The best description of the expression 6(x + 10) is given as follows:
The product of a constant factor 6 and a 2-term factor x + 10.
How to describe the expression?The expression for this problem is defined as follows:
6(x + 10).
The 6 before the parenthesis means that the distributive property is applied, meaning that we have a product of two amounts, which are given as follows:
6.x + 10.Meaning that the second option is the correct option.
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Bethany is driving from her house to her parents’ house. After driving 127.56 miles, her GPS says she is 397.24 miles away from her parents’ house. What was the total distance, in miles, from Bethany’s house to her parents’ house?
The total distance from Bethany’s house to her parents’ house would be = 524.8 miles
How to calculate the total distance covered by Bethany?The first distance covered by Bethany towards the parents house = 127.56 miles.
The distance remaining for her to arrive to ab destination = 397.24 miles
The total distance covered
= 127.56 miles + 397.24 miles
= 524.8 miles.
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The total distance, in miles, from Bethany's house to her parents' house is 524.8 miles.
How is the total distance determined?The total distance is determined using the mathematical operation of addition.
Addition is one of the four mathematical operations, including subtraction, division, and multiplication.
The distance already covered after driving from her house = 127.56 miles
The distance remaining = 397.24 miles
The total distance from Bethany's house to her parents' = 524.8 miles (127.56 + 397.24)
Thus, the total distance is 524.8 miles.
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Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x) = 6/x, c = 1 Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x) = ln(x), c = 1 Find the Maclaurin series for the function. (Use the table of power series for elementary functions.) f(x) = ex9/9
Answer:
Step-by-step explanation: sometimes it is hard to do in school because I'M and 15th-grade class and i got to take my time
which of the following represents the set of possible rational roots for the polynomial shown below? x^3+5x^2-8x-20=0
The possible rational roots of the polynomial are ±1, ±2, ±4, ±5, ±10, ±20.
The correct option is D.
What is the Cubic equation?Cubic equations are polynomials of degree 3. That means the maximum degree of the polynomial is three.
And the standard form of the cubic equation is;
f(x) = ax³ + bx² +cx +d, where a, b, c, and d are constant coefficients a ≠ 0.
Given:
A cubic polynomial,
x³ + 5x² -8x - 20 = 0.
The possible rational roots are;
p/q = -20/1
= -20
The factors of 20 are ±1, ±2, ±4, ±5, ±10, ±20.
Therefore, the possible roots are ±1, ±2, ±4, ±5, ±10, ±20.
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3 three sided dice (with sides labeled 1, 2, and 3) are rolled and their sum is recorded. What is the probability of rolling a sum of 5?
The probability that the sum of numbers we will get will be 6 is 7/27.
What is probability?Probability is simply the possibility that something will happen.
Since we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several.
The study of events that fit into a probability distribution is known as statistics.
Probability, or the likelihood that an event will occur, is calculated by dividing the number of favorable outcomes by the total number of potential possibilities.
A coin toss serves as the most simple illustration.
When you flip a coin, there are only two possible outcomes: heads or tails.
So, the probability formula:
P(E) = Favourable events/Total events
We need to get the probability of getting the sum of 6.
Then, calculate as follows:
P(E) = Favourable events/Total events
P(E) = 7/27
Therefore, the probability that the sum of numbers we will get will be 6 is 7/27.
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Correct question:
3 three-sided dice (with sides labeled 1, 2, and 3) are rolled and their sum is recorded. What is the probability of rolling a sum of 6?
gage stocks two ponds with bass and blue hill. he stocks pond a with 60 fish and pond b with 300 fish. gage stocks pond b with twice the amount of bass and six times the amount of bluegills as pond a. how many bass and bluegills does gage stock in pond w
Finally, we can use the earlier equations to find the number of bass and bluegills in pond B:
2x + 6y = 300
2(15) + 6(45) = 300
30 + 270 = 300
Therefore, pond B has 30 bass and 270 bluegills.
What is a math equation, exactly?In algebra, a statement of mathematics that proves the equality of two mathematical expressions is known as an equation. Consider the equation 3x + 5 = 14, where the word "equal" is used to denote the relationship between the terms 3x + 5 and 14.
Let's denote the number of bass in pond A as "x" and the number of bluegills in pond A as "y".
