A particular shade of paint is made by mixing five parts of red paint with seven parts of blue paint. To make the correct shade, Shannon makes 12 quarts of blue paint with 8 quarts of red paint. Did Shannon mix the correct shade? Explain.
We get that Shannon did not mix the correct shade as the ratios are not equal.
We are given that a particular shade of paint is made by mixing five parts of red paint with seven parts of blue paint.
This means that the ratio of the paints in that shade is
Red : Blue = 5 : 7.
Now, we are also given that to make the correct shade, Shannon makes 12 quarts of blue paint with 8 quarts of red paint.
Here the ratio becomes:
Red : Blue = 8 : 12
= 4 : 6
= 2 : 3
Now, since both the ratios are not equal, he did not mix the correct shade.
Therefore, we get that Shannon did not mix the correct shade as the ratios are not equal.
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How do you write 2204000000 in scientific notation?
Answer:
2.204×[tex]10^{9}[/tex]
Step-by-step explanation:
Convert to scientific notation.
Which variable expression represents the following word phrases?
13 more than two times a number.
13-2n
2n-13
13>2n
13+2n
Answer:
13+2n
Step-by-step explanation:
'two times a number' means 2n
'13 more' means we add 13 to this, so 13+2n is the answer.
If a/b = c, then a = bc converse
To address the issue, we must understand what the converse of a statement implies. The statement's opposite is true if a=bc and a/b=c.
By switching the condition and the result, a conditional statement can be made into its opposite. The converse of a statement is q—->p if the statement is p—->q. In the provided question, the condition is stated as a/b=c, and the answer is a=bc if the condition holds.
We must create the result, the condition, and the condition will be the new result in order to discover the opposite of this assertion. As a result, a=bc will be the condition for converse, and a/b=c will be the outcome if the condition is satisfied.
As a result, if a=bc then a/b=c., the supplied sentence has the opposite meaning.
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The fraction model below shows the steps that a student performed to find a quotient. Which statement best interprets the quotient?
The statement that best interprets the quotient is "there are 6( 1/4 ) two - third in 4( 1/6 )".
In mathematics, the sum obtained by diluting two numbers is known as a quotient. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.
Any integer may be used as the larger number in a fraction, which is a number that represents a percentage of the larger number. It is shaped like a denominator and a numerator.
For step 1:
The shaded part is:
4 + 1/6 = 4(1/6) = 25/6
Now, dividing the shaded part by the unshaded part,
( 25/6 ) / ( 2/3 ) = ( 25/6 ) × ( 3/2 )
( 25/6 ) / ( 2/3 ) = 25/4
( 25/6 ) / ( 2/3 ) = 6( 1/4 )
Hence, there are 6( 1/4 ) two - third in 4( 1/6 ).
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Please help!!!!!!! thx xxx
Start by dividing both sides by G, giving us
[tex]\frac{F}{G}=\frac{m_{1} m_{2} }{d^{2} } }[/tex]. Multiply both sides by d^2. [tex]\frac{F}{G}(d^{2})=m_{1} m_{2}[/tex].
Finally, divide both sides by m2.
[tex](\frac{F}{G}\div{m_{2}}) (\frac{d^{2} }{m_{2} } )=m_{1}[/tex]
Hope this helps! This was a tough problem for me too.
In the 1800s psychologists established______
behavior and mental processes.
Answer:
the scientific approach led to the birth of modern psychology in the 1800's as psychologists argued that ideas about human behavior and mental processes should be supported by this. In the 1800's, psychologists established these for the (scientific study of human behavior and mental processes).
Step-by-step explanation:
An open cylindrical tank is 150 feet in diameter and 180 feet high. The lateral surface area of the tank (no top and no bottom) is to be painted with paint that covers 225 square feet per gallon. When filled each cubic foot of the tank holds approximately 7.5 gallons of gasoline valued at $2.75 per gallon.
a) Find the number of gallons of paint required for a single coat of paint.
b) Find the total value of the gasoline in the filled tank.
In linear equation, the total value of the gasoline in the filled tank = $65605290
What is a formula for linear equations?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b). 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.
Radius = 150/2 = 75 feet
height = 180 feet
A)
lateral surface area = 2 *pi*r*h = 2*pi* 75 *180 =84823
number of gallons of paint=84823/225 = 377 gallons
B)
Volume of cylinder= pi*r²h= pi*75^2*180 =3180862.5618
total value of the gasoline in the filled tank =3180862.5618 *7.5 *2.75 =$65605290
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What is the quotient of 5/6 + 2/7?
Answer:
Step-by-step explanation:
this app is helpful
You may recall that the area of a rectangle is A=L⋅W, where W is the width and L is the length.
