Answer:
see explanation
Step-by-step explanation:
given that V is directly proportional to h³ , then the equation relating them is
V = kh³ ← k is the constant of proportion
to find k use the condition V = 48 when h = 4 , then
48 = k × 4³ = 64k ( divide both sides by 64 )
[tex]\frac{48}{64}[/tex] = k , then k = 0.75
V = 0.75h³ ← equation of proportion
1
when h = 3 , then
V = 0.75 × 3³ = 0.75 × 27 = 20.25 cm³
2
when h = 6 , then
V = 0.75 × 6³ = 0.75 × 216 = 162 cm³
then
162 ÷ 20.25 = 8
the volume will be 8 times bigger
x^2-y=7 and y-5x=-11 The system of equations above has two solutions. The solution in Quadrant 1 is (A,B) and the solution in Quadrant 4 is (C,D) . Find the values of (A,B), (C,D)
By solving the system of equations, we can see that the solutions are:
(A, B) = (4, 9)
(C, D) = (1, -6).
How to solve the system of equations?Here we have the following system of equations:
x^2 - y = 7
y - 5x = -11
If we isolate the variable y in both equations, we get:
y = x^2 - 7
y = -11 + 5x
Now we can equate these two to get:
x^2 - 7 = -11 + 5x
now we have a quadratic equation, this can be rewritten as:
x^2 - 7 + 11 - 5x = 0
x^2 - 5x + 4 = 0
Using the quadratic formula, we will see that the solutions are:
[tex]x = \frac{5 \pm \sqrt{(-5)^2 - 4*1*(4)} }{2*1}[/tex]
Solving that we get:
[tex]x = \frac{5 \pm \sqrt{(9} }{2} \\\\x = \frac{5 \pm 3}{2}[/tex]
So the two solutions for x are:
x = (5 + 3)/2 = 4
x = (5 - 3)/2 = 1
Evaluating the second equation in these x-values we get:
y = -11 + 5*4 = -11 + 20 = 9
y = -11 + 5*1 = -6
Then we have the coordinate pairs: (4, 9) (on the first quadrant) and (1, -6) on the fourth quadrant.
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Kelyse's preschool tuition is $180 per week. She
receives a small discount for honor roll, $50 per
month. Her grandparents help out and pays
20% of her tuition. How much do her
grandparents pay?
$134 is the amount paid by grandparents every month.
What is the percentage?Percentage as the name suggests is a ratio of some particles to 100. In order to get the value of the required amount one has to divide the value by 100.
It is given that the tuition fee is $180 per week = $720 per month
It is also provided that she receives an honour rule of $50 per month.
So, her fees per month is $720- $50= $670.
It is given that 20% of the fees is paid by grandparents.
So, percentage share = 20% of $670 =20/100 x $ 670 = $134
So, $134 is paid by the grandparents every month.
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12 > w + 3 solve the inequality for w and simplify your answer as much as possible
The solution to given inequality 12 > w + 3 is w < 9
In this question, we have been given an inequality 12 > w + 3
We need to solve the inequality for w.
Consider given inequality,
12 > w + 3 ............(Given)
12 - 3 > w + 3 - 3 ...........(Subtract 3 from each side)
9 > w
This means, w is less than 9.
Therefore, the solution to given inequality 12 > w + 3 is w < 9
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7th grade math please help a girl out
In a pasture of grass and other plants, the biomass of insects makes up 5000 kilograms. This is 5% of the total biomass of the pasture. What is the total biomass of the pasture? Set up the problem and solve below.
5000kg------->5%
x------------------>100%
Using Cross-multiplication:
5000/x=5/100
Solving for x:
x=(100*5000)/5 =100000kg
You can verify the answer:
100000kg *5% =100000*0.05= 5000kg
The tuition costs, C, for a local community college are modeled by C(h) = 250 + 200h, where h represents the number of credit hours taken. The local state university has tuition costs, S, modeled by the function S(h) = 300 + 180h.
How many credit hours will a student have to take for the two tuition costs to be equal? Round the answer to the nearest tenth of an hour.
250 + 200h = 300 + 180h
250 + 200h = 300 + 180h
− 180h − 180h
250 + 20h = 300
The credit hours that a student has to take for the two tuition costs to be equal is A. 250 + 200h = 300 + 180h
How to illustrate the information?From the information, the tuition costs, C, for a local community college are modeled by C(h) = 250 + 200h
h = the number of credit hours taken.
The local state university has tuition costs, S, modeled by the function S(h) = 300 + 180h.
Therefore, the credit hours that a student have to take for the two tuition costs to be equal will be:
250 + 200h = 300 + 180h
200h - 180h = 300 - 250
20h = 250
h = 250/20
h = 12.5 hours.
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Under her cell phone plan, Mayerlin pays a flat cost of $55 per month and $5 per gigabyte. She wants to keep her bill under $70 per month. Write and solve an inequality which can be used to determine x x, the number of gigabytes Mayerlin can use while staying within her budget.
The number of gigabytes that Mayerlin can use while staying within her budget is 5.
How many gigabytes can she use?The first step is to determine the appropriate inequality sign to use. Here are the inequality signs:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The sign that would be used is <
The form of the inequality is:
flat cost + (cost per gigabyte x number of gigabytes) < total budget
$55 + $5x < $70
5x < $70 - $55
5x < 25
x < 25 / 5
x = 5
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Subject: geometry btopic: Chords and arcs a. 7.1 inb. 7.8 inc. 6.7 ind. 8.3 in
Chords and arcs
YM is the chord of the circle and it has a length of 12 in
The perpendicular VL bisects the chord in V.
To prove the above statement, please note that triangles VYL and VLM are similar because they have one side in common and the second side of the same length (the radius of the circle).
Let's work with any of those triangles, for example, VLY. It's a right triangle in V. The hypotenuse of the triangle is the radius, one leg is the given distance of 5 in and the other leg is half the length of the chord (6 in).
Thus, applying Pythagora's Theorem:
[tex]r^2=5^2+6^2=25+36=61[/tex]Thus, the radius is
[tex]r=\sqrt{61}[/tex]r=7.8 in
Option b.
Convert to slope-intercept form to graph:
2x + 4y = 8
By converting to slope-intercept form to graph and solving this equation we are get -x/2 +2
What is slope intercept ?
The slope indicates the steepness of a line and the intercept indicates to the location where it intersects are in an axis. The slope and that the intercept define to the linear relationship between the two variables, and can be the used to the estimate an average rate of change.
The slope, m, represents the steepness of a line. The slope of the line is also the termed as gradient, sometimes .and the y-intercept, b, of a line, represents the y-coordinate of the point to where the graph of the line intersects the y-axis.
Sol-
Re write 2x+4y=8 in slope intercept form we are get-
y= -x/2+2
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i need help with this problem i’m struggling with
Translate this sentence into an equation.
78 is the product of Helena's savings and 6.
Use the variable h to represent Helena's savings.
Answer:
786
Step-by-step explanation:
Answer:
Helena',s savings... h=78+6
Aryon has $20. He buys 2 cokes that each cost $1.50. He also buys a sandwich for $5.50. And a bag of chips that cost $2.25. After Aryon pays for his lunch, how much money does he have left.
Aryon is left with $9.25 of money after he has paid for his lunch.
According to the question,
We have the following details:
Total amount Aryon has = $20
The cost of 1 coke = $1.50
So, the cost of 2 cokes = $(2*1.50)
The cost of 2 cokes = $3
The cost of a sandwich = $5.50
The cost of a bag of chips = $2.25
So, the total cost of all the materials = the cost of 2 cokes + the cost of a sandwich + the cost of a bag of chips
The total cost of all materials = $(3+5.50+2.25)
The total cost of all materials = $10.75
Now, the money Aryon has = Total money he has - the total cost of all materials
The money Aryon is left with = $(20-10.75)
The money Aryon is left with = $9.25
Hence, the money Aryon is left with is $9.25.
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Can someone pls help me i will mark for whoever helps me
The answers to all the subparts are:
(A) 0.21 : Rational number(B) 3/12 : Rational number(C) 4.125 : Rational number(D) 8⅒ : Rational number(E) π/3.14/(22/7) : Rational numberWhat are rational numbers?Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number. In other words, p/q, where p and q are both integers and q 0, can be used to represent a rational number.So, the reason for rational or irrational numbers:
(A) 0.21
It is a rational number as it can be represented in fractions.
(B) 3/12
It is a rational number as it is in fractions.
(C) 4.125
It is a rational number as it can be represented in fractions.
(D) 8⅒
It is a rational number as it can be represented in fractions.
(E) π/3.14/(22/7)
It is a rational number as it can be represented in fractions.
Therefore, the answers to all the subparts are:
(A) 0.21 : Rational number(B) 3/12 : Rational number(C) 4.125 : Rational number(D) 8⅒ : Rational number(E) π/3.14/(22/7) : Rational numberKnow more about rational numbers here:
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4. tumbleweed, commonly found in the western united states, is the dried structure of certain plants that are blown by the wind. kochia, a type of plant that turns into tumbleweed at the end of the summer, is a problem for farmers because it takes nutrients away from soil that would otherwise go to more beneficial plants. scientists are concerned that kochia plants are becoming resistant to the most commonly used herbicide, glyphosate. the us department of the interior claims that 20 percent of kochia plants are resistant to glyphosate. in 2017 another study by researchers at university of new mexico, 38.5 percent of 52 randomly selected kochia plants were resistant to glyphosate.
Using the z-distribution, as we are working with a proportion, it is found that since the test statistic is less than the critical value for the right-tailed test, there is not enough evidence to conclude that there has been an increase in the proportion of all kochia plants that are resistant to glyphosate.
What are the hypothesis tested?In null hypothesis, we test if there has been no increase, that is, the subtraction is of 0.
In this problem, we consider that:
p₁ is the proportion in 2014.
p₂ is the proportion is 2017.
H₀=p₂-p₁
By alternative hypothesis,
H₁=p₂-p₁≠0,
we test if there has been an increase
The proportions and standard errors are given by:
p₁=0.97, s₁=√0.97(0.803)/61=0.0509
p₂=0.385, s₁=√0.385(0.615)/52=0.0675
Hence, the distribution has mean and standard error given by:
p=p₂-p₁=0.0675-0.0509
s=√s₁²+s₂²=0.0845
Test static z=p bar-p/s
at p = 0 is the value tested at the null hypothesis,
z=0.0166/0.0845
z=0.2
By a right-tailed test, we are testing is the proportion is greater than a value, with a significance level of 0.05, the critical value is of
z=1.645
0.2<1.645 there is not enough evidence to conclude that there has been an increase in the proportion of all kochia plants that are resistant to glyphosate.
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Carlos is three times as old as Maria.
The sum of their ages is 56 years. How
old is each?
Maria's Age = 14 years old.
Carlos Age = 42 years old
Answer:
Carlos is 42, and Maria is 14.
Step-by-step explanation:
14 x 3 = 42,
14 + 42 = 56,
So, the answer is Carlos = 42, Maria = 14.
Hope this helps!
Btw, Brainliest please, thanks!
Rebecca Sweet was the top scorer in a women's professional basketball league for the 2006 regular season, with a total of 806 points. The number of two-point field goals that Rebecca made was 52 less than double the number of three-point field goals she made. The number of free throws (each worth one point) she made was 28 less than the number of two-point field goals she made. Find how many free throws, two-point field goals, and three-point field goals Rebecca Sweet made during the 2006 regular season.
In the year 2006, the number of free throws is 100, number of 2 point field goals 128 and the number of 3 point field goals 90.
Let x = number of free throws
y = number of 2 point field goals
z = number of 3 point field goals
However given that Rebecca has a total of 806 points,
Thus x + 2y + 3z = 806 ---------- equation 1
Number of 2 point field goals that Rebecca made was 52 less than double the number of three-point field goals she made ;
thus y = 2z - 52 ---------------- equation 2
Number of 3 point field goals that Rebecca made was 28 less than the number of two-point field goals she made ;
thus x = y - 28 ------------------ equation 3
Thus on solving these three above mentioned equations :
we get x = 2z - 52 -28 [ substituting values in eq 3 from eq 2]
x = 2z - 80 ------------- equation 5
So equation 1 becomes ; 2z - 80 + 2y + 3z = 806
5z + 2y = 886 -------------- equation 4
Thus on solving equation 4 and 2 we get
2 X equation 2 = 4z - 2y = 104
5z + 2y = 886
= 11 z = 990
thus z = 90 and so y = 4 × 90 - 104 = 2y
y= 360 - 104 / 2
= 256/2 = 128
thus y = 128 .
And x= 2z -80 from equation 5 ; x = 180 - 80 = 100 .
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Rectangle 1 has an area of 60.81 square centimeters. Rectangle 2 has an area of 61.44 square centimeters. Rectangle 3 has an area of 35.52 square centimeters. Rectangle 4 has an area of 47.88 square centimeters. Part A..Which two rectangles have the greatest difference in area? Part B Look at your answer to part A what is the difference between those two rectangles areas?
The two rectangles that is R3 and R4 have the greatest difference in the area.
How to calculate the area of the rectangle?
In mathematics, the rectangle is a closed polygon shape which has four vertex as well as four sides. And the opposite side are parallel to each other. To calculate the area, multiply the length and breadth. Similarly, for the perimeter means add all the sides.
According to the question, the given data in the form of the area of the rectangle is as follows:
Area of Rectangle1 = 60.81 square centimeters
Area of Rectangle2 = 61.44 square centimeters
Area of Rectangle3 = 35.52 square centimeters
Area of Rectangle4 = 47.88 square centimeters
Now, to calculate the greatest difference in the area of the rectangles:
Difference(Rect2 - Rect1) = 61.44 - 60.81 = 0.63
Difference(Rect1 - Rect3) = 60.81 - 35.52 = 25.29
Difference(Rect1 - Rect4) = 60.81 - 47.88 = 12.93
Therefore, the two rectangles that is R3 and R4 have the greatest difference in the area.
And the differences are as follows:
Area(Rect1 - Rect3) = 60.81 - 35.52 = 25.29 square centimeters
Area(Rect1 - Rect4) = 60.81 - 47.88 = 12.93square centimeters
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A function is modeled by the equation f(x) = 2x + 5.
Which function models a transformation of f (x + 3)?
f(x + 3) = 2x+8
f (x + 3) = 2x + 11
f(x + 3) = 5x + 8
f (x + 3) = 6x + 15
A
B
C
D
"y is a function of x." The input value, or independent variable, is represented by the letter x. The dependent variable or output value is denoted by the letter y, or f(x).
f(x) = 2x + 5.
f(x+3) = 2(x+3) + 5.
f(x+3) = 2x + 11.
What is meant by function ?a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.A function called f is defined by the notation y=f(x). This should be understood as "y is a function of x." The input value, or independent variable, is represented by the letter x. The dependent variable or output value is denoted by the letter y, or f(x).To learn more about : function
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11. What is the value of the expression below?
1-10+6|-|3²-5|
The value of the expression |-10+6|-|3²-5| = 0
The expression given is |-10+6|-|3²-5|.
This contains absolute value which needs to be evaluated.
We will go through the definition of absolute value.
Absolute value for x = x, when x is a positive integer.
i.e., |x| = x, when x >0
Absolute value of (-x) = x, when -x is a negative integer.
So absolute value always gives the positive value of the number inside it.
Now |-10+6|-|3²-5| = |-4| - |9-5|
= 4 - |4| [Since |-4| = 4]
= 4 - 4 [Since |4| = 4]
= 0.
So the value of the expression |-10+6|-|3²-5| = 0
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On a literature exam, there are 6 vocabulary questions for every 7 questions about
a book. If there are 12 vocabulary questions on the test, how many total questions
are on the test?
Answer:
26 total questions
Step-by-step explanation:
6 * 2 = 12
7 * 2 = 14
14 + 12 = 26
Which equation is equivalent to −(5−x)=5−x? Responses
Answer:
x = 5
Step-by-step explanation:
what is 5.3 x 10^2 in standard form?
Answer:
530 x
Step-by-step explanation:
Jessica wants to have a square garden plot in her backyard. She has enough compost to cover an area of 116 ft². Use the
formula s = A to find the length of each side of her garden. Round your answer to the nearest tenth of a foot.
The length of the each side of the square garden of Jessica is found as 10.77 ft.
What is termed as the square?A quadrilateral with 4 equal sides is known as a square. There are numerous objects in our environment that are square in shape. Each square shape is distinguished by it's own equal sides as well as interior angles of 90°.For the given question,
Jessica is making a square garden in her backyard.
The compost bought is to cover the area of the 116 ft².
The formula for the area is given as;
A = s² , where s is the length of the side of the square.
Put the values.
116 = s²
Taking square root both side.
s = √116
s = 10.77
Thus, the length of the each side of the square garden of Jessica is found as 10.77 ft.
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solve for t
275,000 = 300 1-(1 + .038/12 ) ^(-12t)/(.038/12)
In linear equation , 2,932.25 * ( 1.0316)¹²t = (1)t is value of t .
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an uncertain variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.275000 = 3001 - ( 1 + 0.38/12)⁻¹²t/0.038/12
275000 = 3001 - ( 1 + 0.38/12)⁻¹²t/0.0025
275000 * 0.0025 = 3001 - ( 1 + 0.38/12)⁻¹²t
68.75 = 3001 - ( 1 + 0.38/12)⁻¹²t
3001 - 68.75 = ( 1 + 0.38/12)⁻¹²t
2,932.25 = ( 1 + 0.0316)⁻¹²t
2,932.25 = ( 1.0316)⁻¹²t
2,932.25 = 1/ ( 1.0316)¹²t
2,932.25 * ( 1.0316)¹²t = (1)t
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I need help with this question.
Answer:the 2nd choice
Step-by-step explanation:
A survey was taken that asked a total of 400 participants whether or not they were happy withtheir jobs. An overall score was given. 100 of the participants were unhappy while 300 of theparticipants were happy with their job.What percent were happy with their job?
To find the percent of happy people, we just have to divide the number of happy participants by the total number of them.
[tex]\frac{300}{400}=0.75[/tex]Then, we multiply it by 10 to express it as a percentage.
[tex]0.75\cdot10=75[/tex]Hence, 75% of the participants were happy with their job.really need helppp plsssss asap
Answer:
Step-by-step explanation:
The sum of 2 and b is less than or equal to -16 translate the scentence into an inequaltiy
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{G\textsf{uide:}}[/tex]
[tex]\bullet\large\textsf{ Greater than or equal to}\rightarrow\mathsf{\geq}\\\bullet\large\textsf{ Greater than}\rightarrow\mathsf{ > }\\\bullet\large\textsf{ Less than or equal to}\rightarrow\mathsf{\leq}\\\bullet\large\textsf{ Less than}\rightarrow\mathsf{ < }[/tex]
[tex]\star\large\textsf{ The word \boxed{\rm{difference}} means subtract/subtraction}\\\star\large\textsf{The word \boxed{\rm{product}} means multiply/multiplication}\\\star\textsf{The word \boxed{\rm{quotient}} means divide/division}\\\star\large\textsf{The word \boxed{\rm{sum}} means add/addition}[/tex]
[tex]\large\text{Now, let us answer your given question}[/tex]
“[tex]\large\textsf{The \underline{SUM} of 2 and b is \underline{LESS THAN or EQUAL to} }\mathsf{-}\large\textsf{16}[/tex]”
[tex]\large\text{Your equal should possibly look like this:}\large\textsf{ 2 + b }\mathsf{\leq\ -}\large\textsf{16}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{2 + b \leq -16}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
The countdown before a rocket launch is described as –10, –9, –8, . . . After the countdown, the time is described as 1, 2, 3, . . . What is the meaning of zero in this situation?
Answer:dsa
Step-by-step explanation:
sadfdfsaf
jared bought a table and 12 chairs for $2,400. each chair cost $ 165. find the cost of the table?
Answer:
Answer down below!
Step-by-step explanation:
Since we do have the value of the chairs, we can do 12 * 165 to get a total of 1,980
Now, with this, to find the price of the table, you do 2,400 - 1,980
That will give you your answer of 420.