Answers
(13) Angle A, angle B and angle C are collinear and are proved.
(14) Based on corresponding angles theorem, X is bisector of angle A.
What is the proof that A, B, C are collinear?The sum of the measures of collinear angles is always 180 degrees, as they together form a straight angle.
If we consider triangle PCQ;
Since line CP = line CQ; then angle P = angle Q = x
m∠PCQ = 180 - 2x
If we consider triangle PBQ;
Since line PB = line BQ; then angle P = angle Q = x
m∠PBQ = 180 - 2x
If we consider triangle PAQ;
Since line AP = line AQ; then angle P = angle Q = x
m∠PAQ = 180 - 2x
Thus, angle A, angle B and angle C are collinear.
14. To prove that X is a bisector A;
Draw a line parallel to AN from point B to opposite side, call this point Y
Angle formed from line M to line BY, is a corresponding angle to angle formed from line M to line AN.
If X is the bisector of angle B, then it is also a bisector angle A since both angles are equal.
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Related Questions
HELP PLS EXPLAIN THISSSSS
Answers
Plugging in the values given into the expression, and simplifying, we would have our answer as: B. [tex]\frac{9}{25}[/tex]
How to Evaluate an Expression?To evaluate an expression, follow these steps:Identify the variables and constants in the expression.Substitute the given values for each variable in the expression.Simplify the expression until there are no more operations left.Given that, a = 5 and k = -2, substitute the values into the expression given and simplify:
[tex](\frac{3^2(5^{-2})}{3(5^{-1})} )^{-2}[/tex]
Simplify:
[tex](\frac{9 * \frac{1}{25} }{3* \frac{1}{5} } )^{-2}[/tex]
[tex](\frac{\frac{9}{25} }{\frac{3}{5} } )^{-2}\\\\(\frac{9}{25} * \frac{5}{3} } )^{-2}\\\\(\frac{3}{5} )^{-2}\\\\ = \frac{9}{25}[/tex]
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carmen bought 3 cds that were each the same price. including sales tax, she paid a total of $49.50. each cd had a tax of 0.70 . what was the price of each cd before tax?
Answers
If Carmen paid a total of $49.50 for 3 CD's, then the price of each CD before the tax is $15.80.
The "Sales-Tax" is $0.70 per CD, which is added to the original price of each CD to arrive at the total cost of the CDs including sales tax
Let the price of each CD before tax be = "x",
Carmen bought 3 CDs, so the total cost of the CDs without tax would be 3x.
The "Sales-Tax" on each CD is $0.70, and Carmen bought 3 CDs,
The "total-sales" tax will be = 3 × $0.70 = $2.10,
So, the "total-cost" of the CDs including sales tax is "3x + $2.10", and
We know this total cost is = $49.50,
The equation to represent the cost is written as :
⇒ 3x + $2.10 = $49.50
Now, Solving for "x", the price of each CD before tax.
⇒ 3x = $49.50 - $2.10
⇒ 3x = $47.40
⇒ x = ($47.40)/3,
⇒ x ≈ $15.80
Therefore, the price of each CD is $15.80.
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Solve the following problem. Be sure to show all the steps (V. E. S. T. ) and work in order to receive full credit.
The sum of three numbers is 26. The second number is twice the first and the third number is 6 more than the second. Find the numbers.
Please help due tomorrow
Answers
The three numbers are 4, 8, and 14.
Let's use variables to represent the three numbers
Let x be the first number.
Then the second number is twice the first, so it is 2x.
The third number is 6 more than the second, so it is 2x + 6.
We know that the sum of the three numbers is 26, so we can write an equation:
x + 2x + (2x + 6) = 26
Now we can solve for x
5x + 6 = 26
5x = 20
x = 4
So the first number is 4.
To find the second number, we can use the equation we wrote earlier:
2x = 2(4) = 8
So the second number is 8.
To find the third number, we can use the other equation we wrote earlier
2x + 6 = 2(4) + 6 = 14
So the third number is 14.
