Answer:
B & E.
Step-by-step explanation:
$25 is the y value, because she has to pay the fee no matter what.
Integers can be less than or equal to 8 because 65(8) + 25 is equal to 545, which does not exceed the budget.
Hope this helps!
NEED HELP QUICK!! 25 POINTS TO ANSWER
Set up the equation and solve for x:
11x-2 = 9x +2 + 10
11x-2 = 9x +12
2x = 14
X = 7
BOC = 9x +2 = 9(14) +2 = 126+2 = 128
Describe a way of showing that a continuous function on n open interval (a b, ) has a minimum value.
Answer:
See explanation below
Step-by-step explanation:
In fact, the interval has to be closed (just as [a,b], for b>a). Otherwise, this is not neccesarily true. For example, consider the function f(x) = -1/x defined on the open interval (0.1). f is continuous (quotient of continuous functions) but it does not have a minimum value: it decreases infinitely near zero.
To show this result on the interval [a,b], the idea is the following:
We can use a previous theorem. If f is continuous on [a,b], there exists some N>0 such that N≤f(x) (that is, f is bounded below). Now, we take the biggest N such that N≤f(x) for all x∈[a,b] (this is known as the greatest lower bound)
The number N is the candidate for the minimum value of f. Next, we have to show that there exists some p∈[a,b] such that f(p)=N. To do this, we must use the continuty of f on [a,b]. There are many ways to do it, and usually they require the epsilon-delta definition of continuity.
This is just a description of the ideas involved, but of course, a rigorous proof would need more technical details, depending on the theorems you are allowed to use.
Assessment
8. Compare the function with the parent function. Without graphing, what are the vertex, axis of
symmetry, and transformations of the given function?
(1 point)
y= | 10x – 2| -7
A. x = 2: translated to the right - unit and down 7 units
B. translated to the left – unit and up 7 units
C. translated to the left – unit and down 7 units
D. translated to the right – unit and down 7 units
ul
Raphael graphed the functions g(x)=x+2 and f(x)=x−1. How many units below the y-intercept of g(x) is the y-intercept of f(x)? A coordinate plane with 2 lines drawn. The first line is labeled f(x) and passes through the points (0, negative 1) and (1, 0). The second line is labeled g(x) and passes through the points (negative 2, 0) and (0, 2). −3 units −1 units 2 units 3 units
Answer:
3 units below the y-intercept of g(x) is the y-intercept of f(x)
Step-by-step explanation:
[tex]g(x)=x+2[/tex] and [tex]f(x)=x-1[/tex]
In f(x)= mx+b the y intercept is b
In [tex]g(x)=x+2[/tex], the y intercept value is 2
In [tex]f(x)=x-1[/tex], the y intercept value is -1
the difference in y intercept is +2-(-1)=+3
3 units below the y-intercept of g(x) is the y-intercept of f(x)
A company did a quality check on all the packs of trail mix it manufactured. Each pack of trail mix is targeted to weigh 9.25 oz. A pack must weigh within 0.23 oz of the target weight to be accepted. What is the range of rejected masses, x, for the manufactured trail mixes?
a. x < 9.02 or x > 9.48 because |x − 0.23| + 9.25 > 0
b. x < 9.25 or x > 9.48 because |x − 9.25| > 0.23
c. x < 9.25 or x > 9.48 because |x − 0.23| + 9.25 > 0
d. x < 9.02 or x > 9.48 because |x − 9.25| > 0.23
Answer:
d. x < 9.02 or x > 9.48 because |x − 9.25| > 0.23
Step-by-step explanation:
Given,
The standard weight of the pack = 9.25 oz,
The pack must weigh within 0.23 oz of the target weight to be accepted.
i.e. if x represents the weight of the pack,
If x > 9.25 oz
then x - 0.925 ≤ 0.23 ......(1)
if x < 9.25
then 9.25 - x ≤ 0.23
⇒ -(x-9.25) ≤ 0.23 .......(2)
From equation (1) and (2),
The accepted range of mass is,
|x-9.25| ≤ 0.23
Hence, the rejected range mass would be,
|x-9.25| > 0.23
⇒ x - 9.25 > 0.23 or -x + 9.25 < 0.23
⇒ x > 0.23 + 9.25 or -x > 0.23 - 9.25
⇒ x > 9.48 or - x > −9.02
⇒ x > 9.48 or x < 9.02
Can someone help me?
Divide using long division.
Answer:
The answer to your question is -3x² + 29x -150
Step-by-step explanation:
-3x² + 29x -150
x³ + 6x² - 3x - 5 -3x⁵ + 11x⁴ + 33x³ - 26x² - 36x - 6
+3x⁵ +18x⁴ - 9x³ - 15x²
0 29x⁴ +24x³ - 41x² - 36x
-29x⁴ - 174x³ +87x²+145x
0 -150x³ +46x² +109x - 6
+150x³ +900x²-450x -750
0 946x² -341x -756
Quotient = -3x² + 29x -150
Remainder = 946x² -341x -756
It is observed that a certain bacteria culture has a relative growth rate of 15% per hour, but in the presence of an antibiotic the relative growth rate is reduced to 5% per hour. The initial number of bacteria in the culture is 24. Find the projected population after 24 hours for the following conditions. (Round your answers to the nearest whole number.)
In this bacterial growth problem, the population after 24 hours under normal conditions would be approximately 19136 bacteria. With a reduced growth rate due to antibiotics, the population would be approximately 79 bacteria.
Explanation:The subject of the question relates to the concept of exponential growth, as demonstrated by a bacteria population. Given that the initial population is 24, the population P after time t, in this case in hours, is given by the formula P = P0 * (1 + r/100)^t, where P0 is the initial population, r is the relative growth rate (percentage), and t is time.
Under normal growth conditions, after 24 hours the population would be P = 24 * (1 + 15/100)^24 = approximately 19136, rounded to the nearest whole number. However, with the introduction of antibiotics, reducing the growth rate to 5%, after 24 hours the population would be P = 24 * (1 + 5/100)^24 = approximately 79, rounded to the nearest whole number.
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Beneficial terms of trade are the terms or prices that are between the two parties' oppotunity costs
Answer:
Beneficial terms of trade or trading price between two parties are opportunity costs lower than the cost to manufacture them locally which benefits both parties. They must be less enough to cover the freight charges or additional service charges that may arise.
what is the solution of x^2 = 16^x?
Answer:
x = -0.5.
Step-by-step explanation:
x^2 = 16^x
One way to do this is to use 2 graphs y = x^2 and y = 16^x .
The solution is where the 2 graphs intersect.
The answer is x = -0.5.
One warehouse had 185 tons of coal, another one had 237 tons. The first warehouse delivered 15 tons of coal to its clients daily, the second one delivered 18 tons of coal to its clients daily. In how many days will the second warehouse have 1.5 times more coal than the first one?
Answer:
In 9 days will the second warehouse have 1.5 times more coal than the first one
Step-by-step explanation:
The coal left in warehouses after x days can be found using the equation:
first warehouse: 185 - 15xsecond warehouse= 237-18xLet the second warehouse have 1.5 times more coal than the first one after n days then
1.5 ×(185 - 15n)=237-18n which gives: 277,5-22,5n=237-18n and 40,5=4,5n9=nDans sporting goods received a shipment of 120 sweatshirts. Half of the sweatshirts were size large. One-fourth of the large sweatshirts were red. What was the total number of sweatshirts in the shipment that were both large and red?
Answer:
15
sweatshirts were large and red.
Step-by-step explanation:
Hope this helps
Answer:the total number of sweatshirts in the shipment that were both large and red is 15
Step-by-step explanation:
The total number of sweatshirts received by Dans sporting goods is 120. Half of the sweatshirts were size large. This means that the number of sweatshirts that were size large is 120/2 = 60.
One-fourth of the large sweatshirts were red. This means that the number of large sweatshirts that were also red would be
1/4×60 = 15
Using k as the constant of proportionality, write an equation that expresses: Z varies jointly as x and y.
Answer: z= kxy
Step-by-step explanation:
There are three types of variation. We have direct, inverse and joint.
Variation has to do with the manner in which we relate two mor more variables either directly or inversely.
For joint variation, we relate two or more variables to one another. A variable among those variables is written in terms of the remaining variables directly.
According to the question, since we have three variables z, x and y and we are to express z joint as x and y.
Joint variation is a "direct relationship" between variables i.e z will be directly proportional to the product of x and y making k as constant of proportionality. Mathematical relationship will give us;
Z=kxy
The height of the water in a fish pond is 42.5 inches. Water is being drained from the pond at a rate of 3.75 inches per minute. What is the height of the water after 3 minutes?
