the jurassic zoo charged $11 for each adult admission and $8 for each child. the total bill for the 195 people from a school trip was $1713. how many children went to the zoo
Answers
Children : 144
Adults : 51
Explanation
Step 1
Set the equations
let
x represents the number of children
y represents the number of adults
charge per child:8
charge per adult:11
total people:195
then
a)the total people is 195, so
\(x+y=195\rightarrow equation(1)\)b) the total bill was $1713,so
total childrend +total adults=173
but,
total adults cost= rate*number of adults
total children cost= rate*number of childe
replacing
\(8x+11y=1713\rightarrow equation(2)\)Step 2
solve the equations,
\(\begin{gathered} x+y=195\rightarrow equation(1) \\ 8x+11y=1713\rightarrow equation(2) \end{gathered}\)a) isolate the x value from equation 81) and replace in eqaution (2)
\(\begin{gathered} x+y=195\rightarrow equation(1) \\ \text{subtract y in both sides} \\ x+y-y=195-y \\ x=195-y \end{gathered}\)replace in equation (2)
\(\begin{gathered} 8x+11y=1713\rightarrow equation(2) \\ 8(195-y)+11y=1713 \\ 1560-8y+11y=1713 \\ 3y+1560=1713 \\ \text{subtract 1560 in both sides} \\ 3y+1560-1560=1713-1560 \\ 3y=153 \\ \text{divide bothsides by 3} \\ \frac{3y}{3}=\frac{153}{3} \\ y=51 \end{gathered}\)therefore, the number of adults is 51
b) now, replace the y value into equation (1) to find x
\(\begin{gathered} x+y=195\rightarrow equation(1) \\ x+51=195 \\ \text{subtract 51 in both sides} \\ x+51-51=195-51 \\ x=144 \end{gathered}\)so, the number of children is 144
I hope this helps you
Related Questions
What are the solution(s) of the quadratic equation 98 - x2 = 0?
O x = +2/7
O x = +673
O x = +7/2
O no real solution
Answers
Answer:
Solutions are x=7 square 2
The solutions of the quadratic equation 98 - x² = 0 are ±7√2.
What are Quadratic Equations?Quadratic expressions are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
Given quadratic equation is,
98 - x² = 0
This can be written as,
98 = x², or
x² = 98
Now, taking the square root on both sides,
√x² = √98
x = √98
Write 98 as the product of perfect square.
98 = 49 × 2
√98 = √(49 × 2) = √49 × √2 = ±7√2
Hence the solutions are ±7√2.
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Subtract.
−1 3/5 − (−2 7/8)
Enter your answer as a simplified fraction by filling in the boxes.
It shouldn't be a mixed number.
Answers
Consider the following figure.
(Note that the figure is not drawn to scale.)
20°
L
47°
89°
Order the side lengths IK, KL, IJ, IL, and LJ from least to greatest.
Answers
The side lengths from least to greatest as follows:
IK < KL < IJ < IL < LJ
To order the side lengths IK, KL, IJ, IL, and LJ from least to greatest, we can analyze the given figure.
Since the figure is not drawn to scale, we cannot determine the exact lengths of the sides. However, we can make some observations based on the given angles.
Let's analyze the angles:
Angle L: Since angle L is marked as 47°, we know that side KL is the shortest side, as it is opposite to the smallest angle in a triangle.
Angle I: Since angle I is marked as 20°, we can infer that side IJ is longer than side IK, as it is opposite to a larger angle.
Angle LJ: Since angle LJ is marked as 89°, we can conclude that side LJ is the longest side, as it is opposite to the largest angle in the triangle.
Based on these observations, we can order the side lengths from least to greatest as follows:
IK < KL < IJ < IL < LJ
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if three apples cost 45 rupees how much with 5 apples cost?
Answers
if 3 apples cost 45 rupees
1 apple costs 45 : 3 = 15 rupees
how much with 5 apples cost?
5 x 15 = 75 rupees
Answer:
75 rupees
Step-by-step explanation:
Given:
3 apples cost 45 rupees
To Find:
How much with 5 apples cost
Solve:
if 3 apples cost 45 rupees
Since 3 apple cost 45
Thus, Find the cost of 1.
45 ÷ 3 = 15 rupees
Now,
5 x 15 = 75
Thus, 5 apples cost 75 rupees.
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Suppose that X is a binomial random variable with n = 11 and p = 0.28. Find P 5).
Write only a number as your answer. Round to 4 decimal places (for example
0.1849). Do not write as a percentage.
