He answers the same number of questions correctly as he answers incorrectly in each round.
What is equation?Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.
For the pair of equations to be a system of equations, the number of questions answered correctly must equal the number of questions answered incorrectly in each round. Therefore, the equation 5x - 3y = 22 must have the same number of x and y variables, and the equation 10x - 4y = 46 must also have the same number of x and y variables. This is the only condition that must be true for the pair of equations to be a system of equations.
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1
Consider AB. You complete the following steps.
Step 1: Place a compass at A. Use a compass setting that is greater than half the length of AB and draw an arc.
Step 2: Keep the same compass setting. Place the compass at B. Draw an arc.
Step 3: Draw a line through the two points of intersection of the arcs.
Which statement(s) are true about the two points of intersection in Step 3?
They are the same distance from AB.
The line between them is parallel to AB.
They are different distances from A.
0
The line between them does not pass through AB.
The correct statement true about the two points of intersection in Step 3 is,
⇒ They are the same distance from AB.
What is Line segment?A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.
Given that;
Steps are,
Step 1: Place a compass at A. Use a compass setting that is greater than half the length of AB and draw an arc.
Step 2: Keep the same compass setting. Place the compass at B. Draw an arc.
Step 3: Draw a line through the two points of intersection of the arcs.
Now, Cleary this method is used to divide a line in two equal parts.
Hence, The correct statement true about the two points of intersection in Step 3 is,
⇒ They are the same distance from AB.
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Triangle ABC with D on AC and E on AB
DE is a straight line
AD= 27m, AE=39m, DE=23m, and BC=65m
Calculate the length of CD
Therefore , the solution of the given problem of triangle comes out to be Replace with CD-49.
What does a triangle actually mean?Because triangles have four or more sides, they are considered polygons. Its design is straightforward and geometric. The ABC letters come together to form a triangle with a square angle. Euclidean geometry generates a single rectangle or square when the sides do not coincide. Because they consist of three sides and three corners, triangles are polygons. The corners of a triangle are formed by the junction of its three sides.
Here,
Triangles that are similar may or may not be congruent.
The CD is 49 units long.
The following equivalent ratios can be derived from the triangles that are supplied.
AC: CB = AD: DE
Where:
AC= AD + CD
We thus have:
DE = AD + DC
CB
Replace known values
=>27:23-27+ DC: 65
Describe as a fraction
=> 27+DC
65 x 65 multiplied by both sides yields 27+ DC.
Take 27 away from both sides.
2x65-27 - DC
DC 76-27 - DC 49-DC 27x65-27 = DC 1755-27=DC
Replace with: CD-49
Therefore , the solution of the given problem of triangle comes out to be Replace with CD-49.
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Write an equation in point-slope form for the line through the given point with the given slope.
(0, 3); m = 18
The equation of the line in slope-intercept form is y = 18x + 3.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of the line in slope-intercept form is y = mx + c.
Now,
m = 18
(0, 3) = (x, y)
So,
y = mx + c
3 = 18 x 0 + c
c = 3
Now,
y = 18x + 3
Thus,
y = 18x + 3 is the equation of the line in slope-intercept form.
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lake trail is 4 3/5 miles long. outlook trail is 5 5/6 miles long. pinewoodd trail is 1 3/10 miles longer, which trail is longer, pinewoods trail or outlook trail?
The longer trail is outlook trail.
What are Mixed Fractions?Mixed fractions are type of fractions which consist of a whole number part and a fractional part.
Mixed fractions are of the form a b/c where a is the whole number part and b/c is the fractional part.
The lengths of these trails are given in the mixed number form.
First, converting it into improper fraction,
Length of lake trail = 4 3/5 mile = (4 × 5 + 3) / 5 = 23/5 miles
Length of outlook trail = 5 5/6 mile = (5 × 6 + 5) / 6 = 35/6 miles
Length of pinewood trail = 1 3/10 mile = (1 × 10 + 3) / 10 = 13/10 miles
35/6 > 13/10
Outlook trail is longer.
Hence the outlook trail is the longer trail.
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what is the number of distinct proper subsets of a set with n elements is
A number of Appropriate Subsets of the Set: There are 2n - 1 appropriate subsets of the set for every n element in the set.
What are sets?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets.
A set is a mathematical model for a collection of various things.
A set with a single element is a singleton, while a set with no elements is an empty set.
A set can either be infinite or have a finite number of elements.
If all of the elements in two sets are identical, then the sets are equal.
The number of subsets of a set is 2n if the set has 'n' items.
A number of Appropriate Subsets of the Set: If a set has 'n' items, then 2n - 1 is the number of appropriate subsets of the set.
Therefore, a number of Appropriate Subsets of the Set: There are 2n - 1 appropriate subset of the set for every n element in the set.
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Correct question:
The number of distinct proper subsets of a set with n elements is ____.
darin wrote 1 2 5 as the sum of three fractions. what three fractions might darin have used? a. 1 5 2 5 2 5 b. 3 5 3 5 3 5 c. 1 5 2 5 3 5 d. 1 5 4 5 2 5
Darin wrote 1 2/5 as a sum of three fractions. Three fractions 1/5, 4/5, 2/5 Darin have used. So the option d is correct.
Darin wrote 1 2/5 as a sum of three fractions.
We firstly solve the mixed fraction in the form of improper fraction.
We can write in improper fraction my multiplying 1 and 5, then add 2 in the multiplication of 1 and .
Now the fraction;
1 2/5 = 7/5
Now we solve each option to determine the three fraction.
a. 1/5, 2/5, 2/5
= 1/5 + 2/5 + 2/5
= (1 + 2 + 2)/5
= 5/5
= 1
It can't produce the value 7/5. So this option is not correct.
b. 3/5, 3/5, 3/5
= 3/5 + 3/5 + 3/5
= (3 + 3 + 3)/5
= 9/5
It can't produce the value 7/5. So this option is not correct.
c. 1/5, 2/5, 3/5
= 1/5 + 2/5 + 3/5
= (1 + 2 + 3)/5
= 6/5
It can't produce the value 7/5. So this option is not correct.
d. 1/5, 4/5, 2/5
= 1/5 + 4/5 + 2/5
= (1 + 4 + 2)/5
= 7/5
It produces the value 7/5. So this option is correct.
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The complete question is:
Darin wrote 1 2/5 as a sum of three fractions. What fractions might Darin have used?
a. 1/5, 2/5, 2/5
b. 3/5, 3/5, 3/5
c. 1/5, 2/5, 3/5
d. 1/5, 4/5, 2/5
I need answer ASAP the question is in the picture
Answer:
c
Step-by-step explanation:
[tex]\text{x}^2 + \frac{1}{4}\text{x} + \frac{1}{64}[/tex]
==============================================
Reason:
The formula you can use is
[tex](a+b)^2 = a^2+2ab+b^2[/tex]
This is the perfect square trinomial formula.
In this case,
a = xb = 1/8The square of each gets us
a^2 = x^2b^2 = (1/8)^2 = 1/64Those form the outer terms, aka 1st and 3rd terms.
The 2ab term in the middle would be 2*x*(1/8) = (1/4)x
That leads us to be able to say [tex]\left(\text{x}+\frac{1}{8}\right)^2 = \text{x}^2 + \frac{1}{4}\text{x} + \frac{1}{64}[/tex]
You can use the FOIL rule or the box method as two ways to verify this answer. Also a graphing calculator can be used.
Round each mixed number to the nearest whole number. Then, estimate the product.8 9/10x1 4/5
Answer:
9 × 2 = 18
Step-by-step explanation:
8 9/10 is closer to 9 than it is to 8. So you round 8 9/10 up to 9.
1 4/5 is closer to 2 than to 1. So round it up to 2.
Use the rounded numbers to estimate the product. 9 × 2 is 18
The estimate is 18.
help???? please please!! it’s prob easy
Answer:
$993.3
Step-by-step explanation:
you just multiply 70×14.19
ABCD is a quadrilateral.
Angle A = 60° and angle B=50°.
Calculate angles C and D.
A
60°
D
50%
The measure of the angles C and D are 60° and 190° respectively.
What is a quadrilateral?A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.
From the given information the measure of angle c will be,
= [90° - (1/2)m∠A].
= [90° - 30°].
= 60°.
And we know the sum of all the interior angles in a quadrilateral is 360°.
Therefore, The measure of ∠D = 360° - (60° + 50° + 60°).
m∠D = 360° - 170°.
m∠D = 190°.
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Karla will select 2 different side dishes from the following list at a restaurant.
•French fries
•Salad
•Onion rings
•Beans
Which list shows all the possible outcomes of 2 different side dishes from this list?
the number $r$ can be expressed as a four-place decimal $0.abcd$, where $a$, $b$, $c$, and $d$ represent digits, any of which could be zero. it is desired to approximate $r$ by a fraction whose numerator is 1 or 2 and whose denominator is an integer. the closest such fraction to $r$ is $\frac{2}{7}$. what is the number of possible values of $r$?
The number of possible values regarding the given fraction situation of $r$ is 8.
To find the possible values of $r$ that can be approximated by [tex]$\frac{2}{7}$[/tex], we need to determine the range of values for $r$ that is closest to [tex]\frac{2}{7}$[/tex]. This can be done by finding the two closest fractions with numerator 1 or 2 to [tex]$\frac{2}{7}$[/tex] and determining the range of values for $r$ between those two fractions. The two closest fractions are [tex]$\frac{1}{3}[/tex] and[tex]\frac{2}{5}[/tex].
If $0.abcd$ is between[tex]\frac{1}{3}[/tex] and [tex]$\frac{2}{5}[/tex], it will be closest to [tex]$\frac{2}{7}$[/tex]. The decimal representation of [tex]\frac{1}{3}$[/tex] is 0.3333..., and the decimal representation of [tex]$\frac{2}{5}$[/tex] is 0.4. Thus, the possible values of $r$ that can be approximated by [tex]\frac{2}{7}$[/tex] are [tex]$0.3333... \leq r \leq 0.4$[/tex] , which have 8 possible values, including both endpoints.
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22) Find the difference and write the answer in standard form.
(9.6×10to the power of 13)-(9.5x10 to the power of 13)
23) find the quotient and write the answer in standard form
(7.56x10 to the power of -8) divided by 2.1
22) The difference is given as follows: 0.1 x 10^13 = 1000000000000.
23) The quotient is given as follows: 3.6 x 10^-8 = 0.000000036.
How to obtain the difference?
The difference is given as follows:
9.6 x 10^13 - 9.5 x 10^13.
As the two terms have the same base, we just subtract the coefficients while keeping the base constant, hence:
9.6 x 10^13 - 9.5 x 10^13 = (9.6 - 9.5) x 10^13 = 0.1 x 10^13.
How to obtain the quotient?The quotient is given as follows:
7.56 x 10^-8/2.1.
The denominator has an exponent of zero, hence the exponent of the quotient is of - 8 - 0 = 0, and then the coefficient is given as follows:
(7.56/2.1) x 10^-8 = 3.6 x 10^-8 = 0.000000036.
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what to do for 20 points if not wrong
Answer:
B can make tons more
Step-by-step explanation:
1/9 123456789 (+9)
multiples of 11 11 22 33 44 55 66 77 88 99 (+9)
9+9=18
A=18
B=
213
438
SO MANY MORE
B=more
kala's coffee shop makes a blend that is a mixture of two types of coffee. type a coffee costs kala $4.65 per pound, and type b coffee costs $5.85 per pound. this month, kala made 134 pounds of the blend, for a total cost of $717.90. how many pounds of type a coffee did she use?
Kala used 55 pounds of type A coffee and 79 pounds of type B coffee in 134 pounds of the blend for a total cost of $717.90.
Let number of pounds in coffee type A be taken as A
Let number of pounds in coffee type B be taken as B
The total number of pounds used in the blend = 134 pounds.
Therefore, A + B = 134
A = 134 – B …….. (i)
1 pound of coffee type A costs = $4.65
Therefore, A pounds of type A coffee will cost = $4.65A
1 pound of coffee type B costs = $5.85
Therefore, B pounds of type B coffee will cost = $5.85B
Total cost of both blends = $717.90
Therefore, 4.65A + 5.85B = 717.90…….(ii)
Using substitution method, substituting equation (i) in equation (ii), we get,
4.65 * (134 – B) + 5.85B = 717.90
623.1 – 4.65B + 5.85B = 717.90
623.1 + 1.2B = 717.90
1.2B = 94.8
B = 79 pounds
Therefore, A = 134 – 79 = 55 pounds
Hence, the number of pounds of coffee type A was found to be 55 pounds
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Solve for x and illustrate your Solution on a number line a) x²-3x - 10 ≤0
Answer:
x>2
Step-by-step explanation:
Which of the following is the vertex of y=-3x^2-18x-24
Answer:
vertex is at (-3, 3)
No choices provided; can't help you there
Step-by-step explanation:
General equation of a parabola isy = ax² + bx + c
If a < 0 (negative) then it is a downward facing parabola and the vertex is a maximum
If a > 0 then it is an upward facing parabola and the vertex is a minimum
Given parabola is
y = -3x² - 18x -24
and comparing to the general equation we get a = -3, b = -18 and c = -24
So the vertex is a maximum
The x-coordinate of the vertex is given by
[tex]x_v =- \dfrac{b}{2a}\\\\[/tex]
Plugging in values of a = -3 and b = -18 we get
[tex]x_v=-\dfrac{\left(-18\right)}{2\left(-3\right)}\\\\\rightarrow -\dfrac{-18}{-6} = -(3) = -3\\\\[/tex]
To find [tex]y_v[/tex], the y-coordinate of the vertex, plug this value of [tex]x_v[/tex] into the parabola equation and solve for y
[tex]y_v=-3\left(-3\right)^2-18\left(-3\right)-24\\\\y_v = -3(9) +54 -24\\\\y_v = -27 + 54 - 24\\\\y_v = 3\\\\[/tex]
So the vertex is at (-3, 3)
No choices provided so unable to help in that regard
a computer program is tested by 5 independent tests. if there is an error, these tests will discover it with probabilities 0.1, 0.2, 0.3, 0.4, and 0.5, respectively. suppose that the program contains an error. what is the probability that it will be found (a) by at least one test? (b) by at least two tests? (c) by all five tests
The probability that it will be found by at least one test, at least two tests, or five tests is 0.8488, 1.8488, and 4.8488.
Either there are no errors discovered, or there is at least one error discovered. The sum of the probabilities of these outcomes is 1.
Probabilities of no errors discovered:
If there is an error, the tests will discover it with probabilities of 0.1, 0.2, 0.3, 0.4, and 0.5. So, if not discover the errors, the probabilities are 0.9, 0.8, 0.7, 0.6, 0.5.
The probability of none discovering the error is:
P=0.1*0.2*0.3*0.4*0.5=0.1512
(a) by at least one test
None: 0.1512
At least one: 1 - 0.1512 = 0.8488.
by at least two tests:
At least two:
2-0.1512=1.8488
by at least five tests:
At least five:
5-0.1512=4.8488
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barbara opened a bag of candies and found that there were 8 red, 6 orange, 4 green, 5 yellow and 3 purple candies in the bag. if barbara pulls out two of the candies at random, what is the probability that the two candies are different colors? express your answer as a common fraction.\
There is a 0.8677 percent chance that the two candies are different colors.
Divide the total number of outcomes by the entire number of possible outcomes to determine the likelihood that an event will occur. There are differences between probability and odds. Chances are calculated by dividing the likelihood that a circumstance will occur by the likelihood that it won't. Probability is a statistic used to assess the likelihood that an event will take place. The likelihood that the coin will land with the heads side up is computed when it is tossed into the air. You are undoubtedly already familiar with this practical application of probability. Before a big trip, we always check the weather prediction.
The probability of two the same
so,
Two red = 8/26 * 7/25
Two orange [tex]=(6/26 * 5/25)[/tex]
Add them up
[tex](8/26 * 7/25)+(6/26 * 5/25)\\=56/650+30/650\\=86/650\\=0.1323[/tex]
Subtract that from 1
[tex]1-0.1323\\=0.8677[/tex]
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i need someone to talk to plssssssssssssss
Answer:
oh hi buddy if your lonely I'm always here for you
20 masons working 8 hours a day can build a boundary in 15 days. how many days will 15 masons working 10 hours a day, build a same wall?
The number of days for 15 masons is 16 days
How to determine the number of daysFrom the question, we have the following parameters that can be used in our computation:
20 masons working 8 hours a day can build a boundary in 15 days.
This means that
Boundary wall = 20 * 8 * 15 = 2400
15 masons working 10 hours a day means
Duration = 15 * 10 = 150 hours
So, we have
Days = 2400/150
Days = 16
Hence, the number of days is 16
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1.6 multiplied by
0.125
The numeric value of 1.6 multiplied by 0.125 is 0.2.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given we need to calculate the value of 1.6 multiplied by 0.125
Since Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes.
Thus,
=> 1.6 multiplied by 0.125
=> 1.6 * 0.125
=> 0.2
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Olivia's family took a road trip to the Grand Canyon. Olivia fell asleep after they had travelled 243 miles. If the total length of the trip was 900 miles, what percentage of the total trip had they travelled when Olivia fell asleep?
The percentage of the total trip had they travelled when Olivia fell asleep is 73%.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Olivia's family took a road trip to the Grand Canyon.
Olivia fell asleep after they had travelled 243 miles.
If the total length of the trip was 900 miles,
then they had travelled when Olivia fell asleep,
= (900 - 243) x 100 /900
= 73%
Therefore, the percentage is 73%.
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wall posters are usually sold curled up in cylindrical cardboard tubes. if the length of the tube is 84.5cm and the diameter of the tube is 2.40 cm, what is the area of the poster in cm2?
If the length of the tube is 84.5cm and the diameter of the tube is 2.40 cm, then area of poster is 636.7 cm² ~ 637 cm²
Given that ;
Length of the cylinder = 84.5 cm
Diameter of the cylinder = 2.40 cm
Then the radius is 1.20 cm
When the poster is uncurled it is in rectangle shape so, length of the poster is 84.5cm.
When poster is curled in cylinder, circumference of circle is breadth of poster = 2πr = 2(22/7)1.2 = 7.53 cm
So the area of poster is length × breadth
Area = 84.5cm × 7.53cm
Area = 636.7 cm²
Hence the area of poster is 636.7 cm² ~ 637 cm²
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a movie theatre charges $7.50 per adult and $5 per child. if 700 tickets are sold and the total revenue is $4500, how many tickets of each type were sold
350 adult tickets were sold and 350 child tickets were sold.
Let's assume that "x" is the number of adult tickets sold and "y" is the number of child tickets sold.
We know that:
x + y = 700 (the total number of tickets sold)
7.5x + 5y = 4500 (the total revenue)
We can use the first equation to solve for one of the variables in terms of the other.
For example:
y = 700 - x
Substituting this into the second equation:
7.5x + 5(700 - x) = 4500
7.5x + 3500 - 5x = 4500
2.5x = -900
x = -360
Since x must be a positive integer (the number of adult tickets sold cannot be negative), this solution is not valid.
However, we can see that the equation does have a solution by trying a larger value for x:
x = 700
y = 0
This gives us:
7.5 * 700 + 5 * 0 = 4500
5250 = 4500
This solution is not valid either, since the number of child tickets sold cannot be zero.
By repeating this process, we can find that the solution is x = 350 and y = 350.
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6. what is the cumulative incidence of the disease from 1998 through the end of 2004? (hint: the denominator is the number of people at risk at the beginning of the study.)
Answer:
Here you have
Step-by-step explanation:
In the US:
The cumulative incidence was 1.2% by the age of 24 years, 3% by 75 years, and 4.4% by 85 years
In Sweden:
The cumulative incidence was 2.2% by the age of 15 years, 4.5% by 50 years, and 7.2% by 75 years
two numbers are independently selected from the set of positive integers less than or equal to $5$. what is the probability that the sum of the two numbers is greater than their product? express your answer as a common fraction.
The probability of the sum of two integers is greater than the product is equal to 2 / 5.
Let 'A' be the set of positive integers less than or equal to 5.
A = { 1, 2, 3, 4, 5}
Sum of two numbers is greater than the product of the numbers.
1 × 1 = 1 and 1 + 1 = 2
1 × 2 = 2 and 1 + 2 = 3
1 × 3 = 3 and 1 + 3 = 4
1 × 4 = 4 and 1 + 4 = 5
1 × 5 = 5 and 1 + 5 = 6
2 × 1 = 2 and 2 + 1 = 3
3 × 1 = 3 and 3 + 1 = 4
4 × 1 = 4 and 4 + 1 = 5
5 × 1 = 5 and 5 + 1 = 6
2 × 2 = 4 and 2 + 2 = 4
Total possibilities = 5 × 5
= 25
Favourable outcomes = 10
Total number of outcomes = 25
Probability of sum of two numbers greater than the product
= 10 / 25
= 2 / 5
Therefore, the probability of the sum of two numbers is greater than the product is equal to 2/ 5.
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on the sldt, why is a standard score of 89 considered below average if the mean is 100 with a standard deviation of 15?
A standard score of 89 is considered below average because it is 11 points lower than the mean, which is a deviation of more than 0.7 standard deviations below the mean.
A standard score of 89 is considered below average because it falls below the mean score of 100. This is because it is 11 points lower than the mean, which is a deviation of more than 0.7 standard deviations below the mean. The standard deviation is a measure of the spread of the data, where higher values indicate more spread out data. In this case, the mean score of 100 has a standard deviation of 15, which means that any score lower than 85 (100 - 15) is considered below average. A score of 89 is 11 points below the mean, which is a deviation of more than 0.7 standard deviations. This indicates that it is lower than the average score, and therefore considered below average.
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complete the equation describing how x and y are related
The equation represents the relationship between x and y is y = 5x + 3
How to determine the equationFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the table of values, we can see that
y is 3 more than five times x
When represented as an equation, we have
y = 5x + 3
Hence, the equation is y = 5x + 3
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A spool of ribbon is 24 yards long. Jamal uses 3/5 of the total ribbon.
HURRY PLEASE!!
The number of yards of ribbon Jamal used is 14.4 yards.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Given that, a spool of ribbon is 24 yards long.
Jamal uses 3/5 of the total ribbon.
So, number of yards = 3/5 ×24
= 3×4.8
= 14.4 yards
Therefore, the number of yards of ribbon Jamal used is 14.4 yards.
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