The critical point of the function y = 3x² - 40x + 8 is at (6²/₃, -125¹/₃)
What are critical points of a function?The critical points of a function are the point at which there is a maximum or minimum value of the function.
Since we have the function y = 3x² - 40x + 8, we desire to find its ctitical points. We proceed as follows.
To find the critical points of the function y = 3x² - 40x + 8, we differentiate with respect to x and equate to zero.
So, y = 3x² - 40x + 8,
dy/dx = d(3x² - 40x + 8)/dx
= d3x²/dx - d40x/dx + d8/dx
= 2 × 3x - 40 + 0
= 6x - 40
So, equating to zero, we have
dy/dx = 0
6x - 40 = 0
6x = 40
x = 40/6
To determine if this is a maximum or minimum point, we differentiate dy/dx.
so, d(dy/dx) = d(6x - 40)/dx
d²y/dx² = d6x/dx - d40/dx
= 6 - 0
= 6
Since d²y/dx² = 6 > 0. x = 40/6 is a minimum point
So, substituting x = 40/6 into the equation, we have
y = 3x² - 40x + 8
y = 3(40/6)² - 40(40/6) + 8
= 3 × 1600/36 - 1600/6 + 8
= 1600/12 - 1600/6 + 8
= 1600/6(1/2 - 1) + 8
= -1600/12 + 8
= (-1600 + 96)/12
= -1504/12
= -125¹/₃
So, the critical point is at (6²/₃, -125¹/₃)
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Abox of apples weighs 270 kg 500 g. When the box is filled with oranges, it weighs 192 kg 500 g. The same basket when filled with guavas weighs 245 kg. If the fruits together weigh 690 kg, find the weight of the box alone. [some body help me i can't solve it
Answer:
The box alone weighs 6 kg
Step-by-step explanation:
Let, weight of Apple be x, Oranges be y, Guavas be z nd box a.
A box of Apple weighs 270kg and 500g i.e270.5kg
a+x =270.5---(1)
A box of oranges weighs 192.5kg
a+y=192.5---(2)
A box of guavas weighs 245
a+z=245---(3)
Fruits together weigh 690 kg
x+y+z=690---(4)
Combining (1),(2),(3), we get
3a+x+y+z=708---(5)
From 4&5
3a+690=708
3a=18
a=6
So the box weighs 6 kg
Matthew is training to run a marathon. He runs 20 miles his first week of training. Each week, he increases the number of miles he runs by 4 miles. How many total miles did he run in 8 weeks of training
Answer:
52 miles
Step-by-step explanation:
Matthew runs 20 miles in the first week. We want to increase this number by 4 each week. For this question we will use m for a variable for miles.
This will look like
20 + 4m = total miles ran
if he ran 8 miles, we will enter this number into the variable m.
20 + 4 × 8 = 52
The total miles Matthew ran was 52 miles after 8 weeks.
Lin needs to mix a specific shade of orange paint for the set of the school play. The color uses 3 parts yellow for every 2 parts red.
Complete the table to show different combinations of red and yellow paint that will make the shade of orange Lin needs
Combination of red and yellow paint that follows the ratio of 3 parts yellow for every 2 parts red will make the shade of orange Lin needs.
Red Yellow
2 3
4 6
6 9
8 12
The formula for this specific shade of orange paint is 3 parts yellow for every 2 parts red. To calculate the amounts of red and yellow paint that can be used for different combinations we can use the following equation:
Yellow = 2 x Red/3
For the first combination of 2 parts red and 3 parts yellow, the equation can be written as:
Yellow = (2 x 2)/3
Simplified, that is 2/3, or 3 parts yellow.
For the second combination of 4 parts red and 6 parts yellow, the equation can be written as:
Yellow = (2 x 4)/3
Simplified, that is 4/3, or 6 parts yellow.
For the third combination of 6 parts red and 9 parts yellow, the equation can be written as:
Yellow = (2 x 6)/3
Simplified, that is 8/3, or 9 parts yellow.
For the fourth combination of 8 parts red and 12 parts yellow, the equation can be written as:
Yellow = (2 x 8)/3
Simplified, that is 16/3, or 12 parts yellow.
Therefore, any combination of red and yellow paint that follows the ratio of 3 parts yellow for every 2 parts red will make the shade of orange Lin needs.
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Landon is going to invest in an account paying an interest rate of 6. 6% compounded daily. How much would landon need to invest, to the nearest dollar, four the value of the account to reach $3,250 in 18 years
Landon would need to invest approximately $1,150 to reach a future value of $3,250 in 18 years with an interest rate of 6.6% compounded daily.
To determine how much Landon needs to invest, we can use the compound interest formula, which is:
A = P(1 + r/n)^(nt)
where A is the future value of the account, P is the principal amount (the amount Landon needs to invest), r is the interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the interest rate is 6.6% or 0.066, the account is compounded daily, so n = 365, and t = 18. We want to find the principal amount, P, that will result in a future value of $3,250.
Substituting these values into the formula, we get:
3,250 = P(1 + 0.066/365)^(365*18)
Simplifying the right-hand side of the equation, we get:
3,250 = P(1.000181)^6,570
Dividing both sides by (1.000181)^6,570, we get:
P = 3,250 / (1.000181)^6,570
Using a calculator, we can evaluate this expression to find that:
P ≈ $1,150.52
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complete the square for 3x²-12=9
The square form of the given equation as per quadratic equation is: x²=7.
What is the quadratic equation?
A quadratic equation is an equation where the variable has the highest degree of 2.
Given equation:
⇒ [tex]3x^{2} -12 =9[/tex]
⇒ [tex]3x^{2} -12 -9=0[/tex]
⇒ [tex]3x^{2} -21 =0[/tex]
⇒ [tex]3x^{2} =21[/tex]
⇒ [tex]x^{2} =7[/tex]
Therefore, the square form of the given equation is x² = 7
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(12 points ) Find the area of an equilateral triangle with side length 2cm. Show all necessary calculations. Round your answer to the nearest hundredth.
The area of the equilateral triangle with side length 2cm is approximately 1.73 cm².
What is the area of the equilateral triangle?An equilateral triangle with side length 2cm can be divided into two right triangles with hypotenuse equal to 2cm and the other two sides of length 1cm each.
We can then use the Pythagorean theorem to find the length of the height of the equilateral triangle, which is also the height of the right triangles.
Let h be the height of the equilateral triangle, then:
h² = 2² - 1²
h² = 3
h = √3
The area of the equilateral triangle can be found using the formula:
Area = (base × height) / 2
Since the equilateral triangle has three equal sides, the base is also equal to 2cm. Therefore, we have:
Area = ( 2 × √3 ) / 2
Area = √3
Rounding to the nearest hundredth, we get:
Area = 1.73 cm²
Therefore, the area of the equilateral triangle is 1.73 cm².
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A certain type of brass contains 65% copper. How many pounds of copper are contained in 120 pounds of the brass? Please help I’m doing a test I need help T^T
The amount of copper that is contained in 120 pounds of brass is equal to 78 pounds.
Let the amount of copper be C.
Given the following data:
Quantity of brass = 120 pounds
Percentage of copper = 65%
To calculate the amount of cooper that is contained in 120 pounds of the brass:
In this exercise, you're required to determine how many pounds of copper can be found in 120 pounds of brass. Thus, we would solve for the percentage of copper contained in this type of brass.
[tex]Copper=\frac{65}{100}*120\\\\Copper, c=78 ponds.[/tex]
This is correct because 65% of 120 pounds is equal to 78 pounds. 65% can be expressed as a decimal (0.65) and multiplied by 120 pounds to find the number of pounds of copper contained in 120 pounds of the brass.
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Find the value of x.
Answer:
x = -10
Step-by-step explanation:
Note that it is a isosceles triangle. This means that the base angles (the angles that are not forged by the congruent sides) are congruent.
It is given that one of the angle measurements are 67°, meaning that ∠A would also be equal to 67. Set the equation:
m∠A = x + 77
67 = x + 77
Isolate the variable, x. Subtract 77 from both sides of the equation:
67 (-77) = x + 77 (-77)
x = 67 - 77
x = -10
x = -10 is your answer.
~
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A scale drawing of a living room is shown below. The scale is 1 : 40. A rectangle is shown. The length of the rectangle is labeled 6 inches. The width of the rectangle is labeled 4 inches. What is the area?
Julia teaches two dog training classes. The Level 1 class helps dogs learn the basics, while the Level 2 class focuses on more advanced commands. For each class, she kept track of the number of dogs that attended each session. These box plots show the results
On average, slightly more dogs attended the Level 2 class than the Level 1 class.The mean number of dogs attending the Level 1 class was 7.92, and the mean number of dogs attending the Level 2 class was 9.48.
The box plots provided show the results of Julia's two dog training classes. The Level 1 class helps dogs learn the basics, while the Level 2 class focuses on more advanced commands. From the box plots, we can see that the Level 1 class was attended more consistently than the Level 2 class, with the majority of classes having between 5 and 10 dogs attending. The Level 2 class, on the other hand, had more variability in attendance, with some classes having up to 18 dogs and other classes having as few as 3. The median number of dogs attending the Level 1 class was 8, while the median number of dogs attending the Level 2 class was 10. The mean number of dogs attending the Level 1 class was 7.92, and the mean number of dogs attending the Level 2 class was 9.48. This indicates that, on average, slightly more dogs attended the Level 2 class than the Level 1 class.
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If you toss one dime and roll one die. Predict how many time you would flip heads and roll an odd number In 120 tries.
We can predict that in 120 tries, we would expect to get heads and an odd number around 30 times. However, it is important to note that this is just a prediction and the actual number of times this occurs may vary due to chance.
When flipping a dime, there are two possible outcomes: heads or tails. Similarly, when rolling a die, there are six possible outcomes: 1, 2, 3, 4, 5, or 6. An odd number is any number that is not divisible by 2, so the odd numbers on a die are 1, 3, and 5.
The probability of flipping heads on a dime is 1/2, and the probability of rolling an odd number on a die is 3/6 or 1/2. To predict how many times you would flip heads and roll an odd number in 120 tries, we can use the multiplication rule of probability.
The multiplication rule of probability states that the probability of two independent events occurring together is the product of their individual probabilities. Since flipping a dime and rolling a die are independent events, we can multiply the probability of flipping heads and the probability of rolling an odd number to get the probability of both events occurring together.
So, the probability of flipping heads and rolling an odd number is:
P(heads and odd) = P(heads) x P(odd)
P(heads and odd) = (1/2) x (1/2)
P(heads and odd) = 1/4
We can estimate that in 120 trials, we should get heads about 30 times and an odd amount about the same. It is crucial to keep in mind that this is only a prediction and that there is a possibility that the actual frequency of occurrence will differ.
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Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
Graphs allow us to show that the following is true: D. Both plans will be costing the same when 50 texts are sent is accurate.
Describe graphs?The graph is just a organised representation of the data. It helps in our understanding of the data. The numerical information gathered through observation is referred to as data.
The answer is that both plans are same in price when 50 texts are sent because both lines intersect at a cost of $22.5 for 50 texts, indicating that they are equal in price.
The other options are not right:
A-plan Hiroto's costs more than Emilia's plan when more than 50 messages are sent. This is untrue, as you can see from the graph that Emilia's line is higher after 50 texts, indicating that her plan is more expensive.
B-When 22 messages are sent, the cost of both plans is the same. This is false because when 22 texts are sent, the lines do not cross at the same spot.
C-When more than 22 SMS are sent, Emilia's is more expensive than Hiroto's plan. This is untrue because Hiroto's plan is more expensive until they send 50 messages, which is the only time they cost the same. At that moment, Emilia's plan costs about $15.5 and Hiroto's plan costs about $21.
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The complete question is:
Hiroto's texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia's plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
A. Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent.
B. Both plans cost the same when 22 texts are sent.
C. Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent.
D. Both plans cost the same when 50 texts are sent.
A water sample shows 0. 066 grams of some trace element for every cubic centimeter of water. Shandra uses a container in the shape of a right cylinder with a radius of 5. 7 cm and a height of 13. 9 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Shandra collected? Round your answer to the nearest tenth
Shandra has cοllected apprοximately 93.67 grams οf the trace element.
How to Find Amοunt of trace element?The amοunt οf trace element refers tο the tοtal quantity οr mass οf a particular substance οr element that is present in a given sample οr substance. Tο find the amοunt οf trace elements, we can use the fοrmula:
Amοunt οf trace element = cοncentratiοn × vοlume
where the cοncentratiοn is the amοunt οf the trace element per unit vοlume, and the vοlume is the tοtal vοlume οf the sample.
Here we have
A water sample shοws 0. 066 grams οf sοme trace element fοr every cubic centimeter οf water.
Shandra uses a cοntainer in the shape οf a right cylinder with a radius οf 5. 7 cm and a height οf 13. 9 cm tο cοllect a secοnd sample
As we knοw the vοlume οf a right cylinder, V = πr²h
Substituting the given values, we get:
V = π(5.7 cm)²(13.9 cm)
V = 1419.34 cm³
Since the cοncentratiοn οf the trace element is 0.066 g/cm³,
Find the number οf trace elements in the sample by multiplying the vοlume οf the sample by the cοncentratiοn:
Amοunt οf trace element = cοncentratiοn × vοlume
Amοunt οf trace element = 0.066 g/cm³ × 1419.34 cm³
Amοunt οf trace element = 93.67 g
Therefοre,
Shandra has cοllected apprοximately 93.67 grams οf the trace element.
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Work out the value of 4 cubed - 6 squared.
help if can for 10+ points
Answer:
28
Step-by-step explanation:
4 cubed means 4 x 4 x 4, which is 64.
6 squared means 6 x 6, which is 36.
So,
4 cubed - 6 squared = 64 - 36 = 28.
Please help! I need this question to pass my class
Answer:
Step-by-,step explanation:
s.,s
Two balanced and fair dice are rolled. One is six-sided and the other is eight-sided. What is the probability of rolling a sum greater than 12 or a sum that is an odd number? Submit the answer as a simplified fraction. Use the forward slash (/) to separate the numerator from the denominator without spaces before or after. For example, three-fourths should be submitted as
5/6
The probability of rolling a sum greater than 12 or a sum that is an odd number after rolling two balanced and fair dice is 47/96.What is the probability of rolling a sum greater than 12 or a sum that is an odd number?The given information says that there are two balanced and fair dice. One is a six-sided die, and the other is an eight-sided die. We need to find the probability of rolling a sum greater than 12 or a sum that is an odd number after rolling the two dice.It's necessary to know the possible outcomes of the dice game when two dice are rolled. The 6-sided die has possible outcomes {1,2,3,4,5,6}, and the 8-sided die has possible outcomes {1,2,3,4,5,6,7,8}.The possible outcomes for each sum from 2 to 14 are shown below in the following table:The sum of the faces is odd if only one of the dice has an even number. In contrast, the sum of the faces is even if both dice have an even number. The red color represents the sum of the faces, which is an odd number, while the blue color represents the sum of the faces, which is an even number. Now we can easily calculate the total number of sums that are either greater than 12 or an odd number. It is important to note that the sum of 2 and 4 is even, and the sum of 13 and 14 is greater than 12. So the total number of sums that are either greater than 12 or an odd number is: 1 + 4 + 1 + 6 + 8 + 8 + 6 + 1 + 4 + 1 = 40It's also necessary to calculate the total number of possible outcomes when rolling two dice. The number of possible outcomes when rolling two dice is 6 x 8 = 48.We now have everything we need to find the probability of rolling a sum greater than 12 or a sum that is an odd number:Probability = Number of favorable outcomes / Total number of possible outcomes= 40/48 = 5/6Therefore, the probability of rolling a sum greater than 12 or a sum that is an odd number is 5/6.
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A ball is dropped from a height of 10 ft. Assuming that on each bounce, the ball rebounds to one-fifth of its previous height, find the total distance traveled by the ball.
Answer: The ball is dropped from a height of 10 ft, so it first travels down 10 ft until it hits the ground. The distance traveled in this first part is 10 ft.
On the first bounce, the ball rebounds to one-fifth of its previous height, which is 2 ft (since 10/5 = 2). The ball then travels up 2 ft and back down 2 ft to the ground, for a total distance traveled of 10 + 2 + 2 = 14 ft.
On the second bounce, the ball rebounds to one-fifth of its previous height, which is 2/5 ft (since 2/5 x 2 = 4/5). The ball then travels up 4/5 ft and back down 4/5 ft to the ground, for a total distance traveled of 2/5 + 4/5 + 4/5 = 2 ft.
On the third bounce, the ball rebounds to one-fifth of its previous height, which is 4/25 ft (since 4/25 x 2/5 = 8/125). The ball then travels up 8/125 ft and back down 8/125 ft to the ground, for a total distance traveled of 4/25 + 8/125 + 8/125 = 0.32 ft (rounded to two decimal places).
The ball will continue to bounce, getting closer and closer to the ground with each bounce. We can calculate the total distance traveled by summing the distances traveled on each bounce:
10 + 14 + 2 + 0.32 + ...
To calculate the sum of this infinite series, we can use the formula for the sum of an infinite geometric series:
S = a / (1 - r)
where S is the sum, a is the first term, and r is the common ratio.
In this case, a = 10 (the distance traveled on the first drop), and r = 1/5 (the fraction by which the height decreases on each bounce). Plugging in these values, we get:
S = 10 / (1 - 1/5)
= 12.5
So the total distance traveled by the ball is 12.5 ft.
Step-by-step explanation:
suppose you have a set of data with a mean of 50 and a standard deviation of 10. if you add 5 to each data point, what will happen to the mean and the standard deviation of the new set of data?
If you add 5 to each data point in a set of data with a mean of 50 and a standard deviation of 10, the mean of the new set of data will become 55. The standard deviation of the new set of data will remain the same at 10.
What is the standard deviation?The term standard deviation is frequently used in statistics to quantify the dispersion or spread of a set of data. The standard deviation is a measure of the amount of variation or dispersion of a set of data values from the mean. Standard deviation is denoted by the symbol s or σ (sigma).
What is the mean of a set of data?The term mean or arithmetic mean is used in statistics to refer to the value that represents the central tendency of a data set. It is computed by dividing the sum of all data values into a data set by the total number of data points. The formula for computing the mean is given as:
mean = (sum of data values) / (total number of data points)
When you add 5 to each data point in a data set with a mean of 50, the sum of all data values in the data set will increase by (5 * n), where n is the total number of data points. Consequently, the new mean will be given as:
new mean = (sum of new data values) / (total number of data points)
⇒ [(sum of old data values) + (5 * n)] / n ⇒ (50n + 5n) / n ⇒ 55
What is the effect of adding a constant to every data point in a data set?When you add a constant value to each data point in a data set, the measure of central tendency, i.e., mean, median, and mode will also be shifted by the same constant value. This is because the sum of all data values in the data set increases by the product of the constant value and the total number of data points, n.
The measure of variability or spread, i.e., range, interquartile range, variance, and standard deviation, however, remains the same because it is independent of the location of the data values in the data set. Therefore, adding a constant value to every data point in a data set does not change the spread of the data set but shifts the measure of central tendency to a new value.
Hence, the mean of the new dataset will increase by 5, from 50 to 55, and the standard deviation of the new dataset will remain the same at 10.
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A normal distribution has mean =μ57 and standard deviation =σ20. Find and interpret the z-score for =x50.
The z-score for =x50 is. So 50 is standard deviations ▼(Choose one) the mean =μ57
If a normal distribution has mean of 57 and standard deviation as 20, then the z-score for x=50 is -0.35 .
In order to find the z-score for x=50, we can use the formula : z = (x-μ)/σ ;
Where x is = 50, "μ" is = mean of the distribution , and "σ" is = standard deviation of the distribution ;
In this case , x = 50 , mean(μ) = 57 and standard deviation(σ) = 20;
Substituting in the values,
We get,
⇒ z = (50-57)/20,
Simplifying, We get,
⇒ z = -0.35
So, the z-score for x=50 is -0.35.
Interpretation of the z-score is that :
The z-score represents the number of standard deviations that a given value (in this case, x=50) is from the mean of the distribution (μ=57).
A negative z-score means that the value is below mean. In this case, x=50 is 0.35 standard deviations below the mean of 57.
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The given question is incomplete, the complete question is
A normal distribution has mean of 57 and standard deviation as 20. Find and interpret the z-score for x=50.
hw06-MoreProbability: Problem 9 (1 point) Employment data at a large company reveal that 59% of the workers are married, that 39% are college graduates, and that 1/5 of the college graduates are married. What is the probability that a randomly chosen worker is: a) neither married nor a college graduate? Answer =% b) married but not a college graduate? Answer = c) married or a college graduate? Answer = Note: You can earn partial credit on this problem. You have attempted this problem 0 times. You have unlimited attempts remaining.
The answer is 0.68.b) To find the probability that a randomly selected worker is married but not a college graduate, we need to subtract the probability that the person is married and a college graduate from the probability that the person is married.
The probability that a randomly selected worker is neither married nor a college graduate is the complement of the probability that they are either married or a college graduate. The equation for the complement is 1 - P(A).1 - (0.59 + 0.39 - 0.2)1 - (0.78 - 0.2)0.22. The answer is 0.68.b) To find the probability that a randomly selected worker is married but not a college graduate, we need to subtract the probability that the person is married and a college graduate from the probability that the person is married. The equation is P(A ∩ B) = P(A) × P(B|A).0.591 - 0.196 = 0.394.The answer is 0.394.c) To find the probability that a randomly selected worker is either married or a college graduate, we can use the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B).0.59 + 0.39 - 0.196 = 0.784.The answer is 0.784.
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Jacob conducts another survey of students in the school in the Example. This time,
he surveys a random sample of 30 students.
a. In Jacob's sample, 24 students say they will vote for Garrett. Based on this
sample, about how many students in the school should Garrett expect to vote
for him? Show your work.
SOLUTION
Jacob's sample suggests that Garrett should expect approximately 80 percentage of the students in the school to vote for him.
Jacob's sample of 30 students suggests that 24 of them will vote for Garrett, which is an 80% ratio. Applying this ratio to the entire school population, Garrett can reasonably expect that 80% of the students in the school will vote for him. This means that out of the total student population, Garrett can expect approximately 24/30, or 80%, of them to vote for him. This is a useful estimate for how many votes Garrett can expect to receive from the student body. It is important to note, however, that this is only an estimate and may not accurately reflect the actual number of students who will vote for Garrett. Factors such as student opinion or external influences may affect the actual voting results.
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Solve using the Zero Product Property. Give your answer as a decimal, if necessary. A group of friends tries to keep a small bean bag from touching the ground by kicking it. On one kick, the beanbags height can be modeled by the equation h = −(2t − 3) − 8t(2t − 3), where h is the height of the beanbag in feet and t is the time in seconds. Find the time it takes the beanbag to reach the ground. The time it takes for the beanbag to reach the ground is ___ second(s)
As per the given equation, the beanbag will reach the ground after 1.5 seconds.
To find the time it takes for the beanbag to reach the ground, we need to set h equal to zero, since the beanbag will be on the ground when its height is zero. So we have the equation:
0 = −(2t − 3) − 8t(2t − 3)
We can simplify this equation by factoring out the common factor of (2t − 3):
0 = (2t − 3)(−1 − 8t)
Now we can use the Zero Product Property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero. So we can set each factor equal to zero and solve for t:
2t − 3 = 0 or −1 − 8t = 0
Solving the first equation for t, we get:
2t = 3
t = 3/2
Solving the second equation for t, we get:
−1 − 8t = 0
8t = −1
t = −1/8
However, we need to discard the negative value of t, because time cannot be negative. So the time it takes for the beanbag to reach the ground is t = 3/2 seconds or 1.5 seconds
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What is the arc length of an arc with radius 18 inches and central angle 22°? Round to nearest hundredth or leave in terms of π. Show your work.
We calculate the arc length to be 6.86 inches by rounding to the closest hundredth.
What is a Circle's Arc Length?The distance between two places in a curve's section is known as the arc length of a circle. Any portion of a circle's circumference is an arc. The angle formed by the two line segments joining a point to an arc's endpoints at any given position is known as the arc's angle.
An arc with a radius of 18 inches and a centre angle of 22° can be calculated using the formula below:
Arc length = (central angle / 360°) × (2πr)
where r denotes the circle's radius.
Substituting the given values, we get:
Arc length = (22° / 360°) × (2π × 18 inches)
Arc length = (0.0611) × (2π × 18 inches)
Arc length ≈ 6.86 inches
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Refer to exercise 3. 67. What is the expected number of applicants who need to be interviewed in order to find the first one with advanced training?
The expected number of applicants who need to be interviewed in order to find the first one with advanced training is 8.
We can calculate this by using the formula for the geometric series. The formula for the geometric series is given by S = a1(1-rn)/1-r, where a1 is the first term in the series, r is the common ratio, and n is the number of terms. In this problem, a1 = 1 (since the probability of finding the first applicant with advanced training is 1/8), and r = 1/8 (since the probability of finding the next applicant with advanced training is 1/8). Thus, plugging these values into the formula yields S = 1(1-(1/8)^n)/1-(1/8) = 8. Therefore, the expected number of applicants who need to be interviewed in order to find the first one with advanced training is 8.
S = a1(1-rn)/1-r
S =[tex]1(1-(1/8)^n)/1-(1/8)[/tex]
S = 8
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Clty Line What is the measure of the angle formed by the intersection of the River Line and the Northeast Line?
The measure of the angle formed by the intersection of the River Line and the Northeast Line is equal to: C. 42°.
What is a supplementary angle?In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can logically deduce that the sum of the given angles are supplementary angles:
60° + (8x - 18)° + (3x + 6)° = 180°
60° + 8x - 18° + 3x + 6° = 180°
11x = 180° - (18° - 6° - 60°)
11x = 180° - 48°
11x = 132°
x = 132/11
x = 12
For the intersection of the River Line and the Northeast Line, we have:
R = (3x + 6)°
R = 3(12) + 6
R = 36 + 6
R = 42°.
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Complete Question:
What is the measure of the angle formed by the intersection of the River Line and the Northeast Line?
40
41
42
43
Suki took $20 to the carnival she spent one half of her money on rides 1/4 of her money on food and 1/10 of her money on parking how much did Suki spend on rides on food and on parking
Suki spent a total of $17 on rides, food, and parking at the carnival.
The problem states that Suki took $20 to the carnival and spent some portion of it on rides, food, and parking. The first step is to figure out what fractions of her money she spent on each of these things.
The problem tells us that she spent one half of her money on rides, 1/4 of her money on food, and 1/10 of her money on parking. We can write this mathematically and use the multiplication :
Suki spent 1/2 x $20 = $10 on rides
Suki spent 1/4 x $20 = $5 on food
Suki spent 1/10 x $20 = $2 on parking
To find the total amount that Suki spent on rides, food, and parking combined, we simply add up these three amounts:
Total spent = $10 + $5 + $2 = $17
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Me podrían ayudar no entiendo cómo hacerlo
A bisector in math is a line or a line segment that divides an angle or a line segment into two equal parts.
What is bisector?The bisector, also known as the perpendicular bisector, is a geometric concept in mathematics that is used to construct a line that is perpendicular to a given segment and passes through its midpoint. The bisector is an important tool in geometry and is used in a variety of applications, including constructing triangles, circles, and finding the circumcenter.
To construct the bisector of a segment, one must first locate the midpoint of the segment. This is done by dividing the length of the segment in half, using a straightedge to connect the two endpoints, and then drawing a perpendicular line through the midpoint. The resulting line is the bisector of the segment.
The bisector has several important properties. First, it is always perpendicular to the segment it bisects. This means that the angle between the bisector and the segment is always 90 degrees. Second, the bisector always passes through the midpoint of the segment. Finally, any point on the bisector is equidistant from the two endpoints of the segment. This means that the bisector can be used to construct other geometric objects that are equidistant from the endpoints of the segment, such as circles.
In summary, the bisector is a line that is perpendicular to a given segment and passes through its midpoint. It is an important tool in geometry and is used in a variety of applications, including constructing triangles, circles, and finding the circumcenter.
Note: This question is in Spanish. Here is the translation to English.
Bisector: the line by which a segment is divided into two parts perpendicularly.
Please explain this.
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what is the answer to this
Answer:
[tex]\huge\boxed{\sf 10(9n + 8m)}[/tex]
Step-by-step explanation:
Given expression:= 90n + 80 m
Common factor = 10
So, the expression becomes:
= 10(9n + 8m)[tex]\rule[225]{225}{2}[/tex]
Answer: C
Step-by-step explanation: If you factor 10 out of 90n and 80m then you get 9n and 8m for each. to make the equation you get: 10(9n+8n)
Sadie needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 5 hours and charged her $70 for parts. The total was $395. Which equation or tape diagram could be used to represent the context if
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x represents the cost of labor per hour?
