It makes sense that 0 is the domain of y = √x because the square root of any number can never be negative, and 0 is the smallest positive number. Therefore, any values of x less than 0 would result in an undefined answer.
what do you mean by arithmetic series?
Answer:
The sum of the first n terms in an arithmetic sequence is (n/2)⋅(a₁+aₙ). It is called the arithmetic series formula.
Step-by-step explanation:
An arithmetic series is the sum of the terms in an arithmetic sequence with a definite number of terms. Following is a simple formula for finding the sum: Formula 1: If S nrepresents the sum of an arithmetic sequence with terms , then. This formula requires the values of the first and last terms and the number of terms.
Please mark me as Brainliest if possible! Thank you :)
what is the sum of all integer values of $x$ such that $\frac{31}{90} < \frac{x}{100} < \frac{41}{110}$ is true?
In a first-order model with two predictors x1 and x2, an interaction term may be used when the:
a) relationship between the dependent variable and the independent variables is linear.
b) effect of x1 on the dependent variable is influenced by x2.
c) effect of x2 on the dependent variable is influenced by x1.
d) both b and c.
When the effects of x1 and x2 on the dependant variable are influenced by each other in a first-order model with two predictors, x1 and x2, an interaction term may be utilised. The right response is d) both b and c.
A first-order model is a linear equation that involves only one dependent variable and one independent variable. In other words, the equation represents the linear relationship between two variables. The equation can be defined as
Y = β0 + β1X,
where
Y is the dependent variable,
X is the independent variable,
β0 is the y-intercept, and
β1 is the slope of the line.
When attempting to predict the dependant variable based on the independent variable and a linear relationship between them, the first-order model is helpful.
An interaction term is added to a first-order model with two predictors when the effect of x1 on the dependent variable is influenced by x2 as well as the effect of x2 on the dependent variable is influenced by x1. Therefore, the correct answer choice is d) both b and c.
You can learn more about first-order model at
https://brainly.com/question/15585829
#SPJ11
in a large population 54% of the people hav been vaccinated 3 people are randomly selected what is the probability that at least one of them has been vaccinated
The probability that at least one of the three people has been vaccinated is 92.8%.
Step-by-step explanation: Given, In a large population, 54% of the people have been vaccinated. Then, the probability that one person has been vaccinated is 54/100 = 0.54.
The probability that one person has not been vaccinated is 1 - 0.54 = 0.46. The probability that all three people have not been vaccinated is (0.46)³ = 0.097336. The probability that at least one person has been vaccinated is 1 - 0.097336 = 0.902664. Hence, the probability that at least one of the three people has been vaccinated is 92.8%.
See more about probability at: https://brainly.com/question/13604758
#SPJ11
Water is being poured into a large, cone-shaped
cistern. The volume of water, measured in cm³, is
reported at different time intervals, measured in
seconds. A regression analysis was completed and is
displayed in the computer output.
In response to the stated question, we may state that The coefficient equation of -1.327 indicates that the amount of water in the cistern declines at an exponential rate as time passes.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
The least-squares regression line has the following equation:
2.993 - 1.327 In(Volume)* (Time)
The link between the natural logarithm of water volume and the natural logarithm of time is illustrated by this equation. The coefficient of -1.327 indicates that the amount of water in the cistern declines at an exponential rate as time passes.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
Find the rate of change over the interval 2 < x < 5; f(x)= 2x^2+5 (use this function).
Answer: The correct answer to this problem would be C, or 32/3.
Step-by-step explanation:
The average rate of change in a function is the rate at which one value changes with respect to another value.
Given function: f(x) = 2x² + x + 5 on interval [-2, 2]
Therefore,
Average rate of change = f(2)-f(-2)/2-(-2)
f(2) = 2(2)² + 2 + 5
f(2) = 15
f(-2) = 2(-2)² - 2 + 5
f(2) = 11
Substitute the values,
Average rate = 5-11/2+2
Average rate = 4/4
Average rate = 1
So, the average rate of change is
Leading me to believe option C is correct.
