any number raised to a negative exponent is equal to the reciprocal of the base raised to the opposite exponent. Let's consider a number "a" raised to a negative exponent "-n". We can represent it as follows:
[tex]a^(-n) = 1 / (a^n)[/tex] To prove this, we can use the definition of negative exponents. When we have a negative exponent, we are essentially taking the reciprocal of the number raised to the positive version of that exponent. In other words, [tex]a^{-n}[/tex] is the same as 1 / [tex](a^n).[/tex]
For example, let's take the number 2 raised to the exponent -3:
[tex]2^(-3) = 1 / (2^3) = 1 / 8[/tex] We can also represent this as the reciprocal of 2 raised to the opposite exponent:
[tex]1 / (2^{-3}) = 1 / (1 / (2^3)) = 1 / (1/8) = 8[/tex]
As we can see, both approaches yield the same result. This can be generalized to any number "a" and any negative exponent "-n".
In summary, any number raised to a negative exponent is equal to the reciprocal of the base raised to the opposite exponent. This can be proven by using the definition of negative exponents and applying it to a specific example. This property is essential in many areas of mathematics and science, including algebra, calculus, and physics.
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During the first year she owned her car, Barbara spent $732 on repairs and maintenance. She spent $1,377 the second year she owned the car. What was the percentage
increase in maintenance and repair costs from the first year to the second year (to the nearest whole percent)?
79%
84%
88%
92%
None of these choices are correct.
There was 88% increase in maintenance and repair costs from the first year to the second year. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The four fundamental operations, often referred to as "arithmetic operations", are thought to be able to properly represent all real numbers. The mathematical operations quotient, product, sum, and difference come after division, multiplication, addition, and subtraction.
We are given that during the first year she owned her car, Barbara spent $732 on repairs and maintenance and she spent $1,377 the second year she owned the car.
So, the more amount she spent in the second year is obtained using subtraction operation which gives:
⇒ $1,377 - $732
⇒ $645
Now, the percentage increase is
⇒ $645 ÷ 7.32
⇒ 88.11%
Hence, there was 88% increase in maintenance and repair costs from the first year to the second year.
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PLEASE HELP!
Jasmine invests $2658 in a retirement home account with a fixed annual interest rate of 9% compounded 4 times annually what will be the account balance after 5 years?
Work Shown:
A = P*(1+r/n)^(n*t)
A = 2658*(1+0.09/4)^(4*5)
A = 2658*(1+0.0225)^(20)
A = 2658*(1.0225)^(20)
A = 2658*1.56050920068472
A = 4147.83345541997
A = 4147.83
emma buys a gift basket online for 30% off the list price. she has to pay $5.50 for shipping. the total charge is $45.20. what is the list price of the gift basket?
The list price of the gift basket is $65.20. This can be determined by taking the total charge of the gift basket ($45.20) and subtracting the shipping charge of $5.50. The remaining $39.70 is the discounted amount of the gift basket.
Since the gift basket was discounted by 30%, the original list price can be determined by dividing the discounted amount by 70%, which is 0.7. Then, the list price can be calculated by multiplying the discounted amount by 1.43 (the reciprocal of 0.7). Therefore, the list price of the gift basket is $65.20.
This method of calculating the list price of the gift basket is called reverse-discounting. The process of reverse-discounting involves subtracting the discounted amount from the total charge to get the original list price. This method is useful when the discount rate is known and the total charge is given. It allows for the original list price of the item to be determined quickly and accurately.
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the probability that a person in the united states has type b* blood is 12%. four unrelated people in the united states are selected at random. complete parts (a) through (d).
The probabilities of different events related to the type B' blood in four randomly selected people from the United States are 0.000207, 0.0600, 0.400. The events in parts (a) and (b) are considered unusual.
The probability that a person in the united states has type b* blood is 12%. four unrelated people in the united states are selected at random of different scenarios are calculated.
The probability that all four have type B' blood is 0.000207, The probability that none of the four have type B' blood is 0.0600, The probability that at least one of the four has type B' blood is 0.400, The events in parts (a) and (b) can be considered unusual because their probabilities are less than or equal to 0.05.
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_____The given question is incomplete, the complete question is given below:
The probability that a person in the United States has type B' blood is 12 % Four unrelated people in the United States are selected at random Complete parts (a) through (d) The probability that all four have type B' blood is 000207 (Round to six decimal places as needed) (b) Find the probability that none of the four have type B' blood The probability that none of the four have type B' blood is 0600 (Round to three decimal places as needed) (c) Find the probability that at least one of the four has type B' blood The probability that at least one of the four has type B' blood is 400 (Round to three decimal places as needed) (d) Which of the events can be considered unusual? Explain Select all that apply OA The event in part (a) is unusual because its probability is less than or equal to 0.05 OB. The event in part (c) is unusual because its probability is less than or equal to 0.05 O C. None of these events are r uual O D. The event in part (b) is unusual because its probability is less than or equal to 0.05 Click to select your answer and then click Check Answer
Solve the equation by completing the square.
x^2−12x+35=0
After completing the square, the equation is _____, and the solution is x=5,x=7
Answer:
x:5,x:7
x^2-12x+35
x^2-12x=-35
x^2-12x+6^2=-35+36
(x+6)^2=1
insert a radical anywhere
x+6=1
x=1-6
x=-5. x=5
x=-1-6
x=-7. x=7
Which fractions are the equivalent to 4/10 + 40/100 ? A. 80/100 B. 4/5 C. 20/100 D. 8/10 (multiple choice)
A boutique wants to determine how the amount of time a customer spends browsing in the store affects the amount the customer spends. 2 1 The equation of the regression line is Y - 2+0.98 40 30 . A browsing time of 17 minutes is found to result in an amount spent of 40.3 dollars. What is the predicted amount spent? Ex: 7.9 dollars 20 . 10 Where is the observed value in relation to the regression line? Pick 0 10 20 40 50 dollars Pick Browsing time in minutes) A browsing time of 14 minutes is found to result in a amount spent of 10.84 dollars. What is the predicted amount spent? Where is the observed value in relation to the regression line? A browsing time of 28 minutes is found to result in a amount spent of 27.2 dollars. What is the predicted amount spent? Where is the observed value in relation to the regression line? dollars ✓ Pick above below 2 on Check Next
EXPLANTION:
1. For a browsing time of 17 minutes, the predicted amount spent can be calculated using the equation of the regression line:
Y = 2 + 0.98X, where X is the browsing time in minutes.
Step-by-step:
Y = 2 + 0.98(17)
Y = 2 + 16.66
Y = 18.66 dollars
The observed value (40.3 dollars) is above the regression line, as it is higher than the predicted amount spent (18.66 dollars).
2. For a browsing time of 14 minutes, the predicted amount spent can be calculated using the equation of the regression line:
Y = 2 + 0.98X.
Step-by-step:
Y = 2 + 0.98(14)
Y = 2 + 13.72
Y = 15.72 dollars
The observed value (10.84 dollars) is below the regression line, as it is lower than the predicted amount spent (15.72 dollars).
3. For a browsing time of 28 minutes, the predicted amount spent can be calculated using the equation of the regression line:
Y = 2 + 0.98X.
Step-by-step:
Y = 2 + 0.98(28)
Y = 2 + 27.44
Y = 29.44 dollars
The observed value (27.2 dollars) is below the regression line, as it is lower than the predicted amount spent (29.44 dollars).
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Simplify. Remove all perfect squares from inside the square root. 18
A top tv costs r50 000. The dealer offers you two payments options
Option1:20% deposit and the balance paid back over 36 months (3 years) at 12% simple interest p. A
Option 2:no deposit ,but the product needs to be paid off in 42 months (3 1,2years )at 9% compound interest p. A
Calculate the deposit amount if option 1 is chosen
The deposit amount need to be paid in option 1 with 20% of the cost is equal to R10,000.
Cost of a tv = R50,000
Option 1.
Deposit amount = 20% of the cost.
Balance to be paid in 36 months
Simple interest = 12% p.a.
Deposit amount
= 20% of R50,000
= 0.2 x R50,000
= R10,000
Now,
Let x be the balance amount that needs to be paid.
x = R50,000 - R10,000
⇒ x = R40,000
Simple Interest = ( Principal × Rate of interest × time ) / 100
Total amount to be paid = Principal + Simple Interest
= R40,000 + (R40,000 x 0.12 x 3)
= R40,000 + R14,400
= R54,400
Therefore, the deposit amount for option 1 as per the given details is equal to R10,000.
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a new product is being tested by zed electronics to determine if it will continue to operate in a stable fashion under a variety of conditions. a sample of 400 items were tested, and 60 failed the test. determine a 90 percent confidence interval for the population proportion.
The 90% confidence interval for the population proportion is (0.1171, 0.1829).
To calculate the confidence interval, we first need to find the point estimate of the population proportion. The point estimate is the sample proportion which is given by:
p-bar = x/n = 60/400 = 0.15
where x is the number of items that failed the test and n is the sample size.
Next, we need to find the margin of error, which is given by:
ME = z*√(p_bar(1-p_bar)/n)
where z is the z-score corresponding to the confidence level, p_bar is the sample proportion, and n is the sample size.
For a 90% confidence level, the z-score is 1.645 (using a standard normal distribution table). Substituting the values, we get:
ME = 1.645*√(0.15(1-0.15)/400) = 0.0329
Finally, we can construct the confidence interval by adding and subtracting the margin of error from the point estimate:
CI = p_bar ± ME = 0.15 ± 0.0329 = (0.1171, 0.1829)
Therefore, we are 90% confident that the true population proportion of items that will fail the test is between 0.1171 and 0.1829.
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what is the term for 2x + 4y - 2
Answer:
The term 2x+4y-2 is a binomial equation.
Step-by-step explanation:
Factoring said equation: 2(x+2y-1)
x intercepts: (1,0)
y intercepts: (0, 1/2)
the first pentagon is dilated to form the second pentagon. drag and drop the answer to correctly complete the statement.
Hence, the correct answer to the question is: The second pentagon is either an enlargement or a reduction of the first pentagon, depending on the dilation factor.
The first pentagon is dilated to form the second pentagon. Drag and drop the answer to correctly complete the statement.The dilation is a transformation in which a figure is resized without changing its shape. It is an enlargement or a reduction of a geometric figure that maintains its similarity.
Therefore, if the first pentagon is dilated, the second pentagon will be an enlarged or a reduced form of the original pentagon.Since it is a dilation, the ratio of the corresponding sides of the pentagon will remain the same. Also, the angles of the pentagon will remain the same. Hence, both the pentagons will be similar to each other. The second pentagon will either be an enlargement or a reduction of the first pentagon. It will also have the same number of vertices and edges as the first pentagon.However, the size of the second pentagon will depend on the dilation factor. If the dilation factor is greater than 1, then the second pentagon will be an enlargement of the first pentagon. If the dilation factor is less than 1, then the second pentagon will be a reduction of the first pentagon.
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a. For which angle measures, 0, between 0 and
2π radians is cos(0) = 0? Label the
corresponding points on the unit circle.
b. What are the values of sin(x) for these angle
measures?
for the angle measures where cos(0) = 0, sin(x) equals 1 for π/2 radians and -1 for 3π/2 radians.
cos(0) = 0 when the angle is π/2 or 3π/2 radians.
To label the corresponding points on the unit circle, we can use the following conventions:
The angle 0 radians (or 0 degrees) starts at the positive x-axis and goes counterclockwise.
The angle π/2 radians (or 90 degrees) is at the positive y-axis.
The angle π radians (or 180 degrees) is at the negative x-axis.
The angle 3π/2 radians (or 270 degrees) is at the negative y-axis.
So, for cos(0) = 0, the corresponding angle measures are π/2 and 3π/2 radians. On the unit circle, these correspond to the points (0, 1) and (0, -1), respectively.
the values of sin(x) for these angle measures:
sin(π/2) = 1
sin(3π/2) = -1
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In a lab experiment, 80 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 5 hours. How long would it be, to the nearest tenth of an hour, until there are 136 bacteria present?
Answer:
Step-by-step explanation:
We can use the formula for exponential growth to solve this problem:
N = N0 * 2^(t/T)
where N is the final number of bacteria, N0 is the initial number of bacteria, t is the time elapsed, and T is the doubling time.
We know that N0 = 80, and T = 5 hours. We want to find t when N = 136.
136 = 80 * 2^(t/5)
Dividing both sides by 80, we get:
1.7 = 2^(t/5)
Taking the logarithm of both sides (base 2), we get:
log2(1.7) = t/5
Solving for t, we get:
t = 5 * log2(1.7) ≈ 3.4 hours
Therefore, it would take approximately 3.4 hours, to the nearest tenth of an hour, until there are 136 bacteria present.
During a series of spins, a spinner landed on blue 7 times and on other colors 7 times. Considering this data, how many of the next 10 spins should you expect to land on blue?
Answer:
5
Step-by-step explanation:
Landing 7 times on blue and 7 times on other colors means it landed on blue half of the time.
I expect it will land on blue half of the next 10 spins.
Answer: 5
explain how you know which type of feed the zookeeper will run out of first
Answer:
well since there is no math, the first feed that runs out, will be the animal that they have the most of, or the bigger animals. meaning lemurs for multiple or large meaning elephant, or your mother
Step-by-step explanation:
no offense, it's just faster to drive around the world than trying to print a picture of your mom
Eugene had some paper with which to make note cards. on his way to his room he found 3 more pieces to use. in his room he cut each piece of paper in half. when he was done he had 12 half-pieces of paper. with how many sheets of paper did he start with?
On his journey to his room, Eugene first found a few pieces of paper before discovering three more. Let's assume that he began with x bits of paper. Eugene started with [tex]3[/tex] pieces of paper.
What is the equation?Eugene started with some pieces of paper, and then he found 3 more on his way to his room. So, let's say he started with x pieces of paper.
After finding the 3 more pieces, he had a total of [tex]x + 3[/tex] pieces of paper.
He then cut each piece of paper in half, which means he doubled the number of pieces of paper. So, he ended up with [tex]2 \times (x + 3) = 2x + 6[/tex] half-pieces of paper.
We're given that he had 12 half-pieces of paper in the end, so we can set up the equation:
[tex]2x + 6 = 12[/tex]
Solving for x, we get:
[tex]2x = 6[/tex]
[tex]x = 3[/tex]
Therefore, Eugene started with 3 pieces of paper.
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ʙʀᴀɴᴅᴏɴ ᴡᴀs ᴏɴ ᴠᴀᴄᴛɪᴏɴ ꜰᴏʀ 2 weeks ᴀɴᴅ 1ᴅᴀʏ ᴀɴᴅ ʜᴇ sᴘᴇɴᴅ ᴛʜᴇ sᴀɴᴇ ᴀᴍᴏᴜɴᴛ ᴏɢ ᴛɪᴍᴇs ᴡɪᴛʜ ᴇᴀᴄʜ 3 ʙʀᴏ ʜᴏᴡ ᴍᴀɴʏ sᴀʏs ᴅɪᴅ ʜᴇ sᴘᴇɴᴅ ᴡɪʀʜ ᴇᴀᴄʜ ʙʀᴏ ?
Answer:
5 days
Step-by-step explanation:
You want to know the amount of time that is 1/3 of 2 weeks and 1 day.
Total timeThere are 7 days in a week, so 2 weeks and 1 day will be a total of ...
2·7 +1 = 14 +1 = 15 . . . . days
Part timeIf this time is split into 3 equal parts, each part is 1/3 of the total.
1/3 · 15 days = 5 days
Brandon spent 5 days with each of his 3 bro.
A gas station operates two pumps, each of which can pump up to 10,000 gallons of gas in a month. The total amount of gas pumped at the station in a month is a random variable Y (measured in 10,000 gallons) with a probability density function given by
y, 0< y < 1,
f(y) = 2 - y, 1<= y < 2,
0, elsewhere.
a Graph f(y)·
b Find F(y) and graph it.
c Find the probability that the station will pump between 8000 and 12,000 gallons in a
particular month.
d Given that the stati.on pumped more than 10,000 gallons in a particular month, find the probability that the station pumped more than 15,000 gallons during the month.
