To determine the number of minutes you would have to exercise each day to have a resting heart rate of 60 beats per minute, we need to consider the relationship between exercise and heart rate.
Regular exercise can help lower resting heart rate as it strengthens the cardiovascular system. The American Heart Association recommends engaging in moderate-intensity aerobic exercise for at least 150 minutes per week to maintain cardiovascular health.
If we assume that you exercise evenly throughout the week, we can calculate the daily exercise time as follows:
150 minutes per week ÷ 7 days = approximately 21.43 minutes per day.
Therefore, if you exercise for approximately 21.43 minutes per day, it can contribute to maintaining a healthy resting heart rate. It's important to note that individual results may vary, and consulting with a healthcare professional is always recommended before starting or modifying an exercise routine.
However, it's crucial to understand that exercise alone may not be the sole factor affecting resting heart rate. Other factors, such as genetics, overall health, stress levels, and lifestyle choices, can also influence heart rate. Additionally, achieving a resting heart rate of 60 beats per minute may not be feasible or suitable for everyone, as the ideal range can vary based on individual circumstances.
Therefore, while regular exercise can be beneficial for cardiovascular health, it's essential to consider personalized factors and consult with a healthcare professional for tailored advice on achieving and maintaining a healthy resting heart rate.
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Help with this, thank you
The slope of a line perpendicular to the line whose equation is x - 2y = -8 is -2.
What are perpendicular lines?In Mathematics and Geometry, perpendicular lines are two (2) lines that intersect or meet each other at an angle of 90° (right angles).
From the information provided above, the slope for the equation of line m is given by:
x - 2y = -8
2y = x + 8
y = x/2 + 4
slope (m) of line m = 1/2
In Mathematics and Geometry, a condition that is true for two lines to be perpendicular is given by:
m₁ × m₂ = -1
1/2 × m₂ = -1
m₂ = -2
Slope, m₂ of perpendicular line = -2
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4.1 Draw the four different views of the object, as indicated below, on square grid paper. Left Back Front Right
Remember to make use of the grid paper to maintain accuracy and proportionality across all four views.
Certainly! Below is a verbal description of how you can draw the four different views of the object on square grid paper:
Left View: Start by drawing the left side of the object as you would see it from a leftward perspective.
Capture its shape, height, and any visible features. Use the grid lines to maintain proportion and accuracy.
Back View: Move to the back of the object and draw what you see from that viewpoint.
Focus on its rear-facing details, contours, and any distinguishing characteristics. Utilize the grid paper to ensure proper alignment.
Front View: Now, face the object directly and draw its front view. Pay attention to its overall shape, dimensions, and any frontal features or patterns.
Utilize the grid lines to maintain symmetry and precision.
Right View: Finally, position yourself on the right side of the object and draw its appearance from that angle.
Portray the right-facing side, capturing its unique attributes and maintaining consistency with the previous views.
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Read the word problem.
Hershel buys 5 bags of cookies, 3 bags of granola, and
several bags of fruit snacks from a bake sale. In total, he
buys 10 bags from the bake sale. How many bags of
fruit snacks did Hershel buy?
Which type of word problem is shown?
O part-whole
O comparison
Omultiplication
Odivision
Answer:
A) Part Whole
Step-by-step explanation:
This is an Addition Problem, 5+3=8 then you can either count up from 8.
Or Subtract 10 by 8 and Get 2 Fruit Snacks Bought
Jenny and Dan want to save for an RV. They estimate that they will need $15,000 in 8 years. They can get 3% interest compounded semiannually. How much would they need to deposit now in order to have $15,000 in 8 years?
Answer:
$11820.466 ROUNDS TO $11820.47
Step-by-step explanation:
Using the compound interest formula:
X = P(1+r/n)^(nt)
where X = desired amount (15,000 in this case)
P = principle or initial amount
r = interest rate (0.03 or 3% in this case)
n = number of times the interest is compounded each year (2 in this case because interest is compounded semiannually)
t = time in years
you can begin to plug in your numbers
15,000 = P(1+0.03/2)^(2*8) --> this will show you that they are looking to have 15,000 by the end of the 8 years, at a rate of 3% (0.03) with interest compounded semiannually
from here you can simplify (1+0.03/2)^(2*8) to 1.27 (full decimal = 1.26898554765)
and then you have
15,000 = P * 1.26898554765
then divide 15,000 by 1.26898554765
and get P = 11820.466, which rounds to $11820.47
hope this helps!
Answer: P = 11820.47
Step-by-step explanation:
Formula for compound interest:
[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]
A = after amount =15000
P = Principal, initial/deposit amount = find this
r = rate in decimal form = .03
n = number of times it compounds in 1 year = 2 >semiannually
t = time in years > 8
[tex]15000 = P(1+\frac{.03}{2} )^{(2)(8)}[/tex]
[tex]15000 = P(1.015 )^{16}[/tex]
15000 = P(1.015 )^{16}
15000 = P(1.26899)
P = 11820.47
Which of the following ordered pairs represents the solution to the system given below?
x − 4y = 7
5x + 9y = 6
(3, −1)
(3, 1)
(1, −3)
(−1, −3)Which of the following ordered pairs represents the solution to the system given below?
x − 4y = 7
5x + 9y = 6
(3, −1)
(3, 1)
(1, −3)
(−1, −3)
Answer:
Step-by-step explanation:
To determine which of the given ordered pairs represents the solution to the system of equations, we can substitute the values of x and y into the equations and check if they satisfy both equations.
The system of equations is:
Equation 1: x - 4y = 7
Equation 2: 5x + 9y = 6
Let's check each ordered pair:
(3, -1)
Substituting x = 3 and y = -1 into the equations:
Equation 1: 3 - 4(-1) = 7
3 + 4 = 7
7 = 7 (True)
Equation 2: 5(3) + 9(-1) = 6
15 - 9 = 6
6 = 6 (True)
Since both equations are satisfied, (3, -1) is a solution to the system.
(3, 1)
Substituting x = 3 and y = 1 into the equations:
Equation 1: 3 - 4(1) = 7
3 - 4 = 7
-1 = 7 (False)
Equation 2: 5(3) + 9(1) = 6
15 + 9 = 6
24 = 6 (False)
Since one or both equations are not satisfied, (3, 1) is not a solution to the system.
(1, -3)
Substituting x = 1 and y = -3 into the equations:
Equation 1: 1 - 4(-3) = 7
1 + 12 = 7
13 = 7 (False)
Equation 2: 5(1) + 9(-3) = 6
5 - 27 = 6
-22 = 6 (False)
Since one or both equations are not satisfied, (1, -3) is not a solution to the system.
(-1, -3)
Substituting x = -1 and y = -3 into the equations:
Equation 1: -1 - 4(-3) = 7
-1 + 12 = 7
11 = 7 (False)
Equation 2: 5(-1) + 9(-3) = 6
-5 - 27 = 6
-32 = 6 (False)
Since one or both equations are not satisfied, (-1, -3) is not a solution to the system.
Therefore, the ordered pair (3, -1) represents the solution to the system of equations.
if two angle measurements of a triangle are 90 and 60 what is the third angle?
please show all steps
Given
Two out of three angles of a triangle measures 90° & 60° respectivelyTo find
The third angleWe know that,
Measure of all three angles of a triangle = 180°Let the third angle be ,'x'
then,
x + 90° + 60° = 180°x + 150° = 180°x = 180° -150°x = 30°Hence,the third angle would measure 30°
Assume that when adults with smartphones are randomly selected, 42 % use them in meetings or classes. If 30 adult smartphone users are randomly selected, find the probability that exactly 20 of them use their smartphones in meetings or classes.
The probability that exactly 20 out of 30 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.1031, or 10.31%.
To find the probability that exactly 20 out of 30 randomly selected adult smartphone users use their smartphones in meetings or classes, we can use the binomial probability formula.
The binomial probability formula is given by:
P(X = k) = (n C k) * p^k * (1 - p)^(n - k),
where:
P(X = k) is the probability of exactly k successes,
n is the total number of trials (number of smartphone users selected),
k is the number of successes (number of smartphone users using their smartphones in meetings or classes),
p is the probability of success in a single trial (percentage of adults using smartphones in meetings or classes), and
(n C k) represents the binomial coefficient, which can be calculated as n! / (k! * (n - k)!)
Given that the percentage of adults using smartphones in meetings or classes is 42% or 0.42, we have p = 0.42. Also, n = 30 and k =
Substituting these values into the binomial probability formula:
P(X = 20) = (30 C 20) * 0.42^20 * (1 - 0.42)^(30 - 20).
To calculate the binomial coefficient (30 C 20), we can use the formula:
(30 C 20) = 30! / (20! * (30 - 20)!).
Calculating (30 C 20):
(30 C 20) = 30! / (20! * 10!) = (30 * 29 * 28 * 27 * 26 * 25 * 24 * 23 * 22 * 21) / (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) = 30,045,015.
Substituting the values into the formula:
P(X = 20) = 30,045,015 * 0.42^20 * (1 - 0.42)^(30 - 20).
Calculating the expression:
P(X = 20) ≈ 0.1031.
Therefore, the probability that exactly 20 out of 30 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.1031, or 10.31%.
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The probability for this case is P = 0.147
How to find the probability?To solve this problem, we can use the binomial probability formula. In this case, we have a binomial distribution with the following parameters:
n = 30 (number of trials, i.e., number of adult smartphone users selected)p = 0.42 (probability of success, i.e., the probability that an adult smartphone user uses their smartphone in meetings or classes)x = 20 (number of successes we want to calculate the probability for, i.e., exactly 20 adult smartphone users using their smartphones in meetings or classes)The formula for the probability of exactly x successes in n trials is:
[tex]P(X = x) = (N_x) * p^x * (1 - p)^(n - x)[/tex]
Where:
[tex](N_x) = n! / (x! * (n - x)!)[/tex]
Calculating the binomial coefficient:
[tex](30_{20}) = 30! / (20! * (30 - 20)!) = 30! / (20! * 10!)[/tex]
Using the given values, we can calculate the probability as follows:
[tex]P(X = 20) = (30_{20}) * (0.42^{20}) * (1 - 0.42)^{(30 - 20)} = 0.147[/tex]
that is the probability.
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what is inequalities
Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.
Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.
The most common symbols used in inequalities are:
">" (greater than): indicates that the value on the left side is larger than the value on the right side.
"<" (less than): indicates that the value on the left side is smaller than the value on the right side.
"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.
"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.
"≠" (not equal to): indicates that the values on both sides are not equal.
Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.
Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.
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What is the 5th term in the expansion of (4x³y²-1/2y)^9?
The 5th term in the expansion is 126 * (4x³y²)^5 * (-1/2y)^4, which simplifies to 126 * 4^5 * (x³)^5 * (y²)^5 * (-1/2)^4 * y^4.
To find the 5th term in the expansion of (4x³y² - 1/2y)^9, we can use the binomial theorem. The binomial theorem allows us to expand a binomial raised to a positive integer exponent.
The binomial theorem states that for any binomial (a + b)^n, the general term in the expansion can be written as C(n, k) * a^(n-k) * b^k, where C(n, k) represents the binomial coefficient, also known as "n choose k."
In our case, the binomial is (4x³y² - 1/2y)^9. The first term has an exponent of 9, so the last term will have an exponent of 0. Since we are looking for the 5th term, the exponent of y will be 9 - 5 = 4. The exponent of x will be 5, as 4x³ raised to the power of 5 gives x^15.
Using the binomial coefficient, we have C(9, 5) = 126.
Simplifying further, we get 126 * 1024 * x^15 * y^10 * (1/16) * y^4, which can be simplified as 126 * 64 * x^15 * y^14 * (1/16). The final result is 8064 * (x^15 * y^14) * (1/16), which can be further simplified if necessary.
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10 Ten Atlas batteries were tested to find their average life. The times, in hours, that the batteries lasted were as follows: 10.8, 10.6, 11.4, 8.9, 10.1, 10.6, 9.9, 12.6, 10.5, 11.9. a Find, to the nearest tenth of an hour, the average life of the ten batteries. b Which of the following advertisements is more accurate? i Atlas batteries are guaranteed to last 10 hours. ii Atlas batteries have an average life of over 10 hours.
a) To find the average life of the ten batteries, we need to calculate the mean, which is the sum of all the values divided by the number of values.Sum of all values = 10.8 + 10.6 + 11.4 + 8.9 + 10.1 + 10.6 + 9.9 + 12.6 + 10.5 + 11.9 = 106.2
Number of values = 10
Average life = Sum of all values / Number of values = 106.3 / 10 ≈ 10.63
Therefore, the average life of the ten batteries, rounded to the nearest tenth of an hour, is approximately 10.6 hours.
b) Comparing the two advertisements:
i) The first advertisement claims that Atlas batteries are guaranteed to last 10 hours. This means that all Atlas batteries are expected to last at least 10 hours. However, based on the data provided, we can see that the average life of the batteries is approximately 10.6 hours, which is higher than the guaranteed 10-hour minimum
ii) The second advertisement claims that Atlas batteries have an average life of over 10 hours. This statement aligns with the data we have, as the average life of the batteries is indeed over 10 hours.
Based on the information provided, the second advertisement claiming that Atlas batteries have an average life of over 10 hours is more accurate, as the average life calculated from the given data is 10.6 hours.
In summary, the average life of the ten batteries is approximately 10.6 hours, and the second advertisement stating an average life of over 10 hours is more accurate based on the data provided.
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Please help me on this question.
The scientific notation of the number -98, 160, 000,000 is -9.816 × 10¹⁰.
How to change number to scientific notation?Scientific notation is a way of writing very large or very small numbers. The proper way to represent scientific notation is a x 10ᵇ where a is a number or decimal number such that the absolute value of a is greater than or equal to one.
Therefore, let's write the scientific notation of the number as follows:
-98, 160, 000,000.
Hence, the scientific notation is as follows:
We have to move backward(to the left).
-9.816 × 10¹⁰
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Nikhil and Mae work at the same company. Nikhil has been at the company 4 times as long as Mae. Nikhil's time at the company is 8 more than 2 times Mae's time. The following system of equations models the scenario: x = 4y x = 8 + 2y How many years has each person been employed by the company? Nikhil has been with the company for 16 years, while Mae has been there for 4 years. Nikhil has been with the company for 24 years, while Mae has been there for 6 years. Nikhil has been with the company for 20 years, while Mae has been there for 5 years. Nikhil has been with the company for 12 years, while Mae has been there for 3 years
The number of years of employment is A. Nikhil has been with the company for 16 years, while Mae has been there for 4 years.
How to find the years of employment ?The system of equations given is:
x = 4y
x = 8 + 2y
You can solve the system by setting the two expressions for x equal to each other:
4y = 8 + 2y
2y = 8
2y / 2 = 8 / 2
y = 4
Substitute y = 4 into the first equation to solve for x:
x = 4 x 4
= 16
So, Mae (y) has been at the company for 4 years and Nikhil (x) has been at the company for 16 years.
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4tan(x)-7=0 for 0<=x<360
Answer:
x = 65.26 degrees or x = 245.26 degrees.
Step-by-step explanation:
To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:
4tan(x) = 7
Then, we can divide both sides by 4 to get:
tan(x) = 7/4
Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:
x = tan^-1(7/4)
Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).
However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).
To find the solution in the first quadrant, we can simply use the value we just calculated:
x = 65.26 degrees (rounded to two decimal places)
To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:
x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)
So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:
x = 65.26 degrees or x = 245.26 degrees.
The table below shows the year and the number of people unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed first reach 43? (Round your answer down to the nearest year. If the trend does not appear linear, enter NOT LINEAR.) Year 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 Number Unemployed 750 670 650 605 550 510 460 420 380 320
The trend appears to be linear. Assuming the trend continues, the number of unemployed will first reach 43 in the year 2022.
To determine whether the trend appears linear, we can plot the data points on a graph and check for a consistent pattern. Let's create a scatter plot with the years on the x-axis and the number of unemployed on the y-axis.
Year | Number Unemployed
1990 | 750
1992 | 670
1994 | 650
1996 | 605
1998 | 550
2000 | 510
2002 | 460
2004 | 420
2006 | 380
2008 | 320
When we plot these points, we can see that there is a consistent downward trend in the number of unemployed over the years.
Next, we can try to fit a line to the data points to see if it follows a linear pattern. Using a linear regression model or by visual inspection, we can determine that the data points approximately follow a straight line.
Assuming this linear trend continues, we can extrapolate to find the year when the number of unemployed first reaches 43. By extending the line beyond the given data points, we can estimate that it will intersect the y-axis (number of unemployed) at approximately 43.
Therefore, the year when the number of unemployed first reaches 43 would be around 2022.
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A=-1,0,1,2,4,6,7 I=-2,-1,1,2,8
Answer:
A=-1
Step-by-step explanation:
7. Suppose that the discriminating monopolist has the demand functions
P_{1} = 200 - 2Q_{1}; P_{2} = 180 - 4Q_{2} and that the cost function is C = 20(Q_{1} + Q_{2}) .
a) How much should be sold in the 2 markets to maximise profits?
b) What are the corresponding prices?
c) How much profit is lost if it becomes illegal to discriminate?
12 marks]
12 marks]
16 marks]
d) Discuss the consequences of the imposition of a tax of 5 per unit sold in market 1 by
a) To maximize profits, 10 units should be sold in market 1 and 5 units in market 2.
b) The corresponding prices are $180 in market 1 and $160 in market 2.
c) If it becomes illegal to discriminate, the profit loss is $50.
d) The imposition of a tax of $5 per unit sold in market 1 would likely decrease the monopolist's profit and potentially lead to adjustments in prices and quantities sold in both markets.
a) To maximize profits, the monopolist should set marginal revenue equal to marginal cost in each market.
In this case, marginal revenue is equal to the derivative of the demand function with respect to quantity, and it can be calculated as MR = dP/dQ.
For market 1:
MR₁ = dP₁/dQ₁ = -2
For market 2:
MR₂ = dP₂/dQ₂ = -4
Setting MR equal to marginal cost, which is the derivative of the cost function with respect to quantity, gives:
MR₁ = -2 = dC/dQ₁ = 20
MR₂ = -4 = dC/dQ₂ = 20
Solving these equations, we find:
Q₁ = 10
Q₂ = 5
Therefore, the monopolist should sell 10 units in market 1 and 5 units in market 2 to maximize profits.
b) To determine the corresponding prices, we substitute the quantities obtained in part (a) into the demand functions:
For market 1:
P₁ = 200 - 2Q₁ = 200 - 2(10) = 180
For market 2:
P₂ = 180 - 4Q₂ = 180 - 4(5) = 160
Therefore, the corresponding prices are $180 in market 1 and $160 in market 2.
c) To calculate the profit lost if it becomes illegal to discriminate, we need to compare the profits under discrimination with the profits under non-discrimination.
Under discrimination, the monopolist charges different prices in each market, while under non-discrimination, the same price is charged in both markets.
Under discrimination:
Profit = Total revenue - Total cost
For market 1:
Total revenue₁ = P₁ [tex]\times[/tex] Q₁ = 180 [tex]\times[/tex] 10 = $1
For market 2:
Total revenue₂ = P₂ [tex]\times[/tex] Q₂ = 160 [tex]\times[/tex] 5 = $800
Total revenue = Total revenue₁ + Total revenue₂ = $1800 + $800 = $2600
Total cost = C = 20(Q₁ + Q₂) = 20(10 + 5) = $300
Profit = Total revenue - Total cost = $2600 - $300 = $2300
Under non-discrimination:
Since the same price is charged in both markets, we take the average price:
Average price = (P₁ + P₂) / 2 = (180 + 160) / 2 = $170
Total revenue = Average price [tex]\times[/tex] (Q₁ + Q₂) = $170 [tex]\times[/tex] (10 + 5) = $2550
Total cost remains the same at $300.
Profit = Total revenue - Total cost = $2550 - $300 = $2250
Therefore, the profit lost if discrimination becomes illegal is $2300 - $2250 = $50.
d) The imposition of a tax of $5 per unit sold in market 1 would increase the cost per unit for the monopolist.
This would affect the profit-maximizing quantity in market 1 and potentially lead to a change in prices.
The monopolist would compare the new marginal cost, which includes the tax, with the marginal revenue to determine the new profit-maximizing quantities and prices.
The tax would likely reduce the monopolist's profits and could potentially result in adjustments in production and pricing strategies.
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Ben wants to try a new honey-glazed salmon recipe. He starts with 1 - cups of honey. He uses g of it
to make the glaze. How much honey does Ben have left?
The amount of honey that Ben will have left after using some to make the honey-glazed salmon would be = 1⅓.
How to calculate the amount of honey left?To calculate the amount of honey left after making the honey-glazed salmon, the following is carried out:
The quantity of honey he started with = 1⅔ cups of honey
The amount he used for the recipe = ⅕ of 1⅔
That is:
= 1/5× 5/3
= ⅓
The amount that is left ;
= 1⅔-⅓
= 5/3 - 1/3
= 4/3
= 1⅓.
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Consider the two-way table.
Category 1
Group 1 - 30
Group 2 - 90
Category 2
Group 1 - 14
Group 2- 32
Complete the table below to show the relative frequencies of the data in the first row.
Enter numbers in the boxes as decimals to the hundredth place.
Group 1 ____
Group 2____
The relative Frequencies of the data in the first row are 0.25 for Group 1 and 0.75 for Group 2.
Given two-way table.Category 1Group 1 - 30Group 2 - 90Category 2Group 1 - 14Group 2- 32To find the relative frequency of the data in the first row, we need to first calculate the sum of the numbers in the first row.
Then we need to divide each of the individual numbers in the first row by the sum of the numbers in the first row to get the relative frequency of each group. Let's begin by calculating the sum of the numbers in the first row.Sum of the numbers in the first row = 30 + 90 = 120
Relative frequency of Group 1 in the first row = (Number of Group 1 in the first row) / (Sum of the numbers in the first row) = 30/120 = 0.25 (rounded to the nearest hundredth)Relative frequency of Group 2 in the first row = (Number of Group 2 in the first row) / (Sum of the numbers in the first row) = 90/120 = 0.75 (rounded to the nearest hundredth)We can complete the table with the above calculated relative frequencies. Group 1 0.25Group 2 0.75
Therefore, the relative frequencies of the data in the first row are 0.25 for Group 1 and 0.75 for Group 2.
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The Product of two rational numbefs is -15/22.If one of the number is -9?44 what is the other number
Answer:
n = 10/3
Step-by-step explanation:
Let n be the number
[tex]n(-\frac{9}{44}) = -\frac{15}{22} \\ Cross multiply\\n = \frac{-44(-15)}{9(22)} \\n = \frac{660}{198} \\n = \frac{10}{3}[/tex]
A student is trying to solve the system of two equations given below:
Equation P: x + y = 8
Equation Q: 2x + 5y = 24
Which of the following steps can be used to eliminate the x term?
2(x + y = 8)
−2(x + y = 8)
−1(2x + 5y = 24)
−2(2x + 5y = 24)
Answer:
Step-by-step explanation:
To eliminate the x term in the system of equations, you can multiply Equation P by a constant and then add or subtract it from Equation Q. Let's go through the given steps:
2(x + y = 8):
This step is incorrect because it only multiplies the entire Equation P by 2 without changing the other equation. It does not eliminate the x term.
-2(x + y = 8):
This step is incorrect because it multiplies Equation P by -2, but the equation should be subtracted from Equation Q, not multiplied by -2.
-1(2x + 5y = 24):
This step is incorrect because it only multiplies Equation Q by -1 without changing Equation P. It does not eliminate the x term.
-2(2x + 5y = 24):
This step is correct. By multiplying Equation Q by -2 and then adding it to Equation P, the x term will be eliminated. The resulting equation will involve only the y term, allowing you to solve for y.
Therefore, the correct step to eliminate the x term is -2(2x + 5y = 24).
To prove that the step -2(2x + 5y = 24) eliminates the x term in the system of equations, we need to show that when we perform the elimination, the resulting equation involves only the y term.
Given the system of equations:
Equation P: x + y = 8
Equation Q: 2x + 5y = 24
Multiplying Equation Q by -2:
-2(2x + 5y) = -2(24)
-4x - 10y = -48
Now, let's add Equation P and the modified Equation Q:
(x + y) + (-4x - 10y) = 8 + (-48)
Simplifying the left side of the equation:
x - 4x + y - 10y = 8 - 48
-3x - 9y = -40
As we can see, the resulting equation -3x - 9y = -40 involves only the y term. The x term has been eliminated.
Therefore, by performing the step -2(2x + 5y = 24), we have successfully eliminated the x term in the system of equations.
I invested $750 and earned 16% yearly interest
Write the equation
Complete the table
The equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is: Interest = $750 * 0.16.
To write the equation for calculating the yearly interest earned on an investment, we can use the formula:
Interest = Principal * Rate
Where:
- Principal is the initial investment amount.
- Rate is the interest rate expressed as a decimal.
In this case, you invested $750, and the annual interest rate is 16%. To use the decimal form of the interest rate, we divide it by 100:
Rate = 16% = 16/100 = 0.16
Substituting the values into the equation:
Interest = $750 * 0.16
To calculate the interest, we multiply the principal by the interest rate:
Interest = $750 * 0.16 = $120
Therefore, the equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is:
Interest = $750 * 0.16
Now, let's complete a table to show the growth of your investment over multiple years. We'll assume the interest is compounded annually.
Year | Initial Investment | Interest Earned | Total Value
---------------------------------------------------------
1 $750 $120 $870
2 $870 $139.20 $1009.20
3 $1009.20 $161.47 $1170.67
4 $1170.67 $187.31 $1357.98
5 $1357.98 $217.28 $1575.26
In each year, we calculate the interest earned by multiplying the initial investment by the interest rate (16% or 0.16). The total value is obtained by adding the initial investment and the interest earned. This process is repeated for each subsequent year.
The table shows the growth of your investment over five years, demonstrating how the interest compounds and increases the total value each year.
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What is the perimeter of ABC
Answer:
12
Step-by-step explanation:
ABC is a right triangle.
AC = 4
CB = 3
The legs have lengths of 4 and 3.
Now we use the Pythagorean theorem to find AB, the length of the hypotenuse.
a² + b² = c², for legs a and b, and hypotenuse c.
(AC)² + (CB)² = (AB)²
4² + 3² = (AB)²
16 + 9 = (AB)²
25 = (AB)²
AB = 5
perimeter = sum of lengths of sides
perimeter of triangle ABC = AC + CB + AB
perimeter = 4 + 3 + 5
perimeter = 12
if CD is parallel to BE, DC = 4x - 11, BE = 6, AD = 15, and ED = 4, find x. Round to the nearest tenth if necessary.
The value of x is approximately 8.4.To find the value of x, we can use the fact that CD is parallel to BE to establish a relationship between the corresponding sides of the two triangles formed.
Based on the given information, we have:
DC = 4x - 11
BE = 6
AD = 15
ED = 4
Using the corresponding sides in the triangles, we can set up a proportion:
AD/ED = CD/BE
Substituting the known values:
15/4 = (4x - 11)/6
Now we can cross-multiply to solve for x:
6 * 15 = 4 * (4x - 11)
90 = 16x - 44
Adding 44 to both sides:
134 = 16x
Dividing both sides by 16:
x = 8.375
Rounded to the nearest tenth, x ≈ 8.4.
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What is the probability that a random point on AK will be on DF? A B C D E F G H I JK |||||||||||||||||||| -10 -8 -6 -4 -2 0 2 4 P=[?] 6 8 10 Enter
The probability that a random point on AK will be on DF is 0.4 or 40%.
The given line segments have coordinates on a coordinate plane. To find the probability that a random point on AK will be on DF, we have to determine the length of AK and DF.
Firstly, we need to find the coordinates of D and F, which can be determined from the given coordinates. The coordinates of D are (-4, 8) and the coordinates of F are (4, 8).
Therefore, the length of DF can be found by applying the distance formula as shown below: DF = √((4-(-4))² + (8-8)²)DF = √(8² + 0²)DF = √64DF = 8 Similarly, we can find the coordinates of A and K as well.
The coordinates of A are (-10, 6) and the coordinates of K are (10, 6).Therefore, the length of AK can be found by applying the distance formula as shown below: AK = √((10-(-10))² + (6-6)²)AK = √(20² + 0²)AK = √400AK = 20.
Therefore, we can find the probability that a random point on AK will be on DF by using the formula: P = Length of DF / Length of AKSubstituting the values, we get P = 8/20P = 0.4 or 40%
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A 2-mi cab ride costs $5.25. A 5-mi cab ride costs $10.50. Which equation models the cost y of the cab ride for ride that is × miles?
The equation which models the scenario is y = 2.625x
Using the given Parameters
cost for 2 miles = 5.25cost per mile = 5.25/2 = $2.625
cost 'y ' for x miles can be modeled using the Multiplication operator thus :
cost = cost per mile * number of milesHence, we have
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Sera had the number 548.She adds one to the tens and two to the units. What number would Sera end up with??
The number she'd have is:
560Explanation:
First, let's see which number is in the tens place and which number is in the ones place (the units place).
In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).
So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :
550
That's not all, since we also add 1 to the tens:
560
Hence, Sera ends up with 560.Dennis bought some pears for his students. If each 3 student gets pears, there will be 6 pears left. If each student gets 5 pears, 2 students will have no pears. How many students are there in total?
Dennis bought some pears for his students. If every 3 students get pears, there will be 6 pears left. If each student gets 5 pears, 2 students will have no pears. So, there are 2 students in total.
Let's assume the total number of students is 'x'.
According to the first scenario, if each group of 3 students receives pears, there will be 6 pears left. This means that the number of pears must be a multiple of 3 plus 6. So, we can write the equation:
[tex]P = 3n + 6[/tex], where P represents the total number of pears and n is a positive integer.
In the second case, if two students are left out of the distribution of pears and each student receives five, the sum of the pear distributions should be a multiple of five plus two. This can be said as follows:
[tex]P = 5x + 2[/tex], where P represents the total number of pears and x is the total number of students.
Since both equations represent the same number of pears, we can equate them:
[tex]3n + 6 = 5x + 2[/tex]
Rearranging the equation, we get:
[tex]3n - 5x = -4[/tex]
Our next aim is to find a solution where n and x are positive integers. Starting by examining the values of n and x is a smart idea. Trial and error leads us to the conclusion that n = 4 and x = 2 satisfy the following equation:
[tex]3*4 - 5*2 = -4[/tex]
So, there are 2 students in total.
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Urgent please help I am so lost thank you a lot
Therefore, The Speed of the plane is: X = 130 mph
Step-by-step explanation:520 / x = 160 / x - 90
Rearranged the variables:520/x = 160/x - 90
Undefined Variables:x ≠ 90
x ≠ 0 and x - 90 ≠ 0
Cross Multiply:520x - 46800 = x * 160
Now We Solve the problem:
520/x = 160/x - 90
520(x - 90) = 160x
520x - 46800 = 160x
520x - 160x = 46800
360x = 46800
x = 46800/360
x = 130
Draw the conclusion:Therefore, The Speed of the plane is: X = 130 mph
I hope this helps you!
Dividing the sum of (7/8) (15/4) (1/12) by their multiplication gives _________
The Division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).
To find the division of the sum of (7/8), (15/4), and (1/12) by their multiplication, we first need to calculate the sum and multiplication of the given fractions.
The sum of the fractions is:
(7/8) + (15/4) + (1/12)
To add these fractions, we need a common denominator. The least common multiple of 8, 4, and 12 is 24. Let's convert each fraction to have a denominator of 24:
(7/8) = (21/24)
(15/4) = (90/24)
(1/12) = (2/24)
Now we can add the fractions:
(21/24) + (90/24) + (2/24) = (113/24)
The multiplication of the fractions is:
(7/8) * (15/4) * (1/12)
To multiply fractions, we multiply the numerators and denominators:
(7*15*1) / (8*4*12) = (7/96)
Now we can divide the sum of the fractions by their multiplication:
(113/24) / (7/96)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(113/24) * (96/7) = (2712/168)
Therefore, the division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).
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What is the trigonometric ratio for sin C?
Enter your answer, as a simplified fraction, in the boxes.
A
B
O
82
80
O
Applying the sine ratio, the trigonometric ratio of sin C, as a simplified fraction is: sin C = 9/41.
How to Find the Trigonometric Ratio of Sin C?The sine ratio in trigonometry is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. In mathematical notation, the sine ratio is given by sin(∅) = opposite/hypotenuse.
We are given the following:
Reference angle (∅) = C
length of the hypotenuse = 82
length of the opposite side = AB = √(82² - 80²) = 18 [Pythagorean theorem]
Plug in the values:
sin C = 18/82
Simplify:
sin C = 9/41
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