62% of the dancers did not get into the show.
To find the percentage of dancers who did not get into the show.
First, identify the total number of dancers auditioning and the number of dancers who did not get into the show.
In this case, there are 150 dancers in total, and 93 of them did not get in.
Next, divide the number of dancers who did not get into the show by the total number of dancers auditioning.
This will give us the proportion of dancers who did not get in.
Proportion = (Number of dancers who did not get in) / (Total number of dancers)
Proportion = 93 / 150
Finally, to find the percentage, multiply the proportion by 100:
Percentage = Proportion * 100
Percentage = (93 / 150) * 100.
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The Louvre is an art museum in Paris. A glass square base pyramid sits in front of the entrance to the museum. If the pyramid is 35 meters wide at the base and 20. 6 meters tall, what was the minimum amount of glass needed to construct the pyramid?
The minimum amount of glass needed to construct the Louvre pyramid is approximately 3133 square meters.
What is the minimum amount of glass needed to construct the glass pyramid in front of the Louvre museum in Paris, if the pyramid is 35 meters wide at the base and 20.6 meters tall?
The surface area of a square base pyramid can be calculated by adding the area of the base to the sum of the areas of the four triangular faces.
The area of the square base is simply the width of the base squared:
Area_base = (35 m)^2 = 1225 square meters
The area of each triangular face can be calculated using the formula:
Area_triangle = (1/2) * base * height
For the Louvre pyramid, the base of each triangular face is equal to the width of the base of the pyramid, which is 35 meters. The height of each triangular face can be found using the Pythagorean theorem:
[tex]height^2 = (1/2 * width)^2 + height^2[/tex]
[tex]height = sqrt((1/2 * 35 m)^2 + (20.6 m)^2)[/tex]
height = 29.2 m
Therefore, the area of each triangular face is:
Area_triangle = (1/2) * (35 m) * (29.2 m) = 508.5 square meters
The total surface area of the pyramid is:
Surface_area = Area_base + 4 * Area_triangle
Surface_area = 1225 + 4 * 508.5
Surface_area = 3133 square meters
Since the pyramid is made of glass, we need to calculate the minimum amount of glass needed to construct it. Assuming the glass is thin and flat, we can simply use the surface area of the pyramid to estimate the amount of glass needed.
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A basketball coach thinks that as his team progresses through the season, his players are not scoring as many points as they were in the previous weeks. He uses a table to record the number of points that his team scores for the first ten weeks of the season. First drop down box answers( positive,negative, or no correlation) second drop down box (correct or incorrect)
The observed relationship can be described as a negative correlation.
The basketball coach observes a decrease in points scored by his team over the first ten weeks of the season.
This indicates a negative correlation between time (progressing through the season) and points scored. Without seeing the data, we cannot determine if the coach's observation is correct or incorrect. However, the observed relationship can be described as a negative correlation.
However, it is important to note that without actually seeing the data and analyzing it, we cannot conclusively determine if the coach's observation is correct or incorrect.
The observed relationship, as described by the coach, suggests a negative correlation, but the strength and significance of this correlation would need to be evaluated through statistical analysis of the data.
In addition, it is also possible that other factors may be influencing the decrease in points scored, such as changes in team strategy, player injuries, or tougher opponents.
Without considering these other factors and analyzing the data, it would be premature to draw definitive conclusions about the relationship between time and points scored.
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Question 7(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 8(Multiple Choice Worth 2 points)
(Circle Graphs MC)
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
The correct graph to display the data is: C. Bar graph with the title "favorite sport" and the x-axis labeled "sport" and the y-axis labeled....
Why is a Bar Graph appropriate?A bar graph is an appropriate choice for displaying the data collected from the middle school students because it allows us to compare discrete categories (in this case, sports) and their corresponding frequencies (number of students).
In this case, the data is as follows:
Basketball: 17 studentsBaseball: 12 studentsSoccer: 27 studentsTennis: 44 studentsThe correct bar graph has the title "Favorite Sport" to indicate the subject of the data being represented.
