The weight of all of the rocks to the nearest tenth is 6.085 pounds .
Given :
in a science lab, a number of rock samples are weighed. if the scientist finds one of the rocks to weigh 3 pounds and this is 49.3% of the total weight of all of the rocks, what is the weight of all of the rocks if necessary, round your answer to the nearest tenth.
Let x be the total weight or all the weight of rocks .
3 = 49.3 % * x
3 = 49.3 * 1 / 100 * x
3 * 100 = 49.3 * x
300 = 49.3 * x
divide with 49.3 on both sides
300 / 49.3 = 1 * x
x = 300 / 49.3
= 6.085 pounds
Learn more about the number here:
https://brainly.com/question/17429689
#SPJ4
you are to build a rectangular pen with three parallel partitions using 500 feet of fencing. what dimensions will maximize the total area of the pen?
The dimensions required are 125 feet and 50 feet.
The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable. Derivatives can be generalized to functions of several real variables. In this generalization, the derivative is reinterpreted as a linear transformation whose graph is (after an appropriate translation) the best linear approximation to the graph of the original function. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables.
The total length will be x and the height will be y.
Perimeter = 500 = 2x + 5y
Total Area = A = xy
Solve for y using the equation of perimeter:
5y = 500 - 2x
y = 100 - 2x/5
Put y in the equation of the Area
A = x(100 - 2x/5)
A = -2x²/5 +100x
To find the maximum area, find the derivative:
A' = -4x/5 + 100
To maximise the area, we equate A' to zero.
A' = 0
-4x/5 +100 = 0
∴ x = 125
A' is positive when x < 125 and A' is negative when x >125, therefore meaning that x=125 is a maximum. Since this value is a maximum, the area is maximized when the total length is 125ft.
Put x = 125 in equation of perimeter:
500 = 2(125) + 5y
500 = 250 + 5y
5y = 250
∴ y = 50 ft
Thus, the dimensions required are 125 feet and 50 feet.
To learn more about dimensions, visit brainly.com/question/28688567
#SPJ4
8. Graph the function
f(x)=-5/4x+6.
Label the point on the graph that is the
solution to f(x) = -4 by writing
solution" next to it. Then, write the
solution below.
Solution
Show your work
The graph for the given function f(x)=-5/4x+6. is obtained.
What is meant by the term function?A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.For the stated question, the function is defined as;
f(x) = -5/4x + 6.
Put x = 0,
f(0) = -5/4(0) + 6.
f(0) = 6
Coordinate (0, 6)
For, the solution of f(x) = -4, put f(x) = -4
-4 = -5/4x + 6
x = 8
Coordinate (8, -4)
Plot the graph using the obtained points for the function.
Thus, the graph for the given function is obtained.
To know more about the function, here
https://brainly.com/question/25638609
#SPJ1
If 8% of a liquid is 56 mL, what is the whole
amount?
Please help
Answer:
700 mL
Step-by-step explanation:
You want to know the whole amount if 8% of it is 56 mL.
RelationThe problem statement tells you ...
8% × whole = 56 mL
Divide by the coefficient ...
whole = (56 mL)/(0.08) = 700 mL
The whole amount is 700 mL.
A cashier gets a $100 bonus for working on a holiday plus $11/h. The total holiday salary is given by the function y = 11x + 100. How will the graph change if the bonus is raised to $150 and the hourly rate is lowered to $10/h? Choose the answers that describe these transformations.
HELP PLEASE
(50,650) the graph evolve if the hourly rate is reduced to $10/h and the incentive is increased to $150.
Given that,
For working on a holiday, a cashier is given a $100 bonus in addition to $11/h. The equation y = 11x + 100 yields the entire holiday salary.
We have to find how would the graph evolve if the hourly rate is reduced to $10/h and the incentive is increased to $150.
We know that,
We get,
A cashier is given a $100 bonus in addition to $11/h is y=11x+100
The hourly rate is reduced to $10/h and the incentive is increased to $150 is y=10x+150
Now we subtract those two equation
11x+100-10x-150=0
x-50=0
x=50
We get y as y=10x+150
y=10(50)+150
y=500+150
y=650
Therefore, (50,650) the graph evolve if the hourly rate is reduced to $10/h and the incentive is increased to $150.
To learn more about increase visit: https://brainly.com/question/12165844
#SPJ1
. Is x + 2 a factor of the polynomial f(x)=2x^4-3x²-4x+1?
Of(2)=13, so (x + 2) is not a factor.
