A farmer raises chickens and pigs. If his animals have a total of 120 heads and a total of 300 feet, how many chickens does the farmer have?
F. 60 G. 70 H. 80 J. 90

By algebraic simplification, the expression [(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)] is equivalent to the expression 2 · b.

In this question we need to simplify the division of two expressions that comprises powers and square roots, the complete procedure requires the use of algebra properties:

The expression [(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)] is equivalent to 2 · b.

To learn more on algebraic equations: https://brainly.com/question/24875240

#SPJ1

The shortest length of fabric, in inches, that Kirk could use to make the tablecloth without putting any separate pieces of fabric together is 30 inches

Given data

diameter of the table = 3 feet

hang down dimension = 5 inches

sew down dimension = 1 inch

width of rectangular fabric = 60 inches

The question seeks for area of the table cloth, for a circular table area of a circle = pi * r^2

required radius of cloth

= radius of the table + hang down dimension + sew down dimension

= 3 feet / 2 + 5 inches + 1 inch

= 1.5 * 12 inches + 5 inches + 1 inch

= 18 + 5 + 1

= 24 inches

Area of required cloth

= pi * 24^2

= 1809.557 square inches

Area of fabric =  Area of required cloth

length * wide = 1809.557 square inches

length * 60 = 1809.557 square inches

length = 1809.557 / 60 square inches

length = 30.159 inches ≈ 30 inches

Therefore option H which is 30 inches is the answer

Read more on areas here: https://brainly.com/question/25292087

#SPJ1

The solution of the differential equation as given in the task content is; ln(5p +a)/5 + C = t

It follows from the task content that the solution of the differential equation is required.

Given;

dp/dt=5p +a

To find; solution to the differential equation;

By variable separation; the resulting equation is;

dp/(5p +a) = dt

By integrating both sides of the equation; we have;

ln(5p +a)/5 + C = t

Ultimately, although both sides of the equation integrated yield a constant of integration as the integral is indefinite, the two constants have been combined into constant, C as in the equation above.

Read more on differential equations;

https://brainly.com/question/1164377

#SPJ1

Answer:

23 dollars.

Step-by-step explanation:

She spent a total of 174 - 13 = 161 dollars.

So, the cost of each book = 161/7

= 23 dollars.

The width of the message as shown in the image attached is 3 inches.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let b represent the width of the message. The area of the postcard is 24 square inches, hence:

(b + 3)4 = 24

4b + 12 = 24

b = 3

The width of the message as shown in the image attached is 3 inches.

Find out more on equation at: https://brainly.com/question/13763238

#SPJ1

The density of the material is  0.4 kg/cubic cm.

Given that:-

Height of the cylinder = 54.5 mm

Diameter of the cylinder = 53.0 mm

Weight of the cylinder = 1 kg

We have to find the density of the cylinder.

We know that,

Density  = mass/volume

Here, mass = 1 kg

We know that,

Volume of a cylinder = [tex]\frac{1}{3} \pi r^2 h[/tex]

Where,

r is the radius of the cylinder, and

h is the height of the cylinder

Here, h = 54.5 mm, and

r = 53/2 = 26.5 mm

Hence,

Volume of cylinder = (1/3)*(22/7)*(26.5)(26.5)*54.5 ≈ 2566.088 ≈ 2566 cubic mm. = 2566/(10*10*10) cubic cm = 2.566 cubic cm

Density of cylinder = 1kg/2.566 cubic cm  ≈ 0.3897  ≈ 0.4 kg/cubic cm.

To learn more about density, here:-

https://brainly.com/question/15164682

#SPJ4

Step-by-step explanation:

420x1800=756000

so 756k items in 30 minutes

Answer:

x=3/5y-9/5

Step-by-step explanation:

Answer:

5x=7y-4y-9

5x=9-3y

[tex]\frac{5x}{5}[/tex]=[tex]\frac{9-3y}{5}[/tex]

[tex]x=\frac{9-3y}{5}[/tex]

Answer:

it is the first option

Step-by-step explanation:

First step. Switch the greater than sign and turn the linear inequality to slope formula. after that graph the line. it is a dashed line due to not being greater than EQUAL to. if not equaled to then it is dotted. then you need a point as your testing point to see if it is shaded in that area. I chose to(0,0) but you could have chose any point. Once you plug in the zeros you will notice you get the false statement of 0 greater than 15. so obviously that is a no so you shade the opposite side of your testing point. phew

Answer:

A. On a coordinate plane, a dashed straight line has a positive slope and goes through (0, 3) and (10, 7). Everything above and to the left of the line is shaded.

Step-by-step explanation:

Answer:

9.81....

Step-by-step explanation:

x = 432/44

x = 9.81...

How do you find equivalent expressions?

Image result for what is equivalent to (5x/6)

Combine any like terms on each side of the equation: x-terms with x-terms and constants with constants. Arrange the terms in the same order, usually x-term before constants. If all of the terms in the two expressions are identical, then the two expressions are equivalent.

Answer: 816

Step-by-step explanation:

h(3) = 1248 - 160(3) + 16(3)

h(3)= 1248 - 480 + 48

h(3)= 816

Answer:

25

Step-by-step explanation:

180 - 25 = 155

180 - 155 = 25

For an analysis of variance comparing four treatments, msbetween = 12. The value of ssbetween is 36.

A measure of variability is the variance. It is determined by averaging the squared deviations from the mean. Your data set's variability is shown by its variance. The variance is greater in respect to the mean when the data are more dispersed.

Finding the mean will allow you to compute the population's variance (the average). Squaring the result after deducting the mean from each data point in the sample. The outcomes are squared to make the adverse findings positive.

Data points' deviations from the mean are quantified by their variance. Layman defines variance as the degree to which a set of data (numbers) deviates from the mean (average) value.

To learn more about variance from the given link:

brainly.com/question/14116780

#SPJ4

Making a perpendicular bisector on the segment that gives the half length of AB

Given that,
here are 2 points in the plane. Explain how to construct a line segment that is half the length of AB is to explain.

A line can be defined by the shortest distance between two points is called as a line.

Here,
Two points are given on the plane,
Draw line segment joining these two points on the plane,
Now with help of a compass draw a perpendicular bisector on the line, that bisects the segment into two equal halfs.

Thus, making a perpendicular bisector on the segment that gives the half length of AB

Learn more about lines here:

brainly.com/question/2696693

#SPJ1

Using proportions, the coordinates of the point C that partitions segment HE in the ratio of 2:3 are found according to the following equation:

C - H = 2/5(E - H).

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For this problem, we have point C that partitions segment HE in the ratio of 2:3, hence it is 2/5 of the way from H to E, and the rule is given by:

C - H = 2/5(E - H).

Then:

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

after 10days savannah will have 31 pennies

Step-by-step explanation:

arithmetic progression (AP)

(a1) started with, 5 pennies

common difference (d), 3 pennies

formula: Tn = a + (n-1)d

after 10 days, T10 = 5 + (10- 1)(3)

T10 =5 + 27

T10= 31

therefore after ten days savannah has 31 pennies

The circumference of the children's ball to the nearest centimeter is 52 centimeters.

If a regulation volleyball has a circumference of about 66 centimeters, solve for its radius using the formula for the circumference of a circle given by:

C = 2πr

66 centimeters = 2πr

r = 33/π centimeters

Then, solve for the surface area of this regulation volleyball using the formula given by:

A = 4πr^2

A = 4π(33/π centimeters)^2

A = 4356/π square centimeters

If the ratio of the surface area of that ball to the surface area of a children's ball is approximately 1.6 : 1, then

surface area of regulation volleyball : surface area of a children's ball = 1.6 : 1

surface area of a children's ball = 4356/π square centimeters/1.6

surface area of a children's ball = 2722.5/π square centimeters

If  the children's ball has a surface area of 2722.5/π square centimeters, solve for its radius using the formula for the surface area given by:

A = 4πr^2

2722.5/π square centimeters = 4πr^2

r = 26.0887907/π centimeters

Solving for the circumference:

C = 2πr

C = 2π(26.0887907/π centimeters)

C = 52.17758139 centimeters

Rounding off to the nearest centimeter.

C = 52 centimeters

To learn more about circumference: https://brainly.com/question/20489969

#SPJ4

Answer:

x [tex]\leq[/tex] 28

Step-by-step explanation:

lets say you chose 27 . 27 - 13 = 14 . thats not enough . but everything 28 and above would work for x . so x would be equal to or greater than 28 . hope this helps :)

The missing values of the table are a=7, b=18, c=15, d=13, e=42 and  f= 21

We can easily  complete the give table using simple addition and subtraction

            Monday   Tuesday    Wednesday    Total

Year 7       7               18                   13.               38

Year 8     14              15                    13                42

Total        21              33                   26               80

The correct question is 80 students visited the library

over three days. The two-way

table shows some information

about these students.

             Monday   Tuesday   Wednesday   Total

Year 7           a               b                    13.          38

Year 8         14               c                      d          e

Total            f              33                    26          80

Complete the table.

To know more about Tables - https://brainly.com/question/10670417

#SPJ9

Answer:

2

Step-by-step explanation:

[tex] \: \: \: \: \: \: \: \large{\frac{5}{8}} \: \div \large{\frac{5}{16}} \\ \\ = \frac{5}{8} \times \frac{16}{5} \\ \\ = \green 2 \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Answer:

2

Step-by-step explanation:

(5/8) ÷ (5/16)

= (5*16) ÷ (8*5)

= 80 ÷ 40

= 2

Step-by-step explanation:

f(x) = 5|x - 1| - 5

f(x) will be positive that means >= 0, if

5|x - 1| - 5 >= 0

5|x - 1| >= 5

|x - 1| >= 1

that will be true for x <= 0 or x >= 2

f(x) will be negative for the other cases.

so, 0 < x < 2

f(x) is increasing in

[1, infinity)

the value "1" is for sure included, as it starts the increasing part.

f(x) is decreasing in

(-infinity, 1]

"1" is again included, because it ends the decreasing part.

end behavior means for x going to infinity and -infinity : in both cases f(x) goes to infinity.