Height of the water after 3 minutes is 31.25 inches
Solution:Given that height of the water in a fish pond is 42.5 inches
Water is being drained from the pond at a rate of 3.75 inches per minute
To find: height of the water after 3 minutes
According to given information,
Water drained in 1 minute = 3.75 inches
So height of the water after 3 minutes is calculated by following steps:
1) find how much water is drained in 3 minutes
2) subtract value obtained in step 1 from total height of water in fish pond
Step 1:water is drained in 3 minutes = Water drained in 1 minute x 3
[tex]\text {water is drained in } 3 \text { minutes }=3.75 \times 3=11.25[/tex]
Thus water drained in 3 minutes is 11.25 inches
Step 2:height of the water after 3 minutes = total height of water in fish pond - water drained in 3 minutes
height of the water after 3 minutes = 42.5 - 11.25 = 31.25 inches
Thus height of the water after 3 minutes is 31.25 inches
Final answer:
After draining water at a rate of 3.75 inches per minute for 3 minutes, the height of the water in the pond decreases from 42.5 inches to 31.25 inches.
Explanation:
The question is asking for the height of the water in a pond after draining some amount of water for a specified time. Initially, the pond has a water height of 42.5 inches. Water is being drained at a rate of 3.75 inches per minute. To find the height of the water after 3 minutes, we need to calculate the total amount of water drained and subtract it from the initial height.
Total water drained in 3 minutes = Drain rate per minute × number of minutes = 3.75 inches/minute × 3 = 11.25 inches.
Height of water after 3 minutes = Initial height - Total water drained = 42.5 inches - 11.25 inches = 31.25 inches.
Therefore, the height of the water in the pond after 3 minutes is 31.25 inches.
If a supply curve is a vertical line, it is ________, and if it is a horizontal line, it is ________.
what's the answer choices
am I right??
* Show examples & details if I am wrong!! *
Yes, you are correct.
From the image, we can see 3 triangles, the large triangle and the two triangles that make the larger triangle.
All 3 of these triangles are similar since they're angle measurements are the same (can be proven by geometry).
We can gather the following information from the given information.
The largest triangle (the one made up of two triangles) has a hypotenuse of 3+9=12, and a leg length of x. The hypotenuse to leg ratio is 12/xThe second largest triangle has a hypotenuse length x and leg length 9. The hypotenuse to leg ratio is x/9We know the hypotenuse to corresponding leg ratio must be equal since these two triangles are similar. Thus, we have the equation:
12/x = x/9
Using the cross product property gives us:
x² = 9 × 12
x² = 108
Taking the square root of both sides gives us:
x = √108
= 6 √3
Thus, your answer is correct. Great job!
Let me know if you need any clarifications, thanks!
Two concentric circles with radii of 19 and 29 units bound a shaded region. A third circle will be drawn with area equal to that of the shaded area. What must the radius of the third circle be? Express your answer in simplest radical form.
========================================
Work Shown:
Let P and Q be two concentric circles
P = area of circle with radius 19
P = pi*r^2
P = pi*19^2
P = 361pi
-------
Q = area of circle with radius 29
Q = pi*r^2
Q = pi*29^2
Q = 841pi
-------
R = area of shaded region between circle P and circle Q
R = region outside circle P, but inside circle Q
R = Q - P
R = 841pi - 361pi
R = 480pi
------
S = area of circle with area equal to region R's area
S = 480pi
S = pi*r^2
pi*r^2 = 480pi
r^2 = 480
r = sqrt(480)
r = sqrt(16*30)
r = sqrt(16)*sqrt(30)
r = 4*sqrt(30)
How many square shaped tiles of area 25 m2 would you need to cover a rectangular plot of area 700 m2? A. 25 B. 28 C. 175 D.17500
Answer:28 square shaped tiles of area 25 m^2 would be needed to cover the rectangular plot.
Step-by-step explanation:
The area of the rectangular plot is 700m^2
The area of each square tiles is 25m^2
The number of tiles needed to cover a rectangular plot would be
700/25 = 28 square shaped tiles
The 9-1-1 service fee on telecommunications bills is what type of tax?Select all that apply
Service tax
Professional service tax
Ad valorem tax
Fixed tax
Business tax
The 9-1-1 service fee on telecommunications bills is a type of tax such as service tax, fixed tax, business tax. Thus, the option (a), (d) and (e) is correct.
What is tax?
The term tax refers to the government charge the extra money for goods and services. The tax is also called as financial charge. The amount of tax are collect to government account as spent on public welfare. The public pay tax is compulsory. There are two types of tax such as direct tax and indirect tax.