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When Jose had cable TV, he had 120 channels. He switched to satellite TV, and now he has 300 channels. What is the percent increase in the number of channels Jose has to watch? Round to the nearest percent.
Answers
The percent increase in the number of channels Jose has to watch is 150%.
What is percent?To find the percent increase in the number of channels Jose has to watch, we need to find the difference between the new number of channels and the old number of channels, divide that by the old number of channels, and then multiply by 100 to get the percentage increase.
The difference between the new and old number of channels is 300 - 120 = 180.
Dividing that by the old number of channels and multiplying by 100 gives us:
(180/120) x 100% = 150%
Therefore, the percent increase in the number of channels Jose has to watch is 150%. This means that Jose now has 150% more channels to watch than he did before he switched to satellite TV.
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Last year, Big Bill's Department Store sold many pairs of shoes: 118,214 pairs of boots were sold; 37,092 more pairs of sandals than pairs of boots were sold; and 124,417 more pairs of sneakers than pairs of boots were sold.
How many pairs of shoes were sold last year?
Answers
Answer:279,723
Step-by-step explanation: 124,417+118,214+37,092=279,723
James decided to share rocks collection. He gave 13 to Bill, 18 to lill, and 15 to mark. He had 32 left. How many rocks did he have to start with
Answers
James started with 78 rocks, as he gave away 46 rocks and had 32 rocks left.
The problem states that James gave away 13 rocks to Bill, 18 rocks to Lill, and 15 rocks to Mark. Therefore, the total number of rocks he gave away is the sum of these three amounts
13 + 18 + 15 = 46
This means that James had 46 fewer rocks after giving them away. The problem also states that he had 32 rocks left after giving some away. We can use this information to figure out how many rocks he started with by adding the number of rocks he had left to the number he gave away
46 + 32 = 78
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As a nurse working in a hospital one of the jobs is to give appropriate doses of medicine
before surgery so the patient doesn't wake up during surgery. 4cc of this particular medicine is
meant for a 180lb man, what would be the correct dosage for a 145 lb. woman?
Answers
Answer:
the correct dosage of the medicine for a 145 lb. woman would be approximately 3.22 cc
Step-by-step explanation:
To calculate the correct dosage of the medicine for a 145 lb. woman, we can use the following formula:
dosage = (weight of patient / weight of reference patient) x reference dosage
where the weight of the reference patient is 180 lb. and the reference dosage is 4 cc.
Plugging in the given values, we get:
dosage = (145 / 180) x 4
= 3.22 cc (rounded to two decimal places)
Therefore, the correct dosage of the medicine for a 145 lb. woman would be approximately 3.22 cc. However, it's important to note that dosages of medications should only be determined by a qualified medical professional based on a number of factors, including the patient's weight, medical history, and current condition.
Circle A has radius AB and Circle X has radius XY. Points A and X are distinct points. Complete the statements below describing how to prove that the circles are similar.
Translate the center of circle A onto point __ __.
Then dilate the image of circle A about its center by a scale factor of __ __.
Answers
Translate the center of circle A onto point X.Then dilate the image of circle A about its center by a scale factor of XY/AB.
What is circle?A circle is a geometric shape consisting of points in a plane that are equidistant from a fixed point called the center, forming a closed curve.
According to the given information :
To prove that circles A and X are similar, we can follow the steps below:
1) Translate the center of circle A onto point X. This can be done by moving the center of circle A to point X while keeping the radius AB the same.
2) Dilate the image of circle A about its center by a scale factor of XY/AB. This means that we multiply the radius of the image of circle A by XY/AB. The result is a new circle that is similar to circle A and has the same center as circle X.
To summarize, the statements to complete are:
Translate the center of circle A onto point X.
Then dilate the image of circle A about its cent er by a scale factor of XY/AB.
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Translate the center of circle A onto point X.Then dilate the image of circle A about its center by a scale factor of XY/AB.
What is circle?
A circle is a geometric shape consisting of points in a plane that are equidistant from a fixed point called the center, forming a closed curve.
According to the given information :
To prove that circles A and X are similar, we can follow the steps below:
1) Translate the center of circle A onto point X. This can be done by moving the center of circle A to point X while keeping the radius AB the same.
2) Dilate the image of circle A about its center by a scale factor of XY/AB. This means that we multiply the radius of the image of circle A by XY/AB. The result is a new circle that is similar to circle A and has the same center as circle X.
To summarize, the statements to complete are:
Translate the center of circle A onto point X.
Then dilate the image of circle A about its center by a scale factor of XY/AB.
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Need the answer to question 15
Answers
An equation in slope-intercept form for the perpendicular bisector of the segment with endpoints H (-3, 2) and K (7, -5) is y = -0.7x - 0.1.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-5 - 2)/(7 + 3)
Slope (m) = -7/10
Slope (m) = -0.7.
At data point (-3, 2) and a slope of -7/10, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 2 = -7/10(x + 3)
y - 2 = -7x/10 - 21/10
y = -7x/10 - 21/10 + 2
y = -0.7x - 0.1
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in a recent basketball game, shenille attempted only three-point shots and two-point shots. she was successful on 20% of her three-point shots and 30% of her two-point shots. shenille attempted 30 shots. how many points did she score?(2013 amc 12a
Answers
The probability of a score for a recent basketball game, shenille attempted only three-point shots and two-point shots is 18 points in the game. The answer is Option B.
Let x be the number of three-point shots and y be the number of two-point shots attempted by Shenille.
Then, we have:
x + y = 30 (total number of shots attempted)
Let's solve for one of the variables. For example, we can solve for x by subtracting y from both sides of the equation:
x = 30 - y
Now, we can express Shenille's points in terms of x and y:
Points = 3x + 2y
Substituting x = 30 - y, we get:
Points = 3(30 - y) + 2y
Points = 90 - y
Shenille's success rate for three-point shots is 20%, so the number of successful three-point shots she made is 0.2x. Similarly, the number of successful two-point shots she made is 0.3y.
Total points scored = (0.2x)(3) + (0.3y)(2)
Substituting x = 30 - y, we get:
Total points scored = (0.2(30 - y))(3) + (0.3y)(2
Total points scored = 18 + 0.4y
Now we need to maximize the total points scored by Shenille. Since she attempted 30 shots in total, we have:
y = 30 - x
Substituting this into the equation for total points, we get:
Total points scored = 18 + 0.4(30 - x)
Total points scored = 30 - 0.4x
This is a linear function, which is maximized at its endpoint. The maximum value of this function occurs at x = 0, which means Shenille attempted all two-point shots. In this case, y = 30, and the total points scored would be:
Total points scored = 0 + 0.3(30)(2)
Total points scored = 18
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The question is -
In a recent basketball game, Shenille attempted only three-point shots and two-point shots. She was successful on 20% of her three-point shots and 30% of her two-point shots. Shenille attempted 30 shots. How many points did she score?
(A) 12
(B) 18
(C) 24
(D) 30
(E) 36
A car travels 3 miles in 5 minutes. A subway train travels 4 miles in 6 minutes. How much longer does it take to travel 7 miles in the slower vehicle
Answers
The slower vehicle is the car, and it would take (11.67 - 10.5) = 1.17 minutes longer to travel 7 miles compared to the subway train.
To find out how much longer it would take to travel 7 miles in the slower vehicle, we need to calculate the speed of
each vehicle first.
The car travels 3 miles in 5 minutes, which means it travels at a speed of 3/5 miles per minute.
The subway train travels 4 miles in 6 minutes, which means it travels at a speed of 4/6 miles per minute. Simplifying
this, we get a speed of 2/3 miles per minute.
Now, we can calculate how long it would take each vehicle to travel 7 miles:
The car travels at a speed of 3/5 miles per minute, so it would take (7 / (3/5)) = 11.67 minutes to travel 7 miles.
The subway train travels at a speed of 2/3 miles per minute, so it would take (7 / (2/3)) = 10.5 minutes to travel 7 miles.
Therefore, the slower vehicle is the car, and it would take (11.67 - 10.5) = 1.17 minutes longer to travel 7 miles compared to the subway train.
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90%; n = 10; σ is unknown; population appears to be normally distributed
Answers
With 90% confidence, we can estimate that the true population mean lies between 13.96 and 16.04.
If the population appears to be normally distributed, and σ (population standard deviation) is unknown, we can use a t-distribution to calculate the confidence interval.
To find the confidence interval, we need to use the following formula
CI = X' ± t_(α/2, n-1) × (s/√n)
Where X' is the sample mean, t_(α/2, n-1) is the critical t-value based on the desired confidence level (α) and the sample size (n-1), s is the sample standard deviation, and √n is the square root of the sample size.
Given that we have a confidence level of 90%, α = 0.10, and we need to find the critical t-value for a two-tailed test with 10-1=9 degrees of freedom. Using a t-distribution table, we find that the critical t-value is approximately 1.833.
Assuming that we have a sample mean of X' = 15 and a sample standard deviation of s = 2, we can now calculate the confidence interval
CI = 15 ± 1.833 × (2/√10)
CI = 15 ± 1.04
CI = (13.96, 16.04)
Therefore, with 90% confidence, we can estimate that the true population mean lies between 13.96 and 16.04.
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A rectangular plece of paper with length 28 cm and width 14 cm has two semicircles cut out of it, as shown below. Find the area of the paper that remains. Use the value 3.14 for 1, and do not round your answer. G ✓6 14 cm 0 00 H cm X 2023 McGraw Hill LLC As Rights Reserve
Answers
The area of the paper remains is 238.14 cm².
What is area?Area is the region bounded by a plane shape.
To calculate the area of the paper that remains, we use the formula below.
Formula:
Area of the paper that remains(A) = Area of the rectangle(LW)-Area of the two semi circles [π(W/2)²]A = LW- [π(W/2)²]................ Equation 1Where:
L = Length of the rectangleW = Width of the rectangle = Diameter of the semi circleFrom the diagram in the question,
Given:
L = 28 cmW = 14 cmSubstitute these values into equation 1
A = (28×14)-[3.14(14/2)²A = 392-153.86A = 238.14 cm²Hence, the area is 238.14 cm².
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the in song the twelve days of christmas, my true love gave to me first 1 gift, then 2 gifts and 1 gift, then 3 gifts, 2 gifts and 1 gift, and so on. how many gifts did my true love give me all together during the twelve days?
Answers
In a song the twelve days of christmas, my true love gave to me, then total number of possible gifts that my true love give me all together during the twelve days is equal to the 364.
We have There are twelve days of Christmas in a song and my true love gives me presents every day. We have to calculate total number of gifts my true love give me all together during the twelve days. Now, according to the song, on the first day of Christmas my true love gave me: a partridge on a pear tree 1 gift. On the second day of Christmas, my love really gave me: two doves and a gift. cake etc. Mathematically, gifts by true love are written as 1+2+3+... n gifts per day. Number of gifts per day: 1 to 1, 2 to 3, 3 to 6 and 4 to 10. The amount of mis N (N + 1) (N + 2) / 6. Number of parts This form is called tetrahedral number. Change the value N = 12, then N (N + 1) (N + 2) / 6
= 12 × 13 × 14 / 6
= 364
Hence, 364, the total number of gifts, almost one for each day of the year.
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Find the volume of the prism.
The volume is
cubic feet.
Answers
Answer: 8/125 or 0.064
Step-by-step explanation:
volume of a cube is w^3
(2/5)*(2/5)*(2/5)
8/125 or 0.064
The data for the height and weight of different people was collected the line of best fit for this date it was determined to be Y equals 0. 9 1X -65. 5 where X is the height in centimeters and why is the weight in kilograms is in the equation predict the height of a person who weighs 63 kg
Answers
According to the equation, a person who weighs 63 kg is predicted to be approximately 141 centimeters tall.
The equation given is Y = 0.91X - 65.5, where X represents the height in centimeters and Y represents the weight in kilograms. To predict the height of a person who weighs 63 kg, we need to solve for X, the height in centimeters.
To do this, we can plug in the given weight of 63 kg for Y in the equation and then solve for X. So, we have:
63 = 0.91X - 65.5
Adding 65.5 to both sides, we get:
63 + 65.5 = 0.91X
Simplifying, we have:
128.5 = 0.91X
Finally, to solve for X, we divide both sides by 0.91, giving:
X = 141.21
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call a positive integer kinda-prime if it has a prime number of positive integer divisors. if there are $168$ prime numbers less than $1000$, how many kinda-prime positive integers are there less than $1000$?
Answers
There are 173 kinda-prime positive integer less than 1000.
To find the number of kinda-prime positive integer less than 1000, we'll follow these steps:
1. Understand the definition of a kinda-prime number: A positive integer is kinda-prime if it has a prime number of positive integer divisors.
2. Determine the number of prime numbers less than 1000: There are 168 prime numbers less than 1000, as given.
3. Determine the possible prime number of divisors: Since 168 is not too large, we only need to consider 2 and 3 as possible prime numbers of divisors for a kinda-prime number.
4. Analyze the cases:
Case 1: Kinda-prime numbers with 2 divisors (prime numbers)
All prime numbers have exactly 2 divisors (1 and itself). Thus, all 168 prime numbers less than 1000 are kinda-prime.
Case 2: Kinda-prime numbers with 3 divisors
Let N be a kinda-prime number with 3 divisors. Then, N = p^2 for some prime number p. To find the suitable prime numbers p, we need[tex]p^2 < 1000[/tex]. The prime numbers that meet this condition are 2, 3, 5, 7, and 11 (since 13^2 = 169 > 1000). Therefore, there are 5 additional kinda-prime numbers ([tex]2^2, 3^2, 5^2, 7^2, and 11^2[/tex]).
5. Add the total number of kinda-prime numbers from both cases: 168 + 5 = 173.
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[tex]$(\pi(1000)-1)+11=\boxed{177}$[/tex] "kind a-prime" positive integers less than $1000$.
Let [tex]$n$[/tex] be a positive integer with[tex]$k$[/tex] positive integer divisors.
If [tex]$k$[/tex] is prime, then.
[tex]$n$[/tex] is a "kind a-prime" integer.
[tex]$k$[/tex] must be of the form.
[tex]$k=p$[/tex] or [tex]$k=p^2$[/tex] for some prime [tex]$p$[/tex].
If [tex]$k=p$[/tex], then [tex]$n$[/tex] must be of the form.
[tex]$p^{p-1}$[/tex] for some prime [tex]$p$[/tex]. Since [tex]$p < 1000$[/tex], there are.
[tex]$\pi(1000)$[/tex]possible values of [tex]$p$[/tex].
[tex]$p=2$[/tex] gives [tex]$2^1$[/tex], which is not prime, so we have to subtract.
[tex]$1$[/tex] from [tex]$\pi(1000)$[/tex] to get the number of possible.
[tex]$p$[/tex].
[tex]$\pi(1000)-1$[/tex] values of [tex]$p$[/tex] that give a "kind a-prime" integer of this form.
If [tex]$k=p^2$[/tex], then [tex]$n$[/tex] must be of the form.
[tex]$p^{p^2-1}$[/tex] for some prime[tex]$p$[/tex].
There are.
[tex]$\pi(31)=11$[/tex] primes less than [tex]$31$[/tex], and each of them gives a different "kind a-prime" integer of this form.
Since [tex]$31^5 > 1000$[/tex], no primes larger than [tex]$31$[/tex]can be used to form a "kind a-prime" integer of this form.
[tex]$11$[/tex] possible values of [tex]$p$[/tex] that give a "kind a-prime" integer of this form.
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From a horizontal distance of 80.0 m, the angle to the top of a flagpole is 18°. Calculate the height of the flagpole to the nearest tenth of a meter.
1. 24.7 meters
2. 76.1 meters
3. 26.0 meters
4. 25.3 meters
Answers
Answer:
The figure is omitted--please sketch it to confirm my answer.
Set your calculator to degree mode.
Let h be the height of the flagpole.
[tex] \tan(18) = \frac{h}{80} [/tex]
[tex]h = 80 \tan(18) = 25.994[/tex]
The height of the flagpole is approximately 26.0 meters. #3 is correct.
Evaluate the expression when x = 7 (4x + 9) - 4(x - 1) + x use the answer choices in the diagram
Answers
Answer:
The answer is 20
Step-by-step explanation:
when x=7
(4x+9)-4(x-1)+x
(4(7)+9)-4(7-1)+7
28+9 -4(6)+7
37+7-24
44-24
=20
If r=0.5 m, A = ???
(Use the r key.)
Answers
The calculated value of the angular velocity of the object is 2 rad/s.
Calculating the angular velocityThe angular velocity, denoted by the Greek letter omega (ω), represents the rate of change of the angle with respect to time.
For an object moving in a circular path, the angular velocity is related to the linear speed and the radius of the circle by the equation:
ω = v/r
where v is the linear speed and r is the radius.
In this case, the radius is 0.5m and the speed is 1ms−1. Thus, the angular velocity is:
ω = v/r = 1/0.5 = 2 radians per second (rad/s)
Therefore, the angular velocity of the object is 2 rad/s.
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Complete question
An object moves in a circular path of radius 0.5m with a speed of 1ms−1. What is its angular velocity (A)?
If r = 0.5 m, A = ???
Given the following code fragment, which of the following expressions is always true?
int x;
scanf("%d", &x);
A) if( x = 1)
B) if( x < 3)
C) if( x == 1)
D) if((x/3) > 1)
Answers
If the expressions given, only C) if( x == 1) is always true.
In the given code fragment, the value of x is read from the user using the scanf() function. The value of x can be any integer value, depending on what the user enters. After the value of x is read, the program checks the value of x using a conditional statement (if statement) and executes the code inside the if statement only if the condition is true.
Expression A) if( x = 1) assigns the value 1 to x and then checks if x is true. This means that the condition is always true, because the assignment operation (=) returns the assigned value (in this case, 1), which is a non-zero value and therefore considered true in C programming.
Expression B) if( x < 3) checks if x is less than 3. This expression is not always true, as x can be any value greater than or equal to 3, in which case the condition would be false.
Expression C) if( x == 1) checks if x is equal to 1. This expression is always true if the user enters the value 1 for x.
Expression D) if((x/3) > 1) checks if the integer division of x by 3 is greater than 1. This expression is not always true, as x can be any value less than or equal to 3, in which case the result of the integer division by 3 would be 1 or less, in which case the condition would be false.
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the only expression that is always true in this code fragment is option C) if( x == 1).
The expression that is always true in this code fragment is option C) if( x == 1).
Option A) if( x = 1) is not always true because it is an assignment statement instead of a comparison statement. It assigns the value 1 to x instead of checking if x is equal to 1.
Option B) if( x < 3) is also not always true because x could be any number less than 3.
Option D) if((x/3) > 1) is not always true because x could be any number less than or equal to 3, in which case the expression would evaluate to false.
Therefore, the only expression that is always true in this code fragment is option C) if( x == 1).
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Find the surface area and the volume of the cement block in the figure shown.
Answers
The surface area and volume of cement block is 1336 in² and 880 in³
What is Surface area of Cuboid ?To find the total surface area of a cuboid, add the areas of all six faces. Suppose l, b and h be the length, breadth and height of a cuboid, then the total surface area will be 2(lb + bh + hl). The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object.
Surface area of given cement block is = 10×8×2+20×10×2+(20×8 - 6×4×3)×2 + 4×10×2×3 +6×10×2×3
= 160 + 400 + 176 + 240 + 360
= 1336 in²
Volume of cement block is 20 × 8× 10 - 3×6×4×10
= 1600 - 720
= 880 in³
Hence, the surface area and volume of cement block is 1336 in² and 880 in³
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What is the slope of the line?
-2
-1
1
2
Answers
Answer: positive 2
Step-by-step explanation:
was solving an equation, but when he checked his answer, he saw his solution was incorrect.
He knows he made a mistake, but he can't find it. Where is Diego's mistake and what is the solution to the equation?
- 4(7 - 2x) = 3(x + 4)
-28-8x = 3x + 12
- 28 = 11x + 12
- 40 = 11x
06
11
ーン
Answers
The solution to the equation is x = 16/11.
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.
Diego's mistake is in the step where he subtracts 3x from both sides of the equation. The correct subtraction should be 28, not 12.
Here's the correct solution:
4(7 - 2x) = 3(x + 4)
28 - 8x = 3x + 12
28 - 12 = 3x + 8x
16 = 11x
x = 16/11
Therefore, the solution to the equation is x = 16/11.
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three machines, a, b, c produce a large number of identical products. 60% of the products come from machine a, 30% from b and 10% from c. historical records indicate that 10% of the parts produced by machine a are defective, compared with 30% for machine b and 40% for machine c. what is the probability that a randomly chosen part is defective?
Answers
The probability that a randomly chosen part is defective is 0.16, or 16%.
The probability that a randomly chosen part is defective, we need to use the law of total probability.
Let [tex]$D$[/tex] be the event that a part is defective and let [tex]$M_i$[/tex] be the event that the part came from machine [tex]$i$[/tex], for [tex]$i = A, B, C$[/tex].
Then we have:
[tex]$P(D) = P(D|M_A)P(M_A) + P(D|M_B)P(M_B) + P(D|M_C)P(M_C)$[/tex]
60% of the products come from machine A, 30% from machine B, and 10% from machine C.
Therefore:
[tex]$P(M_A) = 0.6$[/tex]
[tex]$P(M_B) = 0.3$[/tex]
[tex]$P(M_C) = 0.1$[/tex]
The probability of a part being defective is 10% if it comes from machine A, 30% if it comes from machine B, and 40% if it comes from machine C.
Therefore:
[tex]$P(D|M_A) = 0.1$[/tex]
[tex]$P(D|M_B) = 0.3$[/tex]
[tex]$P(D|M_C) = 0.4$[/tex]
Substituting these values into the law of total probability, we get:
[tex]$P(D) = 0.1 \cdot 0.6 + 0.3 \cdot 0.3 + 0.4 \cdot 0.1 = 0.16$[/tex]
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Eli's house is due west of Yardley and due south of Salem. Yardley is 7 miles from Eli's house and 9 miles from Salem. How far is Salem from Eli's house, measured in a straight line? If necessary, round to the nearest tenth
Answers
By Pythagorean , Eli's home is thus roughly **11.4 miles** from Salem when viewed from a straight line.
Define Pythagorean theorem?A fundamental relationship between a right triangle's three sides in Euclidean geometry is known as the Pythagorean theorem. The hypotenuse is the side that forms the right angle, and the rule says that the square of its length is equal to the sum of the squares of the lengths of the other two sides. In other words, if the hypotenuse is length c and the legs of a right triangle are lengths a and b, then a²+ b² = c² .
Call Yardley Y, Salem S, and Eli's home E. As far as we are aware, Y is located 7 miles from E and 9 miles from S.
We can check that the distance between Eli's house and Salem is the hypotenuse of a right triangle with Yardley as one of the vertices because Eli's house is located due west of Yardley and due south of Salem. The Pythagorean theorem can be used to determine this distance.
Eli's home is 11.4 miles from Salem at a distance of√(7 + 9 ) = √(130).
√(130) = 11.4miles
Eli's home is thus roughly **11.4 miles** from Salem when viewed from a straight line.
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a slide caliper has 32 divisions per inch and a vernier of 8 divisions per major division. for this instrument the smallest resolution and uncertainty are:
Answers
The smallest resolution for this instrument is 1/256 inches.
This is also the instrument's uncertainty, as it represents the smallest measurable increment.
Let's first understand the terms mentioned:
Slide caliper:
A measuring instrument with a main scale and a vernier scale for taking precise measurements.
Divisions per inch:
The number of equal divisions on the main scale in one inch.
Vernier:
A short auxiliary scale that slides along the main scale, allowing for more precise readings.
Divisions per major division:
The number of equal divisions on the vernier scale that correspond to one division on the main scale.
Now, let's determine the smallest resolution and uncertainty for this instrument.
Calculate the main scale resolution
Main scale resolution = 1 inch / 32 divisions per inch = 1/32 inches
Calculate the vernier scale resolution
Vernier scale resolution = Main scale resolution / Vernier divisions per major division = (1/32 inches) / 8 = 1/256 inches.
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For the first half of a baseball season, a player had 90 hits out of 270 times at bat. The player's batting average was
90
270
≈ 0. 333. During the second half of the season, the player had 64 hits out of 276 times at bat. The player's batting average was
64
276
≈ 0. 232. (Round your answers to three decimal places. )
(a) What is the average (mean) of 0. 333 and 0. 232?
Answers
The issue inquires to discover the normal (cruel) of two values:
0.333 and 0.232. To do this, able to essentially include the two values together and partition them by 2. Including the two values gives us:
0.333 + 0.232 = 0.565
Separating by 2 gives us:
0.565 / 2 = 0.2825
So the normal of 0.333 and 0.232 is 0.2825.
In any case, the issue inquires to circular our answer to three decimal places, which suggests we have to be circular 0.2825 to the closest thousandth. The third decimal put maybe a 2, which implies we circular down. Hence, the ultimate reply is roughly 0.283, adjusted to three decimal places.
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6. ____ tales and _____ tales
folk tales are storues with no known creator. they were originally passed down from one generation to another by word of mouth.
fairytales were often created to teach children behavior in an entertaining way.
what is the blank fictions/nonfictions?
Answers
The complete statement is folk tales and fairy tales
Both folk tales and fairy tales are types of fiction because they are imaginative stories that are not based on factual events or characters.
Explaining fictions and nonfictions?Folk tales
Folk tales are stories with no known creator. They were originally passed down from one generation to another by word of mouth. Folk tales are a type of traditional literature that is deeply rooted in the culture of a particular region or community.
They often feature supernatural elements, and their origins can be traced back many centuries.
Because they were passed down orally, different versions of the same tale may have developed in different regions, with variations in characters, plot, and theme.
Fairy tales
Fairy tales were often created to teach children behavior in an entertaining way. Fairy tales are a type of story that typically features magical creatures or events and often have a moral or lesson to teach. They were originally intended for both adults and children and were used as a way to teach moral values, societal norms, and important life lessons in an entertaining way.
The fairy tale genre has evolved over time, and modern fairy tales may have different themes and messages than traditional ones.
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A store is giving out cards labeled 1 through 10 when customers enter the store. If the card is an even number, you get a 10% discount on your purchase that day. If the card is an odd number greater than 6, you get a 40% discount. Otherwise, you get a 25% discount. The table shows the results of 500 customers. What is the relative frequency for each discount? Use pencil and paper. If the manager of the store wants approximately half of the customers to receive the 25% discount, does this seem like an appropriate method? Explain.
Answers
Answer: We can use the data given in the table to calculate the relative frequency of each discount as follows:
- For a 10% discount: 160 customers received even-numbered cards, so the relative frequency is 160/500 = 0.32, or 32%.
- For a 25% discount: 222 customers received odd-numbered cards less than or equal to 6, so the relative frequency is 222/500 = 0.444, or 44.4%.
- For a 40% discount: 118 customers received odd-numbered cards greater than 6, so the relative frequency is 118/500 = 0.236, or 23.6%.
Regarding the question about whether this method will lead to approximately half of the customers receiving a 25% discount, we can see that the relative frequency for a 25% discount is actually higher than the desired 50%. Therefore, this method is not appropriate if the manager wants approximately half of the customers to receive a 25% discount.
To achieve this, the store can change the rule to offer a 25% discount for odd-numbered cards less than or equal to 5 and a 50% discount for odd-numbered cards greater than 5. This will result in the relative frequency for a 25% discount to be close to 50%.
Step-by-step explanation: