A large milling machine shaves 2-in. from a plate that is 1 in. thick. What is the thickness of the plate after one pass? What is the thickness of the plate after three passes?
Answers
The thickness of the plate after one pass is 1 21/ 32 and after three pass is 1 7/32 in.
How to convert mixed fractions?A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
An inappropriate fraction is created by adding the numerator to a mixed fraction after multiplying the denominator of the proper fraction by the whole number it is related to.
How change a fraction into a mixed fraction?
By denominator, divide the numerator.
Take the quotient as a whole number and use the remaining amount as the proper fraction's numerator while maintaining the original denominator.
Given that the thickness of the plate is 1 7/8 in.
Convert the mixed fraction into improper fraction:
1 7/8 = 15/8
The machine shaves of 7/32 in, thus after one pass we have:
15/8 - 7/32
Take the LCM:
60/32 - 7/32 = 53/32
Covert the fraction into mixed fraction:
53/32 = 1 21/ 32 in
After three passes through the machine the thickness of the plate is:
15/8 - 3(7/32)
60/32 - 21/32 = 39/32
Covert into mixed fraction:
39/32 = 1 7/32 in
Hence, the thickness of the plate after one pass is 1 21/ 32 and after three pass is 1 7/32 in.
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The correct question is:
Related Questions
#7. Tyler llenó su bañera, se bañó y luego drenó la bañera. La función B da la profundidad del agua,
pulgadas, t minutos después de que Tyler comenzó a llenar la bañera.
Explique el significado de cada declaración en esta situación.
a. B(0) = 0
b. B(1)
C. B(9) = 11
d. B(10) = B(22)
e. B(20) > B(40)
Answers
The explanation of each statement in each given situation is given below:
How to solve for thisa. B(0) = 0
depth in inches 0 minutes after filling began is 0; that is at time =0; depth =0
b. B(1) < B(7)
B(1) represents the function one minus after filling began
c. B(9) = 11
depicts that the depth in inches of water 5 minutes after filling is 11
d. B(10) = B(22)
depicts that the depth in inches of water 10 minutes after filling began is 22.
e. B(20) > B(40)
represents the function 20 minutes after filling began
These are the required answers
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The question translated in English is: "#7. Tyler filled his tub, took a shower, and then drained the tub. Function B gives the depth of the water,
inches, t minutes after Tyler started filling the tub.
Explain the meaning of each statement in this situation.
to. B(0) = 0
b. B(1) C.B(9) = 11
d. B(10) = B(22)
and. B(20) > B(40)"
The frequency of people compared to the number of monthly text messages sent and received by a class are shown in the histogram.
A histogram titled Daily Text Messages. The x-axis is labeled Number of Sent Texts and has intervals of 1 to 15, 16 to 30, 31 to 45, 46 to 60, 61 to 75, 76 to 90, and 91 to 105. The y-axis is labeled Frequency and starts at 0, with tick marks every 2 units up to 12. There is a shaded bar for 1 to 15 that stops at 1, for 31 to 45 that stops at 3, for 46 to 60 that stops at 4, for 61 to 75 that stops at 4, for 76 to 90 that stops at 5, and for 91 to 105 that stops at 8. There is no shaded bar for the 16 to 30 interval.
Which of the following best describes the shape of the data, and why?
The data is symmetric because the majority of students sent fewer than 45 text messages.
The data is symmetric because some students have phones and some do not.
The data is skewed because most text messages are replied to and cause the number to be at least twice what it was originally.
The data is bimodal because the popular number of text messages to send is between 91 and 105.
Answers
The data is symmetric because some students have phones and some do not. The correct option is B.
What does histogram mean?A histogram is a simplified representation of the distribution of numerical data. The phrase was first used by Karl Pearson at the outset.
Rectangles are used in a histogram, a type of visual representation of statistical data, to show how frequently data points occur throughout a range of subsequent numerical intervals of equal width.
In the most common sort of histogram, the independent variable and dependent variable are shown along the horizontal axis and the vertical axis, respectively.
The histogram is a frequently used graphing tool. It is used to summarize data that is measured on an interval scale, whether it be continuous or discontinuous.
It is widely applied to give the primary properties of the data distribution a practical way to be illustrated.
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Answer: B. The data is symmetric because some students have phones and some do not.
Step-by-step explanation:
Polaris, the North Star, is very important in navigation because it does not appear to move in the sky.
True
False
Answers
a two-tailed test is a hypothesis test in which the rejection region is . a. only in the upper tail of the sampling distribution b. in both tails of the sampling distribution c. in one tail of the sampling distribution d. only in the lower tail of the sampling distribution
Answers
A two-tailed test is a hypothesis test in which the rejection region is option (B) in both tails of the sampling distribution
The hypothesis test is defined as the statistic approach checking the results of a research study support a particular theory when we apply that result to population
A two-tailed test is a hypothesis test that defined in which the critical area of the distribution is two sided, so the sample will be greater than or less than a certain range of values
Therefore, the rejection region of a two-tailed test is a hypothesis test is in both tails of the sampling distribution.
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solve the problem and then click on the correct answer choice. jane must select 3 different items for each dinner she will serve. the items are to be chosen from among 5 different vegetarian and 4 different meat selections. if at least one of the selections must be vegetarian, how many different dinners can jane create?
Answers
Jane can select 80 different types of dinner consisting of 3 different items from 5 different vegetarian items and 4 different meat items available.
For finding the various combination of dinners available which has atleast one vegetarian item we will apply combination formula with the given data i.e., [tex]^{n} C_{r} = \frac{n!}{(n-r)!.r!}[/tex]
A combination is a way of selecting items from a collection where the order of selection does not matter.
We will have to apply the formula separately for vegetarian and meat items.
Combinations available
A. 1 vegetarian item and 2 meat items
[tex]^{5} C_{1} and ^{4} C_{2}[/tex] (In combination "and" means to multiply)
= [tex]\frac{5!}{(5-1)!.1!} . \frac{4!}{(4-2)!.2!}[/tex]
= [tex]\frac{5!}{(4)!.1!} . \frac{4!}{(2)!.2!}[/tex]
= [tex]\frac{5.4.3.2.1}{(4.3.2.1).(1)}. \frac{4.3.2.1}{(2.1).(2.1)}[/tex]
= 5.3.2
= 5.6
= 30
B. 2 vegetarian items and 1 meat item
[tex]^{5} C_{2} and ^{4} C_{1}[/tex]
= [tex]\frac{5!}{(5-2)!.2!} . \frac{4!}{(4-1)!.1!}[/tex]
= [tex]\frac{5!}{(3)!.2!} . \frac{4!}{(3)!.1!}[/tex]
= [tex]\frac{5.4.3.2.1}{(3.2.1).(2.1)}. \frac{4.3.2.1}{(3.2.1).(1)}[/tex]
= 5.2.4
= 10.4
= 40
C. 3 vegetarian items and no meat item
= [tex]^{5} C_{3} and ^{4} C_{0}[/tex]
= [tex]\frac{5!}{(5-3)!.3!} . \frac{4!}{(4-0)!.0!}[/tex]
= [tex]\frac{5.4.3.2.1}{(2.1).(3.2.1)}. 1[/tex]
= 5.2
= 10
Now, we will add all the different combination
Total combinations = 30+40+10
= 80 different type of dinners
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three numbers a, b, and c between 0 and 1 are selected independently and at random. what is the probability that these numbers appear in increasing order?
Answers
The probability of selecting three numbers in increasing order is 1/3, which means that in one out of every three trials, we will select three numbers in increasing order.
Probability is a branch of mathematics that deals with the measurement of the likelihood or chance of an event occurring. In this problem, we are asked to find the probability of selecting three numbers in increasing order from a range of 0 to 1.
Let's compute the probability of selecting three numbers in increasing order. Since the total number of possible outcomes is infinite, we need to use a continuous probability distribution to compute the probability. In this case, we can use the uniform distribution, which assumes that each number between 0 and 1 is equally likely to be selected.
The probability of selecting "a" as the smallest number is a/1 = a.
The probability of selecting "a" as the largest number is (1-a)/1 = 1-a.
The probability of selecting "a" as the middle number is 2(1-a)a, which is the product of the probability of selecting "a" and the probability of selecting "b" or "c" from the remaining range.
Therefore, the probability of selecting three numbers in increasing order is the sum of these probabilities:
P(increasing order) = ∫₀¹ (a * (1 - a) + (1 - a) * a + 2a(1 - a))da
P(increasing order) = ∫₀¹ 2a(1 - a)da
P(increasing order) = 2∫₀¹ a - a²da
P(increasing order) = 2[(a²/2) - (a³/3)] from 0 to 1
P(increasing order) = 2[(1/2) - (1/3)] = 1/3
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Ken has just retired. His Roth IRA has a present value of $524,856.00 and has an interest rate of 3.4%, compounded annually. In addition, he receives a yearly pension of $32,615.12. Given that Ken plans to draw from his Roth IRA for the next fifteen years, find his total annual income.
Answers
Ken total annual income is $ 55,401.98.
What has compounded annually?
The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound and simple interest is this.
The completely randomized design, in which participants are assigned to treatment groups at random, is the most basic type of experimental design. The main benefit of using this method is that it minimizes the influence of chance and eliminates bias. This approach makes use of probability theory, which gives statistical analysis a strong foundation.
Given that Roth IRA has a present value of $524,856.00. The rate of interest is 3.4% per annum.
A = P(1+r)^t
A = amount
P = principal
r = rate of interest
t = time
The amount after 15 years is
A = 524,856.00(1+3.4%)¹⁵
A = 866658.9925
The total interest is 866658.9925 - 524,856.00 = $341802.99
The average interest per annum is (341802.99 /15) =22786.866
The annual income is 22786.866 + 32,615.12 = 55,401.986
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the city's pr manager, who never took statistics, claimed the mean score of all ninth graders in the city was 81 . of course, that is incorrect. what
Answers
The mean score of all the ninth graders in the city is equal to 81.84 ( round to two decimal places )
Number of schools in the city = 3
Result of the mean score of the ninth grade students are
Glenwood 78 269
Central City 93 321
Lincoln High 66 161
Given mean score by PR manager = 81
Correct mean score is calculated as
= ( 78 × 269 + 93 × 321 + 66 × 161 ) / ( 269 + 321 + 161 )
= ( 20982 + 29853 + 10626 ) / 751
= 61461 / 751
= 81.84 ( round to two decimal places )
Therefore, the mean score of the ninth grade students of all the schools in the city is given by 81.84 ( round to two decimal places ).
The above question is incomplete , the complete question is:
In a city with three high schools, all the ninth graders took a Standardized Test, with these results: High School Mean score on test Number of ninth graders
Glenwood 78 269
Central City 93 321
Lincoln High 66 161
The city's PR manager, who never took statistics, claimed the mean score of all ninth graders in the city was 81 . Of course, that is incorrect.
a. What is the mean score for all ninth graders in the city? Round to two decimal places.
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subsitute (-3,3) 2y+x=3 y=x+0
Answers
Answer:
Point (-3, 3) is not a solution to the system of equations
2y+x=3
y=x+0
Step-by-step explanation:
2y + x = 3
y = x + 0
2(3) + (-3) = 3
6 - 3 = 3
3 = 3
The point works in the first equation.
3 = -3 + 0
3 = -3
The point does not work in the second equation.
My parents give me an allowance of $60 every month. To earn some extra money I get a job. I make $7.50 an hour at this job. In order to have a social life and hang out with my friends, I am going to need at least $260 every month.
What is the APPROXIMATE minimum amount of hours I will have to work to accomplish my goal? (HINT: use whole numbers for your answer)
Answers
I would need to work at least 27 hours to make enough money to reach my goal.
What are arithmatic operations?
Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.
Let's start by finding the amount of money I receive from my allowance and how much more money I need to make to reach my goal:
Allowance per month = $60
Amount of money I need for social life = $260
Additional amount of money I need to make = $260 - $60 = $200
Now, let's divide the additional amount of money I need to make by the amount I make per hour to find how many hours I need to work:
$200 ÷ $7.50 per hour = 26.67 hours
Since we can't work a fraction of an hour, we need to round up to the nearest whole number.
Therefore, I would need to work at least 27 hours to make enough money to reach my goal.
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in the sketch A is an x-intercept and B is the turning point of the parabola, f(x) =ax^2+bx+c the straight line AB is defined as g(x) =3x+6.D(-1\3:35/6) is a point of f and CD is perpendicular to t x-axis B in the y intercept of f and g
Determine the coordinates of B
Answers
The required coordinates of B are (0, 6) for the given parabola.
What is x-Intercept?The x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses.
To determine the coordinates of B, we can use the information given in the problem.
A is an x-intercept, which means that the y-coordinate of A is 0, and it can be found by setting x = 0 in the equation for f(x).
The line AB is g(x) = 3x + 6. This line is a straight line and it is perpendicular to the x-axis at B, which means that the x-coordinate of B is 0.
Therefore, we can set x = 0 in both equations to find the y-coordinate of B.
For f(x), we have:
f(0) = a × 0² + b × 0 + c = c
For g(x), we have:
g(0) = 3 × 0 + 6 = 6
Since the line AB passes through the turning point B, we know that the y-coordinate of B is equal to both f(0) and g(0). Therefore, we have:
c = 6
So, the coordinates of B are (0, 6).
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Find sin a + cos a if sin a * cos a = 3/8
Answers
The value of sin a + cos a is √7/2.
Trigonometric identities:Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
Based on the right-triangle theorem, which is known as Pythagoras theorem, there are three Pythagorean trigonometric identities in trigonometry as follows
sin² a + cos² a = 11+tan² a = sec² acosec² a = 1 + cot² aHere we have
sin a × cos a = 3/8
Multiply with 2 on both sides
=> 2(sin a × cos a) = 2(3/8)
=> 2 sin a cos a = 3/4
Add sin²a + cos²a on both sides
=> sin²a + cos²a + 2 sin a cos a = 3/4 + sin²a + cos²a
As we know (a + b)² = a²+ b² + 2ab
=> (sin a + cos a)² = 3/4 + 1
=> (sin a + cos a)² = 7/4
=> sin a + cos a = √7/2
Therefore,
The value of sin a + cos a is √7/2.
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Select all the angle relationships in △
△
ABC that are correct.
Answers
In ΔABC, we can conclude that m∠A < m∠C and m∠B < m∠A < m∠C. Hence, options a. and d. are the accurate solutions.
The angle opposite to the longest side of the triangle is the largest angle of the triangle, similarly, the angle opposite to the smallest side of the triangle is the smallest angle of the triangle.
In the given ΔABC, we have,
The longest side = AB = 3.1
The angle opposite to side AB = m∠C
The smallest side = AC = 2.9
The angle opposite to side AC = m∠B
side CB = 3
The angle opposite to side CB = m∠A
We have,
side AC < side CB < side AB
m∠B < m∠A < m∠C
From the given relations in the options provided, we get,
a. m∠A < m∠C
d. m∠B < m∠A < m∠C
are correct interpretations.
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The complete question is -
Select all the angle relationships in △ABC that are correct.
What is the value of
3/10^3
Answers
Answer:
c
Step-by-step explanation:
9/10
Clarissa cycled at 12 1/2 miles per hour for 2 1/2 hours. How far did she travel?
Answers
She travel 31.25 miles we calculate it by multiply by speed and time
Speed indicates how quickly something or someone is moving. If you know how far something has travelled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in metres per second (m/s) in this example because the distance is measured in metres (m) and the time is measured in seconds (s).The formula can be rearranged in three ways:
speed = distance ÷ time
distance = speed × time
time = distance ÷ speed
To calculate one of the variables (speed, distance or time) we need the other two.
As given in Question she cycled at speed 12 1/2 miles per hours
12 1/2 can be written as 12.5 miles per hours
and she cycled for 2 1/2 hours which can be written as 2.5 hours
and to find the distance how much she total travel we have to multiply the speed and time
distance = 12.5x2.5 = 31.25 miles
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A water sample shows 0.04 grams of some trace element for every cubic centimeter of water. Samir uses a container in the shape of a right cylinder with a radius of 8.1 cm and a height of 17.9 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Samir collected? Round your answer to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
To find the volume of the container, we can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height. Plugging in the given values, we get:
V = π * 8.1^2 * 17.9 = 1146.4 cm^3
Since the sample contains 0.04 g of the trace element per cubic centimeter of water, the amount of trace element in the entire container can be found by multiplying the volume of the container by the concentration of the trace element:
0.04 g/cm^3 * 1146.4 cm^3 = 45.86 g
So Samir has collected approximately 45.9 g of the trace element, rounded to the nearest tenth.
Answer:147.6g
Step-by-step explanation
Pls show your work thank you will mark the Brainliest
Answers
Answer:
second option
Step-by-step explanation:
an exponential function modelling the situation has the form
y = a [tex](b)^{x}[/tex]
to find a and b use ordered pairs from the table
using (0, 11000 )
11000 = a [tex](b)^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ] , then
a = 11000 , so
y = 11000 [tex]b^{x}[/tex]
using (1, 9350 )
9350 = 11000 [tex]b^{1}[/tex] = 11000b ( divide both sides by 11000 )
[tex]\frac{9350}{11000}[/tex] = b
b = 0.85
then exponential function is
y = 11000 [tex](0.85)^{x}[/tex]
Which of the following is equal to √16 x 4
A. √16 x √4
B. 32
C. √16/4
D. 64
Answers
Answer:
None
Step-by-step explanation:
Let's clarify that a radical symbol beside a number means what number squared (or to the power of 2) can give me the number in the symbol.
In this case it would be 4 because
[tex]4*4=16[/tex]
A method I use is to find the square root is dividing the number in the radical symbol 2 times
First by the original number, and then by the product of the last equation. It will not always work, but it works in some cases like this one.
[tex]\frac{16}{2} = 8\\ \\\frac{8}{2}=4\\ \\\sqrt{16}=4[/tex]
Second step, multiply 4 by 4, which equals 16.
Since the square root of 16 is 4, you can substitute 4 in the rest of the equations instead of the radical expression.
None of the following equations equal 16, which means none of the following equations if equal to [tex]\sqrt{16} *4[/tex]
Let A={2,4,6} and B={135}
R={(2,2),(4,4),(6,6)} is a relation on A. Express the relation
Answers
The relation:
{x = y : x, y ε A}.
And this relation is a function.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given:
A={2,4,6} and B={135}
R={(2,2), (4,4), (6,6)} is a relation on A.
That means, each value of set A connects to the same point.
The relation:
{x = y : x, y ε A}
Hence, {x = y : x, y ε A}.
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y=-1/2x-1
y=1/4x-4
graphing method
Answers
The solution of the system of equations is (4, -3)
How to solve the system of equations graphically?Here we want to solve the next system of equations:
y = -(1/2)x - 1
y = (1/4)x - 4
Graphically.
To do so, we just need to graph both of these lines on the same coordinate axis and find the point where the lines intersect. Below is the graph of the system of equations, there we can see that the lines intersect at the point (4, -3), so that is the solution of the system.
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8 more than the quotient of a number b and 25 is greater than 6
Answers
When eight more than the quotient of a number 'b' and 25 is greater than 6 then the inequality representing the value of b is b > -50.
The expression used to represents :
Quotient of a number b and 25 is equal to b / 25
Next step is :
8 more than the b / 25 is equal to ( b / 25 ) + 8
Then ,
( b / 25 ) + 8 is greater than 6 is given by
⇒ ( b / 25 ) + 8 > 6
Simplify the above inequality for 'b' we get,
⇒ ( b / 25 ) > 6 - 8
⇒ ( b / 25 ) > -2
Multiply both the side by 25 we get,
⇒ b > - 2 × 25
⇒ b > -50
Therefore, the inequality representing the value of 'b' for the condition of quotient and a number is equal to b > -50.
