Answer:
Step-by-step explanation:
This is a word problem involving percentages. To solve it, we need to follow these steps:
Identify the given information and the unknown quantity. In this problem, we are given that Natalie has $330 to spend at the amusement park, 5% is spent on games, 5/11 is for food and drinks, and she spends $13 on parking. The unknown quantity is the price of one ticket.
Write an equation that relates the given information and the unknown quantity. We can use the fact that the sum of all parts of the whole is 100%1. Let x be the price of one ticket. Then we have:
games+food and drinks+parking+tickets0.05×330+115×330+13+2x=total amount=330
Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:
16.5+150+13+2x2x2xxx=330=330−16.5−150−13=150.5=2150.5=75.25
Therefore, the price of one ticket is $75.25.
Eve works out every 6 days and Jenna
works out every 4 days. If both Eve and
Jenna work out today, how many days will it
be until they work out on the same day
again?
In 12 days, both Eve and Jenna will work out on the same day again.
Calculating the number of days to work out againTo find the number of days until Eve and Jenna work out on the same day again, we need to find the least common multiple (LCM) of 6 and 4.
One way to find the LCM is to list the multiples of each number until we find a multiple that they have in common:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, ...
From this list, we see that the least common multiple of 6 and 4 is 12.
This means that in 12 days, both Eve and Jenna will work out on the same day again.
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1. Which is the best estimate of
7,625,750,263?
A 7x1010
B 7x10⁹
C 8x10 to power of 10
D 8x10⁹
The best estimate of 7,625,750,263 is 7x10⁹. So the correct option is B.
The given number is 7,625,750,263.
To express the above number in words, it is "seven billion six hundred twenty-five million seven hundred fifty thousand two hundred sixty-three". So, the given value ultimately has a billion value.
To find the correct answer let's see the given options and eliminate each one to find the correct answer. Option A is 7 x 1010 = 7070 which is not even coming to a close, so option A is eliminated.
Let's see the second option which is 7x10⁹ which is 7000000000, which is 7 billion. So, option B is very near to the answer.
Let's see the third option which is 8x10¹⁰ which is 80 billion, it is not an estimated value. So, it is also eliminated and the final option is 8x10⁹ which is 8 billion which is also high value So, it is also eliminated.
From the above analysis, we can conclude that the best estimated value for 7,625,750,263 is 7x10⁹ which is option B.
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PLEASE SOMEONE HELP ME DO THIS MATH PROBLEM
i am having a mental breakdown rnn :(.
Check the picture below.
Pre calculus trigonometry
The result of the division of the two complex numbers is equal to z₁ / z₂ = (8 / 9) · [cos (π / 10 - π / 12) + i sin (π / 10 - π / 12)].
How to find the division of two complex numbers
In this problem we find two complex numbers in rectangular form, whose division must be found. This can done by easily by means of complex numbers in polar form and definition of division:
Complex number (rectangular form)
z = r · (cos θ + i sin θ)
Complex number (polar form)
[tex]z = r\cdot e^{i\cdot \theta}[/tex]
Where:
r - Normθ - DirectionDivision between two complex numbers in polar form:
[tex]\frac {z_{1}}{z_{2}} = \left(\frac{r_{1}}{r_{2}}\right)\cdot e^{i\cdot (\theta_{1}-\theta_{2})}[/tex]
This number is equivalent to the following expression in rectangular form:
z₁ / z₂ = (r₁ / r₂) · [cos (θ₁ - θ₂) + i sin (θ₁ - θ₂)]
If we know that r₁ = 8, r₂ = 9, θ₁ = π / 10 and θ₂ = π / 12, then the division of the two complex numbers is:
z₁ / z₂ = (8 / 9) · [cos (π / 10 - π / 12) + i sin (π / 10 - π / 12)]
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Ignatio and his two friends each bought a ticket to play lazer tag and each spent $15 on game tokens at Fun Mountain. Let t represent the cost of a lazer tag ticket. Enter an expression that represents the total amount that Ignatio and his friends spent.
The expression that represents the total amount that Ignatio and his friends spent is 15t
From the question, we have the following parameters that can be used in our computation:
Each spent $15 on game tokens at Fun MountainEach cost = tAfter spending on t games, we have
f(t) = Rate * t
Substitute the known values in the above equation, so, we have the following representation
f(t) = 15 * t
Evaluate
f(t) = 15t
Hence, the expression that represents the total amount that Ignatio and his friends spent is 15t
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6 yards 2 feet 5 inches equals
Answer:
245 inches
Step-by-step explanation:
Yards->Inches
1 yard = 36 inches
Therefore, 6 yards = 36 x 6 = 216 inches
Feet->Inches
1 feet = 12 inches
Therefore, 2 feet = 2 x 12 = 24 inches
Adding all inches,
=> 216 + 24 + 5
=> 245 inches
The hypotenuse of an isosceles right triangle is 13 centimeters longer than either of its legs. Find the exact length of
each side. (Hint: An isosceles right triangle is a right triangle whose legs are the same length.)
The length of one leg is
the length of the other leg is
(Simplify your answers. Type exact answers, using radicals as needed.)
and the length of the hypotenuse is
The length of the other legs of the isosceles right triangle is 13 + 13√2 centimetres.
How to find the sides of a right triangle?The hypotenuse of an isosceles right triangle is 13 centimetres longer than either of its legs.
An isosceles right triangle is a right triangle whose legs are the same length. The sides of a right triangle can be found using Pythagoras's theorem.
Therefore,
let
y = other legs
Therefore,
(x + 13)² = x² + x²
(x + 13)(x + 13) = 2x²
x² + 13x + 13x + 169 = 2x²
x² - 26x - 169 = 0
Therefore, using the quadratic formula,
[tex]\frac{-b+\sqrt{b^{2} - 4ac } }{2a}[/tex]
where
a = 1b = -26c = -169x = 13 ± 13√2
Therefore, we can only use positive values
x = 13 + 13√2
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where should the linear inequality y ≤ 3/2x + 3 be shaded?
Answer:
Step-by-step explanation:
it should be shaded at the 76
Help pleaseee
Expand the logarithm as much as possible
logy^10
The expanded form of log y^10 is either 10 log y or 10 ln y
Expanding the logarithmAssuming that the base of the logarithm is not specified, we can use the change of base formula to expand the logarithm:
log y^10 = log (y^10) / log (base)
Using base 10:
log y^10 = log (y^10) / log 10
= 10 log y / 1
= 10 log y
Using natural logarithm:
log y^10 = log (y^10) / log e
= 10 log y / 1
= 10 ln y
Therefore, the expanded form of log y^10 is either 10 log y or 10 ln y, depending on the base used.
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A small country emits 80,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by 2.5% per year for the next 7 years. In the first year of the agreement, the country will keep its emissions at 80,000 kilotons and the emissions will decrease 2.5% in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the 7 year period, to the nearest whole number?
Using an exponential function and integration, it is found that over the entire 11 year period, the country will emit 763,968 kilotons of carbon dioxide.
Exponential function:
A decaying exponential function is modeled by:
⇒ A (t) = A (0) (1 - r)ⁿ
In which:
A(0) is the initial value.
r is the decay rate, as a decimal.
In this problem:
In the first year, the country emits 80,000 kilotons, hence . A (0) = 8000
Emissions will decrease 2.5% in each successive year, hence r = 0.026
Then, the equation for the amount emitted each year is:
⇒ A (t) = A (0) (1 - r)ⁿ
⇒ A (t) = 80000 (1 - 0.025)ⁿ
⇒ A (t) = 80,000 (0.975)ⁿ
The total amount emitted over the course of the 11 year period is:
T = ∫ 0 to 11 ( A (t) ) dt
Hence:
T = ∫ 0 to 11 ( 80000 (0.974)ⁿ ) dt
Applying the Fundamental Theorem of Calculus:
T = 763,968 kilotons
Hence, Over the entire 11 year period, the country will emit 763,968 kilotons of carbon dioxide.
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Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle.
questions 1)
m
question 2)
m
question 3)
m
The triangle has one solution. The remaining side c ≈ 4 and remaining angles B = 30°; C = 31°.
Option D is correct.
How to solveif angle A is obtuse and if a > b then the triangle has one solution
We are given ∠ = 119° which is obtuse and side a= 7 and side b - 4 i.e 7>4 so, the triangle has one solution.
Finding remaining sides c and ∠B and ∠C
Using the Law of sines to find ∠B
a/sin A = b/sin B
7/sin 119° = 4/sin B
7 * sin B = 4 * sin 119
7*sin B = 4(0.874)
sin B = 3.496/7
B = sin^-1(0.4994)
B = 29.96 = 30°
We know that sum of angles of triangle = 180°
So, 180° = 119° + 30° +∠C
180° = 149° + ∠C
=> ∠C = 180° - 149°
∠C = 31°
Now finding c
b/sin B = c /sin C
4/Sin 30 = c/sin 31
4* sin 31 = c*sin 30
4*0.515 = c* 0.5
=> c = 4*0.515/0.5
c = 4.12 ≈ 4
So, Option D one solution; c ≈ 4; B = 30°; C = 31° is correct.
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Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest degree
A = 119°, a=7, b=4
Question 7 options:
one solution; c ≈ 7; B = 30°; C = 119°
no solution
one solution; c ≈ 4; B = 31°; C = 30°
one solution; c ≈ 4; B = 30°; C = 31°
PLEASE HELP SO CONFUSING PLEASE HELP WITH THE WHOLE PROBLEM THOUGH‼️‼️
When a student is chosen at random, the student is more likely to be from Mrs Johnson's class.
The probability that the student got A in the first semester will be 0.15.
How to calculate the probabilityWhen a student is chosen at random, the student is more likely to be from Mrs Johnson's class. It should be noted that this is because 152 students out of 300 are from her class compared to Dixon who has 148 students.
The probability that the student got A in the first semester will be:
= 46 / 300
= 0.15
The probability for the last question will be:
= 14 / 148
= 0.095.
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Hypothesis testing question.
From a sample of 30 patients, Divoc Health Group found that the mean days for a patient to discharge is 25 days. The hospitalization duration was assumed to follow a normal distribution. Last year, the mean days for a patient to discharge was 20 days with a standard deviation of 5 days. Divoc Health Group suspects that the mean days for a patient to discharge has increased because of Covid-19 cases and other health-related issues. Divoc Health Group decides to carry out a hypothesis test.
a) State the null and alternative hypotheses.
b) At a 5% significance level, is there sufficient evidence to conclude that the mean days for a patient to discharge has increased? Show all steps clearly. [Express your answers up to 3 decimal places]
Based on the information, Divoc Health Group now samples an additional 10 clients. The mean days for a patient to discharge were 22 days.
c) Using the new information, construct a 95% confidence interval for the mean days for a patient to discharge. [Express your answers up to 3 decimal places]
d) What is the minimum sample size required if Divoc Health Group wants to estimate the mean days for a patient to discharge to within 2 days of error with a 99% confidence?
a) Null: Mean = 20 days; Alt: Mean > 20 days. b) supported by t-value 6.708 > critical value at α=0.05. c) 95% confidence interval for mean patient discharge time is between 20.528 and 23.472 days, d) 99% confidence, a minimum sample size of 67 patients is required.
a) The null hypothesis is that the mean days for a patient to discharge is still 20 days, while the alternative hypothesis is that the mean days for a patient to discharge has increased and is now greater than 20 days.
Null hypothesis: 0: = 20
Alternative hypothesis: 1: > 20
b) We can use a one-sample t-test to test the hypothesis. We will use a significance level of 0.05.
The test statistic is given by:
t = (x - ) / (s / √n)
where x is the sample mean, is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
Here, x = 25, = 20, s = 5, and n = 30. Plugging these values into the formula, we get:
t = (25 - 20) / (5 / √30) = 6.708
The degrees of freedom (df) for the t-distribution is n - 1 = 29. Using a t-table or calculator, the p-value for a one-tailed test with df = 29 and t = 6.708 is < 0.0001.
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis. There is sufficient evidence to conclude that the mean days for a patient to discharge has increased.
c) To construct a 95% confidence interval for the mean days for a patient to discharge, we use the formula:
CI = x ± tα/2 * (s/√n)
where x is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the critical value for a t-distribution with df = n-1 and α = 0.05/2 = 0.025.
Here, x = 22, s = 5, and n = 40 (30 from the first sample + 10 from the second sample). The critical value for tα/2 with df = 39 is 2.022.
Plugging these values into the formula, we get:
CI = 22 ± 2.022 * (5/√40) = (20.528, 23.472)
Therefore, we can be 95% confident that the true mean days for a patient to discharge is between 20.528 and 23.472 days.
d) To find the minimum sample size required to estimate the mean days for a patient to discharge to within 2 days of error with a 99% confidence, we use the formula:
n = (zα/2 * s / E)²
where zα/2 is the critical value for a z-distribution with α = 0.01/2 = 0.005, s is the sample standard deviation (which we assume is the same as before, i.e., s = 5), and E is the desired margin of error (which is 2 days).
Plugging in the values, we get:
n = (2.576 * 5 / 2)² = 66.18
Therefore, the minimum sample size required is 67 patients.
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Helppppppp anyoneeee?
Answer:
( -6, 6)
Step-by-step explanation:
A scale drawing for an apartment is shown below. In the drawing, 3cm represents 4cm. Assuming the bedroom is rectangular, find the area of the real room
The calculated value of the area of the real room is 10.67 cm²
Finding the area of the real roomFrom the question, we have the following parameters that can be used in our computation:
In the drawing, 3cm represents 4cm
This means that
Scale factor = 4/3
Also, we have the dimension of the scale drawing to be
Dimension = 3cm by 2 cm
So, the area of the bedroom in the scale is
Area = 3cm * 2cm
For the actual room, we have
Area = 3cm * 2cm * (4/3)²
Evaluate the exponent
Area = 3cm * 2cm * (16/9)
Evaluate the products
Area = 10.67 cm²
This means that the real area is 10.67 cm²
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Can someone help me please
Chapter 13/14. The Civil War. Watch the Hari Jones TED talk. Then, answer the following questions in 7-10 sentences. Then, respond to two different classmates' posts by asking a question or challenging their assertions (respectfully). Try to make sure everyone has a response to their post. Finally, respond to the question or assertion your classmate(s) replied to you. Responses are meant to acknowledge what the other student has communicated, and either expand on their ideas, or push back on them, then offer positive feedback. Consider using the following template: "Hi _____. I was interested in ______ about your post because _______. Also/However, ______. I think ______ because _____. Do you think/feel _____/? I feel _____. "
In serving in the military, what contributions did African Americans make to the Union war effort?
What kinds of discrimination did they face? What kind of heroism did they exhibit, and when?
Write a reaction to Dr/ Jones' TED talk. What did you know/not know? What surprised/amazed/angered/made you proud/saddened/made you happy?
Hi Annie. I was interested in engaging you about your post because of my differing view. However, I think I am open to changing my views because I am not dogmatic. Do you think I am too pliable?
How did African Americans contribute?Throughout the Civil War, African Americans assumed crucial roles in the Union war effort. From enlisting as soldiers to acting as laborers and even spies, their contributions left an indelible impact on history.
Despite being subjected to rampant discrimination and racism from both Confederacy and Union forces, these individuals exhibited incredible heroism and bravery.
Excelling in dangerous missions that often led them to become prisoners of war, they persevered as they fought for the freedoms of themselves and others.
Hari Jones' TED talk shines a much-needed light on this overlooked aspect of history, revealing not only the extensive involvement of African American soldiers but also the pivotal role played by women in areas such as nursing, cooking, and espionage.
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pls pls help me with answer(correct it)
Determine the equation of the circle with center (6,-2)containing the point (14,6).
Answer:
(x -6)² +(y +2)² = 128
Step-by-step explanation:
You want the equation of the circle centered at (6, -2) through point (14, 6).
Circle equationThe equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
For center (h, k) = (6, -2), we can find the value of r² knowing that it will be the value that lets the point (14, 6) satisfy the equation.
(14 -6)² +(6 -(-2))² = r² = 8² +8² = 128
The circle equation is ...
(x -6)² +(y +2)² = 128
The combined math and verbal scores for females taking the SAT-I test are normally distributed with a mean of 998 and a standard deviation of 202 (based on date from the College Board). If a college includes a minimum score of 1025 among its requirements, what percentage of females do not satisfy that requirement?
I have already tried 64.8% as my answer!!
The percentage of females that do not satisfy the requirement is given as follows:
55.17%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation are given as follows:
[tex]\mu = 998, \sigma = 202[/tex]
The proportion that does not satisfy the requirement is the p-value of Z when X = 1025, hence:
Z = (1025 - 998)/202
Z = 0.13
Z = 0.13 has a p-value of 0.5517.