Your Answer:
Answers
Answer:
Step-by-step explanation:
To find P(X = 5), we can use the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
where n is the number of trials, p is the probability of success on each trial, k is the number of successes we want to find, and (n choose k) is the binomial coefficient, which can be calculated as:
(n choose k) = n! / (k! * (n - k)!)
Plugging in the values n = 11, p = 0.28, and k = 5, we get:
P(X = 5) = (11 choose 5) * 0.28^5 * (1 - 0.28)^(11 - 5)
Using a calculator to evaluate this expression, we get:
P(X = 5) ≈ 0.1397
Therefore, the probability of getting exactly 5 successes in 11 trials, where the probability of success on each trial is 0.28, is approximately 0.1397, rounded to 4 decimal places.
Can someone please help
Answers
Answer:
340
Step-by-step explanation:
The risk-free rate is 8%, and the expected return on the market is 16%. As an analyst, you are preparing a recommendation report on the following stock:
Stock S
Beta 0.85
Expected dividend next year $1.10
Growth rate (g) 8%
Current Price (p0) $22
Using the SML, would you recommend to buy or sell the stock?
A) Sell, because the required rate is greater than the expected rate.
B) Sell, because the expected rate is greater than the required rate.
C) Buy, because the required rate is greater than the expected rate.
D) Buy, because the expected rate is greater than the required rate.
Answers
Correct Option is,
D) Buy, because the expected rate is greater than the required rate.
Now, Based on the information you've provided,
To calculate the required rate of return, we can use the SML formula as;
Required rate of return = risk-free rate + beta x (expected market return - risk-free rate)
Plugging in the numbers, we get:
Required rate of return = 8% + 0.85 x (16% - 8%)
= 14.6%
Since the expected rate of return for Stock S is,
= dividend yield + growth rate
= (1.1 / 22 + 8%),
= 9.4%
which is higher than the required rate of return of 14.6%,
Here, the stock is undervalued and would be a good buy.
Therefore, the answer is, option D) Buy, because the expected rate is greater than the required rate.
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Evaluate S8: 2+6+10+14
Answers
Evaluate S8: 2+6+10+14
2+6+10+14 = 32
Instructions: Identify the key features of the following graph. If the Domain is all real numbers, type in 'All Real" into the Domain box
Answers
Key features for the graph given in the problem will be-:Vertex (-1, -5), Axis of symmetry=> (x = -1), y-intercept (0,-3), Minimum=> (y=-5), Domain=> (All Real), Range=>( y >= -5)
How to determine the key features?Refering to the graph given in the problem(refer image attached).The key features of the graph can be given as:
Vertex: The graph's vertex is at (-1, -5), which indicates that the graph extends upwards (because y = -5 is the minimal value).A vertical line at x = -1 serves as the graph's axis of symmetry. The graph is split into two symmetrical sections by this line.Y-intercept: The graph's y-intercept is at (0, -3), which indicates that here is where the graph and y-axis connect.The graph has a minimum point at y = -5, which is also the vertex of the graph and the lowest point on it.The graph's domain is set as "All Real" or "(-, )", which signifies that it spans all real values on the x-axis horizontally.Range: The graph's range is defined as y -5, which indicates that it climbs vertically from -5 and above on the y-axis.The graph has an upward-opening form, an axis of symmetry at x = -1, a y-intercept at (0, -3), a minimum point at y = -5 (which is also the vertex), and it spans all real numbers on the x-axis (domain) while being larger than or equal to -5 on the y-axis (range).
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What is the product of 3 x4/5
Answers
Answer:
2 2/5
Step-by-step explanation:
3 * 4/5
~Make the whole number a fraction by adding a 1 as the denominator
3/1 * 4/5
~Multiply both numerators and denominators
12/5 or 2 2/5
Best of Luck!
Answer:
12/5 :)
Step-by-step explanation:
3/1 x 4/5
3x4/1x5
12/1x5
12/5
Sixth-grade students were asked, "What grade are you in?" Explain why this is not a statistical question.
Answers
You already know that everyone you ask is in 6th grade so there is no point in asking because anyone who says no is lying.
Un trabajo puede ser realizado por 30 obreros durante 40 días. si el plazo para terminarlo es de 12 días, ¿cuántos obreros más se deben contratar?
Answers
To complete the job in 12 days, they need 100 workers.
How many works are needed?We know that 30 workes can complete 1 job in 40 days, then if each worker works at a rate R, then we can write:
30*R*40 days = 1 job
R = (1/1200) job/day
Then if they need to complete the job in 12 days, the number N of workers needed is:
N*(1/1200)*12 = 1
N = (1200/12) = 100
100 workers are needed.