B. F(y) = 1, 2 ≤ y
C. P(8000 < Y < 12000) = 1 - 0.4 = 0.6
D. P(Y > 15000) = 1 - 1 = 0
A detailed explanation of the answer.
A. The graph of the probability density function, f(y), is shown below:
B. The cumulative probability distribution function, F(y), is given by:
F(y) = 0, 0 ≤ y < 1
F(y) = (y-1)/2, 1 ≤ y < 2
F(y) = 1, 2 ≤ y
The graph of F(y) is shown below:
C. The probability that the station will pump between 8000 and 12,000 gallons in a particular month is calculated by subtracting the cumulative probability at 8000 (0.4) from the cumulative probability at 12,000 (1):
P(8000 < Y < 12000) = 1 - 0.4 = 0.6
D. Given that the station pumped more than 10,000 gallons in a particular month, the probability that the station pumped more than 15,000 gallons during the month is calculated by subtracting the cumulative probability at 10,000 (1) from the cumulative probability at 15,000 (1):
P(Y > 15000) = 1 - 1 = 0
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Find the measure of angle DBC.
The measure of angle DBC based on the information given will be 115°.
How to calculate the angleA circle is a geometric shape that consists of all the points in a plane that are equidistant from a fixed point called the center. The distance between any point on the circle and the center is called the radius. A circle can also be defined as the set of all points that are a fixed distance away from the center point.
The total circle is 360 degrees. The sum of the arcs of the circle is 360
Arc DC = 360 - Arc CB - Arc BC
DC = 360 -30-100
DC =230
Inscribed Angle =1/2 Intercepted Arc
<DBC = 1/2 CD
<DBC = 1/2 (230)
= 115
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PLS HELP ASAP .a vacuum cleaner costs the owner $220 to buy. They then mark up the cost to sell it by 30%. What as the amount of the mark up? What is the selling price?
The amount of the mark up is $66 and the selling price is $286.
What is markup percentage?The amount by which a product's cost is raised to determine its selling price is known as the markup percentage. Usually, it is represented as a percentage of the item's price. Markup percentage is determined by the following equation:
Markup percentage = (Selling price - Cost price) / Cost price x 100%
Given that, the mark up is 30%.
Thus,
Mark up = 0.3 x $220 = $66
The selling price is:
Selling price = $220 + $66 = $286
Hence, the amount of the mark up is $66 and the selling price is $286.
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A softball base is 15 inches long and 15 inches wide. How long is the diagonal? Leave your answer as a
simplified radical.
15 in
15 in
Length of diagonal =
h(t) = -16t ² + 110t + 72
The function above models the height, h, in feet, of an object above the ground t seconds after being launched straight up in the air. What does the number 72 represent in the function?
*
1 point
A The initial height, h, in feet, of the object.
B The maximum height, h, in feet, of the object.
C The initial speed, in ft per second, of the object.
D The maximum speed, feet per second, of the object.
Answer:
A. The initial height, h, in feet, of the object.
Answer:
A The initial height, h, in feet, of the object.
Step-by-step explanation:
Let t = 0
h(t) = -16t ² + 110t + 72
h(0) = -16(0)² + 110 × 0 + 72
h(0) = 72
The height at time zero is 72.
72 is the initial height.
Answer: A The initial height, h, in feet, of the object.
What is the weight of a 48 kg girl on Earth? Round the answer to the nearest whole number.
___N
Answer:
remember, in order to calculate the weight on earth, we need to multiply the mass of the object with the force of Gravity (9.8 m/s^2 on earth)
so, her weight would be:
48 x 9.8 = 470.4 >>>>>>> Will be 470 if we round it to the nearest whole number.
Step-by-step explanation: Hope this helps. Mark me brainliest!! :)))
Answer: 470
Step-by-step explanation:
if m<4 = 15, find the measure of <2
75°
Step-by-step explanation:Angle properties can help us find the measure of an unknown angle.
Vertical Angles
Before we find the measurement of angle 2, we need to find angle 1. Angle 1 and angle 4 are vertical angles.
Vertical angles are angles formed by 2 intersecting lines.We know that 1 and 4 are vertical angles because they are formed by the same lines. Vertical angles are always congruent. This means that if angle 4 is 15°, then angle 1 must equal 15°.
Complementary Angles
Now that we know angle 1, we can find angle 2. Angles 1 and 2 are complementary angles.
Complementary angles are angles that sum to 90°.We can tell that 1 and 2 are complementary angles because together they form a right angle. Using this information, we can set up an equation.
15 + x = 90x = 75This shows that angle 2 must equal 75°.
if the cycle time is 2 minutes/customer then how many customers are served per hour? multiple choice question. 15 20 30 60
If the cycle time is 2 minutes per customer, 30 customers can be served per hour.
The given cycle time is 2 minutes per customer. To calculate how many customers can be served per hour, we need to calculate the number of minutes in an hour as follows: 60 minutes = 1 hour.
The time taken for each customer is 2 minutes. Therefore, the number of customers that can be served per hour can be calculated as follows:
Number of customers per hour = (60 minutes/hour) ÷ (2 minutes/customer)
Number of customers per hour = 30 customers.
Therefore, the number of customers that can be served per hour is 30, according to the given cycle time of 2 minutes per customer.
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Please help with 7! Thankyou :)
-12 will be the value of the variable x.
The given expression is:
-9 = (-6 +x)/2
Simplifying the expression,
-6+x = -18
x = -18 +6
x = -12
Therefore, the value of the variable x will be -12.
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A factory produces components of which 1% are defective. The components are
packed in boxes of 10. A box is selected at random
the probability that there are at most 2 defective components in the box is approximately 0.9044 and the probability of having at most 3 defective components out of 250 boxes is very close to zero.
a) Let X be the number of defective components in a box of 10 components. Then X follows a binomial distribution with n=10 and p=0.01, since the probability of a component being defective is 0.01. We want to find the probability that there are at most 2 defective components in the box, i.e., P(X ≤ 2).
Using the binomial probability formula, we get:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
= (10 choose 0) × 0.01⁰ × 0.99¹⁰ + (10 choose 1) × 0.01¹ × 0.99⁹ + (10 choose 2) × 0.01² × 0.99⁸
= 0.90438222
Therefore, the probability that there are at most 2 defective components in the box is approximately 0.9044 (rounded to four decimal places).
b) We want to find the probability of having at most 3 defective components out of 250 boxes, each containing 10 components. Since np = 100.01 = 0.1 < 5 and n × (1-p)=10 × 0.99=9.9 > 5, we can use the normal approximation to the binomial distribution, with mean μ = np = 2.5 and standard deviation σ = √np(1-p) = 1.577.
Let X be the number of boxes with at most 3 defective components. Then X follows an approximate normal distribution with mean μ' = np=2.5250 = 625 and standard deviation σ' = √np(1-p)) = 12.5 × 1.577 = 19.712.
We want to find P(X ≤ 250), which can be written as P(X < 251) since X is a discrete variable. Using the continuity correction, we can approximate this probability as P(X < 251.5). Then we standardize the variable:
z = (251.5 - μ')/σ' = (251.5 - 625)/19.712 = -18.919
Using a standard normal table or calculator, we find that P(Z < -18.919) is a very small number, practically zero. Therefore, the probability of having at most 3 defective components out of 250 boxes is very close to zero.
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Complete Question
factory produces components of which 1% are defective. The components are packed in boxes of 10. A box is selected by random a) Find the probability that there are at most 2 defective components in the box b) Use a suitable approximation to find the probability of having at most 3 defective (inclusive 3 cases) components out of 250.
I need help with question
Check the picture below.
so the ball hits the ground when g(x) = 0
[tex]\stackrel{g(x)}{0}=-16t^2+30t\implies 0=-2t(8t-15) \\\\[-0.35em] ~\dotfill\\\\ 0=-2t\implies \boxed{0=t} \\\\[-0.35em] ~\dotfill\\\\ 0=8t-15\implies 15=8t\implies \cfrac{15}{8}=t\implies \stackrel{ seconds }{\boxed{1.9\approx t}}\qquad \textit{falls to the ground}[/tex]
we get two values for "t", once at 0, because that's when the ball was at rest before being kicked.
Solve the system of equations by elimination.
Answer:
(-1,1)
Step-by-step explanation: