Answer:
I think the answer is A.
Step-by-step explanation:
Have a good day ;-).
and please give me brainliest if you can.
Classify the states of the following Markov chain and select all correct statements. [1 0 0 0 0 0 0 ]
[7/8 1/8 0 0 0 ]
[0001/3 1/2 1/6]
[0 0 1/3 2/3 0]
a)State 1 is absorbing b) States 4 and 5 are periodic c) State 1 is transient d) State 1 is recurrent e) States 3, 4 and 5 are recurrent f) Only state 3 is recurrent
In the given Markov chain, State 1 is absorbing, State 4 is periodic, State 1 is recurrent, and States 3, 4, and 5 are recurrent.
A Markov chain is a stochastic model that represents a sequence of states where the probability of transitioning from one state to another depends only on the current state. Let's analyze the given Markov chain to determine the properties of each state.
State 1: This state has a probability of 1 in the first row, indicating that it is an absorbing state. An absorbing state is one from which there is no possibility of leaving once it is reached. Therefore, statement a) is correct, and State 1 is absorbing.
State 2: There are no transitions from State 2 to any other state, which means it is an absorbing state as well. However, since it is not explicitly mentioned in the question, we cannot determine its status based on the given information.
State 3: This state has non-zero probabilities to transition to other states, indicating that it is not absorbing. Furthermore, it has a loop back to itself with a probability of 1/6, making it recurrent. Hence, statements c) and e) are incorrect, while statement f) is correct. State 3 is recurrent.
State 4: State 4 has a transition probability of 1/3 to State 3, which means there is a possibility of leaving this state. However, there are no outgoing transitions from State 4, making it an absorbing state. Moreover, since there is a loop back to itself with a probability of 2/3, it is also recurrent. Therefore, statement b) is correct, and State 4 is periodic and recurrent.
State 5: Similar to State 4, State 5 has a transition probability of 2/3 to State 3 and no outgoing transitions. Hence, State 5 is also an absorbing and recurrent state. Consequently, statement e) is correct.
To summarize, State 1 is absorbing and recurrent, State 4 is periodic and recurrent, and States 3 and 5 are recurrent.
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a new car cost ₹ 4,20,000 .After one year ,its value decreased by 20% for the second year its value further decreased by 10% what is the value of the car after 2 years
The value of the car after 2 years is ₹ 3,02,400.
After one year, the car's value decreased by 20%.
To find the new value, we need to multiply the original cost by
\((100\% - 20\%) or 80\%.\)
So, the value of the car after one year is
\(4,20,000 \times 0.8 = 3,36,000.\)
For the second year, the car's value decreased by 10%.
Again, we need to multiply the previous year's value by
\((100\% - 10\%) or 90\%\).
Therefore, the value of the car after the second year is
\(3,36,000 \times 0.9 = 3,02,400\).
Thus, the value of the car after 2 years is ₹ 3,02,400.
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Jim bought 2 packs of batteries from a store. The price of each pack was the same. After he bought the batteries, his account balance showed a change of −$23.94. What would have been the change to Jim's account balance had he only bought 1 pack of batteries from the store?
−$21.94
−$11.97
$11.97
$21.94
Answer: B
Step-by-step explanation: The answer is 11.97 hope this helps
if -9 is added to a number and the sum is doubled, the result is 11 less than the number. Find the number
Answer: 7
let x be the number
2(-9 + x) = x - 11
-18 + 2x = x - 11
2x - x = -11 + 18
x = 7
Suppose that x is the number we want :
- 9 added to it means :
\(x + ( - 9) = x - 9\)
And sum is doubled means :
\(2 \times (x - 9)\)
The result is 11 less than the number which means :
\(2 \times (x - 9) = x - 11\)
Now let's find the x ...
\(2x - 18 = x - 11\)
Add both sides 18
\(2x - 18 + 18 = x - 11 + 18\)
\(2x = x + 7\)
Subtract both sides x
\(2x - x = x + 7 - x\)
\(2x - x = x - x + 7\)
\(x = 7\)
Thus that number is 7
Sierra left $17.75 as a tip for a waiter. This was 20% of the bill before the tip. How much was her total bill before the tip
Answer:
$31.95 Before tip.
Step-by-step explanation:
I believe you should just add 17.75+80%=31.95
please help jssjdbrbensbsjshwha
Answer:
0dh 8/6
Step-by-step explanation:
Answer:
-8/27
Step-by-step explanation:
First, make all fractions an improper fraction.
-2/3 / 9/4
Flip the right fraction over.
-2/3 * 4/9
multiply
and you get -8/27
1/3 as a percent
0.43 as a percent
2/17 as a percent
1.25 as a percent
All rounded to the nearest whole
find the inverse. check your answer algebraically and graphically. f(x) = x2 − 2x, x ≤ 1
The blue curve represents the original function f(x), and the red curve represents its inverse f^(-1)(x). We can see that the two curves are reflections of each other across the line y=x, which confirms that we have found the correct inverse function.
To find the inverse of the function f(x) = x^2 - 2x, we can follow these steps:
Step 1: Replace f(x) with y, so that we have y = x^2 - 2x.
Step 2: Solve for x in terms of y. To do this, we can use the quadratic formula:
x = [2 ± sqrt(4 - 4y)] / 2 = 1 ± sqrt(1 - y)
Note that we have used the fact that x ≤ 1, which means that the solution with the minus sign in front of the square root is not valid. Therefore, the inverse function is:
f^(-1)(y) = 1 + sqrt(1 - y)
To check our answer algebraically, we can verify that f(f^(-1)(y)) = y and f^(-1)(f(x)) = x for all values of x and y.
f(f^(-1)(y)) = f(1 + sqrt(1 - y)) = (1 + sqrt(1 - y))^2 - 2(1 + sqrt(1 - y)) = y
f^(-1)(f(x)) = 1 + sqrt(1 - (x^2 - 2x)) = 1 + sqrt(3 - (x - 1)^2)
Both of these checks confirm that we have found the correct inverse function.
To check our answer graphically, we can plot the original function and its inverse on the same set of axes:
graph of f(x) = x^2 - 2x and its inverse function
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Find the mean, median, mode, range, and standard deviation of each data set that is obtained after adding the given constant to each value. 56, 37, 41, 50, 38, 44, 32, 54; +(-7)
After adding (-7) to each value in the given data set, the mean is 38.25, the median is 38, the mode does not exist, the range is 24, and the standard deviation is approximately 8.85.
To find the mean of the data set, add all the values together (49, 30, 34, 43, 31, 37, 25, 47) and divide the sum by the total number of values (8). The mean is the average value of the data set.
To determine the median, arrange the values in ascending order (25, 30, 31, 34, 37, 43, 47, 49) and find the middle value. In this case, the median is the average of the two middle values (34 and 37).
The mode refers to the value(s) that appear most frequently in the data set. In this case, there is no mode since no value appears more than once.
The range is calculated by subtracting the smallest value (25) from the largest value (49). Thus, the range is 24.
To calculate the standard deviation, subtract the mean from each value, square the differences, calculate the mean of those squared differences, and finally take the square root of the resulting value. This provides a measure of the dispersion or spread of the data around the mean.
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Find an equation for the perpendicular bisector of the line segment whose endpoints
are (8, 7) and (-4,3)
Answer:
y = -3x + 11.
Step-by-step explanation:
The slope of the given line segment is (3-7)/(-4-8) = -4/-12 = 1/3.
The midpoint of the line has coordinates (8-4)/2, (7+3)/2.
= (2, 5).
The slope of the perpendicular bisector = -1/ 1/3 = -3.
So it's bisector has equation:
y - y1 = m(x - x1)=
y - 5 = -3(x - 2)
y = -3x + 6 + 5
y = -3x + 11.
Noise levels at 5 airports were measured in decibels yielding the following data:
162,176,162,141,159
Construct the 90% confidence interval for the mean noise level at such locations. Assume the population is approximately normal.
Step 1 of 4:
Calculate the sample mean for the given sample data. Round your answer to one decimal place.
Step 2 of 4:
Calculate the sample standard deviation for the given sample data. Round your answer to one decimal place.
Step 3 of 4:
Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Step 4 of 4:
Construct the 90% confidence interval. Round your answer to one decimal place.
The 90% confidence interval for the mean noise level at these airport locations is approximately (148.1, 171.9).
Step 1 of 4:
To calculate the sample mean for the given sample data, we sum all the values and divide by the sample size.
Sample mean = (162 + 176 + 162 + 141 + 159) / 5 ≈ 160.0 (rounded to one decimal place)
Step 2 of 4:
To calculate the sample standard deviation, we need to find the differences between each data point and the sample mean, square those differences, sum them up, divide by the sample size minus 1, and then take the square root.
Deviation from mean: (162 - 160)^2, (176 - 160)^2, (162 - 160)^2, (141 - 160)^2, (159 - 160)^2
Sum of squared deviations = (2^2 + 16^2 + 2^2 + (-19)^2 + (-1)^2) = 590
Sample standard deviation = sqrt(590 / (5 - 1)) ≈ 9.6 (rounded to one decimal place)
Step 3 of 4:
To find the critical value for a 90% confidence interval, we need to look up the t-value in the t-distribution table with (n-1) degrees of freedom. Here, n is the sample size, which is 5.
Degrees of freedom = 5 - 1 = 4
Looking up the t-value for a 90% confidence level and 4 degrees of freedom, we find it to be approximately 2.776 (rounded to three decimal places).
Step 4 of 4:
To construct the 90% confidence interval, we use the formula:
Confidence interval = sample mean ± (critical value * (sample standard deviation / sqrt(sample size)))
Confidence interval = 160.0 ± (2.776 * (9.6 / sqrt(5)))
Calculating this expression will give us the lower and upper bounds of the confidence interval.
Confidence interval = 160.0 ± (2.776 * 4.297) ≈ 160.0 ± 11.9 (rounded to one decimal place)
Using the sample mean, standard deviation, and critical value, we constructed a 90% confidence interval for the mean noise level, which is approximately (148.1, 171.9) decibels. This confidence interval provides an estimate of the range within which the true mean noise level at these airports is likely to fall with 90% confidence.
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Find the value of both expressions below when x = 5.
4x
Answer:
The expression below, 4x=20 when x=5.
Step-by-step explanation:
4(5)=20
will give briniest.
Create a two-way table from the diagram:
1
Match the values with their correct places in the table:
1
Question 1 options:
22
6
8
19
25
55
14
30
41
1.
a)
2.
b)
3.
c)
4.
d)
5.
e)
6.
f)
7.
g)
8.
h)
9.
i)
wo way frequency tables
Two-way frequency tables show how many data points fit in each category.
Here's an example:
Preference Male Female
Prefers dogs 363636 222222
Prefers cats 888 262626
No preference 222 666
The columns of the table tell us whether the student is a male or a female. The rows of the table tell us whether the student prefers dogs, cats, or doesn't have a preference.
Each cell tells us the number (or frequency) of students. For example, the 363636 is in the male column and the prefers dogs row. This tells us that there are 363636 males who preferred dogs in this dataset.
Notice that there are two variables—gender and preference—this is where the two in two-way frequency table comes from.
Want a review of making two-way frequency tables? Check out this video.
Want to practice making frequency tables? Check out this exercise.
Want to practice reading frequency tables? Check out this exercise
Two way relative frequency tables
Two-way relative frequency tables show what percent of data points fit in each category. We can use row relative frequencies or column relative frequencies, it just depends on the context of the problem.
For example, here's how we would make column relative frequencies:
Step 1: Find the totals for each column.
Preference Male Female
Prefers dogs 363636 222222
Prefers cats 888 262626
No preference 222 666
Total 464646 545454
Step 2: Divide each cell count by its column total and convert to a percentage.
Preference Male Female
Prefers dogs \dfrac{36}{46}\approx78\%
46
36
≈78%start fraction, 36, divided by, 46, end fraction, approximately equals, 78, percent \dfrac{22}{54}\approx41\%
54
22
≈41%start fraction, 22, divided by, 54, end fraction, approximately equals, 41, percent
Prefers cats \dfrac{8}{46}\approx17\%
46
8
≈17%start fraction, 8, divided by, 46, end fraction, approximately equals, 17, percent \dfrac{26}{54}\approx48\%
54
26
≈48%start fraction, 26, divided by, 54, end fraction, approximately equals, 48, percent
No preference \dfrac{2}{46}\approx4\%
46
2
≈4%start fraction, 2, divided by, 46, end fraction, approximately equals, 4, percent \dfrac{6}{54}\approx11\%
54
6
≈11%start fraction, 6, divided by, 54, end fraction, approximately equals, 11, percent
Total \dfrac{46}{46}=100\%
46
46
=100%start fraction, 46, divided by, 46, end fraction, equals, 100, percent \dfrac{54}{54}=100\%
54
54
=100%start fraction, 54, divided by, 54, end fraction, equals, 100, percent
Notice that sometimes your percentages won't add up to 100\%100%100, percent even though we rounded properly. This is called round-off error, and we don't worry about it too much.
Two-way relative frequency tables are useful when there are different sample sizes in a dataset. In this example, more females were surveyed than males, so using percentages makes it easier to compare the preferences of males and females. From the relative frequencies, we can see that a large majority of males preferred dogs (78\%)(78%)left parenthesis, 78, percent, right parenthesis compared to a minority of females (41\%)(41%)left parenthesis, 41, percent, right parenthesis.
What is the yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons if this bond is currently trading for a price of $884?
5.02%
6.23%
6.82%
12.46%
G
5.20%
The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct
Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.
The formula for calculating YTM is as follows:
YTM = (C + (F-P)/n) / ((F+P)/2) x 100
Where:
C = Interest payment
F = Face value
P = Market price
n = Number of coupon payments
Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.
First, let's calculate the semi-annual coupon payment:
Semi-annual coupon rate = 5.2% / 2 = 2.6%
Face value = $1000
Market price = $884
Number of years remaining until maturity = 10 years
Number of semi-annual coupon payments = 2 x 10 = 20
Semi-annual coupon payment = Semi-annual coupon rate x Face value
Semi-annual coupon payment = 2.6% x $1000 = $26
Now, we can calculate the yield to maturity using the formula:
YTM = (C + (F-P)/n) / ((F+P)/2) x 100
YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100
YTM = 6.23%
Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.
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can someone send the answer that on the picture and show your work
Answer:
k = 52
Step-by-step explanation:
- 8 = \(\frac{k-4}{-6}\) ( multiply both sides by - 6 to clear the fraction )
48 = k - 4 ( add 4 to both sides )
52 = k
Answer: k=52
Step-by-step explanation:
-8= k-4/-6
multiply by -6
48=k-4
add 4 to both sides
k=52 :)
g the physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. the distribution of the number of daily requests is bell-shaped and has a mean of 57 and a standard deviation of 8. using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 57 and 73?
The approximate percentage of bulb replacement requests between 57 and 73 is 95%.
How do we calculate the approximate percentage?The empirical rule, also known as the 68-95-99.7 rule, is used to determine the percentage of observations that lie within a specified number of standard deviations of the means in a normal distribution. The rule states that approximately:
68% of the observations are within one standard deviation of the means
95% of the observations are within two standard deviations of the mean
99.7% of the observations are within three standard deviations of the mean
The given problem states that the distribution of the number of daily requests for fluorescent light bulbs at a university is bell-shaped and has a mean of 57 and a standard deviation of 8. Therefore, to find the approximate percentage of light bulb replacement requests between 57 and 73, we need to find the number of standard deviations of the means that are 73 and 57.
\(z-score = (x - \mu) / \sigma\)
Where
\(z-score\) is the number of standard deviations from the mean.\(x\) is the value of the observation\(\mu\) is the population mean\(\sigma\) is the population standard deviationFor x = 73,
\(z-score = (73 - 57) / 8\\z-score = 2\)
For x = 57,
\(z-score = (57 - 57) / 8\\z-score = 0\)
Therefore, observations 57 and 73 are separated by two standard deviations.
Using the empirical rule, we can say that approximately 95% of the observations lie within two standard deviations of the mean. Therefore, approximately 95% of the daily requests for replacement of fluorescent bulbs in the university are between 57 and 73.
Thus, the approximate percentage of bulb replacement requests between 57 and 73 is 95%.
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7. MP Persevere with Problems The greenhousetemperatures at certain times are shown in the table.The greenhouse maintains temperatures between 65°Fand 85°F. Suppose the temperature increases at a constantrate. Create a graph of the time and temperaturesat each hour from 1:00 P.M. to 8:00 P.M. Is the relationshipproportional? Explain.
We are given a table of temperatures that are being maintained at different times in a greenhouse . We are to consider that the temperatures increase at a constant rate and we are asked to create a graph for this.
After leaving his house, Nate drove fifteen minutes to take his oldest daughter to the middle school and then drove ten minutes to take his two younger daughters to the elementary school. Next, Nate drove twenty-five minutes to work. If Nate arrived at work at 9:30 a.M., what time did he leave his house?
The time Nate left his house is 8 : 40 am
After leaving his house, Nate drove 15 minutes to take his oldest daughter to the middle school . Therefore,
Time spent to middle schoolt = 15 minutesThen he drove ten minutes to take his two younger daughters to the elementary school. Therefore,
Time spent to elementary schoolt = 10 minutesHe drove twenty-five minutes to work. Therefore,
Time spent to workt = 25 minutesHe arrived at work at 9:30 am. The time he left home can be calculated as follows:
Total time spent on the road = 15 + 10 + 25 = 50 minutes
Therefore,
Time he left home = 9:30 - 50 = 8 : 40 am
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Calculate the length of ED and BE
Felicia ran a 4-mile race in 28 minutes. Complete the table to represent Felicia’s average rate of speed during the race.
Answer:
she runs an average 1mile every 7 minutes
Step-by-step explanation:
sorry if this does not help if this is not what u r looking for maybe clarify
hope this helps also i don't see where the chart is for the question
23.-28. In a manner similar to Example 1, (a) identify input and
output consistent with the general proportional model; (b) write
an equation for the model; (c) determine a numerical value for the
constant k; and (d) solve the problem.
24. The speed of a skidding car is directly proportional to the
square root of the length of the skid. On a snowy road, a car
with good brakes traveling at 40 mph would skid approxi-
mately 178 ft. If the skid marks of a similar car on a similar
road were 400 ft, how fast would this car be traveling?
24. If the skid marks of a similar car on a similar road were 400 ft, how fast would this car be
traveling?
The direct variation that of the speed to the skid length implies that the speed increases as the length increases
The car would be traveling at 59.96 mph
How to determine the speed of the skidding car?A direct variation that illustrates the speed of the skidding car is:
s = k√l
Where:
s represents the speed of the carl represents the length of the skidk represents the proportionality constantMake k the subject in s = k√l
k = s /√l
Rewrite as:
s₁ /√l₁ = s₂ /√l₂
Substitute known values
40 /√178 = s₂ /√400
Evaluate the square root of 40
40 /√178 = s₂ /20
Multiply both sides by 20
800 /√178 = s₂
Evaluate the quotient
s₂ = 59.96
Hence, the car would be traveling at 59.96 mph
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A deli wraps its cylindrical containers of hot food items with plastic wrap. The containers have a diameter of 3.5 inches and a height of 4 inches. What is the minimum amount of plastic wrap needed to completely wrap 6 containers? Round your answer to the nearest tenth and approximate using iT = 3.14. O
A)44.0 in?
B)63.2 in2
C)379.2 in?
D)505.5 in?
The minimum amount of plastic wrap needed to completely wrap 6 containers is option C: 286.4 square inches.
What is the minimum amount of plastic wrap?Area of a circle is the area that is occupied by the given circle in a kind of two-dimensional plane. The total surface area of a cylindrical container is solved by the equation:
A = πr²
where r is the radius of the end. The diameter of each container is given as 3.5 inches, so the radius is half of that, or 1.75 inches. Using π = 3.14, we get:
A = 3.14 x (1.75in)²
=3.14 x 3.06
= 9.61 in² (rounded to two decimal places)
The area of the rectangular side is:
A = h x circumference
where: h = height of the container and circumference is the distance around the circular end. The circumference is equal to the diameter times π, so we have:
circumference = 3.5in x π
= 3.5 x 3.14
= 10.99in
Using the given height of 4 inches, we get:
A = 4in x 10.99in
A = 43.96 (rounded to two decimal places)
Therefore, the total surface area of each container is:
A = 2 x 9.61 in² + 43.96in²
A = 63.2in²
To wrap 6 containers, we need to multiply the surface area of each container by 6:
total surface area = 6 x 63.2in²
=379.2
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see correct text below
A deli wraps its cylindrical containers of hot food items with plastic wrap. The containers have a diameter of 3.5 inches and a height of 4 inches. What is the minimum amount of plastic wrap needed to completely wrap 6 containers? Round your answer to the nearest tenth and approximate using π = 3.14.
A. 44.0 in2
B. 63.2 in2
C. 379.2 in2
D. 505.5 in2
PLS FIND X ASAP PLS PLS
Answer:
1- the figure doesn't provide enough information from what I'm aware of
2- x= 17.78
3- x=12
4- x=19
Step-by-step explanation:
Given the following classification confusion matrix, what is the overall error rate?
Classification Confusion Matrix
Predicted Class
Actual Class 1 0
1 224 85
0 28 3,258
0.033 0.0298 0.0314 0.025
The overall error rate of the following classification confusion matrix is 0.0314.
To calculate the overall error rate using the given classification confusion matrix, you can follow these steps:
STEP 1. Find the total number of predictions:
Sum of all elements in the matrix = 224 + 85 + 28 + 3,258 = 3,595
STEP 2. Determine the number of incorrect predictions:
Incorrect predictions are the off-diagonal elements, i.e., False Positives (FP) and False Negatives (FN) = 85 + 28 = 113
STEP 3. Calculate the overall error rate:
Error rate = (Incorrect predictions) / (Total predictions) = 113 / 3,595 = 0.0314
So, the overall error rate is 0.0314 of the given confusion matrix.
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help please...what is the locus of the midpoints of all chords that can be drawn from a given point on a circle with a radius of 6. be exact with your answer.
Answer:
the answer is a
Step-by-step explanation:
sory lawl
i mean e
answer e!
good luck w summer geometoery
Let S represent monthly sales of Bluetooth headphones. Write a statement describing S' and S" for each of the following. (a) The rate of change of sales is increasing. S' is increasing SO S" > 0.
S" > 0 indicates that the rate of change of sales is increasing.
What is rate?
A rate is a measure of the amount of change of one quantity with respect to another quantity, typically expressed as a ratio.
The derivative of a function represents its rate of change at a particular point. In this case, S represents the monthly sales of Bluetooth headphones, and its derivative S' represents the rate of change of sales. If S' is increasing, it means that the rate of change of sales is getting larger over time.
Mathematically, this means that the second derivative S" (which represents the rate of change of the rate of change) is positive, since an increasing slope of the original function (S') corresponds to a positive value for the second derivative.
Therefore, S" > 0 indicates that the rate of change of sales is increasing.
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Solve 2 log x = log 64. (1 point)
Answer:
8
Step-by-step explanation:
2log(x)=log(64)
By logarithms properties
\(xlog_{a}(b)=log_{a}(b^{x} ) \\\)
log(x²)=log(64)
When you have log or ln in both sites, you delete them and...
x²=64
\(\sqrt[]{x^{2} } =\sqrt{64} \\x=8\)
$69 shoes with a 6% tax
6% of 69 is 4.14
So 69 + 4.14 = $73.14
Answer:
Step-by-step explanation:
69.00(1.06) = 73.14
On average, Mary can drive to the supermarket in 10 minutes.
but depending on Mathie the drive can vary from the average by minutes Which absolute Value equation can be used to calculate wary's maximum and minimum drive times?
Let x represent the maximum and minimum time.
|x+10|=5
|x-10|=5
|x+5|=10
|x-5|=10
Answer:
it is going to have to be the 3rd one
Answer:
|x−10|=5
Step-by-step explanation:
just took the test
1. What are two numbers that multiply to make -24 and sum to make -5?
2. What are two numbers that multiply to make 40 and sum to make -13?