The x-axis is labeled "Sport" and lists the four sports - basketball, baseball, soccer, and tennis - in separate, distinct categories. The y-axis is labeled "Number of Students" and displays the frequency or count of students who chose each sport as their favorite.
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i cant do math no more
Answer:
(1, 4)
Don't worry, I feel the same way sometimes, :)
Please give me Brainliest :)Step-by-step explanation:
Substitute the bottom equation into the top.
If y=3x+1, than the first y will equal 3x+1.
3x+1 = x+3
Subtract 1 from 3
3x = x+2
Subtract x from 3x.
2x=2
Divide everything by 2.
x=1
Now substitute it in the equation.
1. y=1 + 3
y=4
2. y= 3(1) + 1
y=3+1
y=4
(1, 4)
what is 34.16 as a fraction
Answer:
make me brainalist
Step-by-step explanation:
34.16
[tex] \frac{3416}{100} [/tex]
If there is one to one correspondence between two sets, we say that the sets have the same "size" or the same ____________________
If there is a one-to-one correspondence between two sets, we say that the sets have the same "size" or the same "cardinality."
Cardinality is a term used in mathematics and set theory to describe the size or number of elements in a set. It refers to the property of a set that determines how many objects it contains. For example, the cardinality of the set {1, 2, 3} is 3, because it contains three elements. The cardinality of a set can be finite (if it has a specific number of elements) or infinite (if it contains an uncountable number of elements).
Cardinality is usually denoted using the vertical bar notation |A|, where A is the set in question. For example, if A = {a, b, c}, then |A| = 3.
Cardinality is an important concept in mathematics, especially in areas such as set theory, combinatorics, and number theory. It is used to compare the sizes of different sets and to determine the properties of operations that involve sets, such as union, intersection, and complement.
If there is a one-to-one correspondence between two sets, we say that the sets have the same "size" or the same "cardinality."
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Suppose there are 5 people and 4 waffle. What is each person's share of 4 waffles?
Answer:
4/5 or 0.8 Waffles per person
Step-by-step explanation:
Divide the 4 waffles among 5 people, 4/5
0.8 waffle.
ANSWER THE QUESTIONS A AND B ! 1ST ONE WHO ANSWERS WITH A CORRECT ANSWER WILL BE MARkED BRAINLIEST!
Answer:
A is -4.5,2 and B is 0,-3.5
Step-by-step explanation:
Answer:
Coordinates of A: (-4.5, 2), Coordinates of B: (0, -3.5)
northview swim club has a number of members on monday. on tuesday, 22 new members joined the swim clun on wednesday 17 members cancled their membership or left the swim clun northview swim club has 33 members on thursday morning the equation m+22-17=33 repersents the situation solve the equation
There were 28 members in the Northview Swim Club on Monday before any new members joined or any current members left.
What is the solution of the equation?The equation "m+22-17=33" represents the situation where "m" is the number of members in the Northview Swim Club on Monday.
To solve the equation, we can start by simplifying it:
m + 5 = 33
Next, we can isolate "m" on one side of the equation by subtracting 5 from both sides:
m = 33 - 5
m = 28
Thus, the solution of the equation for the Northview Swim Club on Monday before any new members joined is determined as 28 members.
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Suppose clay, a grocery store owner, is monitoring the rate at which customers enter his store. after watching customers enter for several weeks, he determines that the amount of time in between customer arrivals follows an exponential distribution with mean 15 s. what is the 60 th percentile for the amount of time between customers entering clay's store
Following an exponential distribution with a mean of 15 seconds, the 60th percentile for the amount of time between customers entering Clay's store is approximately 13.74 seconds.
Based on the information provided, Clay's grocery store experiences customer arrivals following an exponential distribution with a mean of 15 seconds. To find the 60th percentile for the amount of time between customers entering the store, we can use the following formula:
Percentile = Mean * ln(1 / (1 - Percentile in Decimal Form))
In this case, the 60th percentile in decimal form is 0.6. Plugging the values into the formula, we get:
60th Percentile = 15 * ln(1 / (1 - 0.6))
60th Percentile ≈ 15 * ln(1 / 0.4)
60th Percentile ≈ 15 * ln(2.5)
60th Percentile ≈ 15 * 0.9163
60th Percentile ≈ 13.74 seconds
Thus, the 60th percentile for the amount of time between customers entering Clay's store is approximately 13.74 seconds.
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Fill in the blank: as the number of trials gets ____________, the experimental probability of an event approaches the theoretical probability of the event.
As the number of trials gets larger, the experimental probability of an event approaches the theoretical probability of the event.
The Law of Large Numbers, a key idea in probability theory, holds that as trials or experiments are conducted, the experimental probability of an occurrence tends to converge toward the theoretical or predicted probability of that event.
In other words, the experimental results improve in accuracy and reliability as the sample size grows when forecasting the actual course of an event. This is because a bigger sample size reduces the significance of random changes or data errors and increases the likelihood that the experimental results will accurately reflect the true underlying probability of the event.
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A bowl contains four balls numbered 1 through 4. You select the four balls successively,
without replacement, until none remain in the bowl.
a) What is the probability that the two even numbered balls are selected before the odd
numbered balls?
b) What is the probability that the balls are not selected in size order (i. E. 1, 2, 3, 4 or 4, 3, 2,1) ?
a) The probability of selecting two even numbered balls before odd numbered balls is 1/6.
b) The probability of not selecting balls in size order is 22/24 or 11/12.
a) There are 4! (24) ways to arrange the four balls. There are 2! ways (2) to arrange the even balls and 2! ways (2) to arrange the odd balls, so there are 2x2=4 favorable ways (2,4,1,3 and 4,2,1,3). The probability is 4/24, which simplifies to 1/6.
b) There are only 2 ways to select balls in size order (1,2,3,4 and 4,3,2,1). Subtracting these from the total arrangements (24-2) results in 22 non-size ordered selections. The probability is 22/24, which simplifies to 11/12.
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As a result of complaints from both students and faculty about lateness, the registrar at a large university is ready to undertake a study to determine whether the scheduled break between classes should be changed. Until now, the registrar has believed that there should be 30 minutes between scheduled classes. What are the null and alternative hypotheses?
The null hypothesis (H0) is that the scheduled break between classes of 30 minutes is appropriate and does not need to be changed. The alternative hypothesis (Ha) is that the scheduled break between classes of 30 minutes is not appropriate and needs to be changed.
In hypothesis testing, the null hypothesis (H0) is a statement that assumes there is no significant difference between two population parameters or that there is no relationship between two variables. It is the default assumption that is initially assumed to be true and is tested against the alternative hypothesis.
The alternative hypothesis (Ha) is a statement that contradicts the null hypothesis and suggests that there is a significant difference between two population parameters or that there is a relationship between two variables. It is the hypothesis that we want to prove, and it is supported if the null hypothesis is rejected.
In the case of the registrar's study, the null hypothesis could be "There is no significant difference in lateness between classes with a 30-minute break and classes with a break of a different length,"
While the alternative hypothesis could be "There is a significant difference in lateness between classes with a 30-minute break and classes with a break of a different length."
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A video game player is creating a user identification to play a game. The identification must consist of one vowel (A, E, I, O, U) followed by any one number (2, 4, 6, 8). What is the probability that the user identification will contain both an E and an 8?
The probability that the user identification will contain both an E and an 8 is 1/20, or 5%.
To determine the probability of a user identification containing both an E and an 8, we will break down the problem step-by-step.
1. Identify the total number of possibilities:
There are 5 vowels (A, E, I, O, U) and 4 even numbers (2, 4, 6, 8). To calculate the total number of possible user identifications, multiply the number of vowels by the number of even numbers:
Total possibilities = 5 vowels × 4 even numbers = 20 combinations
2. Determine the desired outcome:
In this case, we are interested in the combination that has an E followed by an 8. There is only one such combination: E8.
3. Calculate the probability:
To find the probability of the desired outcome, divide the number of desired outcomes by the total number of possible outcomes:
Probability = Desired outcomes / Total possibilities
Probability = 1 / 20
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Nicholas cleans his room in 10 hour. Gloria
cleans her room for 3 minutes and 18 seconds. How many seconds longer does Nicholas clean his room than Gloria?
To determine how many seconds longer Nicholas cleans his room than Gloria, we first need to convert both their cleaning times into seconds.
1. Convert Nicholas's cleaning time to seconds:
Nicholas cleans his room in 10 hours. There are 60 minutes in an hour and 60 seconds in a minute. So, we multiply 10 hours by 60 minutes and then by 60 seconds:
10 hours * 60 minutes/hour * 60 seconds/minute = 36,000 seconds
2. Convert Gloria's cleaning time to seconds:
Gloria cleans her room for 3 minutes and 18 seconds. We convert 3 minutes into seconds by multiplying it by 60 seconds/minute:
3 minutes * 60 seconds/minute = 180 seconds
Now, add the 18 seconds to the 180 seconds:
180 seconds + 18 seconds = 198 seconds
3. Subtract Gloria's cleaning time from Nicholas's cleaning time:
36,000 seconds (Nicholas) - 198 seconds (Gloria) = 35,802 seconds
In conclusion, Nicholas cleans his room for 35,802 seconds longer than Gloria.
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stys
ACA
2. A square with one side length represented by an
expression is shown below.
6(3x + 8) + 32 + 12x
Use the properties of operations to write three
different equivalent expressions to represent the
lengths of the other three sides of the square. One
of your expressions should contain only two terms.
We want to use properties to write expressions for the length of the other sides of the square.
Remember that the length of all the sides in a square is the same, so we only need to rewrite the above expression in two different ways.
First, we can use the distribute property in the first term:
[tex]\sf 6\times(3x + 8) + 32 + 12\times x[/tex]
[tex]\sf = 6\times3x + 6\times8 + 32 +12\times x[/tex]
[tex]= \sf 18\times x + 48 + 32 + 12\times x[/tex]
So this can be the length of one of the sides.
Now we can keep simplifying the above equation:
[tex]= \sf 18\times x + 48 + 32 + 12\times x[/tex]
To do it, we can use the distributive and associative property in the next way:
[tex]\sf 18\times x + 48 + 32 + 12\times x[/tex]
[tex]= \sf 18\times x + 12\times x + 48 + 32[/tex]
[tex]= \sf (18\times x + 12\times x) + (48 + 32)[/tex]
[tex]= \sf (18 + 12)\times x + 80[/tex]
[tex]= \sf 30\times x + 80[/tex]
This can be the expression to the other side.
Chris wants to order DVD's over the internet. Each DVD costs $15. 99 and shipping the entire order costs $9. 99. If he can spend no more than $100, how many DVD's could he buy?
Since Chris can only buy whole DVDs, he can purchase a maximum of 5 DVDs within his $100 budget.
Each DVD costs $15.99, and the shipping for the entire order is $9.99.
We can use the following inequality to represent Chris's budget constraint:
15.99x + 9.99 ≤ 100
Here, x represents the number of DVDs he can buy.
To find the maximum value of x, we can rearrange the inequality:
x ≤ (100 - 9.99) / 15.99 x ≤ 90.01 / 15.99 x ≤ 5.63
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The enrollment of students at a school is decreasing at a constant rate of 5 % per year what percent remains after one year
Answer: depends but just subtract 5 from the original rate
Step-by-step explanation:
example
100 to 95 to 90 to 85 to 80 and etc.
Part A Convert the mixed fraction into an improper fraction. 5 9 17 5 17 9 = = 94 17 Part B Select the decimal equivalent to the improper fraction in PART A approximated to two decimal places: (b) A 5.525 B 5.535 C 5.55 D 5.625
Part A: To convert the mixed fraction 5 9/17 to an improper fraction, we first multiply the whole number (5) by the denominator of the fraction (17), and then add the numerator (9). This gives us:
5 x 17 + 9 = 94
So 5 9/17 as an improper fraction is 94/17.
