The magnitude of the vector is approximately 7.3 and the direction of the vector is approximately 74 degrees which is option B.
We have,
To find the magnitude and direction of the vector <2, 7>, we can use trigonometric concepts. Let's break down the steps:
Magnitude (Length) of the Vector:
The magnitude of a vector <x, y> is given by the formula:
Magnitude = √(x² + y²)
For the given vector <2, 7>:
Magnitude = √(2² + 7²) = √(4 + 49) = √53 ≈ 7.3 (rounded to the nearest tenth)
Direction (Angle) of the Vector:
The angle θ that the vector makes with the positive x-axis can be found using trigonometric functions:
θ = arctan(y / x)
For the given vector <2, 7>:
θ = arctan(7 / 2) ≈ 74° (rounded to the nearest degree)
Thus,
The magnitude of the vector is approximately 7.3 and the direction of the vector is approximately 74 degrees which is option B.
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Need help to solve this please!!
Answer:
0.999
Step-by-step explanation:
If the driver wore a seat belt, that is the only column we have to look at.
The chance the driver survived is number survived / number total.
Plugging in, we get 412,042/412,493, or about 0.999.
Hope this helps!
Kendall will find the total surface area of the prism below. Assuming the base is the shaded surface (the bottom), drag an
drop the correct values for the variables P, h, B that she should use in her formula.
1.2 ft
P.⠀
h:
B:
feet
feet
8.8 ft
square feet
nwore mangslugnsits arts to come sostua eri bait of absan y
So
2 ft
Answer:
Step-by-step explanation:
is 8,15,24
a. in the sample: i. what is the average value of birthweight for all mothers? ii. for mothers who smoke? iii. for mothers who do not smoke? b. i. use the data in the sample to estimate the difference in average birth weight for smoking and nonsmoking mothers. ii. what is the standard error for the estimated difference in (i)? iii. construct a 95% confidence interval for the difference in the average birth weight for smoking and nonsmoking mothers.
a. In the sample:i. The average value of birth weight for all mothers is 7.17 pounds.
ii. For mothers who smoke is 6.82 pounds.
iii. For mothers who do not smoke is 7.28 pounds.b. i. The difference in average birth weight for smoking and nonsmoking mothers can be estimated using the sample data. The difference is given by the formula:
Difference = X1 – X2, where X1 is the average birth weight of mothers who smoke and X2 is the average birth weight of mothers who do not smoke.Using the sample data, the estimated difference in average birth weight for smoking and nonsmoking mothers is: 7.28 – 6.82 = 0.46 pounds.ii. The standard error for the estimated difference can be calculated using the formula:SE(Difference) = sqrt[(SE1)^2 + (SE2)^2]where SE1 and SE2 are the standard errors of the two sample means.Using the sample data, the standard error for the estimated difference is:SE(Difference) = sqrt[(0.23)^2 + (0.12)^2] = 0.26 pounds.iii. The 95% confidence interval for the difference in average birth weight for smoking and nonsmoking mothers can be calculated using the formula:CI(Difference) = Difference ± (t-value) × (SE(Difference))where (t-value) is the value from the t-distribution table for a 95% confidence level with n1 + n2 – 2 degrees of freedom (where n1 and n2 are the sample sizes for smoking and nonsmoking mothers).Using the sample data, the 95% confidence interval for the difference in average birth weight is:CI(Difference) = 0.46 ± (2.048) × (0.26) = (0.04, 0.88) pounds.
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Question 2
On a bicycle, Ivanna rides for 5 hours and is 12 miles from her house. After riding for 9 hours, she is 20 miles
away.
What is Ivanna's rate?
By answering the presented question, we may conclude that As a result, expressions Ivanna's average speed is approximately 2.311 miles per hour.
what is expression ?In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
We can use the formula:
rate = distance / time
Let's calculate Ivanna's rate for the first part of her journey:
rate = distance divided by time = 12 miles divided by 5 hours = 2.4 miles per hour
Let us now compute Ivanna's rate for the second leg of her journey:
rate = distance divided by time = 20 miles divided by 9 hours = 2.222... miles per hour
As a result, Ivanna's overall rate is the average of these two rates:
rate = (2.4 miles per hour + 2.222... miles per hour) / 2 = 2.311... miles per hour
As a result, Ivanna's average speed is approximately 2.311 miles per hour.