The total number of houses sold in January by Coventry Estates are 18.

As per the given question;

Let the total sales of the houses in January be 'x'.

In February they sold twice as many houses as in January.

February = 2x.

In March they sold 10 more houses than in February.

March  = February + 10

March  = 2x + 10

In April they sold half as many houses as in March.

April = March/2

April = (2x + 10)/2 = x + 5

The total sold houses = 123.

Add all the sold houses;

x + 2x + 2x + 10 + x + 5 = 123

6x + 15 = 123

On simplification;

x = 18

Thus, the total number of houses sold in January by Coventry Estates are 18.

To know more about twice of number, here

https://brainly.com/question/13966934

#SPJ9

The hypotenuse of the right triangle is the diameter of the circle then the circumference of the circle is 17[tex]\pi[/tex] centimeters.

The midpoint is the point in the middle of a line segment in geometry. It serves as the segment and endpoint centroid because it is equidistant from both endpoints. The segment is cut in half.

The diameter of the circle is the hypotenuse of the right triangle.

Use the Pythagorean Theorem to find the diameter.

By using Pythagorean theorem we get

[tex]$$c^2 = a^2 +b^2[/tex]

substituting the values in the above equation, we get

[tex]$$c^2 = 8^2 +15^2[/tex]

simplifying the equation

[tex]$$c^2[/tex] = 289

c = 17

The diameter of the circle is 17 cm.

The circumference C of a circle is given by C = [tex]\pi[/tex] d.

Circumference of a circle = [tex]\pi[/tex]d

=  [tex]\pi[/tex] (17) = (17) [tex]\pi[/tex]

Therefore, the circumference of the circle is 17[tex]\pi[/tex] centimeters.

The correct question is:

Find the exact circumference of each circle by using the given inscribed or circumscribed polygon.

To learn more about the circumference of a circle refer to:

https://brainly.com/question/20489969

#SPJ4

The reactants in the chemical equation C7H16 + O2 = CO2 + H2O have a total of 7 atoms in them.

The chemical formula of a compound indicates how many atoms are present in the substance.

The number of atoms of each element present in a molecule is noted in a chemical formula.

The answer to this query provides the following description of the chemical interaction between heptane and oxygen:

O2 + C7H16 = CO2 + H2O

Hexane's chemical composition reveals that the reactant side of the reaction has 7 carbon atoms.

Therefore, there are 7 atoms total in the reactants of the chemical equation C7H16 + O2 = CO2 + H2O.

To learn more about chemical formula from given link

https://brainly.com/question/11995171

#SPJ1

If Mrs. Chavez put $8,000.00 in her IRA savings account that offers 8.62% interest compounded annually, then she will earn $3136 interest at the end of the 4 years

Total invested amount = $8000

Interest rate = 8.62%

The interest is compounded annually

Time period = 4 years

We know

[tex]A=P(1+\frac{r}{100})^{t}[/tex]

Where,

A = Final amount

P = Principal

r = Interest rate

t = Time period

Substitute the values in the equation

A= [tex]8000(1+\frac{8.62}{100})^{4}[/tex]

A= $11136

Compounded interest = 11136-8000

=$3136

Hence, If Mrs. Chavez put $8,000.00 in her IRA savings account that offers 8.62% interest compounded annually, then she will earn $3136 interest at the end of the 4 years

Learn more about Compound interest here

brainly.com/question/14295570

#SPJ1

Answer: -50

Step-by-step explanation:

2a-2a+5c

2(-3)-2(-3)(-4)+5(-4)=

-6-24-20=-50

The dimensions of the 1000-square-foot rectangular enclosure with the least amount of fencing should be 25ft by 40ft.

The amount of fencing needed can be calculated by getting the perimeter of each choice of dimensions.

Perimeter is defined as the distance that surround any two-dimensional shape. For a rectangle, the perimeter is given by the formula

P = 2l + 2w

Solving for the perimeter of each of the following choices:

F. 8ft by 125ft

P = 2l + 2w

P = 2(8) + 2(125)

P = 16 + 250

P = 266ft

G. 10ft by 100ft

P = 2l + 2w

P = 2(10) + 2(100)

P = 20 + 200

P = 220ft

H. 20ft by 50ft

P = 2l + 2w

P = 2(20) + 2(50)

P = 40 + 100

P = 140ft

J. 25ft by 40ft

P = 2l + 2w

P = 2(25) + 2(40)

P = 50 + 80

P = 130ft

The dimensions with the least perimeter will require the least amount of fencing.

Hence, a 1000 -square-foot rectangular enclosure, with dimensions 25ft by 40ft, will require the least amount of fencing.

To learn more about perimeter: https://brainly.com/question/17297081

#SPJ4

The value of Square root √16 is equals to 4, and the number 16 is larger than the number 4 then 16 > √16.

Let the value of √16 be 4 then 16 > √16.

To know more about Square root, refer to the following link:

https://brainly.com/question/3617398

#SPJ4