In the following question, among the conditions given, The greatest value in the data set is 21, the mean is 13.4, the mode is 12, and the median is 12.
The greatest value is the highest number in the set, 21.
The mean is the average of the set, and is calculated by adding all the numbers together and dividing by the number of values, which in this case is 11. 11 + 11 + 12 + 12 + 12 + 12 + 13 + 15 + 17 + 21 + 21 + 21 = 163, and 163 / 11 = 13.4.
The mode is the number that appears the most often, which is 12 in this set.
The median is the middle number when all the numbers are put in order from least to greatest, which is also 12 in this set.
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The diagram shown is two intersecting lines. The measure of <5 is 42°.
Two intersecting lines. Not perpendicular. Angles labeled from far left counterclockwise are labeled 5 then 6 then 7
What is the measure of <7 ? How do you know. Explain your answer in complete sentences.
Suppose the measure of <6 can be represented by(3x-9). What equation can be written to solve for the value of x?
What is the value of x?
Hence, x has a value of 49 as to find x, we add 9 to both sides and divide the result by 3.
what is angle ?The distance between two intersecting lines or planes is measured in terms of angles. The amount of rotation required to align one of the lines or planes with the other is usually expressed in terms of degrees. The range of an angle is 0 degrees (i.e., no rotation) to 360 degrees (corresponding to a complete rotation).
given
As angles 5 and 7 are a pair of linear angles, their sum must be 180 degrees. Angle 7 therefore has a measure of 180 - 42 = 138 degrees.
We can use the fact that angles 6 and 7 are vertical angles and have the same measure to find the value of x. As a result, we can set the following phrase to indicate that the measure of angle 6 is equal to angle 7:
3x - 9 = 138
In order to find x, we add 9 to both sides and divide the result by 3:
3x = 147
x = 49
Hence, x has a value of 49 as to find x, we add 9 to both sides and divide the result by 3.
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Solve for X.
x² + 4x + 4 = 8
Step-by-step explanation:
We can also solve the equation x² + 4x + 4 = 8 by rearranging the terms and using the quadratic formula:
x² + 4x + 4 - 8 = 0
x² + 4x - 4 = 0
Applying the quadratic formula, we have:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 4, and c = -4. Substituting these values, we get:
x = (-4 ± √(4² - 4(1)(-4))) / 2(1)
x = (-4 ± √32) / 2
Simplifying the square root of 32, we get:
x = (-4 ± 4√2) / 2
x = -2 ± 2√2
Therefore, the solutions to the equation x² + 4x + 4 = 8 are x = -2 + 2√2 and x = -2 - 2√2.
this is so confusing. i have to round to either 106 or 67 in.
The circumference of a circle with a radius of 15 inches is 30π inches, or 94.25 inches
How to calculate the circumferenceThe circumference of a circle can be calculated using the formula:
C = 2πr
where C is the circumference, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14159.
In this case, the radius is 15 inches. Substituting this value into the formula, we get:
C = 2π(15) = 30π
So the circumference of a circle with a radius of 15 inches is 30π inches, or approximately 94.2478 inches.
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DUE TOMORROW PLEASE HELP!!!!
The center of an airplane propeller is 13 feet off the ground and the radius of the propeller is 3 feet. The blades of the propeller are set at π/6, 5π/6, and 3π/2 radians from 0 radians directly to the right of the center of the propeller.
What is the height of the tip of each propeller in this position?
The heights of the tips of the propeller blades at π/6, 5π/6, and 3π/2 radians are 15.5 feet, 11.5 feet, and 10 feet, respectively.
What is the equation of a circle in parametric form?
The equation of a circle in parametric form is given by x=acosθ,y=asinθ.
We can use the equation for a circle in standard form:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius.
In this case, the center of the propeller is (0, 13) and the radius is 3. So the equation of the circle is:
x² + (y - 13)² = 9
We can use this equation to find the x and y coordinates of the tip of each propeller.
For the blade at π/6 radians, we can use the parametric equations for a circle:
x = r cos(t) + h
y = r sin(t) + k
where t is the angle in radians.