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11x + 9y=-20 x= -5y-6
Use substitution method pls
The solution to the system of equations is (x, y) = (1, -1) where the given equations are 11x+9y=-20 and x=-5y-6.
What is substitution method?The substitution method is a technique used in algebra to solve systems of equations by replacing one variable with an expression containing another variable. The goal is to eliminate one of the variables so that we can solve for the other one.
According to question:We are given the following system of two equations with two variables:
11x + 9y = -20 (equation 1)
x = -5y - 6 (equation 2)
To solve the system using the substitution method, we need to solve one of the equations for one of the variables, and then substitute the expression for that variable into the other equation. Let's solve equation 2 for x:
x = -5y - 6
Now we can substitute this expression for x into equation 1, and solve for y:
11x + 9y = -20
11(-5y - 6) + 9y = -20 (substituting x = -5y - 6)
-55y - 66 + 9y = -20
-46y = 46
y = -1
Now that we have found y = -1, we can substitute this value back into equation 2 and solve for x:
x = -5y - 6
x = -5(-1) - 6
x = 1
Therefore, the solution to the system of equations is (x, y) = (1, -1).
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please help I need this complete
Answer: [tex]c-34=21[/tex]; 55 cups of lemonade.
Step-by-step explanation:
We are given the amount sold and the amount leftover so we need to figure out how many cups were there at the start. Since you are subtracting the amount of cups you sold from the amount you start with and it equals an end amount, the cups can be modeled by the equation [tex]c-34=21[/tex] rather than [tex]21+c=34[/tex].
Now to solve for c
[tex]c-34=21\\[/tex]
add 34 to both sides
[tex]c=55[/tex]
Helppppppppppp me please
Answer:
Step-by-step explanation:\Write an expression for the sequence of operations describe below Add C and the quotient of 2 and D do not simplify any part of the expression
A restaurant at the food court in a mall is offering a lunch special. The table shows the relationship between the number of side dishes and the total cost of the special.
Restaurant
Number of Side Dishes Total Cost
2 $6.75
4 $8.25
5 $9.00
8 $11.25
Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 6 and 75 hundredths through the point 3 comma 9
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 25 hundredths through the point 5 comma 9
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 6 and 75 hundredths through the point 1 comma 8 and 25 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 75 hundredths through the point 1 comma 7 and 25 hundredths
The correct answer is graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 6 and 75 hundredths through the point 3 comma 9.
What is axis?Axis refers to the number of dimensions in a graph, chart, or plot. It is an imaginary line that is used to measure and plot values in a graph. In a line graph, the x-axis is the horizontal line and the y-axis is the vertical line.
The first graph shows a relationship between the number of side dishes and the total cost of the special that does not match the data given in the table.
The second graph does not reflect the data given in the table, as the total cost of the special increases from $5.25 to $9.00 when the number of side dishes increases from 0 to 5.
The third graph also does not reflect the data given in the table, as the total cost of the special increases from $6.75 to $8.25 when the number of side dishes increases from 0 to 4.
The fourth graph also does not reflect the data given in the table, as the total cost of the special increases from $5.75 to $7.25 when the number of side dishes increases from 0 to 1.
Therefore, the correct answer is mentioned above. This graph accurately reflects the relationship between the number of side dishes and the total cost of the special.
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The correct answer is "graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0,6 and 75 hundredths through the point 3,9".
What is axis?Axis refers to the number of dimensions in a graph, chart, or plot. It is an imaginary line that is used to measure and plot values in a graph.
This graph correctly illustrates the relationship between the number of side dishes and the total cost of the special as shown in the table.
The line starts at 0 side dishes and $6.75
and ends at 4 side dishes and $8.25, both of which are in the table.
The graph accurately reflects this by having a line that starts at 2 side dishes and $6.75 and ends at 5 side dishes and $9.00.
This shows that as the number of side dishes increases, the cost also increases.
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What is the exact value of the trigonometric expression? State your answer in simplified radical form and include all work.
*Please reference included picture for problem. Thank you!
Answer:
The exact value of the given trigonometric expression is undefined.
Step-by-step explanation:
Given trigonometric expression:
[tex]\dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)[/tex]
To find the exact value of the given trigonometric expression, begin by finding the exact values of each of the trigonometric functions in the expression
The exact value of cos(2π/3) is:
[tex]\implies \cos\left(\dfrac{2 \pi}{3}\right)=-\dfrac{1}{2}[/tex]
The exact value of tan(-7π/4) is:
[tex]\implies \tan\left(-\dfrac{7 \pi}{4}\right)=1[/tex]
Since the cosecant function is the reciprocal of the sine function, the exact value of csc(π) is:
[tex]\implies \csc (\pi)=\dfrac{1}{\sin(\pi)}=\dfrac{1}{0}=\textsf{unde\:\!fined}[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)&=\dfrac{-\dfrac{1}{2}}{1}+\dfrac{1}{0}\\&=-\dfrac{1}{2}+\dfrac{1}{0}\\\\&=\textsf{unde\:\!fined}\end{aligned}[/tex]
An article reports that in a sample of 123 hip surgeries of a certain type, the average surgery time was 136.9 minutes with a standard deviation of 24.1 minutes.
find
A. The 95% confidence interval is (,)
B.The 99.5% confidence interval is(,)
C. A surgeon claims that the mean surgery time is between 133.71 and 140.09 minutes. With what level of confidence can this statement be made? Express the answer as a percent and round to two decimal places.
D. Approximately how many surgeries must be sampled so that a 95% confidence interval will specify the mean to within ±3 minutes? Round up the answer to the nearest integer.
F.Approximately how many surgeries must be sampled so that a 99% confidence interval will specify the mean to within ±3 minutes? Round up the answer to the nearest integer.
The minimum sample size required to get a 99% confidence interval that will specify the mean to within ±3 minutes is 597 (Rounded up to the nearest integer).
A) The 95% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (130.82, 142.98).Explanation:Given,Sample size, n = 123Average surgery time, μ = 136.9 minutesStandard deviation, σ = 24.1 minutesWe know that for a sample of size n, the 95% confidence interval is given by, (Formula1)Where, z is the z-score, α/2 = 0.05/2 = 0.025 is the level of significance and n - 1 = 122 degrees of freedom.Now, substituting the given values in (Formula1), we get the 95% confidence interval as(130.82, 142.98)Thus, the 95% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (130.82, 142.98).B) The 99.5% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (127.93, 145.87).Explanation:We know that for a sample of size n, the 99.5% confidence interval is given by, (Formula2)Where, z is the z-score, α/2 = 0.005/2 = 0.0025 is the level of significance and n - 1 = 122 degrees of freedom.Now, substituting the given values in (Formula2), we get the 99.5% confidence interval as (127.93, 145.87).Thus, the 99.5% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (127.93, 145.87).C) The surgeon's claim that the mean surgery time is between 133.71 and 140.09 minutes is equivalent to the confidence interval (133.71, 140.09). The surgeon's claim falls inside the 95% confidence interval, (130.82, 142.98), therefore we can say that the surgeon's claim can be made with 95% confidence.D) The formula to find the minimum sample size for a 95% confidence interval that will specify the mean to within ±3 minutes is given by (Formula3)Where, n is the sample size and σ is the standard deviation.Now, substituting the given values in (Formula3), we get the minimum sample size as 424.15.The minimum sample size required to get a 95% confidence interval that will specify the mean to within ±3 minutes is 425 (Rounded up to the nearest integer).F) The formula to find the minimum sample size for a 99% confidence interval that will specify the mean to within ±3 minutes is given by (Formula4)Where, n is the sample size and σ is the standard deviation.Now, substituting the given values in (Formula4), we get the minimum sample size as 596.73.The minimum sample size required to get a 99% confidence interval that will specify the mean to within ±3 minutes is 597 (Rounded up to the nearest integer).
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2 Rema has two jobs. In one year, she worked 276 hours at her first job. In the same year, she worked 3 times the number of hours at her second job. How many hours did Rema work that year at her second job?
Answer:
Step-by-step explanation:
Kind of like rema from the song calm down calm down!!
you an find it on youtub
The population of a city was 20000. The next year it increased by 2% find the new population
The city had 20,000 residents. The next year, it went up by 2%. The new population of the city after a 2% increase is 20400.
To find the new population of the city after a 2% increase from 20000, we need to use the following formula:
New population = Old population + (Percentage increase x Old population)
Substituting the given values into the formula, we get:
New population = 20000 + (2/100 x 20000)
New population = 20000 + 400
New population = 20400
It is important to note that this calculation assumes that the increase in population is the only factor affecting the total population. In reality, there may be other factors that affect the population, such as migration, birth rates, and mortality rates.
Additionally, this calculation only gives the estimated population based on the percentage increase, and the actual population may differ due to various factors.
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a red cap fire hydrant provides 1700 liters per minute of water. how long (in minutes to the nearest minute) will it take to fill a water truck with a tank of the following dimensions: 68 inches diameter and 24 feet long? when the tank is full of water, how heavy will the water load be in pounds (lbm) to the nearest pound?
It will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.
How to find out how long it will take to fill the tank.First, we need to convert the dimensions of the tank from inches to feet:
68 inches diameter = 68/12 feet = 5.67 feet diameter
24 feet long = 24 feet long
Next, we can calculate the volume of the tank in cubic feet:
Volume = [tex]pi x (diameter/2)^2 x length[/tex]Volume = [tex]3.14 x (5.67/2)^2 x 24[/tex]Volume = [tex]485.15 cubic feet[/tex]Since 1 cubic foot of water weighs 62.4 pounds, we can calculate the weight of the water in the tank in pounds:
Weight = Volume x DensityWeight = 485.15 x 62.4Weight = 30,296.16 poundsTo find out how long it will take to fill the tank, we can use the flow rate of the fire hydrant:
Flow rate = 1700 liters per minute1 liter = 0.264172 gallonsFlow rate = 1700 x 0.264172 = 449.10 gallons per minute1 gallon = 0.133681 cubic feetFlow rate = 449.10 x 0.133681 = 60.05 cubic feet per minuteFinally, we can divide the volume of the tank by the flow rate to find out how long it will take to fill the tank:
Time = Volume / Flow rateTime = 485.15 / 60.05Time = 8.08 minutesTherefore, it will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.
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If x is a positive integer , 4x^1/2 is equivalent to
If x is a positive integer , 4x^1/2 is equivalent to product of 2 and square root of x, wherein it would surely be a positive value greater than 2.
Positive integers are the numbers on the number line which are greater then zero and extend on the right hand side of the number line till infinity. These numbers are also whole numbers in itself such as 1, 2, 3...,∞. When 4x^1/2 is calculated, it is assumed that 4x is raised to power half, which will provide the answer as 2√x.
It is because square root of 4 will be 2 and that of x will be √x. Square roots are the numbers obtained by multiplying a specific number by the number itself. For example: 3×3 = 9 or square root of 9 is 3.
If some positive integer is fixed in the equation, the desired outcome would be obtained as follows:
If x=4, (4×4)^1/2 = 4
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Chang each expression into radical form and then give the value. no calculators should be necessary.
The value of the given expressions are as follows: a. 25 b. 4 c. 1/4 d. 1/3.
What is expression?In mathematics, an expression is a combination of symbols and/or numbers that represents a mathematical object or quantity. Expressions can be written using variables, operations, functions, and mathematical symbols such as parentheses, exponents, and radicals. An expression can represent a value, an equation, or a formula, and can be evaluated or simplified using mathematical rules and properties. Examples of expressions include 2x + 5, sin(θ), and (a + b)².
Here,
a. [tex]125^{2/3}[/tex]
radical form:
[tex]\sqrt{ (125^2)} = 125^{1/2}[/tex]
[tex]125^{1/2}[/tex] = √125
= 5√5
Therefore, [tex]125^{2/3} = (125x^{1/3})^{2}[/tex]
= [tex](5^3)x^{2/3}[/tex]
= [tex]5x^{3*2/3}[/tex]
= 5²
= 25
b. √16
In radical form:
√16 = 4
Therefore, [tex]16x^{-1/2} = \sqrt{16}[/tex]
= 4
c. [tex]16^{1/2}[/tex]
In radical form:
1/√16 = 1/4
Therefore, [tex]16^{-1/2} = 1/\sqrt{16}[/tex]
= 1/4
d.[tex]\sqrt[4]{81}[/tex]
In radical form:
[tex]\sqrt[4]{81}[/tex] = √(√81)
= √9
= 3
Therefore, [tex]\sqrt[4]{81} = 1/\sqrt[4]{81}[/tex]
= 1/3
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Place the three sets of conditions in order. Begin with the set that gives the greatest number of triangles, and end with the set that gives the smallest number of triangles. Condition A: One side is 6 inches long, another side is 5 inches long, and the angle between them measures 50°. Condition B: One angle measures 50°, another angle measures 40°, and a third angle measures 90°. Condition C: One side is 4 inches long, another side is 9 inches long, and a third side measures 5 inches.
The order from the greatest number of triangles to the smallest is: Condition A, Condition B, Condition C.
What is triangle inequality theorem?According to the Triangle Inequality Theorem, any two triangle sides' sums must be bigger than the length of the third side.
The triangle inequality theorem can be used to determine the order of the greatest to smallest triangle.
Condition A: Under this condition, we have two sides with lengths 5 and 6, and their angle is 50°. Using these requirements, we may create two separate triangles since 5 + 6 = 11, which is more than the third side.
Condition B: This condition results in a right triangle with a third angle that is 90° and two sharp angles that measure 40° and 50°. According to the Pythagorean theorem, the triangle's two legs must be 30 and 40 inches long, respectively, meaning that the hypotenuse must be 50 inches long. We can only create one triangle as a result.
Condition C: This condition provides us with three sides that are 4, 5, and 9 lengths long. Any two sides must have a length total larger than the third side in order for a triangle to be formed. The three sides provided, however, do not satisfy this since 4 + 5 = 9. Hence, under these circumstances, a triangle cannot be formed.
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Determine whether the following statement is true or false. If it is false, explain why. The probability that event A or event B will occur is P(A or B)= P(A) + P(B) - P(A or B). Choose the correct answer below. A. True B. False, the probability that A or B will occur is P(A or B)= P(A) middot P(B). C. False, the probability that A or B will occur is P(A or B)= P(A) + P(B). D. False, the probability that A or B will occur is P(A or B)= P(A) + P(B) - P(A and B).
False, the probability that A or B will occur is P(A or B) = P(A) + P(B) - P(A and B).
Define probabilityProbability refers to the measure of the likelihood or chance of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event, and 1 indicates a certain event.
This formula is known as the Addition Rule for Probability and states that to calculate the probability of either event A or event B occurring (or both), we add the probability of A happening to the probability of B happening, but then we need to subtract the probability of both A and B happening at the same time to avoid double counting.
Option A is not the correct answer because it is missing the subtraction of P(A and B), options B and C are incorrect because they omit the subtraction and only add the probabilities of the events. Option D is close, but it is missing the addition of the probabilities of A and B.To know more about event, visit:
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find the z-score such that the interval within standard deviations of the mean for a normal distribution contains 87% of the probability.
The Z-score of the interval within standard deviations of the mean for a normal distribution contains 87% of the probability is 1.11 (rounded to two decimal places).
To find the z-score such that the interval within standard deviations of the mean for a normal distribution contains 87% of the probability, we need to use the standard normal distribution table (Z-table) or a calculator that has the inverse normal function.
The standard normal distribution is a normal distribution with a mean of zero and a standard deviation of 1. It is denoted by the letter Z. Z-scores measure the number of standard deviations a data point is from the mean of the data set. A positive Z-score indicates a data point is above the mean, while a negative Z-score indicates a data point is below the mean.
To find the Z-score such that the interval within standard deviations of the mean for a normal distribution contains 87% of the probability, we first need to find the probability that is outside the interval. Since the interval is within standard deviations of the mean, we can use the empirical rule or the 68-95-99.7 rule to find the probability that is outside the interval.
The 68-95-99.7 rule states that 68% of the probability lies within 1 standard deviation of the mean 95% of the probability lies within 2 standard deviations of the mean 99.7% of the probability lies within 3 standard deviations of the mean. Since we are interested in the interval within standard deviations of the mean that contains 87% of the probability, we can assume that the interval is 1 standard deviation away from the mean.
Using the 68-95-99.7 rule, we can find the probability that is outside the interval:
100% - 68% = 32%
Since the probability that is outside the interval is 32%, we want to find the Z-score that corresponds to the probability of 16% on either side of the mean. We use the Z-table or a calculator that has the inverse normal function to find the Z-score that corresponds to a probability of 0.16.
From the Z-table, the Z-score that corresponds to a probability of 0.16 is 1.11 (rounded to two decimal places).
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It’s not 1507 please help me
Answer:
Below
Step-by-step explanation:
Mass of bouncies + box = 17342 subtract mass of box from both sides
mass of bouncies = 17342 - 429 = 16913 g
Unit mass per bouncy = 505 g / 45 bouncy
Number of Bouncies = 16913 gm / ( 505 g / 45 bouncy ) = 1507.1 bouncies
With the given info, I am afraid it IS 1507 bouncies in the box
maybe since the question asks for APPROXIMATE number, the answer is 1510 bouncies ( rounded answer) ....or 1500
A number subtracted from 80 gives — 30. Find the number
The number which, when subtracted from 80, results in -30 is equal to 110.
To solve this problem, we can use algebraic equations to represent the given information. Let x be the number that we want to find.
According to the problem, when we subtract x from 80, we get -30:
80 - x = -30
To solve for x, we can isolate it on one side of the equation by adding x to both sides, and then simplify:
80 - x + x = -30 + x
80 = -30 + x
Next, we can isolate x by subtracting -30 from both sides:
80 - (-30) = x
Simplifying the right-hand side:
80 + 30 = x
110 = x
Therefore, the number that was subtracted from 80 and gave -30 as the result is 110.
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What is the solution to the trigonometric inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2pi radians?
From the given information provided, the solution to the given trigonometric inequality is (π/4, 5π/4).
To solve the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians, we can use the following steps:
Rewrite the inequality in terms of tangent:
Divide both sides by cos(x) to get:
tan(x) > 1
Find the solutions of the equation tan(x) = 1:
tan(x) = 1 when x = π/4 or x = 5π/4.
Check the sign of tangent in the intervals between the solutions:
We need to check the sign of tan(x) for x values in the following intervals:
(0, π/4), (π/4, 5π/4), and (5π/4, 2π).
In the interval (0, π/4), tan(x) is positive and less than 1.
In the interval (π/4, 5π/4), tan(x) is positive and greater than 1.
In the interval (5π/4, 2π), tan(x) is negative and less than -1.
Determine the solution set:
Since we are looking for x values that satisfy tan(x) > 1, the only interval that contains such values is (π/4, 5π/4). Therefore, the solution to the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians is:
π/4 < x < 5π/4
In interval notation, we can write:
(π/4, 5π/4)
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trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 11 miles per day. the mileage per day is distributed normally. find the probability that a truck drives between 99 and 128 miles in a day. round your answer to four decimal places.
The probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.
What is the standard deviation?Standard deviation is a statistical measurement that depicts the average deviation of each value in a dataset from the mean value. It tells you how much your data deviates from the mean value. It represents the typical variation between the mean value and the individual data points.
The formula for the probability that a truck drives between 99 and 128 miles in a day is:
[tex]Z = (X - \mu) /\sigma[/tex]
where, X is the number of miles driven per day; μ is the mean of the number of miles driven per day; σ is the standard deviation of the number of miles driven per day. The value of Z for 99 miles driven per day is:
[tex]Z = (99 - 120) / 11 = -1.91[/tex]
The value of Z for 128 miles driven per day is:
[tex]Z = (128 - 120) / 11 = 0.73[/tex]
Using a standard normal distribution table or calculator, the probability of a truck driving between 99 and 128 miles per day is:
[tex]P(-1.91 < Z < 0.73) = 0.7734[/tex]
Therefore, the probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.
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What is the contrapositive of the following statement? "If it is not a lion, then it is a cat
The contrapositive of the given statement is "If it is not a cat, then it is a lion."
The contrapositive of the statement "If it is not a lion, then it is a cat" can be obtained by negating the original statement and switching the positions of the antecedent (the "if" part) and the consequent (the "then" part).
The contrapositive takes the form:
"If it is not a cat, then it is a lion."
So, the contrapositive of the given statement is "If it is not a cat, then it is a lion."
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Will give brainly award
Using the other endpoint of the diameter, and the center of the circle write an equation of the circle
Answer:
Step-by-step explanation:
C(1,2), radius=6
Equation using [tex](x-h)^2+(y-k)^2=r^2[/tex]:
[tex](x-1)^2+(y-2)^2=36[/tex]
Part A: Graph the system of equations {−2x+y=6x−y=1
Part B: Determine the solution from Part A.
Answer:
Step-by-step explanation:
An important math tool is graphing. It can be a straightforward method for introducing more general concepts like most and least, greater than, or less than. It can also be a great way to get your child interested in math and get them excited about it. Using graphs and charts, you can break down a lot of information into easy-to-understand formats that quickly and clearly convey key points.
Given equation 2x + y = 6 we can drive from this equation that at x = 0 y will be 6 and y =0 x will be 3 hence we have two points of the line (0,6) and (3,0)
From the Given equation (2) 6X + 3Y = 12 we can drive from this equation that at x = 0 y will be 4 and y =0 x will be 2 hence we have two points of the line (0,4) and (2,0).
1. Describe the relationship you see between elevation and temperature in these data sets.
In response to the stated question, we may state that The scatter plot indicates a clustering pattern in the data, and as elevation increases, temperature drops.
What exactly is a scatter plot?"Scatter plots are graphs that show the association of two variables in a data collection. It is a two-dimensional plane or a Cartesian system that represents data points. The X-axis represents the independent variable or characteristic, while the Y-axis represents the dependent variable. These plots are sometimes referred to as scatter graphs or scatter diagrams."
"A scatter plot is also known as a scatter chart, scattergram, or XY graph. The scatter diagram plots numerical data pairings, one variable on each axis, to demonstrate their connection."
Because the graph is a scatter plot, the data displays a clustering pattern.
We may deduce from the figure that as height increases, temperature falls.
As a result, C and E are the proper choices.
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The correct question is -
The scatter plot shows the relationship between elevation and temperature on a certain mountain peak in North America. Which statements are correct?
A. The data shows one potential outlier
B. The data shows a linear association
C. The data shows a clustering pattern
D. The data shows a negative association
E. As elevation increases, temperature decreases
an arm wrestler is the champion for a period of 75 hours. (here, by an hour, we mean a period starting from an ex- act hour, such as 1 p. m ., until the next hour.) the arm wrestler had at least one match an hour, but no more than 125 total matches. show that there is a period of consec- utive hours during which the arm wrestler had exactly 24 matches.
In the following question, among the conditions given, There must have been at least one 24-hour period in the 75-hour period in which the arm wrestler had exactly 24 matches.
The arm wrestler had at least 75 matches and no more than 125 total matches. This means that the arm wrestler had a maximum of 50 matches in any consecutive period of 75 hours. Therefore, there must be a period of consecutive hours during which the arm wrestler had exactly 24 matches.
To show this, let us consider the following: in the 75-hour period, there must have been at least 3 periods of consecutive 24-hour periods (24 matches per period). If we subtract 3 x 24 matches from the total of 75 matches, we are left with 3 matches. Therefore, there must have been at least one 24-hour period in the 75-hour period in which the arm wrestler had exactly 24 matches.
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At the start of 2014
Mikes car was worth 12000 the value of the car decreased by 30%
Answer:
If the value of Mike's car decreased by 30%, we can calculate the new value of the car as follows:
New value = Original value - (Percentage decrease × Original value)
Percentage decrease = 30%
Original value = 12000
New value = 12000 - (0.30 × 12000)
New value = 12000 - 3600
New value = 8400
Therefore, at the end of the decrease, the value of Mike's car was 8400.
Angela made 23 cards for her friends. She wants to make 19 more cards. How many cards will she make in all?
By using addition calculation, we determine that Angela will end up making 42 cards in total.
Angela made 23 cards for her friends, but she wants to make even more to share with others. To determine how many cards she will make in total, we need to add the number of cards she has already made with the number of cards she plans to make.
So, we add 23 (the number of cards she has made) and 19 (the number of cards she plans to make) so in total, she will make:
23 + 19 = 42
Therefore, Angela will make 42 cards in all.
By using simple arithmetic calculation of basic addition, we find that Angela will make 42 cards in all.
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Exercise 16.8. Prove Theorem 16.8 following the outline below: Let p be a prime number that is irreducible in Zi]. We wish to show that Z,[i] is a field. Let [c] + [d]i be a nonzero element of Zp[i], with [c] and [d] in Zp. (Thus we may take c and d to be integers representing their congruence classes.) We need to prove that [cl+ Idi is a unit. 1. Notice that [c +(di is a unit if one of [e and [d is [0 and the other is not. 2. Having taken care of the case in which one of [c and [d is the zero congruence class in Zp, suppose now that [cj and [d are both nonzero elements of Zp[i]. Observe that in Zj, the prime p cannot divide c + di (why?), so that p and c+ di are relatively prime. 3. Deduce that in this case, by Theorem 16.7, there exist Gaussian integers r and s such that (c + d)r = 1 + ps. 4. Supposer e fi for integers e and f. Deduce that in Zp[l. 5. Conclude that Zpli] is a field.
The theorem is Every nonzero element in the ring has an inverse, hence we deduce that Z[i]/(p) is a field. For any prime number p that is irreducible in Z[i], as asserted, Z[i]/(p) is a field.
Proof of Theorem is Let p be a prime number that is irreducible in Z[i]. We want to show that Z[i]/(p) is a field, where (p) denotes the ideal generated by p.
Suppose that [c] + [d]i is a nonzero element of [tex]Z[i]/(p)[/tex], where [c] and [d] are congruence classes in Zp.
If one of [c] and [d] is [0], then [c] + [d]i is a unit, since the other element is nonzero. So, suppose that [c] and [d] are both nonzero in Zp.
We observe that p cannot divide c + di in Z[i] since p is irreducible in Z[i] and it cannot divide both c and d. Therefore, p and c + di are relatively prime in Z[i].
By Theorem 16.7, there exist Gaussian integers r and s such that [tex](c + di)r = 1 + ps.[/tex]
Now, suppose that [e] + [f]i is another nonzero element of Z[i]/(p), where [e] and [f] are congruence classes in Zp. We want to show that [e] + [f]i is also a unit.
Since p and c + di are relatively prime, there exist integers u and v such that [tex]pu + (c + di)v = 1[/tex] , by Bezout's identity.
Multiplying both sides by e + fi, we get:
[tex]pue + (c + di)ve + (ce - df) + (cf + de)i = e + fi[/tex]
Therefore, [tex](e + fi)(ue + vi(c + di)) = (e + fi)(1 - (cf + de)i)[/tex]
Multiplying both sides by the conjugate of (e + fi), we get:
[tex](e + fi)(e - fi)(ue + vi(c + di)) = (e^2 + f^2)[/tex]
Since p is irreducible in Z[i], it is also prime. Thus, Z[i]/(p) is an integral domain, which means that the product of two nonzero elements is nonzero. Therefore, [tex]e^2 + f^2[/tex] is nonzero in Zp, and
so [tex](e + fi) (ue + vi(c + di))[/tex] is a unit in Z[i]/(p).
We conclude that Z[i]/(p) is a field since every nonzero element has an inverse in the ring.
Therefore, Z[i]/(p) is a field for any prime number p that is irreducible in Z[i], as claimed
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