^2[/tex]b. The area of new patio is 4 times the area of current patio.
[tex]1500\times4=6000ft^2[/tex]
Examine the pattern of socks Above:
If the pattern continues, how many socks would b in figure 5?
(A.) 29
(B.) 41
(C.) 50
(D.) 52
23. According to the Guinness Book of World Records, the world’s smallest horse is Thumbelina. Thumbelina is 42.5 cm tall and eats about 0.3 kg of food per day. A former world record holder ate food in the same proportion to its height. If it was 46.25 cm tall, how much did it eat? Give your answer to the nearest hundredth of a kilogram.
The food that the former world record holder should eat per day is 0.33kg.
How much should should the horse eat?The first step is to determine the ratio of the smallest horse's food per day to the height of the horse. This can be determined by dividing the food eaten per day by the height of the horse.
Division is the operation used in mathematics that is used to determine the quotient of two or more numbers
Ratio of the height and food eaten per day = 0.3 / 42.5
The next step is to multiply the ratio gotten in the previous step by the height of the former world holder
Food the former holder should eat = (0.3 / 42.5) x 46.25 = 0.33 kg
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Identify the pair of numbers that represents the boiling point of water in degrees Fahrenheit and the boiling point of water in degree Celsius
Let's begin by identifying key information given to us:
The boiling point of water is 100 degrees Celsius
We will convert this temperature to Fahrenheit to obtain its equivalent using the formula:
[tex]\begin{gathered} F=\frac{9}{5}C+32_{} \\ C=100^{\circ} \\ F=\frac{9}{5}(100)+32=180+32 \\ F=212^{\circ} \end{gathered}[/tex]Therefore, the first option is the correct answer (212 degrees Fahrenheit & 100 degrees Celsius)
Prove that: [tex](a+b)^{-1} . (a^{-1} + b^{-1} ) = (ab)^{-1}[/tex]
Step-by-step explanation:
[tex] \frac{1}{a + b} \times ( \frac{a + b}{ab}) = \frac{1}{ab} [/tex]
Answer with step-by-step explanation:
[tex](a+b)^-^1*(a^-^1+b^-^1)=(ab)^-^1[/tex]
First, convert these into positive indices.
[tex]\frac{1}{(a+b)} *(\frac{1}{a} +\frac{1}{b})=\frac{1}{ab}[/tex]
And now, let us solve the left side.
[tex]\frac{1}{(a+b)} *(\frac{1}{a} +\frac{1}{b})\\\\[/tex]
First, solve the brackets. That is add the fractions inside the brackets.
[tex]\frac{1}{(a+b)} *(\frac{1}{a} +\frac{1}{b})\\\\\frac{1}{(a+b)}*(\frac{1*b}{a*b} +\frac{1*a}{b*a})\\\\\frac{1}{(a+b)}*(\frac{b}{ab} +\frac{a}{ab})\\\\\frac{1}{(a+b)}*\frac{(a+b)}{ab}[/tex]
Now multiply the fractions.
[tex]\frac{1}{ab}[/tex]
So, it's clear that the left side equals the right side.
Left side = Right side
[tex]\frac{1}{ab}=\frac{1}{ab}[/tex]
∴ [tex](a+b)^-^1*(a^-^1+b^-^1)=(ab)^-^1[/tex]
AB. CD. EF are three chords of a circle, P and Q are two points inside the circle such that AB and CD meet at P, and AB and EF meet at Q. If CP = 2, PD = 7, EQ = 3, QF = 6 and
AP = 2, then QB may be
A. 2 B. 3 C. 4 D. 5 E. 7
Answer:
Step-by-step explanation:
I think it is option E) 7
A boat traveled 240 miles downstream, then 240 miles back upstream. The trip downstream took 20 hours. The trip back upstream took 60 hours. Use this information to fill in the following blanks. Note: Express your answers as integers.
The boat is moving at 2 miles per hour and current is 4 miles per hour.
In calm water, the boat travels at a 2 mph pace.
4 miles per hour is the current's speed.
One such computation is as follows.
Let a be a representation of the boat's speed.
Allow b to be the current's speed.
20(a + b) = 240, according to equation 1.
Equation 2: 60(a + b)
Equation 3: a + b = 12
Equation 4: a - b Equals 4.
Equation 3 and equation 4 combined
(a + b) + (a - b)= 12+4
2x = 16
a= 16/2
a= 8
Calculate equation 4 minus equation 3
(a + b) - (a-b)= 12-4
2b= 8
b= 8/2
b= 4
As a result, the boat is moving at 2 miles per hour, while the current is moving at 4 miles per hour.
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Van graphed f(x) = x and h(x) = f(x-10) on
the same grid. Which is not a true statement about the graphs of the two functions?
A The lines have the same slope.
B The lines are parallel.
C The lines do not have the same x-intercept.
D h(x) is located 10 units left of f(x).
Answer:
Step-by-step explanation:
"D" would be the correct answer. "f(x-10)" means that the "10" would be moving right-- the positive direction. Therefore, h(x) would be located 10 units RIGHT of f(x), which passes through the origin, (0,0). Statement A is correct because, on a graph, you'd have line f(x) passing through the origin, and towards the right, 10 units, (positive) you would have h(x) making them identical. So yes, same slope. Statement B is also correct, they're obviously parallel if they're beside each other. Statement C is correct as well. Although they're parallel, they don't share the same X-intercept. f(x)'s x-intercept would be (0,0), origin. h(x)'s x-intercept would be (10,0). These three statements, A,B, & C are correct statements therefore they're not our answers since we're looking for the incorrect statement....... STATEMENT D!