Substituting r = 3, h = 0, k = 13, and t = π/6, we get:
x = 3 cos(π/6) + 0 = 3√3/2
y = 3 sin(π/6) + 13 = 13 + 3/2 = 15.5
So the height of the tip of the propeller blade at π/6 radians is 15.5 feet.
Using the same method for the blades at 5π/6 and 3π/2 radians, we get:
Blade at 5π/6 radians:
x = 3 cos(5π/6) + 0 = -3√3/2
y = 3 sin(5π/6) + 13 = 13 - 3/2 = 11.5
Height of tip: 11.5 feet
Blade at 3π/2 radians:
x = 3 cos(3π/2) + 0 = 0
y = 3 sin(3π/2) + 13 = 10
Height of tip: 10 feet
Therefore, the heights of the tips of the propeller blades at π/6, 5π/6, and 3π/2 radians are 15.5 feet, 11.5 feet, and 10 feet, respectively.
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Solve for z.
d³ = −27
ANSWER FAST PLEASE
Answer:
d=-3
Step-by-step explanation:
d^3=-27
d=[tex]\sqrt[3]{-27} \\[/tex]
d=-3
Answer:
d=-3
Step-by-step explanation:
You must that 3rd root of -27, which is -3
Terrance and his three friends earned $359 in August, $522 in July, and $420 in September selling lemonade. How much would they each earn if they divided their earnings equally?
In Linear equation, 260.2 would they each earn if they divided their earnings equally.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Equations with variables of power 1 are referred to be linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
three friends earned $359 in August, $522 in July, and $420 in September
= $359 + $522 $ 420
= 1301/5 = 260.2
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you need to have a password with 4 letters followed by 2 even digits between 0 and 9 , inclusive. if the characters and digits cannot be used more than once, how many choices do you have for your password?
There are 6,354,000 choices for the password.
To generate a password, you need to have 4 letters followed by 2 even digits between 0 and 9, inclusive.
If the characters and digits cannot be used more than once,
Solution: We have to find the number of choices of the password with given conditions.
To find the number of choices, let us follow the following steps:
Step 1: Choose the first letter in 26 ways
Step 2: Choose the second letter in 25 ways (excluding the letter that we have already chosen)
Step 3: Choose the third letter in 24 ways (excluding the 2 letters that we have already chosen)
Step 4: Choose the fourth letter in 23 ways (excluding the 3 letters that we have already chosen)
Step 5: Choose the first even digit in 5 ways (from 0, 2, 4, 6, and 8)
Step 6: Choose the second even digit in 4 ways (excluding the even digit that we have already chosen)
Therefore, the total number of choices for the password with the given conditions is given by:
Total number of choices = 26 × 25 × 24 × 23 × 5 × 4= 6,354,000.
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full-time high school students spend approximately 30 hours per week in class, and full-time college students only spend about half of that in class. true or false: full-time high school students spend more time per week on their courses than full-time college students.
Answer:
The answer to your question would be true.
The given statement 'full-time high school students spend more time per week on their courses than full-time college students' is true because full-time high school students spend approximately 30 hours per week in class, and full-time college students only spend about half of that in class.
Full-time high school students spend more time per week on their courses than full-time college students. It is because full-time high school students spend approximately 30 hours per week in class, and full-time college students only spend about half of that in class.
College courses usually last for one hour per day, whereas high school students attend classes for 5-6 hours per day. Hence, college students spend around 15-18 hours per week attending classes, while high school students spend around 30 hours per week in the classroom.
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i need help on this question :(((
The Polynomials that are listed in the question are the options labelled;
B, C, E
What is a polynomial?
A polynomial is a mathematical expression that consists of variables, coefficients, and exponents.
The variables represent unknown values, while the coefficients are constants that multiply the variables or their exponents. The exponents indicate the power to which the variables are raised.
Polynomials can be added, subtracted, multiplied, and divided to create more complex expressions, and they are used in a wide range of mathematical applications, including algebra, calculus, and geometry.
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8. the z-table gives the area under the standard normal curve to the left of z. what does the t-table give?
Answer:
The z-Table gives the area under the standard normal curve to the left of z. What does the t-Table give? The t-Table gives the area under the t-curve with n degrees of freedom to the left of it
HOPE THIS HELPSSS!
What are the steps to express 0.15 as a fraction in simplest form ? Order the following from 1-5
Answer:
0.15 expressed as a fraction in its simplest form is 3/20.
Step-by-step explanation:
To express a terminating decimal as a fraction:
Step 1Write the decimal as a fraction by dividing it by 1:
[tex]\boxed{\dfrac{0.15}{1}}[/tex]
Step 2Multiply the numerator and denominator by 10 for every number after the decimal point.
As there are two numbers after the decimal point, multiply the numerator and denominator by 100:
[tex]\boxed{\dfrac{0.15 \times 100}{1 \times 100}=\dfrac{15}{100}}[/tex]
Step 3Find the highest common factor (HCF) of the numerator and denominator.
Factors of 15: 1, 3, 5 and 15.Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100.Therefore, the HCF of 15 and 100 is 5.
Divide the numerator and denominator by the HCF to reduce the fraction to its simplest form:
[tex]\boxed{\dfrac{15 \div 5}{100 \div 5}=\dfrac{3}{20}}[/tex]
Conclusion0.15 expressed as a fraction in its simplest form is 3/20.
Answer:
See below, please.
Step-by-step explanation:
Write 0.15 as the fraction 15/100.Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of 15 and 100 is 5.Divide both 15 and 100 by 5. This gives 3/20.The resulting fraction 3/20 is in its simplest form, as 3 and 20 have no common factors other than 1.The final answer is 3/20.So the order would be:Write 0.15 as the fraction 15/100.Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of 15 and 100 is 5.Divide both 15 and 100 by 5. This gives 3/20.The resulting fraction 3/20 is in its simplest form, as 3 and 20 have no common factors other than 1.The final answer is 3/20.identify three strategies that the federal government could implement to encourage the use of bevs. assume that the fuel efficiency of the ice vehicle is 235 miles per gallon and that gasoline costs $3.75 per gallon.calculate the cost of gasoline per mile.
Three strategies that implement to encourage the use of BEVs are incentives, Infrastructure and Regulations. The cost of gasoline per mile for an ICE vehicle is $0.016 per mile.
Incentives: The federal government could offer financial incentives such as tax credits, rebates, or grants to consumers who purchase BEVs. This would make BEVs more affordable and help to offset the higher upfront cost of these vehicles.
Infrastructure development: The federal government could invest in the development of charging infrastructure for BEVs, such as public charging stations. This would help to alleviate range anxiety and make BEVs more convenient and practical for consumers.
Regulations: The federal government could implement regulations that incentivize or require automakers to produce more BEVs. This could include emissions standards that are more favorable to BEVs, or mandates for automakers to produce a certain percentage of their vehicles as electric.
To calculate the cost of gasoline per mile for an ICE vehicle with fuel efficiency of 235 miles per gallon and gasoline cost of $3.75 per gallon, we divide the cost of gasoline by the fuel efficiency:
Cost per mile = $3.75 / 235 miles per gallon
Cost per mile = $0.016 per mile
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The function f(x) is defined as f(x) = One-third(6)x. Which table of values could be used to graph g(x), a reflection of f(x) across the x-axis? A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, one-third, 2, 12. The third column is labeled g (x) with entries 12, 2, one-third, one-eighteenth, StartFraction 1 Over 108 EndFraction. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, 0, 2, 12. The third column is labeled g (x) with entries 12, 2, 0, one-eighteenth, StartFraction 1 Over 108 EndFraction. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, one-third, 2, 12. The third column is labeled g (x) with entries negative StartFraction 1 Over 108 EndFraction, negative one-eighteenth, negative one-third, negative 2, negative 12. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, 0, 2, 12. The third column is labeled g (x) with entries negative StartFraction 1 Over 108 EndFraction, negative one-eighteenth, negative one-third, negative 2, negative 12.