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Solve proportion round it to the nearest hundredth
Answers
Answer:
7.7 = 2.3
3.6 b
7.7b= 8.28
7.7 7.7
b = 1.075324675
b = 1.08
A) If the last digit in the fractional part of 1.080 is less than 5, then simply remove the last the digit of the fractional part. With 1.080, rule A applies and 1.08 rounded to the nearest hundredth is:
14 + 3 [81 - (4x6)]
Please Show Your Work!
Answers
Answer:
185
Step-by-step explanation:
first multiply to get 14+3(81-24)
then calculate to get 14+3*57
multiply and get 14+171
the calculate to get your final answer which is 185
Answer:
969
Step-by-step explanation:
4x6+=24
81-24=57
14+3(57)
17(57)
969
Need help with this one
Answers
Answer:
The answer is a.2x/9Step-by-step explanation:
\( \frac{x {}^{2} }{3y} \div \frac{3x}{2y} \\ \frac{x {}^{2} }{3y} \times \frac{2y}{3x} \\ \frac{x {}^{2} }{3} \times \frac{2}{3x} \\ \frac{x}{3} \times \frac{2}{3} = \frac{2x}{9} \)
What is 30x2? Id love to know
Answers
The easiest way to do multiplication is to add the number to itself by the number your multiplying it by.
So if your multiplying 30 by 2 you just need to add 30 to itself twice so it's
30 + 30
Which also gives you the same answer
Based on the graph how many bottles will be filled in 80 seconds? 
Answers
Answer:
Below
Step-by-step explanation:
Find unit rate (since it starts at 0,0)
at 45 seconds it is 900 bottles
900 bottles / 45 seconds = 20 bottle / sec
20 bottles / sec * 80 sec = 1600 bottles
using the digits -9 to 9, without repeating any numbers, place a number in each box to create a system of equations that has a solution in quadrant 2. Tip: in quadrant 2, the x - coordinate is negative and the y-coordinate is positive.
Answers
Okay, here we have this:
Considering the provided information and options, we are going to find the requested numbers, so we obtain the following:
So first we will choose two values for x and y that meet the given tip: in quadrant 2, the x - coordinate is negative and the y-coordinate is positive.
For our case we will take x=-1 and y=1, then we can write the following two equations:
1x+3y=2 -> 1(-1)+3(1)=2 -> -1+3=2 -> 2=2
y=7x+8 -> 1=7(-1)+8 -> 1=-7+8 -> 1=1
Add. 4 7/12 plus 2 3/4 plus 7 5/12 =
Answers
Answer:
12 9/12
Step-by-step explanation:
Answer:
exact form- 59/4
mixed numbers- 14 3/4
decimal- 14.75
Which expression is equivalent to...
Answers
Detailed Answer:
Following the Laws of Exponents,
• a^n * a^m = a^(n + m)
Therefore,
= 5^10 * 5^5
= 5^(10 + 5)
=> 5^15
How many degrees Fahrenheit is -3°C?
Answers
Answer:
26.6°
Step-by-step explanation:
Answer: 26.6
Step-by-step explanation:
All you have to do i search the answer. They will give it to you automatically
Which sequence shows the numbers in order from least to greatest?
A. -2.14<3.16227766017<2.8
B. 2.8<3.16227766017<2.14
C. 2.14<3.16227766017 <2.8
D. 2.14<2.8<3.16227766017
Answers
The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.
The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.What is the meaning of the inequality symbols?The inequality symbols are mathematical symbols that are used to compare two values.
They indicate the relationship between two values that are not equal to each other. Here are the inequality symbols:
< (less than)≤ (less than or equal to)> (greater than)≥ (greater than or equal to)What is the meaning of the sequence?
A sequence is a set of numbers arranged in a particular order. The order of the numbers in a sequence can be from smallest to largest or largest to smallest.
The sequence D. 2.14 < 2.8 < 3.16227766017 is arranged from smallest to largest because the first number in the sequence, 2.14, is the smallest, and the last number in the sequence, 3.16227766017, is the largest.
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LaVilla is a village in the Italian Alps. Given its enormous popularity among Swiss, German, Austrian, and Italian skiers, all of its beds are always booked in the winter season, and there are, on average, 1465 skiers in the village. On average, skiers stay in LaVilla for 11 days. How many new skiers are arriving - on average - in LaVilla every day
Answers
Answer:
There are approximately 133 new skiers arriving every day
Step-by-step explanation:
Total number of skiers = 1465
time of stay for skiers = 11 days
How many new skiers are arriving on average = ???
To keep the average number of skiers available at each time constant, the number of skiers coming in and going out are fairly constant, and this is gotten by using the flow rate formula.
flow rate = amount available ÷ flow time
flow rate = 1465 ÷ 11
flow rate = 133.18
flow rate = 133
∴ There are approximately 133 new skiers arriving every day
pls help with this..
Answers
Answer:
B
Step-by-step explanation:
given scale is 1 inch represents 7.5 feet
then we require to calculate how many 7.5 feet there are in each dimension.
to obtain this divide each dimension by 7.5, that is
13 ÷ 7.5 ≈ 1.73 ( to 2 decimal places )
26 ÷ 7.5 ≈ 3.47 ( to 2 decimal places )
then dimensions are approximately 1.73 inches by 3.47 inches
You measure 48 backpacks' weights, and find they have a mean weight of 70 ounces. Assume the population standard deviation is 6.4 ounces. Based on this, construct a 99% confidence interval for the true population mean backpack weight.
Give your answers as decimals, to two places
Answers
The 99% confidence interval for the true population mean backpack weight is approximately (68.15, 71.85) ounces, rounded to two decimal places.
To construct a 99% confidence interval for the true population mean backpack weight, we can use the formula:Confidence Interval = Sample Mean ± (Critical Value * Standard Deviation / √Sample Size).
Since the population standard deviation is known, we can use the z-distribution and find the critical value corresponding to a 99% confidence level. The critical value for a 99% confidence level is approximately 2.576.
Given that the sample mean weight is 70 ounces, the population standard deviation is 6.4 ounces, and the sample size is 48, we can calculate the confidence interval:
Confidence Interval = 70 ± (2.576 * 6.4 / √48).
Simplifying the expression, we get:
Confidence Interval ≈ 70 ± 1.855.
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What is the value of x? 2.5x=35 Answer ASAP
Answers
Answer:
14
Step-by-step explanation:
x=35÷2.5 will devide 35 by 2.5 to get x
Answer: x = 14
Step-by-step explanation: To find the value of x, you can simply divide 35 by 2.5, which gives you a final result of 14. Therefore, x = 14.
*Tip: To divide whole numbers by decimals or decimals by decimals, then you’ll have to just divide regularly and align the decimal point where it originally was, as shown in the bracket where the dividend is.
what is the equation of a line that passes through the points (2,5) and (4,3)
Answers
The equation of a line that passes through points (2,5) and (4,3) is
y = -x+7.
Finding the equation of a line:
First, we need to find out the slope for the given points.
(X1,Y1) = (2,5)
(X2,Y2) = (4,3)
formula for slope(m) = \(\frac{Y2 - Y1}{X2 - X1}\)
substitute the points in the above formula
\(\frac{3 - 5}{4 - 2}\) = \(\frac{-2}{2}\)
\(\frac{-2}{2}\) = -1
slope for the given points(m) = -1.
m = -1
The equation of a line is y-y1 = m(x-x1), where x and y are variables.
substituting the values in the above equation then :
y-5 = -1(x-2)
y-5 = -x+2
y+x = 2+5
x+y = 7
y = -x+7
Therefore, the equation of the line passing through the points (2,5) and (4,3) is y = -x+7
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One hundred samples of five data points were randomly selected from each of four populations. The medians of each population's samples were plotted as shown below. Another random sample was then taken from one of the populations and recorded as follows: {1, 20, 5, 0, 5} From which population was this sample MOST likely selected? A. Population A B. Population B C. Population C D. Population D
Answers
From the dot plot, it can be seen that the median of the sample {1, 20, 5, 0, 5} is 5. This value falls in the range of the medians of samples from Population C. Therefore, it is most likely that this sample was selected from Population C.
What is median?The median is a measure of central tendency in a dataset, it is the middle value when a data set is ordered from least to greatest. If the dataset has an odd number of observations, the median is the middle value. If the dataset has an even number of observations, the median is the average of the two middle values. The median is a useful measure of central tendency when the data set contains outliers or extreme values, which can skew the mean.
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what is √ 169 please answer fast and the correct answer please
Answers
Answer:
Step-by-step explanation:
Answer:13
Step-by-step explanation:
A line passes through the point (6, -1) and has a slope of 3/2 Write an equation in slope-intercept form
Answers
9514 1404 393
Answer:
y = 3/2x -10
Step-by-step explanation:
The point-slope equation can be written ...
y = m(x -h) +k . . . . . for a line with slope m through point (h, k)
Using the given values, this is ...
y = (3/2)(x -6) -1 = 3/2x -9 -1
y = 3/2x -10 . . . . . slope-intercept equation