PLS HELP ASAP THIS QUESTION IS REALLY EASY
Answer:
point form : (-2 , -1)
equation form : x = -2 , y = -1
Step-by-step explanation:
( 5x + 9 = -2x - 5)
for y = 5x + 9 (substitute x = -2)
y = 5(-2) + 9 = -1
Write a function g whose graph represents the indicated transformation of the graph f.
f(x)=∣x+2∣−1; translation 1 unit to the right followed by a vertical stretch by a factor of 2 and a translation of 4 units down.
g(x) = ?
The transformed function is:
g(x) = 2*|x + 1| - 6
How to write the transformed function?
We start with the original function f(x), and we define the transformed function as g(x).
First, we have a translation of 1 unit to the right, so we have:
g(x) = f(x - 1)
Then, we have a vertical stretch by a factor of 2.
g(x) = 2*f(x - 1)
A translation of 4 units down:
g(x) = 2*f(x - 1) - 4
And we know that f(x) = |x + 2| - 1
Replacing that, we get:
g(x) = 2*( |x -1 + 2| - 1) - 4
g(x) = 2*|x + 1| - 2 - 4
g(x) = 2*|x + 1| - 6
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40 POINTS PLEASE ASAP!!!
A soccer Practice is 90 minutes long, write an
expression for the number of minutes left after
m minutes have elapsed.
Answer:
Given that the information,
Length of a soccer practice = 90 minutes
Time that has elapsed = m minutes
Let "y" be the minutes left
Expression for the number of minutes left is
[tex]y = (90 - m) min[/tex]
(PLEASE ANSWER THIS!!! I NEED THE ANSWER ASAP!!!) How many numbers are in this equation: 5, 7, 9 . . . 39, 41
The number of terms in the sequence is 19
How to determine the number of terms in the sequence?The sequence is given as
5, 7, 9 . . . 39, 41
In the above sequence, we can see that
Type of sequence: Arithmetic sequenceFirst term, a = 5Last term, Tn = 41Common difference, d = 2The nth term of an arithmetic sequence is
Tn = a + (n - 1)d
So, we have
5 + (n - 1) * 2 = 41
This gives
(n - 1) * 2 = 36
Divide by 2
n - 1 = 18
Add 1 to both sides
n = 19
Hence, there are 19 numbers in the sequence
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a graph shows a proportional relationship. what is the constant of proportionality
The constant of proportionality is known as the slope of the line.In the graph constant of proportionality is 1/2
What is constant of proportionality?The constant of proportionality is known as the slope of the line.
Constant of proportionality is nothing but slope of a line
The formula for calculating slope is expressed as:
m = y₂-y₁/x₂-x₁
Given the coordinate points (2/3, 3/4 ) and (0,0).
y₂=0, y₁=3/4, x₂=0,x₁ =2/3
substitute the values of y₂=0, y₁=3/4, x₂=0,x₁ =2/3 in slope formula to get constant of proportionality.
The constant of proportionality is expressed as:
m = 3/4 × 2/3
m =6/12
m=1/2
Hence the constant of proportionality is 1/2
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Subtract (-2)-(-1) using number line
Answer:
picture
Step-by-step explanation:
everything in the picture
i hope that this helps
Answer:
the answer is -1 .........
The team needs new uniforms. The students plan to sell plush toy s (the school mascot) for $5 each. The students find three companies on-line that sell stuffed mascots. Company A sells s for $. Company B sells s for $. Company C charges $ for s. Which company has the best buy?
Company B has the best buy with a selling price of $2.79
Given: Company A sells 16 lions for $44.32
Company B sells 18 lions for $50.22
Company C sells 12 lions for $ 32.88
To find : The selling price of each lion
By using unitary method we get,
Company A sells 1 lion for $ 2.77
Company B sells 1 lion for $2.79
Company C sells 1 lion for $ 2.74
From the above statistics it is clear that Company B has the best buy .
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A rectangle is shown below.
measurements are to the nearest cm.
17 cm
9 cm
Calculate the lower bound for the area of the rectangle.
Calculate the upper bound for the perimeter of the rectangle
Answer:
lower bound for area = 140.25 square cm
upper bound for perimeter = 54 cm
======================================================
Explanation:
L = length
W = width
The unknown length L is rounded to the nearest cm to get to 17
This means it's in the interval [tex]16.5 \le L < 17.5[/tex]
The smallest it can get is L = 16.5 since that rounds to 17
It doesn't reach 17.5 since that would round to 18. But it could be L = 17.49 or L = 17.499 or L = 17.4999 and so on.
Similarly, if the unknown width W rounds to 9 cm, then its unrounded value is somewhere in the interval [tex]8.5 \le W < 9.5[/tex]
------------------------
Select the lower bounds of L and W to compute the lower bound of the area
length*width = L*W = 16.5*8.5 = 140.25
The smallest area possible is 140.25 square cm.
--------------------------
Use the upper bounds of each L and W to find the upper bound of the perimeter.
P = 2(L+W)
P = 2(17.5 + 9.5)
P = 54
In the previous example, we could have a true area of 140.25 square cm. However in this case, there's no way to reach this upper bound 54 itself. This is the so called "ceiling" which we can think of as an electric fence or asymptote value.
We could have the following example perimeter values that approach 54 but not actually reach it
perimeter = 53.9perimeter = 53.99perimeter = 53.999perimeter = 53.9999and so on.