Answer: 5
Step-by-step explanation:
You could multiply every number but that would take too much time
Instead you have to logic through the problem
Numbers in multiplication follow cyclical sets. i.e. the ones place in the multiples of 3 goes 3,6,9,2,5,8,1,4,7,0,3 forever. (That is why 3 is a "mod 10" number there are 10 possible 1s place values)
The helpful number here is 5
5 is mod 2 because any multiple ends in a 5 or a 0. Given that you are doing all of the odd numbers, five times any odd number will end in a 5, and any odd number ending in 5 times another odd number will also end in 5 so the ones place for all odd numbers multiplied from 1 to 2023 is 5.
When multiplying all the odd numbers from 1 to 2023, inclusive, the last digit of the product will be 5. This is based on the pattern observed in the last digits of the products of odd numbers.
Explanation:In mathematics, specifically in number theory, we often make use of patterns to solve problems. When you're asked to find the last digit of the product when you multiply all the odd numbers from 1 to 2023, inclusive, it is helpful to look for a pattern in the last digits of the products of odd numbers.
Let's start small. The first five odd numbers are 1, 3, 5, 7, and 9. The product of these numbers is 945, and the last digit, or unit digit, is 5. Let's add another odd number to the product, 11. The product becomes 10395, and again, the unit's digit is 5. As you can see, the pattern is that no matter how many odd numbers you multiply together, the unit's digit (or the last digit) of the product is always 5.
Therefore, when you multiply all the odd numbers from 1 to 2023, inclusive, the last digit of the product will be 5.
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One of the interior angles of an n-sided polygon is 126° and the remaining interior angles are 162° each. Find the value of n.
The number of sides of the polygon will be 6.
In any closed polygon, the number of sides is equal to the number of interior angles.
Let the number of sides is n in the given polygon.
Sum of angles = 90° + 126° × (n - 1)
The sum of angles is given as, 180(n - 2)
90° + 126° × (n - 1) = 180(n - 2)
90 + 126n - 126 = 180n - 360
180n - 126n = 90 - 126 + 360
54n = 324
n = 6
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Determine if W is a basis for R^3 and check the correct answer(s) below. [-2,3,0] , [6,-1,5] A. W is a basis. B. W is not a basis because it is linearly dependent. C. W is not a basis because it does not span R^3.
We can then perform row reduction to determine the rank of the matrix. After performing row reduction, we can see that the rank of the matrix is 2, which is less than the dimension of R^3, which is 3. Therefore, the two vectors in W do not span R^3, and so W is not a basis for R^3.
First, let's check for linear independence. We can set up the following equation:
c1[-2,3,0] + c2[6,-1,5] = [0,0,0]
This gives us the system of equations:
-2c1 + 6c2 = 0
3c1 - c2 = 0
5c2 = 0
The last equation tells us that c2 must be 0, which means the first equation simplifies to c1 = 0. Substituting these values into the second equation gives us 0 = 0, which is always true. This tells us that the only solution to the system is c1 = c2 = 0, meaning that W is linearly independent.
Next, let's check if W spans R^3. We can do this by checking if any vector in R^3 can be written as a linear combination of the two vectors in W. That is, we need to solve the equation:
c1[-2,3,0] + c2[6,-1,5] = [x,y,z]
This gives us the system of equations:
-2c1 + 6c2 = x
3c1 - c2 = y
5c2 = z
Solving for c1, c2, and z, we get:
c2 = z/5
c1 = (y + c2)/3 = (y + z/5)/3
x = -2c1 + 6c2 = -(2/3)(y + z/5) + 6z/5 = (-2/3)y + (22/15)z
This means that any vector [x,y,z] in R^3 can be written as a linear combination of the vectors in W. Therefore, W spans R^3.
Since W is both linearly independent and spans R^3, it is a basis for R^3. Therefore, the correct answer is A. W is a basis.
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Consider the line and three rays that intersect as shown.
Answer:
Expression 1: 3y+x+52+(2x-60)+(x+15)+52=360
Expression 2: 4x+3y+59=360 or if you want just "x"'s and "y"'s on one side, you would do 4x+3y=301
Step-by-step explanation:
Expression 1: Add up all the angles to get expression 1.
Expression 2: Combine like terms.
