Answer:
0.333333
Step-by-step explanation:
0.333 yards are in one foot
Use De Moivre's Formula to compute the three complex cubic roots of 2-2i List your answers in the form (a + bi). Show all steps.
Using c we can compute the three complex cubic roots of 2-2i. The roots are (-1 + i), (1 - i), and (-2). The explanation below provides the step-by-step process of finding these roots.
De Moivre's Formula states that for any complex number z = r(cos θ + i sin θ), the nth root of z can be calculated as z^(1/n) = r^(1/n)(cos(θ/n + 2πk/n) + i sin(θ/n + 2πk/n)), where k is an integer.
In this case, we have z = 2-2i, which can be represented in polar form as r = √(2^2 + (-2)^2) = 2√2 and θ = tan^(-1)(-2/2) = -π/4.
To find the cubic roots, we need to compute z^(1/3) = (2√2)^(1/3)[cos((-π/4)/3 + 2πk/3) + i sin((-π/4)/3 + 2πk/3)].
For k = 0:
z^(1/3) = (2√2)^(1/3)[cos((-π/4)/3) + i sin((-π/4)/3)] = (∛2)[cos(-π/12) + i sin(-π/12)] = (-1 + i).
For k = 1:
z^(1/3) = (2√2)^(1/3)[cos((-π/4)/3 + 2π/3) + i sin((-π/4)/3 + 2π/3)] = (∛2)[cos(7π/12) + i sin(7π/12)] = (1 - i).
For k = 2:
z^(1/3) = (2√2)^(1/3)[cos((-π/4)/3 + 4π/3) + i sin((-π/4)/3 + 4π/3)] = (∛2)[cos(-5π/12) + i sin(-5π/12)] = (-2).
Therefore, the three complex cubic roots of 2-2i are (-1 + i), (1 - i), and (-2)
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The box plots show data about test
scores for two classes.
Test Scores
Class 1
Class 2.
+
t
60
70
90
100
80
Score
Which statement is best supported by the
information in the box plots? (7.1A, 7.18,
7.1E, 716)
Answer:
t = r n − 2 1 − r 2 = 0.45 25 − 2 1 − 0.45 2 = 2.417 The critical value for α = 0.05 for a two-tailed test using the t 24 distribution is 2.064. Your value is greater than this, so you reject the null hypothesis and conclude that the study produced evidence that the variables are significantly correlated
Step-by-step explanation:
Divide the larger square into 10 equal columns or rectangles. Shade one rectangle. What part of the whole is the shaded rectangle? Write that part as a decimal and a fraction.
Answer:
[tex]Part=\frac{1}{10}[/tex]
[tex]Part=0.10[/tex]
Step-by-step explanation:
Given
[tex]Columns = 10[/tex]
[tex]Shaded = 1[/tex]
Required
Part of the whole
This is calculated as:
[tex]Part=\frac{Shaded}{Columns}[/tex]
Substitute [tex]Columns = 10[/tex] and [tex]Shaded = 1[/tex]
[tex]Part=\frac{1}{10}[/tex]
[tex]Part=0.10[/tex]
Piscine is replacing the paving stones around her inground pool. Her pool is 10 cm by 5 cm, and is surrounded by a 1.5m border of paving stones.
a) How many square metres of paving stones will she need in total?
b) If each paving stone is 25 cm by 40 cm, in theory, how many paving stones will she need?
c) Will your answer in part b) actually be enough? Try fitting the stones in the space to see whether Piscine can complete the border with exactly that number of stones, or whether there will be waste, requiring some extras.
During a blind taste test of 8 different sodas, some people were asked to choose a favorite. Each dot represents one person. If the ratio of people choosing B to people choosing H stays the same, he many people will choose H if the number of people who choose B increases to 20
Answer:
20:5
Step-by-step explanation:
1. What is the ratio for B and H?
Ratio = 4 to 1 or 4:1
2. What is the question asking?
The question is increasing 5 to 20. What is the quotient of 20 and 5? 4! The question is basically multiplying B by 5. Now, since math is a very jealous subject, it needs to be done on the other side too! So you need to multiply the B, which is 1, by 5.
3. 1 x 5?
5
4. Answer
So, since B is 20 and H is 5, the ratio would be 20:5!
Hiii, so I REALLY want to rank up, and I just need 4 more Branliests, so if you liked my answer, can you please give me one? Thank you so much, and thanks for the points!!
Answer:
Step-by-step explanation:
J
Maria made $192 for 12 hours of work.
At the same rate, how much would she make for 17
hours of work?
Answer:
192/12=16 per hour
16 x 17 = 272
Step-by-step explanation:
Please help.
Is algebra.
B and B simple math and simplification of the problems : (2x-5y)(2x-5y) and (x+7)(x+7)
HURRY! ANSWER QUICK PLEASEEE
Answer:
See explanation below
Step-by-step explanation:
Total number = (Rate)(time)
---------------------------------------
t = cd
t = qh
t = wm
what does a research means to be amenable to scientific study
Being amenable to scientific study means that a research topic can be investigated using scientific methods and principles.
When a research topic is described as being amenable to scientific study, it means that it can be effectively examined and analyzed using scientific methods and principles. This implies that the research question or phenomenon can be studied through systematic observation, data collection, experimentation, and analysis within the framework of scientific inquiry.
To be amenable to scientific study, a research topic should be measurable, testable, and capable of producing empirical evidence. It should lend itself to rigorous investigation, allowing for the formulation of hypotheses, the collection of data, and the application of statistical analysis or other scientific methodologies.
Furthermore, the topic should be well-defined and specific enough to be studied systematically, allowing for replication and peer review, which are essential aspects of scientific research.
Overall, being amenable to scientific study means that the research topic can be examined and understood using the established principles and methods of scientific inquiry.
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Consider the situation where the maximum temperature in degrees Farenheit for the seven successive days in a certain week is the vector random variable, (T1,..., 77), where T₁ ~ N(75,0² = 4), Tj+1=14+0.87, +3Xj, j = 1,...6, where X₁,..., X6 i.i.d. U[-1,1]. A weather derivative pays $100 if there are two or more days with maximum temperatures below 70 degrees. Using Monte Carlo simulation com- pute the fair price of this derivative with n= 105 sample paths. Ignore the time value of money for a week. [Hint: Generate the sample temperature paths using the iterative formula step by step. Create a matrix to store sample temperature paths using command "ma- trix(NA,nrow-n,ncol=7)", then fill in each column (each day) of the sample paths. Think about how to write the code to check the number of days with maximum temperature below 70. The option price is estimated using the sample mean of payoffs.]
To determine the fair price of a weather derivative, use Monte Carlo simulation to generate sample temperature paths, count the number of days below 70 degrees for each path, calculate the payoffs, and estimate the derivative price using the sample mean.
To compute the fair price of the weather derivative using Monte Carlo simulation, you can follow these steps:
Generate n sample paths for the maximum temperature using the given iterative formula and the specified distribution of X₁,...,X₆. Create a matrix to store the sample temperature paths.
For each sample path, count the number of days with a maximum temperature below 70 degrees.
Calculate the payoff for each sample path: If the number of days below 70 degrees is two or more, the payoff is $100; otherwise, the payoff is $0.
Estimate the option price by taking the sample mean of the payoffs.
Here's a summary of the steps to determine the fair price of the derivative:
Generate n sample paths for maximum temperature using the iterative formula and the specified distribution.
Count the number of days below 70 degrees for each sample path.
Calculate the payoff for each sample path: $100 if the count is two or more, $0 otherwise.
Estimate the fair price of the derivative by taking the sample mean of the payoffs.
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5. Find the area of the isosceles trapezoid in square centimeters.
14 cm
12 cm
10 cm
24 cm
Answer:
60 because I added all of them
Find the area of rhombus with diagonals 6 mm and 9 mm.
One hundred draws will be made at random with replacement from one of the following boxes. Your job is to guess what the sum will be, and you win $1 if you are right to within 10. Which box is best? Worst?
(i) 1 9 (ii) 4 6 (iii) 5 5
A. Box (i) is the best and Box (iii) is worst.
B. Box (i) is the best and Box (ii) is worst.
C. Box (ii) is the best and Box (i) is worst.
D. Box (ii) is the best and Box (iii) is worst.
E. Box (iii) is the best and Box (ii) is worst.
F. Box (iii) is the best and Box (i) is worst.
The answer is:Option (F) Box (iii) is the best and Box (i) is worst, for the given one hundred draws will be made at random with replacement from one of the following boxes based on expected-probability.
Given the three boxes:
(i) 1 9(ii) 4 6(iii) 5 5
One hundred draws will be made at random with replacement from one of the above boxes.
Let us now calculate the expected value of the sum for each of the boxes:
(i) Expected value of sum = (1+9)/2 × 100
= 500.
(ii) Expected value of sum = (4+6)/2 × 100
= 500.
(iii) Expected value of sum = (5+5)/2 × 100
= 500.
Box (i) and (ii) have the same expected value, so we can choose either of them.
However, it is important to note that in Box (ii) the numbers are closer together than in Box (i),
so the sum is more likely to be near the expected value.
This makes Box (ii) the best option.
Box (iii) is the worst option as it has a smaller range than the other two boxes,
Which means that it is less likely to produce a sum close to the expected value.
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Read through the list of points about robots. Determine main points, subpoints, and sub-subpoints. Drag each point to its appropriate place on the outline to the right. If using a tablet, please turn your device horizontally In 1773, Pierre and Henri Jaquet-Droz built dolls that could write, play music, and draw pictures. They allow surgeons to operate on patients from thousands A. of miles away They can navigate hospital corridors to deliver pharmaceuticals, X-rays, and bandages Robots have captured the human imagination for centuries. Astronauts use robots to perform maintenance on the International Space Station In 1937, Westinghouse created a seven-foot robot that could walk, talk, blow up balloons, and smoke cigarettes A. Today robots are used in many fields, including space 1. exploration and medicine Robots have become indispensable to space exploration. 2 Robots are becoming more and more important in medicine. 1. In 1497, Leonardo da Vinci designed a mechanical suit of armor that could sit up and move its arms, neck, and jaw. In addition, NASA sends robotic spacecraft to explore distant planets 2
Robots have captured the human imagination for centuries and have become indispensable in many fields, including space exploration and medicine. They have evolved from simple mechanical devices to advanced machines that assist in complex tasks.
Robots have been a source of fascination for humans for centuries. From Leonardo da Vinci’s mechanical suit of armor in 1497 to Westinghouse’s seven-foot robot in 1937, robots have come a long way. Today, robots are used in many fields, including space exploration and medicine. They allow surgeons to operate on patients from thousands of miles away and navigate hospital corridors to deliver pharmaceuticals, X-rays, and bandages. Astronauts use robots to perform maintenance on the International Space Station and NASA sends robotic spacecraft to explore distant planets.
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A yogurt company claims that it prints a free yogurt coupon under a randomly selected 20% of its lids. A loyal customer purchases 85 yogurt cups, and records whether each was a winner. After consuming all 85 cups, he is disappointed to see that only 12 (14.1%) of his yogurt cups contained coupon codes. He performs a 99% confidence interval for the proportion of yogurt cups containing coupon codes, obtaining (0.044, 0.238). What conclusion can the customer draw about the yogurt company’s claim?
Answer:
The customer can conclude that the company's claim is correct
Step-by-step explanation:
The percentage of lids that has a free yogurt coupon = 20%
The number of cups a loyal customer purchases = 85 yogurt cups
The number of cups that contained a coupon = 12 (14.1%)
The confidence interval performed = 99% confidence interval for the proportion of yogurt cups containing coupon codes
The interval obtained = (0.044, 0.238)
Therefore, the range of proportion within which the true proportion exists is 0.044 < [tex]\hat p[/tex] < 0.238
The range of percentage within which the true percentage exist is therefore;
0.044 × 100 = 4.4% < [tex]\hat p[/tex] × 100 < 0.238 × 100 = 23.8%
Given that the possible true percentage of lids that has a coupon is between 4.4% and 23.8% at 99% confidence level, the customer can conclude that only 12 of his yogurt cup contained coupon by chance and that the company's claim is correct.
Answer:
A, the company’s claim may be justified because 0.2 is in the confidence interval.
Step-by-step explanation:
HELP please!!
What would the container look like for this depth vs height graph??
The distance from the
coffee shop to the
school is 10 miles. On
the map, the coffee
shop is 7.5 inches from
the school. Which one
of the following gives
the scale used
on the map?
A. 5 inches = 2 miles
B. 4 inches = 3 miles
C. 2 inches = 5 miles
D. 3 inches = 4 miles
PLEASE HELP! 15 POINTS! Select the statement that describes this expression: fraction 1 over 2 x (734 − 246). (2 points)
Group of answer choices
Half the sum of 734 and 246
fraction 1 over 2 the difference between 734 and 246
fraction 1 over 2 the quotient of 734 and 246
2 times the difference between 734 and 246
Answer:
fraction 1 over 2 the difference of 734 and 246.
A patient is given 3 mg of morphine to control pain. About 31% of any morphine in the blood is washed out every hour. (a) Construct a function that models the level M of morphine (in mg) in the blood t hours after one dose. M = (b) How much morphine (in mg) remains in the blood after 5 hours? (Round your answer to two decimal places.) mg (c) Estimate how long, in hours, it will take for the amount of morphine left to drop to 0.1 mg. (Round your answer to two decimal places.) h
a) the function that models the level M of morphine (in mg) in the blood t hours after one dose is M = [tex]3 * (0.69)^t[/tex]
b) 0.50 mg of morphine remains in the blood after 5 hours.
c) it will take approximately 14.67 hours for the amount of morphine left to drop to 0.1 mg.
(a) To construct a function that models the level M of morphine (in mg) in the blood t hours after one dose, we can use the formula for exponential decay:
M = [tex]initial amount * (1 - decay rate)^t[/tex]
Given that the patient is initially given 3 mg of morphine and 31% (0.31) of any morphine is washed out every hour, we can write the function as:
M = [tex]3 * (1 - 0.31)^t[/tex]
Simplifying further, we have:
M = [tex]3 * (0.69)^t[/tex]
Therefore, the function that models the level M of morphine (in mg) in the blood t hours after one dose is M = [tex]3 * (0.69)^t[/tex]
(b) To find out how much morphine remains in the blood after 5 hours, we can substitute t = 5 into the function and calculate the value of M:
M = 3 * (0.69)⁵
M ≈ 3 * 0.1681
M ≈ 0.5043
So, approximately 0.50 mg of morphine remains in the blood after 5 hours.
(c) To estimate how long it will take for the amount of morphine left to drop to 0.1 mg, we need to find the value of t when M = 0.1 in the function:
0.1 = [tex]3 * (0.69)^t[/tex]
Dividing both sides by 3:
0.0333 ≈ [tex](0.69)^t[/tex]
Taking the logarithm of both sides:
log(0.0333) ≈ [tex]log[(0.69)^t][/tex]
Using the logarithm properties, we can bring down the exponent:
log(0.0333) ≈ t * log(0.69)
Now, we can solve for t by dividing both sides by log(0.69):
t ≈ log(0.0333) / log(0.69)
Calculating this expression:
t ≈ -2.3859 / -0.1625
t ≈ 14.67
So, it will take approximately 14.67 hours for the amount of morphine left to drop to 0.1 mg.
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Use the provided dropdown menus to construct a translation of the given compound statement into propositional logic notation. Enter a sentence letter, a propositional operator, or a parenthetical mark into each blank space. By convention, parentheses () go inside brackets [], if more than one level of parentheses are needed.
Statement: Today is Thanksgiving Day, but I will eat the turkey if and only if the turkey is free range and it has not been tortured.
Key: E = I will eat the turkey.
F = The turkey is free range.
O = The turkey has been tortured.
T = Today is Thanksgiving Day.
The translation of the compound statement into propositional logic notation is as follows: T ∧ (E ↔ (F ∧ ¬O)).
In propositional logic notation, the compound statement is broken down into individual propositions using sentence letters and logical operators. Here, T represents "Today is Thanksgiving Day," E represents "I will eat the turkey," F represents "The turkey is free range," and O represents "The turkey has been tortured." The compound statement can be translated as T ∧ (E ↔ (F ∧ ¬O)), where ∧ represents the logical AND operator, ↔ represents the logical biconditional operator (if and only if), and ¬ represents the logical NOT operator (negation). This notation captures the conjunction of the conditions and the relationships between them.
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A quality control inspector selects 12 bottles of apple juice at random from a single day’s production. The mean amount of apple juice in the bottles is 298.3 milliliters, and the 95% confidence interval for the true mean amount of juice dispensed per bottle is (296.4, 300.2). Does this interval give the quality control inspector reason to believe that the mean amount of juice in today’s bottles differs from 300 milliliters, as the juice label promises?
Answer:
The juice label (300ml) is in the confidence interval.
So, the 95% CI does not give the inspector the reason to believe the amount of juice differs from 300ml
Step-by-step explanation:
Given
[tex]95\%\ CI = (296.4, 300.2)[/tex]
[tex]Juice\ label = 300ml[/tex]
From the 95% confidence interval value, we have: 296.4 to 300.2
Within this interval, we can find the juice label 300
i.e. 296.4 < 300 < 300.2
In other words, the juice label (300ml) is in the confidence interval.
So, the 95% CI does not give the inspector any reason to believe the amount of juice differs from 300ml.
Question 1 Find the first six terms of the sequence. a1 -4, an -an-1+ 8 (1 point)
0,8, 16, 24, 32, 40
12.20,28, 36, 44, 52
4, 12, 20, 28, 36,44
4.8. 16, 24, 32,40
Question 2 Find the first six terms of the sequence. a1 -8, an 5 an-1(1 point)
-8,-40, -200,-1000,-5000, -25,000 .
8,-40-35,-30,-25,-20
0,5,-40, -35, -30,-25
40, -200, -1000, -5000, -25,000, -125,000
The correct answer is option is 3) 4, 12, 20, 28, 36, 44 and option is 1) -8,-40, -200,-1000,-5000, -25,000.
Question 1= The given sequence is a1 = -4 and an = an-1 + 8.
Here, to find the first six terms of the given sequence, we need to substitute the values of n from 1 to 6.
So, the first six terms of the given sequence are as follows:
The first term, a1 = -4.
Second term, a2 = a1 + 8 = -4 + 8 = 4.
Third term, a3 = a2 + 8 = 4 + 8 = 12.
Fourth term, a4 = a3 + 8 = 12 + 8 = 20.
Fifth term, a5 = a4 + 8 = 20 + 8 = 28.
Sixth term, a6 = a5 + 8 = 28 + 8 = 36.
So, the first six terms of the given sequence are -4, 4, 12, 20, 28 and 36.
Hence, the correct option is 3) 4, 12, 20, 28, 36, 44.
Question 2= The given sequence is a1 = -8 and an = 5an-1.
Here, to find the first six terms of the given sequence, we need to substitute the values of n from 1 to 6.
So, the first six terms of the given sequence are as follows:
First term, a1 = -8.
Second term, a2 = 5a1 = 5(-8) = -40.
Third term, a3 = 5a2 = 5(-40) = -200.
Fourth term, a4 = 5a3 = 5(-200) = -1000.
Fifth term, a5 = 5a4 = 5(-1000) = -5000.
Sixth term, a6 = 5a5 = 5(-5000) = -25,000.
So, the first six terms of the given sequence are -8, -40, -200, -1000, -5000 and -25,000.
Hence, the correct option is 1) -8,-40, -200,-1000,-5000, -25,000.
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Find the length of the missing side.
7
24
A 25
B.168
C 31
D. 625
Answer: C
Step-by-step explanation: #1 because if you add 24 and 7 it looks like the other side.
Answer:
A. 25
Step-by-step explanation:
By Pythagoras theorem,
[tex] {25}^{2} = {24}^{2} + {7 }^{2} \\ 625 = 576 + 49 \\ 62 5= 625 \\ therefore \: 25 \: is \: the \: correct \: \: answer.[/tex]
Estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints. (Round your answers to four decimal places.)
R4 =
R4 ≈ 1.5535. The given function is f(x) = 5 cos(x).
We have to estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints.
(Round your answers to four decimal places.)
Here is the given function graphically and the approximating rectangles: [tex]\text{graph}\left(5\cos\left(x\right),\ \left(0,\ \frac{\pi}{2}\right)\right)[/tex]
Now, let's find the value of ∆x:∆x = [b-a]/n, here n is the number of rectangles.
∆x = [π/2 - 0]/4= π/8
First, we will find the right endpoints of four approximating rectangles: x1 = ∆x+x0 = π/8+0 = π/8x2 = ∆x+x1 = π/8+π/8 = π/4x3 = ∆x+x2 = π/8+π/4 = 3π/8x4 = ∆x+x3 = π/8+3π/8 = π/2
Now, we will find the height of each rectangle: For rectangle 1: f(x1) = 5 cos(π/8) ≈ 4.8729
For rectangle 2: f(x2) = 5 cos(π/4) ≈ 3.5355For rectangle 3: f(x3) = 5 cos(3π/8) ≈ 1.4645
For rectangle 4: f(x4) = 5 cos(π/2) = 0
Therefore, the area under the curve using four approximating rectangles and right endpoints is:R4 = ∆x (f(x1) + f(x2) + f(x3) + f(x4))R4 = π/8(4.8729 + 3.5355 + 1.4645 + 0)≈ 1.5535 (rounded to four decimal places)
Hence, R4 ≈ 1.5535.
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Dose anyone know this question I will give brainless bc I dont know this
Answer:
3.5
Step-by-step explanation:
Answer:
LxWxH
Step-by-step explanation:
thats how you find area
Which mapping represents y as a function?
Answer:
a
Step-by-step explanation:
Answer: J
Step-by-step explanation:
Which of the following are Statistical Inference methods?
• Significance Tests
• Confidence Intervals
• Normal and Binomal Summaries
• Sampling Distributions
• Graphs and Numerical Summarie
Statistical inference methods include significance tests, confidence intervals, and sampling distributions.
Statistical inference refers to the process of drawing conclusions and making predictions about a population based on sample data. It involves using various methods and techniques to make inferences and generalize findings to the larger population.
Significance tests are statistical inference methods that help determine if there is enough evidence to reject or accept a specific hypothesis about a population parameter. They involve calculating a test statistic and comparing it to a critical value to make a decision.
Confidence intervals are another statistical inference method that provides a range of plausible values for a population parameter. They estimate the parameter with a certain level of confidence and are based on sample data and the sampling distribution of the statistic.
Sampling distributions are fundamental to statistical inference as they describe the distribution of a statistic based on repeated sampling. They provide information about the variability and properties of the statistic under different sample scenarios.
Normal and binomial summaries, as well as graphs and numerical summaries, are tools and techniques used in statistical inference to summarize and analyze data but are not specific methods themselves. They help in understanding and visualizing data, which in turn informs the application of statistical inference methods.
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#8 Tessa has a plan for a set of stairs made of concrete, as shown. Each stair is 1 point the same width and height and is taller than the previous one by the same amount. What is the volume of concrete needed for the set of stairs?
Picture below:
Answer: 2.43m^3
Step-by-step explanation:
2 5/6 divided by 3 1/4 please explain .
Answer:
[tex]\frac{34}{39}[/tex]
Step-by-step explanation:
[tex]2\frac{5}{6}[/tex] can be rewritten as [tex]\frac{17}{6}[/tex]
[tex]3\frac{1}{4}[/tex] can be rewritten as [tex]\frac{13}{4}[/tex]
So now
[tex]\frac{17}{6} / \frac{13}{4}[/tex]
Flip the second fraction and multiply
[tex]\frac{17}{6} * \frac{4}{13} = \frac{68}{78}[/tex]
Now reduce the fraction
[tex]\frac{34}{39}[/tex]
Need help plz asap im hoping on an answer quick thank you <3
Answer:
I believe the answer is 10
Step-by-step explanation:
Answer:
I think that it might be ten
Step-by-step explanation: