In the graph, line k with equation y = -k makes a 45° angle with the x- and y- axes. The correct option is 1. (-2, 5).
What is a graph?The angle formed by the line y = - x with the x-axis is 45 degrees, and the angle formed by the y-axis with the positive x-axis is 135 degrees.
The coordinates of the reflected point, when a point (p,q) is reflected over the line y=x, are (q,p)
Moreover, the coordinates of the reflected point, when point (p,q) is reflected over the line y= -x, will be (-q, -p).
Hence, the coordinates of the reflected point when point (2,5) is reflected over the line y= - x will be (-5,-2).
The point (2,5) will change to if it is reflected across the line y=x (5,2).
Therefore, the correct option is 1. (-2, 5).
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An article on the relation of cholesterol levels in human blood to aging reports that average cholesterol level for women aged 70-74 was found to be 230m/dl. If the standard deviation was 20mg/dl and the distribution normal, what is the probability that a given woman in this age group would have a cholesterol level
a) Less than 200mg/dl
b) More than 200mg/dl
c) Between 190mg/dl and 210mg/dl
d) Write a brief report on the guidance you would give a woman having high cholesterol level in this age group
a) The probability of a given woman in this age group having a cholesterol level less than 200mg/dl is 6.68%.
b) The probability of a given woman in this age group having a cholesterol level more than 200mg/dl is 93.32%.
c) The probability of a given woman in this age group having a cholesterol level between 190mg/dl and 210mg/dl is 15.87%.
d) If a woman in this age group has a cholesterol level higher than 230mg/dl, it is considered high and puts her at risk of heart disease
To calculate the probability of a given woman in this age group having a cholesterol level less than 200mg/dl, we need to find the z-score first. The z-score is the number of standard deviations that a given value is from the mean. The formula to calculate the z-score is:
z = (x - μ) / σ
where x is the given value, μ is the mean, and σ is the standard deviation.
For a cholesterol level of 200mg/dl, the z-score is:
z = (200 - 230) / 20 = -1.5
We can then use a z-table or calculator to find the probability of a z-score being less than -1.5, which is 0.0668 or approximately 6.68%.
Next, to find the probability of a given woman in this age group having a cholesterol level more than 200mg/dl, we can use the same process but subtract the probability of a z-score being less than -1.5 from 1 because the total probability is always 1.
So, the probability of a given woman in this age group having a cholesterol level more than 200mg/dl is:
1 - 0.0668 = 0.9332 or approximately 93.32%.
Finally, to find the probability of a given woman in this age group having a cholesterol level between 190mg/dl and 210mg/dl, we need to find the z-scores for both values.
For a cholesterol level of 190mg/dl, the z-score is:
z = (190 - 230) / 20 = -2
For a cholesterol level of 210mg/dl, the z-score is:
z = (210 - 230) / 20 = -1
We can then use the z-table or calculator to find the probability of a z-score being between -2 and -1, which is 0.1587 or approximately 15.87%.
Finally, a brief report on the guidance that you would give a woman having high cholesterol levels in this age group is:
It is essential to make lifestyle changes such as eating a healthy diet, exercising regularly, quitting smoking, and managing stress to lower cholesterol levels.
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The function f is given by f(x) = 10x + 3 and the function g is given by g(x) = 2×. For each question, show your reasoning
1. Which function reaches 50 first
2. Which function reaches 100 first?
1. x = 4.7 for f(x) and x = 25 for g(x), f(x) reaches 50 first.
2. x = 9.7 for f(x) and x = 50 for g(x), f(x) reaches 100 first.
1. Which function reaches 50 first?
To answer this, we need to solve for x in each function when the output is 50:
For f(x): 50 = 10x + 3
47 = 10x
x = 4.7
For g(x): 50 = 2x
x = 25
Since x = 4.7 for f(x) and x = 25 for g(x), f(x) reaches 50 first.
