The value of the given expression is -2.
The given expression is -14-(-12).
Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
Here, -14+12 (Because -×- = +)
= -2
Therefore, the value of the given expression is -2.
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Penelope selects an earring from a jewelry boxes the earrings color is gold. The colors of the remaining earrings are: 11 gold, 16 silver, and 13 black She randomly selects a second earring from the jewelry box. Is it likely that Penelope selects earrings of the same color?
No, it is not likely that Penelope selects earrings of the same color.
We have,
Gold Earrings= 11
Silver Earrings= 16
Black Earrings = 13
So, if she picked a earring already of any of the color.
Then, there is chance if she picked the second earring then the earring can be different or same.
Thus, No it is likely that Penelope selects earrings of the same color as there 50% chance of getting different earrings too.
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The two-way table shows the number of births, in thousands, in the United States for the years 2010 and 2011. A baby born in 2011 is randomly selected. What is the probability that the baby was born in February?
The probability that the baby was born in February if a baby born in 2011 is randomly selected is 0.0754 or 7.54%.
What is the probability that the baby was born in February?The probability that the baby was born in February if a baby born in 2011 is randomly selected is calculated from the formula below:
Probability(February) = number of babies born in February/total number of babies born in 2011Probability(February) = 299 / 3966
Probability(February) = 0.0754
Hence, the probability that a baby born in 2011 was born in February is equal to 0.0754 or 7.54%.
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5. Four times the sum of a number and three is equal to fifteen less than seven times the
number. Find the number.
Answer:
The Answer is 1Step-by-step explanation:
1. 2x-4=10
2x=14
x=7
2. 3x+3=2x-1
3x-2x=-1-3
x=-4
3. 7x+x=24
8x=24
x=3(
4. 5+x=-18
x=-18-5
x=-23
5. -14=10-6x
6x=10+14
6x=24
x=4
6. 2x-2=x+12
2x-x=12+2
x=14
7. 3x-31=2
3x=2+31
3x=33
x=11
8. 5x-14=16
5x=16+14
5x=30
x=6
9. 2x+8=4(5-x)
2x+8=20-4x
2x+4x=20-8
6x=12
x=2
10. 2x-3=3(1+x)
2x-3=3+3x
2x-3x=3+3
-x=6
g 4. you are using an unreliable wi-fi connection. you send three emails - one to your bank, one to a magazine, and one to your professor. each email has an 92.5% chance of going through, independently of whether the other emails go through. a. what is the chance that all three emails go through? b. what is the chance that the emails to the bank and magazine go through but not the one to your professor? c. what is the chance that exactly two emails go through?
There is a 20.7% chance that exactly two emails will successfully go through.
a. The probability that all three emails go through is the product of the individual probabilities of each email going through:
P(all three go through) = 0.925^3 = 0.779
Therefore, there is a 77.9% chance that all three emails will successfully go through.
b. The probability that the emails to the bank and magazine go through but not the one to your professor is the product of the probability that the bank and magazine emails go through and the probability that the email to your professor does not go through:
P(bank and magazine go through, professor does not) = 0.925^2 x (1 - 0.925) = 0.069
Therefore, there is a 6.9% chance that the emails to the bank and magazine will go through, but not the one to your professor.
c. The probability that exactly two emails go through can occur in three different ways: the bank and magazine emails go through and the professor's does not, the bank and professor's emails go through and the magazine's does not, or the magazine and professor's emails go through and the bank's does not.
The probability of each of these events happening can be calculated as follows:
P(bank and magazine go through, professor does not) = 0.925^2 x (1 - 0.925) = 0.069
P(bank and professor go through, magazine does not) = 0.925^2 x (1 - 0.925) = 0.069
P(magazine and professor go through, bank does not) = 0.925^2 x (1 - 0.925) = 0.069
Therefore, the total probability that exactly two emails go through is the sum of these probabilities:
P(exactly two go through) = 0.069 + 0.069 + 0.069 = 0.207
Therefore, there is a 20.7% chance that exactly two emails will successfully go through.
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using the answers to the previous parts, we would conclude that, on average, the population of all ferrets tend to [ select ] weight when exposed to the virus.
Based on these results, we would conclude that on average, the population of all ferrets tend to decrease in weight when exposed to the virus.
Based on the results of the hypothesis test in part (b) and the confidence interval in part (c), we can conclude that the population mean weight of ferrets tends to decrease when exposed to the virus.
In part (b), we found that the p-value was less than the significance level of 0.05, which means that we reject the null hypothesis that the mean weight of ferrets is not affected by the virus. This indicates that there is strong evidence that the virus has a significant effect on the weight of ferrets.
In part (c), we constructed a 95% confidence interval for the difference between the mean weight of ferrets before and after exposure to the virus. The interval was (−0.643,−0.057), which does not contain 0. This means that we are 95% confident that the true difference between the mean weights is negative, indicating that the weight tends to decrease after exposure to the virus.
Therefore, based on these results, we would conclude that on average, the population of all ferrets tend to decrease in weight when exposed to the virus.
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A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. y'' - y = 17t, yp(t) = - 17t The general solution is y(t) = (Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.)
The given nonhomogeneous equation is:
y'' - y = 17t
To find the general solution, we need to find the complementary solution and particular solution separately.
Complementary Solution:
The associated homogeneous equation is:
y'' - y = 0
The characteristic equation for this is:
r^2 - 1 = 0
Solving for the roots, we get:
r = ±1
So the complementary solution is:
y_c(t) = c1e^t + c2e^(-t)
where c1 and c2 are constants.
Particular Solution:
The particular solution is given as:
y_p(t) = -17t
We can substitute this into the nonhomogeneous equation to find the value of the constant:
y'' - y = 17t
(-17)'' - (-17) = 17t
0 + 17 = 17t
t = 1
Therefore, the constant is -17.
So the particular solution is:
y_p(t) = -17t
General Solution:
The general solution is the sum of the complementary solution and the particular solution:
y(t) = y_c(t) + y_p(t) = c1e^t + c2e^(-t) - 17t
where c1 and c2 are constants.
Therefore, the general solution to the given nonhomogeneous equation y'' - y = 17t with particular solution yp(t) = -17t is:
y(t) = c1e^t + c2e^(-t) - 17t
where c1 and c2 are constants.
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The scale for the drawing of a rectangular playing field ismath 2 i n c h e s = 5 f e e t . a.Write an equation you can use to find the dimensions of the actualfield, wherexis a dimension of the scale drawing (in inches) andyisthe corresponding dimension of the actual field (in feet). b.What is the area of the field?
The equation to find dimensions of the actualfield is y= 5/2x.
We have,
2 inch = 5 feet
So, the equation can be
y= 5/2 x
Now, width = 10 inch
So, y= 5/2(10)
y= 25 feet
and, length = 20 inch
So, y= 5/2(20)
y= 50 feet
So, the Area of field is
= 10 x 20
= 20 inch²
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sketch the following region and write an iterated integral of a continuous function f over the region. use the order dy dx. r is the region in the first quadrant bounded by a circle of radius 5 centered at the origin.
we write the iterated integral of a continuous function f over the region using the order dy dx. Since the region is symmetric with respect to the x-axis, we can integrate over the top half of the region and then multiply by 2.
Here, "region" refers to the part of the circle of radius 5 centered at the origin that lies in the first quadrant, "integral" refers to the calculation of the area or volume under a curve or surface, and "quadrant" refers to one of the four regions obtained by dividing a plane into four equal parts by the x- and y-axes.
Step 1: Sketch the region
The region (R) is in the first quadrant, which means x ≥ 0 and y ≥ 0. The region is bounded by a circle with radius of 5 centered at the origin (0,0). This circle can be represented by the equation x^2 + y^2 = 25.
Step 2: Write the iterated integral
To find the iterated integral of a continuous function f over the region R using the order dy dx, we first need to find the bounds for y and x.
The limits of integration for y are from 0 to the y-coordinate of the top half of the circle, which is √(25-x^2). The limits of integration for x are from 0 to 5. Therefore, the iterated integral is:
∫ from 0 to 5 ∫ from 0 to √(25-x^2) f(x,y) dy dx
For y: Since R is in the first quadrant and bounded by the circle, the lower bound for y is y = 0. The upper bound for y, given x, is the equation of the circle's top half, solving for y: y = sqrt(25 - x^2).
For x: Since R is in the first quadrant, the lower bound for x is x = 0, and the upper bound is x = 5 (the radius of the circle).
Now we can write the iterated integral using these bounds:
∫(from x=0 to x=5) ∫(from y=0 to y=sqrt(25-x^2)) f(x,y) dy dx
This iterated integral represents the continuous function f over the specified region R in the first quadrant, using the order dy dx.
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1. Does the table represent values of a function? Explain.
Input
Output
Input, x
10
2. Consider the table shown.
Output, y
32
0
-10
20
64
15
10
64
10
40
30
96
20
90
40
64
50
32
30
a.
Complete the table to include values of a function represented by the equation y = 5x - 10.
b. If the table included the input value 55, what output would you expect the rule to assign?
a
Answer: if the input value 55 were included in the table, we would expect the rule to assign an output value of 265. However, since this value is not currently included in the table, we cannot verify its accuracy based on the given data.
Step-by-step explanation: a. To complete the table using the equation y = 5x - 10, we can substitute each input value of x into the equation and solve for the corresponding output value of y:
Input, x Output, y
10 40
Copy code
2 | 0
-10 | -60
20 | 90
64 | 310
15 | 65
10 | 40
64 | 310
10 | 40
40 | 190
30 | 140
96 | 470
20 | 90
90 | 440
40 | 190
64 | 310
50 | 240
32 | 150
30 | 140
b. If the table included the input value 55, we can use the same equation to find the corresponding output value:
y = 5x - 10
y = 5(55) - 10
y = 275 - 10
y = 265
Therefore, if the input value 55 were included in the table, we would expect the rule to assign an output value of 265. However, since this value is not currently included in the table, we cannot verify its accuracy based on the given data.
What is the domain of the function?
y = √5x-10
O A. x2-2
O B. x≤-2
O C. x22
O D. x≤2
The domain of the function y = √(5x-10) is: D. x ≥ 2.
What is the domain of the function?In order to find the the domain of the function we have to first of all find or determine the values of x that make the function undefined.
Let solve the inequality 5x-10 ≥ 0 to find the values of x that make the function defined:
5x-10 ≥ 0
5x ≥ 10
Divide by 5x
x ≥ 10/5
x ≥ 2
Therefore the correct option is D.
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H.: u = 47.6 and H.: u < 47.6 where u = the mean age of teachers at Ravenwood High School. The calculated p-value is 0.023. What conclusion will you make at a = 0.10? Reject the H. Fail to reject the H. Reject the H. Fail to reject the Ha
This suggests that the mean age of teachers at Ravenwood High School is less than 47.6. Based on the given information, we have two hypotheses, H.: u = 47.6 and H.: u < 47.6, where u represents the mean age of teachers at Ravenwood High School.
The calculated p-value is 0.023, and we need to make a conclusion at a significance level of 0.10.
If we compare the p-value with the significance level, we see that the p-value is less than the significance level (0.023 < 0.10). This means that we have strong evidence to reject the null hypothesis H.: u = 47.6 in favor of the alternative hypothesis H.: u < 47.6.
Therefore, we can conclude that the mean age of teachers at Ravenwood High School is significantly less than 47.6 years at a significance level of 0.10.
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What is the yield on a corporate bond with a $1000
face value purchased at a discount price of $925, if
it pays 8% fixed interest for the duration of the
bond?
yield = [?] %
Give your answer as a percent rounded to the nearest
hundredth.
The yield on the corporate bond is 8.65%.
What is the yield on the corporate bond?A bond yield is a general term that relates to the return on the capital you invest in a bond. To calculate the yield of a bond, the forumula to use is "yield = (annual interest payment / purchase price) x 100%".
Data:
Face value of the bond is $1000
Fixed interest rate is 8%.
Annual interest payment = 8% x $1000
Annual interest payment = $80
The purchase price is $925.
we can substitute these values to find the yield:
= ($80 / $925) x 100%
= 0.0864864865 * 100%
= 8.65%
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One serving of takis weighs 1.4 ounces how many servings are in 20.3 ounces of takis
Select whether the equation has a solution or not.
no roots
roots
The equation √(12x - 25) = √(3x -11) + √(3x) has a solution at x = 5.444
Selecting whether the equation has a solution or not.From the question, we have the following parameters that can be used in our computation:
√(12x - 25) = √(3x -11) + √(3x)
To do this, we solve graphically
When plotted on a graph, we have the value of x to be
x = 5.444
This means that the equation has a root
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A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate A. The 95% confidence interval for the true proportion of people who favors Candidate a isa. 0.419 to 0.481 b. 0.40 to 0.50 0.45 to 0.55 d. 1.645 to 1.96
The 95% confidence interval for the true proportion of people who favors Candidate a is (a) 0.419 to 0.481.
We can use the formula for a confidence interval for a population proportion:
p ± zsqrt(p(1-p)/n)
where p is the sample proportion, z* is the critical value from the standard normal distribution for the desired level of confidence (95% in this case), and n is the sample size.
Substituting the given values, we have:
450/1000 ± 1.96sqrt((450/1000)(1-450/1000)/1000)
= 0.45 ± 1.96*0.0225
= 0.45 ± 0.0441
Therefore, the 95% confidence interval for the true proportion of people who favor Candidate A is:
0.45 ± 0.0441
= (0.4059, 0.4941)
or approximately:
(0.41, 0.49)
So the answer is (a) 0.419 to 0.481.
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Here is an equation that is true for all values of x: 5(x + 2) = 5x + 10. Elena saw this equation and says she can tell 20(x + 2) + 31 = 4(5x + 10) + 31 is also true for any value of x. How can she tell? Explain your reasoning.
The equation 20(x + 2) + 31 = 4(5x + 10) + 31 is also true for all the values of x by the addition and multiplication property of equality.
Given equation which is true for all the values of x is,
5(x + 2) = 5x + 10
We have to explain the reason behind the equality of the other equation through this equation.
Using multiplication property of equality, multiplying both sides of the equation with the same number will hold the equation true.
Multiplying both sides by 4,
4 [5(x + 2)] = 4 [5x + 10]
20(x + 2) = 4(5x + 10)
By the addition property of equality, adding both sides by 31,
20(x + 2) + 31 = 4(5x + 10) + 31
which gives the required equation.
Hence the equation 20(x + 2) + 31 = 4(5x + 10) + 31 is true for all x.
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When squaring a complex number using De Moivre's theorem, there is only one answer.
OA. True
OB. False
It is true to claim that when squaring a complex number using De Moivre's theorem, there is only one answer. Option B is correct.
What is De Moivre's theorem?It is a theorem developed by the mathematician Abrahan Moivre. Its purpose is to establish a formula for calculating powers of complex numbers in trigonometric or polar form. The first de Moivre formula is given by:
wn=z=ρ(cosθ+isenθ)Therefore, this theorem is used to find roots of complex numbers, and after application in formulas, we have that when squaring a complex number using De Moivre's theorem, there is only one answer.
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Perform regression on the number of laborers in construction sites. Site Project Safety Location No. of laborers Sponsor 1 Govt High Urban 45 2 Private High Rural 40 3 Govt Low Urban 42 4 Govt High Rural 43
5 Private High Urban 38
6 Private Low Urban 55 7 Govt High Urban 35 8 Govt Low Rural 27 9 Govt High Urban 43 10 Private High Rural 41 11 Private Low Rural 43 12 Govt Low Rural 29 13 Private High Rural 39 14 Govt Low Rural 55 15 Private Low Urban 19
To perform a regression analysis on the number of labourers in construction sites, we first need to identify the independent variables that may have an impact on the number of labourers (dependent variable).
Based on the provided data, the independent variables are Site Project, Safety, Location, and Sponsor. Here's a step-by-step explanation:
1. Encode categorical variables: Convert the categorical variables (Site Project, Safety, Location, and Sponsor) into numerical values. For example, assign 1 for Govt and 0 for Private in the Sponsor column.
2. Organize the data: Create a table or a spreadsheet with the encoded data, with each column representing an independent variable and the last column being the dependent variable (No. of labourers).
3. Perform regression analysis: Use a statistical software or tool (e.g., Excel, R, or Python) to perform a multiple linear regression analysis on the organized data. The software will generate a regression model in the form of an equation that best describes the relationship between the independent and dependent variables.
4. Interpret the results: Analyze the regression coefficients, p-values, and R-squared value provided by the software to determine the significance of each independent variable on the dependent variable. A lower p-value (usually below 0.05) indicates a stronger relationship, while a higher R-squared value suggests that the model can better explain the variability in the number of labourers.
5. Make predictions: Use the generated regression model to make predictions on the number of labourers for new construction sites based on the Site Project, Safety, Location, and Sponsor factors.
By following these steps, you can perform a regression analysis on the number of labourers in construction sites and better understand the factors affecting the number of workers at a site.
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A social psychologist is interested measuring the effect of the age of the author on the persuasiveness of an opinion about Social Security. 18 research participants read a controversial essay about Social Security. Each participant rated the extent to which he or she agreed with the author (the higher the number, the more the person agreed with the author).
The study involved 18 participants who were asked to read a controversial essay on Social Security and rate their level of agreement with the author's opinion.
In this scenario, a social psychologist conducts research to measure the effectiveness of the author's age on the persuasiveness of an opinion about Social Security.
Measuring the participants' level of agreement on a numerical scale allows the researcher to quantitatively analyze the data and determine if there is a correlation between the age of the author and the persuasiveness of their opinion on Social Security. Overall, this study aims to provide insights into the factors that influence individuals' opinions and beliefs about Social Security.
1. The social psychologist gathers 18 participants to read a controversial essay about Social Security.
2. Each participant reads the essay and is informed of the author's age, which might be manipulated or varied across different groups of participants.
3. After reading the essay, each participant rates the extent to which they agree with the author on a scale. The higher the number, the more they agree with the author's opinion.
4. The researcher then collects these ratings and analyzes the data to determine if there is a significant relationship between the age of the author and the persuasiveness of the essay as measured by the participants' agreement scores.
5. Based on the findings, the social psychologist can draw conclusions about the influence of the author's age on the persuasiveness of opinions about Social Security among the participants.
Complete Question:
A social psychologist is interested measuring the effect of the age of the author on the persuasiveness of an opinion about Social Security. 18 research participants read a controversial essay about Social Security. Each participant rated the extent to which he or she agreed with the author (the higher the number, the more the person agreed with the author).
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if n1 = 6, n2 = 8 and a = 0.052 tail, ucrit value is ____. _____
To find the ucrit (critical value) for a two-sample t-test with the given information, you need to use a t-distribution table.
Since a = 0.052 tail, the significance level (α) is 0.052. You need to find the degrees of freedom (df) first:
Step 1: Calculate the degrees of freedom:
df = n1 + n2 - 2
df = 6 + 8 - 2
df = 12
Step 2: Look up the ucrit value in the t-distribution table using α and df:
For a one-tailed test at α = 0.052 and df = 12, the ucrit value is approximately 1.782.
Your answer: The ucrit value for n1 = 6, n2 = 8, and a = 0.052 tail is approximately 1.782.
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Find the indicated area under the standard normal curve. To the left of z = 1.22 Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table. The area to the left of z = 1.22 under the standard normal curve is (Round to four decimal places as needed.) Find the indicated area under the standard normal curve. To the left of z = 0.43 Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table. The area to the left of z=0.43 under the standard normal curve is (Round to four decimal places as needed.)
For z = 1.22, The area to the left of z = 1.22 under the standard normal curve is approximately 0.8888. For z = 0.43, The area to the left of z = 0.43 under the standard normal curve is approximately 0.6664.
To find the indicated area under the standard normal curve to the left of a given z-value, we can use a standard normal table. For the first question, we need to look up the area to the left of z = 1.22 in the table. From page 1, we find the row for 1.2 and the column for 0.02, which gives us the value 0.88493. Adding the area to the left of z = 1.2 (0.88493) to the area between z = 1.20 and z = 1.22 (0.04846), we get the area to the left of z = 1.22 as 0.9334 (rounded to four decimal places).
For the second question, we need to look up the area to the left of z = 0.43 in the table. From page 1, we find the row for 0.4 and the column for 0.03, which gives us the value 0.66640. Adding the area to the left of z = 0.4 (0.65542) to the area between z = 0.40 and z = 0.43 (0.01392), we get the area to the left of z = 0.43 as 0.6693 (rounded to four decimal places).
To find the indicated area under the standard normal curve, follow these steps:
1. Locate the z-score in the standard normal table.
2. Read the corresponding decimal value for the given z-score.
3. Round the decimal value to four decimal places as needed.
For z = 1.22:
1. Find the intersection of the row labeled 1.2 and the column labeled 0.02 in the standard normal table.
2. The corresponding decimal value for z = 1.22 is 0.8888.
3. The area to the left of z = 1.22 under the standard normal curve is approximately 0.8888.
For z = 0.43:
1. Find the intersection of the row labeled 0.4 and the column labeled 0.03 in the standard normal table.
2. The corresponding decimal value for z = 0.43 is 0.6664.
3. The area to the left of z = 0.43 under the standard normal curve is approximately 0.6664.
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College students average 7 hours of sleep per night with a standard deviation of 40 minutes. If the amount of sleep is normally distributed, what proportion of college students sleep for more than 8.3 hours?
Approximately 2.62% of college students sleep for more than 8.3 hours.
To determine the proportion of college students who sleep for more than 8.3 hours, we need to use the provided information: the average sleep time is 7 hours per night with a standard deviation of 40 minutes (which is equivalent to 2/3 of an hour or 0.67 hours). Since the sleep time is normally distributed, we can use the Z-score formula to find the proportion.
First, calculate the Z-score: Z = (X - μ) / σ, where X is the desired sleep time (8.3 hours), μ is the average sleep time (7 hours), and σ is the standard deviation (0.67 hours).
Z = (8.3 - 7) / 0.67 ≈ 1.94
Now, we can use a Z-table to find the proportion of students who sleep for more than 8.3 hours. The table value for a Z-score of 1.94 is approximately 0.9738. However, this value represents the proportion of students who sleep 8.3 hours or less. To find the proportion of students who sleep more than 8.3 hours, subtract the table value from 1:
Proportion = 1 - 0.9738 ≈ 0.0262
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The area of a rectangular garden is given by the trinomial x
2 − 3x + 2. What are the possible dimensions of the
rectangle? Show your work.
Answer:
Step-by-step explanation:
50 possible dimensions
Answer:
Step-by-step explanation:
Please answer this question
The slope of the line, based on the information given in the table is: the cost of purchasing one pencil.
How to Interpret the Slope of a Line?In a given situation, the slope of a line can be defined as the unit rate between two variables. It is calculated as the rate of change of the dependent variable over the rate of change of the independent variable.
In this scenario, to find the slope, use two pairs of values from the table, (3, 1.05) and (7, 2.45):
Slope in this case = cost of purchasing one pencil (unit rate) = 2.45 - 1.05 / 7 - 3
Slope = $0.35 per pencil.
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Find the amount in the account for the given principal, interest rate, time, and compounding period. P = $500, r=4%, t = 4 years; compounded quarterly
With quarterly compounding and an interest rate of 4%, the account balance after 4 years will be around $587.44.
From the formula for compound interest to find the amount in the account:
[tex]A = P(1 + r/n)^{nt}[/tex]
where A is the amount in the account, P is the principal, r is the annual interest rate (as a decimal), t is the time (in years), and n is the number of compounding periods per year.
In this case, P = $500, r = 0.04 (since 4% = 0.04), t = 4 years, and the interest is compounded quarterly, so n = 4.
Substituting the values, we get:
[tex]A = $500(1 + 0.04/4)^{4*4}\\A = 500(1 + 0.01)^{16}\\A = 500(1.01)^{16}\\A = 500(1.1749)[/tex]
A = 586.29 (rounded to two decimal places)
Therefore, the amount in the account after 4 years with a quarterly compounding period and a 4% interest rate is approximately $587.44.
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\The graph represents a functional relationship.
On a coordinate plane, a straight line with a negative slope begins at point (1, 3), crosses the x-axis at (4, 0), and exits the plane at (18, negative 14).
Which value is an input of the function?
–14
–2
0
4
The value of 4 is an input of the function.
Now, we know that;
In a linear equation, the variable x represent the independent variable or input value and the variable y represent the dependent variable or output value
Hence, In this problem we have that the given line passes through the points (1,3), (4,0) and (18,-14)
So, we get;
The input values are (1,4,18)
And, The output values are (3,0,-14)
Therefore, The value of 4 is an input of the function.
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A line passes through (-1,1) and 3,9 what is the equation of the line in slope intercept form
The equation of the line in slope intercept form based on the location of two points is (2x + 3).
To find the equation of line in slope intercept form, we need to calculate the slope first. The formula is -
Slope = ([tex] y_{2}[/tex] - [tex] y_{1}[/tex])/([tex] x_{2}[/tex] - [tex] x_{1}[/tex])
Keep the values in formula
Slope = (9-1)/(3-(-1))
Add the values in numerator and denominator
Slope = 8/4
Divide the values
Slope = 2
The equation of line in slope intercept form is -
y - [tex] y_{1}[/tex] = m(x - [tex] x_{1}[/tex)
Again keeping values
y - 1 = 2(x - (-1))
Multiply the values on RHS
y - 1 = 2(x + 1)
y - 1 = 2x + 2
Simplify the equation
y = 2x + 3
Hence, the equation is 2x + 3.
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Easy geometry "Law of Sines" question.
The values of x and y are 67.4 degrees and 18. 78 respectively.
How to determine the value
Using the sine rule, we have;
sin A/a = sin B/b = sin C/c
Given that;
A, B and C are the angles in the triangle.a,b, c are the length of the sides of the triangle.From the diagram shown, we have;
sin 38/12 = sin x/18
Cross multiply the values, we get;
sin x = sin 38(18)/12
Find the value and multiply
sin x = 0. 9234
x = 67. 4 degrees
To determine the side y
sin 38/12 = sin 74. 6/y
Then,
y = 18. 78
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latona did an experiment at a military barracks over the space of a few months to examine the effect of group size on group morale. he randomly assigned soldiers to the experimental and control groups and did a prettest and posttest. midway through the experiment, some of the soldiers were re-assigned to different stations across the u.s. causing the sample size to drop. which source of internal invalidity does this example reflect? question 8 options: a) maturation b) testing c) experimental mortality d) history
The source of internal invalidity reflected in this example is experimental mortality, as the drop in sample size due to soldiers being reassigned to different stations across the U.S. can lead to a decrease in statistical power and increased risk of bias in the results.
This example reflects the source of internal invalidity known as c) experimental mortality. Experimental mortality refers to the loss of participants during an experiment, which may cause issues with the overall validity of the results. In this case, the reassignment of soldiers to different stations across the U.S. caused the sample size to drop, potentially affecting the outcome of the study on the effect of group size on group morale.
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line p contains the points (-2 -5) and (3,25) write the equation of the line that is parallel to line p and passes through the point (1,—9)
Answer:
Step-by-step explanation: