Use the equation and type the ordered-pairs.
y = log 3 x
{(1/3,____,)(1,___), (3,___),(9,____),(27,____),(81,___)}
Answer:
[tex]{(1/3, 0) , ( 1, 0.477), (3, 0.954), (9, 1.43), (27, 1.90), (81, 2.385)}\\[/tex]
Step-by-step explanation:
Here the "X" Values are given, thus the corresponding "Y" values will be
[tex]Y = log (3 X)\\a) X = \frac{1}{1} , Y = log (3 * \frac{1}{3} ) = log (1) = 0\\b) X = 1, Y = log (3*1) = log (3) = 0.477\\c) X = 3, Y = log (3*3) = log (9) = 0.954\\d) X = 9, Y = log (3*9) = log (27) = 1.43\\e) X = 27, Y = log (3* 27) = log (81) = 1.90\\f) X = 81, Y = log (3 * 81) = log (243) = 2.385\\[/tex]
So the pattern would be
[tex]{(1/3, 0) , ( 1, 0.477), (3, 0.954), (9, 1.43), (27, 1.90), (81, 2.385)}\\[/tex]
help me create an extraneous radical equation please using this model!! :) thank you.
[tex]a \sqrt{x}+b + c = d[/tex]
I don't need you to solve it, just help me pick numbers for variable a, b, c, and d to create an extraneous solutuion
Find the volume of a sphere that has a surface area of 16 sq. in.
A. (32/3) cubic inches
B.8 cubic inches
C.(4/3) cubic inches
Answer:
A is the answer
The population of a town in 2000 was 430. The population is increasing at a rate of 0.9% every year. What will be the projected population of the town in 2010? Round your answer to the nearest whole number
You are required to take five courses, one each in humanities, sociology, science, math, and music. you have a choice of 2 humanities courses, 2 sociology courses, 6 science courses, 6 math courses, and 8 music courses. how many different sets of five courses are possible?
By multiplying the course options together for Humanities, Sociology, Science, Math and Music (2*2*6*6*8), we found that there are a total of 576 different sets of five courses.
Explanation:To answer this question, we have to calculate the number of different sets of five courses. This can be done by multiplying the number of choices available for each requirement. So, if you have 2 humanities courses, 2 sociology courses, 6 science courses, 6 math courses, and 8 music courses to decide from, the calculation would be as follows:
We then multiply these options together (2*2*6*6*8) to get the total number of different sets of courses possible, which is 576.
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To find the total number of different sets of five courses, multiply the number of choices for each course category: 2 (Humanities) × 2 (Sociology) × 6 (Science) × 6 (Math) × 8 (Music). This results in 1152 different sets of five courses.
To determine the number of different sets of five courses possible, we need to consider the choices available for each category:
- Humanities: 2 choices
- Sociology: 2 choices
- Science: 6 choices
- Math: 6 choices
- Music: 8 choices
The total number of different sets of five courses can be found by multiplying the number of choices in each category together. Here is the calculation:
2 × 2 × 6 × 6 × 8
Let's calculate this step-by-step:
1. 2 × 2 = 4
2. 4 × 6 = 24
3. 24 × 6 = 144
4. 144 × 8 = 1152
Therefore, the number of different sets of five courses possible is: 1152
write the number 32.56 corrrect to one decimal place
A sample of size 40 is taken from an infinite population whose mean and standard deviation are 68 and 12 respectively. the probability that the sample mean is larger than 70 equals:
To solve this problem, we can use the z statistic to find for the probability. The formula for z score is:
z = (x – u) / s
Where,
u = the sample mean = 68
s = standard deviation of the samples = 12
x = sample value = 70
In this case, what is asked is the probability that the sample mean is larger than 70, therefore this corresponds to the right of z on the graph of normal distribution.
z = (70 – 68) / 12
z = 2 / 12
z = 0.17
Therefore finding for P at z ≥ 0.17 using the standard distribution tables:
P (z = 0.17) = 0.5675
But this is not the answer yet since this is the P to the left of z. Therefore the correct one is:
P (z ≥ 0.17) = 1 - 0.5675
P (z ≥ 0.17) = 0.4325 = 43.25%
The probability that the sample mean is larger than 70 is 43.25%
The probability that the sample mean is larger than 70 for a sample size of 40 from a population with a mean of 68 and standard deviation of 12 is approximately 14.69%.
To determine this probability, we can use the Central Limit Theorem (CLT), which states that the distribution of sample means will be approximately normal if the sample size is large enough (n ≥ 30 is a common benchmark).
The standard error of the mean is calculated using the formula:
SE = σ / √n
Where σ is the population standard deviation and n is the sample size.
In this case:
σ = 12
n = 40
Therefore,
SE = 12 / √40 ≈ 1.8974
The z-score is calculated using the formula:
z = (M - μ) / SE
Where M is the sample mean,
μ is the population mean,
SE is the standard error.
Given,
μ = 68
M = 70
Therefore,
z = (70 - 68) / 1.8974 ≈ 1.054
Using the z-table, we find the probability that a z-score is less than 1.054 is approximately 0.8531.
However, we need the probability that the sample mean is greater than 70, so we subtract this from 1,
1 - 0.8531 ≈ 0.1469
Thus, the probability that the sample mean is larger than 70 is approximately 0.1469, or 14.69%.
Four students get 90s on a test, three get 70s, 2 get 60s and one gets an 80. what is the mean test score in this group?
Final answer:
The mean test score for the group is calculated by summing the products of each unique score and the number of students who received it, then dividing by the total number of students. In this case, the mean test score is 77.
Explanation:
To calculate the mean test score for the group, you multiply each score by the number of students who received it, then sum all those products, and finally divide by the total number of students. Four students scoring 90 would contribute 4 x 90 = 360 to the total sum. Three students scoring 70 contribute 3 x 70 = 210. Two students scoring 60 contribute 2 x 60 = 120. One student scoring 80 adds 80 to the sum. The total sum of all scores is 360 + 210 + 120 + 80 = 770. Since there are a total of 10 students (4 + 3 + 2 + 1), the mean score is calculated as 770 ÷ 10 = 77. Therefore, the mean test score in this group is 77.
Express the number as a ratio of integers. 7.5336
Determine the factors of 15x2 + 3xy + 10x + 2y. (4 points)
(3x + 2)(5x + y)
(5x + y)(2x + 3)
(3x + y)(5x + 2)
(5x + 3)(2x + y)
Answer:
the answer is the first option : A
Step-by-step explanation:
Find the period of the function. y = 5 cos one divided by twox
Video studying aboard and she's requested required to pay $3,500 in u.s. dollars per year to the university however she must pay in Euros how many euros can be there except to pay per month to the university round to the nearest Point 7306equals one u.s. dollar
Foe the AP given by a1,a2,......,an,...with non zero common difference, the equation satisfied are
Use newton's method to find the absolute minimum value of the function f(x)=x2+sinx correct to six decimal places.
The solution would be like this for this specific problem:
f(x) = x^2 + sin(x)
f '(x) = 2x + cos(x)
The minimum value is at f '(x) = 0,
So, let g(x) = 2x + cos(x)
Thus, g '(x) = 2 - sin(x)
x(new) = x - g(x) / g '(x)
or
x(new) = x - [2x + cos(x)] / [2 - sin(x)]
Calculation
x1 = -0.5 - [2 * -0.5 + cos(-0.5)] / [2 - sin(-0.5)]
= -0.4506266931
x2 = -0.4501836476
x3 = -0.4501836113
x4 = -0.4501836113
This value for x, f(x) = -0.2324655752.
After converting to 6 decimal places: the minimum point is (-0.450184,
-0.232466).
Final answer:
To find the absolute minimum value of f(x)=x^2+sin(x), use Newton's method with Newton-Raphson iteration x_{n+1} = x_n - f(x_n)/f'(x_n). Start with an initial guess and iterate until the result converges to six decimal places, ensuring the second derivative at the critical point is positive.
Explanation:
To find the absolute minimum value of the function f(x)=x^2+sin(x) correct to six decimal places, we can use Newton's method. Newton's method helps to find successively better approximations to the roots (or zeroes) of a real-valued function. First, we need to find the derivative of the function, which gives us f'(x) = 2x + cos(x). We are looking for a critical point where the derivative is zero because this could indicate a potential minimum (or maximum).
Starting with an initial guess, we can apply the Newton iteration formula x_{n+1} = x_n - f(x_n)/f'(x_n) to find a better approximation. In this case, let's choose an initial guess close to the root of f'(x). Since we do not have the specific initial guess, we would theoretically pick a value near the expected minimum and iterate until the difference between consecutive approximations is less than the desired tolerance, which is the change in six decimal places.
The Newton-Raphson iteration would be applied repeatedly until convergence is seen at six decimal places. Note that in practice, one must also check the second derivative f''(x) at the found critical point to confirm it is a minimum (it should be positive).
geometry. helppp!!! please explain this
What is the value of 10 C 2
PLEASE HELP 50 POINTS
A sports club rewards teams based on overall points earned in a season. The data for points are shown in the table, where Low represents the fewest points scored and High represents the highest points scored by a single team member.
Team Low High Range Mean Median IQR σ
Team A 22 58 36 42.1 44 18.25 10.35
Team B 38 49 11 43.9 44.5 3.5 2.97
Team C 27 36 9 31.8 32 3.75 2.55
Part A: If the club wants to award the team that has the most consistent scoring among its team members, which team should it choose and why? Justify your answer mathematically. (5 points)
Part B: If the club wants to award the team with the highest average score, which team should it choose and why? Justify your answer mathematically. (5 points)
WILL GIVE BRAINLIEST PLEASE HELP!!
What is the fifth term of the recursive formula an=2an-1 with the first term of 3?
A.
7
B.
17
C.
33
D.
65
How many cubic feet of space is there in a warehouse that is 610 feet wide by 140 feet deep and has an 18 foot ceiling?
Final answer:
The warehouse has a volume of 252,000 cubic feet, calculated using the corrected dimensions of 140 feet in length, 100 feet in width, and an 18-foot ceiling.
Explanation:
To calculate the volume of a warehouse, we use the formula for the volume of a rectangular prism, which is length × width × height. However, the question contains a typo about the width of the warehouse.
We are informed that the correct width is 100 feet, not 610 feet.
Given the corrected dimensions (140 feet by 100 feet with an 18 foot ceiling), we can now calculate the volume of the warehouse.
Volume = length × width × height
= 140 feet × 100 feet × 18 feet
= 252,000 cubic feet.
Therefore, the warehouse has a volume of 252,000 cubic feet of space.
The graph and table shows the relationship between y, the number of words Jean has typed for her essay and x, the number of minutes she has been typing on the computer.
According to the line of best fit, about how many words will Jean have typed when she completes 60 minutes of typing?
2,500
2,750
3,000
3,250
The number of words Jean will type when she completes 60 minutes of typing is 3,000, This is further explained below Option C is correct
What is correlation?Correlation is simply a relationship that exists between events or objects, A relationship between mathematical variables that are subject to variation.
In conclusion, The graph and table show the relationship between y and x
And the graph shows 3000 at "the number of words Jean has typed for her essay" axis denoted by y, for what she completes 60 minutes.
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the ratio of the corresponding side of two regular polygons is 3:4 the area of the larger polygon is 320 m squared what is the area of the smaller polygon?
The area of the smaller polygon with a side ratio of 3:4 is 180 m2 for the smaller polygon.
When dealing with the areas of similar polygons, if the ratio of corresponding sides is given, such as 3:4 in this case, the ratio of their areas is the square of the ratio of their sides. This is because the area is a two-dimensional measure, so each dimension is scaled by the ratio.
Given that the area of the larger polygon is 320 , we establish that the scale factor is 3 for the smaller polygon and 4 for the larger one.
To find the area of the smaller polygon, we use the fact that the ratio of the areas is (3/4)2 = 9/16.
This means that the area of the smaller polygon is 9/16 times the area of the larger polygon. Therefore, focusing on the comparison of areas, we calculate:
Area of smaller polygon = (9/16) x Area of larger polygon
= (9/16) x 320
Area of smaller polygon = 180
Which of the following statements are true? I. -(-6) = 6 and -(-4) > -4 III. 5 + 6 = 11 or 9 - 2 = 11 II. -(-4) < 4 or -10 > 10 - 10 IV. 17 > 2 or 6 < 9
The answer would be an option (D) 17 > 2 or 6 < 9 because 17 is greater than 2 and 6 is less than 9 is always true.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
I. -(-6) = 6 and -(-4) > -4
Here -(-4) > -4 is incorrect
-(-4) = 4 is correct
These statements are not true
III. 5 + 6 = 11 or 9 - 2 = 11
Here 9 - 2 = 11 is incorrect
So 9 - 2 = 7 is correct
These statements are not true
II. -(-4) < 4 or -10 > 10 - 10
Here -(-4) < 4 is incorrect
So -(-4) = 4 is correct
These statements are not true
IV. 17 > 2 or 6 < 9
Here 17 is greater than 2 and 6 is less than 9 is always true.
Hence, the correct answer would be an option (D)
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To the nearest degree what is the measure of each exterior angle of a regular hexagon ?
a.60°
b.45°
c.30°
d.51°
Answer:
A
Step-by-step explanation:
The sum of measures of all the exterior angles of ANY POLYGON is 360°.
The measure of each exterior angle of ANY POLYGON is [tex]\frac{360}{n}[/tex]
where [tex]n[/tex] is the number of sides of the polygon
A hexagon has 6 sides, thus the measure of each exterior angle of a hexagon is:
[tex]\frac{360}{6}=60[/tex] degrees
Answer choice A is correct.
What is the next number in the sequence 5 10 3 15 20 13 25 30?
What reference angle in the first quadrant corresponds to theta = -120? Answer in radians.
Answer:
Answer: Reference angle is π/3 Radians
Step-by-step explanation:
If f(x)=x-7 and g(x)=x^3, what is G(f(x))?
A. x^3+x-7
B. x^3(x-7)
C. X^3-7
D. (x-7)^3
Answer:
D. [tex](x-7)^3[/tex]
Step-by-step explanation:
Given functions are,
[tex]f(x) = x-7-----(1)[/tex]
[tex]g(x)=x^3-----(2)[/tex]
Now,
[tex]g(f(x))=g(x-7)[/tex] ( From equation (1) ),
[tex]=(x-7)^3[/tex] ( From equation (2) ),
[tex]\implies g(f(x)) = (x-7)^3[/tex]
Hence, Option D is correct.
please help, show me the steps
Find 3 consecutive even intergers if the sum is 108
Please Help!! Find the measure of angle 2. Image Attached
opposite angles = 180 degrees
180-111 = 69
angle 2 = 69 degrees
In science class, Savannah measures the temperature of a liquid to be 50∘ Celsius. Her teacher wants her to convert the temperature to degrees Fahrenheit. What is the temperature of Savannah's liquid to the nearest degree Fahrenheit
Final answer:
To convert the temperature of Savannah's liquid from Celsius to Fahrenheit, use the equation °F = (°C × 9/5) + 32. Savannah's temperature in Celsius is 50°, so her temperature in Fahrenheit is 122°F.
Explanation:
To convert the temperature from Celsius to Fahrenheit, you can use the equation:
°F = (°C × 9/5) + 32.
In this case, Savannah's temperature in Celsius is 50°. Using the equation, we can calculate her temperature in Fahrenheit as:
°F = (50 × 9/5) + 32 = 122°F.
Therefore, the temperature of Savannah's liquid to the nearest degree Fahrenheit is 122°F.
Savannah's liquid, initially measured at 50°C, converts to 122°F using the formula F = C x (9/5) + 32.
Explanation:Converting Celsius to FahrenheitTo convert the temperature from degrees Celsius to degrees Fahrenheit, we use the conversion formula: F = \( C \times \frac{9}{5} + 32 \), where F is the temperature in degrees Fahrenheit and C is the temperature in degrees Celsius.
In Savannah's case, she measured the temperature as 50°C. Applying the conversion formula:
First, multiply the Celsius temperature by \( \frac{9}{5} \)50 \times \frac{9}{5} = 90Then, add 32 to this result to find the Fahrenheit temperature.90 + 32 = 122Therefore, the temperature of Savannah's liquid to the nearest degree Fahrenheit is 122°F.