2. Which function reaches 100 first?
Similarly, we'll solve for x in each function when the output is 100:
For f(x): 100 = 10x + 3
97 = 10x
x = 9.7
For g(x): 100 = 2x
x = 50
Since x = 9.7 for f(x) and x = 50 for g(x), f(x) reaches 100 first.
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scenic cinemas surveyed its audience and found that while most movie goers prefer weekends, seniors visit on weekdays. how should the theatre respond?
Scenic Cinemas should offer discounted weekday matinee showings for seniors and continue to focus on weekend showings for their broader audience.
How should Cinemas tailor their offerings to accommodate both preferences?Based on the survey results, it would be wise for Scenic Cinemas to tailor their offerings to accommodate both preferences.
One option would be to offer discounted weekday matinee showings targeted toward seniors. This could incentivize them to visit on weekdays while also offering them a more affordable option. At the same time, Scenic Cinemas could continue to focus on weekend showings to cater to their broader audience.
Another approach would be to offer more diverse programming during the weekdays, such as classic films or independent movies that may appeal more to seniors. This could create a niche for Scenic Cinemas and attract a more loyal customer base.
Ultimately, it's important for Scenic Cinemas to balance the needs of their different audience segments to maximize revenue and customer satisfaction. By offering targeted promotions and programming, they can ensure that both seniors and other moviegoers feel valued and have a reason to visit the theatre.
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What is the mean of this data set?
Please help
Answer:
Step-by-step explanation:
Find the area of the circle with a circumference of
. Write your solution in terms of
.
Area in terms of
: ______
The length of one leg of a right triangle is 2 times the length of the other, and the
length of the hypotenuse is 12. What is the length of the longest leg?
Answer:
[tex]\frac{24\sqrt{5} }{5}[/tex]
Step-by-step explanation:
Let's start by assigning one of the unknown legs with the variable x.
We know that the other leg is 2 times the length of x, so we can write:
2x
We also know that the length of the hypotenuse is 12.
From here, we can use the Pythagorean Theorem.
Recall that the Pythagorean Theorem is:
[tex]a^2+b^2=c^2[/tex]
where a is the length of one leg, b is the length of the other leg, and c is the length of the hypotenuse.
Let's substitute the values. We have:
[tex]x^2+(2x^2)=12^2=\\x^2+4x^2=144=\\5x^2=144=\\x^2=\frac{144}{5}=\\x=\frac{12}{\sqrt{5} }[/tex]
Let's rationalize the denominator by multiplying the numerator and denominator by [tex]\sqrt{5}[/tex], like so:
[tex]\frac{12}{\sqrt{5} } =\\\frac{12\sqrt{5} }{5}[/tex]
Therefore, [tex]x=\frac{12\sqrt{5} }{5}[/tex]
Let's solve for 2x:
[tex]2x=\\2(\frac{12\sqrt{5} }{5})=\\ \frac{24\sqrt{5} }{5}[/tex]
So, the length of the longest leg is [tex]\frac{24\sqrt{5} }{5}[/tex]
sue works 5 out of the 7 days of the week. how many possible schedules are there to work on tuesday or friday or both?
Sue works 5 out of 7 days a week, which implies that she has two days off. We need to discover how numerous conceivable plans there are for her to work on Tuesday or Friday or both.
There are two cases to consider:
1. Sue works on Tuesday as it were, Friday as it were, or both Tuesday and Friday.
2. Sue does not work on Tuesday or Friday.
For the primary case, there are three conceivable outcomes:
1. Sue works on Tuesday as it were and has Friday off.
2. Sue works on Friday as it were and has Tuesday off.
3. Sue works on both Tuesdays and Fridays.
For the moment case, there are two conceivable outcomes:
1. Sue works on one of the other 5 days of the week and has both Tuesday and Friday off.
2. Sue has Tuesday and Friday off.
In this manner, there are added up to 3 + 2 = 5 conceivable plans for Sue to work on Tuesday or Friday or both.
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Please help offering 15 points
More people that rode the roller coaster are between the ages of 11 and 30, than people that are between the ages of 41 and 60 is the best description of the data which is obtained by using the arithmetic operations.
What are arithmetic operations?
Any real number may be explained using the four basic operations, also referred to as "arithmetic operations." Operations like division, multiplication, addition, and subtraction come before operations like quotient, product, sum, and difference in mathematics.
We are given a chart. From the chart we get the following data:
Number of people aged 11 - 20 riding roller coaster = 20
Number of people aged 21 - 30 riding roller coaster = 15
Number of people aged 31 - 40 riding roller coaster = 10
Number of people aged 41 - 50 riding roller coaster = 5
Number of people aged 51 - 60 riding roller coaster = 0
Using addition operation, we get
Total people = 20 + 15 + 10 + 5 + 0
Total people = 40
Now,
Total riders between 11 - 30 = 20 + 15
Total riders between 11 - 30 = 35
Similarly,
Total riders between 41 - 60 = 5 + 0
Total riders between 41 - 60 = 5
Hence, the fourth option is the correct answer.
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data from a sample of randomly selected students is shown below. the variables collected are: exercise - the number of hours a student exercise per week debt - the amount of student loan debt (in thousands of dollars) a student is expected to graduate with age - the age of a student gpa - the gpa of a student descriptive statistics exercise debt age gpa n 241 196 254 248 lo 95% ci 7.0769 8.8655 20.069 3.2702 mean 7.8133 11.311 20.500 3.3200 up 95% ci 8.5497 13.757 20.931 3.3822 sd 5.8032 17.361 3.5000 0.3400 minimum 0.0000 0.0000 17.000 1.7500 1st quartile 4.0000 0.0000 19.000 3.0200 median 7.0000 3.0000 20.000 3.3600 3rd quartile 10.000 20.000 21.000 3.6950 maximum 35.000 100.00 41.000 4.0000 someone claims that the mean exercise time of all students is 10 hours per week. how would you respond? group of answer choices at the 95% confidence level, the mean exercise time of all students might be 10 hours per week. i am 95% confident that the mean exercise time of all students equals 7.8133 hours per week. i am 95% confident that the mean exercise time of all students is greater than 10 hours per week. i am 95% confident that the mean exercise time of all students is less than 10 hours per week.
The most appropriate response to the claim would be: "At the 95% confidence level, the mean exercise time of all students might not be 10 hours per week based on the sample data."
How do you 95% confident about the claim?Based on the given data, we can see that the sample mean exercise time is 7.8133 hours per week. The standard deviation of the exercise time is 5.8032, indicating that there is some variability in the data.
To determine whether the claim that the mean exercise time of all students is 10 hours per week is reasonable, we can conduct a hypothesis test.
Our null hypothesis would be that the mean exercise time of all students is equal to 10 hours per week, and the alternative hypothesis would be that the mean exercise time is different from 10 hours per week.
We can then calculate a test statistic and compare it to a critical value based on a t-distribution with n-1 degrees of freedom, where n is the sample size.
Alternatively, we can use the confidence interval provided in the table to make a statement about the claim.
We can see that the 95% confidence interval for the mean exercise time is [7.0769, 8.5497]. Since 10 is outside of this interval, we can say that at the 95% confidence level, the claim that the mean exercise time of all students is 10 hours per week is not supported by the data.
Therefore, the most appropriate response to the claim would be: "At the 95% confidence level, the mean exercise time of all students might not be 10 hours per week based on the sample data."
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Given a circle has a center at (-6, 14) and a diameter of 30, write the equation of the circle
Answer:
The center of the circle is at (-6, 14), and the radius is 15, so we have this equation:
[tex] {(x + 6)}^{2} + {(y - 14)}^{2} = 225 [/tex]
the ricardo household used w cubic feet of water during a summer month express the number of ccf of water they used algebraically
Ricardo used w/100 Ccf of water.
Given that, Ricardo household used w cubic feet of water in a month of summers,
we need to express the number of ccf of water they used algebraically,
Ccf = A CCF is a unit of measurement of volume.
The CCF is used to measure gas consumption, used in the billing of natural gas and water delivered to households.
1 CCF = 100 cubic feet
CCF means Centum Cubic Feet.
1 cubic feet = 0.01 Ccf
Therefore,
w cubic feet = 0.01 × w Ccf
= w / 100
Hence, Ricardo used w/100 Ccf of water.
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A factory has two assembly lines, M and N, that make the same toy. On Monday, only assembly line M was functioning and it made 900 toys.
On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and line N made 480 toys per hour. Line N made as many toys on Tuesday as line M did over both days.
Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.
Answer: First choice 480t = 300t + 900
Step-by-step explanation:
A factory has two assembly lines, M and N, that make the same toy. On Monday, only assembly line M was functioning and it made 900 toys.
On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and line N made 480 toys per hour. Line N made as many toys on Tuesday as line M did over both days.
Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.
ANS
Let say t is time in hrs for Which Both Assembly line worked
M made 300 toys per hr on Tuesday
Toys made on Tuesday at Assembly line M = 300 × t = 300t toys
N made 480 toys per hr on Tuesday
Toys made on Tuesday at Assembly line N = 480 × t = 480t toys
Toys Made by N on Tuesday = Toys made by M on Tuesday + Toys made by M on Monday
480t = 300t + 900
=> 180 t = 900
=> t = 900/180
=> t = 5 hr
N capacity on tuesday Per hour * t = M capacity on tuesday per hour * t + Toys made by M on Monday
N = N capacity on tuesday Per hour
M = M capacity on tuesday Per hour
=> t (N - M ) = 900
=> t = 900/(N-M)
Frank and Joey ordered a large pizza. Frank ate 20% of rye pizza and Joey at 4/5 of the pizza. What percentage of the pizza did they eat in all
The percentage of the large pizza they ate is 100%
To calculate the percentage of pizza they both ate we have to add and then covert the fractions to percentage.
Given from the question
Frank ate 20% of the large pizza and Joey ate 4/5 portion of the large pizza
Converting 4/5 into percentage
For converting into percentage we have to multiply 100 to the fraction
= 4/5 x 100
= 80%
Now, let us proceed by adding the collected two percentages to find out the total percentage of pizza consumed by Frank and Joey
20% + 80%
= 100%
The percentage of the large pizza they ate is 100%.
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4. The radius of a cylinder is 3x-2 cm. The height of the cylinder is x +3 cm. What is the
surface area of the cylinder? Use the formula A=2x²+2xrh.
02x (3x2+10x-8)
O 27(12x+7x-2)
O 27(12x²-2x+13)
O 27(12x²-5x-2)
Answer:
D: 27(12x² - 5x - 2).
Step-by-step explanation:
The formula for the surface area of a cylinder is: A = 2πr² + 2πrh
Given that the radius of the cylinder is 3x - 2 cm and the height is x + 3 cm, we can substitute these values in the formula and simplify:
A = 2π(3x - 2)² + 2π(3x - 2)(x + 3)
A = 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6)
A = 18πx² - 24πx + 8π + 6πx² + 14πx - 12π
A = 24πx² - 10πx - 4π
A = 2π(12x² - 5x - 2)
Therefore, the answer is option D: 27(12x² - 5x - 2).
Answer:
D
Step-by-step explanation:
Please only do 9,11, and 13! And please help!! 40 points!!!
9. The volume of the triangular pyramid is given by:
V = (1/3)Bh
Here, B is the base area.
The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:
h = sqrt(26.7² - 11.7²) = 23.274 km
The area if the base is:
B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km
Now, the volume is:
V = (1/3)(136.89)(15) = 2053.35 cubic km
Hence, the volume of the triangular pyramid is 2053.35 cubic km.
9. The volume of the triangular pyramid is 2053.35 cubic km. 11. The area of the shaded portion is 348.19 cubic in 13. The slant height of the cone is 8.53 meters.
What is Pythagoras Theorem?A fundamental conclusion in geometry relating to the lengths of a right triangle's sides is known as Pythagoras' theorem. According to the theorem, the square of the length of the hypotenuse, the side that faces the right angle, in any right triangle, equals the sum of the squares of the lengths of the other two sides, known as the legs.
9. The volume of the triangular pyramid is given by:
V = (1/3)Bh
Here, B is the base area.
The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:
h = √(26.7² - 11.7²) = 23.274 km
The area if the base is:
B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km
Now, the volume is:
V = (1/3)(136.89)(15) = 2053.35 cubic km
Hence, the volume of the triangular pyramid is 2053.35 cubic km.
11. The volume of a cone is given by:
V = (1/3)πr²h
The dimension of the bigger cone is radius is 9 in, and height 15 in:
V1 = (1/3)π(9 in)²(15 in) = 381.7 cubic in
The dimension of the smaller cone is radius is 4 in, and height 10 in:
V2 = (1/3)π(4 in)²(10 in) = 33.51 cubic in
Now, the area of the shaded portion is:
V1 - V2 = 381.7 - 33.51 = 348.19
13. The volume of a cone is given by:
V = (1/3)πr²h
Substituting the values we have:
542.87 = (1/3)π(6 m)²h
h = 542.87 / [(1/3)π(6 m)²] = 6.05 m
Now, using the Pythagoras Theorem for the slant height we have:
s² = r² + h²
s² = (6 m)² + (6.05 m)²
s² = 72.9
s = √(72.9) = 8.53 m
The slant height of the cone is 8.53 meters.
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Can please someone help me ASAP? It’s due tomorrow. I will give brainliest if it’s all correct!!
Please do part a, b, and c
The sample space are:
{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}
The favorable outcomes care:
{RS, RT, SR, ST, TR, TS}
The probability is 0.3 or 30%
How to find the sample spacePart A:
The sample space represents all possible outcomes that can occur when two cards are randomly selected without replacement from the given pile of cards.
The sample space can be represented as follows:
{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}
Part B:
The favorable outcomes are those outcomes in which both cards are consonants. In this case, the consonants are R, S, and T.
The favorable outcomes can be represented as follows:
{RS, RT, SR, ST, TR, TS}
Part C:
To calculate the probability of selecting 2 cards that are consonants, we need to find the ratio of favorable outcomes to the sample space.
The number of favorable outcomes is 6, and the size of the sample space is 20.
Therefore, the probability of selecting 2 cards that are consonants is:
P(consonants) = favorable outcomes / sample space
P(consonants) = 6 / 20
P(consonants) = 0.3 or 30%
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Complete the table using the information given.
Using the above information, we can calculate the missing figures in the table and this is shown on the table attached.
What is the table about?For the "Shorts" row: It's given that 42 people were wearing shorts.
Since it's mentioned that twice as many people were wearing closed-toed shoes as open-toed shoes, and 30 people were wearing open-toed shoes, we can deduce that 30 people were also wearing closed-toed shoes.So, the total number of people wearing closed-toed shoes is 30, and the total number of people wearing shorts is also 42, since they are the same group of people.Therefore, the "Close-Toed Shoes" column in the "Shorts" row is also 42, and the "Total" column is the sum of open-toed and closed-toed shoes, which is 84.
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See text below
30 people surveyed were wearing open-toed shoes.
1/3 of the people with open-toed shoes were wearing
pants.
• 42 people were wearing shorts.
Twice as many people were wearing closed-toed shoes
than open-toed shoes.
Complete the table using the information given.
Open-Toed Shoes Close-Toed Shoes Total
Shorts ------- ------ --------
Pants ------ ---------- ------
Total ------ ---------- ---------
A primary credit cardholder's card has an APR of 22. 99%. The current monthly balance, before interest, is $4,528. 34. Determine how much more the cardholder will pay, making monthly payments of $200, until the balance is paid off, instead of paying off the current balance in full
The cardholder will pay an additional $1,471.66 in interest by making monthly payments of $200 until the balance is paid off instead of paying off the current balance in full.
First, we need to calculate the total interest that will accrue on the current balance of $4,528.34. We can do this using the formula
Interest = Balance x (APR/12)
where APR is the annual percentage rate and is divided by 12 to get the monthly interest rate. Plugging in the values, we get:
credit card Interest = $4,528.34 x (22.99%/12) = $87.80
So the total interest that will accrue on the current balance is $87.80.
Next, we need to calculate how long it will take to pay off the balance by making monthly payments of $200. We can use a credit card repayment calculator to do this, but we'll use a simplified formula here
Months = -log(1 - (Balance x (APR/12))/Payment) / log(1 + (APR/12))
where Payment is the monthly payment amount. Plugging in the values, we get
Months = -log(1 - ($4,528.34 x (22.99%/12))/$200) / log(1 + (22.99%/12)) = 29.6 months
So it will take about 30 months (or 2.5 years) to pay off the balance by making monthly payments of $200.
Finally, we can calculate how much more the cardholder will pay in total by subtracting the current balance from the total amount paid over 30 months
Total amount paid = $200 x 30 = $6,000
Total interest paid = $6,000 - $4,528.34 = $1,471.66
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A 30 pack of copy paper cost $48.30 a 32 pack cost $49.60 which is the better buy (help me explain it)
Answer:
Step-by-step explanation:
the 32 pack because it costs just slightly more
Ms. Yamato's gross pay is $2644. Her deductions total $548.30.
What percent of her gross pay is take-home pay?
A. 84%
B. 79%
C. 21%
D. 18%
Thus, the correct Percent response is B) 79%.
what is a percent?Percentage refers to a portion of every hundred. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, it is frequently shown using the percent sign, "%".
If you have 100 apples and distribute 10 of them, for instance, you have distributed 10% of your total apple supply.
We deduct Ms. Yamato's deductions from her gross income to determine her take-home pay:
$2644 - $548.30 = $2095.702.
By dividing her take-home pay by her gross pay and multiplying the result by 100%, we can determine what proportion of her gross pay is taken home:
($2095.70 / $2644) * 100% = 79%
Thus, the correct response is B) 79%.
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n.2 multi-step word problems with positive rational numbers jvu you have prizes to reveal! go to your game board. on friday night, suzie babysat her cousin for 3 1 2 hours and earned $8.50 per hour. on saturday, she babysat for her neighbors for 4 1 2 hours. if she made a total of $72.50 from both babysitting jobs, how much did suzie earn per hour on saturday?
Answer:
$9.50
Step-by-step explanation:
You want Suzie's hourly rate on Saturday if she babysat for 3.5 hours on Friday, earning 8.50 per hour, and for 4.5 hours on Saturday, earning a total of 72.50 from both jobs.
EarningsFor (hours, rates) of (h1, r1) and (h2, r2), Suzie's total earnings for the two jobs are ...
earnings = h1·r1 +h2·r2
Filling in the known values, we can find r2:
72.50 = 3.5·8.50 +4.5·r2
72.50 = 29.75 +4.5·r2 . . . . . . . simplify
42.75 = 4.5·r2 . . . . . . . . . . . subtract 29.75
9.50 = r2 . . . . . . . . . . . . divide by 4.5
Suzie earned $9.50 per hour on Saturday.
__
Additional comment
The steps of the "multistep" problem are ...
find Friday's earningssubtract that from the total to find Saturday's earningsdivide by Saturday's hours to find the hourly rateEffectively, these are the steps to solving the equation we wrote.
HELP ME PLEASE!!!!!!!
Answer:
Step-by-step explanation:
Graph # Matching equation
1 |-3x|
2 |-x|
3 -|2x|
You can tell which one matches by finding the slope and whether the V points up or down
Send total home runs during the baseball season for over five other home runs during the first half of the season what is the fraction of home run hit through and a half of the season as a decimal
Terrell hit 0.8 of his home runs during the first half of the baseball season, which is the decimal equivalent of the fraction (4)/(5).
A fraction is a way of representing a part of a whole, where a whole is divided into equal parts and the fraction represents the number of those equal parts that are being considered.
A decimal number is a number expressed in the base-ten positional system, where each digit can take one of ten possible values and the value of each digit is determined by its position relative to the decimal point.
To write a fraction as a decimal, you simply divide the numerator (the top number) by the denominator (the bottom number). In this case, the fraction is (4)/(5), which means Terrell hit 4 out of 5 home runs during the first half of the season
(4)/(5) = 0.8
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The given question is incomplete, the complete question is:
Terrell hit a total of 10 home runs during the baseball season. He hit (4)/(5) of the home runs during the first half of the season. Write the fraction of home runs hit during the first half of the season as a decimal.
I NEED HELP ON THIS ASAP!! PLEASE IT'S DUE TODAY!
The exponential function to represent the number of new participants of the challenge as a function of the day number, is f(x) = 12 × 4ˣ.
How to find the exponential function ?Let f(x) be the number of new participants on day x.
On day 0 (today), Aliyah, Kim, and Reese are the only participants. They each send selfies to 4 friends, so there will be 3 x 4 = 12 new participants on day 1.
From day 1 onwards, each new participant will send selfies to 4 friends. Therefore, the number of new participants will quadruple each day. This gives us an exponential growth function:
f(x) = 12 × 4ˣ
where f(x) represents the number of new participants on day x.
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Find the number of permutations with of the letters in each word
The trigonometry functions when calculated are sin(A) = 18/34 and cos(A) = 30/34
Calculating the trigonometry functionsFrom the question, we have the following parameters that can be used in our computation:
The right triangle
Where we have
Opposite = 18Adjacent = 30Hypotenuse = 34Using the above as a guide, we have the following:
sin(A) = 18/34
cos(A) = 30/34
Hence, the values are sin(A) = 18/34 and cos(A) = 30/34
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the table shows several packages of assorted spools of thread available at a store. what is the price per spool of each kind of thread?
I'm sorry, but I cannot provide a definitive answer to your question as I do not have access to the table you are referring to.
However, in general, to find the price per spool of each kind of thread, you would need to know the total price of the package and the number of spools in the package.
To calculate the price per spool, you would divide the total price of the package by the number of spools in the package. For example, if a package costs $10 and contains 50 spools of thread, the price per spool would be $0.20 ($10 ÷ 50 = $0.20).
You can use this method to find the price per spool for each type of thread in the table you are looking at.
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What is the equation of the line 2x+3y+1=0 after it has been reflected across y=-1 and rotated about o(2,3) by 180
The equation of the line 2x + 3y + 1 = 0 after it has been reflected across y = -1 and rotated about O(2,3) by 180 degrees is -2x + y = 15.
To reflect the line 2x + 3y + 1 = 0 across the line y = -1, we need to subtract twice the y-coordinate of each point on the line from the equation of the line.
This is because the reflection of a point across a line is obtained by reflecting it across the line's perpendicular bisector, which is also the line with the same x-coordinates and twice the distance from the point to the line.
Subtracting twice the y-coordinate, we get:
2x + 3(-2y - 1) + 1 = 0
Simplifying the equation, we get:
2x - 6y - 5 = 0
Now, to rotate the line about the point O(2,3) by 180 degrees, we can use the rotation formula:
x' = 2a - x
y' = 2b - y
where (x,y) are the coordinates of a point on the original line, and (x',y') are the coordinates of the same point after rotation about the point (a,b).
Substituting the coordinates of two points on the line, we get:
(0,-1) → x' = 2(2) - 0 = 4, y' = 2(3) - (-1) = 7
(-1/2,0) → x' = 2(2) - (-1/2) = 4 1/2, y' = 2(3) - 0 = 6
Now, we can use the two points (4,7) and (4 1/2,6) to find the equation of the rotated line using point-slope form:
slope = (6-7) / (4 1/2 - 4) = -2
y - 7 = -2(x - 4)
y = -2x + 15
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ASAP Please help me do a two column proof for this. I am struggling
∠A = ∠C in trapezoid ABCD with arcAB = arcCD, can be proven with the property of isosceles triangles.
How to prove the relation?Since arcAB = arcCD, the lengths of the two arcs are equal. This implies that the lengths of the segments subtended by these arcs, AB and CD, are also equal.
Let E and F be the midpoints of the non-parallel sides AD and BC, respectively. Connect E and F with a line segment EF.
Since E and F are midpoints, DE = EA and BF = FC. In addition, since AB = CD = L, we can say that:
DE + EA = BF + FC
EA = FC
So, by the Hypotenuse-Leg (HL) theorem of congruence, triangles AEF and CFE are congruent:
ΔAEF ≅ ΔCFE
Now, since the triangles are congruent, their corresponding angles are equal:
∠A = ∠C
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rewrite the following without an exponent 4^-3
Step-by-step explanation:
4^-3 = 1/4^3 = 1/64
Solve the IVP given by y''+y=t, y(0)=1, y'(0)=-2
The solution to the IVP given by y''+y=t, y(0)=1, y'(0)=-2 is y(t) = cos(t) - (3/2) sin(t) + (1/2) t.
To solve the Initial Value Problem, we can use the method of undetermined coefficients, which involves assuming a particular form for the solution to the non-homogeneous equation y'' + y = t, and then finding the coefficients of the terms in that form by substituting it back into the equation.
First, we find the general solution to the homogeneous equation y'' + y = 0
The characteristic equation is r² + 1 = 0, which has solutions r = ±i. Therefore, the general solution to the homogeneous equation is
y_h(t) = c₁ cos(t) + c₂ sin(t),
where c₁ and c₂ are constants determined by the initial conditions.
Next, we assume a particular form for the non-homogeneous solution, based on the form of the right-hand side t. Since t is a linear function, we assume that the particular solution has the form
y_p(t) = a t + b.
Substituting this into the differential equation, we get
y''_p + y_p = t
2a + (at+b) = t.
Equating coefficients, we get
a = 1/2, b = 0.
Therefore, the particular solution is
y_p(t) = (1/2) t.
The general solution to the non-homogeneous equation is then the sum of the homogeneous and particular solutions
y(t) = y_h(t) + y_p(t)
= c₁ cos(t) + c₂ sin(t) + (1/2) t.
To determine the constants c₁ and c₂, we use the initial conditions:
y(0) = c₁ cos(0) + c₂ sin(0) + (1/2) (0) = c₁ = 1,
y'(0) = -c₁ sin(0) + c₂ cos(0) + (1/2) (1) = c₂ - (1/2) = -2,
so c₂ = -3/2.
Therefore, the solution to the IVP is
y(t) = cos(t) - (3/2) sin(t) + (1/2) t.
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a bacteria culture starts with 40 bacteria and grows at a rate proportional to its size. after 2 hours there are 180 bacteria. find the number of bacteria after 5 hours.
The number of bacteria after 5 hours is approximately 1013.8.
We can use the formula for exponential growth to solve this problem. If a population grows at a rate proportional to its size, then we can writ
N(t) = N₀ × e^(rt),
where N(t) is the size of the population at time t, N₀ is the initial size of the population, r is the growth rate, and e is the mathematical constant approximately equal to 2.71828.
We know that the culture starts with 40 bacteria, so N₀ = 40. We also know that after 2 hours, the size of the population is 180. We can use this information to solve for r:
180 = 40 × e^(2r)
180/40 = e^(2r)
ln(180/40) = 2r
r = ln(180/40)/2
r ≈ 0.6931
Now we can use the formula to find the size of the population after 5 hours:
N(5) = 40 × e^(0.6931×5)
N(5) ≈ 1013.8
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