Suppose that the length of a rectangle is 4 times the width. If the area is 900 square feet, then what is the width of the rectangle, in feet?
Answer:
Width = 15 ft
Step-by-step explanation:
Given formula,
→ A = L × W
Let us assume that,
→ Length = 4x
→ Width = x
→ Area = 900 ft²
Then the value of width will be,
→ A = L × W
→ 900 = 4x × x
→ 4x² = 900
→ x² = 900/4
→ x = √225
→ [ x = 15 ft ]
Hence, the value of width is 15 ft.
All whole numbers can also be classified as
integers and rational numbers.
True
False
Answer:
True
Step-by-step explanation:
We use definitions to help us in this problem. The definition of an integer is a whole number that is not a fraction or has any fractional value. This definition includes all whole numbers, so we know that all whole numbers can be classified as integers. That's one condition done. The definition of a rational number is a number that can be written as a fraction. All whole numbers can be written as a fraction (i.e. 12/1, -3/1, 10000/1). This means that all whole numbers are also rational numbers, giving us our final answer of True.
FINAL ANSWER: True
A company is designing boxes to ship their product to stores. The design team decides that the width of the box should be five feet shorter than the length, and the height of the box should be three feet longer than the width. Due to shipping constraints, the length of the box can be no greater than six feet.
The volume of the box, V(x), can be modeled by a polynomial function, where x is the length of the box. Which of the following correctly models the situation above and gives the correct domain?
The polynomial function is V(x) = x^3 - 7x^2 + 10x and domain of x is (5,6]
Here we are given that the length of the box is x
Also, the width of the box should be 5 feet shorter than the length
Thus, width = x - 5
and the height should be 3 feet longer than the width
Thus, height = x - 5 + 3
= x - 2
Now the volume of the box = length × width × height
Volume = x (x-5) (x-2)
V(x) = (x^2 - 5x) (x-2)
V(x) = x^3 - 2x^2 - 5x^2 + 10x
V(x) = x^3 - 7x^2 + 10x
Now, looking at the options, we see that option C is eliminated.
Now, let us look at the domain of x
Since width cannot be negative (x-5) > 0
⇒ x > 5
Now in option A domain is (0, 6], but x cannot take values from (0,5). Thus, option A is eliminated.
Similarly, we can eliminate option B also since x cannot take values from (0, 2)
Thus, option 4 is the correct answer.
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Your question was incomplete. Check for the missing options below, in the figure attached.
Help! Quadratic Word Problems!
Answer:
Step-by-step explanation:
Ch. 1. Problems 6, 7 & 9
6. The only swimmng pool at a motel is outdoors. It is 5.0 m wide and 12.0 m long. If the weekly
evaporation is 2.35 inches how many gallons of water must be added to the pool if it does not rain? If during the next week the pool still loses two. 35 inches of water to evaporation, even with 20 mm of rainfall, how many liters of water must be added?
Answer:
946 gal
629 gal
Step-by-step explanation:
volume that evaporates = LWH
volume = (5.0 m × 100 cm/m × inch / 2.54 cm) × (12.0 m × 100 cm/m × inch / 2.54 cm) × 2.35 inch
volume = 218,550 in.³
volume = 218,550 in.³ × 1 gal / 231 in.³
volume = 946 gallons
You must add 946 gallons.
The loss to evaporation is 2.35 in.
The amount of rain is 20 mm
The net loss is
2.35 in. × 25.4 mm / inch - 20 mm = 39.69 mm
39.69 mm × 1 inch / 25.4 mm = 1.563 in.
The net loss now is 1.563 in. instead of 2.35 in.
We find the fraction of the the previous loss is the loss with rain and multiply by the previous loss.
1.563/2.35 × 946 gal = 629 gal
With rain, then 629 gallons of water must be added.
One cubic foot holds7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much dose 6 cubic feet of water weigh in Tons
We can use the concept of unitary method to solve the question.The weight of 6 cubic feet of water is 0.19 Ton.
Unitary method helps us in finding the solution to seemingly complicated problems, here we have been given the amount of water that one cubic foot can hold, first we need to find out how much water 6 cubic feet can hold.
1 cubic foot hols 7.48 gallons of water
6 cubic feet holds 7.48x6 gallons of water=44.88 gallons
Next we know how much 1 gallon of water weighs in pounds,we need to find out how much 44.88 gallons of water weigh in pounds first and then convert it to tons.
1 gallon weighs 8.33 pounds
44.88 gallons weighs 8.33x44.88=373.8504 pounds
1 Ton=2000 pounds
373.8504 pounds=[tex]\frac{373.8504}{2000}[/tex]=0.1869 Ton≈0.19 Ton
Thus we can see that 6 cubic feet of water weighs 0.19 Ton, we used unitary method step by step to reach this result.
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Find the union of the sets (22, 33, 44, 55) and (66, 44, 22}
Application of Finite Mathematics
The union of the sets is { 22, 33, 44, 55, 66 }
What is the union of sets?The union of sets can be defined as the sum of the elements of two or more sets without repetition of those elements.
It is also known as the combination of the all the elements of two or more sets.
It is denoted using the symbol , ' ∪ '
Given the sets;
(22, 33, 44, 55)(66, 44, 22}The union of the sets is:
{ 22, 33, 44, 55, 66 }
Thus, the union of the sets is { 22, 33, 44, 55, 66 }
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State the cardinality of the set.
The set of subsets of {2, 3, 5, 9, 11}
c
ℵ0
32
25
none of these
Answer:
32
Step-by-step explanation:
The given set has 5 elements, meaning it has 2⁵ = 32 subsets.
This means the cardinality of the desired set is 32.
Determine the intercepts of the line. Do not round your answers. y − 6 = 4 ( x + 5 )
Answer:
x = (- [tex]\frac{13}{2}[/tex], 0)
y = (0,26)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
8. A figure has two pairs of parallel sides and four right angles. The figure is
translated 4 units down. How many parallel sides does the image have?
The image would also have two pairs of parallel sides
How many parallel sides does the image have?The given parameters are:
Two pairs of parallel sides Four right angles. Translation down by 4 unitsThe translation transformation is a rigid transformation
This means that, it keeps the orientation that is being transformed
The initial figure has two pairs of parallel sides
Hence, the image would also have two pairs of parallel sides
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What are the coordinates of the point on the directed line segment from (−5,8)(−5,8) to (−1,−8) (−1,−8) that partitions the segment into a ratio of 3 to 1?
The coordinates of the point on the directed line segment is (-2, 4)
How to determine the coordinates of the point on the directed line segment?The points are given as
(-5, 8) and (-1, -8)
The ratio is given as
m : n = 3 : 1
The coordinates of the point are calculated as
Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)
So, we have
Point = 1/(3+ 1) * (3 * -1 + 1 * -5, 3 * -8 + 1 * 8)
Evaluate
Point = 1/4 * (-8, 16)
So, we have
Point = (-2, 4)
Hence, the coordinates of the point on the directed line segment is (-2, 4)
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A cyclist his bike at a speed of 40 kilometers per hour what is this speed in miles? How many miles will the cyclist travel in 5 hours ? In your computations assume that 1 mile is equal to 1.6 kilometers. do not round your answers.
The cyclist cover 200 kilometer in 5 hours and his speed in miles are 25 miles per hour.
According to the statement
We have to find that the speed of the cyclist.
So, For this purpose, we know that the
Speed is the time rate at which an object is moving along a path
From the given information:
A cyclist his bike at a speed of 40 kilometers per hour
Then
The distance he covered in 5 hours = 40*5
The distance he covered in 5 hours = 200.
And then
The speed in miles :
We have given that the 1 mile is equal to 1.6 kilometers
Then
If he covers a 40 kilometers in a hour then
in miles it becomes = 40/1.6
In other words,
Speed in miles = 40/1.6
Speed in miles = 25 miles per hour.
So, The cyclist cover 200 kilometer in 5 hours and his speed in miles are 25 miles per hour.
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can someone help me with this?
The value of the function f(-4) = 16.
What is termed as the function?A function is categorized as a relationship between a set of inputs that each have one output.
A function is an association between inputs in which each input is connected to exactly one output. Each function has a domain as well as a co domain, as well as a range. In general, a function is denoted by f(x), where x is really the input.For the given function in the question;
f(x) = x ² , if x < 0.
f(x) = 0 , if x = 0.
f(x) = 2x + 1 , if x > 0
Now, estimate the values;
(a) f(-4)
As, the value of the x to be substitute is negative, the function used will be.
f(x) = x ² ,for x < 0.
Put the value x = -4
f(-4) = (-4)²
f(-4) = 16
The value of f(-4) = 16.
(b) f(0)
As the value of function is zero.
Then,
f(x) = 0 , if x = 0.
Put x = 0 in function we will get.
f(x) = 0.
(c) f(2)
As the value to be substituted is positive, the function used is;
f(x) = 2x + 1 , if x > 0
Put x = 2
f(2) = 4 + 1
f(2) = 5
Thus, the value of f(2) is 5.
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Q2. The diagram shows the position of town A.
Scale: 1 cm represents 10 km
Town B is 64 km from town A on a bearing of 070°.
Mark the position of town B, with a cross (*).
Use a scale of 1 cm represents 10 km.
The position of town B in cartesian plane is 6.4 cm in 1st quadrant at an angle of 70°.
As per the question statement, we are given that a diagram which shows the position of town A and the scale of 1 cm representing 10 km.
Town B is 64 km from town A on a bearing of 070°. We are supposed to tell the position of town B.
Let's assume that town A lies at origin in cartesian plane and as 1 cm represents 10 km therefore,
[tex]1cm = 10 km\\1 km = 0.1 cm\\64 km = 64*0.1=6.4 cm[/tex]
The town B is 6.4 cm from the origin and as the angle is given as 70° so the position of town B is in 1st quadrant.
Therefore the position of town B is 6.4 cm in 1st quadrant at an angle of 70° when town A lies at origin in the cartesian plane.
Cartesian Plane: The cartesian coordinate system includes a two-dimensional plane known as the Cartesian Plane. Numerical coordinates can be used to describe any point on a cartesian plane.To know more about cartesian plane, click on the link given below:
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What is the value of A on the number line below?
Answer:
the answer is 435
Step-by-step explanation:
the change between each line is 105, so we start to add and then you get the resul
The value of A in the number line is the in-between of 225 and 645 so it is 435.
What is a number line?In mathematics, a number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.
In another word, a number line is basically a line in which infinite numbers have been written in ascending order or increasing order.
A horizontal number line is the most common representation and can be extended infinitely in any direction.
Given the number line,
Now if we count the interval of A between 225 and 645 it is 2(same).
So A must be between 225 and 645.
So,
225 - A = A - 645
2A = 870
A = 435
Hence "The value of A in the number line is the in-between of 225 and 645 so it is 435".
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Which is the best approximation for the solution of the system of equations?
y= -2/5x + 1
Y = 3x -2
A: (0.45, 0.88)
B:(0.88, 0.65)
C:(0.88, 1.11)
D:(1.3, 0.88)
Graph pictured below
Simplify (2.8 × 10−9) − (6.9 × 10−8). Write the final answer in scientific notation.
−6.62 × 10−9
−6.62 × 10−8
−4.1 × 10−1
−4.1 × 101
The solution to the expression (2.8 × 10⁻⁹) − (6.9 × 10⁻⁸) gives -6.62 * 10⁻⁸
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
(2.8 × 10⁻⁹) − (6.9 × 10⁻⁸)
Making the exponents to be similar gives:
(2.8 × 10⁻⁹) − (69 × 10⁻⁹)
Simplifying gives:
-6.62 * 10⁻⁸
The solution to the expression (2.8 × 10⁻⁹) − (6.9 × 10⁻⁸) gives -6.62 * 10⁻⁸
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Compare the square root of one hundred forty and one hundred five ninths using <, >, or =.
square root of one hundred forty is greater than one hundred five ninths
square root of one hundred forty is equal to one hundred five ninths
one hundred five ninths is greater than square root of one hundred forty
square root of one hundred forty is less than one hundred five ninths
The square root of one hundred forty is less than one hundred five ninths. So, option D is correct.
According to this question we have to compare the square roots of both numbers One Hundred Forty and One Hundred Five Ninths. So, we have to calculate their square roots.
The square root of One hundred Forty: √140
The square root of One hundred Forty: 11.832
The square root of One Hundred Five Ninths: √159
The square root of One Hundred Five Ninths: 12.609
Comparing both of their square roots we can clearly see that :
(11.832) < (12.609)
The square root of 140 < Square root of 159
Hence, option D is correct. The square root of 140 is less than 159.
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Which ordered pair is a solution to every linear equation of the form y = mx, where m is a real
number?
The ordered pair which is a solution to every linear equation of the form given is; (0, 0).
Which ordered pair is a solution to the linear equation?It follows from the task content that the ordered pair which satisfies the equation of the form y =Mx be determined.
On this note, since the product of any real number, slope in this scenario and 0 is; 0.
Ultimately, it follows that the required ordered pair is; (0, 0) for any real number value of the slope, m.
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ASAP help will mark you brainliest 5 likes
f(x)=1f ( x ) = 1 ,
f(x)=x+1f ( x ) = x + 1 ,
f(x)=x−1f ( x ) = x − 1 ,
f(x)=−1
A rectangle's width is 6 feet less than its length. Write a quadratic function
that expresses the rectangle's area in terms of its length.
A. A(1)=1²-61
B. A(7)=7w
c. A(1)=12+61
D.A(7)=1-6
Answer:
A. A(l) = l² -6l
Step-by-step explanation:
You want a quadratic function for the area of a rectangle whose width is 6 feet less than its length.
Rectangle areaLet l (ell) represent the length of the rectangle in feet. Then the width will be 6 feet less, or (l -6). The area is the product of length and width:
A = LW
A(l) = l(l -6)
A(l) = l² -6l . . . . . . use the distributive property to eliminate parentheses