19. There are 18 more students in the 7th grade class than the number x in the 8th grade class. The 7th
grade class has 140 students. Write and solve an equation to find x, the number of students in the
8th grade class.
The number of students in the 8th grade class = 122
In this question, we have been given the number of students in the 8th grade class = x
The 7th grade class has 140 students.
Also, we have been given, there are 18 more students in the 7th grade class than the number x in the 8th grade class.
So, from given information we get an equation,
x + 18 = 140
We need to find the value of x i.e., the number of students in the 8th grade class.
We solve above equation,
x + 18 = 140
x = 140 - 18
x = 122
Therefore, the number of students in the 8th grade class = 122
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the coordinate of an object is given as a function of time by x = -2 12t, where x is in meters and t is in seconds. its average velocity over the interval from t = 1 to t = 6 s is
The average velocity of an object between two points can be determined by the following equation:
Average velocity = Δx/Δt
where Δx is the change in position or displacement of the object over the time interval Δt.
Here, the coordinate of an object is given as a function of time by x = -2 12t, where x is in meters and t is in seconds. Its average velocity over the interval from t = 1 to t = 6 s is calculated as follows:
Substituting t = 1 in the given equation x = -2 12t,x = -2 12(1) = -2 12 = -24 m
Substituting t = 6 in the given equation x = -2 12t,x = -2 12(6) = -2 72 = -144 m
Therefore, the change in position or displacement is given by Δx = (-144) - (-24) = -120 m. The time interval Δt between
t = 1 s and t = 6 s is given by Δt = 6 - 1 = 5 s. Therefore, the average velocity of the object over the time interval from t = 1 to t = 6 s is: Average velocity = Δx/Δt = (-120) / (5) = -24 m/s. The correct answer is -24.
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you and your friend are saving money to go on an end-of-the-year school trip. You have $25 in your savings account and add $15 each week. Your friend has $10 in a savings account and adds $15 each week.
a) Write a system of linear equations that represents the amounts of money y (in dollars) in each savings account after x weeks.
b) Will there be a day which you and your friends have the same amount of money in your savings accounts? Explain.
c) If your friend were able to add $29 each week, would there be a day when you and your friend have the same amount of money in your savings accounts? Explain.
a)
b) no, you will never be able to have the same amount because you started off with $25, and the friend started with $10. and you both are putting the same amount away each week which is $15.
c) also no, because although you started off with more, it was $10 more only while the friend is putting in almost twice as much as you each week.
write the equivalent fractions for 4/9 and 10/11 using the least common denominator
Answer:
4/9 = 44/99
10/11 = 90/99
Step-by-step explanation:
44/99=90/99
Answer:
Step-by-step explanation:
4/9 = 8/18 or 36/81
10/11= 20/22 or 30/33
solve for b 1/4(b-8)=2. I hope you have time to answer this. Thank you so much for your time you guys make me so happy
Answer:
16
Step-by-step explanation:
1/4(b-8)=2
b-8=2/(1/4)
b-8=2(4/1)
b-8=8
b=8+8
b=16
Answer:
b=16
Step-by-step explanation:
1/4(b-8)=2
(b-8)=2(4)
b-8=8
b=8+8
b=16
Check
1/4(16-8)=2
1/4(8)=2
2=2
ANSWER FAST PLZ!! what does it look like when you take the cumulative exam? Can they see your screen or if you are on your phone? How many questions are there? Plz help, I will help you with whatever you need in return!
you are skiing down a mountain with a vertical height of 1250 feet. the distance that you ski as you go from the top down to the base of the mountain is 3050 feet. find the angle of elevation from the base to the top of the mountain. round your answer to a whole number as necessary. degree
Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.
What is polynomial?
A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.
Here,
When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.
This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.
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31. One serving of party drink is comprised of 3oz of syrup, 4oz of water, and 3oz of apple juice. If a large bowl of the drink contains 237oz of apple juice, how much of the total drink is in the bowl
Answer:
790 oz
Step-by-step explanation:
Ratio:
3oz syrup : 4oz water : 3oz apple juice: 1 serving: 10oz total mixture
We know there is 10oz total mixture because 3oz of syrup + 4oz of water + 3oz of apple juice = 10oz total mixture
We want to find
237oz apple juice: ?oz total mixture
To do this, we can multiply the ratio
3oz apple juice: 10oz total mixture by 237/3, because 237/3 * 3 = 237, getting us to 237oz apple juice on one side and maintaining the ratio so that we can find the total mixture amount, so we have
237oz apple juice: 10*237/3 oz total mixture = 10*79 = 790 oz
if x=-1, x^5+x+4+x^3+x
Answer:
-2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
x⁵ + x⁴ + x³ + x
x = -1
Step 2: Evaluate
Substitute in variable: x⁵ + x⁴ + x³ + x = (-1)⁵ + (-1)⁴ + (-1)³ - 1Exponents: x⁵ + x⁴ + x³ + x = -1 + 1 - 1 - 1Add/Subtract: x⁵ + x⁴ + x³ + x = -2help i hate math pls
Answer:
31.5
cubic inches of sand will fit in the container because 4.5 x 3.5 • 2 = 31.5in.^3
While on the trip to Galveston the boys got
hungry and sent Spencer to the store. Spencer
paid $9.03 for 2.1 pounds of flounder. What was
the price per pound Spencer paid for the
flounder?
Answer:
4.3 dollars per pound
Step-by-step explanation:
price / pound = ?
$9.03 / 2.1 lbs. = 4.3
r.i.p walter wallace Jr
7. show that if a ≡ b (mod m) and c ≡ d (mod m), where a, b, c, d, and m are integers with m ≥ 2, then a − c ≡b − d (mod m) (10 pts).
We can prove this statement using the definition of congruence. According to the definition of congruence, a ≡ b (mod m) means that a - b is divisible by m.
Similarly, c ≡ d (mod m) implies that c - d is divisible by m. Therefore, we can write:
a - b = km
c - d = lm
where k and l are integers. Then we can add the two equations together to get:
a - c = (k + l)m
which implies that a - c is divisible by m, thus a - c ≡ b - d (mod m). This completes the proof.
To show that a − c ≡ b − d (mod m), we need to use the definition of congruence modulo m.
Definition: Two integers a and b are congruent modulo m if and only if there exists an integer k such that a − b = km.
From the given information, we have:
a ≡ b (mod m) → a − b = km for some integer k
c ≡ d (mod m) → c − d = lm for some integer l
Now, we can rearrange the equations and subtract them from each other:
a − b = km → a = km + b
c − d = lm → c = lm + d
a − c = (km + b) − (lm + d) = km − lm + b − d = (k − l)m + (b − d)
Since k − l is an integer, we can let k − l = n, where n is an integer. Then we have:
a − c = nm + (b − d) = (b − d) + nm
This shows that a − c ≡ b − d (mod m), as required. Therefore, if a ≡ b (mod m) and c ≡ d (mod m), then a − c ≡ b − d (mod m).
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What is 603/25 as a mixed number
Answer: 24 3/25
Step-by-step explanation:
Divide 600 by 25, giving you 24. The rest goes into the fraction part.
Lengths of pregnancies of women are normally distributed with a mean of 266 days and a standard deviation of 16 days.
What percentage to the nearest hundredth of children are born from pregnancies lasting more than 274 days?
What percentage to the nearest hundredth of children are born from pregnancies lasting less than 246 days?
To solve this problem, we need to use the z-score formula to convert the given values to standard units. This will allow us to use the normal distribution table to find the percentage of pregnancies that fall within a certain range of lengths.
First, let's find the z-score for a pregnancy lasting more than 274 days:
z = (274 - 266) / 16 = 0.5
Next, let's use the normal distribution table to find the percentage of pregnancies that are longer than 274 days. Since the z-score we calculated is positive, we need to look in the right tail of the distribution. From the table, we find that the percentage of pregnancies that are longer than 274 days is approximately 30.85%.
Now let's find the z-score for a pregnancy lasting less than 246 days:
z = (246 - 266) / 16 = -1.25
To find the percentage of pregnancies that are shorter than 246 days, we need to look in the left tail of the distribution. From the table, we find that the percentage of pregnancies that are shorter than 246 days is approximately 8.38%.
Therefore, the percentage of children that are born from pregnancies lasting more than 274 days is approximately 30.85%, and the percentage of children that are born from pregnancies lasting less than 246 days is approximately 8.38%.
To find the percentage of children who are born from pregnancies lasting more than 274 days or less than 246 days, we need to use the z-score formula to convert the lengths of pregnancies to standard units and the standard normal distribution to find the percentage of children who fall within the given range of pregnancy lengths.
The z-score formula is:
z = (x - mu) / sigma
where z is the z-score, x is the raw score, mu is the mean, and sigma is the standard deviation.
In this case, we are given that mu = 266 days and sigma = 16 days. We can use this information to find the z-score for the lower and upper bounds of the pregnancy length range, 246 days and 274 days, respectively.
For the lower bound of the pregnancy length range, we have:
z = (246 - 266) / 16
= -20 / 16
= -1.25
For the upper bound of the pregnancy length range, we have:
z = (274 - 266) / 16
= 8 / 16
= 0.5
Now we can use the standard normal distribution to find the percentage of children who have a z-score between -1.25 and 0.5. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1, so the percentage of children who fall within the given pregnancy length range is the same as the percentage of children who have a z-score within this range.
To find the percentage of children who have a z-score between -1.25 and 0.5, we can use a standard normal distribution table to look up the z-scores and find the corresponding probabilities. The standard normal distribution table shows the percentage of values that fall within a given range of z-scores, so to find the percentage of children who have a z-score between -1.25 and 0.5, we need to look up the percentage of values that fall within this range.
According to the standard normal distribution table, the percentage of values that fall within the range of z-scores -1.25 to 0.5 is approximately 0.38. Therefore, the percentage of children who are born from pregnancies lasting more than 274 days or less than 246 days is approximately 38%, to the nearest hundredth.
the mean wait time for a drive-through chain is 193.2 seconds with a standard deviation of 29.5 seconds. what is the probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds? (write answer round to whole number like 91%).
The probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.
To solve this problem, we can use the Central Limit Theorem, which states that the distribution of sample means is approximately normal for large sample sizes.
First, we need to calculate the standard error of the mean (SEM) using the formula
SEM = standard deviation / sqrt(sample size)
SEM = 29.5 / sqrt(45) = 4.4
Next, we can standardize the sample mean using the formula
z = (x - μ) / SEM
where x is the sample mean, μ is the population mean, and SEM is the standard error of the mean.
For the lower limit, we have
z = (185.7 - 193.2) / 4.4 = -1.70
For the upper limit, we have
z = (206.5 - 193.2) / 4.4 = 3.02
We can use a standard normal distribution table or calculator to find the probabilities associated with these z-scores.
The probability of z being between -1.70 and 3.02 is approximately 0.9429 or 94%. Therefore, the probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.
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the amount of food prepared for a catered event depends on the number of people attending. which variable is the explanatory variable? [1 point]
The number of people attending affects how much food is prepared for a catered event. The number of people attending is the explanatory variable in this scenario.
One kind of independent variable is an explanatory variable. Both words are frequently used interchangeably. This is the variable that changes as we change it or watch it change. In other words, it is a factor that a researcher has changed in an experiment.
In the given situation, the number of people attending is an explanatory variable and the amount of food prepared is a dependent variable. As the number of people attending increases, the amount of food prepared also increases. This means the effect of one variable alters the effect of another variable. The change of one variable is called an independent variable while the change that occurs because of the independent variable is a dependent variable.
Therefore, the required answer is the number of people attending.
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amy, beth, and jo listen to four different songs and discuss which ones they like. no song is liked by all three. furthermore, for each of the three pairs of the girls, there is at least one song liked by those two girls but disliked by the third. in how many different ways is this possible?(2012 amc 12b
If there is at-least one-song liked by those two girls but disliked by the third, then the "different-ways" this is possible is 132 ways.
There are ⁴C₃ ways to choose the "3-songs" which are liked by "3-pairs" of girls.
There are 3! ways to find the three songs are liked by which pair of girls.
In total, there are ⁴C₃×3! possibilities for the first "3-songs".
There are "3-cases" for fourth song, let that song be "D".
Case 1: Song "D" is disliked by all three girls means there is only one possibility.
Case 2: Song "D" is liked by exactly one girl means there are three possibility.
Case 3: Song "D" is liked by exactly two girls means there are three pairs of girls to choose from.
However, there is an overlap when "other-song" is liked by "same-pair" of girl is counted as "fourth-song" at some point, in which "case-D" will be counted as one of first "three-songs" liked by same girls.
Counting the overlaps, there are "three-ways" to choose pair with overlaps and 4×3=12 ways to choose what the other "two-pairs" like independently.
In total, there are 3×12=36 over-lapped possibilities,
Therefore, there are ⁴C₃ × 3! ×(3+1+3)-36 = 132 ways for the songs to be likely by the girls.
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Please hurry I will mark you brainliest
What is the slope of the line with an x-intercept of 4 and a y-intercept of -3?
the answer to this question is the slope is 43
Answer:
Therefore, the slope is 3/4
Step-by-step explanation:
An x -intercept is the value of x when y=0 , so an x-intercept of 4 can be written as a coordinate on the graph as (4,0)
Likewise, an
y -intercept is the value of y when x=0 , so an y -intercept of −3can be written as a coordinate on the graph as (0,-3)
Now we have two points(4,0) (0,-3)
To find the slope given two points, we use the formula
rise÷run , or y2−y1÷x2−x1 .
Plug in the given points into the formula
-3-0/0-4
-3/-4
3/4
Therefore, the slope is 3/4
Hope this helps!
Please help me with this
Answer:A or C
Step-by-step explanation: i guessed plus 19 hours ago
What is the area of square whose side is 12 cm
A. 144 square cm
B. 121 square cm
C. 104 square cm
D. 48 square cm
Answer:
144cm2
Step-by-step explanation:
I just looked it up and it's 144
Point V lies between points U and W on Line segment U W. A line has points U, V, W. The length between U V is 2 x minus 4. The length between V W is 4 x + 10.
Answer:
UW = 36 units
Step-by-step explanation:
The question is incomplete. Here is the complete question
Point V lies between points U and W on Line segment U W. A line has points U, V, W. The length between U V is 2 x minus 4. The length between V W is 4 x + 10. If UW = 9x – 9, what is UW in units?
If a point V lies between points U and W on line segment UW, then based on vector notation, UV + VW = UW.
Given parameters
The length between U and V i.e UV = 2x-4
The length between V and W i.e VW= 4x + 10.
UW = 9x – 9
Required
The length between U and W in units
Since UW = UV+VW, we will substitute the given functions into the formula as shown;
9x-9 = 2x-4+4x + 10.
9x-9 = 2x+4x-4+10
9x-9 = 6x+6
collect like terms on both sides;
9x-6x = 6+9
3x = 15
x = 15/3
x = 5
Substitute x = 5 into the function UW = 9x-9 to ge the length of UW in units.
UW = 9(5)-9
UW = 45-9
UW = 36 units
Hence the required length between line segment U and W in units is 36units.
Answer:
36 units, edge 2020-21
Step-by-step explanation:
aka D/last answer
1/3 X 12 = 12 X ___ = __
Wendell is building a doghouse using these pieces of wood:
The pieces of wood to build a doghouse with the highest point to the lowest point of 28 inches.
Each length with one mark (I) is 36 inches. Each length with two marks (II) is 18 inches. Each length with three marks (III) is 30 inches. Each end has a height (from the highest point to the lowest point) of 28 inches.
The doghouse will have the shape shown once it is built.
The shape of the doghouse.
Part A
If Wendell were to slice the doghouse in half with a slice parallel to the pentagonal bases, what shape would the slice be?
If Wendell were to slice the doghouse in half with a slice parallel to the pentagonal bases, the shape of the slice would be a pentagon.
