Jamal is correct ( ½+⅓ =⅚), when he says that when adding two unit fractions, the numerator is found by adding the denominators, and the new denominator can be found by multiplying the previous denominators.
State what is denominator with example?A denominator is the lowest number in a fraction that indicates how many equal parts are divided into a whole. It is a fraction's divisor. In this case, the denominator is 4, thus there are four components overall.
What is an illustration of a numerator?In a fraction, the number above the line is the numerator. For instance, the numerator of the fraction 3/5 is 3. A fraction's numerator displays the number of pieces that make up the whole while the denominator.
Adding 2 unit fractions example ½ and ⅓
By Jamal’s theory, 2+3=5
2*3=6
½+⅓ =⅚
Hence the theory is proved right.
Drawbacks of Jamal’s Shortcut,
It is only for the unit fraction and not for any other type of fractions.
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What calculation is showed on the number line
The calculation shown in the number line is -4/10 + ( -7/10) = - 1 1/10
What is a number line?
This is a sequential arrangement of numbers in a straight line. The scale of number line is shown to suit the problem at hand.
The number line in the question here has a scale of 1. This means that every number represent a unit. However in between the numbers are 10 strokes.
The value of each stroke is gotten from division of one by ten which is
1 ÷ 10 = 1/10
So every line in the number line represent 1/10. The positive side is 1/10 while the negative side is -1/10
The calculation done here is counting from 0 in the negative direction to get -4/10. Then adding -7/10 units to arrive at the point which is -1 1/10
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Compute the probability that a five-card poker hand is dealt to you that contains all hearts.
The probability of getting all 5 cards hearts 13C₅/ 52C₅.
What is probability?The probability of an event occurring is defined by probability.
There are many instances in real life where we may need to make predictions about how something will turn out.
The outcome of an event may be known to us or unknown to us.
When this happens, we say that there is a chance that the event will happen or not.
Given : A five card poker card
To find : the probability of all hearts
Let E be the events of getting all 5 cards of hearts
therefore n(E)= [tex]13C[/tex]₅
As we know that probability is defined as total number of favourable outcomes divided by total number of possible outcomes.
Thus the required probability is 13C₅/ 52C₅
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There are 2 different maps of North Carolina. The scale on the first map is 1 cm to 2 km. The distance from Durham to Cary is 15 cm. The scale of the second map is 1 cm to 5 km. What is the distance from Durham to Cary on the second map
Two separate maps exist for North Carolina. The first map has a scale of 1 cm to 2 km. Durham and Cary are separated by 15 cm. The second map has a scale of 1 cm to 5 km. On the second map, the separation between Durham and Cary is 18 cm.
What do you mean by distance?The measurement of the distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common language can refer to physical length or an assumption based on other factors (e.g. the "two counties over"). Given that spatial thinking is rich source of conceptual metaphors in human thought, the term is also frequently used metaphorically to denote a measure of the degree of separation or statistical distance between two similar objects (such as edit distance between strings of text or probability distributions) (as exemplified by distance between people in a social network). A metric space is mathematical concept that is used to define the majority of these conceptions of distance, both literal and figurative.
In social sciences, distance can refer to a qualitative measurement of separation, such as social distance or psychological distance.
if
1cm to 2km map= 15cm distance
1cm to 5km map= 15+3cm distance
= 18cm
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Solve 2x^2+3x-1=0 by completing the square
Answer:
x=(-3-√17)/4
x=(-3+√17)/4
Step-by-step explanation:
2x^2+3x-1=0
it can rewrite as,
x^2+3x/2-1/2=0
now adding and subtracting (3/4)^2 , in R.H.S,
x^2+3x/2+9/16-9/16-1/2=0
(x+3/4)^2-17/16=0
(x+3/4)^2-((√17)/4)^2=0
(x+3/4+√17/4)(x+3/4-√17/4)=0
x=(-3-√17)/4
x=(-3+√17)/4
Can someone help me with this?
From the function table and verbal description of the two functions, we can say that; Function 2 has a greater y-intercept
How to interpret the y-intercept?
The y -intercept of a graph is the point where the graph crosses the y -axis. Now, due to the fact that a function must pass the vertical line test , it means that a function can have at most one y -intercept .
The y -intercept is often referred to with just the y -value.
Now, we are told given table representing function1 which is an exponential function and we can see the x and y-values. Now, the y-intercept occurs when x = 0 and in this case, at x = 0, y = 20. Thus, the y-intercept of function 1 is 20.
Now, for the second function, we are told that it has 15 pitches but that it crosses the vertical axis at y = 22. Thus, from, y-intercept definition, we can say that the y-intercept of function 1 is 22.
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-5/9 multiplied by (-4)
Answer:
Step-by-step explanation:
-5/9* -4 = 20/9
Answer=20/9
When you multiply them, there is nothing to simplify in any of them. So when you multiply, the negatives become a positive because -*- is + so the answer is 20/9.
Dilate point D by a scale factor of 3.
Answer:
according to the image, it looks like you would move 6 more points to the right, but i might be wrong.
Step-by-step explanation:
If the point that you are dilating is directly above the point of dilation and you are dilating by 3, you take the distance from the point of dilation and the point you are dilating and you multiply it by 3.
If f(x)=1-x, which value is equivalent to f1?
0
√√√2
Answer: f(1)=0
Step-by-step explanation:
f(x)=1-x
f(1)=1-1
f(1)=0
the amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 35 and 56 minutes. one student is selected at random. find the probability of the following events.
The amounts of time it takes for a student to complete a statistics quiz uniformly distributed between 30 and 60 minutes. One student is selected at random. Find the probability of the following events.
a) the student requires more than 55 minutes to complete quiz
b) the student completes the quiz in a time between 30 and 40 minutes
c) the student completes the quiz in exactly 37.23 minutes
A student to complete a statistics quiz uniformly distributed between 30 and 60 minutes The probability of the events are a) 1/6, b )1/3 c) 0
Given, X similar U( a = 30, b = 60)
f(x) =1/60-30, 30 ≤ X ≤60
f(x) = 1/30, 30 ≤ X ≤60
a) the student requires more than 55 minutes to complete quiz
P(X > 55) = ∫_55^60▒f(x)dx = ∫_55^60▒〖1/30dx〗 = 1/30[x]6055 = 1/6
b) the student completes the quiz in a time between 30 and 40 minutes P (30 < X < 40) = ∫_30^40▒f(x)dx == ∫_30^40▒〖1/30dx〗 = 1/30[x]4030 = 1/3
C) the student completes the quiz in exactly 37.23 minutes P(X = 37.23) = ∫_37.23^37.23▒f(x)dx=∫_37.23^37.23▒〖1/30dx〗 = 0
A student to complete a statistics quiz uniformly distributed between 30 and 60 minutes The probability of the events are a) 1/6, b )1/3 c) 0
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A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t2 + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s. Which solution can be eliminated and why?
The solution –0.2 s can be eliminated because time cannot be a negative value.
The solution –0.2 s can be eliminated because the pass was not thrown backward.
The solution 2.7 s can be eliminated because the pass was thrown backward.
The solution 2.7 s can be eliminated because a ball cannot be in the air for that long due to gravity.
The solution that will be eliminated when a quarterback throws an incomplete pass is –0.2 s can be eliminated because time cannot be a negative value
What is parabolic equation?This is the equation used to trace the path made by a parabola. It is another name for quadratic equation.
We can say that the football traced a parabolic path represented by the equation h(t) = –16t2 + 40t + 7.
Parabolic equation will always produce two solutions then depending on the applicability of the solution the best option will be picked.
In this case time, which cannot be a negative value hence option A is the correct answer
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Complete each statement from the information given and state the reasons and the triangle criterion you used
[tex]\angle TIG \cong \angle AIN[/tex] by vertical angles, so [tex]\triangle TIG \cong \triangle NIA[/tex] by SAS.
Write 3 functions. In the first function, y should vary directly with x. In the second function, y should vary inversely with x. In the third function, the relationship between x and y should be neither inverse variation nor direct variation. Describe the graph of each function and give a real-world example for each.
first function: y = ([tex]\frac{3}{4}[/tex])x
Second function: y=[tex]\frac{12}{x}[/tex]
Third function y = 30 + 2x.
A) In the first function, y directly depends on x.
first formula: y = ([tex]\frac{3}{4}[/tex])x
2) Graph: It has a slope of ([tex]\frac{3}{4}[/tex]) and is a straight line that goes through the origin. According to the slope, the function changes at a rate of 3 units for every 4 units of x-value growth, or 0.75 units for every additional unit of x-value growth.
3) Use a real-world example
According to a cake recipe, 3 cups of sugar should be combined with every 4 cups of flour. Therefore, if you have 12 cups of sugar, how much flour do you need?
Y = ([tex]\frac{3}{4}[/tex])x, so if x = 3, y =([tex]\frac{3}{4}[/tex])×12= 9.
Given that : the variation is direct, you must multiply the number of cups of sugar by the constant rate, which is ([tex]\frac{3}{4}[/tex])x, to determine how many cups of flour correspond to the specified amount of sugar.
B) The second equation has an inverse relationship between y and x.
Inverse variation causes either y = constant / x or y*x = constant.
In other words, if x increases, y will decrease by the same amount as x increases.
1) formula: y=[tex]\frac{12}{x}[/tex]
2) Graph: The hyperbola, a diminishing line extending from left to right, is the shape of this graph. Both the x-axis and the y-axis asymptote to zero. This implies that neither x nor y can be zero.
As the x-value gets closer to 0, the y-value gets closer to positive or negative infinity; conversely, as the y-value gets closer to 0, the x-value gets closer to positive or negative infinity.
The graph is a declining curve in the first quadrant if you pick the positive numbers (x and y are positive).
The graph has a declining slope in the third quadrant if you pick the negative values (x and y are negative)
3) An actual world instance.
a uniform motion's relationship between time and velocity.
If an object runs a constant distance, time slows down proportionately as velocity rises.
Give the distance between cities A and B as 100 kilometers.
How long will it take to get from point A to point B traveling at 50 km/h or 25 km/h?
100 kilometers = speed * time
at 50 km/h: t = [100 km] / [50 km/h] = 2 hours 100 km = 50 km/h * t
at 25 km/h: t = [100 km] / [25 km/h] = 4 hours; 100 kg = 25 km/h * t.
C) In the third scenario, x and y should not have an inverse variation or a direct variation.
There are infinite types of functions that are neither inverse variations nor direct variations, including trigonometric sine, exponential, logarithmic, exponential, linear (that do not pass through the origin), and exponential, quadratic, and exponential.
1) A function illustration is y = 30 + 2x.
2) Graph: The line has a slope of 2 and a y-intercept of 30.
3) A case in point
In order to create chairs, it costs 30 dollars to rent the facility plus 2 dollars for each chair, for a total cost of 30 + 2x.
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Joven's scores in five of his quizzes in mathematics are 85, 88, 95, 86, and 92. if he needs an average quiz grade of 90 to be able to maintain his required grade for his scholarship, what score must he get for his sixth quiz?
Answer:
If, he got 94 marks for his sixth quiz, then, he will be able to maintain his required grade for his scholarship.
Step-by-step explanation:
given-
Joven's scores in five of his quizzes in mathematics are 85, 88, 95, 86, and 92.
let, the x score he gets for his sixth quiz.
then, he will be able to maintain his required grade for his scholarship.
he needs an average quiz grade of 90 to maintain his required grade for his scholarship.
according to the question--
using the formula of average=>
(85+88+95+86+92+x)/6=90
=>x=540-446
=>x=94
if, he got 94 marks for his sixth quiz, then, he will be able to maintain his required grade for his scholarship.
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The two legs of a right triangle are 9 and 7. Find the hypothesis of the triangle. Draw a Picture! Leave your answer in radical form.
The value of the hypotheses of the right angled triangle is found as √130.
What is meant by the right angled triangle?A right triangle is one in which one of interior angles is 90°. The hypotenuse is the longest side of the right triangle and also the side opposite this same right angle, while the height and base are the two arms of the right angle.In a right triangle, the right angle always has the largest.The longest side is the hypotenuse, which is the side opposite this same right angle.For the given right angled triangle,
The two side legs are given as 7 and 9.
By the Pythagorean theorem;
H² = P² + B²
Put the values;
H² = 7² + 9²
Simplifying;
H² = 49 + 81
H² = 130
Taking square root both sides.
H = √130
Thus, the value of the hypotheses of the right angled triangle is found as √130.
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Use digits and symbols to write ''The product of one and two is less than the sum of one and two''
Answer:
1 + 3 < 1 · 2
Step-by-step explanation:
anyone boredddddddddddd?
Answer:
gay
Step-by-step explanation:
gay gay gay gay gay gay
Answer: i am
Step-by-step explanation:Black parents
when you are finding the perimeter of a shape do you cancel out the negatives
Answer:
Yes, you would cancel them out.
Step-by-step explanation:
You cannot have negatives on the sides of a shape for perimeter.
What is the least integer? explain.
Answer:
The function whose value at any number x is the smallest integer greater than of equal to x is called the least integer function.
Step-by-step explanation:
It is denoted by ⌈x⌉ It is also known as ceiling of x. For example ⌈3.578⌉ = 4 , ⌈0.78⌉ = 1 , ⌈-4.64⌉ = - 4.
I’m struggling with my guided notes practice questions
The shaded angles in the given diagram can be named as:
1. ∠ABC; ∠1; and ∠B.
2. ∠JKM; ∠2; ∠K.
3. ∠CBJ ≅ ∠DHG
4. ∠FJH ≅ ∠AJB
5. m∠JAB = 75°.
6. m∠JBC = 130°.
How to Name an Angle?We can name a given angle by:
Using the three letters that form the angle, i.e. ∠ABC.Naming the angle using numbers, i.e. ∠1By using the letter of the vertex of the angle only, i.e. ∠B.1. The three angles can be named as:
Angle ABC or ∠ABC
Angle 1 or ∠1
Angle ∠B or ∠B.
2. The shaded angle can be named as:
Angle JKM or ∠JKM
Angle 2 or ∠2
Angle ∠K or ∠K.
Two angles with the same marks on a diagram are congruent to each other. Therefore:
3. ∠CBJ ≅ ∠DHG
4. ∠FJH ≅ ∠AJB
Angles that are congruent to each other have the equal angle measure, therefore:
5. ∠EFD ≅ ∠JAB
Therefore, If m∠EFD = 75°, then m∠JAB = 75°.
6. ∠GHF ≅ ∠JBC
Therefore, If m∠GHF = 130°, then m∠JBC = 130°.
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Which statement is true about the graph of the line whose equation is y = 8?
Answer:
A. the line is parallel to the x axis
Step-by-step explanation:
B is incorrect because it will be intersecting the y axis therefore not being parallel
C is incorrect because It doesn't pass through the origin (origin is (0, 0) btw) it actually passes thru the point (0, 8) so this choice is wrong
D is incorrect because It doesn't give us enough info that the slope is 8 so we can't tell. Also if y = 8 it will just be a straight line so the slope will actually be 0 im pretty sure
A is correct because it is parallel if y = 8 and x axis kept going in a straight line they will never touch so that means it it parallel
Doughnuts are sold in bags and bags and doughnuts. a bag holds 10 doughnuts and a carton holds 10 doughnuts. tom buys b bags of doughnuts and c cartons of doughnuts he buys a total of t doughnuts write down a formula for t in terms of b and c
Answer:
t = 10b + 10c
Step-by-step explanation:
As stated in the problem, 1 bag holds 10 doughnuts so that give us 10b since we don't know how many bags were bought/sold but we do know how many comes in each. Same goes for cartons.
Were asked to write a formula for t, and since we don't know how many bags(b) or cartons(c) were sold, our t remains t.
73.261-2.852 =______
Answer:70.409
Step-by-step explanation:73.261-2.852
Mark wants to buy a new laptop that costs $699. He earns $65 for mowing lawns. What
is the minimum number of lawns he can mow to have enough money to buy the laptop?
Answer:
11 lawns
Step-by-step explanation:
$65 × 10 = $650
$695 - $650 = $45
So Mark will need to mow at least 11 lawns.
A plane flew at a constant speed between Boston and Philadelphia. An equation relating the distance traveled in miles, d, to the number of hours flying, t, is d=350t. How long will it take the airplane to travel 280 miles?
The time it take for the plane to travel at 280 miles is 0.8 hours.
How to find the time it will take the plane to cover a distance?The plane flew at a constant speed between Boston and Philadelphia.
An equation relating the distance travelled in miles, d, to the number of hours flying, t, is d = 350t.
Therefore,
d = 350t
where
t = time travelledd = distanceTherefore, let's find the time it will take to travel for 280 miles
d = 350t
d = 350 × t
280 = 350t
divide both sides by 350
t = 280 / 350
t = 0.8 hours
Therefore,
the time it will take to travel = 0.8 hours
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Find two consecutive whole numbers that √72 lies between.
The two consecutive whole numbers that √72 lies between are 8 and 9.
As per the question statement, we are supposed to find two consecutive whole numbers that √72 lies between.
We know,
8 squared is 64 and 9 squared is 81
since 72 lies in between 64 and 81, then the square root must lie between 8 and 9 which are also whole numbers and consecutive too.
Hence we accept out answer to be 8 and 9.
Hence the two consecutive whole numbers that √72 lies between are 8 and 9.
Whole numbers: Whole Numbers are all numbers, including zero and the natural numbers but not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …}To learn more about whole numbers, click on the link given below:
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The Roman Empire began in 31 B.C. and fell to the Goths in A.D. 476 How long did the Roman civilization last?
In case whereby the the Roman Empire began in 31 B.C. and fell to the Goths in A.D. 476,the Roman civilization lasted for 445 years.
What was Roman Empire?The Roman Empire can be described as the post-Republican period that can be associated with the ancient Rome , it can be described as the empire that came into the lime light around the 8th century BC , and actually came to an end around 5th century AD and the period it laste can be calculated below as :
In this case as regards to the question, we can calculate how long the Roman civilization lasted as [476+(-31)]
=445 years.
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What is the image of the point (-6,4) after a rotation of 180° counterclockwise about the origin?
By using the rotation formula, the image of the point (- 6, 4) after rotating 180° counterclockwise about the origin is equal to point (6, - 4).
How to determine the image of a point by using rotation rule about the origin
In this problem we find the coordinates of the image, which is the result of rotating a point 180° counterclockwise (+ 180°) about the origin. Let be P(x, y) = (x, y) the coordinates of the point set on Cartesian plane, then the coordinates of the image are defined by the following expression:
P'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)
Where θ is the angle of rotation, in degrees.
If we know that P(x, y) = (- 6, 4) and θ = 180°, then the coordinates of the image are, respectively:
P'(x, y) = (- 6 · cos 180° - 4 · sin 180°, - 6 · sin 180° + 4 · cos 180°)
P'(x, y) = (6, - 4)
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Jose fue a una papeleria y saco 10 fotocopias a color tamaño carta a 2.75 cada una y 100 fotocopias blanco y negro tamaño carta a 0.75 cada una ¿cuanto pago en total por todas las fotocopias?
The total cost that Jose will pay for the photocopies is $102.50.
How to calculate the amount?From the information, the following can be deduced:
Number of letter size photocopies = 10
Amount for each color photocopies = 2.75
Number of black and white photocopies = 100
Amount for each = 0.75
Therefore, the total cost will be:
= Cost of colored + Cost of black and white
= (10 × 2.75) + (100 × 0.75)
= 27.5 + 75
= $102.50
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Jose went to a stationery store and took out 10 letter size color photocopies at 2.75 each and 100 letter size black and white photocopies at 0.75 each. How much did he pay in total for all the photocopies?
16. If 45/n, what other whole numbers divide n? Why?
Answer:
1,3,5,9,15,45
Step-by-step explanation:
All factors of 45 to get a whole number
Answer:
90, 135, 180, 225, 270... ∞
Step-by-step explanation:
All multiples of 45 are divisible by n
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Graph the line that represents a proportional relationship between d and t with the property
that an increase of 5 units in t corresponds to an increase of 8 units in d.
What is the unit rate of change of d with respect to t? (That is, a change of 1 unit in t will
correspond to a change of how many units in d?)
The unit rate is
Graph the relationship.
-9-8
9
8-
7+
6-
5
44
3
2
1
+2+
-3-
-4+
-5-
-6-
-7
-8-
-9-
The proportional linear equation relationship has a unit rate of 1.6
How to plot the graph the line of the relationship?From the question, we have the statement to be:
The relationship between d and t is a proportional relationship An increase of 5 units in t causes an increase of 8 units in d.The above means that
5 * t = 8* d
Evaluate the products
So, we have the following equation
5t = 8d
Divide both sides of the equation by 5
So, we have the following equation
t = 1.6d
Next, we plot the graph of the equation
See attachment for the graph of the equation t = 1.6d
Also, we have
t = 1.6d
The above equation is a proportional linear equation
A proportional linear equation is represented as
t = md
Where m represents the unit rate
So, we have
m =1.6
Hence, the unit rate of the relationship is 1.6
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