Hope this helps! :)
Answer:
1: 3y+x+52+(2x-60)+(x+15)+52=360
2: 24x+3y+59=360
Step-by-step explanation:
REVIEW FROM 4.01
What are the zeros of the function?
f(x) = 2x² + x - 15
X1=
X2=
Answer:
x=5/2, -3
Step-by-step explanation:
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.
have a great day and thx for your inquiry :)
A rectangular prism has a length of 10 centimeters, a width of
6 centimeters, and a height of
8 cm
8 centimeters.
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data. 10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55 A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49. Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The charity should use the range as a measure of variability to accurately represent the data. Range is the difference between the largest and smallest values in a dataset. So, the range as a measure of variability is appropriate for this dataset because it gives a sense of how spread out donations are from the smallest to the largest.
In this case, the largest donation was $55 and the smallest was $10, so the range is $55 - $10 = $45. Using the range as a measure of variability is appropriate for this dataset because it gives a sense of how spread out the donations are from the smallest to the largest.
It is also easy to calculate and understand, which makes it useful for reporting to donors and stakeholders.
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the probability that sergeant mendez hits its target each time he shoots is 0.8. suppose that sergeant mendez shoots at a target 10 times. a. find the probability he hits the target 3 times. b. what is the probability he hits his target at least twice? c. what is the probability he hits the target at most 4 times? d. what is the expected number of shots that hit the target
a. The probability he hits the target 3 times is 0.2013. b. The probability he hits his target at least twice is 0.9984. c. The probability he hits the target at most 4 times is 0.1074. d. The expected number of shots that hit the target is 8.
a. The probability he hits the target 3 times = (10C3) * (0.8)^3 * (0.2)^7 = 0.2013
b. To calculate the probability he hits his target at least twice, we need to calculate the probability of hitting it twice, hitting it thrice, hitting it four times, ..., hitting it ten times.
So, P(hitting at least twice) = P(hitting twice) + P(hitting thrice) + ... + P(hitting ten times).
Therefore,
P(hitting at least twice) = (10C2) * (0.8)^2 * (0.2)^8 + (10C3) * (0.8)^3 * (0.2)^7 + ... + (10C10) * (0.8)^10 * (0.2)^0 = 0.9984
c. The probability he hits the target at most 4 times = P(hitting 0 times) + P(hitting 1 time) + P(hitting 2 times) + P(hitting 3 times) + P(hitting 4 times)
= (10C0) * (0.8)^0 * (0.2)^10 + (10C1) * (0.8)^1 * (0.2)^9 + (10C2) * (0.8)^2 * (0.2)^8 + (10C3) * (0.8)^3 * (0.2)^7 + (10C4) * (0.8)^4 * (0.2)^6
= 0.1074
d. The expected number of shots that hit the target can be calculated as:
Expected number = 10 * 0.8 = 8
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Zeus eats 1/2of dog food Shiva eats 1 box of dog food and Apollo eats the same amount as Zeus how many pounds do they all eat one week
Answer:
They eat 2 pounds in one week
Step-by-step explanation:
Lets write down what we know:
Zeus eats: 1/2
Shiva eats: 1
Apollo eats: Same amount as Zeus, 1/2.
How many do they eat in one week?
In order to answer this question, we just need to add all of our numbers together.
[tex]\frac{1}{2}+\frac{1}{2}+1[/tex]
Add the halves together. 1/2 + 1/2 = 1
[tex]1+1[/tex]
Add the 1s
[tex]2[/tex]
They eat 2 pounds in one week
liam wants to estimate the percentage of people who lease a car. he surveys 240 individuals and finds that 54 lease a car. find the margin of error for the confidence interval for the population proportion with a 95% confidence level.
The margin of error for the confidence interval for the population proportion, with a 95% confidence level, is approximately 0.0513 (or 5.13%).
To find the margin of error for the confidence interval for the population proportion, we can use the formula:
Margin of Error = Z * sqrt((p * (1 - p)) / n)
Where:
Z is the critical value for the desired confidence level (95% confidence level corresponds to a Z-value of approximately 1.96)
p is the sample proportion (54/240 in this case)
n is the sample size (240 in this case)
Plugging in the values, we have:
Margin of Error = 1.96 * sqrt((54/240 * (1 - 54/240)) / 240)
Calculating this expression, we find:
Margin of Error ≈ 0.0513
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a statistics instructor collects the gpa and major of each student in a statistics class. major is which level of measurement?
The major variable in this statistics class is considered a nominal variable.
The major variable is considered a nominal level of measurement because it represents a categorical characteristic that cannot be ordered or measured in a quantitative manner.
In other words, the values assigned to different majors (e.g. Engineering, English, History) do not represent numerical quantities or differences.
The level of measurement of a variable determines the type of statistical analyses that can be conducted with that variable. In this case, the major variable is considered a nominal variable because it represents a categorical characteristic that cannot be ordered or measured in a quantitative manner.
Nominal variables are often used to categorize or group data based on non-numeric characteristics, such as gender, race, or occupation. By collecting data on both GPA and major, the statistics instructor can explore relationships between these variables, such as whether certain majors tend to have higher or lower GPAs.
In conclusion, the major variable in this statistics class is considered a nominal variable.
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John draws a circle with a radius of 26 centimeters. What is the circumference of the circle
Answer:163.362817987
Step-by-step explanation:
Circumference = (rx2)π
= (26x2)π
= 52π
= 163.362817987cm
you want to obtain a sample to estimate a population proportion. at this point in time, you have no reasonable estimate for the population proportion. you would like to be 99.9% confident that you estimate is within 5% of the true population proportion. how large of a sample size is required?
Since you cannot have a fraction of a sample, you should round up to the nearest whole number. Therefore, a sample size of 542 is required to be 99.9% confident that your estimate is within 5% of the true population proportion.
To estimate a population proportion with a high degree of confidence (99.9%) and a margin of error (5%), you need to determine an appropriate sample size. Since you have no reasonable estimate for the population proportion, it's common to use 0.5 as a conservative estimate to ensure the largest possible sample size.
For this calculation, you can use the formula:
n = (Z^2 * p * (1-p)) / E^2
Where n is the sample size, Z is the Z-score associated with the desired confidence level (99.9%), p is the estimated population proportion (0.5), and E is the margin of error (0.05).
For a 99.9% confidence level, the Z-score is 3.291. Plugging the values into the formula:
n = (3.291^2 * 0.5 * (1-0.5)) / 0.05^2
n ≈ 541.16
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a diver jumps off a diving board 26 feet above the water.
The time it takes for the diver to reach the water is 1.7 seconds.
To find the time it takes for the diver to reach the water, we need to determine when the height of the diver, as modeled by the function
h(x) = -16x² + 6x + 36, becomes 0.
So, h(x)= 0
-16x² + 6x + 36 = 0
We can either factor the equation or use the quadratic formula to find the solutions. Let's use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
x = (-6 ± √(36 + 2304)) / (-32)
x = (-6 ± √2340) / (-32)
x ≈ (-6 ± 48.38) / (-32)
This gives us two possible solutions:
x ≈ (-6 + 48.38) / (-32) ≈ 42.38 / (-32) ≈ -1.32
x ≈ (-6 - 48.38) / (-32) ≈ -54.38 / (-32) ≈ 1.7
Since time cannot be negative in this context, the time it takes for the diver to reach the water is 1.7 seconds.
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for which value of theta is csc (theta) undefined?
The function csc(theta), which stands for cosecant, is defined as the reciprocal of the sine function: csc(theta) = 1/sin(theta).
In trigonometry, the sine function is undefined when the denominator is zero, which occurs at angles where the sine function equals zero. The sine function equals zero at angles that are multiples of pi (180 degrees), such as 0, pi, 2pi, etc.
Since csc(theta) is the reciprocal of sin(theta), csc(theta) is undefined at angles where sin(theta) equals zero. Therefore, csc(theta) is undefined at theta = 0, pi, 2pi, etc., or in general, at any angle where the sine function equals zero.
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A cube with 2.0-cm sides is made of material with a bulk modulus of 4.7 x 10^5 N/m^2. When it is subjected to a pressure of 2.0 x 10^5 Pa is the length of its any of its sides is
The answer is 2.6825 cm, which is not one of the given options. Therefore, the correct answer is E. none of these.
What is the bulk modulus?The bulk modulus, B is defined as:
B = (P / ΔV / V), where P is the pressure applied, ΔV is the change in volume, and V is the original volume.
For a cube, the change in volume, ΔV is related to the change in length, ΔL by:
[tex]\sf \Delta V = \Delta L^3[/tex].
Given that the cube has 2.0 cm sides, the original volume, V is:
[tex]\sf V = (2.0 \ cm)^3 = 8.0 \ cm^3[/tex].
The pressure applied is [tex]\sf P = 2.0 \times 10^5[/tex] Pa and the bulk modulus is [tex]\sf B = 4.7 \times 10^5 \ N/m^2[/tex].
We can rearrange the bulk modulus formula to solve for ΔL as:
[tex]\sf \Delta L = \huge \text(\dfrac{P}{B} \huge \text) \times \dfrac{V}{3}[/tex].
Substituting the values, we get:
[tex]\sf \Delta L = (2.0 \times 10^5 \ \dfrac{Pa}{4.7} \times 10^5\ N/m^2) \times \dfrac{8.0 \ cm^3}{3} = 0.6825 \ cm[/tex]
Therefore, the final length of any side of the cube is:
[tex]\sf L = 2.0 \ cm + \Delta L = 2.0 \ cm + 0.6825 \ cm = 2.6825 \ cm[/tex]
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Complete Question:
A cube with 2.0-cm sides is made of material with a bulk modulus of4.7 × 10^5 N/m2. When it is subjected to a pressure of 2.0 × 10^5 Pa the length of its any of its sides is:
A. 0.85 cm
B. 1.15 cm
C. 1.66 cm
D. 2.0 cm
E. none of these
C
2 mm
9 mm
What is the length of the hypotenuse? If
necessary, round to the nearest tenth.
C =
millimeters
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{2}\\ o=\stackrel{opposite}{9} \end{cases} \\\\\\ c=\sqrt{ 2^2 + 9^2}\implies c=\sqrt{ 4 + 81 } \implies c=\sqrt{ 85 }\implies c\approx 9.2[/tex]
last year, the personal best high jumps of track athletes in a nearby state were normally distributed with a mean of 221 cm and a standard deviation of 11 cm. use technology to find each probability. what is the probability a randomly selected high jumper has a personal best of no more than 230 cm?
Using the given mean and standard deviation, we can calculate the probability of a randomly selected high jumper having a personal best of no more than 230 cm. By using the normal distribution and the cumulative distribution function (CDF), we can find this probability.
To find the probability, we can standardize the value of 230 cm using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (230 - 221) / 11 = 0.818. This standardized value represents the number of standard deviations that 230 cm is away from the mean.
Next, we use a standard normal distribution table or a calculator to find the cumulative probability associated with the standardized value of 0.818. This probability represents the area under the normal curve to the left of 0.818. Using technology, we can find this probability to be approximately 0.7910.
Therefore, the probability that a randomly selected high jumper has a personal best of no more than 230 cm is 0.7910, or 79.10%.
This means that approximately 79.10% of the high jumpers in the nearby state have a personal best height of 230 cm or lower.
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Please help me solve this, and ignore my eraser marks lol
Answer:
[tex]( { {(x + 4)}^{2}) }^{3} = {(x + 4)}^{6} [/tex]
which of the following accurately describes the expected frequencies for a chi-square test? a. they are always whole numbers. b. they can contain fractions or decimal values. c. they can contain both positive and negative values. d. they can contain fractions and negative numbers.
Among the given alternatives, the following option accurately describes the expected frequencies for a chi-square test: They can contain fractions or decimal values.
The answer is B.
What is Chi-Square test?A chi-square test is a statistical method used to measure the relationship between two categorical variables. The null hypothesis for a chi-square test is that there is no relationship between the variables.
The expected frequency (EF) is the number of times an outcome is expected to occur during a trial based on probabilities. In a chi-square test, the expected frequencies are calculated based on probabilities and sample sizes.
The expected frequency can be a fraction or a decimal, and it is determined by multiplying the row total and column total of each cell by the overall total and dividing it by the total number of observations.
The chi-square test statistic is calculated by comparing the observed frequencies to the expected frequencies. The test statistic is then compared to a critical value in a chi-square distribution table to determine whether to accept or reject the null hypothesis.
Hence, the answer of the question is B.
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A group of 49 randomly selected students has a mean age of 22.4 years. Assume the population standard deviation is 3.8. Construct a 98% confidence interval for the population mean.
a) (19.8, 25.1)
b) (21.1, 23.7)
c) (20.3, 24.5)
d) (18.8, 26.3)
This means the confidence interval for the population mean is approximately (21.135, 23.665).
To construct a confidence interval for the population mean, we can use the formula:
CI = ± Z * (σ/√n)
Where:
is the sample mean (22.4),
Z is the Z-score corresponding to the desired confidence level (98% corresponds to a Z-score of approximately 2.33),
σ is the population standard deviation (3.8), and
n is the sample size (49).
Plugging in the values, we have:
CI = 22.4 ± 2.33 * (3.8/√49)
Calculating this expression will give us the confidence interval for the population mean. Evaluating the expression, we find:
CI ≈ 22.4 ± 2.33 * 0.543
Simplifying further, we get:
CI ≈ 22.4 ± 1.265
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exercise 3 (10 points) listed below are the weights (in pounds) and the highway fuel consumption amounts (in mi/gal) of randomly selected cars. weight 3175 3450 3225 3985 2440 2500 2290 fuel consumption 27 29 27 24 37 34 37 what is the correlation coefficient? correlation coeff
Therefore, the correlation coefficient is -2.19.
To calculate the correlation coefficient, we first need to find the mean and standard deviation of both sets of data.
Weight:
Mean = (3175 + 3450 + 3225 + 3985 + 2440 + 2500 + 2290) / 7 = 2995
Standard Deviation = 633.72
Fuel Consumption:
Mean = (27 + 29 + 27 + 24 + 37 + 34 + 37) / 7 = 30
Standard Deviation = 5.73
Next, we need to find the covariance between the two sets of data.
Covariance = Σ[(weight - mean weight) * (fuel consumption - mean fuel consumption)] / (n - 1)
= [(3175-2995)(27-30) + (3450-2995)(29-30) + (3225-2995)(27-30) + (3985-2995)(24-30) + (2440-2995)(37-30) + (2500-2995)(34-30) + (2290-2995)*(37-30)] / 6
= -84317.62
Finally, we can calculate the correlation coefficient using the formula:
Correlation Coefficient = Covariance / (Standard Deviation of Weight * Standard Deviation of Fuel Consumption)
= -84317.62 / (633.72 * 5.73)
= -2.19
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In a coin game, you toss a coin three times. If all three coin tosses are heads or all three tosses are tails, you win $15. Otherwise, you lose $3. What is the expected profit for one round of the coin game?
Round your answer to the nearest cent.
Enter an expected loss as a negative number.
Rounding to the nearest cent, the expected profit for one round of the coin game is approximately -$0.38.
To calculate the expected profit for one round of the coin game, we need to consider the probabilities of winning and losing, as well as the corresponding amounts won or lost.
There are 2 possibilities for winning: either getting all three heads or all three tails. Each of these outcomes has a probability of (1/2) * (1/2) * (1/2) = 1/8.
The amount won in each winning case is $15. Therefore, the expected profit from winning is:
(1/8) * $15 = $1.875
The probability of losing is 1 - probability of winning. In this case, it is 1 - (1/8 + 1/8) = 6/8 = 3/4.
The amount lost in each losing case is $3. Therefore, the expected loss from losing is:
(3/4) * (-$3) = -$2.25
Finally, we can calculate the expected profit by subtracting the expected loss from the expected profit from winning:
$1.875 - $2.25 = -$0.375
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Suppose that a detailed study has revealed that for romance novels the number of pages has mean 364 and standard deviation 47, and that for detective novels the number of pages has mean 404 and standard deviation 173. A reader is going to select at random one romance novel, independently select at random one detective novel, and read both books. What is the standard deviation of the total number of pages the person will read? (A) 14.8 (B) 110.0 (C) 179.3 (D) 220.0 (E) 321.4
The standard deviation of the total number of pages the person will read is approximately 179.3.
To find the standard deviation of the total number of pages the person will read, we need to consider that the number of pages in the romance novel and the number of pages in the detective novel are independent random variables.
The variance of the sum of two independent random variables is equal to the sum of their variances. Therefore, the variance of the total number of pages is the sum of the variances of the romance novel and the detective novel.
For the romance novel:
Mean = 364
Standard Deviation = 47
For the detective novel:
Mean = 404
Standard Deviation = 173
Variance of the total number of pages = Variance of romance novel + Variance of detective novel
Variance = (47^2) + (173^2)
Standard Deviation = √Variance = √(47^2 + 173^2) ≈ 179.3 (rounded to one decimal place)
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Two parallel lines are shown below. Describe the result of the lines after the translation (x, y) -> (x+ 2,y - 1)
The result of the lines after the translation is given as follows:
They do not intersect.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The vector notation is given as follows:
(g,h).
The meaning is given as follows:
g < 0 moves g units left left, g > 0 moves g units right.h > 0 moves h units up, h < 0 moves h units down.The vector for this problem is given as follows:
(2,1).
Meaning that the lines are shifted 2 units right and one unit down.
Both lines, that do not intersect, are translated, hence the lines continue not intersecting.
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M5]L15
Dive Into Dimensions
Irene's window store made a mosaic for the community center. The mosaic had a 7 x 7 array of
different color square tiles. If each tile is 1 ft long, what is the area of the whole mosaic? ➜
3
Solve on paper. Then check your work on Zearn. 4)
Step-by-step explanation:
To find the area of the whole mosaic, we need to multiply the length by the width. In this case, the mosaic is a 7 x 7 array of square tiles, and each tile is 1 ft long.
Area = Length × Width
Area = 7 ft × 7 ft
Area = 49 square feet
So, the area of the whole mosaic is 49 square feet.
2. The volume of a sphere can be given by the formula V = 4.18879r³. You have to design a spherical container that will hold a volume of 100 cubic inches. What should the radius of your container be? (SHOW ALL STEPS AND WORK PLS)
The radius of the spherical container should be approximately 2.87941 inches to hold a volume of 100 cubic inches.
What is the radius of the spherical container?A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.
Given the formula for volume of sphere in the question:
V = 4.18879r³
If a spherical container has a volume of 100 cubic inches, the we can calculate its radius using the above formula.
V = 4.18879r³
r³ = V/4.18879
r = ∛( V/4.18879 )
Plug in the volume of the container:
r = ∛( 100in³ / 4.18879 )
r = 2.87941 in
Therefore, the radius is approximately 2.87941 inches.
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what is the slope of the line that passes through the pair of points (1 7) (10 1)
The line that passes through the points (1, 7) and (10, 1) has a slope of -2/3.
The slope of a line is a measure of its steepness and is defined as the change in the y-coordinate over the change in the x-coordinate between any two points on the line.
The slope of the line that passes through the pair of points (1, 7) and (10, 1) can use the slope formula.
The slope formula states that the slope of a line passing through two points, (x1, y1) and (x2, y2), is given by:
slope = (y2 - y1) / (x2 - x1)
(x1, y1) = (1, 7) and (x2, y2) = (10, 1).
Substituting the values into the formula, we get:
slope = (1 - 7) / (10 - 1)
= -6 / 9
= -2/3
The slope of the line as follows:
For every one unit increase in the x-coordinate the y-coordinate decreases by 2/3 units.
Alternatively for every one unit increase in the x-coordinate the line drops by 2/3 units.
The slope of a line is useful in many applications such as calculating the rate of change of a quantity over time measuring the angle between two lines and determining whether lines are parallel or perpendicular.
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Explain how to do this too please
Answer:
point on the line (3, 1). slope = -1/5
Step-by-step explanation:
straight line equation format is y -y1 = m(x - x1)
where y1 is y-coordinate of a point, x1 is x-coordinate of the same point, m is the slope (gradient).
we have y - 1 = -1/5 (x - 3)
y1 is 1, x1 is 3 and slope is -1/5
The average price of 80 mobile phones if $30,000.If the highest price and lowest price are sold out then the average price of the remaining 78 mobile phones is $29500.If the highest price is 80000,what is the lowest price?
Answer:
$19,000
Step-by-step explanation:
Let's start by finding the sum of the prices of all 80 mobile phones:
80 × 30,000 = 2,400,000
Next, we can find the sum of the prices of the remaining 78 mobile phones by multiplying the new average by 78:
78 × 29,500 = 2,301,000
We know that the highest price is $80,000. Let's assume that the lowest price is x dollars. We can set up an equation to solve for x:
2,400,000 - 80,000 - x = 2,301,000
Simplifying the equation:
2,320,000 - x = 2,301,000
Subtracting 2,301,000 from both sides:
19,000 = x
Therefore, the lowest price of the mobile phone is $19,000.
Find two rational and irrational number between 2.37 and 2.41
The two rational and irrational number that can be found between 2.37 and 2.41 would be given below;
Rational numbers= 2.38 and 2.4.
Irrational numbers = √2 + 2.37 and √3+2.37
What are rational numbers and irrational numbers?A rational number can be defined as the type of number that can be written as the ratio of two integers or any number that can be written as a fraction, where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not equal to zero.
Therefore,Rational numbers between 2.37 and 2.41 = 2.38 and 2.4.
An irrational number is defined as the number that is a real number that cannot be expressed as a ratio of integers; for example,
Therefore that Irrational numbers between 2.37 and 2.41 = √2 + 2.37 and √3+2.37
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