We get the equation as : 5y + 70 = 395 if the computer for 5 hours and charged her $70 for parts. The total was $395.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let's use the variable "y" to represent the cost of labor per hour.
The technician worked on the computer for 5 hours, so the cost of labor would be 5y. Additionally, the technician charged $70 for parts. The total cost was $395. We can set up the following equation to represent the context:
5y + 70 = 395
This equation represents the total cost Sadie paid for the repair, which includes the cost of labor and parts.
Alternatively, we can use a tape diagram to represent the context. We can draw a rectangle and divide it into two parts, one representing the cost of labor and the other representing the cost of parts. The length of the labor part would be Five times the cost per hour (5y), and the length of the parts part would be $70.
]The length of the whole rectangle would represent the total cost ($395). We can label the unknown cost per hour as "y".
Therefore, we get the equation as : 5y + 70 = 395 if the computer for 5 hours and charged her $70 for parts. The total was $395.
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Let \underset{v}{\rightarrow}= (4, 2) and \underset{w}{\rightarrow}= (1, -3).
1. Find 7\underset{v}{\rightarrow} - 3\underset{w}{\rightarrow} and state the result in component form
2. State the exact magnitude (length) of \underset{v}{\rightarrow} and the exact magnitude of \underset{w}{\rightarrow}
3. State the dot product \underset{v}{\rightarrow}\cdot \underset{w}{\rightarrow}
4. Find proj_{\underset{w}{\rightarrow}}(\underset{v}{\rightarrow})proj_{\underset{v}{\rightarrow}}(\underset{w}{\rightarrow}) in component form. Give exact values. Show work.
5. Determine the angle between \underset{v}{\rightarrow} and \underset{w}{\rightarrow}. Show work. Write the exact angle as the arccosine of an appropriate number. Also, use a calculator to approximate the value of the angle, rounding the result to the nearest degree.
The approximate angle is $\approx 135^{\circ}$, rounded to the nearest degree
\underset{v}{\rightarrow} - 3\underset{w}{\rightarrow} = (7 \cdot 4, 7 \cdot 2) - (3 \cdot 1, 3 \cdot -3) = (28, 12). The result in component form is (28, 12).
The exact magnitude of \underset{v}{\rightarrow} is $\sqrt{4^2 + 2^2} = \sqrt{20}$ and the exact magnitude of \underset{w}{\rightarrow} is $\sqrt{1^2 + (-3)^2} = \sqrt{10}$.
The dot product \underset{v}{\rightarrow}\cdot \underset{w}{\rightarrow} is (4 \cdot 1) + (2 \cdot -3) = -10.
proj_{\underset{w}{\rightarrow}}(\underset{v}{\rightarrow}) = (\frac{\underset{v}{\rightarrow}\cdot \underset{w}{\rightarrow}}{\Vert \underset{w}{\rightarrow} \Vert^2})\underset{w}{\rightarrow} = (\frac{-10}{10}) \cdot (1, -3) = (-1, 3).
proj_{\underset{v}{\rightarrow}}(\underset{w}{\rightarrow}) = (\frac{\underset{v}{\rightarrow}\cdot \underset{w}{\rightarrow}}{\Vert \underset{v}{\rightarrow} \Vert^2})\underset{v}{\rightarrow} = (\frac{-10}{20}) \cdot (4, 2) = (-2, -1). The results in component form are (-1, 3) and (-2, -1).
The angle between \underset{v}{\rightarrow} and \underset{w}{\rightarrow} can be found using the formula $\cos\theta = \frac{\underset{v}{\rightarrow}\cdot \underset{w}{\rightarrow}}{\Vert \underset{v}{\rightarrow} \Vert \cdot \Vert \underset{w}{\rightarrow} \Vert}$.
Plugging in the values, $\cos\theta = \frac{-10}{\sqrt{20}\cdot\sqrt{10}} = -\frac{1}{\sqrt{2}}$. The exact angle is $\arccos(-\frac{1}{\sqrt{2}})$. Using a calculator, the approximate angle is $\approx 135^{\circ}$, rounded to the nearest degree.
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