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.

Answer:

177

Step-by-step explanation:

A=3.14r^2

A=3.14(7.5)

A=~177

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.

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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

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;

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

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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

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Answer:

4 1/2

Step-by-step explanation:

add 1 1/5 and 3/10 and then multiply your answr by 3

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.

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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.

At the end of the year, there will be $2200.in her 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.

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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

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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

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Mila will receive 68 EUROS of money after the exchange of 80 US dollar.

USD is the official money currency of united states of America.. its symbol of representation is $., also value of 1 US$ =82 rupee.

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

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For a polynomial function statements that need to be true are different end behavior for different degree and different sign of leading coefficient.

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:

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Answer:

B because I had learned this at school.

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.

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

Answer:

3 grams

Step-by-step explanation:

g(5)-2g(1)

g × 5- 2g(1)

5g - 2g×1

5g - 2g

3g

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

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

The slicing of the equation 8x - 4y = 20 for y is y = 2x - 5

From 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

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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

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

Answer:

  700 mL

Step-by-step explanation:

You want to know the whole amount if 8% of it is 56 mL.

The 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.

(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).

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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 )

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

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

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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.

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(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.

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Expression for Number of t shirts in each package = [tex]\frac{8}{p}[/tex]

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]

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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.

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.

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The graph for the given function f(x)=-5/4x+6. is obtained.

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.

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5% of $1100 = 55

Year given = 7

So, 55 × 7 = 385

She would get after 7 years all total  = (1100 + 385) = $1485