According to the problem, Gage stocks pond B with twice the amount of bass as pond A, so the number of bass in pond B is 2x. He also stocks pond B with six times the amount of bluegills as pond A, so the number of bluegills in pond B is 6y.
We know that Gage stocks pond A with a total of 60 fish, so:
x + y = 60
We also know that Gage stocks pond B with a total of 300 fish, so:
2x + 6y = 300
x + 3y = 150
Now we have two equations:
x + y = 60
x + 3y = 150
We can solve for x in the first equation:
x = 60 - y
Substitute this expression for x into the second equation:
(60 - y) + 3y = 150
2y = 90
y = 45
Now that we know that pond A has 45 bluegills, we can use the equation x + y = 60 to find that pond A has 15 bass (since 45 + 15 = 60).
2x + 6y = 300
2(15) + 6(45) = 300
30 + 270 = 300
Therefore, pond B has 30 bass and 270 bluegills.
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PLEASE HELP!
Over the course of 24 hours, the tides on Earth complete one full cycle from low tide to high tide and back down again. On one particular beach, the tide drops to 2 feet below sea level for low tide and reaches 4 feet above sea level for high tide. Write a possible trigonometric function that would model the tide situation for
this beach.
Answer:
Step-by-step explanation:
A possible trigonometric function that would model the tide situation for this beach is:
h(t) = -2 + 3sin(πt/12)
where h(t) represents the height of the tide at time t in hours, and πt/12 represents the angle (in radians) corresponding to the time t on a unit circle with a period of 24 hours.
The constant -2 represents the lowest point of the tide (2 feet below sea level), and the coefficient of 3 in front of the sine function determines the amplitude of the tide, which is 3 feet (half the difference between the highest and lowest points of the tide, which is 4 - (-2) = 6 feet). The sine function oscillates between -1 and 1, so the range of the function h(t) is between -2 - 3 = -5 feet (when the sine function takes on its minimum value of -1) and 4 - 2 = 2 feet (when the sine function takes on its maximum value of 1), as expected for the given tidal range.
Because the Earth rotates through two tidal “bulges” every lunar day, coastal areas experience two high and two low tides every 24 hours and 50 minutes. High tides occur 12 hours and 25 minutes apart. It takes six hours and 12.5 minutes for the water at the shore to go from high to low, or from low to high.
4. If you are comparing a single proportion statistic to the populations parameter, what type of test should you use?
a. Two-proportion z-test
b. one-propotion z-test
c. one sample t-test
d. 2 sample t-test
When two-proportion z-test if you're evaluating the populations parameter against a single proportion statistic.
what is proportionality ?Relationships generally regarded to as symmetrical when they continuously maintain a similar ratio. For instance, the number of trees in a vineyard and the number of apples in a yield of apples depend upon that average number of apples delivered by each tree. A linear relationship among two quantities or variables is described to as being proportional in mathematics. If the initial quantity doubles, the other amount does do so. Once one of the variables is reduced to 1/100th of its previous value, the other decreases as well. If two quantities be proportional, it means that if one grows, the other climbs as well, and their connection is constant at all values. The size and circumference of a sphere are used as an example.
given
To compare a proportion of replies or values in a sample of data to a (hypothesized) proportion in the population .
from which our sample data are obtained, one can use the single proportion (or one-sample) binomial test.
We rarely have access to statistics for a whole population, so this is significant.
when two-proportion z-test if you're evaluating the populations parameter against a single proportion statistic.
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Equivalent function for .5=2^-1
The equivalent function for .5=2⁻¹ is: 2x = 1 or log2(0.5) = -1 These are alternative ways of expressing the same relationship between 0.5 and 2⁻¹.
Understanding the Exponential Function
In mathematics, the exponential function is a function that is defined as f(x) = a^x, where 'a' is a constant called the base of the exponential function, and 'x' is the exponent. The exponential function is an important function in mathematics and is used in many different fields, such as finance, physics, and engineering.
To understand the relationship between an exponential function and a power of a number, we can consider the example of 0.5 = 2⁻¹ This means that 2 raised to the power of -1 is equal to 0.5.
To prove this, we can use the definition of the exponential function as f(x) = a^x. In this case, a = 2 and x = -1. So, we have:
f(-1) = 2⁻¹
We can simplify this expression using the property of negative exponents that states that a^-n = 1/a^n. Therefore:
f(-1) = 1/2¹
Simplifying further, we get:
f(-1) = 1/2
So, we see that 2 raised to the power of -1 is indeed equal to 0.5.
In conclusion, understanding the exponential function is important in mathematics and many other fields. The example of 0.5 = 2⁻¹ helps to illustrate the relationship between an exponential function and a power of a number, and how we can use the properties of exponents to simplify expressions involving exponential functions.
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Please help me!! <3
Find the equation of the circle represented by the given figure.
*Use y as a variable in the equation y + 16 = 0 to help solve for the radius.*
The equation of the circle has the following format:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In which:
[tex](x_0, y_0)[/tex] are the coordinates of the center.r is the radius.What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by the equation presented as follows:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
From the figure, you must identify the coordinates of the center, and then replace the given point [tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex] into the equation to solve for the radius r.
Missing InformationThe problem is incomplete, hence the procedure to obtain the equation of the circle was presented.
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Consider the following points.
(−2,−3),(3,3)
and (3,−3)
Step 1 of 2 : Determine whether or not the given points form a right triangle. If the triangle is not a right triangle, determine if it is isosceles or scalene.
The perimeter of a triangle is the sum of the lengths of its three sides.
What is triangle?Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.
In the case of triangle HGI, the perimeter is calculated by adding the three side lengths together. For example, if the three sides are labeled a, b, and c, the perimeter would be calculated as a + b + c.
The perimeter of triangle HGI can be calculated by knowing the lengths of its three sides. If the lengths of the three sides are 7, 8, and 9 units respectively, the perimeter of triangle HGI is 7 + 8 + 9 = 24 units.
The perimeter of triangle HGI can also be calculated using the Pythagorean Theorem if the lengths of two sides and the measure of the included angle are known. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side. Using this theorem, the lengths of the other two sides can be calculated if the length of one side and the measure of the included angle is known.
In summary, the perimeter of triangle HGI can be calculated by adding the lengths of its three sides or by using the Pythagorean Theorem if the lengths of two sides and the measure of the included angle are known.
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Find and interpret the average rate of change illustrated in the following graph
Answer:
Step-by-step explanation:
Average rate of change is the same thing as the slope. Ours here is negative. Our rate of change then goes down $5000 per year, so it is -5 per year. That means that the value of the machine decreases $5000 for every year that goes by.
please help me with tgis
The value of x is 11. 18
The value of y is 8. 67
How to determine the valueUsing the Pythagorean theorem, we have that;
x² = y² + z²
Substitute the values, we get;
x² = 10² + 5²
find the squares
x² = 100 + 125
Add the values
x² = 125
Find the square root
x = 11. 18
Using the Pythagorean theorem, we have;
y² = 9² - (√6)²
Find the squares
y² = 81 - 6
substract the values
y² = 75
Make 'y' the subject
y = 8. 67
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7. Alexis has 145 stickers. She wants to divide the stickers evenly among 5 of her friends. How
many stickers will each friend get?
Write your answer in the box.
stickers.
8. There are 2,472 seats in the school auditorium. The seats are divided into 6 equal sections.
How many seats are in each section? Write your answer in the box.
seats
Explain how you found your answer. Show your work.
Answer: 7: 29 stickers for each friend
8: 412 seats in each section
Step-by-step explanation:
We will have to divide 145 (stickers) by 5 (friends) to get 29
We will have to divide 2472 by 6 to get 412
7.) 145 ÷ 5 = 29 → Each friend will get 29 stickers
8.) 2,472 ÷ 6 = 412 → There are 412 seats in each second.
I divided for both problems using the long division method and multiplied which is the inverse operation, to check my work.
PLS ANSWER MY QUESTION QUICKLY
Answer:
The answer is D.
Step-by-step explanation:
difference of cubes
Formula for the difference of cubes are,
⇒ x³ - y³ = (x - y) (x² + xy + y²)
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
To find the difference of cubes of two numbers.
Now, Let two numbers are x and y.
Hence, Formula for the difference of cubes of numbers x and y are,
⇒ x³ - y³ = (x - y) (x² + xy + y²)
Thus, Formula for the difference of cubes are,
⇒ x³ - y³ = (x - y) (x² + xy + y²)
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During the summer, Curran and AJ
started their own business mowing
lawns. Before starting any work, Curran
spent $20 to ! ll up the gas tank for the
lawnmower. The boys agreed that each
person would earn the same amount
after Curran was reimbursed the money
he spent for gas. After a week of work,
the boys were paid a total of $177.
Curran ! lled up the gas tank just once.
How much did each boy earn?
The boys agreed that each person would earn the same amount after Curran was reimbursed the money he spent on gas. After a week of work, the boys were paid a total of $177. thus each boy earned $88.50.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
Let's denote the amount each boy earns by x.
According to the given information, Curran spent $20 for gas, which he should be reimbursed for. This means that the total revenue of the business was $177 + $20 = $197.
Since each person earns the same amount, we can set up an equation:
2x + $20 = $197
Simplifying and solving for x, we get:
2x = $177
x = $88.50
Therefore, each boy earned $88.50.
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Help Please!!!
That partitions the segments into a ratio of 3 to 2
let's say the segment with A(-5 , -8) and B(10 , 7) gets partitioned by point C
[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-5,-8)\qquad B(10,7)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{2}\implies \cfrac{A}{B} = \cfrac{3}{2}\implies 2A=3B\implies 2(-5,-8)=3(10,7)[/tex]
[tex](\stackrel{x}{-10}~~,~~ \stackrel{y}{-16})=(\stackrel{x}{30}~~,~~ \stackrel{y}{21}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-10 +30}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-16 +21}}{3+2} \right)} \\\\\\ C=\left( \cfrac{ 20 }{ 5 }~~,~~\cfrac{ 5}{ 5 } \right)\implies C=(4~~,~~1)[/tex]
Answer:
( 4, 1 )
Step-by-step explanation:
A regular deck of playing cards is well shuffled. Please answer the following questions. All answers should be in fraction form.
On a single draw, what would be the probability of drawing the Ace of Hearts?
On a single draw, what would be the probability of drawing an Ace?
On a single draw, what would be the probability of drawing a red card?
On a single draw, what would be the probability of drawing a face card? A face card is a Jack, Queen or King.
What would be the probability of not drawing an Ace?
On the first draw, the Ace of Hearts is removed and not replaced. What would the probability be that on the next draw you draw another Ace?
Answer:
1/52
4/52 == 1/13
13/52 == 1/4
12/52 == 6/26 == 3/13
48/52 == 12/13
3/51
FIND THE PRODUCT
(x - y)(8x + y)
Answer:
Step-by-step explanation:
8x^2 + xy - 8xy - y^2
8x^2 - 7xy - y^2
Find the value of each variable, help pls??
Answer:
x = 145
Step-by-step explanation:
We are given a polygon that has 7 sides. We can use the formula [tex]S=(n-2) * 180[/tex] which allows us to write an algebraic expression to solve for x where n = number of sides.
[tex]S=(7-2) * 180[/tex]
Evaluate
[tex]S=5*180[/tex]
[tex]S=900[/tex]
Now that we have our number, lets write an algebraic expression that will help us find the value of x.
[tex]x+116+129+120+130+135+125=900[/tex]
Add like terms
[tex]x+755=900[/tex]
Subtract 755 on both sides
[tex]x=145[/tex]
We can check our work by adding all the angle measures together
[tex]145+116+129+120+130+135+125=900[/tex]
Thus we know 145 is the correct answer.
Macy has 27 red stickers and 33 blue stickers. She gives away 50
stickers. How many stickers does she have left? Choose the two
operations needed to solve the problem.
First add, then subtract
First add, then divide
First multiply, then subtract
Answer:
First add, then subtract
10
Step-by-step explanation:
First subtract, then determine the result:
27 + 33 = 60
60 - 50 = 10
Macy has 10 stickers left.
The operations needed to solve the problem are:
First add, then subtract.
Which data set has two values for the mode?
2, 2, 2, 5, 6, 7, 9, 10
5, 6, 8,10, 11, 11, 15, 18
12, 12, 13, 13, 14, 14, 15, 15
21, 22, 22, 24, 25, 26, 28, 28
The data set: 21, 22, 22, 24, 25, 26, 28, 28 have two values of mode, which are, 22 and 28.
What is meant by the mode of a data set?
The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. Yet, occasionally there is either no mode or more than one mode. When every observed value occurs exactly once in a data collection, there is no mode. When the highest frequency was noted for more than one value in a data collection, there are many modes. The mode cannot be utilised in either of these examples to identify the distribution centre. Categorical variables can be summarised using the mode.
a)2, 2, 2, 5, 6, 7, 9, 10
Here most repeated value is only 2.
So the mode is 2.
b) 5, 6, 8,10, 11, 11, 15, 18
Here most repeated value is only 11.
So the mode is 11.
c)12, 12, 13, 13, 14, 14, 15, 15
Here the values 12,13,14 and 15 are repeated twice.
So this has 4 values as mode.
d) 21, 22, 22, 24, 25, 26, 28, 28
Here 22 and 28 are repeated twice.
So this data set has 2 values for the mode.
Therefore the data set: 21, 22, 22, 24, 25, 26, 28, 28 have two value of mode, which are, 22 and 28.
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Answer:
D
Step-by-step explanation:
here is a pic for proof
A nurse administers 25 milligrams of a drug to a patient. The amount of the drug, A, in milligrams, left in the patient after t hours can be modeled by the function A(t) = 25e 0.354 How many hours will it take for the amount of the drug left in the patient to drop to 0.25 milligrams? Round your answer to the nearest tenth of an hour.
As a result, it will take around 4.9 hours for the quantity of medicine remaining in the body to decline to 0.25 milligrams.
What is exponent?In mathematics, an exponent (also known as power or index) is a number that indicates how many times a base number is multiplied by itself. It is written as a superscript to the right of the base number. For example, in the expression 2³, 2 is the base number and 3 is the exponent. The exponent 3 indicates that the base number 2 is multiplied by itself 3 times, resulting in the value 8. Exponents are a shorthand notation for repeated multiplication and are used in many areas of mathematics and science.
Here,
The given model for the amount of the drug left in the patient after t hours is:
A(t) = 25e*(0.354t)
We need to find the time t when the amount of the drug left in the patient is 0.25 milligrams. So we can set A(t) = 0.25 and solve for t:
0.25 = 25e*(0.354t)
Dividing both sides by 25, we get:
0.01 = e*(0.354t)
Taking the natural logarithm of both sides, we get:
ln(0.01) = 0.354t
Simplifying, we get:
t = ln(0.01)/0.354 ≈ 4.9 hours
Therefore, it will take about 4.9 hours for the amount of the drug left in the patient to drop to 0.25 milligrams.
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1. Suppose a new tennis ball drops downward from a height of 30 feet onto a paved parking lot and keeps
bouncing up and down, again and again. Rebound height of the ball should be of its drop height. Make
a table and plot the data showing expected heights of the first ten bounces of the tennis ball.
Bounce Number 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10
Rebound Height (in feet) ??
Answer: Let's assume that each time the ball rebounds, it bounces back up to exactly 2/3 of its previous height. We can use this information to create a table and plot the expected rebound heights for the first ten bounces.
Bounce Number Rebound Height (feet)
0 30.0
1 20.0
2 13.3
3 8.9
4 5.9
5 3.9
6 2.6
7 1.7
8 1.1
9 0.7
10 0.5
To plot this data, we can use a scatter plot with the bounce number on the x-axis and the rebound height on the y-axis. The points should be connected by a line to show the trend.
Tennis ball bounce heights
Note that the rebound heights decrease quickly and approach zero, but they never actually reach zero due to the rounding in our calculations.
Step-by-step explanation:
I Really Need Help ASAP!!!
To draw the inequality on a number line first select an open point and mark at 3 and then click on ray and draw a ray from point 3 to the right side of the number line.
What is inequality?
It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have an inequality:
0.3(x - 4) > -0.3
After simplifying:
0.3x - 1.2 > -0.3
0.3x > -0.3 + 1.2
0.3x > 0.9
x > 3
Select open point and mark at 3.
Click on ray and draw a ray from point 3 to the right side of the number line.
Thus, to draw the inequality on a number line first select an open point and mark at 3 and then click on ray and draw a ray from point 3 to the right side of the number line.
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pls help i need the answer
Answer:
6
Step-by-step explanation:
to be very honest I'm not very good at mathematics but Im here to learn
There were 28 students in the RSM Math Challenge class. Over the year, eight students were late to class 12 times, 9 students were late 10 times, and the rest of the students were late
heeeeeeeelp
Answer:
3 students
Step-by-step explanation:
Now for RSM Olympiad are 8 math kangaroo are 7 studs that did both are 4
Total number of studs that participated are
(8-4) + 4 + (7-4)
4+4+3=11
those who didn't participate are
11-14-13
All 155 students in the math club went on a field trip some students rode in cars which hold five students each and some students wrote in buses which holds 30 students each how many of each type of vehicle do they use if there were only 11 vehicles total
7 cars and 4 buses were used on the trip
How to find how many of each type of vehicle do they use if there were only 11 vehicles total
Let's start by defining some variables to represent the unknowns in the problem:
Let x be the number of cars used.
Let y be the number of buses used.
We know that there were a total of 11 vehicles used, so we can write an equation based on that:
x + y = 11
We also know that the total number of students who went on the trip is 155.
We can use this information to set up another equation:
5x + 30y = 155
This equation represents the fact that the total number of students in cars (5x) plus the total number of students in buses (30y) equals the total number of students (155).
Now we have two equations with two unknowns. We can solve for x and y using a method like substitution or elimination.
Let's use substitution. Solve the first equation for x in terms of y:
x + y = 11
x = 11 - y
Substitute this expression for x into the second equation:
5x + 30y = 155
5(11 - y) + 30y = 155
Simplify and solve for y:
55 - 5y + 30y = 155
25y = 100
y = 4
Now that we know y, we can use the first equation to find x:
x + y = 11
x + 4 = 11
x = 7
Therefore, there were 7 cars and 4 buses used on the trip.
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The way entertainment is sold and viewed has changed drastically in the past decade. In the year
2011, there were 6.1 billion DVDs sold worldwide. In the year 2021, the number had declined to
1.2 billion.
a. What is the average rate of change in DVD sales during this period?
b. Using the numbers in 2011 as an initial value, write a linear model that models the
number of DVD sales worldwide. Make sure to define the variables.
c. If the rate stays the same, predict the number of DVD sales in the
year 2023.
Answer:
Step-by-step explanation:
a. The average rate of change in DVD sales during this period can be calculated as:
average rate of change = (change in DVDs sold) / (change in years)
We are given that in 2011, 6.1 billion DVDs were sold, and in 2021, 1.2 billion DVDs were sold. The change in DVDs sold is:
change in DVDs sold = 1.2 billion - 6.1 billion = -4.9 billion
The change in years is:
change in years = 2021 - 2011 = 10
So the average rate of change in DVD sales during this period is:
average rate of change = (-4.9 billion) / 10 = -0.49 billion DVDs per year
Therefore, DVD sales declined by an average of 0.49 billion per year during this period.
b. Using the numbers in 2011 as an initial value, we can write a linear model that models the number of DVD sales worldwide as:
DVD sales = -0.49(t - 2011) + 6.1
where t is the year and DVD sales are measured in billions.
c. If the rate stays the same, we can predict the number of DVD sales in the year 2023 by substituting t = 2023 into the linear model and solving for DVD sales:
DVD sales = -0.49(2023 - 2011) + 6.1 ≈ 0.5 billion DVDs
Therefore, if the rate of decline in DVD sales stays the same, we can predict that there will be about 0.5 billion DVDs sold worldwide in 2023.
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The last number in Row 8 is 56.
The number in Row 12 and column 3 is 80.
The row and column that will contain the number 400 is Row 58 Column 1
What does the figure shown in the image represent?The figure shown in the image represents the multiplication table 7.
Each column contains 7 numbers.
Beginning with the first Row and column, 7 numbers are added until the next row. At the end of each row is a multiple of 7.
The last number in Row 8 will be the product of 7 and 8 = 56
The number in Row 12 and Column 3 will be:
7 * 11 + 3 = 80
The row and column that will contain the number 400 will be:
400/7 = 77 remainder 1
Hence, it will be Row 58 Column 1.
Learn more about multiplication tables at: https://brainly.com/question/29069569
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