Part B: To find the decimal equivalent of 94/17, we divide the numerator (94) by the denominator (17) using a calculator or long division. The answer is approximately 5.53 when rounded to two decimal places.
Therefore, the decimal equivalent of the improper fraction 94/17 approximated to two decimal places is option B: 5.535.
What is the average rate of change for the number of shares from 2 minutes to 4 minutes?
The average rate of change for the number of shares from 2 minutes to 4 minutes is 25 shares per minute.
To find the average rate of change for the number of shares from 2 minutes to 4 minutes, we need to know the initial number of shares at 2 minutes and the final number of shares at 4 minutes. Once we have those values, we can use the formula:
average rate of change = (final value - initial value) / (time elapsed)
Let's say the initial number of shares at 2 minutes was 100 and the final number of shares at 4 minutes was 150. The time elapsed between 2 minutes and 4 minutes is 2 minutes. Plugging these values into the formula, we get:
average rate of change = (150 - 100) / 2
average rate of change = 50 / 2
average rate of change = 25
Therefore, the average rate of change is 25 shares per minute.
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MARK YOU THE BRAINLIEST! If
Answer:
∠ D = 38°
Step-by-step explanation:
given Δ ABC and Δ DEF are similar, then corresponding angles are congruent, so
∠ A and ∠ D are corresponding , so
∠ D = ∠ A = 38°
1. If a 20 inch pizza costs $13, how many square inches of pizza do you
for 1 dollar? In other words, what is the unit rate per one dollar?
Answer:
I think you get 0.65 inches of pizza for 1 dollar
Step-by-step explanation:
$13 divided by 20 inches = 0.65
Four gallons of paint are used to paint 20 chairs and 5 small tables. If each chair and table used the same amount of paint, how many gallons are used to pain each piece of furniture? between what two wholes numbers lie?
Answer:
0.16 gallons of paint
the number lies between 0 and 1
Step-by-step explanation:
Chairs and tables used the same amount of paint,
20x + 5x = 4
25x = 4
x = 0.16
So, each piece of furniture will use 0.16 gallons of paint.
Please help me with this math problem!! Will give brainliest!! :)
part a.
the percentage of eggs between 42 and 45mm is 48.48%
part b.
The median width is approximately (42+45)/2 = 43.5mm.
The median length is approximately (56+59)/2 = 57.5mm.
part c.
The width of grade A chicken eggs has a range of about 24mm.
part d.
I think its impossible to determine because we don't have the value for the standard deviation.
The second option should be correct.
What is a histogram?A histogram is described as an approximate representation of the distribution of numerical data.
part a.
From the histogram, we see that the frequency for the bin that ranges from 42 to 45mm is 4 and we have a total of 33 eggwe use this values and calculate the percentage of eggs between 42 and 45mm is 48.48%.
part b.
we have an estimation that the median of the width is 48mm and the median of the length is around 60mm.
part c.
Also from the histogram, we notice that the smallest value is around 36mm and the largest value is around 66mm, hence the width of grade A chicken eggs has a range of about 24mm.
In a histogram, the range is the width that the bars cover along the x-axis and these are approximate values because histograms display bin values rather than raw data values.
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A local amusement park found that if the admission was $7, about 1000 customers per day were admitted. When the admission was dropped to $6, the park had about 1200 customers per day. Assuming a linear demand function, determine the admission price that will yield maximum revenue.
The admission price that will yield maximum revenue is $6.
To determine the admission price that will yield maximum revenue, we'll first find the linear demand function using the given data points: ($7, 1000) and ($6, 1200).
Let x represent the admission price and y represent the number of customers per day. We can calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given data points:
m = (1200 - 1000) / (6 - 7) = 200 / (-1) = -200
Now, we have the slope and a point, so we can use the point-slope form to find the linear demand function:
y - y1 = m(x - x1)
Using the point ($7, 1000):
y - 1000 = -200(x - 7)
Now, let's rewrite the equation to the slope-intercept form (y = mx + b):
y = -200x + 2400
The revenue (R) is equal to the product of the admission price (x) and the number of customers (y):
R = xy
Substitute the linear demand function (y = -200x + 2400) into the revenue equation:
R = x(-200x + 2400)
To maximize the revenue, we need to find the vertex of the parabola represented by this equation. The x-coordinate of the vertex is given by:
x_vertex = -b / 2a
In this case, a = -200 and b = 2400:
x_vertex = -2400 / (2 * -200) = 6
The admission price that will yield maximum revenue is $6.
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What does each angle equal?
Given : Angle 2 measures x+12 degrees
Angle 5 measures 49 degrees
Using the fact that the sum of the angles in a triangle is 180 degrees we do know that their sum is 119 degrees.
What is the measure of angle 2 and angle 5, given that angle 2 is x + 12 degrees and angle 5 measures 49 degrees?To understand why we used the fact that the sum of angles in a triangle is 180 degrees, let's take a closer look at the diagram.
We see that Angle 2 and Angle 5 are on the same side of a transversal and are therefore supplementary angles. This means that their sum is 180 degrees:
Angle 2 + Angle 5 = 180
We can substitute the value of Angle 5 (49 degrees) for Angle 5 and x + 12 for Angle 2 to get:
x + 12 + 49 = 180
Simplifying the equation, we get:
x = 119 - 49 - 12
x = 58
This gives us the value of x, but not the measure of Angle 2. To find the measure of Angle 2, we need to use the fact that the sum of angles in a triangle is 180 degrees.
We can write an equation using angles 2, 3, and 4 (which we now know is 49 degrees) as follows:
Angle 2 + Angle 3 + Angle 4 = 180
Substituting the known values, we get:
x + 12 + Angle 3 + 49 = 180
Simplifying the equation, we get:
x + Angle 3 = 119
So, we know that the sum of Angle 3 and x is 119 degrees, but we still don't know the measure of either angle on its own.
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You have $20 to spend. You go to the store and buy a bouncy ball for an unknown amount of money and then you buy a glider airplane for $3. If you have $15 left over, how much did you spend on the bouncy ball?
Step-by-step explanation:
$20-$3-$15= $2
the amount of money spent on the bouncy ball is $2
Mr. vara is designing post caps in the shape of a square pyramid for a fence that he just built in his backyard. the caps are solid wood and each one has a volume of 94.5 cubic centimeters.
If Mr. Vara's square pyramid post caps have a volume of 94.5 cubic centimeters, and he assumes that the height and side length are equal, then the side length of each cap should be approximately 6.04 centimeters.
Mr. Vara is designing post caps in the shape of a square pyramid for his fence. The caps are solid wood and have a volume of 94.5 cubic centimeters. To calculate the dimensions of the pyramid, we need to use the formula for the volume of a square pyramid, which is V = (1/3)bh, where b is the area of the base and h is the height of the pyramid.
Since the caps are square pyramids, the base is a square. Let's call the side length of the base s. Then the area of the base is s². We can rearrange the formula for volume to get h = (3V)/b. Plugging in the given volume of 94.5 cubic centimeters, we get:
h = (3 x 94.5) / s²
h = 283.5 / s²
We still need to find the side length s. We can use the fact that the volume of the pyramid is also equal to [tex](1/3)s^{2h[/tex]. Plugging in the volume and height from above, we get:
94.5 = (1/3)s²(283.5 / s²)
94.5 = 94.5
This equation simplifies to 1 = 1, which doesn't give us any information about s. However, we can make an assumption about the dimensions of the pyramid. Let's say that the height h is equal to the side length s. Then we can solve for s using the volume formula:
[tex]94.5 = (1/3)s^{2s[/tex]
94.5 = (1/3)s³
283.5 = s³
s = 6.04
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Determine whether the Mean Value there can be applied to to the dosed intervalectal that apply 100-V2--14:21 A. Yes, the Moon Value Theorem can be applied B. No, because is not continuous on the dosed inter
Based on the given information, we need to determine whether the Mean Value Theorem can be applied to the dosed interval [100-V2, 14:21].
The Mean Value Theorem states that for a function that is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), there exists at least one point c in (a, b) where the slope of the tangent line to the function at c is equal to the average rate of change of the function over the interval [a, b].