The telecommunications bills are also included tax such as service tax, fixed tax, and business tax etc. The service tax is an indirect tax as charge on exchange of services. The fixed tax are apply on lump sum amount. The business tax is included income tax, and other expenses tax (wages, salaries etc.)
Therefore, option (a) (d) and (e) is correct.
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The double number line shows that in 222 minutes, Pogo the dog can fetch a frisbee 666 times. Based on the ratio shown in the double number line, how many times will Pogo fetch the frisbee in 444 minutes?
Answer:
Dog Pogo will fetch the frisbee 12 times in 4 minutes.
Step-by-step explanation:
Given:
Number of minutes required =2 minutes.
Number of times frisbee fetch by dog = 6 times
We need to find Number of times the dog can fetch the frisbee in 4 minutes.
First we will find number of frisbee fetch in minute.
In 2 minutes = 6 times frisbee fetched by the dog
so in 1 minute = Number of times frisbee fetched by the dog in 1 minute.
By using Using Unitary method we get;
Number of times frisbee fetched by the dog in 1 minute = [tex]\frac{6}{2} =3[/tex]
Hence in 1 minutes the dog can fetch frisbee 3 times.
for 1 min = 3 times frisbee is been fetched by dog
So for 4 minutes = Number of times frisbee is been fetched by dog in 4 min.
Again by using Unitary Method we get;
Number of times frisbee is been fetched by dog in 4 min = [tex]3\times4 = 12[/tex]
Hence Dog Pogo will fetch the frisbee 12 times in 4 minutes.
Answer:12
Step-by-step explanation:
In 2001 , chipper had 102 runs batted in. In 2008 , Chipper had only 75 runs batted in. Calculate the percent change in runs batted in from 2001 to 2008
Answer: There is decrease in percent of 26.47% from 2001 to 2008.
Step-by-step explanation:
Since we have given that
Number of runs that chipper had batted in 2001 = 102
Number of runs that chipper had batted in 2008 = 75
So, the year gap = 7 years
Difference in runs = 102- 75 =27
So, the percent change in runs batted from 2001 to 2008 is given by
[tex]\dfrac{27}{102}\times 100\\\\=\dfrac{2700}{102}\\\\=26.47\%[/tex]
Hence, there is decrease in percent of 26.47% from 2001 to 2008.
If a dog was 7 weeks old 5 days ago when was it born?
What is its birth date
Like if it was born today its birthdate would be 12/19/19, and you could even go more into detail and say for instance Thursday 12/19/19
AB = 4x DC = x + 9 AD = 6 BC = 2y Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Show that quadrilateral ABCD is a parallelogram by finding the lengths of the opposite side pairs.
Answer:
Therefore the lengths of the opposite side pairs, AB and BC are 12 units and 6 units .
Step-by-step explanation:
Given:
[] ABCD is a Parallelogram.
∴ pairs of opposite sides are congruent
∴ AB = DC and
BC = AD
To Find:
Length of AB = ?
Length of BC = ?
Solution:
[] ABCD is a Parallelogram. .............Given
∴ pairs of opposite sides are congruent
∴ AB = DC and BC = AD
On substituting the values we get
For 'x' i.e AB = DC
[tex]4x=x+9\\\\4x-x=9\\\\3x=9\\\\x=\frac{9}{3}\\ \\x=3[/tex]
For 'y' i.e BC = AD
[tex]2y=6\\\\y=\frac{6}{2} \\\\y=3\\[/tex]
Now substituting 'x' and 'y' in AB and BC we get,
[tex]Length\ AB=4\times 3 =12\ units\\\\Length\ BC=2\times 3 =6\ units[/tex]
Therefore the lengths of the opposite side pairs, AB and BC are 12 units and 6 units .
C) 12, 6
Set opposite sides equal to each other and solve for x or y.
AB = DC → 4x = x + 9 → 3x = 9 → x = 3
So, AB = DC = 12
And,
AD = BC → 6 = 2y → y = 3
So, AD = BC = 6
An online music club has a one- time registration fee of $13.95 and charges $0.49 to buy each song. If Emma has $50.00 to join the club and buy songs, what is the maximum number of songs she can buy?