O f(-2)=29, so (x + 2) is not a factor.
O f(-2)=0,so (x + 2) is a factor.
Of(2)=0,so (x+2) is a factor.
(x + 2) is not a factor of the given polynomial f(x).
What is factor of polynomial?
A polynomial with coefficients in a specific field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization.
Consider, the given polynomial
f(x)=2x^4-3x²-4x+1
We have to check that (x + 2) is a factor of polynomial or not.
Since, if (x - a) is a factor of polynomial then 'a' is a zero of polynomial.
Here if (x + 2) is a factor of f(x) then f(-2) = 0
Plug x = -2 in f(x).
⇒
f(-2) = 2(-2)^4 - 3(-2)^2 - 4(-2) + 1
= 32 - 12 + 8 + 1
= 20 + 9
f(-2) = 9
f(-2) ≠ 0
Hence, (x + 2) is not a factor of the given polynomial f(x).
To learn more about factor of polynomial, click on the link
https://brainly.com/question/24351176
#SPJ1
PLEASE I NEED HELP!!!!!!!!
Answer:
161 square inches.
Step-by-step explanation:
The surface area of a pyramid is the sum of the areas of all of its faces. Since the base of the pyramid is a square with an edge length of 7 inches, the area of the base is 49 square inches (7 inches x 7 inches).
To find the surface area of the pyramid, you also need to find the area of the lateral faces of the pyramid. The lateral faces of a pyramid are the triangular faces that are not the base. The lateral faces of a pyramid are all congruent, meaning that they are all the same size and shape.
To find the area of a lateral face of the pyramid, you can use the formula for the area of a triangle: A = 1/2bh, where A is the area of the triangle, b is the base of the triangle, and h is the height of the triangle.
In this case, the base of the triangle is 7 inches (the edge length of the base of the pyramid) and the height of the triangle is 8 inches (the slant height of the pyramid). The area of each lateral face of the pyramid is therefore 1/2 x 7 inches x 8 inches = 28 square inches.
Since there are 4 lateral faces on the pyramid, the total area of the lateral faces is 4 x 28 square inches = 112 square inches.
To find the surface area of the pyramid, add the area of the base to the area of the lateral faces: 49 square inches + 112 square inches = 161 square inches. Therefore, the surface area of the pyramid is 161 square inches.
According to online realtor Zillow a 30 year $200,000, 4. 5%, fixed rate mortgage on your house will currently set your estimated monthly payments at about $1,020 per month. A 15-year fixed rate $200,000 mortgage would drop to 4. 0% with monthly payments of $1,480. Approximately how much would the 15-year fixed rate mortgage save you over the length of both loans?
The 15-year fixed rate mortgage save $ 100,800 more than in the case of the 30-year mortgage.
We must compute the total payments to be made in order to determine the amount saved by getting a 15-year mortgage rather than a 30-year mortgage.
Payments for a 30-year mortgage with a fixed rate of 4.5% are due every month in the amount of $1,020. The total payment is then determined as follows:
Total payment = 1020 * 12* 30 = 367,200
Difference according to lone = 367,200 - 200,000
difference = $167,200
Now, the monthly payments for the 15-year mortgage at a 4% rate will be $1,480.
Then total final payment = 1480*12*20 = $266,400
so in this case, the difference from The loan will be
266,400 - 200,000 = $66,400
Thus, we can draw the conclusion that, when comparing the two loans, the 15-year option will result in savings of $ 100,800 more than the 30-year mortgage.
To know more about mortgage and saving here,
https://brainly.com/question/14408794
#SPJ4
What is the value of g(5)-2g(1)
Answer:
3 grams
Step-by-step explanation:
g(5)-2g(1)
g × 5- 2g(1)
5g - 2g×1
5g - 2g
3g
Me. Ramirez writes the equation shown. He asks four students to slice the equation for y 8x-4y=20
The slicing of the equation 8x - 4y = 20 for y is y = 2x - 5
How to slice the equation for yFrom the question, we have the following parameters that can be used in our computation:
8x-4y=20
Rewrite the above equation properly
So, we have the following representation
8x - 4y = 20
Divide through the equation by 4
So, we have the following representation
2x - y = 5
Make y the subject of the equation in the above equation
This gives
y = 2x - 5
Hence, the solution is y = 2x - 5
Read more about subject of formula at
https://brainly.com/question/657646
#SPJ1
Which function represents the graph below?
The graph represents the function
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6.
Option(B) is the correct answer.
What is a graph of a function?
A graph of a function is a visual representation of the relationship between the input values and the output values of the function. It is typically plotted in the form of a set of points on a coordinate plane, with the input values plotted on the horizontal axis and the output values plotted on the vertical axis.
From the given graph we can conclude that
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6
Hence, the graph represents the function
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6
To learn more about the function, visit:
https://brainly.com/question/10439235
#SPJ1
The graph represents the function
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6.
Option(B) is the correct answer.
What is a graph of a function?
A graph of a function is a visual representation of the relationship between the input values and the output values of the function. It is typically plotted in the form of a set of points on a coordinate plane, with the input values plotted on the horizontal axis and the output values plotted on the vertical axis.
From the given graph we can conclude that
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6
Hence, the graph represents the function
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6
To learn more about the function, visit:
brainly.com/question/10439235
#SPJ1
when the philies play the dodgers, the tickets for three adults and three children are $75. for two adults and four children the total admission cost is $62. find the cost of each adult and each child ticket.
when the philies play the dodgers, the tickets for three adults and three children are $75. for two adults and four children the total admission cost is $62. So, by using equation formula:
the cost of each adult is $19
and each child ticket is $6
What is an equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.
The relationship between the two expressions on each side of the sign is represented by a mathematical equation. One variable and an equal sign are often present.
Let us assume,
tickets for adults = a
tickets for children = c
Now,
3a + 3c = $75 ........ (i)
2a + 4c = $62 ......... (ii)
Multiply the equation (i) ×2 and equation (ii) × 3, we get -
6a + 6c = $150 ........ (iii)
6a + 12c = $186 .........(iv)
Now, subtract equation (iv) from (iii) we get -
or, 6c = $36
or, c = $6
Now, putting the value of c in equation (iii) we get -
6a + 6×6 = $150
6a = $114
a = $19
Thus, the cost of each adult is $19
and each child ticket is $6
To know more about equation formula refer to:
https://brainly.com/question/22688504
#SPJ4
Lester bought 8 t-shirts. The shirts came in p packages. Write an expression that shows how many t-shirts were in each package.
Expression for Number of t shirts in each package = [tex]\frac{8}{p}[/tex]
What is Unitary Method ?The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
Total number of shirts bought = 8 T- shirts
Total number of packages = p
So,
According to unitary method
In p packages we have t shirts = 8
In one package number of t shirts we will have = [tex]\frac{8}{p}[/tex]
Expression for Number of t shirts in each package = [tex]\frac{8}{p}[/tex]
To know more about Unitary method
https://brainly.com/question/28276953
#SPJ4
help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
5% of $1100 = 55
Year given = 7
So, 55 × 7 = 385
She would get after 7 years all total = (1100 + 385) = $1485
given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line. State True or False your answer:
a. True
b. False
It is true that given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.
A parabola is a quadratic function graph .A parabola is a curve equation in which a point on the curve is equidistant from a fixed point and a fixed line.
The fixed point is known as the parabola's focus, and the fixed line is known as the parabola's directrix. It is also worth noting that the fixed point does not lie on the fixed line.
A parabola is a locus of any point that is equidistant from a given point (focus) and a given line (directrix). The parabola is a significant curve of the coordinate geometry's conic sections.
The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h,k) denotes the vertex.
The standard equation of a regular parabola is y² = 4ax.
It's true that given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.
To know more about Parabola here
https://brainly.com/question/21685473
#SPJ4
Pls Help Got to do this right now!!!
Which expression is the additive inverse of - 13/6?
A) 13/6
B) 6/13
C) - 6/13
D) - 13/6
WILL MARK BRAINLIEST!!
Two piece of metal meaure one and one fifth yard and three tenth yard each. Three time the amount of metal i needed for a project. How many total yard of metal i needed? one and one half yard one and nine fifteenth yard four and one half yard four and one fifth yard
As per the area of the rectangle, the amount of metal need for the total yard is 4.68
Area of rectangle
In geometry, the area of rectangle is written as,
A = l x b
where l refers the length and b refers the breadth of the rectangle.
Given,
Here we have given that the 1 1/5 and 3 1/10 is the measure of yard.
While we looking into the given question, we have identified that,
3 time of metal is need for the project,
So, as per the area of the rectangle formula, it can be written as,
=> 3 x 1 1/5 x 3 1/10
=> 3 x 6/5 x 13/10
=> 234/50
=> 4.86
To know more about Area of rectangle here.
https://brainly.com/question/20693059
#SPJ4
Answer:
4 1/2
Step-by-step explanation:
add 1 1/5 and 3/10 and then multiply your answr by 3
Dylan has $14.00 to spend at the book fair. He decides to buy two paperbacks for $4.50 each. Then, he sees some sticker books. At most, how much can he spend on sticker books?
A $5.50
B $6.00
C $5.01
D $5.00
Answer:
B because I had learned this at school.
A new Youth Activity Center is being built in Ook Valley. The perimeter of the rectangular playing field is 272 yards. The length of the field is 8 yards less than double the width. What
are the dimensions of the playing field?
Answer:
w = 48 and l = 88
Step-by-step explanation:
A new Youth Activity Center is being built in Ook Valley. The perimeter of the rectangular playing field is 272 yards. The length of the field is 8 yards less than double the width. What are the dimensions of the playing field?
P = 2w + 2l
w = w
l = 2w - 8
272 = 2w + 2(2w - 8)
272 = 2w + 4w - 16
272 = 6w - 16
288 = 6w
w = 48
remember that: l = 2w - 8
l = 2w - 8 when w = 48
l = 2(48) - 8
l = 96 - 8
l = 88
CHECK: w = 48 and l = 88
P = 2w + 2l
272 = 2(48) + 2(88)
272 = 96 + 176
272 = 272
so: w = 48 and l = 88
Really need help on this I do not understand how to do anything
Answer:
y = 6x + 12
Step-by-step explanation:
(2, $24)
(4, $36)
(6, $48)
Find slope (y2-y1) / (x2-x1)
m = ($36 - $24) / (4 - 2)
m = 12 / 2
m = 6
Put into formula y = mx + b
y = 6x + b
Substitute values to find b (the y offset)
$24 = 6(2) + b
$24 = 12 + b
b = $12
y = 6x+12
5. Mila is preparing to travel from the United States to Belgium, a member of the European Union, and wants to exchange $80 USD to euros. She finds that the curren exchange rate is €0.85 EUR to $1 USD. If Mila exchanges $80 USD, how much mone will she receive in euros? (Example 4)
Mila will receive 68 EUROS of money after the exchange of 80 US dollar.
What is meant by USD?USD is the official money currency of united states of America.. its symbol of representation is $., also value of 1 US$ =82 rupee.
What is meant by EURO?Unit of money used in other countries of European union is known as euro, also value of 1 EURO=87 rupee.
According to the given data in the question,
1 USD =0.85 EURO
80 USD = 0.85*80 EURO
80 USD= 68 EURO
Hence 80USD will be converted to 68 EUROS
To learn more about currencies conversion visit to the given link;
https://brainly.com/question/11171380
#SPJ1
Silvia puts $1000 in an account. She puts 10% of the account each month for a year how much is in her account at the end of the year?
At the end of the year, there will be $2200.in her account
Describe account.A list of debit and credit entries for transactions involving a specific object (such as cash or notes payable), a certain person or business, or both. a financial period's transaction statement that displays the final balance
The most typical kinds of bank accounts are as follows: Checking accounts and Savings accounts
Silvia invests $1,000 in an account over the course of a year, contributing 10% per month.
Because there are 12 months in a year,
She puts 10% of the account each month for a year
that is 10 * 1000/100 = 100 each month she puts in her account.
so for 12months in a year 100*12 = $1200
$1200 in her account over the course of the year she has deposited
Thus, at the end of the year,
Silvia has $1000 + $1200 = $2200 in her account.
At the end of the year, there will be $2200.in her account.
To know more about account click :
brainly.com/question/24261944
#SPJ1
Given: ∠BCD is right; BC ≅ DC; DF ≅ BF; FA ≅ FE
Triangles A C D and E C B overlap and intersect at point F. Point B of triangle E C B is on side A C of triangle A C D. Point D of triangle A C D is on side C E of triangle E C D. Line segments B C and C D are congruent. Line segments B F and F D are congruent. Line segments A F and F E are congruent.
Which relationships in the diagram are true? Select three options.
△ACF ≅ △ECF by HL
ΔCBF ≅ ΔCDF by SSS
ΔBFA ≅ ΔDFE by SAS
ΔCFD ≅ ΔEFD by SSS
ΔCBE ≅ ΔCDA by HL
SAS
The three relationships in the diagram that are true include the following;
B. ΔCBF ≅ ΔCDF by SSS
C. ΔBFA ≅ ΔDFE by SAS
E. ΔCBE ≅ ΔCDA by HL
What is the Right Triangles Similarity Theorem?In Mathematics, the Right Triangles Similarity Theorem states that when the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then, the two (2) triangles that are formed would be similar to each other, as well as the original triangle.
Based on the Right Triangles Similarity Theorem, we have the following;
ΔCBF ≅ ΔCDF by side, side, side (SSS).ΔBFA ≅ ΔDFE by side, angle, side (SAS).What is HL?In Mathematics, HL is an abbreviation for hypotenuse leg and it can be defined as a theorem which states that if the hypotenuse and one (1) leg in a right-angled triangle are congruent to the hypotenuse and leg of another right-angled triangle, then the two (2) triangles would be congruent.
By applying the hypotenuse leg (HL) theorem across right-angle BCD (∠BCD), we have the following;
ΔCBE ≅ ΔCDA
Read more on a triangle here: brainly.com/question/11544842
#SPJ1
Average employee salary?
Answer:
$67,680
Step-by-step explanation:
average is calculated as
average = [tex]\frac{sum}{count}[/tex]
Denver
[tex]\frac{sum}{137}[/tex] = 67,013 ( multiply both sides by 137 )
sum = 9,180,781
Anchorage
[tex]\frac{sum}{25}[/tex] = 71,332 ( multiply both sides by 25 )
sum = 1,783,300
total sum for both = $9,180,781 + $1,783,300 = $10,964,081
then average salary across both companies is
average = [tex]\frac{10,964,081}{162}[/tex] = $67,680 ( to the nearest dollar )
write an eqation of the line that passes throught the points (0,-2), (4,-2),
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
The equation of the line is y = -2.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of the line is given as,
y = mx + c
The line passes through the points (0, -2) and (4, -2).
Now,
Slope = m
m = (-2 + 2) / (4 - 0)
m = 0 / 4
m = 0
Now,
(x, y) = (0, -2)
y = mx + c
-2 = 0 x 0 + c
c = -2
Now,
m = 0 and c = -2
y = 0x -2
y = -2
Thus,
The equation of the line is y = -2.
Learn more about equation of a line here:
https://brainly.com/question/23087740
#SPJ1
The diameter of a circle is 15 cm. Find its area to the nearest whole number.
Answer:
177
Step-by-step explanation:
A=3.14r^2
A=3.14(7.5)
A=~177
7 divided by 1 over 2
Answer: 3.5
Step-by-step explanation: hope it helps :)
Answer: 14
Step-by-step explanation: using cross multiplication, 7 times 2=14 and 1 time 1=1. so it would be 14/1 which can be simplified to 14.
Which of the following statements must be true about the polynomial function f(x)
For a polynomial function statements that need to be true are different end behavior for different degree and different sign of leading coefficient.
What is polynomial function?A function that can be expressed as a polynomial is referred to as a polynomial function.
A polynomial equation's definition can be used to derive the definition.
A polynomial is typically denoted by P (x).
The degree of the variable in P(x) is its maximum power.
The degree of a polynomial function is crucial because it reveals how the function P(x) will behave when x is very large.
Whole real numbers make up a polynomial function's domain (R).
For a polynomial function following statements to be true:
Function that has different degrees have different end behaviors because due to different degrees the graph will be different, and their x-intercept will be different.Function that has leading coefficient of different sign have different end behavior because if we take even degree polynomial leading coefficient.To know more about polynomial follow link:
https://brainly.com/question/7693326
#SPJ1
Find compound interest on 15,625 at 4% for 3 years.
Help! With steps
Answer:
P=15,625
Rate=4%
Time=3 years
CI=P(1+R/100)^T
=15,625(1+4/100)^3
=15,625*1.124864
=17576 Ans
Step-by-step explanation:
hope it helps
(10)
Write the equation
of the line in
Slope-Intercept
Form.
Answer:
y = -x
Step-by-step explanation:
The slope of this line is -1 (rise/run = -1/1 = -1). We can plug this value into the slope-intercept form equation:
y = mx + b
y = -1x + 0
and simplify.
y = -x
What is the equation of the blue line
Answer:
y = -1/2 x + 2
Step-by-step explanation:
A (0,2)
B (4,0)
(y-2)/(0-2) = (x-0)/(4-0)
(y-2)/-2 = x/4
(-y+2)/2 = x/4
4 * (-y+2)/2 = x/4 * 4
-2y+4 = x
-2y = x -4
2y = -x + 4
y = - 1/2 x + 4/2
y = -1/2 x + 2