In this case, we do not have enough information about the function or its continuity on the interval [100-V2, 14:21]. Therefore, we cannot determine whether the Mean Value Theorem can be applied or not.
However, we do know that for the Mean Value Theorem to be applicable, the function must be continuous on the closed interval. If the function is not continuous on the closed interval, then the Mean Value Theorem cannot be applied.
Therefore, the answer to the question is B. No, because we do not have enough information about the function's continuity on the dosed interval [100-V2, 14:21].
I understand you're asking about the Mean Value Theorem and whether it can be applied to a given interval. Due to some typos in your question, I'm unable to identify the specific interval and function. However, I can provide general guidance.
The Mean Value Theorem can be applied to a function if:
A. The function is continuous on the closed interval [a, b]
B. The function is differentiable on the open interval (a, b)
If the given function meets these two conditions, then the Mean Value Theorem can be applied. Otherwise, it cannot be applied.
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Two spacecraft are following paths in space given by rt sin(t),t,02 and rz cos(t) , -t,73) . If the temperature for the points is given by T(x, y.2) = x y(5 2) , use the Chain Rule to determine the rate of change of the difference D in the temperatures the two spacecraft experience at time =4 (Use decimal notation. Give your answer to two decimal places )
To find the rate of change of the temperature difference between the two spacecraft, we need to first find the temperature at each spacecraft's position at time t=4.
For the first spacecraft, rt sin(t) = r4sin(4) and t=4, so its position is (4sin(4), 4, 0). Using the temperature function, we have T(4sin(4), 4, 0) = (4sin(4))(4)(5-2) = 48.08.
For the second spacecraft, rz cos(t) = r3cos(4) and t=-4/3, so its position is (3cos(4), -4/3, 7). Using the temperature function, we have T(3cos(4), -4/3, 7) = (3cos(4))(-4/3)(5-2) = -9.09.
Therefore, the temperature difference D between the two spacecraft at time t=4 is D = 48.08 - (-9.09) = 57.17.
To find the rate of change of D with respect to time, we use the Chain Rule. Let x = 4sin(t) and y = 4, so D = T(x, y, 0) - T(3cos(t), -4/3, 7). Then,
dD/dt = dD/dx * dx/dt + dD/dy * dy/dt
We already know that D = 48.08 - 9.09 = 57.17, so dD/dx = dT/dx = y(5-2x) = 4(5-2(4sin(4))) = -31.64.
We also have dx/dt = 4cos(4) and dy/dt = 0, since y is constant.
To find dD/dy, we take the partial derivative of T with respect to y, holding x and z constant: dT/dy = x(5-2y) = (4sin(4))(5-2(4)) = -28.16.
Putting it all together, we get:
dD/dt = dD/dx * dx/dt + dD/dy * dy/dt
= (-31.64)(4cos(4)) + (-28.16)(0)
= -126.56
Therefore, the rate of change of the temperature difference between the two spacecraft at time t=4 is -126.56.
Given the paths of the two spacecraft: r1(t) = (t sin(t), t, 0) and r2(t) = (t cos(t), -t, 7), and the temperature function T(x, y, z) = x * y * z^2, we want to determine the rate of change of the temperature difference D at time t=4 using the Chain Rule.
First, let's find the temperature for each spacecraft at time t:
T1(t) = T(r1(t)) = (t sin(t)) * t * 0^2
T1(t) = 0
T2(t) = T(r2(t)) = (t cos(t)) * (-t) * 7^2
T2(t) = -49t^2 cos(t)
Now, find the temperature difference D(t) = T2(t) - T1(t) = -49t^2 cos(t)
Next, find the derivative of D(t) with respect to t:
dD/dt = -98t cos(t) + 49t^2 sin(t)
Now, we need to evaluate dD/dt at t=4:
dD/dt(4) = -98(4) cos(4) + 49(4)^2 sin(4) ≈ -104.32
Thus, the rate of change of the temperature difference D at time t=4 is approximately -104.32 (in decimal notation, rounded to two decimal places).
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