Write the following expression using the fewest possible terms (2/5 * t - 7 + 2/3 * t) - (5/6 * t + 14)
Answers: 7/30*t + (-7)
7/30*t + (-21)
-57/30*t + (-7
57/30*t + (-21)
The expression using the fewest possible terms in (2/5*t - 7 + 2/3 * t) - (5/6 * t + 14) is (7/30)*t + (-21) .
In the question
the given expression is (2/5 * t - 7 + 2/3 * t) - (5/6 * t + 14)
Simplifying the expression further
we get ,
[tex]= \frac{2}{5} t-7+\frac{2}{3} t-\frac{5}{6} t-14[/tex]
writing the like terms together
= t * (2/5+2/3-5/6)-7-14
taking LCM of 5,3,6 as 30 and simplifying further we get ,
= t * (12/30 + 20/30 -25/30) - 21
= t * (7/30) - 21
which can also be written as (7/30)*t + (-21) .
Therefore , the expression using the fewest possible terms in (2/5*t - 7 + 2/3 * t) - (5/6 * t + 14) is (7/30)*t + (-21) .
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12. Determine whether the given number belongs
to each set.
Whole
Integers
Rational
Numbers
Numbers
-34
Answer:
-34 is an integer and a rational number
Step-by-step explanation:
whole numbers do not include negative numbers
Plot the points in a coordinate plane and sketch ∠X Y Z. Then classify it as right, acute, or obtuse.
X(6,7), Y(2,3), Z(4,1)
The points X(6,7), Y(2,3), Z(4,1) can be plotted as given below. From the obtained graph ∠XYZ is the right angle.
The given coordinates are X(6,7), Y(2,3) and Z(4,1).
We need to classify ∠XYZ whether it is right, acute, or obtuse.
How to plot the points in a cartesian plane?A cartesian plane or coordinate plane can be defined as a plane formed by the intersection of two coordinate axes that are perpendicular to each other. The horizontal axis is called the x-axis and the vertical one is the y-axis. These axes intersect with each other at the origin whose location is given as (0, 0). Any point on the cartesian plane is represented in the form of (x, y). Here, x is the distance of the point from the y-axis and y is the distance from the x-axis.
Now, X(6,7), Y(2,3), Z(4,1) can be plotted as given below:
All points X(6,7), Y(2,3), Z(4,1) have the positive x and y coordinates.
So, all the points X(6,7), Y(2,3) and Z(4,1) lie in the first quadrant.
From the graph, we can see at the two lines are perpendicular to each other.
So, the angle between two lines is the right angle which is 90°.
From the obtained graph ∠XYZ is the right angle.
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A linear function is shown on the graph. a linear function beginning with closed circle at 1 comma 3 and ending with a closed circle at 8 comma 7 What is the domain of the function? {y | 3 ≤ y ≤ 7} {y | 3 < y < 7} {x | 1 ≤ x ≤ 8} {x | 1 < x < 8}
The domain of the function is {x | 1 ≤ x ≤ 8}
The x-coordinates form the domain.
We know the x-coordinates of the end points of the line, the first numbers in pair of coordinates:
x = 1 and x = 8
Also, since both points are closed circles, the endpoints are included.
So the domain is the interval between 1 and 8, both inclusive.
This is shown as:
{x | 1 ≤ x ≤ 8}
A domain name is a string that identifies a realm of administrative autonomy, authority or control within the web . Domain names are utilized in various networking contexts and for application-specific naming and addressing purposes. generally , a website name identifies a network domain or an Internet Protocol (IP) resource, like a personal computer used to access the Internet, or a server computer. Domain names are often wont to identify services provided through the Internet, like websites and email services. As of 2017, 330.6 million domain names had been registered.
Domain names are formed by the principles and procedures of the Domain Name System (DNS). Any name registered within the DNS is a domain name. Domain names are organized in subordinate levels (subdomains) of the DNS root domain, which is nameless.
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Answer:
The domain of the function is {x | 1 ≤ x ≤ 8}
The x-coordinates form the domain.
We know the x-coordinates of the end points of the line, the first numbers in pair of coordinates:
x = 1 and x = 8
Also, since both points are closed circles, the endpoints are included.
So the domain is the interval between 1 and 8, both inclusive.
This is shown as:
{x | 1 ≤ x ≤ 8}
A domain name is a string that identifies a realm of administrative autonomy, authority or control within the web . Domain names are utilized in various networking contexts and for application-specific naming and addressing purposes. generally , a website name identifies a network domain or an Internet Protocol (IP) resource, like a personal computer used to access the Internet, or a server computer. Domain names are often wont to identify services provided through the Internet, like websites and email services. As of 2017, 330.6 million domain names had been registered.
Domain names are formed by the principles and procedures of the Domain Name System (DNS). Any name registered within the DNS is a domain name. Domain names are organized in subordinate levels (subdomains) of the DNS root domain, which is nameless.
Step-by-step explanation:
34. marissa hiked 1 3/4 miles in 3/4 hours. at that rate, how far can she hike in one hour?
By unitary method, Marissa can hike 7/3 miles in an hour.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Given:
[tex]1\frac{3}{4}[/tex] = 7/4miles are hiked in 3/4 hours.
To find: the number of miles hiked in one hour
Finding:
By unitary method,
Miles hiked in 3/4 hours = 7/4
Miles hiked in 1 hour = 7/4(4/3) = 7/3
Hence, by unitary method, Marissa can hike 7/3 miles in an hour.
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PLEASE HELP!
Alissa has already made $15 in the last week selling rubber band bracelets. She earns $5 for each bracelet she makes.
Complete the table to show how much money Alissa will have in total if she continues selling bracelets this week.
Using a linear function, the table for her earnings y of producing x bracelets is given as follows:
x = 1, y = 20.x = 2, y = 25.x = 3, y = 30.x = 4, y = 35.x = 5, y = 40.What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For this problem, we have that:
She has already made $15, hence the intercept is of b = 15.She earns $5 for each bracelet, hence the slope is of m = 5.Hence her earnings are modeled as follows:
y = 5x + 15.
The the numeric values are given as follows:
y(1) = 5(1) + 15 = 20.y(2) = 5(2) + 15 = 25.y(3) = 5(3) + 15 = 30.y(4) = 5(4) + 15 = 35.y(5) = 5(5) + 15 = 40.Then the table for her earnings y of producing x bracelets is given as follows:
x = 1, y = 20.x = 2, y = 25.x = 3, y = 30.x = 4, y = 35.x = 5, y = 40.More can be learned about linear functions at https://brainly.com/question/24808124
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13. Using the information from the previous problem, calculate the amount of taxes Monica owes.
This is the problem above
Monica falls into the 10% bracket.
What is tax?
The tax refers to the money that a person is expected to pay to the government as part of your responsibilities as citizen of the country. The tax that is paid by the citizens is used in the provision of basic amenities for the people of a community.
Now, there are certain legal exemptions that apply to different people in different tax brackets. In this case, Monica has an income of $14000 with a deduction of $5700. This leaves her taxable income at $8300.
From the computation above, it then follows that Monica falls into the 10% bracket.
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Answer:
$465
Step-by-step explanation:
just multiply 4650 (the taxable income) and .10 (the tax bracket she falls into) which equals 465! i hope it helped ^_^
PLEASE HELP!!
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Based on the figure on the graph, match the described transformations with the transformed figures.
reflected across the x-axis
rotated 180° clockwise
translated 9 units to the
right and 2 units down
reflected across the y-axis
The transformation of the given image follows the pattern; Reflection across the x-axis, then translation by 2 units downwards, the reflection across the y-axis.
How to carry out transformation reflection?
From the given first image, we see that it is in the first quadrant but by the second image, we see that it is now mirrored along the horizontal axis. Thus, we can say that it is reflected across the x-axis.
After reflection, across the x-axis, we see that it was translated down by 2 units.
The last transformation is that we see it is now in quadrant 3 which means it was now reflected across the y-axis.
The transformation of the given image follows the pattern; Reflection across the x-axis, then translation by 2 units downwards, the reflection across the y-axis.
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the sum of both digits, of either of two two-digit numbers, in whatever order the digits are written, is 9. the square of either of the digits of either number, minus the product of both digits, plus the square of the other digit is the number 21.
a = 5 and a = 4 are the sum of both digits, of either of two two-digit numbers.
What is square number in math?
When a number is multiplied by itself, the result is a square number. For instance, 25 is a square number since it is composed of 5 lots of 5, or 5 × 5. This is also known as "five squared," or 52. Because it is 102 (10 x 10, or "ten squared"), the number 100 is likewise a square.This can also be solved algebraically. Let the 2 digits be a and b, going left to right. The number itself is then
N = 10a + b. And it's given that a + b = 9, and a2 - ab + b2 = 21. Substitute for b = 9 - a, combine all terms of a2 and a, and you get
3a2 - 27a + 60 = 0. Divide by 3
a2 - 9a + 20 = 0. Factor
(a - 5)(a - 4) = 0. So the roots are a = 5 and a = 4.
The actual numbers N are 54 and 45.
The digits can be changed since the equations including only a and b are symmetric. (If a = 5, then b must be 4; inverse)
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Bob solved the equation \large A=2x-xyz^2-w for y . Which variable is incorrect in his solution below?
Bob's solution: {A-2x}/{w-xz^2} =y
a
A
b
x
c
w
d
z
The variable which is incorrect in his solution as given in the task content is; Choice C; variable w.
Which variable is incorrect in his solution?It follows from the task content that the equation is to be solved for y.
Given; A = 2x -xyz² -w
Add w-2x to both sides of the equation;
A+w-2x = -xyz²
Divide both sides by; -xz²
y = {A+w-2x}/{-xz²}
Hence, the variable which is placed incorrectly in the task content is; w as it should appear Inthe numerator instead of the denominator.
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Reena bought a jacket for £45. Six
months later, she sold it for £34.65.
What was her percentage loss?
Determine the written description of the complement of the given event. when are , of them .
The correct option is D. More than one of them test negative.
More than one of them tests negative in the written explanation of the given event.
What are conditional statements?We have a conditional statement that states that if it rains, we will not play. Let's say A: it's raining and B: we're not going to play. If A is true (it is raining) and B is false (we played), therefore the statement A implies B is false.
Now, as per the question;
The sentence states that seven people have been tested and that at least one of them tested positive, which means that the minimum number of positive outcomes is one, making options A, B, and C incorrect in aspects of probabilities and statistics. Option A and C state that ALL of them are positive or negative, respectively, which can be supported by the expression "at least," and option B is a restatement of option A.Option D correctly paraphrases the sentences by stating that there was at least one, though there could be more, but this does not guarantee that all.
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The complete question is -
Determine the written description of the complement of the given event. When seven job applicants are tested for a certain ability, at least one of them tests positive. Choose the correct answer below.
A. All of them test positive
B. None of them test negative
C. All of them test negative
D. More than one of them test negative
What is 1+1? I really need help
calculate the circumference of a circle with a: radius of 72,5mm
Answer:
4553
Step-by-step explanation:
2 x pi x r
At maximum speed, an airplane travels
Let x be the maximum speed of the plane and y
2100 miles against the wind in 6 hours.
be the speed of the wind. What is the speed of
Flying with the wind, the plane can
the plane with no wind?
travel the same distance in 4 hours.
Enter the correct answer.
express 121,200 in exponential (powers of 10) notation. express the earth sun distance in kilometers in powers of 10 notation.
1.5·10⁸ kilometers
As a result, the Earth Sun distance is 150 million kilometers. To use scientific notation, pick a value between 1 and 10, then multiply it by 10ˣ.
So the number between 1 and 10 in 150,000,000 is 1.5, with 8 decimal points.
As a result, the solution is 1.5·10⁸
State the distance between The Earth and The Sun?
The benefits of Earth's prime placement in the solar system are numerous. We are just far enough away from the Sun for life to thrive.
Venus is excessively hot. Mars is quite chilly. Scientists refer to our region of space as the "Goldilocks Zone" because it looks to be ideal for life.
As previously stated, Earth's average distance from the Sun is around 93 million miles (150 million kilometers). That's one AU.
On this hypothetical scale, these so-called "linebackers" resemble minuscule specks rather than the massive linebackers of the NFL.
If all of the known asteroids in our solar system were combined, their total mass would be less than 10% that of Earth's moon.
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Please Help I will Mark Brainlist !!!!! Help its a geometry Question (MATH) Find the length of b.
Thank you for your Help!!! it is appreciated
what is the range of this absolute value function
Answer:
5<y< infinity
Step-by-step explanation:
a rectanglualr box has a volume of 100 cubic units. let x be the length of the sides of its square bases. express the surface area a of the box in terms of x
According to the given statement the surface area a of the box is S1= 2× x ×(h+4).
What is the surface area?An object's surface area is the total area that all of its surfaces occupy. The formulas we will learn in this post make it simple to determine the various surface areas that various 3D shapes in geometry have.
According to the given data:Vol = W*L*H = 100
Vol = X*(X+4)*H = 100
H = 100/(X^2 + 4X)S
A = 2*(X*(X+4) + X*H + H*(X+4))
Let h = the height× x ×(h+4)=100
h=100/x^{2} +4x
The top and bottom surfaces are:
S1= 2× x ×(h+4)
The following are the front as well as back areas:
S2= 2× (x+4)× h
The area for the sides is:
S3= 2x × h
Choose a value for x to check this as one method.
x=9x+ 4=13
h=100/x^{2} +4
h=100/81+4
h=100/117
According to the given statement the surface area a of the box is S1= 2× x ×(h+4).
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Solve for the missing length
Answer:
10
Step-by-step explanation:
All sides are divided by 2 on corresponding sides.
Emily claims that a tree height of 43 inches is an outlier for the distribution. Based on the 1. 5×iqr rule for outliers, is there evidence to support the claim?.
Emily claims that a tree height of 43 inches is an outlier for the distribution.
What is the 1.5 IQR rule for outliers?
Add 1.5 to the interquartile range (IQR) (a constant used to discern outliers). The third quartile is increased by 1.5 times (IQR). Any figure above this is thought to be an outlier.
The starting and the end of the box in box plot are first and third quartile respectively.
From the given box plot it is clear that, Q₁ = 34 and Q₃ = 38
IQR = Q₃ - Q₁
IQR = 38 - 34
IQR = 4
According to 1.5x IQR rule for outliers, all the data values lies outside the interval [ Q₁ - 1.5 × IQR , Q₃ + 1.5 × IQR ] are outliers..
Q₃ + 1.5 × IQR = 38 + 1.5(4)
Q₃ + 1.5 × IQR = 38 + 6
Q₃ + 1.5 × IQR = 44
We know that, 43<44.
Since, 43 is not greater than Q₃ + 1.5 × IQR therefore, 43 is not an outlier and there is no evidence to support the claim.
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A box of book has a mass of 4.1 kilograms for every meter of its height . Convert your this ratio into pound per inch
Answer:
9 pounds per inch
Step-by-step explanation:
There are approximately 2.2 pounds in a kilogram. So, 4.1 kilograms is approximately 9 pounds. Therefore, the ratio is 9 pounds per inch. The step by step for this is, 4.1 kg/m * 2.2 lb/kg = 9 lb/m * 1 in/m = 9 lb/in
plese help me with this work
Step-by-step explanation:
Mark is 18, as his 8th birthday was 10 years ago
Aunt Jess is 36 since Jess is twice as old as Mark
Julie is 28 because 36+18=54, and 54-26=28
Gwen is 30 since she's 2 years older than Julie
The twins are 8 (1/3 of 30 is 10, then do -2)
Answers:
1. 8
2. 10
3. Mark will be 23
4. Gwen was twice Julie's age when she was 4 (26 years ago)
(Gwen is 2 years older than Julie)
I hope this helps, Brainliest and Thanks would be very much appreciated
Answer: 1. 8 years old
2. 10 years
3. 23 years old
4. 26 years ago
Step-by-step explanation:
G=Gwen's age.
J=Julie's age.
A=Aunt Jess's age
U=Uncle Mark's age
T=twins' ages
1. G=J+2
A=U*2
J=A+U-26
T=G/3 - 2
U-10=8
U+10-10=8+10 ==> Add 10 on both sides to single out U.
U=18
A=U*2
A=18*2
A=36
J=A+U-26
J=36+18-26
J=54-26
J=28
G=J+2
G=28+2
G=30
T=G/3 - 2
T=30/3 - 2
T=10-2
T=8 ==> 8 years old
2. 8+x=18
8-8+x=18-8
x=10 years
3. U=18
18+5=23 years old
4. G=J+2
G=J*2
J*2=J+2
2J=J+2
J=2 ==> subtract J on both sides
G=2+2
G=4
30-4=26 years ago
11/13% of a quantity is equal to what fraction of the quantity?
11/13% of a quantity is equal to 11/1300 fraction of the quantity.
What is Percent to Fraction?Percentage signifies for every hundred or for each. We display it as %. Since a percentage is expressed on a scale of 1 to 100, it is easy to comprehend. Converting percentage data to fractions is known as "percent to a fraction." As per the percent to fraction conversion instructions, the percentage can be written as a fraction by deleting the percent symbol and placing 100 in the denominator. Any percent can easily be converted to a fraction, and the opposite is also true.
How to Convert Percent to Fraction?To convert a percentage to a fraction, follow these three simple steps. Let's examine these three processes in more detail.
Leave out the percent sign.divide it by 100.Reduce the obtained fraction.Divide the given percentage by 100
[tex]\frac{11}{13}[/tex]% [tex]=\frac{11}{13} \times \frac{1}{100} \\=\frac{11}{1300}[/tex]
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The length of a rectangle is 99 centimeters. Find all possible values for the width of the rectangle if the perimeter is at least 240 centimeters.
So the width should be 21 cm, to have a length of 99 cm and a perimeter of 240 cm in linear equations.
What are instances of linear equations?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.240 = 2(99) + 2x
240 = 198 + 2x
42 = 2x
21 = x
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You have a coupon for your favorite clothing store for $20 off any purchase of more than $75. The store is
also running a 15%-off sale on its entire inventory. Let x be the original price,
f x( )
be the price with the $20
coupon applied, and
g x( )
be the price with the 15% discount applied.
(a) Write an expression for
f x( ) . (3 points)
(b) Write an expression for
g x( ) . (3 points)
(c) Write the expression
(f g x )( )
and explain what it represents? (3 points)
(d) Write the expression
(g f x )( )
and explain what it represents? (3 points)
(e) If the store allows you to apply both the 15% discount and the $20-off coupon, does it matter which
you apply first? How do you know? (3 points
Answer:
f(x) = (1 - 0.25)x = 0.75x
f(x) = 0.75x
g(x) = (1 - 0.2)x = 0.8x
g(x) = 0.8x
(f o g)(x) = f(g(x)) = 0.75(0.8x) = 0.6x
(f o g)(x) = 0.6x
(g o f)(x) = 0.8(0.75x) = 0.6x
(g o f)(x) = 0.6x
Step-by-step explanation:
It does not matter which one you apply first.
13/8 x 11=
3/5 x 5/7=
2/5 x 5/6=
Answer:
Hope this helps :)
13/8 x 11 = 143/7 = 17 7/8 (simplified and converted into mixed number)
3/5 x 5/7 = 15/35 = 3/7 (simplified)
2/5 x 5/6 = 10/30 = 1/3 (simplified)
19
Type A batteries and type B batteries were tested.
The cumulative frequency diagram shows information about the battery life of type A.
19 (a)
80
70
60
50
Cumulative
frequency 40
30
20
10
of
0
Type A
800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800
Battery life (hours)
Estimate the interquartile range for type A.
Answer
hours
[2 marks]
300 Hours will be the Interquartile range for type A batteries.
In the given question, we have 11 terms in Hours, So we get N = 11, and the formula can calculate the Median for the allotted Hours [tex]\frac{n+1}{2}[/tex]
Since the Median is 6th term i.e. we get Middle Quartile Q2 = 1300Hours
Q1 is the Lower quartile of the graph and the Median divides the graph into 8 equal parts. And we get the value of Q1 = 1100 Hours. Whereas, The upper quartile is the upper quarter. So, Q3 = 1400 Hours.
We have the formula to calculate the Interquartile range :
IQR = Q3 - Q1
Putting values of Q3 and Q1 into the formula, We get :
IQR = 1400 - 1100
IQR = 300
Hence, the Interquartile range IQR = 300 Hours.
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What is an equation of the line that passes through the point (−2,7) and is perpendicular to the line x−4y=24?
Answer:
y=-4x-1
Step-by-step explanation:
x-4y=24
-x -x
-4y=-x+24
Divide -4
y=-1/-4x-6
Simplify the slope.
y=1/4x-6
Perpendicular slope
m = 1/4
m = -4
The point is (-2,7)
-2 is the x intercept
7 is the y intercept
Slope Point Form is y-y1=m(x-x1)
Plug it in
y-7=-4(x+2)
Solve and put it into slope intercept form
y-7=-4x-8
+7 +7
y=-4x-1
There's your answer.
Hope that helps.
A model of a golf course says that hole #9 is 175 yards long. If the scale for the model is 2in.:20 yards, how many inches are there between the tee and the hole on the model.
There is 17.5 inches distance between the tee and the hole on the model.
According to the question we have been given that
length of hole#9 is = 175 yards
the scale for the model is given as = 2 inch : 20yards
We need to find the inches between the tee and the hole.
Let the length between the tee and the hole on the model be x inches
Thus the above condition can be written as
2 inches / 20yards = x inches/175 yards
We have to solve this proportion for x we get
x inches = 175*2/20
x = 17.5 inches
Hence there is 17.5 inches distance between the tee and the hole on the model.
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