The department should offer 80 sections of finite math and 90 sections of applied calculus to fill all sections and accommodate all of the students.
Let x be the number of sections of finite math and y be the number of sections of applied calculus. Then we have:
x + y = 170 (total number of sections offered)
90x + 80y = 14400 (total number of students)
To solve for x and y, we can use elimination or substitution.
Let's use elimination by multiplying the first equation by 80 and subtracting it from the second equation:
90x + 80y = 14400
-80x - 80y = -13600
-----------------
10x = 800
x = 80
Now we can substitute x = 80 into either equation to solve for y:
80 + y = 170
y = 90
Therefore, the department should offer 80 sections of finite math and 90 sections of applied calculus to fill all sections and accommodate all of the students.
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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
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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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?
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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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?
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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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)
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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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
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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bout 1.02 X 102 times farther away from the sun than Mercury.
out how many kilometers is Pluto from the sun?
about 5.91 X 1014 kilometers
about 4.77 X 10⁹ kilometers
about 5.91 X 10⁹ kilometers
about 5.68 x 105 kilometers
wa chose D as the correct answer. How did she get that answer?
Show work
If bout 1.02 X 102 times farther away from the sun than Mercury. The number of kilometers is: C. about 5.91 X 10⁹ kilometers.
How many kilometers is Pluto from the sun?If Pluto is 1.02 x 10² times farther away from the Sun than Mercury, we can use the average distance of Mercury from the Sun, which is approximately 57.91 million km (5.791 x 10⁷ km) to calculate the distance of Pluto from the Sun.
Distance of Pluto from the Sun = (1.02 x 10²) x (57.91 x 10⁶ km)
Distance of Pluto from the Sun = 5.91 x 10⁹ km
Therefore, the correct option is: about 5.91 x 10⁹ kilometers.
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Determine the reduced exact values for the root of f(x) = x^2+10x-5
The reduced exact values for the root of f(x) = x² + 10·x - 5, obtained using the quadratic formula are; x = (-5 + √(30)) and x = (-5 - √(30))
What is the quadratic formula?The quadratic formula is a formula that is used to find the roots of a quadratic equation, by plugging in the coefficients of a quadratic equation into the formula.
The roots of the quadratic function, f(x) = x² + 10·x - 5, can be obtained using the quadratic formula as follows;
The quadratic formula, which can be used to find the roots of the quadratic function, f(x) = a·x² + b·x + c is; x = (-b ± √(b² - 4·a·c))/(2·a)
The function f(x) = x² + 10·x - 5, indicates;
a = 1, b = 10, and c = -5, therefore;
x = (-10 ± √(10² - 4 × 1 × (-5)))/(2 × 1) = (-10 ± √(120))/2
(-10 ± √(120))/2 = (-5 × 2 ± 2 × √(30))/2
(-5 × 2 ± 2 × √(30))/2 = (-5 ± √(30))/2
The roots of the quadratic function are;
x = (-5 + √(30))/2, and x = (-5 - √(30))/2
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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 $1000$?
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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Find the surface area and the volume of the cement block in the figure shown.
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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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?
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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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
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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Please help Which of the following is equal to 2?
Answer:
The third equation is equal to 2.
Step-by-step explanation:
6 times one third is equal to 6 divided by three, which equals two. Using order of operations, 5 times 2 equals 10, and that divided by 5 is 2, so that equation is equal to 2.
from his house, duncan could drive due north to get to his parents' house or he could drive due east to get to his grandparents' house. it is 6 kilometers from duncan's house to his parents' house and a straight-line distance of 9 kilometers from his parents' house to his grandparents' house. how far is duncan from his grandparents' house? if necessary, round to the nearest tenth.
Duncan is approximately 10.8 kilometers away from his grandparents' house, if necessary, rounding to the nearest tenth.
Based on the given information, we can use the Pythagorean theorem to find the distance between Duncan's house and his grandparents' house. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the distance from Duncan's house to his parents' house (6 km) and the distance from his parents' house to his grandparents' house (9 km) form the two shorter sides of the triangle. To find the distance between Duncan's house and his grandparents' house, we will calculate the hypotenuse:
h² = 6² + 9²
h² = 36 + 81
h² = 117
h ≈ 10.8
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Duncan is approximately 6.7 km from his grandparents' house (rounded to the nearest tenth).
We can use the Pythagorean theorem to find the distance between Duncan's house and his grandparents' house.
Identify the triangle
In this problem, we have a right triangle with legs of 6 km (due north) and an unknown length (due east).
The hypotenuse is the straight-line distance of 9 km from his parents' house to his grandparents' house.
Apply the Pythagorean theorem.
The Pythagorean theorem states that a² + b² = c², where a and b are the legs of the triangle, and c is the hypotenuse. In this case, a = 6 km, b = unknown, and c = 9 km.
Solve for the unknown distance (b)
6² + b² = 9²
36 + b² = 81
b² = 81 - 36
b² = 45
b = √45
b ≈ 6.7 km.
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. imagine you had a research question in which you wanted to compare a sample mean to the mean of a population. under these circumstances you would either do a z-test or a one-sample t-test. what key piece of information would be missing if you needed to do a one-sample t-test?
Sample size and sample standard deviation are the key information needed for a single-sample t-test.
In the event that you need to compare the test cruel with the populace cruel, and you perform a single-sample t-test rather than a z-test, the vital piece of data that will be lost is the populace standard deviation.
Within the z-test, the populace standard deviation is known and the standard mistake of the cruel is calculated utilizing the populace standard deviation.
In a single-sample t-test, the populace standard deviation is obscure, and the standard mistake of the cruel is evaluated from the test standard deviation.
Therefore, sample size and sample standard deviation are the key information needed for a single-sample t-test.
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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?
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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Gloria and Seth have each set a goal Gloria plans to walk 30,000 feet each day. Seth plans to walk 6 miles each day. Who plans to walk farther? How many yard father
Thus, from the given data, Seth plans to walk farther as 10560 yards is greater than 10020 yards.
Explain about unit conversion:Unit conversion is the process of translating a measurement from one set of units to a measurement in a different set of units that is equivalent.
The ideas that everything multiplied by one is equal to itself and that anything split by one is equal to itself are the foundational ideas for unit conversions.Conversion factors those fractions when the denominator and numerator are equal, effectively bringing the fraction to a value of 1.Given data:
Gloria walks - 30,000 feet each day.Seth walks - 6 miles each day.-Covert feet into yards-
1 foot = 0.33 yards
30,000 feet = 0.334* 30,000 yards
30,000 feet = 10020 yards
-Covert miles into yards-
1 mile = 1760 yards
6 miles = 6*1760 yards
6 miles = 10560 yards
Thus, from the given data, Seth plans to walk farther as 10560 yards is greater than 10020 yards.
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There are 10 councillors and 12 planning department staff available to serve on a committee to look into re- establishing two way traffic on the streets of St. Catharines. If the committee will consist of 3 councillors and either 1 or 2 planning staff, how many different committees could the council choose?
The council could choose 14,040 different committees.
To form a committee, we need to choose 3 councillors out of 10 and either 1 or 2 planning staff out of 12.
Number of ways to choose 3 councillors out of 10 = 10C3 = (1098)/(321) = 120
Number of ways to choose 1 planning staff out of 12 = 12C1 = 12
Number of ways to choose 2 planning staff out of 12 = 12C2 = (1211)/(21) = 66
Therefore, the total number of different committees that the council could choose is the sum of the number of ways to choose 3 councillors and either 1 or 2 planning staff:
Total number of committees = (Number of ways to choose 3 councillors) x (Number of ways to choose 1 planning staff) + (Number of ways to choose 3 councillors) x (Number of ways to choose 2 planning staff)
Total number of committees = 120 x 12 + 120 x 66
Total number of committees = 14,040
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in a study of the treatment of congestive heart failure (chf), a new surgical procedure was compared to the standard surgical procedure. the study enrolled 550 people with chf and randomly assigned half to receive the new procedure and half to receive the standard procedure. among those that received the new procedure, 98 died within 5 years. among those that received the standard procedure, 190 died within 5 years. what is the result for the appropriate measure to describe the strength of the association between surgical procedure and death?
The result for the appropriate measure, relative risk, is approximately 0.515.
This indicates that the risk of death within 5 years is about 51.5% lower in the new procedure group compared to the standard procedure group.
This suggests a strong association between the surgical procedure and the reduction in the risk of death.
To determine the strength of the association between the surgical procedures and death, we can calculate the relative risk.
Identify the numbers given in the question.
- Total participants: 550
- New procedure group: 275 (half of 550)
- Deaths in new procedure group: 98
- Standard procedure group: 275 (half of 550)
- Deaths in standard procedure group: 190
Calculate the death rate (proportion of deaths) in each group.
- Death rate in new procedure group = (Number of deaths in new procedure group) / (Total in new procedure group) = 98/275 ≈ 0.356
- Death rate in standard procedure group = (Number of deaths in standard procedure group) / (Total in standard procedure group) = 190/275 ≈ 0.691
Calculate the relative risk.
- Relative risk = (Death rate in new procedure group) / (Death rate in standard procedure group) = 0.356/0.691 ≈ 0.515.
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Carlos has 32 iris bulbs and 40 tulip bulbs to plant. He wants to plant them in rows with one
type of bulb in each row. He wants all of the rows to have the same number of bulbs.
Carlos can plant 8 bulbs in each row.
Given that, Carlos is having 32 iris bulbs and 40 tulip bulbs he wants to plant them, he chose to plant them in rows with alternate pattern, also wants all of the rows to have the same number of bulbs.
So, we need to find the number of the rows to have the same number of bulbs,
To find the same we will find the GCF of the two number,
GCF = The GCF is also known as the Highest Common Factor (HCF).
Find the GCF of 32, and 40
32 = 2 × 2 × 2 × 2 × 2
40 = 2 × 2 × 2 × 5
The greatest common factor = 2 × 2 × 2 = 8
Hence, he can plant 8 bulbs in each row.
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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
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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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
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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What is the length of XW and what is the length of WV?
The value of length XW and WV are 20 and 25 respectively.
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. The ratio of corresponding sides of similar triangles are equal.
Therefore XW/VW = XY/XZ
= XW/45 = 24/54
54(XW) = 45× 24
54(XW) = 1080
divide both sides by 54
XW = 1080/54
XW = 20
Therefore WV can be found by subtracting XW for VX
= 45-20 = 25
therefore the value of XW and WV are 20 and 25 respectively.
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evaluate the limit. please help thank you
Answer:
[tex] \frac{(3n + 4)(1 - n)}{ {n}^{2} } = \frac{ - 3 {n}^{2} - n + 4 }{ {n}^{2} } [/tex]
As n approaches infinity, this quotient approaches -3.
A is the correct answer.
What are the vertex, the axis of symmetry, the minimum or the maximum, the domain, and the range of y = −5(x + 2)2 − 8?
The quadratic function y = −5(x + 2)² − 8 has a vertex at (-2, -8),
an axis of symmetry at x = -2,
a maximum value of -8,
a domain of (-∞, ∞),
and a range of (-∞, -8].
A function is a rule that assigns a unique output to every input. In the case of the given quadratic function, y = −5(x + 2)² − 8, the input is the value of x, and the output is the corresponding value of y. Now let's look at the different properties of this function:
Vertex: The vertex is the point on the graph where the function reaches its minimum or maximum value. To find the vertex of the given function, we need to convert it into vertex form, y = a(x - h)² + k. Here, a is the coefficient of the squared term, h and k are the x and y coordinates of the vertex, respectively. By comparing the given function with the vertex form, we get a = -5, h = -2, and k = -8. Therefore, the vertex is (-2, -8).
Axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex of a parabola. For a quadratic function in vertex form, the axis of symmetry is x = h. Therefore, for the given function, the axis of symmetry is x = -2.
Minimum or maximum: The minimum or maximum value of a quadratic function depends on the sign of the coefficient of the squared term. If a is positive, the function has a minimum value, and if a is negative, the function has a maximum value. In the given function, a = -5, which is negative. Therefore, the function has a maximum value. The maximum value is the y-coordinate of the vertex, which is -8.
Domain: The domain of a function is the set of all possible input values for which the function is defined. For the given function, there are no restrictions on the input value of x. Therefore, the domain of the function is all real numbers, or (-∞, ∞).
Range: The range of a function is the set of all possible output values that the function can take. For the given function, since the function has a maximum value of -8 and there are no restrictions on the input values, the range of the function is (-∞, -8].
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coin is heads with probability p and tails with probability 1-p. how many independent flips x until first heads?
The expected number of flips until getting the first heads is equal to the reciprocal of the probability of getting heads on a single flip, which is 1/p.
How to find the probability of flips until getting the first heads?The number of independent flips x until the first heads follows a geometric distribution. In general, the probability of getting the first heads on the kth flip is given by [tex](1-p)^(^k^-^1^)[/tex]p. Thus, the expected value or mean of the geometric distribution is E(x) = 1/p.
This means that on average, we need to flip the coin 1/p times until we get the first heads. For example, if the probability of getting heads is 0.5, then on average we need to flip the coin 2 times until we get the first heads. If the probability of getting heads is 0.1, then on average we need to flip the coin 10 times until we get the first heads.
The geometric distribution is a fundamental concept in probability theory and has many applications in fields such as finance, engineering, and computer science.
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find the missing value of x,y and z
Answer:
x=60
y=30
z=64
Step-by-step explanation:
By using triangle sum theorem, 84+36+x=180
You then isolate the variable, resulting in x=60
x and y are complementary, therefore, x+y=90
Since x is already known, y must be isolated, resulting in 60+y=90 then y=30
By using triangle sum theorem, 86+y+z=180
Since y is already known, z must be isolated, resulting in 86+30+z=180 then z=64
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Answer: 12 and sqaure root of 194
Step-by-step explanation:
solution 1: 12 because if 13 is the missing side length of the hypotenuse then you would do 5^2 - 13^2 which is 169-25 = 144. the square root of 144 is 12
solution 2: the other solution is trying to get the hypotenuse. you would do 5^2 + 13^2 which is 25 + 169.. therefore the sum is 194. the answer would be the square root of 194
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 __ __.
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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the starting sales price of a new car on monticello car lot is normally distributed with a mean of $40,000 and a standard deviation of $5,000. what is the probability that a randomly selected individual will buy a car that costs at least $30,000?
The chance that a randomly selected individual will buy a car that charges at the least $30,000 is 0.9772, or approximately 97.72%.
To clear up this problem, we need to discover the probability that a randomly selected person will purchase a vehicle that prices as a minimum $30,000, given that the starting income rate of a new automobile on the Monticello vehicle lot is usually dispensed with a mean of $forty,000 and a preferred deviation of $5,000.
We can use the same Standard normal distribution to solve this problem with the aid of changing the beginning sales price of $30,000 to a z-score, and then using a standard normal distribution table or calculator to discover the corresponding opportunity.
The z-rating for a starting sales rate of $30,000 is:
z = (30,000 - 40,000) / 5,000 = -2
Using a standard normal distribution table or calculator, we will locate that the opportunity of a z-score less than or identical to -2 is approximately zero.0228.
But, we need to find the possibility that the starting sales price is at the least $30,000, so we want to subtract this chance from 1:
P(X ≥ 30,000) = 1 - P(X < 30,000)
P(X ≥ 30,000) = 1 - 0.0228
P(X ≥ 30,000) = 0.9772
Therefore, the chance that a randomly selected individual will buy a car that charges at the least $30,000 is 0.9772, or approximately 97.72%.
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What is the mode for the data set? 49, 47, 46, 40, 48, 41, 44, 49, 45, 42, 43
Answer:
49
Step-by-step explanation:
The mode is the number that appears most often in a set of data. In this case, 49 appears twice while all the other numbers only appear once.