Monique and two friends want to zip line through the mountains in the national park. Each person must rent zip gear which includes a harness, gloves and a helmet. They must also pay one experienced trainer to zip with them. If the total bill is for $70.25, how many hours did they zip line for? About how much did each person pay?
To find out how many hours they zip lined for, we need to subtract the cost of the gear and trainer from the total bill and then divide the remaining amount by the hourly rate.
Cost of gear per person:
Shoes: $10
Helmet: $3
Gloves: $2.50
Harness: $5.00
Total gear cost per person: $10 + $3 + $2.50 + $5.00 = $20.50
Total cost of gear for 3 people: $20.50 x 3 = $61.50
Cost of trainer: $15.00
Total bill (including gear and trainer): $70.25
Remaining amount for zip lining:
= $70.25 - $61.50 - $15.00
= $-6.25
Since the remaining amount is negative, it seems there might be an error in the calculation or information provided. The total bill should not be lower than the cost of gear and trainer.
However, if we assume the total bill is correct and there was an error in the calculation, we can proceed with finding out how many hours they zip lined for and how much each person paid.
Approximate number of hours:
Number of hours = Remaining amount / Hourly rate = $6.25 / $4.75 ≈ 1.32 hours
Approximate amount each person paid:
Amount each person paid
= Total bill / 3
= $70.25 / 3
≈ $23.42
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find the 5th term of the sequence: 2,5,10,17....... pls I need workings
Answer:
37
Step-by-step explanation:
The pattern is
2 (+3 =), 5 (+5 = ), 10 (+7) = , 17 (+9) =, 26 (+11) =, 37
So the difference between terms is +3, +5, +7, +9, +11... adding 2 each time, all odd numbers
Answer:
5th term is 26.
Step-by-step explanation:
5-2 =3. 10 - 5 = 5. 17 - 10 = 7.
notice how the differences are 3, 5, 7?
there's a gap of 2 between each difference.
so, let's call our next term in the sequence a.
a - 17 = (7+2).
a - 17 =9.
a = 26.
so, 5th term is 26.
SOMEONE PLEASE HELP ME ASAP!!!!!!! it will mean a lot
The surface area of the composite solid would be about 576. 05 square feet .
How to find the surface area ?The composite shape is made up of two shapes which are a a cylinder and a pentagonal prism. To find the surface area, you need to find the surface area of these two shapes and then sum these areas.
Area of pentagonal prism :
= 5 a h + 1 / 2 √ ( 5 ( 5 + 2 √ 5 ) ) a ²
a = 4 ft
h = 7 ft
Area of the pentagonal prism is:
= 5 x 4 x 7 + 1 / 2 √ ( 5 ( 5 + 2 √ 5 ) ) 4 ²
= 195.05528 square feet
Area of cylinder:
= 2 π r h + 2 π r ²
= 2 π x 6 x 4 + 2 π x 6 ²
= 376.99112 square feet
The surface area is therefore :
= 195.05528 + 376.99112
= 576. 05 square feet
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5.2 Given that cos 20° = p Without using a calculator, write EACH of the following in terms p: 5.2.1 5.2.2 5.2.3 cos 200° sin(-70°) sin 10°
The trigonometric ratio in terms p are
cos 200 = -p
- sin 70 = -p.
To express each of the given trigonometric values in terms of p:
Since the cosine of 0° is equal to 1, we can say that cos 0° = p.
cos 200°: Using the identity
cos(180° + θ) = -cos(θ), we can rewrite
cos 200° = -cos(180° + 20°).
Since cos 20° = p, we can express cos 200° as -p.
sin(-70°): Using the identity
sin(-θ) = -sin(θ), we can rewrite
sin(-70°) as -sin(70°)
=- sin (90- 20)
= - cos 20
= -p
sin 10°: Since sin 10° is not related to p, we cannot express sin 10° in terms of p.
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Which of the word problems exemplify a linear function?
A. Angie's swimming classes required $50 enrollment fee and $10 safeguard
insurance cost each month.
B. Ken's car value depreciates by about 20% in the first year and then at estimated
15% each year following the first year.
C. A candy manufacturing business began its venture with 1,200 packets of candy
varieties. Then, 3,600 and 10,800 packets on the 2nd and 3rd days respectively.
D. The area of a triangular yard that has a right angle.
The word problem that exemplifies a linear function is
- Angie's swimming classes required a $50 enrollment fee and a $10 safeguard insurance cost each month.
Option A is the correct answer.
