The exponential function that shows the relationship between the city's population y and the number of years t since the start of the study is [tex]y = 390000 * (1.073)^t[/tex]
Population tends to change with time. It might increase or decrease. Let y be the city's population after t years since the start of the study, and let [tex]Po[/tex] be the initial population at the start of the study. We can use the formula for exponential growth to represent the relationship between y and t:
Final population = Initial population x (growth rate)^years
[tex]y = Po*(1+0.073)^t[/tex]
[tex]y = Po* (1.073)^{(t)[/tex]
Substituting the values in the above equation we get the following equation:
[tex]y = 390,000*(1.073)^t[/tex]
The above function when represented in exponential form will be equal to [tex]y=390,000*(e)^{(0.073t)[/tex]
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Refer to complete question below:
At the beginning of a population study, a city had 390,000 people. Each year since, the population has grown by 7.3% . Let t be the number of years since start of the study. Let y be the city's population. Write an exponential function showing the relationship between y and t .
a restaurant offers a special pizza with any 6 toppings. if the restaurant has 16 topping from which to choose, how many different special pizzas are possible?
To calculate the number of different special pizzas possible with any 6 toppings out of 16, we can use the combination formula:C(16,6) = 16! / (6! * (16-6)!) = (161514131211) / (654321) = 8008
there are 8,008 different special pizzas possible with any 6 toppings out of 16.
To calculate the number of different special pizzas possible with any 6 toppings out of 16, we need to use the combination formula, which is given by:
C(n, k) = n! / (k! * (n - k)!)
where n is the total number of items to choose from, and k is the number of items we want to choose.
In this case, n = 16 (the total number of toppings available), and k = 6 (the number of toppings we want to choose).
Plugging these values into the formula, we get:
C(16, 6) = 16! / (6! * (16 - 6)!)
= (16 * 15 * 14 * 13 * 12 * 11) / (6 * 5 * 4 * 3 * 2 * 1)
= 8008
Therefore, there are 8,008 different special pizzas possible with any 6 toppings out of 16.
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the shortest side of a triangle with angles 50o, 60o, and 70ohas length of 9 furlongs. what is the approximate length, in furlongs, of the longest side?
The longest side of a triangle with angles of 50°, 60°, and 70° and a length of 9 furlongs on the shortest side is approximately 12.2 furlongs.
What is the Law of Cosines?The Law of Cosines is used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two sides and the measure of the included angle are known (SAS) or the lengths of the three sides (SSS) are known.
To calculate this, using the Law of Cosines formula,
which is:
[tex]c^2 = a^2 + b^2 - 2abcosC[/tex]
where c is the longest side, a is the shortest side, b is the other side of the triangle, and C is the angle
between a and b.
In this case, c = 12.2 furlongs,
a = 9 furlongs,
b is the side opposite the angle 70°, and C = 70°.
So the formula becomes:
[tex]c^2 = 92 + b^2 - 2(9)(b)cos70^{o}[/tex]
Solving for b gives us b = 12.2 furlongs, which is the length of the longest side.
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An office building casts a shadow that is 15 feet long. A nearby tree casts a showdown that is 2/5 feet long. If the tree is 5 feet tall how tall is the office building.
The height of the office building is 187.5 feet.
What are some other names for height?It is typically measured horizontally along the X-axis. Height is defined as the distance between the bottom and top of an object. In Geometry, it is sometimes referred to as altitude.
Let's call the office building's height h. We can use a proportion to find h:
height of office building / length of shadow cast by office building = height of tree / length of shadow cast by tree
h / 15 = 5 / (2/5)
The right side of the equation can be simplified as follows:
5/(2/5) = 5 * 5/2 = 12.5
When we plug this into the proportion and solve for h, we get:
h / 15 = 5 / (2/5)
h / 15 = 12.5 \sh = 15 * 12.5 \sh = 187.5
As a result, the office building's height is 187.5 feet.
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the time it takes a person to wash the dishes is uniformly distributed between 8 minutes and 17 minutes. what is the probability that a randomly selected event of washing dishes will take a person between 12 and 15 minutes? round your answer accurate to two decimal places.