Answer:
The correct table of values that could be used to graph g(x), a reflection of f(x) across the x-axis, is:
x f(x) g(x)
-2 1/108 12
-1 1/18 2
0 1/3 1/3
1 2 1/18
2 12 1/108
To reflect a function across the x-axis, we need to change the sign of the y-coordinate for every point on the function. Therefore, to find g(x), we take the negation of f(x) for every value of x. The second column in the third option is the negation of f(x), so it is the correct table of values for g(x).
Answer:
Its A.
Step-by-step explanation:
Other one was not clear enough lol ^
lisa and daisy work at a hair salon. the salon charges $18 fir a hair styling session with lisa and $12 for a session with daisy. the income on a certain day is projected to be $216. this situation can be represented by the equation 18x+12y=216, where x is the number of lisa's customers and y is the number of daisy's customers would lisa need to serve to attain the projected income if daisy calls in sick that day?
Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day
What is linear function ?
A linear function is a mathematical function that can be represented by a straight line on a graph. It has the form of:
y = mx + b
where m is the slope of the line, which determines how steeply the line rises or falls, and b is the y-intercept, which is the point where the line crosses the y-axis.
According to the question:
If Daisy calls in sick, then Lisa will be the only stylist at the salon, and all customers will go to her. Let's use x to represent the number of Lisa's customers. Then the income generated by Lisa's customers can be represented by the equation:
18x = projected income
We can solve for x by dividing both sides of the equation by 18:
x = projected income / 18
Substituting the given projected income of $216, we get:
x = 216 / 18 = 12
Therefore, Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day.
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In the figure, the vertices of ∆ ABC are A ( 0, 6 ), B ( 8, 0 )
and C ( 5, 8 ). If CD ⊥ AB, then find the length of altitude CD.
The length of altitude CD is 133/25 units.
What is the length if altitude?
To find the length of altitude CD, we need to find the length of the line segment CD, which is perpendicular to AB and passes through the point C.
First, let's find the equation of the line AB. We can use the two-point form:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is one of the points on the line. Using points A and B, we get:
m = (0 - 6)/(8 - 0) = -3/4
y - 6 = (-3/4)(x - 0)
y = (-3/4)x + 6
Next, let's find the slope of the line CD, which is the negative reciprocal of the slope of AB. This is because perpendicular lines have slopes that are negative reciprocals of each other. Therefore:
m_CD = 4/3
Now we can use the point-slope form to find the equation of line CD. We know that the line passes through point C (5, 8), so:
y - 8 = (4/3)(x - 5)
Simplifying, we get:
y = (4/3)x - 4/3 + 8
y = (4/3)x + 20/3
Now we need to find the intersection of line CD with line AB. We can solve the system of equations:
y = (-3/4)x + 6
y = (4/3)x + 20/3
Setting the two expressions for y equal to each other, we get:
(-3/4)x + 6 = (4/3)x + 20/3
Multiplying both sides by 12, we get:
-9x + 72 = 16x + 80
25x = -8
x = -8/25
Substituting this value of x into either equation, we get:
y = (-3/4)(-8/25) + 6 = 57/25
Therefore, the point of intersection is (-8/25, 57/25).
Finally, we can use the distance formula to find the length of CD, which is the distance between C and the point of intersection:
d = √[(5 - (-8/25))² + (8 - 57/25)²]
d = √[(125/25 + 8/25)² + (200/25 - 57/25)²]
d = √[(133/25)² + (143/25)²]
d = √(17689/625)
d = 133/25
Therefore, the length of altitude CD is 133/25 units.
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the sampling distribution becomes approximately normal, for all statistics, if there is a large enough sample size. a. false b. true
The given statement "the sampling distribution becomes approximately normal, for all statistics, if there is a large enough sample size" is True as it is proved by the central limit theorem.
The central limit theorem (CLT) states that for large enough sample sizes, the distribution of the sample means approximates a normal distribution regardless of the shape of the initial population distribution.
It is a statistical theory that clarifies how the mean of a random sample of independent observations drawn from a non-normal population converges in distribution to a normal population.
According to this theory, the sample size should be at least 30 for the sample mean to have an approximately normal distribution. The following are the fundamental assumptions of the central limit theorem:
A large enough sample size is requiredPopulation must be random and independentThe variance of the population must be finiteThe sampling must be done with replacement.Therefore, we can say that the sampling distribution becomes approximately normal, for all statistics, if there is a large enough sample size. The statement is true.
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Kira has $2.20 in dimes and quarters. If the number of dimes
is the number of quarters, how many dimes does she have?
Answer:
There are 2 dimes in the purse that contains $2.20
What is an equation?
An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
Let quarters be = x
The dimes be = 1/4 * x
25x+10x/4 = 220
(100x + 10x) /4 = 220
110x/4 = 220
110x = 220*4
110x = 880
x = 880/110
x = 8
The dimes be = 1/4 * x
The dimes be = 1/4 * 8
The dimes be = 2
Step-by-step explanation:
Pls ad brainliest!!!
Write a cosine function that has an amplitude of 3, a midline of y = 4 and a period of 2/3
Answer:
[tex]y=3cos(3\pi x)+4[/tex]
Step-by-step explanation:
[tex]f(x)=cos(x)\\[/tex]
[tex]A(f(Bx+C)+D)[/tex]
The outside constants, A & D stretch and shift vertically. The inside constants, B & C stretch and shift horizontally. B & C work oppositely, basically multiplying by B stretches by a factor of 1/B and similarly adding C shifts f(x) horizontally to the left.
[tex]f(x)=cos(x) \text{ The function which we are transforming}\\\text{It currently has a amplitude of 1, time period of $2\pi$ and mid line at $y=0$}[/tex]
[tex]A=3 \text{ As we want to stretch it by 3 units vertically.}\\\text {To find B:}\\T' = T*(1/B)\\\text{Where $T'$ is new time period and T is existing time period}\\2/3=2\pi*(1/B)\\B=3\pi\\\text{C is not needed}\\D=4 \text{ To shift function by 4 units up}[/tex]
I hope this helps
Help open up a jewelry store, Tom borrowed money from an online lending company He took out a personal, amortized loan for 44,000, at an interest rate of 6. 25\% with monthly payments for a term of 7 years For each part, do not round any intermediate computations and round your final answers to the nearest cent necessary, refer to the list of financial formulas (a) Find Tom's monthly payment (b) Tom pays the monthly payment each month for the full term , his total amount to repay the () Tom pays the monthly payment each month for the full termfind the total amount of interest he will pay
Tom will pay a total of $13,424.20 in interest over the term of the loan.
The formula to calculate the monthly payment for an amortized loan is given by: `P = r(PV) / [1 - (1 + r)^(-n)]`Where P is the monthly payment, r is the interest rate per month, PV is the present value of the loan, and n is the number of payments or the total number of months.
Substituting the given values, we get:P = 0.0052083333 × 44,000 / [1 - (1 + 0.0052083333)^(-7×12)]P = 632.32Therefore, Tom's monthly payment is $632.32 (rounded to the nearest cent).b. Since Tom pays the monthly payment each month for the full term, his total amount to repay the loan is equal to the present value of the loan.
Therefore, the total amount to repay the loan is $44,000 (rounded to the nearest cent).c. The total amount of interest paid over the term of the loan can be calculated as the difference between the total amount repaid and the principal amount of the loan.
Therefore, the total interest paid is: Total interest paid = Total amount repaid - Principal amount of the loan Total interest paid = $57,424.20 - $44,000Total interest paid = $13,424.20
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If you have 4 purple marbles and 8 yellow marbles in a bag. What is the probability of getting a purple marble
You have a 4/12 probability.
The directions and example is in the photo, I really need help with this stuff
The height of the BD for the house using Pythagorean theorem is obtained as: 4.23 m.
Explain about the Pythagorean theorem?According to the Pythagorean Theorem, for any triangle which is a right triangle, the squares of the legs added together equal the square of the hypotenuse.
In the given triangle ABC.
AB = BC = 6 cm
So, ∠A = ∠C (by isosceles triangle)
Then, AD = DC = 8.5/2
So, in right angles triangle ABD, applying Pythagorean theorem:
AB² = AD² + BD²
6² = (8.5/2)² + BD²
36 - 18.0625 = BD²
BD = √17.9375
BD = 4.23
Thus, the height of the BD for the house using Pythagorean theorem is obtained as: 4.23 m.
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If the limit as n goes to infinity of the quotient of the absolute value of the quantity a sub n plus 1 times the n plus 1 power of the quantity x minus 7 and the absolute value of the product of a sub n and the nth power of x minus 7 for the power series the summation from n equals 1 to infinity of a sub n times the nth power of the quantity x minus 7, then what is the interval over which the power series converges absolutely? You do not need to consider the endpoints.
In conclusion, the power series converges absolutely over an interval given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex]is a natural number.
The interval over which the power series converges absolutely is given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex] is a natural number.
In other words, for any given N, the series will converge absolutely over the interval \left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n>N.
This means that the series will converge absolutely over a larger interval as N increases, since the terms \frac{\left|a_n+1\right|}{\left|a_n\right|} get closer to 1 for larger values of n.
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A castle has to be guarded 24 hours a day. Five knights are ordered to split each day's guard duty equally. how long will each knight spend on guard duty in one day???? Please help I am very stuck on this
Answer:
Step-by-step explanation:
If there are five knights and they need to divide the guard duty equally for the 24 hours in a day, each knight would spend 24/5 = 4.8 hours on guard duty in one day.
However, since it's not possible to guard for a fraction of an hour, they would need to round that number to the nearest whole number. In this case, each knight would spend 5 hours per day on guard duty.
A quadratic equation is usually written in the form ax² + bx+c = 0. What are a, b, and c for the following quadratic equations? Separate your answers with a comma. (a) 13x²14x + 5 = 0 a, b, c (b) 5x² 13x - 10 = 0 (c) x² - 4 = 0 (d)-9x² = 0
Answer:
a) a is 13
b is 14
c is 5
b) a is 5
b is 13
c is-10
c) a is 1
b is 0
c is -4
d) a is -9
b is 0
c is 0
Step-by-step explanation:
hope this will be helpful:)
This is due tomorrow so please help me ASAP! Thanks!
The value of the given lengths are as follows:
a.) KL = 11.1ft
LO = 5.7ft
b.) m<OMN = 45°
How to calculate the missing length of the given triangles?For Side LO ;
7/11 = 7√2/7√2+LO
7(7√2+LO) = 11×7√3
69.3+7LO = 108.9
7LO = 108.9-69.3
LO = 39.6/7
LO = 5.7 ft
For KL ;
This can be solved using the Pythagorean theorem;
c²= b²+a²
C = 5.7+7√2 = 15.6
b = 11
a²= 15.6²-11²
= 243.36 - 121
= 122.36
a= √122.36
a= 11.1ft
For angle OMN;
This can be solved using SOHCAHTOA.
Sin∅ = opposite/hypotenuse
opposite = 7
hypotenuse = 7√2
sin∅ = 7/7√2
sin∅ = 0.707106781
∅= sin-1 0.707106781
∅ = 45°
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assume that 20% of criminal suspects who agree to take lie detector tests are actually guilty while 80% of those who agree to take the test are innocent. of those who are guilty, 70% fail the lie detector test. of those who are innocent, only 15% fail the test. suppose a person is arrested and takes a lie detector test. given that the person fails the test, what is the probability that the person is actually innocent?
The probability that the person is actually innocent given that they have failed the test is 0.4615... or approximately 0.462.
The question asks us to calculate the probability that the person is actually innocent given that they have failed the test. The probability that the person is actually innocent is given by the formula: P(innocent | fails test) = P(innocent and fails test) / P(fails test).
Now we need to calculate the values of the probabilities on the right-hand side of this equation. P(fails test) is equal to the sum of the probabilities that a guilty person fails the test and that an innocent person fails the test. Hence, P(fails test) = P(guilty and fails test) + P(innocent and fails test). P(guilty and fails test) = 0.2 × 0.7 = 0.14P(innocent and fails test) = 0.8 × 0.15 = 0.12. Therefore, P(fails test) = 0.14 + 0.12 = 0.26.
Finally, we can calculate the probability that the person is actually innocent given that they have failed the test: P(innocent | fails test) = P(innocent and fails test) / P(fails test)= 0.12 / 0.26= 0.4615 (rounded to four decimal places).
Therefore, the probability that the person is actually innocent given that they have failed the test is 0.4615... or approximately 0.462.
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please help me and I will give a branlist.
The vertices of the image of QRTW for a dilation with center (0, 0) and a scale factor of 1/4 include the following:
Q' (-0.5, 0.75).
R' (-0.75, 0.25).
T' (0.5, -0.25).
W' (0.25, 1).
What is dilation?In Mathematics and Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/4 centered at the origin (0, 0) as follows:
Ordered pair Q (-2, 3) → Ordered pair Q' (-2 × 1/4, 3 × 1/4) = (-0.5, 0.75).
Ordered pair R (-3, 1) → Ordered pair R' (-3 × 1/4, 1 × 1/4) = (-0.75, 0.25).
Ordered pair T (2, -1) → Ordered pair T' (2 × 1/4, -1 × 1/4) = (0.5, -0.25).
Ordered pair W (2, 4) → Ordered pair W' (2 × 1/4, 4 × 1/4) = (0.25, 1).
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A bank offers a CD that pays a simple interest rate of 11. 0%. How much must you put in this CD now in order to have $2500 for a home-entertainment center in 6 years. The present value that must be invested to get $2500 after 6 years at an interest rate of 11. 0% is $__?
The present value that must be invested to get $2500 after 6 years at a simple interest rate of 11.0% is $1509.64.
In this case, we know the final amount that we want to have after 6 years, which is $2500. We also know the interest rate, which is 11.0%. What we need to find is the principal amount, which is the present value that we must invest now to achieve the desired future value.
Using the formula for simple interest, we can rearrange it to solve for the principal:
Principal = Simple Interest / (Rate x Time)
We know that the simple interest is the difference between the final amount and the principal amount. Therefore, we can substitute the values into the formula:
$2500 - Principal = (Principal x 0.11 x 6)
Simplifying the equation, we get:
$2500 = Principal + (0.66 x Principal)
$2500 = 1.66 x Principal
Dividing both sides by 1.66, we get:
Principal = $1509.64
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if the area of a circle is less than $60\pi$ square inches, what is the greatest possible integer value in inches of the radius of the circle?
The greatest possible integer value of the radius of the circle is 7 inches.
The area of a circle is given by the equation[tex]$A = \pi r^2$[/tex]. We know that the area is less than [tex]$60\pi$[/tex] square inches, so the equation can be written as [tex]$60\pi > \pi r^2$[/tex]. We can solve for the radius by dividing both sides by [tex]$\pi$[/tex], which gives us [tex]$60 > r^2$[/tex]. Taking the square root of both sides gives us [tex]$r < \sqrt{60}$[/tex], which is approximately 7.74 inches. Therefore, the greatest possible integer value of the radius of the circle is 7 inches.
To explain this further, we can start with the equation for the area of a circle, which is[tex]$A = \pi r^2$[/tex]. Since the area is less than [tex]$60\pi$[/tex]square inches, this equation can be rewritten as[tex]$60\pi > \pi r^2$[/tex]. We can then divide both sides by [tex]$\pi$[/tex] to get [tex]$60 > r^2$[/tex]. Taking the square root of both sides gives us [tex]$r < \sqrt{60}$[/tex]. This result can then be rounded down to the nearest integer, which is 7. Therefore, the greatest possible integer value of the radius of the circle is 7 inches.
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At a school of 550 children 80% walk to school
If at a school of 550 children 80% walk to school, the 110 children come to school by other means.
If 80% of the children walk to school, then the remaining 20% of children must arrive at school by other means (such as being driven by a parent, taking public transportation, etc.).
To find out how many children come to school by other means, we can use the following formula:
Number of children who come to school by other means = Total number of children x Percentage who don't walk to school
In this case, we have:
Number of children who come to school by other means = 550 x 20% = 110
Therefore, 110 children come to school by other means.
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The given question is incomplete, the complete question is:
At a school of 550 children 80% walk to school, how many comes in other way ?