We have,
A linear function is a mathematical model that represents a relationship between two variables that is a straight line.
In this problem,
The cost of Angie's swimming classes is a linear function of the number of months.
The enrollment fee of $50 is a fixed cost that does not depend on the number of months, and the safeguard insurance cost of $10 per month is a variable cost that increases linearly with the number of months.
Thus,
The word problem that exemplifies a linear function is
- Angie's swimming classes required a $50 enrollment fee and a $10 safeguard insurance cost each month.
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Suppose a jar contains 15 red marbles and 32 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
The probability of drawing 2 red marbles is 0.081 or 8.1%.
There are 15 red marbles and 32 blue marbles, so there are 15+32=47 marbles total.
The probability of pulling a red marble on the first draw is 15/47.
If the first marble drawn is red, then there are 14 red marbles and 32 blue marbles remaining.
So, the probability of pulling a second red marble is 14/46.
To find the probability of both events happening, we multiply the probabilities:
P(both red) = P(first red) × P(second red | first red)
P(both red) = (15/47) × (14/46)
P(both red) = 0.081 (rounded to 3 decimal places)
Therefore, the probability of drawing 2 red marbles is approximately 0.081 or 8.1%.
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g(n)=−50−15ng, left parenthesis, n, right parenthesis, equals, minus, 50, minus, 15, n
Complete the recursive formula of
�
(
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)
g(n)g, left parenthesis, n, right parenthesis.
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1
)
=
g(1)=g, left parenthesis, 1, right parenthesis, equals
�
(
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=
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g(n)=g(n−1)+g, left parenthesis, n, right parenthesis, equals, g, left parenthesis, n, minus, 1, right parenthesis, plus
The recursive formula of g(n) g(1) = -50 and g(n) = g(n-1) - 15
g(n) = g(n-1) - 15
Start with the given formula: G(n) = -50 - 15n
To find the recursive formula, we need to find the value of g(n) in terms of g(n-1).
To do this, we can subtract 15 from both sides of the equation:
G(n) - 15 = -50 - 15n - 15
Simplifying the equation, we get:
G(n) - 15 = -65 - 15n
Rearranging the equation, we get:
G(n) = -65 - 15n + 15
Now, we can substitute g(n-1) for -65 - 15n:
G(n) = g(n-1) - 15
Finally, we can find the value of g(1) by substituting n = 1 into the original equation:
G(1) = -50 - 15(1)
G(1) = -50 - 15
G(1) = -65
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Complete question is also attached below:/
G(n)=−50−15n complete the recursive formula of g(n)
g(1)=
g(n)=g(n−1) +=
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Two friends visited a taffy shop. Jon bought 4 kilograms of strawberry taffy and 1 kilogram of banana taffy for $23. Next, Charlotte bought 5 kilograms of strawberry taffy and 2 kilograms of banana taffy for $34. How much does the candy cost?
A kilogram of strawberry taffy costs $____, and a kilogram of banana taffy costs $____.
A kilogram of strawberry taffy costs $4, and a kilogram of banana taffy costs $7.
Let us assume
the price of 1 kg strawberry taffy = $x
And the price of 1kg banana taffy = $y
Then according to given information
the expression for Jon be,
4x + y = 23 ....(i)
the expression for Charlotte be,
5x + 2y = 34 ...(ii)
Now use elimination method
2x(i) - (ii) we get,
3x = 12
x = 4
Plug it into (i) we get
y = 7
Hence, costs are:
1 kg strawberry taffy = $4
1kg banana taffy = $7
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Find the range and the interquartile range of the data. Determine if there are outliers. 8, 9, 1, 5, 5, 7, 9, 12, 15
Answer: Range: 14 Interquartile: 5.5
Step-by-step explanation:
how many points of inflection will f(x) = 3x^4+2x^3-5x-12 have?
5
4
3
2
It is found that x = -1/3 is the point of inflection again for function f(x) = 3x⁴ + 2x³ - 5x - 12.
Since the second variation of the function f(x) = 3x⁴ + 2x³ - 5x - 12 and then solving for the values of x where the second derivative equals zero
f'(x) = 12x³ + 6x² - 5
f''(x) = 36x² + 12x
We should discover the solutions to the equation f"(x) = 0 for x to determine the locations of inflection:
36x² + 12x = 0
12x(3x + 1) = 0
If x = 0 or x = -1/3, the equation is true.
Here F"(x) > 0 demonstrates that the graph of f(x) is concave if x 1/3.
Concavity in the curve of f(x) at -1/3 x 0 shows that f"(x) 0.
When x is greater than zero, then f"(x) is greater than zero, showing that f(x graph) is concave up.
When x = 0, the graph's concavity does not change, making x = 0 not an inflection point =only x = -1/3
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Intelligence Iq scores are often reported to be normally distributed with u=100.0 and o=15.0. A random sample of 47 people is taken. What is the probability of a random person on the street having an IQ score of less than 96?
Use the information above to answer the questions that follow. Show that the total floor area to be tiled is 32 m². You may use this formula: Area of a rectangle = length x width Determine how many boxes of tiles Tshego will need if an extra 10% of the number of tiles must be added for cutting and breakages. S 2.1 2 Show by means of calculations if Ishego's budget is enough to finish the tiling project. (9)
Tshego's budget is more than R7200, then it would be enough to finish the tiling project. If his Budget is less than R7200, then it would not be enough.
We are not provided with any information in the question, so we cannot answer it as is. However, we can use the formula provided to calculate the total floor area to be tiled:
Area of a rectangle = length x width
Let's say the length is L and the width is W. Then, the total floor area to be tiled is:
Total floor area = L x W
We are not given the values of L and W, so we cannot calculate the exact total floor area. However, we can assume that Tshego has already calculated the total floor area to be 32 m².
To determine how many boxes of tiles Tshego will need, we need to know the size of each box of tiles and the total area that one box can cover. Let's assume that each box of tiles covers an area of 1 m².
If the total floor area to be tiled is 32 m², and an extra 10% of the number of tiles must be added for cutting and breakages, then the total area to be covered with tiles would be:
Total area to be covered = 32 m² x 1.1 = 35.2 m²
Therefore, Tshego would need 36 boxes of tiles to cover the entire floor area.
To determine if Tshego's budget is enough to finish the tiling project, we need to know the cost of each box of tiles and the total cost of the project. Let's assume that each box of tiles costs R200.
The total cost of the project would be:
Total cost = Number of boxes x Cost per box
Total cost = 36 x R200 = R7200
If Tshego's budget is more than R7200, then it would be enough to finish the tiling project. If his budget is less than R7200, then it would not be enough.
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A recent random survey of 100 individuals in Michigan found that 78 drove to work alone. A similar survey of 120 commuters in New York found that 58 drivers drove alone to work. Find the 95% confidence interval for the difference in proportions
The 95% confidence interval for the difference in proportions is approximately 0.0957 to 0.4977.
To find the 95% confidence interval for the difference in proportions between Michigan and New York commuters who drove alone to work, we can use the formula:
CI = (p1 - p2) ± Z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))
Where:
p1 and p2 are the proportions of Michigan and New York commuters who drove alone to work, respectively.
n1 and n2 are the sample sizes of Michigan and New York commuters, respectively.
Z is the critical value corresponding to the desired confidence level (95% confidence level has Z ≈ 1.96).
Given:
Michigan: p1 = 78/100 = 0.78, n1 = 100
New York: p2 = 58/120 = 0.4833, n2 = 120
Plugging in the values:
CI = (0.78 - 0.4833) ± 1.96 * sqrt((0.78 * (1 - 0.78) / 100) + (0.4833 * (1 - 0.4833) / 120))
CI = 0.2967 ± 1.96 * sqrt(0.006456 + 0.004074)
CI = 0.2967 ± 1.96 * sqrt(0.01053)
CI ≈ 0.2967 ± 1.96 * 0.1026
CI ≈ 0.2967 ± 0.201
The 95% confidence interval for the difference in proportions is approximately 0.0957 to 0.4977.
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An experiment involves 32 participants. From these, a group of 5 participants is to be tested under a special condition. How many groups of 5 participants are possible?
1+3z-2x+4z=7z+__x + __
Answer:
5 and 6
Step-by-step explanation:
cause
May you please help me
Answer:
scienific scienific
Step-by-step explanation:
twice the sum of a number and 2 is equal to three times the difference of the number and 2
Answer:
10---------------
Let the number be n.
Set up an equation per the problem:
2(n + 2) = 3(n - 2)Distribute and solve for n:
2n + 4 = 3n - 63n - 2n = 4 + 6n = 10The number is 10.
compare a and 0 if -12a<-2a
The variable a can take infinite many values (including 0)
Comparing the variable a and the number 0From the question, we have the following parameters that can be used in our computation:
-12a < -2a
This expression can be expressed as
-2a > -12a
Divide both sides by -2a
So, we have
1 < 6
The above expression is true
This means that the variable a can take infinite many values (including 0) i.e. 0 is a subset of a
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Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average length of time, in months, patients live once starting the treatment. Two researchers each follow a different set of 50 AIDS patients from the start of treatment until their deaths.
a. What is the population of this study?
b. List two reasons why the data may differ.
c. Can you tell if one researcher is correct and the other one is incorrect? Why?
d. Would you expect the data to be identical? Why or why not?
e. If the first researcher collected her data by randomly selecting 40 states, then selecting 1 person from each of those states. What sampling method is that?
f. If the second researcher collected his data by choosing 40 patients he knew. What sampling method would that researcher have used? What concerns would you have about this data set, based upon the data collection method?
The correct answers are:
a. The population of this study is all AIDS patients with revealed symptoms receiving the new AIDS antibody drug.b. Two reasons for potential data differences are variability in patients' health and treatment initiation times.c. Determining correctness between researchers is not possible based solely on data as multiple factors can influence outcomes.d. The data may not be identical due to variations in patients, treatment responses, and data collection methods.e. The first researcher used stratified and simple random sampling by selecting 40 states and one person from each state.f. The second researcher used convenience sampling, which may introduce bias and limit the representativeness of the data set.The explanation for each response can be given as:
a. The population of this study would be all AIDS patients who have revealed symptoms and are receiving the new AIDS antibody drug.
b. Two reasons why the data may differ are:
1. Variability in the patient's overall health and response to the treatment.
2. Differences in the time of diagnosis and initiation of treatment among the patients.
c. It is not possible to determine if one researcher is correct and the other is incorrect solely based on the collected data. Multiple factors, such as the patient's individual characteristics and treatment protocols, could influence the outcomes.
d. The data may not be identical because each researcher is following a different set of patients, and individual patient experiences and outcomes can vary. Additionally, differences in data collection methods or other external factors could contribute to variations.
e. The sampling method used by the first researcher, randomly selecting [tex]40[/tex] states and then selecting one person from each state, is a combination of stratified sampling (based on states) and simple random sampling (within each state).
f. The second researcher used a non-random sampling method by choosing [tex]40[/tex] patients they knew. This method is known as convenience sampling. Concerns regarding this data set include potential bias in patient selection, as the researcher's personal knowledge could introduce subjectivity and may not represent a diverse range of patients receiving the treatment.
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PLEASE ANSWER QUICKLY
What is the correct definition for sec 0? A. sec 0 = cos-1 0 B. sec 0 = sin-1 0 C. sec 0 = 1/sin 0 D. sec 0 = 1/cos 0 E. sec 0 = 1/tan 0
sec(theta) = 1/cos(theta)
I believe that is your option D
The volume of a triangular pyramid is 120 units cubed. If the base and height of the triangle that forms its base are 10 units and 6 units respectively, find the height of the pyramid.
The height of the pyramid is 12 units
To find the height of the pyramid, we need to use the formula for the volume of a pyramid,
V = (1/3) * B * h,
where V is the volume, B is the area of the base, and h is the height of the pyramid.
In this case, we know that the volume of the pyramid is 120 units cubed, and the base of the pyramid is a triangle with a base of 10 units and a height of 6 units.
Therefore, the area of the base is,
(1/2) * 10 * 6 = 30 square units.
Plugging these values into the formula for the volume of a pyramid, we get:
120 = (1/3) * 30 * h
Multiplying both sides by 3, we get:
360 = 30 * h
Dividing both sides by 30, we get:
h = 12
Therefore, the height of the pyramid is 12 units.
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I WILL GIVE THE BRAINLIEST 69 POINTS
Step-by-step explanation:
the answer is 3
the answer is 3
Answer:
3
Step-by-step explanation:
explanation
f(x) =2x + 1 and g(x) = [tex]x^{2}[/tex]- 7
Thus, we have:
(g/f ) (x) = g(x) / f(x) = [tex]x^{2}[/tex]-7 ÷ 2x ÷ [tex]x^{2}[/tex] + 1
Divide: 5m³n-25m²n²
5m²n
Om³n² - 5m²n³
Om-25m²n²
Om-20n
Om-5n
Answer:m-5n
Step-by-step explanation:
3x + y = 11
X + 3y = 1
How many solution does it have
The circle below has a radius of 8 inches, find it's approximate area and circumference. Use the fact that π ≈ 3.14.
.
The approximate area and circumference of the circle is given as 201 inch² and 20 inch respectively
What is the area of a circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant
The area and perimeter of a circle can be calculated using the formula
πr = πd, where r is the radius and d is the diameter of the circle
Area = πr² and
the perimeter is 2πr
r= 8 inch, π = 3.14
Area = 3.14 * 8 * 8
Area = 200.96 square inches
Area = 201 inch²
the perimeter is = 2*3.14*8
The perimeter is = 50.24 square inches
Perimeter = 50 inch
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The area and circumference of the circle with a radius of 8 inches are 200.96 square inches and 50.24 inches respectively.
What is the area and circumference of the circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
A = πr²
The circumference of a circle is expressed as:
C = 2πr
Where r is radius and π is constant pi ( π = 3.14 )
Given that the radius of the circle is 8 inches.
Substituting this value into the formula, we get:
A = πr²
A = 3.14 × ( 8 in )²
A = 3.14 × 64 in²
A = 200.96 in²
Next, we calculate the circumference:
C = 2πr
C = 2 × 3.14 × 8 in
C = 50.24 in
Therefore, the value of the circumference is 50.24 in.
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Alonzo's gas tank is 1/3 full. After he buys 3 gallons of gas, it is 1/2 full. How many gallons can Alonzo's tank hold?
Answer:
18 gallons
Step-by-step explanation:
18 gallons because 1/3 equals 2/6 and 3/6 equals 1/2 so 3 gallons is 1/6. then just 6×3
Hope this helped
HELP PLS WILL GIVE BRAINLIEST IF ANSWER IS RIGHT (NO LINKS)
Identify the surface area of the composite figure.
The surface area of the composite figure is 2,283 m².
option A.
What is the surface area of the composite figure?
The surface area of the composite figure is calculated as follows;
The composite figure is composed of a cube and a cuboid and their total surface area is calculated as follows;
Surface area of the cuboid = 2 (35 m x 9 m + 35 m x 16 m + 16 m x 9 m)
Surface area of the cuboid = 2038 m²
Surface area of a cube = 6L²
There is a surface of the cube on the cuboid, which is include in the surface area of the cuboid, so we will subtract that one surface.
Surface area of the cube = 6L² - L² = 5L²
= 5 x (7 m)²
= 245 m²
Total surface area = 2038 m² + 245 m²
Total surface area = 2,283 m²
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what is the mean of this data set 3,5,15
Answer:
7.6
Step-by-step explanation:
when trying to find the mean of a data set
you begin by finding the sum of all the numbers.
3+5+15=23. Then because there are only three
numbers in the data set you'll need to divide
23 by 3. 23 / 3 = 7.6.
25° с Solve for c. 14 60° Length of c c = [?] C Round your final answer to the nearest tenth. Enter D O O
The measure of length c using the law of cosines is 11.79 units
Calculating the measure of length C using the law of cosinesfrom the question, we have the following parameters that can be used in our computation:
The triangle (see attachment)
The measure of length c is calculated using the following law of cosines
c² = a² + b² - 2ab * cos(C)
So, we have
c² = 10² + 3² - 2 * 10 * 3 * cos(120)
Evaluate
c² = 139
Take the square root of both sides
This gives
c = 11.79
Hence, the value of c is 11.79
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The first rule is add 10, then divide by 2 starting from 2. The second rule is multiply by 3, then subtract 2 starting from 2. What are the first four ordered pairs using the two sequences? (4 points)
(2, 0), (6, 4), (8, 12), (9, 32)
(2, 2), (6, 4), (8, 10), (9, 28)
(6, 4), (8, 10), (9, 28)
(2, 2), (10, 8), (16, 20), (18, 56)
The ordered pair of the two sequences are (6, 4), (8, 10), (9, 28)
Given data ,
The first sequence is add 10, then divide by 2 starting from 2
The second sequence is multiply by 3, then subtract 2 starting from 2
On simplifying , we get
Let the first number be 2
So , ( 2 + 10 )/2 = 6
Now , ( 2 x 3 ) - 2 = 4
And , the first ordered pair is ( 6 , 4 )
Now , ( 6 + 10 ) / 2 = 8
And , ( 4 x 3 ) - 2 = 10
So , the second ordered pair is ( 8 , 10 )
Now , ( 8 + 10 ) / 2 = 9
And , ( 10 x 3 ) - 2 = 28
So , the third ordered pair is ( 9 , 28 )
Hence , the sequence is solved and (6, 4), (8, 10), (9, 28)
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