Find the surface area of the rectangular pyramid.
1 = 12 ft, w = 8 ft, sh = 10 ft
a 194 ft²
b 182 ft²
c 272 ft²
d 296 ft²
Check it
In response to the stated question, we may state that As a result, the rectangular pyramid has a surface area of 296 ft2. 296 ft2 is the correct answer.
What is rectangle?In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle" at times. A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.
To determine the surface area of a rectangular pyramid, first calculate the area of each face and then add them together.
Given the rectangular pyramid's dimensions:
Slant height= 10 ft base length (l) = 12 ft base width (w) = 8 foot
Then, calculate the area of the base. The area of the base is simply l w: because it is a rectangle.
Base area = [tex]12 ft x 8 ft = 96 ft^2[/tex]
A triangle face's area equals 1/2 its base height, where base = w or l and height = sh.
[tex]1/2 *8 ft *10 ft = 40 ft^2[/tex] area of the first triangle face
[tex]1/2 *12 ft *10 ft = 60 ft^2[/tex]area of the second triangular face
Third triangular face area = [tex]1/2 *8 ft *10 ft = 40 ft^2[/tex]
The area of the fourth triangular face is equal to [tex]1/2 *12 ft *10 ft = 60 ft^2.[/tex]
Now put the areas of all the faces together to get the entire surface area:
Total surface area = base area + sum of all triangular face areas
Surface area total =[tex]96 ft^2 + (40 ft^2 + 60 ft^2 + 40 ft^2 + 60 ft^2)[/tex]
296 ft2 total surface area
As a result, the rectangular pyramid has a surface area of 296 ft2.
296 ft2 is the correct answer.
To know more about rectangle visit:
https://brainly.com/question/29123947
#SPJ1
by rounding both numbers to 2dp approximate an answer to 0.028 x 0.043
Answer:0.001204
Step-by-step explanation:
0.028x0.043
what is the x? please help its very important
Answer:
73°
Step-by-step explanation:
As it is a hexagon, the sum of the interior angles in 720°
4x+165+132+131=720 4x=292 x=73°
Megan's standard pay is £17.70 per hour. She gets paid 1.5 times this rate for working overtime. How much will Megan get paid for working 11 hours of overtime? Give your answer to the nearest pound.
Answer:
Step-by-step explanation:
Overtime Rate = [tex]17.70 \times 1\frac{1}{2}[/tex]
[tex]= 17.70 \times \frac{3}{2}[/tex]
[tex]=\frac{53.10}{2}[/tex]
[tex]=\pounds26.55[/tex]
Pay [tex]=11*26.55=\pounds 292.05[/tex] (I assume you can use a calculator for this)
Solution: [tex]\pounds 292[/tex]
Tara and Jack share a sum of money in the ratio 7: 8
Jack got £18 more than Tara.
How much did Tara receive?
Answer:
Step-by-step explanation:
Let's represent the amount of money Tara received by "7x", since the ratio of Tara's share is 7:8. Similarly, let's represent the amount Jack received by "8x".
We know that Jack received £18 more than Tara, so we can set up an equation:
8x - 18 = 7x
Solving for x, we get:
x = 18
Now we can find Tara's share by substituting x into our expression for Tara's share:
7x = 7(18) = £126
Therefore, Tara received £126.
The simple exponential smoothing model can be expressed asA)a simple average of past values of the data
.B)an expression combining the most recent forecast and actual data value. ***
C)a weighted average, where the weights sum to zero.
D)a weighted average, where the weights sum to the sample size.
E)None of the above.
The simple exponential smoothing model can be best described as (B) "an expression combining the most recent forecast and actual data value". B is the correct answer.
Simple exponential smoothing is a time series forecasting technique that creates predictions using a weighted average of previous observations. As the observations get older, the weights decrease exponentially. The forecast for the next period is created by fusing the most recent forecast with the most recent actual data value using the smoothing parameter alpha. This can be mathematically stated as:
F_t+1 = αY_t + (1-α)F_t
where F_t is the forecast for period t, Y_t is the actual value for period t, α is the smoothing parameter, and F_t+1 is the forecast for period t+1.
Option B is the correct answer.
You can learn more about Simple Exponential Smoothing (SES) at
https://brainly.com/question/14783222
#SPJ11
Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem. (Round your answer to four decimal places.) y' = x^2 + xy y(0) = 4
By using Euler's method with a step size of 0.2, we estimate that y(1) = 4.5429.
The Euler's method is used to estimate a numerical solution of a first-order differential equation. The formula of Euler's method is given by:
y_1 = y_0 + hf(x_0, y_0)
Where: y_1 is the next value of y after one iterationy
0 is the initial value of yy' = f(x, y)h is the step size
This method is an iterative procedure that advances the estimate of y by one step by approximating the curve using a tangent line at each point along the curve.
Given that y(0) = 4 and h = 0.2, we can use Euler's method to estimate y(1) where y(x) is the solution of the initial-value problemy' = x2 + xy, y(0) = 4
Using Euler's method with a step size of 0.2, we get:
1) When x = 0, y = 4
y_1 = y_0 + hf(x_0, y_0) = 4 + 0.2(0 + 4(0))= 4.02
When x = 0.2, y = 4.02
y_2 = y1 + hf(x_1, y_1) = 4.02 + 0.2(0.2^2 + 0.2(4.02))= 4.10523
When x = 0.4, y = 4.1052
y_3 = y_2 + hf(x_2, y_2) = 4.1052 + 0.2(0.4^2 + 0.4(4.1052))= 4.1994144
When x = 0.6, y = 4.1994
4 = y_3 + hf(x_3, y_3) = 4.1994 + 0.2(0.6^2 + 0.6(4.1994))= 4.3032545
When x = 0.8, y = 4.3033
y_5 = y_4 + hf(x_4, y_4) = 4.3033 + 0.2(0.8^2 + 0.8(4.3033))= 4.4174496
When x = 1, y = 4.4174
y_6 = y_5 + hf(x_5, y_5) = 4.4174 + 0.2(1^2 + 1(4.4174))= 4.5429404
Therefore, using Euler's method with a step size of 0.2, we estimate that y(1) = 4.5429 (rounded to four decimal places).
To know more about Euler's method: https://brainly.com/question/14286413
#SPJ11
Samir and Ayisha are on one side of a river. Katia is on the other side. The distance between Samir and Katia is 82 ft. The distance between Ayisha and Katia is 80 ft. If the angle from Samir to Katia to Ayisha is 18°, how far apart are Samir and Ayisha?
Using Law of Cosines, the square root of a negative number is not a real number, there is no solution for x.
We can use the Law of Cosines to solve this problem. Let's label the distance between Samir and Ayisha as "x". Then, using the Law of Cosines, we have:
cos(18°) = (80² + x² - 82²) / (2 * 80 * x)
Simplifying this equation, we get:
cos(18°) = (x² - 2x + 3996) / (160x)
Multiplying both sides by 160x, we have:
160x * cos(18°) = x² - 2x + 3996
Simplifying, we get:
0 = x² - 2x + 3996 - 160x * cos(18°)
Now we can use the quadratic formula to solve for x:
[tex]x = [2 \pm \sqrt{(4 - 4(1)(3996 - 160cos(18^o))) ]} / 2[/tex]
[tex]x = [1 \pm \sqrt{(1 - (3996 - 160cos(1^o°)))} ]\\x = [1 \pm \sqrt{(160cos(18^o) - 3995)]}[/tex]
Plugging in the value of cos(18°) (which is approximately 0.951), we get:
[tex]x = [1 \pm \sqrt{(160(0.951) - 3995)}]x = [1 \pm \sqrt{(-2494.4)}][/tex]
Since the square root of a negative number is not a real number, there is no solution for x. Therefore, the problem may be incorrect or incomplete.
To learn more about law of cosines from given link
https://brainly.com/question/13409288
#SPJ1
Q3 NEED HELP PLEASE HELP
Answer:
C. Rachel is saving $5 per week.
Step-by-step explanation:
The initial savings are $10, as it is the y-intercept.
And to obtain the slope we can take 2 points from the graph.
A(0,10)
B(1,15)
m=(y2-y1)/ (x2-x1)
m=(15-10)/ (1-0)
m= 5/1
m= 5 savings in dollars per (1) week
Winning the jackpot in a particular lottery requires that you selet the correct four numbers between 1 and 59 and, in a separate drawing, you must also select the correct single number between 1 and 41. Find the probability of winning the jackpot.
The probability of winning the jackpot is __ .
The probability of selecting the correct four numbers out of 59 is solved by the formula :
P(4 correct numbers) = (number of ways to choose 4 correct numbers) / (total number of possible 4-number combinations)
The total number of possible 4-number combinations out of 59 is:
C(4,59) = (59 choose 4) = 190,578
P(jackpot) = P(4 correct numbers) * P(1 correct number)
P(jackpot) = 1/41
thus, the probability of winning the jackpot in this particular lottery is 1/41.'
To learn about probability visit:
https://brainly.com/question/16484393?referrer=searchResults
#SPJ4
Interpreting a Z score from a sample proportion. Suppose that you conduct a hypothesis test about a population proportion and calculate the Z score to be 0.47. Which of the following is the best interpretation of this value? For the problems which are not a good interpretation, indicate the statistical idea being described. 19 a. The probability is 0.47 that the null hypothesis is true. b. If the null hypothesis were true, the probability would be 0.47 of obtaining a sample proportion as far as observed from the hypothesized value of the population proportion. c. The sample proportion is 0.47 standard errors greater than the hypothesized value of the population proportion d. The sample proportion is equal to 0.47 times the standard error. e. The sample proportion is 0.47 away from the hypothesized value of the population. f. The sample proportion is 0.47
If the null hypothesis were correct, there would be a 0.47 percent chance of getting a sample proportion that deviates from the population proportion's hypothesised value
What is proportion?Proportion refers to the relationship between two quantities or numbers, indicating how they are related to each other in size or amount.
According to question:The best interpretation of a Z score of 0.47 for a sample proportion is:
b. If the null hypothesis were correct, there would be a 0.47 percent chance of getting a sample proportion that deviates from the population proportion's hypothesised value.
This interpretation is in line with the definition of a Z score, which is a measure of how many standard deviations a sample statistic (in this case, the sample proportion) is not what would be anticipated if the null hypothesis were true. A Z score of 0.47 means that the sample proportion is 0.47 standard deviations away from the expected value under the null hypothesis. Therefore, the interpretation that the probability of obtaining a sample proportion as far or farther than observed from the hypothesized value of the population proportion is 0.47, assuming the null hypothesis is true, is the most appropriate.
To know more about proportion visit:
https://brainly.com/question/7066283
#SPJ1
Use the table to answer the following question. The table shows pairs of values for a linear function. A different function is defined by the equation y = 4x. Which of the following statements is TRUE? The functions both have a slope of 4. The functions are both proportional. The functions have opposite slopes. The functions both have a y-intercept of 4.
A statement which is true include the following: C. The functions have opposite slopes.
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the vertical intercept, y-intercept or initial number.Based on the information provided above, an equation that models one of the function is given by;
y = 4x
mx = 4x
Slope, m = 4.
For the other function, the slope can be calculated as follows;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (0 - 4)/(1 - 0)
Slope (m) = -4/1
Slope (m) = -4.
Read more on slope-intercept here: brainly.com/question/7889446
#SPJ1
8. A department store
buys 300 shirts for
a total cost of $7,200 and sells them for
$30 each. Find the percent markup.
The percent markup is 25%.
What is percent markup?Markup percentage is calculated by dividing the gross profit of a unit (its sales price minus it's cost to make or purchase for resale) by the cost of that unit.
Given that, A department store buys 300 shirts for a total cost of $7,200 and sells them for $30 each.
Cost of one shirt [tex]= 7200 \div 300 = \$24[/tex]
And they sold at $30 each,
Percent markup [tex]= 30-24 \div 24 \times 100[/tex]
[tex]= 25\%[/tex]
Hence, the percent markup is 25%.
Learn more about Markup percentage, click:
https://brainly.com/question/28945726
What true statement can be made about the data distributions shown in the box-and-whisker plots below(attached image)
A
Box 1 is negatively skewed, and Box 2 is symmetric
B
Box 1 is negatively skewed, and Box 2 is positively skewed
C
Box 1 is positively skewed, and Box 2 is negatively skewed
D
Box 1 is positively skewed, and Box 2 is symmetric.
The statement "Box 1 is negatively skewed, and Box 2 is symmetric" is true.
Looking at shown the box-and-whisker plots, we can make the following observations:
Box 1 has a longer whisker on the left side than on the right side, which indicates that the data is skewed to the left.
Therefore, Box 1 is negatively skewed.
Box 2 has whiskers that are approximately the same length on both sides, which indicates that the data is symmetric.
Therefore, Box 2 is symmetric.
Based on these observations, we can conclude that:
A) Box 1 is negatively skewed, and Box 2 is symmetric.
Therefore, the correct answer is A.
To learn more about the box and whisker plot click here:
https://brainly.com/question/11859288
#SPJ12
The missing figure is attached below.
HELP PLEASE … Assuming the input of energy continues for another 2.5 seconds, where will the particle be?
A) cannot be determined
B) positive maximum
C) negative maximum
D) equilibrium
Answer:
To determine the position of a particle given the input of energy, we need to know the type of energy input and the initial position and velocity of the particle. Without this information, we cannot determine the position of the particle after 2.5 seconds.
Therefore, the answer is A) cannot be determined.
Step-by-step explanation:
ABOVE
Find the surface area of the rectangular prism.
6 km
4 km
4 km
Answer: 88km is your answer
Step-by-step explanation: We just had this on a test
Find the value of tan � N rounded to the nearest hundredth, if necessary.
After solving the given problem the value of tan N rounded to the nearest hundredth is 0.95.
What is trignometry?Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of the triangles.
It is used to calculate distances, heights, and angles, and is used extensively in fields such as engineering, physics, and architecture.
We can use the tangent function to find the value of tan N in the right triangle LMN.
tan N = ML/MN
We know that MN = 6 and ∠LMN is 90°, so we can use the Pythagorean theorem to find ML:
NL² = ML² + MN²
√77² = ML² + 6²
77 = ML² + 36
ML²= 77 - 36
ML² = 41
ML = √41
Now we can substitute the values for ML and MN into the equation for tangent:
tan N = ML/MN = (√41)/6
Using a calculator, we can evaluate this expression and round to the nearest hundredth:
tan N ≈ 0.95
To know more about tangent visit:
https://brainly.com/question/23185930
#SPJ1
The complete question is given below.
What is 25.71 rounded to 2 Decimal Place?
The rounded value of 25.71 to 2 decimal places is 25.71 itself.
How to find 25.71 rounded to 2 Decimal PlaceTo round 25.71 to 2 decimal places, we need to look at the third decimal place, which is 1.
If the third decimal place is 5 or greater, we round up the second decimal place. If the third decimal place is less than 5, we simply drop it and keep the second decimal place as is.
In this case, the third decimal place is 1, which is less than 5, so we simply drop it and keep the second decimal place as is. Therefore, 25.71 rounded to 2 decimal places is:
25.71 ≈ 25.71 (no rounding necessary)
So, the rounded value of 25.71 to 2 decimal places is 25.71 itself.
Learn more about decimal at https://brainly.com/question/703656
#SPJ1
3. A triangle has side of 5, angle of 85*, and an angle of 40
Triangle
The length of the side opposite the 85° angle is approximately 7.75 units.
How to determine the side length opposite the angleTo solve this problem, we can use the law of sines, which states that for any triangle ABC:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the side lengths of the triangle opposite the angles A, B, and C, respectively.
In this case, we know the side length b = 5 and the angles A = 85° and B = 40°.
Let's call the unknown side length opposite the angle A as a.
Then, we have:
a/sin(85°) = 5/sin(40°)
Multiplying both sides by sin(85°), we get:
a = 5*sin(85°)/sin(40°)
Using a calculator, we get:
a ≈ 7.75
Therefore, the side length opposite the angle of 85 degrees is
Read more about law of sines at
https://brainly.com/question/4372174
#SPJ1
Complete question
A triangle has side of 5, angle of 85*, and an angle of 40 opposite the side length of 5. What is the length of the side opposite the 85° angle?
apply the triangle inequality theorem to determine the possible whole number measures of the third side of a triangle if the first two sides measure 6 and 2. list them in ascending order.
By applying the triangle inequality theorem, the possible whole number measures of the third side in ascending order, are 5, 6, and 7.
The Triangle Inequality Theorem is a theorem that states that the sum of the lengths of two sides of a triangle is greater than the length of the third side.
We can use the triangle inequality theorem to determine the possible whole number measures of the third side of a triangle if the first two sides measure 6 and 2.
The Triangle Inequality Theorem can be written as:
a + b > c where a, b, and c are the sides of a triangle. If a = 6 and b = 2, then the inequality is:
6 + 2 > c
8 > c
So, the third side must be less than 8 units long. On the other hand, the length of the third side must be greater than the difference between the lengths of the other two sides. So, we can set up another inequality:
6 - 2 < x
Simplifying, we get:
4 < x
So, the length of the third side must be greater than 4 units long.
Therefore, applying the triangle inequality theorem, the possible whole number measures of the third side of the triangle are the integers from 5 to 7, inclusive.
So, the list of possible whole number measures of the third side in ascending order is 5, 6, and 7.
To know more about the "triangle inequality theorem" :https://brainly.com/question/309896
#SPJ11
Compute the measure of the angle between 0 and 360 degrees swept counterclockwise from 3 o'clock position on the unit circle whose terminal ray intersects the circle at the point with given y-coordinate and in the given quadrant. a. D 05 in Quadrant I degrees Preview 6 in Quadrant II Preview egrees Preview uadrant I degreesPreview License Points possible: 1 Unlimited attempts. Submit
The angle between 0 and 360° swept counterclockwise from the 3 o'clock position on the unit circle is 33.69°.
For point D with a y-coordinate 0.5 in Quadrant I, we can use the trigonometric functions to find the angle it makes with the positive x-axis. Since the point is on the unit circle, we have:
x^2 + y^2 = 1
Substituting y = 0.5, we get:
x^2 + (0.5)^2 = 1
x^2 = 1 - (0.5)^2
x = ±√(1 - 0.25)
x = ±√0.75
Since the point is in Quadrant I, we know that x is positive. Therefore, x = √0.75. Now, we can use the inverse tangent function to find the angle θ that the point makes with the positive x-axis:
θ = tan^(-1)(y/x)
θ = tan^(-1)(0.5/√0.75)
θ ≈ 33.69°
Since the point is in Quadrant I, the angle swept counterclockwise from the 3 o'clock position is simply θ:
Angle = 33.69°
To know more about the "swept counterclockwise": https://brainly.com/question/30147251
#SPJ11
Un número tiene 8 divisores. Además, cada uno de la mitad y la tercera parte de él tienen cuatro divisores. Si la suma de todos los divisores del número es 216, obtén tal número
The number we are looking for is N = 2 × 2^3 × 3^2 = 72.
Let's first recall some properties of the number of divisors of an integer. If we factorize an integer n as a product of prime powers, say
n = p_1^a_1 × p_2^a_2 × ... × p_k^a_k
then the number of divisors of n is given by
d(n) = (a_1 + 1) × (a_2 + 1) × ... × (a_k + 1).
Using this fact, we can deduce some information about the number we are looking for. Let's call it N. We know that N has 8 divisors, so it must be of the form
N = p_1^2 × p_2^2, or N = p_1^7,
where p_1 and p_2 are distinct prime numbers.
Now, we are told that each of N/2 and N/3 has four divisors. We can use the same fact about the number of divisors to conclude that
N/2 = q_1^3 × q_2, or N/2 = q_1^1 × q_2^3,
and
N/3 = r_1^3 × r_2, or N/3 = r_1^1 × r_2^3,
where q_1, q_2, r_1, and r_2 are distinct prime numbers.
To simplify the notation, let's introduce the variables a, b, c, d, e, and f, defined by
p_1 = q_1^a × q_2^b,
p_2 = r_1^c × r_2^d,
N/2 = q_1^e × q_2^f,
N/3 = r_1^g × r_2^h.
Using the information we have so far, we can write down equations for a, b, c, d, e, f, g, and h in terms of unknown exponents:
a + 1 × (b + 1) = e + 1 × (f + 1) = 4,
c + 1 × (d + 1) = g + 1 × (h + 1) = 4,
2a × 2b = ef,
2c × 2d = gh.
We can solve this system of equations by trial and error. For example, we can start by trying all possible values of a and b such that 2a × 2b = 4. This gives us two possibilities: a = 0, b = 2, or a = 1, b = 1. Using the first possibility, we get e = 3, f = 1, which leads to N/2 = q_1^3 × q_2, and hence N = 2 × q_1^3 × q_2^2. Substituting this into the equation for the sum of divisors, we get
(1 + q_1 + q_1^2 + q_1^3) × (1 + q_2 + q_2^2) = 216.
We can solve this equation by trial and error as well, or by observing that 216 = 2^3 × 3^3, and hence the two factors on the left-hand side must be equal to 2^3 and 3^3, respectively. This gives us the unique solution q_1 = 2 and q_2 = 3, and hence N = 2 × 2^3 × 3^2 = 72.
Learn more about divisor here
brainly.com/question/17879555
#SPJ4
Please help me with the following questions I will give brainiest
The exponential equation that fits the provided point distribution is [tex]y = 5(2)^x[/tex] . Thus, option A is correct.
What do exponential equations work?An exponential equation is one in which the exponent contains a variable.
For instance, the exponential equation [tex]y = 5x[/tex] has the variable x as the exponent (also known as "5 to the power of x"),
whereas, the exponential equation y = x5 has the number 5 as the exponent instead of a variable, making the latter equation not exponential.
If we calculate the initial differences, we can determine the exponential equation that corresponds to the given pattern of points as follows:
[tex](2-1) = 5[/tex]
[tex](3-2) = 10[/tex]
[tex](4-3) = 20[/tex]
If we calculate the second differences, we obtain:
[tex](10-5) = 5[/tex]
[tex](20-10) = 10[/tex]
The fact that the second differences are constant shows that the exponential equation's coefficient is 5.
Therefore, The exponential equation that fits the provided point distribution is [tex]y = 5(2)^x[/tex] .
Learn more about exponential here:
https://brainly.com/question/29506679
#SPJ1
Help with geometry with rhombus. Given rhombus ABCD with m
For the given rhombus the value of x = 3/2 and the measure of angle EAB and angle EBA = 2.5 degrees.
What is a rhombus?A rhombus is a specific instance of a parallelogram. In a rhombus, opposite sides are parallel and the opposite angles are equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is also referred to as a diamond or rhombus. Rhombi or rhombuses are the plural forms of rhombus.
The adjacent angles of a rhombus are supplementary, and diagonals bisect the angles.
Using this property we have:
2(7x - 8) + 2(3x - 2) = 180
14x - 16 + 6x - 4 = 180
20x - 20 = 180
x = 180/20
x = 9
Substituting the value of x:
angle EAB = 7(9) - 8 = 55
angle EBA = 3(9) - 2 = 25
Hence, the value of x = 9 and the measure of angle EAB = 55 degrees and angle EBA = 25 degreed.
Learn more about rhombus here:
https://brainly.com/question/9637480
#SPJ1