What is a solid figure?A solid figure is a three dimensional shape having length, width and height. Examples of solid figures are cylinders, cone, pyramid and prism.
The shape represented by the doghouse would be a pentagonal prism. If Wendell were to slice the doghouse in half with a slice parallel to the pentagonal bases, the shape of the slice would be a pentagon.
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Randy wants to save $21 to buy a basketball. He saves $7 each week. Which array represents the number of weeks randy needs to save $21?
Tickets to a local basketball team’s games cost $12 each. Brendon and Ed each bought tickets to four games. How much did they spend on tickets altogether? (Let t stand for the amount spent on tickets.)
The total amount spent is $96 altogether on tickets.
What is basketball?Basketball is a team sport in which two teams, most commonly of five players each, opposing one another on a rectangular court, compete with the primary objective of shooting a basketball through the defender's hoop.
Now,
Game tickets bought by Brendon = 4Game tickets bought by Ed = 4Total number of tickets = 8
Cost of each ticket = $12Thus, total money spent = 12 \(\times\) 8 = $96
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solve for m please will give brainlest
Answer:
55 degrees
Step-by-step explanation:
sum of all angles of a triangle equal 180
to find x we add them all and set them equal to 180
(57+x)+(72+x)+55=180
129+2x+55=180
184+2x=180
-184. -184
2x= -4
/2. /2
x=-2
now to find angle A
57+(-2)
55
hopes this helps
The complex numbers $z_1$ and $z_2$ are such that $|z_1| = 5,$ $|z_2| = 13,$ and
\[13z_1 - 5z_2 = 27 - 99i.\]find $z_1 z_2.$
By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.
How to determine two complex numbers based on their norms and a given operation
In this question we must derive two complex numbers such that the following conditions are fulfilled:
a² + b² = 5² (1)
c² + d² = 13² (2)
13 · (a + i b) - 5 · (c + i d) = 27 - i 99 (3)
If we assume that a, b, c, d are integers, then we can suppose that (a, b) = (4, -3) and (c, d) = (5, 12) and we check if these values satisfy (3):
13 · (4 - i 3) - 5 · (5 + i 12)
52 - i 39 - 25 - i 60
27 - i 99
By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.
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What is the equation of the line graphed below? Write your answer in slope-intercept form. (y = mx + b)
Don't forget to simply if you can!
Answer:
y = 2x + 2
Step-by-step explanation:
Slope = (change in y-values)/(change in x-values)
Slope = (-6 - 6)/(-4 - 2)
Slope = -12/-6
Slope = 2
Use the slope = 2 and point (2, 6) and substitute into y = mx + b to solve for b.
y = mx + b
6 = 2(2) + b
6 = 4 + b
b = 2
The equation is y = 2x + 2
Please explain the law of detachment and the law of syllogism.
Please also give 1 example for each law.
Law of Syllogism
The law of syllogism, also called reasoning by transitivity, is a valid argument form of deductive reasoning that follows a set pattern. It is similar to the transitive property of equality, which reads: if a = b and b = c then, a = c.There are also three parts involved in the law of syllogism, and each of these parts is called a conditional statement. A conditional statement has a hypothesis, which follows after the word if, and it has a conclusion, which follows after the word then. A letter is used to represent each phrase of the conditional statement. Let me introduce the pattern, and then we can look at some examples. Statement 1: If p, then q. Statement 2: If q, then r. Statement 3: If p, then r. Statements 1 and 2 are called the premises of the argument. If they are true, then statement 3 must be the valid conclusion.Law of Detachment
The law of detachment states that if a conditional statement is true and its antecedent is true, then the consequence must also be true.There are endless examples both in mathematics and beyond of the law of detachment. One example is a coffee shop that gives a free drink to every 25th customer. As a conditional statement, this is “If someone is the 25th customer, then they get a free drink. ”Thus, if you are the 25th customer, you know you will get a free drink. Likewise, if your friend is the 25th customer, you know he will get a free drink.Sources: https://www.storyofmathematics.com/law-of-detachment/
https://study.com/academy/lesson/law-of-syllogism-in-geometry-definition-examples.html
Refer to the attachment