Hence the percentage is given as follows:
0.5517 x 100% = 55.17%.
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17. The Amethyst Woodstar species of
hummingbird beats its wings about
80 times per second. If there are
60 seconds in a minute, about how
many times does the Amethyst
Woodstar beat its wings in
9 minutes?
A 12,600
B 37,800
C50,400
D 43,200
If the Amethyst Woodstar species of hummingbird beats its wings about 80 times per second and there are 60 seconds in a minute, it beats its wings D. 43,200 times in 9 minutes.
How is the number of times determined?The number of times that the Amethyst Woodstar species of hummingbird beats its wings in 9 minutes can be determined using the mathematical operation of multiplication.
The number of times it beats its wings = 80 seconds per second
The total number of minutes involved = 9 minutes
1 minute = 60 seconds
The total number of times it beats in 9 minutes = 43,200 (80 x 60 x 9)
Thus, using multiplication operation, the number of times the bird beats its wings is Option D.
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Math homework assignment
The finance charge for Sandra Lazzaro, using the average daily balance method, is $13.63.
What is the Average Daily Balance Method?The average daily balance is one of the methods for computing the finance charges (interest and other fees).
The average daily balance method uses the balance owed at the end of each day of the billing period, and not the balance owed at the end of the week, month, or year.
Billing period for the credit card = 31 days
Unpaid credit card balance = $750
Payment made three days before month-end = $600
Finance charge rate per month = 2.2%
Method = Average daily balance
Day Description Amount Average Balance
1 - 28 Balance $750 $21,000 ($750 x 28 days)
29 - 31 Payment -$600 $-1,800 ($600 x 3 days)
31 Total $19,200
Average daily balance = $619.35 ($19,200 ÷ 31)
Finance charge = $13.63 ($619.35 x 2.2%)
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Angle 3 is 120°.
What is the
measure of 25?
m45 = [?]°
Answer in degrees.
[?]°
1/2
4/3= 120°
5/6
8 7
Enter
Answer:
angle 5 is 120 since there is Z shape with angle 3
Consider the following graph: What is the average slope/rate of change between (0, 1) and (2, 4)? 2/3 What is the average slope/rate of change between (-2, 1/4) and (-1, 1/2)? -1/4 Is the slope/rate of change constant (not changing/the same)? No Is the function linear? No
a) The average slope or rate of change between (0, 1) and (2, 4) is 3/2.
b) The average slope or rate of change between (-2, 1/4) and (-1, 1/2) is 1/4.
c) The slope or rate of change is not constant between these two pairs of points, since the average slopes are different.
d) The function connecting these pairs of points is not a linear function.
Define a slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
The average slope or rate of change between two points (x1, y1) and (x2, y2) on a line is given by:
average slope = (y2 - y1) / (x2 - x1)
For the points (0, 1) and (2, 4), the average slope is:
average slope = (4 - 1) / (2 - 0) = 3/2
For the points (-2, 1/4) and (-1, 1/2), the average slope is:
average slope = (1/2 - 1/4) / (-1 - (-2)) = 1/4
When the average slopes of these two pairs of points differ, the slope or rate of change is not constant. As a result, the function connecting these point pairs is not linear.
Because a linear function has a constant slope, a function with a variable slope cannot be linear.
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Rebecca invests 600 into an account with a 2.7% interest rate that is compounded quarterly. How much money will she have in this account if she keeps it for 10 years
The accrued value of the account in 10 years is $641.75
Determining the accrued value of the account in 10 yearsFrom the question, we have the following parameters that can be used in our computation:
Rebecca invests 600 in an account2.7% interest compounded quarterlyUsing the above as a guide, we have the following:
Amount = P * (1 + 0.25r)ᵗ
Where
P = Principal = 600
r = Rate = 2.7% = 0.27
t = time = 10
Substitute the known values in the above equation, so, we have the following representation
Amount = 600 * (1 + 0.25 * 0.27)¹⁰
Evaluate
Amount = 641.75
Hence, the amount is 641.75
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Fully factorise 3h² + 12h
Answer: To factorize 3h² + 12h, we can first find the greatest common factor (GCF) of the two terms, which is 3h:
3h(h + 4)
This is the fully factorized form of 3h² + 12h.
please hurry thats all i ask
The value of A, B, C,D are 33, 36,25 and 16 respectively
What is word problem?A word problem is a math problem written out as a short story or scenario. We use this word problem to solve the unknowns.
The total number of students is 60 and 24 students prefer volley ball. therefore the number of students that prefer basketball = 60-24 = 36 students
Since 11 student are girls that prefer basketball, therefore the number of boys that prefers basketball = 36-11 = 25
C = 25
and B = 36
55% of the students are boys, therefore the number of boys = 55/100 × 60 = 33
A = 33
therefore the number of boys that prefer volley ball= 33-25 = 8
Number of girls = 60-33 = 27
therefore number of girls that prefer volley ball = 27-11 = 16
D= 16
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Select all the equations that have no real solutions.
A. 2x2 – 3x + 7 = 0
B. x2 – 5x + 3 = 0
C. 2x2 + 8x + 7 = 0
D. –x2 + 6x + 4 = 0
E. x2 – x + 5 = 0
Answer:
B
D
E
( all of the answers (E, D, B) have no real solutions)
h(x) = 2x + 3
Complete the function table.
X. H(x)
-4
0
1
2
3
Answer:
X H(x)=2x+3
-4 -5
0 3
1 5
2 7
3 9
P(RI-T) = 0.25, P(-R|T) = 0.2, P(T) = 0.1
What is P(R)?
O 0.245
O insufficient information
O 0.1060
O 0.305
Answer:
We can use Bayes' theorem to calculate P(R), which states that the probability of an event A given event B is equal to the probability of B given A multiplied by the probability of A, divided by the probability of B:
P(R|T) = P(T|R) * P(R) / P(T)
We can rearrange this equation to solve for P(R):
P(R) = P(R|T) * P(T) / P(T|R)
We are given that P(RI-T) = 0.25, which can be written as:
P(R∩T) = P(R|T) * P(T) = 0.25
We are also given that P(-R|T) = 0.2, which can be written as:
P(-R∩T) = P(-R|T) * P(T) = 0.2 * 0.1 = 0.02
We can use the law of total probability to find P(T|R):
P(T|R) = P(RI-T) / P(R) = 0.25 / P(R)
We can substitute these values into the equation for P(R) to get:
P(R) = P(R|T) * P(T) / P(T|R)
= 0.25 / [P(T|R) * P(T) + P(-R|T) * P(T)]
= 0.25 / [0.25 + 0.02]
= 0.1060
Therefore, the answer is option C: 0.1060.
The table shows the home state of the 175 high school students who attended a tri-state debate tournament. The ratio of Illinois students to Michigan students was 6:5. How many students were from Indiana?
Let's start by setting up a proportion to represent the ratio of Illinois students to Michigan students:
Illinois students / Michigan students = 6/5
We can simplify this proportion by multiplying both sides by 5:
Illinois students = 6/5 * Michigan students
Next, we can use the information in the table to set up an equation that relates the number of Illinois students, Michigan students, and Indiana students:
Illinois students + Michigan students + Indiana students = 175
We can substitute the expression we obtained for the number of Illinois students into this equation:
6/5 * Michigan students + Michigan students + Indiana students = 175
Multiplying both sides by 5 to eliminate the fraction, we get:
6 * Michigan students + 5 * Michigan students + 5 * Indiana students = 875
Combining like terms, we get:
11 * Michigan students + 5 * Indiana students = 875
Now we can use the fact that the ratio of Illinois students to Michigan students is 6:5 to set up another equation:
Illinois students / Michigan students = 6/5
Substituting the values from the table, we get:
Illinois students / Michigan students = 24/20
Cross-multiplying, we get:
Illinois students * 20 = Michigan students * 24
Simplifying, we get:
Illinois students = 6/5 * Michigan students = 24/20 * Michigan students = 6/5 * 24 Michigan students = 28.8 Michigan students
Since the number of students must be a whole number, we can round 28.8 up to 29. This means that there were 29 Michigan students.
Substituting this into the equation we obtained earlier, we get:
11 * 29 + 5 * Indiana students = 875
Solving for Indiana students, we get:
5 * Indiana students = 875 - 11 * 29 = 546
Dividing both sides by 5, we get:
Indiana students = 546/5 = 109.2
Since the number of students must be a whole number, we can round 109.2 up to 110. This means that there were 110 Indiana students.
Therefore, the answer is 110 students from Indiana.