The above question is incomplete , the complete question is:
8 more than the quotient of a number b and 25 is greater than 6 , then the value of b is ?
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A procedure for using sample data to find the estimated regression equation is
a. point estimation. b. interval estimation.
c. the least squares method. d. extrapolation.
Answers
Option C. the least squares method is a procedure for using sample data to find the estimated regression equation.
The procedure for using sample data to find the estimated regression equation is called the least squares method. This method involves finding the line that minimizes the sum of the squared vertical distances between the observed data points and the line. The estimated regression equation is used to predict the value of the dependent variable based on the value of the independent variable. This method is commonly used in regression analysis to model the relationship between two variables. It is a useful tool for making predictions and understanding the relationship between variables.
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the multiple linear regression predictive model is thus: and the least squares optimization target is we can find the least squares solution by finding the gradient of with respect to and setting it to zero: what kind of object is ? a real number a vector with the same size as . a matrix of the same size as . a vector with the same size as . unanswered what is ? . . . unanswered savesave your answer submit you have used 0 of 3 attempts
Answers
Object is kind of a vector with the same size as the coefficients in the linear regression model.
In the least squares optimization target, the sum of squared errors (SSE) is typically minimized with respect to the coefficients of the linear regression model. The gradient of the SSE with respect to the coefficients is a vector that provides the direction of steepest ascent, or the direction in which the SSE increases the most rapidly. Setting this gradient vector to zero and solving for the coefficients yields the least squares solution to the linear regression problem.
Therefore, in this context, " " is likely a vector of coefficients that are being optimized to minimize the SSE.
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hat
The distance around a circle is 36
meters long. What is the diameter of the
circle?
Answers
Answer: [tex]36/\pi[/tex] or approximately 11.4592
Step-by-step explanation:
The distance around a circle equals its circumference.
The circumference equation is: C = 2[tex]\pi[/tex] * r where r = radius.
Now, we know that the distance around the circle is 36 so C = 36
Using the equation, we have 36= 2[tex]\pi[/tex]*r
Now, we solve for r by dividing by 2[tex]\pi[/tex] to both sides.
r = [tex]36/2\pi[/tex] which equals [tex]18/\pi[/tex] which is approximately 5.7296
Now, since radius is half of the diameter, we need to multiply this by 2.
This finally gives us the answer of diameter = [tex]36/\pi[/tex] which is approximately 11.4592
raven is planning a bridal shower for her best friend. at the party, she wants to serve 3 beverages, 3 appetizers, and 2 desserts, but she does not have time to cook. she can choose from 19 bottled drinks, 12 frozen appetizers, and 8 prepared desserts at the supermarket. how many different ways can raven pick the food and drinks to serve at the bridal shower?
Answers
To get the total number of different ways, multiply 1,536 x 18 = 7,344.
7,344 different ways. Raven has 19 choices for drinks, 12 choices for appetizers, and 8 choices for desserts. The formula for calculating the number of different ways is 19 x 12 x 8 = 1,536. Since Raven needs to pick 3 drinks, 3 appetizers, and 2 desserts, the formula is 3 x 3 x 2 = 18. To get the total number of different ways, multiply 1,536 x 18 = 7,344.
The formula can be used to calculate the number of different ways to combine any number of choices. For example, if Raven had 24 choices for drinks, 15 choices for appetizers, and 7 choices for desserts, the formula would become 24 x 15 x 7 = 3,240. If Raven still had to pick 3 drinks, 3 appetizers, and 2 desserts, the total would be 3 x 3 x 2 = 18. Multiplying 3,240 x 18 = 57,720 different ways.
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Answers
X^2-4x+2=x+2
Then we will have
X1= 0
X2= 5
For finding y
Y=x+2
1) y=0+2, y=2
2) y= 5+2, y=7
So we will have the final answer:
(X1,y1)= (0,2)
(X2,y2)= (5,7)
Answer:
i think it x = 0 and x = 5
Step-by-step explanation:
[tex]y = {x}^{2} - 4x + 2[/tex]
[tex]y = x + 2[/tex]
[tex]x + 2 = {x}^{2} - 4x + 2[/tex]
[tex]0 = {x}^{2} - 4x + 2 - x - 2[/tex]
[tex]0 = {x}^{2} - 5x[/tex]
[tex]0 = x(x - 5)[/tex]
[tex]x = 0[/tex]
(or)
[tex]x - 5 = 0[/tex]
[tex]x = 5[/tex]
Let a function f A B be defined by f(x) 11 B-1-2, 1, 0,2- 4¹5) 0. can you make it one to one and onto both? x-1 F x*-2 with A = {-1, 0, 1, 2, 3, 4) and x+2 find the range off. Is the function one to one and onto both? If not, how a whother each of the functions below is one to one, onto both?
Answers
Answer:
The function f: A -> B is defined by:
f(x) = { 11, if x = -1 or x = 2,
-1, if x = 0,
-2, if x = 1,
0, if x = 3 or x = 4 }
The range of the function is the set of all possible values of f(x). In this case, the range of f is B = {-2, -1, 0, 11}.
To determine if the function is one-to-one, we need to check if each element in the range has only one pre-image. In other words, we need to check if no two elements in A map to the same element in B. Since each element in B has a unique pre-image in A, the function is one-to-one.
To determine if the function is onto, we need to check if each element in B is the image of some element in A. In this case, every element in B is the image of exactly one element in A, so the function is onto.
Therefore, the function f is one-to-one and onto both.
A company makes short-sleeved and long-sleeved T-shirts. The company checks a random sample of 60 T-shirts of each type. It finds that 4 short-sleeved shirts have problems and 1 long-sleeved shirt has problems. How many T-shirts should the company predict have problems in a shipment of 3,000 shirts of each type?
Answers
The company should predict that there will be an estimated 201 short-sleeved T-shirts and 51 long-sleeved T-shirts with problems in a shipment of 3,000 shirts of each type.
To predict the number of T-shirts with problems in a shipment of 3,000 short-sleeved and 3,000 long-sleeved T-shirts, we can use the proportion of T-shirts with problems in the random sample as an estimate of the proportion of T-shirts with problems in the population.
For short-sleeved T-shirts, the proportion of T-shirts with problems in the sample is 4/60 = 0.067. For long-sleeved T-shirts, the proportion of T-shirts with problems in the sample is 1/60 = 0.017.
To estimate the number of short-sleeved T-shirts with problems in a shipment of 3,000, we can multiply the proportion by the total number of short-sleeved T-shirts in the shipment:
Estimated number of short-sleeved T-shirts with problems = 0.067 x 3,000 = 201
Similarly, to estimate the number of long-sleeved T-shirts with problems in a shipment of 3,000, we can multiply the proportion by the total number of long-sleeved T-shirts in the shipment:
Estimated number of long-sleeved T-shirts with problems = 0.017 x 3,000 = 51
Therefore, the company should predict that there will be an estimated 201 short-sleeved T-shirts and 51 long-sleeved T-shirts with problems in a shipment of 3,000 shirts of each type.
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Where n = 1: 1 + 6 = 7, so 7 would go in the first box.
Where n = 2: 2 + 6 = 8, so 8 would go in the second box.
Where n = 3: 3 + 6 = 9, so 9 would go in the third box.
This pattern can be continued for other positional values as well!
What coordinates did we plot when we graphed the function y = 3x - 4?
You should have 4 answers selected.
1. (-1, -7)
2. (-1, 8)
3. (0, -4)
4. (0, 9)
5. (1, -1)
6. (2, 2)
Answers
The solution is, (-1, -7), (0, -4), (1, -1), satisfies the graph function, the coordinates did we plot when we graphed the function y = 3x - 4
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
we graphed the function y = 3x - 4
now, the required coordinates are, which satisfies the graph function.
as, we get,
(-1, -7), satisfies the graph function
(0, -4) , satisfies the graph function
(1, -1), satisfies the graph function
Hence, The solution is, (-1, -7), (0, -4), (1, -1), satisfies the graph function, the coordinates did we plot when we graphed the function y = 3x - 4
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