Answer: 73 songs
Step-by-step explanation:
The online music club has a one- time registration fee of $13.95 and charges $0.49 to buy each song. Let x represent the number of songs that a member buys. This means that the amount that a member who just joins the music club pays for x songs would be
0.49x + 13.95
If Emma has $50.00 to join the club and buy songs, the maximum number of songs she can buy would be expressed as follows
0.49x + 13.95 = 50
0.49x = 50 - 13.95 = 36.05
x = 36.05/0.49 = 73.57
the maximum number of songs she can buy is 73 since the number of songs cannot be a fraction.
50.00 - 13.95 = 36.05 (subtract the registration fee)
36.05/0.49 = 73.57 so she can buy 73 songs
A leaky faucet drips 356,755 mL of water over the course of the year. There are approximately 3,785 mL in 1 gallon. How many gallons of water are leaked in one year
Gallons of water are leaked in one year is 94.253 gallons
Solution:Given that leaky faucet drips 356,755 mL of water over the course of the year
There are approximately 3,785 mL in 1 gallon.
To find: gallons of water are leaked in one year
From given information,
Amount of water leaked in one year in ml = 356,755 mL
Also given in question that,
1 gallon = 3785 ml[tex]1 \text{ ml} = \frac{1}{3785} \text{ gallons}[/tex]
Now we can convert 356,755 mL to gallons
[tex]356,755 \text{ ml} = \frac{1}{3785} \times 356755 \text{ gallons}\\\\356,755 \text{ ml} = 94.253 \text{ gallons}[/tex]
Thus gallons of water are leaked in one year is 94.253 gallons
Calculate the slope of the line given the following two points. Point 1 (0, 0) and Point 2 (6, 12)
M = _______
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slope = difference in y / difference in x
slope = (12 - 0) / (6 - 0)
slope = 12/6
slope = 2
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slope
m=y2-y1/x2-x1m=12-0/6-0m=12/6m=2Done
onsider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes
Answer:
V (max) = 2 ft³
and x side of the base is x = 0,5 feet
Step-by-step explanation: See annex ( two different cubes)
We have a square piece of cardboard of 3 inches wide
Let x be lenght of side to cut in each corner
Then the base of the (future cube) is 3 - 2x, and the area is
( 3 - 2x )²
And the height is x Then volume of the cube as a function of x is:
V(x) = ( 3 - 2x )² *x or V(x) = ( 9 + 4x² - 12x )*x
V(x) = 4x³ - 12x² + 9x
Taking derivatives on both sides of the equation
V´(x) = 12x² - 24x + 9
V´(x) = 0 12x² - 24x + 9 = 0 simplifying 4x² - 8x + 3 = 0
Second degree equation solving for x
x₁,₂ = [ 24 ± √( 576) - 432 /24
x₁,₂ = [24 ±√144 ]/24
x₁,₂ = ( 24 ± 12) /24 x₁ = 1.5 feet x₂ = 0,5 feet
Of these two values we have to dismiss x₁ because if x = 1.5 we don´t have a cube ( 0 height )
Then we take x = 0,5 feet
And
V (max) = (2)²*0,5 = 4*0,5
V (max) = 2 ft³
3x-4y>12 which order pair (x,y) satisfies the inequality?
Since in the question, there are no ordered pairs given so you can consider the below explanation to check which ordered pairs satisfies the inequality 3x-4y>12
Step-by-step explanation:
We need to identify which ordered pair(x,y) satisfies the inequality 3x-4y>12
The ordered pair (x,y) which satisfies the inequality will be the values of x and y that satisfies the inequality given 3x-4y>12
So, if x= 2 and y = 2 then the inequality will be:
3x-4y>12
3(2)-4(2)>12
6-8>12
-2>12 is false because -2 is not greater than 12
So, ordered pair (2,2) doesn't satisfy the inequality 3x-4y>12
Now if x = 10 and y = 2 then the inequality will be:
3x-4y>12
3(10)-4(2)>12
30-8>12
22>12 is true because 22 is greater than 12.
So, ordered pair (10,2) satisfies the inequality 3x-4y>12
Since in the question, there are no ordered pairs given so you can consider the above explanation to check which ordered pairs satisfies the inequality 3x-4y>12
Keywords: Solving inequalities
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To find the order pair (x,y) satisfying the inequality 3x - 4y > 12, substitute potential order pairs for x and y and evaluate. If the result is greater than 12, then the order pair satisfies the inequality.
Explanation:The inequality given is 3x - 4y > 12. To find the order pair (x,y) that satisfies this inequality, let's plug in some potential solutions and see which one works.
For example, let's try the order pair (6, 1): 3(6) - 4(1) = 18 - 4 = 14, which is greater than 12, so (6,1) does satisfy the inequality.
But if we try the order pair (2, 3): 3(2) - 4(3) = 6 - 12 = -6, which is not greater than 12, so (2,3) does not satisfy the inequality.
Through these examples, you can see how we can find potential solutions to the inequality by substituting different order pairs for x and y.
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The original price of a computer is $599.99. Suzie has a 15%-off coupon for the computer. A sales tax of 7% will be added to the sale price of the computer. Which expression would calculate how much Suzie will pay for the computer?
The required cost of a computer Suzie will pay is $545.69.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
The original price of a computer is $599.99.
Suzie has a 15%-off coupon for the computer.
Discounted price = (1 - 0.15)×599.99
Discounted price = 0.85×599.99
A sales tax of 7% will be added to the sale price of the computer.
Price of the computer after taxes = (1 + 0.07)0.85×599.99
= $545.69
Thus, the required cost of a computer Suzie will pay is $545.69.
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Final answer:
To find how much Suzie will pay for a computer with a 15% discount and a 7% sales tax, first calculate the discount, then subtract it from the original price, calculate the sales tax on the sale price, and add it to the sale price. The total payment is the original price reduced by the discount and increased by the sales tax, rounded to the nearest cent would be approximately $545.69.
Explanation:
Calculation of Total Payment for the Computer with a Discount and Sales Tax
To calculate how much Suzie will pay for the computer after applying a 15%-off coupon and adding a 7% sales tax, you will need to perform two main calculations. First, calculate the discount amount by converting the percentage to a decimal and multiplying it by the original price. Second, calculate the sales tax on the discounted price by again converting the percentage to a decimal and multiplying it. Finally, add the sales tax to the discounted price to arrive at the total cost.
Here's a step-by-step breakdown of the calculations:
Add the sales tax to the sale price to find the total cost: $509.9915 + $35.699405 = $545.690905.
Therefore, the expression to calculate Suzie's total payment for the computer is ($599.99 times (1 - 0.15)) times (1 + 0.07). When actually performing the calculation, the total payment, rounded to the nearest cent, would be approximately $545.69.
Determine whether the sampling method described below appears to be sound or is flawed. In a survey of 714 subjects, each was asked how often he or she read a book.read a book. The survey subjects were internet users who responded to a question that was posted on a news website.
a) it is flawed because it is a census
b) it is flawed because it is not statistically significant.
c) it appears to be sound because the data are not biased in anyway.
d) it is flawed because it is a voluntary response sample.
Answer:
Option D) It is flawed because it is a voluntary response sample.
Step-by-step explanation:
We are given the following information in the question:
The subjects of the survey were internet users who responded to a question that was posted on a news website.
A total of 714 subjects responded to this question, answering the question, how often he or she read a book.
Option D) It is flawed because it is a voluntary response sample.
Voluntary response sample:
A sample in which the subjects themselves decide whether to be included in the study.People chose to be a part or not to be a part of the survey since the question was posted on website.Some maybe interested some may not in answering this question.A voluntary sample is made up of people who self-select into the survey. Often, these folks have a strong interest in the topic of the survey thus creating a bias.Voluntary response bias occurs when sample members are self-selected volunteers.The admission fee at an amusement park is $2.50 for children and $5.80 for adults. On a certain day, 343 people entered the park, and the admission fees collected totaled $1369. How many children and how many adults were admitted?
188 children and 155 adults were admitted that day.
Step-by-step explanation:
Given,
Cost of one children admission = $2.50
Cost of one adult admission = $5.80
Number of people entered = 343
Total admission fees collected = $1369
Let,
Number of children admission = x
Number of adult admission = y
According to given statement;
x+y=343 Eqn 1
2.50x+5.80y=1369 Eqn 2
Multiplying Eqn 1 by 2.50
[tex]2.50(x+y=343)\\2.50x+2.50y=857.50\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](2.50x+5.80y)-(2.50x+2.50y)=1369-857.50\\2.50x+5.80y-2.50x-2.50y=511.50\\3.30y=511.50[/tex]
Dividing both sides by 3.30
[tex]\frac{3.30y}{3.30}=\frac{511.50}{3.30}\\y=155[/tex]
Putting y=155 in Eqn 1
[tex]x+155=343\\x=343-155\\x=188[/tex]
188 children and 155 adults were admitted that day.
Keywords: linear equation, subtraction
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