The probability that a randomly selected event of washing dishes will take a person between 12 and 15 minutes is 0.33 or 33%.
Uniform distribution is a probability distribution where all outcomes are equally likely. In this case, the time it takes to wash dishes is uniformly distributed between 8 and 17 minutes. This means that any time between 8 and 17 minutes is equally likely to occur.
To find the probability that a randomly selected event of washing dishes will take a person between 12 and 15 minutes, we need to find the area under the curve of the uniform distribution function between 12 and 15 minutes.
Since the distribution is uniform, the area under the curve between 12 and 15 minutes is simply the width of the interval divided by the total width of the distribution. Mathematically, we can express this as:
P(12 ≤ X ≤ 15) = (15 - 12) / (17 - 8)
P(12 ≤ X ≤ 15) = 3 / 9
P(12 ≤ X ≤ 15) = 0.33 or 33%.
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Solve the system of equations. \begin{aligned} &-4y+11x - 67=0 \\\\ &2y+5x-19=0 \end{aligned}
−4y+11x−67=0
2y+5x−19=0
The solution to the system of equations is x = 5 and y = -3.
We can use the elimination method by multiplying the second equation by 2 and adding it to the first equation to eliminate y:
= -4y + 11x - 67 + 2(2y + 5x - 19) = 0
-4y + 11x - 67 + 4y + 10x - 38 = 0
21x - 105 = 0
Dividing both sides by 21, we get:
x - 5 = 0
So x = 5.
Now we can substitute x = 5 into either of the original equations:
2y + 5x - 19 = 0
2y + 5(5) - 19 = 0
y = -3
Thus, the solution to the system of equations is:
x = 5, and y = -3.
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Find the surface area of a rectangular prism
The surface area of this rectangular prism is equal to 68 mm².
How to calculate the surface area of a rectangular prism?In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:
SA = 2(WH + LW + LH)
Where:
SA represents the surface area of a rectangular prism.L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given parameters into the formula for the surface area of a rectangular prism, we have the following;
SA = 2(1 × 4 + 6 × 1 + 6 × 4)
SA = 2(4 + 6 + 24)
SA = 2(34)
SA = 68 mm².
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4. Alex wants to go Go Karting. There are two options for pricing:
i. $30 for 25 laps
or ii. $75 for 2 hours.
a) Convert each to UNIT RATES.
The statements when converted to unit rates are $1.20 per lap and $37.50 per hour
How to calculate the unit ratesTo compare the pricing options, we can convert each to a unit rate, which is a rate with a denominator of 1.
This allows us to compare the cost of each option per lap or per hour.
i. $30 for 25 laps:
To find the unit rate, we can divide the total cost by the number of laps:
Unit rate = $30 ÷ 25 laps = $1.20 per lap.
ii. $75 for 2 hours:
To find the unit rate, we can divide the total cost by the number of hours:
Unit rate = $75 ÷ 2 hours = $37.50 per hour.
So, the unit rate for option i is $1.20 per lap and the unit rate for option ii is $37.50 per hour.
By comparing the unit rates, we can determine which pricing option is more cost-effective based on the number of laps or hours Alex wants to ride.
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At Rachel's 11th birthday party, 8 girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the jumping would not affect their times, on average. Test their hypothesis at the 5% level. Relaxed time (seconds) Jumping time (seconds) 27 20 49 43 31 28 22 21 23 25 45 43 37 35 29 32 NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) What is the p-value? (Round your answer to four decimal places.)
The p-value is (0.0297)
To test the hypothesis that jumping does not affect the girls' breath-holding times, we will conduct a paired t-test using the given data. Here's a step-by-step explanation:
Solution:
1. Calculate the difference between relaxed and jumping times for each girl:
(27-20), (49-43), (31-28), (22-21), (23-25), (45-43), (37-35), (29-32)
The differences are: 7, 6, 3, 1, -2, 2, 2, -3
2. Compute the mean and standard deviation of the differences:
Mean = (7+6+3+1-2+2+2-3)/8 = 16/8 = 2
Standard Deviation = sqrt[((7-2)^2+(6-2)^2+(3-2)^2+(1-2)^2+(-2-2)^2+(2-2)^2+(2-2)^2+(-3-2)^2)/7] = sqrt(42/7) = sqrt(6)
3. Calculate the t-statistic:
t = (Mean - Hypothesized Mean) / (Standard Deviation / sqrt(N))
t = (2 - 0) / (sqrt(6) / sqrt(8)) = 2 / (sqrt(6) / 2.828) ≈ 2 / 0.748 ≈ 2.675
4. Determine the p-value using the t-distribution table or calculator for a two-tailed test with 7 degrees of freedom (N-1) at the 5% level:
The p-value is 0.0297 (rounded to four decimal places).
Since the p-value (0.0297) is less than the significance level of 0.05, we reject the null hypothesis that jumping does not affect the girls' breath-holding times, on average.
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How long is each side of the box if the volume is 1,000,000?
Step-by-step explanation:
[tex]volume = {x}^{3 \\} \\ so \: 1000000 = {x}^{3 \\} \\ x = \sqrt[3]{1000000} \\ x = 100[/tex]
X-y=1/5 in slope-intercept form
The equation in slope- intercept form is y = x - 1/5
How to write the expressionIt is important to note that the expression representing the equation of a line in slope- intercept form is written as;
y = mx + c
Such that the parameters are;
y is a point on the y - axis of the graph.m is the slope of the line.x is a point on the x - axis.c is the intercept on the y -axis of the graph.From the information given, we have;X-y=1/5collect the variables and constants, we have;
- y = 1/5 - x
reconstruct the expression
- y = -x + 1/5
Divide both sides by the coefficient of y , we have;
y = x - 1/5
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in a baseball league of 10 teams, how many games are needed to complete the schedule if each team plays 11 games with each other?
at 3:25 p.m., two trains left kalamazoo, michigan. one train traveled westward at a constant rate of
When they are 111 miles apart, the current time is 4:10 p.m.
If the time taken for two trains to be apart by 111 miles by "t" time.
Then at that time, t, the train which is at 82 mph, should have traveled a distance of 82T miles.
d1 = 82t
At the same time, t, the train which is at 66 mph, should have traveled a distance of 66T miles.
d2= 66t
The total distance traveled by both trains is d1 + d2 = D
D = 82t + 66t
D = 148t
From the given data, D = 111
Hence, 148t = 111
Solving the equation, the time t
t = 111÷148
t = 0.75
Converting it into minutes,
t = 0.75*60
t = 45 mins.
The current time ( T ) = the time at which both the trains left ( t1 ) + 45 mins.
T = t1+t
T = 3:25 + 45 min.
T =4:10 pm
Therefore, the current time is 4:10 p.m
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The complete question is-
At 3:25 p.m., two trains left Kalamazoo, Michigan. one train traveled westward at a constant rate of 82 miles per hour, while the other traveled eastward at a constant rate of 66 miles per hour. if they are now 111 miles apart, what time is it now? show your work on how you solved this situation.
you have six bottles of paroxetine 10 mg in stock. the par level is four bottles, and the maximum quantity is ten bottles. how many bottles should be ordered?
The order quantity should be 4 bottles.
There are 6 bottles of paroxetine 10 mg in stock, and the par level is 4 bottles, while the maximum quantity is 10 bottles. The question is asking how many bottles should be ordered.
This can be found by calculating the difference between the current stock level and the par level and then adding this difference to the current stock level. If the result exceeds the maximum quantity, the order quantity is equal to the difference between the maximum quantity and the current stock level.
Otherwise, the order quantity is equal to the difference between the current stock level and the par level.In this case, the difference between the current stock level and the par level is 6 - 4 = 2 bottles. Adding this difference to the current stock level gives us a total of 6 + 2 = 8 bottles.
Since 8 is less than the maximum quantity of 10, the order quantity is 8 - 4 = 4 bottles. Therefore, 4 bottles should be ordered to maintain the par level of 4 bottles. Therefore, the order quantity should be 4 bottles.
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from the position of the bus on the street, the l'arc de triomphe is at an angle of 34 degrees. if the arc is 162 feet tall, how far away is the bus? round to the nearest tenth.
The bus is approximately 373.8 feet away from the base of the l'Arc de Triomphe
To solve this problem, we can use trigonometry. Let's assume that the bus is at point A on the street, and the top of the l'Arc de Triomphe is at point B. The height of the arc is 162 feet.
We want to find the distance AB, which is the horizontal distance from the bus to the base of the arc. We know that the angle of elevation from the bus to the top of the arc is 34 degrees. Let's call the height of the bus H, and the distance AB D.
From the perspective of the bus, we can see that the height of the arc and the height of the bus together form a right triangle with angle of elevation 34 degrees. Therefore, we have:
tan(34) = (162 + H)/D
We can solve this equation for D:
D = (162 + H)/tan(34)
We need to find H to solve for D. To do this, we can use similar triangles. The triangle formed by the bus, the base of the arc, and the top of the arc is similar to the triangle formed by the bus, the ground, and the point directly beneath the top of the arc. Let's call the distance from the base of the arc to the point directly beneath the top of the arc x.
From the perspective of the bus, we can see that the height of the arc and the distance from the base of the arc to the point directly beneath the top of the arc together form a right triangle with angle of elevation 34 degrees. Therefore, we have:
tan(34) = 162/x
Solving for x, we get:
x = 162/tan(34)
Now, the height of the bus is simply H = x*tan(34). Substituting this into the equation for D, we get:
D = (162 + x*tan(34))/tan(34)
Substituting the value of x, we get:
D = (162 + (162/tan(34))*tan(34))/tan(34) = 373.8 feet (rounded to the nearest tenth)
Therefore, the bus is approximately 373.8 feet away from the base of the l'Arc de Triomphe.
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What is the value of k?
127.3°
0.
Ryan checked out 3 books from the library: one mystery (M), one history book (H), and one biography (B). Which tree diagram shows all the possible orders in which Ryan can read the 3 books?
...
This tree diagram shows all possible orders in which Ryan can read the 3 books, including reading the mystery book (M) first, the history book (H) second, and the biography (B) last, as well as reading the biography first, the mystery second, and the history last.
What is mystery?Mystery is an intriguing and often baffling phenomenon or situation. It is something that is not easily explained or understood and often involves a puzzle or secret that needs to be solved. It can be an event, an entity, or a situation that evokes curiosity, suspense, and a desire to uncover the truth. Mystery can be found in everyday life, literature, films, and other forms of entertainment. It is often used to create a sense of anticipation and wonder, and can be a powerful tool in storytelling. Mystery can also be used to explore deeper truths and to connect with our own inner mysteries.
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Complete Question is attached below:
If you flipped a coin 550 times, how many times would you expect it to land on heads?
Answer:
275
Step-by-step explanation:
You have a 1 in 2 chance
550/2
275 times
The function g(x) is shown on the graph.
The graph shows an upward opening parabola with a vertex at negative 3 comma negative 2, a point at negative 5 comma 2, and a point at negative 1 comma 2.
What is the equation of g(x) in vertex form?
g(x) = (x − 3)2 − 2
g(x) = (x − 3)2 + 2
g(x) = (x + 3)2 − 2
g(x) = (x + 3)2 + 2
The equation of g(x) in vertex form include the following: C. g(x) = (x + 3)² - 2.
What is the vertex form of a quadratic equation?In this exercise, you are required to determine the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the graph of this quadratic function, we can reasonably infer and logically deduce that a mathematical expression which quickly reveals the vertex of the quadratic function is given by:
y = a(x - h)² + k
y = (x - (-3))² + (-2)
y = g(x) = (x + 3)² - 2
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nug
a vat with 900 gallons of beer contains 4% alcohol (by volume). beer with 6% alcohol is pumped into the vat at a rate of 9 gal/min and the mixture is pumped out at the same rate. what is the percentage of alcohol after an hour? (round your answer to one decimal place.)
The percentage of alcohol in the vat after an hour will be 4.8%.
Explanation:
Given that a vat with 900 gallons of beer contains 4% alcohol (by volume), beer with 6% alcohol is pumped into the vat at a rate of 9 gal/min and the mixture is pumped out at the same rate. We need to find the percentage of alcohol after an hour.
Let's consider V be the volume of the vat and x be the percentage of alcohol in the vat. Now, the total amount of alcohol in the vat will be Vx.
Let A be the volume of alcohol added in the vat per minute by the pump. Now the volume of alcohol in the vat after a minute will be Vx + A and the volume of the mixture will be V+ 9.
Now the volume of alcohol in the mixture will be (Vx + A)×(x%) and the total amount of alcohol in the mixture will be Vx(x%) + 9A×(6%).
So, the volume of alcohol in the mixture after a minute will be (Vx(x%) + 9A×(6%))/(V + 9).
The rate of change of x will be given by (Vx(x%) + 9A×(6%))/(V + 9) - x/(V + 9). On solving this we get the differential equation:
dx/dt = 0.06 - 0.000067x
On solving the differential equation we get:
x = 80 + 8200/(75e^(0.000067t))
At t = 60 minutes, x = 80 + 8200/(75e^(0.000067×60)) = 4.8%.
Therefore, the percentage of alcohol in the vat after an hour will be 4.8%.
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what is the smallest font size doug should use in the text on his slides? group of answer choices 20 points 24 points
The smallest font size that Doug should use in the text on his slides is 24 points.
The reason for this is that smaller font sizes can make the text difficult to read, especially from a distance.
According to industry standards, the recommended minimum font size for slide presentations is 24 points.
This is because smaller font sizes can be challenging to read, especially if the audience is sitting at the back of the room or if the slides are being viewed on a small screen.
While 20 points may seem like a reasonable font size, it's still small enough to make it difficult for some people to read the text.
Therefore, to ensure that all members of the audience can read the text on the slides, it's best to use a font size of at least 24 points.
In addition to using a larger font size, it's also essential to use a clear and legible font.
Sans-serif fonts such as Arial, Helvetica, or Calibri are recommended for presentations as they are easy to read, even from a distance.
It's also important to keep the contrast between the text and the background high to make it easier to read the text.
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please help dude i have no clue what to do
Answer:94.2
Step-by-step explanation: here is a answer i think
Answer:
C= 94.2
Step-by-step explanation:
To find the circumference you would multiply 15 and 2 and then multiply that answer by pi, or 3.14.
Decide if each of the following is a minor arc, major arc, or semicircle by circling the correct answer .
Answer:
Step-by-step explanation:
minor, semi, minor, major (in that order)
minor is smaller than a semi-circle while major is larger than a semi-circle.
Solve for x (please help me with this I’m willing to give 20 points)
Answer:
75°
Step-by-step explanation:
The angle in the given figure is 90°.
x + 15 = 90
x = 90 - 15
x = 75°
Grace plans on going to the amusement park this Friday. It costs $10.00 to enter the park, and then $2.50 for every ride that Grace goes on. What will be the total cost if Grace goes on 7 rides?
Answer: 27.50
Step-by-step explanation: 2.50 X 7 =17.50 + 10 = 27.50
AP Statistics Hypothesis Testing
The average amount of rainfall in the Amazon Rainforest for a year is recorded to be normally distributed with a
mean of 200 cm. Twelve regions in the Amazon Rainforest are randomly sampled. The total yearly rainfalls, in
centimeters, for these regions were reported as follows:
188 232 210 198 202. 193. 219. 202, 252, 156, 184, 222
Do this data provide sufficient evidence that the annual rainfall in the Amazon rainforest is different than 200 cm?
Therefore, based on this collection of data during a significance level of 0.05, there is insufficient proof to draw the conclusion that the average annual precipitation in the Amazonian rain forest is less than 200 cm.
What kind of hypothesis would you use?Hypothesis The amount of pleasure increases with daily solar exposure. The presumed reason in this case and the factor that is independent is sun exposure. The expected impact, or dependent variable, is the degree of happiness.
To determine if the data provide sufficient that the annual rainfall in the Amazon rainforest is different than 200 cm, we can perform a hypothesis test with the following hypotheses:
Null hypothesis: The true mean annual rainfall in the Amazon rainforest is equal to 200 cm.
Alternative hypothesis: The true mean annual rainfall in the Amazon rainforest is different than 200 cm.
We can use a two-sided t-test with a significance level of 0.05 to test this hypothesis.
We must first determine the population mean and standard variation.
x = (188 + 232 + 210 + 198 + 202 + 193 + 219 + 202 + 252 + 156 + 184 + 222)/12 = 202.17 cm
Sample standard deviation, s = 26.770 cm
Next, we can calculate the t-statistic:
t = (x - μ) / (s / sqrt(n)) = (202.17 - 200) / (26.770 / sqrt(12)) = 0.491
Using a t-distribution table with 11 degrees of freedom (n-1), at a significance level of 0.05, we find the critical values to be ±2.201. Since the calculated t-statistic of 0.491 is within the range of -2.201 to 2.201, we fail to reject the null hypothesis.
Therefore, there is not sufficient evidence to conclude that the annual rainfall in the Amazon rainforest is different than 200 cm based on this sample data at a significance level of 0.05.
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find value of 0 for which the statement is true. sin = cos (0 + 60°)
Answer:
KN bisects <K calculate MN
if 2400 dollars is invested in an account for 10 years. find the value of the investment at the end of 10 years if the interest is:
The value of the investment at the end of 10 years would be $3,905.76 if the interest rate is 5% per year and compounds annually.
The value of an investment after a certain number of years depends on several factors, including the initial amount invested, the interest rate, and the compounding frequency.
Assuming a fixed interest rate and compounding frequency, we can use the formula for compound interest to calculate the value of the investment after 10 years.
For example, if the interest rate is 5% per year and the investment compounds annually, the formula would be:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
Plugging in the given values, we get:
A = 2400(1 + 0.05/1)^(1*10)
A = 2400(1.05)^10
A = 2400(1.6289)
A = $3,905.76
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PLEASE HELP FOR 20 POINTS!
Which expression is equivalent to 1/2 x -1
A. 1/3(3/2 x -1)
B. 2/3(3/2 x - 3/2)
C. -2/3(3/2 - 3/4x)
D. -2/3(-3/4 x - 3/2
Tammy said the product of 5/7
and 1 1/4
is 1 3/4
.
How can you tell that this answer is wrong?
Answer:
Step-by-step explanation:
To determine if Tammy's answer of 1 3/4 for the product of 5/7 and 1 1/4 is correct, we can perform the multiplication ourselves.
First, we need to convert 1 1/4 to an improper fraction:
1 1/4 = (4 x 1 + 1)/4 = 5/4
Then, we can multiply the fractions:
5/7 x 5/4 = 25/28
As we can see, 25/28 is not equal to 1 3/4. Therefore, Tammy's answer of 1 3/4 is incorrect. The correct answer is 25/28, which is an improper fraction. We can also express this as a mixed number: 0 25/28.
Ignore everything above look at bottom of pic for question
The surface area of the triangular prism Milo paints red is equal to 186 square centimeters.
How to evaluate for the surface area of the triangular prismThe triangular prism have two triangle and three rectangle faces, so we shall calculate for each area of the faces and add them to get the surface area of the triangular prism as follows:
area of triangle = 1/2(base × height)
area of one triangle face = 1/2(6 cm × 4 cm)
area of one triangle face = 12 cm²
area of two triangle faces = 2 × 12 cm² =24 cm²
area of one rectangle face = 10.8 cm × 5 cm
area of one rectangle face = 54 cm²
area of three rectangle faces = 162 cm²
area of the triangular prism = 24 cm² + 162 cm³
area of the triangular prism = 186 cm²
Therefore, the surface area of the triangular prism Milo paints red is equal to 186 square centimeters.
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