Three pairs of fractions that have a sum of 5/6 are;
1/3 + 2/3 = 5/6
1/4 + 3/4 = 5/6
2/6 + 3/6 = 5/6
How to calculate this?1/3 + 2/3 = 5/6: The fractions have a common bottom number of 3 because they both have the same bottom number.
Adding the top numbers: 1 plus 2 equals 3.
The total is three divided by three, which can also be written as one.
However, we need to show the total with a bottom number of 6 to match the original part. So, we make the top and bottom numbers twice as big to get 2/6. Hence , 1/3 + 2/3 = 2/6.
1/4 + 3/4 = 5/6:The fractions have the same bottom number, so their common denominator is 4.
When you add 1 and 3 together, you get 4.
The sum is four over four, and when simplified, it equals one.
Once again, we have to find a way to write the sum with a bottom number of 6 so that it is the same as the first number in the fraction. So, we take the top number and the bottom number and multiply them both by 3 to get the fraction 3/6. Hence, 1/4 + 3/4 = 3/6.
2/6 + 3/6 = 5/6:In this situation, the fractions already have the same bottom number which is 6.
Adding the top numbers together: 2 + 3 = 5.
The answer is 5/6, which is what we wanted to get.
Therefore each pair shows a different way to add numbers together, either by finding a number that both denominators can divide evenly into or by using numbers that already work well together.
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these are two angles that are formed by two coplanar lines and a transversal. they occupy the same relative positions.
Corresponding angles are two angles that are formed by two coplanar lines and a transversal and they occupy the same relative positions.
What pairs of angles are formed when two parallel lines are cut by a transversal?There are numerous pairs of angles that are created when a transversal cuts any two parallel lines. These angles include consecutive interior angles, alternate interior and exterior angles, and comparable angles.
Which of these pairs of angles is always equal when a transversal cuts two parallel lines?Each set of comparable angles are equal when a transversal cuts two parallel lines.
The angles that occupy the same relative location when a transversal cuts two or more lines are known as corresponding angles. The matching angles are equivalent when the lines are parallel.
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four feet of wire is used to form a square and a circle. how much wire should be used for the square and how much should be used for the circle to enclose the maximum total area
The total maximum area enclosed by both the shapes square and a circle using given wire is equal to 2.27 square feet.
As given in the question,
Let 'x' be the side length of the square
And 'r' be the radius of the circle.
Length of the wire = 4 feet
Maximum side length of the square is:
4x = 4
⇒ x = 1feet
Maximum area of the square = x²
= 1²
= 1
Maximum radius of the circle is:
2πr = 4
⇒ r = 2 / π
Maximum area of the circle = πr²
= π × (2/π)²
= 4 / π
Total maximum area enclosed by square and a circle
= 1 + (4/π)
= 1 + 1.27
= 2.27 square feet.
Therefore, the total maximum area enclosed by square and a circle from the given wire is equal to 2.27 square feet.
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Triangle ABC is reflected over the x-axis. What are the coordinates of the image of the vertex A?
The image of vertex A will be at point (2,-5).
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The perimeter will be P = sum of all three side.
Point A is located at (2, 5), thus you look at the y-coordinate since you are reflecting it across the x-axis.
Given that it is five above the x-axis, you must travel five below it, or you can simply enter the opposite of five, which is -5.
So, A' is at (2, -5).
Hence, The image of vertex A will be at point (2,-5).
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Learning curve: In psychological tests, it is found that students can memorize a list of words after t hours, according to the learning curve y = 50 - 50e^-0.3t, where y is the number of words a student can learn during the t^th hour of study. Find how many words a student would be expected to learn in the ninth hour of study.
A student is expected to learn approximately 46.535 words in the ninth hour of study.
What is the number of words a student would be expected to learn in the ninth hour of study.?Generally, To find the number of words a student is expected to learn in the ninth hour of study, we can substitute 9 for t in the learning curve equation:
y = 50 - 50e^-0.3(9)
Simplifying the exponent, we have:
y = 50 - 50e^-2.7
To calculate the value of e^-2.7, we can use a calculator or lookup the value in a table of common exponent values. The value of e^-2.7 is approximately 0.0693.
Substituting this value back into the equation, we have:
y = 50 - 50(0.0693)
Simplifying, we find:
y = 50 - 3.465
y = 46.535
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ssdfmsfamong treatments1743 435.751.27error total5503.4615step 6 of 8: what is the variation of the individual measurements about their respective means? please round your answer to two decimal places.
The variation of the individual measurements about their respective means is 2295.04.
Given that,
The table of the treatments and total amount is
SS DF MS F
Among Treatments 4974.88 621.86 2.98
Error ?
Total 7269.92 19
We have to find how do the various measurements differ from their respective means.
We know that,
We know the formula
SSE= SSTotal -SST
= 7269.92-4974.88
=2295.04
The variation of the individual measurements about their respective means is SSE that is 2295.04
Therefore, The variation of the individual measurements about their respective means is 2295.04.
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Two dice are rolled. Determine the probability of the following. ("Doubles" means both dice show the same number. Enter your probability as a fraction.)
rolling a number greater than 5 or doubles
The probability of rolling a number greater than 5 or doubles will be 0.78.
What is probability? What is a mathematical equation? What do you mean by domain and range of a function?The formula to calculate the probability of occurrence of an event [A] can be written as -P(A) = n(A)/n(S)
where -
n(A) = Number of outcomes favorable to event A.
n(S) = Total number of outcomes.
A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have two dices are rolled.
The sample space for sum greater than 5 will be 26. For doubles, we will add 2 pairs (1, 1) and (2, 2) to 26 to get a total sample space of 28. Remaining doubles are already in 26. So, the probability of rolling a number greater than 5 or doubles will be -
P(A) = 28/36 = 0.78
Therefore, the probability of rolling a number greater than 5 or doubles will be 0.78.
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[Question in english -
From a point on the ground located 4m from a pole, its upper part can be seen with an elevation angle of 37°. What is the height of the pole?]
Which of the following pairs of linear equations are consistent or inconsistent XY 8 3x -- 3y 16?
The equations have no solutions and run parallel to one another. The pair of linear equations is hence inconsistent.
What are linear equations?Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.
The definition of linear equations, the standard form for linear equations involving one variable, two variables, or three variables, and examples of each will all be covered in detail in this article.
Find the value of the variable that causes the equation to be true in order to solve linear equations.
Utilize the inverse of the variable's multiplier and divide or multiply both sides by it.
To obtain the variable value, simplify the result. Put your solution back into the equation to verify it.
So, we have the pair of linear equations:
x – y = 8 and 3x – 3y = 16
(a1/a2) = 1/3
(b1/b2) = -1/-3 = 1/3
(c1/c2) = 8/16 = 1/2
Since, we know that (a1/a2) = (b1/b2) ≠ (c1/c2).
The equations have no solutions and run parallel to one another. The pair of linear equations is hence incoherent.
Therefore, the equations have no solutions and run parallel to one another. The pair of linear equations is hence inconsistent.
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Complete question:
Find out whether the following pairs of linear equations x – y = 8 and 3x – 3y = 16 are consistent/inconsistent.
Andrea is 165 cm tall, correct to the nearest cm. Joel is 170 cm tall, correct to the nearest 10 cm. Calculate the upper and lower bound for each person.
Andrea lower bound =
Andrea upper bound =
Joel lower bound =
Joel upper bound=
Answer:
Step-by-step explanation:
andrea lb: 164.5cm
andrea ub: 165.5 cm
joel lb: 165
joel ub: 175
one apple and six bananas cost £2.70
one apple and eight bananas cost £3.50
Work out the cost of an apple and a banana
PLSSS HELP TYSM
Answer:
An apple costs 0.30 pounds and a banana costs 0.40 pounds.
Step-by-step explanation:
Let's think of apples as x and bananas as y.
Using the given information, you can write two equations.
[tex]x+6y=2.70[/tex]
[tex]x+8y=3.50[/tex]
x can also be written as
[tex]x=2.70-6y[/tex]
We can plug this equation into the second one to solve for y, or the cost of a banana.
[tex](2.70-6y)+8y=3.50[/tex]
[tex]2y=0.8[/tex]
[tex]y=0.4[/tex]
Now that we know the cost of a banana, we can go back to the first equation and solve for x, or the cost of an apple.
[tex]x+6(0.4)=2.70[/tex]
[tex]x=0.30[/tex]
Therefore, an apple costs 0.30 pounds and a banana costs 0.40 pounds.
The cost of 7 sandwiches and 5 milkshakes is $79. The cost of 2 sandwiches and 5 milkshakes is $44. How much does one sandwich cost and one milkshake cost?
Cost of one sandwich is $7 and cost of milkshake $5.
What is an equation?
In arithmetic, associate equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
According to question:
let cost of one sandwich be x and cost of milkshake be y .
7x + 5y = $79 -------(1)
2x + 5y = $44 -------(2)
subtracting equation 2 from 1 , we get
5x = 35
x = $7
so cost of one sandwich is $7.
now substituting value of x in equation 1 , we get
7(7) + 5y = 79
49 +5y = 79
5 y = 20
y = 4
so cost of one milkshake is $5.
Hence cost of one sandwich is $7 and cost of milkshake $5.
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Graph the line that passes through the coordinates below and determine which statement is true.
A.
The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
B.
The line that passes through the given coordinates represents a proportional relationship because the line does not pass through the origin.
C.
The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.
D.
The line that passes through the given coordinates represents a proportional relationship because the line passes
Answer:
The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
Do anyone know the answers?
Answer:
e is 9x D is 4x c is 1× and a is 5× and b is 2×
Find the equation of a line parallel to 4x + 4y = -28 that passes
through the point (−4, –4).
Oy-4=x-4
Oy+4= x +4
○y-4=− (x − 4)
Oy+4= (x+4)
Submit Answer
The equation of the line that passes through the point (-4,-4) is y=-x-8.
How to find equation of line?The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y -axis).
What are three equations of line?The three equation of line are slope-intercept form, standard form and point-intercept form.
4x+4y=-28
Taking 4 common and dividing both sides by 4 gives
x+y= -7
y=-x-7
This means slope that is m=-1.
Now to find c in y=mx+c we need to use points (-4,-4).
-4=(-1)(-4)+c
c=-8
So the equation of line is y=-x-8.
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what is the quadratic equation in standard form with rational coefficents that has a root of 5+4i?
Answer:
x^2 -10x + 41 = 0
Step-by-step explanation:
They gave you a root. A root is a solution, is a zero, is an x-intercept(if real).
This is a working backwards problem. They gave you an answer and want the equation back again.
x = 5 + 4i
working backwards:
x - (5 + 4i) = 0
x - 5 - 4i = 0
This left side is a factor of your equation.
If 5+4i is a root then 5-4i is also a root. So do the same thing:
x = 5 - 4i
x - (5 - 4i) = 0
x - 5 + 4i = 0
x - 5 + 4i and
x - 5 - 4i are the factors. Multiply them together to find the quadratic equation. Use distributive property or difference of squares or an area model to model. See image.
Answer:
x² - 10x + 41 = 0
Step-by-step explanation:
complex roots occur as a conjugate pair.
given x = 5 + 4i , then x = 5 - 4i is also a root
the corresponding factors are
(x - (5 + 4i) ) , (x - (5 - 4i) ) , that is
(x - 5 - 4i) and (x -5 + 4i)
the quadratic equation is then the product of the factors, that is
(x - 5 - 4i)(x - 5 + 4i) = 0
multiply each term in the second factor by each term in the first factor.
x² - 5x + 4ix - 5x + 25 - 20i - 4ix + 20i - 16i² = 0 ← collect like terms
x² - 10x + 25 - 16i² = 0 [ note i² = - 1 ]
x² - 10x + 25 + 16 = 0
x² - 10x + 41 = 0 ← in standard form
Does the picture represent a function?
Yes or No
Answer: Yes
Step-by-step explanation: To determine if this graph represents a function, we use what is called the vertical line test.
In other words, if we can draw a vertical or straight up and down line that passes through more than one point on the graph, the relation is not classified as a function.
In this case, it's impossible to draw such a line that hits more than one point on the graph so the relation is a function.
Which of the following equations has the sum of its roots as 3?
A. 2x2-3x+6=0
B. -x2+3x-3=0
C. 3x2-3x+3=0
D. x2+5x+6=0
-x2+3x-3=0 is the equation that has the sum of its roots as 3.
What is meant by sum of roots?A quadratic equation's roots are equal to the second term's coefficient negated, divided by the leading coefficient. The constant term (the third term), divided by the leading coefficient, is equivalent to the product of the roots of a quadratic equation.
Write general formula for the sum of roots.Sum of roots= -b/a
Sum of root is defined as:
Sum of root = -b/a
Consider option B -x^2+3x-3
a=-1 , b=3
Sum of root= - 3/(-1)=3
So B is the correct option of the following question.
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What is 8/15 simplyfied??
Answer:
8/15
Step-by-step explanation:
There is no GCF (greatest common factor) in this. These numbers are relatively prime.
the cdc estimated that 12% of women who have recently given birth suffer from ppd. however, this research only reflected self-reported cases. therefore, one group dedicated to helping women and their families with ppd believes that the true percentage of women who suffer from ppd is much higher. the group conducts a simple random sample of 139 women who had given birth in the last year and discovers that 25 of them report having ppd. based on this evidence, can the group claim that the true percentage of women who have ppd is greater than 12%? use a 0.05 level of significance. step 2 of 3 : compute the value of the test statistic. round your answer to two decimal places.
The actual percentage of female people with ppd is more than 12%.
What is ppd ?Many women experience postpartum depression (commonly known as PPD), which is a medical disorder. After giving delivery, there are intense emotions of sadness, anxiety (concern), and exhaustion that persist for a long time. You may find it challenging to care for both you and your infant as a result of these feelings. PPD can occur at any point following childbirth. Within 1 to 3 weeks of giving birth, it frequently begins. To get better, it need treatment.
What does true percentage mean in statistics?And that's basically what TS% is. A measure of scoring efficiency based on the number of points scored over the number of possessions in which they attempted to score. The actual TS% formula multiplies the denominator by 2 to put the number into a percentage scale, but it's the same result on a different scale
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3 times 1 1/2 times 2 1/2 
Answer:
6
Step-by-step explanation:
Trust the process
an automobile assembly line runs for 9 3/4 hours each day. employees work 3/4-hour shifts. how many shifts are there in each day
A. 9 shifts
B. 10 shifts
C. 12 shifts
D. 13 shifts
Answer:
D 13 shirt
Step-by-step explanation:
9 [tex]\frac{3}{4}[/tex] ÷ [tex]\frac{3}{4}[/tex]
[tex]\frac{39}{4}[/tex] x [tex]\frac{4}{3}[/tex] = 13
if angle A=125 in the parallelogram below, what is the measure of angle B?
Answer:
angle B = 55°
.............
Five times a number is 375. What is the number?
Answer:
75.
Step-by-step explanation:
We need to divide 375 by 5 since we are looking for 5 times a number. This will give us the answer, 75.
Answer:
75.
Step-by-step explanation:
We need to divide 375 by 5 since we are looking for 5 times a number. so the answer is 75
Mitch sells thingamabobs. His revenue is modeled by the function
R(h) = 5h+8 for every h hours he spends working. His overhead cost is
modeled by the function C'′(h) = h² + 7h − 16. After how many hours does
he break even?
The number of hours to breakeven will be 5 hiurs
How to calculate the breakeven?The breakeven is the point at which the cost and the revenue are equal.
Since Mitch sells thingamabobs. His revenue is modeled by the function R(h) = 5h+ + 8 for every h hours he spends working and his overhead cost is modeled by the function C'′(h) = h² + 7h − 16.
This wll be:
Revenue = Cost
5h + 8 = h² + 7h - 16
Collect like terms
h² + 7h - 5h - 16 = 0
h² - 2h - 16 = 0
Solving the equation will give h as 5.
The number of hours will be 5 hours.
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How do you write the equation for a line that passes through points (2,1) and (0,7)?
The equation for a line that passes through points (2,1) and (0,7) is y-7 = -3x or y= -3x+7
To find the equation of a line passing through two points you must first find the slope of the line.
The slope can be found by using the formula: [tex]m=\frac{y2-y1}{x2-x1}[/tex]
Where m is the slope and (x1,y1) and (x2,y2) are the two points. Substituting the two points given in the problem allows us to calculate the slope as:
[tex]m=\frac{7-1}{0-2} \\m= \frac{6}{-2} \\m= -3[/tex]
Next, we have to use the point-slope formula to find the equation for the line passing through these two points.
The point-slope formula states: (y-y1)=m(x-x1)
Where m is the slope and x1, and y1 are points from which the line passes.
Substituting the value of m and x1 and y1 in the given equation,
y-7=-3(x-0)
y-7= -3x-3*0
y-7+-3x
Solving for the slope-intercept form gives:
y-7+7= -3x+7
y-0 + -3x+7
y= -3x+7
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(2x^2 - 4x + 3) + (5x - 6x^2 - 1)
Answer:
The answer is (-4x² + x + 2)
Step-by-step explanation:
(2x² - 4x + 3) + (5x - 6x² - 1)
open the brackets
2x² - 4x + 3 + 5x - 6x² - 1
rearrange the priority order
2x² - 6x² - 4x + 5x + 3 - 1
combine like terms
-4x² + x + 2
Thus, The answer is (-4x² + x + 2)
Find x, given
AD = BC = 6m.
The value of x in the trapezium is 60 degrees.
How to find the angle of a trapezium?A trapezium is a quadrilateral . The sum of angles in the trapezium is 360 degrees. The legs of the trapezium ABCD are congruent.
The length AB and CD are parallel to each other.
Let's find the angle x as follows:
Therefore, using trigonometric ratios,
cos x = adjacent / hypotenuse
Where
adjacent side = 3 m
hypotenuse side = 6 m
Hence,
cos x = 3 / 6
cos x = 1 / 2
x = cos ⁻¹ 0.5
x = 60 degrees
Therefore,
x = 60 degrees.
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In the United States, the common paper size is called letter size and measures 8. 5 by 11 inches. Let
V(x)= (8. 5-2x)(11-2x) (x) be the volume in cubic inches of a box made from a letter size paper
by cutting out squares of side length x in inches from each corner and then folding up the sides.
What is a reasonable domain for V in this context? Explain or show your reasoning.
PLs help
Answer:
0 < x < 4.5
Step-by-step explanation:
You want the reasonable domain of V(x) = (8.5 -2x)(11 -2x).
Reasonable domainThe equation describes volume (V) and cut length (x), so both need to be positive. Volume will be positive when ...
8.5 -2x > 0
4.25 > x
The reasonable domain is 0 < x < 4.5.
Determine the x and y intercept:
X -3 -2 -1 0 1
y 0 2 4 6 8
Wendy spent 1/4of her paycheck on Monday and
3/7of it on Tuesday. She spent the rest of her
paycheck over the next 3 days. If Wendy spent $18 on each of the 3 days, what was the amount of
her paycheck
Answer:
$56.00
Step-by-step explanation:
Check:
1/4(56) + 3/7(56) + 18 =
14 + 24 + 18 = 56
See the picture below. I wanted to figure out what fraction of the paycheck was the 18.
I took 1 which is the whole pay check and subtracted out the fractions that I knew were spent 1/4 and 3/7. That left me with 9/28. So I knew 9/28 of the paycheck was 18 dollars. I drew out 28 squares. 9 of those squares was worth $18. That meant that each square was worth $2. 2 x 28 = 56
Write the equation of the circle with a radius of 10 and a center at (3,-1)
Answer:
[tex]\textsf{b)} \quad (x-3)^2+(y+1)^2=100[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Given:
center = (3, -1)radius = 10Substitute the given center and radius into the formula to create the equation of a circle with the given parameters:
[tex]\implies (x-3)^2+(y-(-1))^2=10^2[/tex]
[tex]\implies (x-3)^2+(y+1)^2=100[/tex]
