Ben, Cam, and Justin are lumberjacks. The number of trees they chop down is given by b+2c+3jb+2c+3j where b is the number of hours Ben spends chopping, c is the number of hours Cam spends chopping, and j is the number of hours Justin spends chopping.
How many trees do they chop down after Ben spends 88 hours chopping, Cam spends 33 hours chopping, and Justin spends 44 hours chopping?

Answer:

Triangles are congruent because all the corresponding sides and interior angles are congruent.

Step-by-step explanation:

In ΔWXY  and ΔBCD

Given Sides are congruent:

[tex]WX \cong BC[/tex]  

[tex]XY \cong CD[/tex]

[tex]YW \cong DB[/tex]

Also,

Angles are congruent i,e:

[tex]\angle W \cong \angle B[/tex]

[tex]\angle X \cong \angle C[/tex]

[tex]\angle Y \cong \angle D[/tex]

By congruence statement: If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then those triangles are congruent.

[tex]\triangle WXY \cong \triangle CBD[/tex]

Therefore, we can say the two triangles WXY and BCD are congruent because every corresponding side are of equal length and every corresponding angle has the same measure.

The given triangles WYX and BDC are congruent as all the sides as well as the angles are equal.

From the given figures,

[tex]WY=BD\\WX=BC\\YX=DC[/tex]

Also,

[tex]\angle{W}=\angle{B}\\\angle{Y}=\angle{D}\\\angle{X}=\angle{C}[/tex]

Hence, the triangles WYX and BDC are congruent to each other.

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Answer:

15/5= x. x=3.

Step-by-step explanation:

Miles ran in total divided by days spent running equals miles ran each day.

The liquid height in the new cylinder will be 4 cm after the volume of liquid from the original cylinder is transferred.

In the context of this problem, we are dealing with the concept of the volume of a cylinder. The volume of a cylinder is given by the formula V=πr²h, where r is the radius of the base and h is the height of the cylinder. The given volume in the problem is 36π cm³ and the radius of the second cylinder is 3 cm. We will use the volume formula to find the height.

We know that V=36π cm³ and r=3 cm. Substituting these values into the volume formula, we get 36π=π(3)²h. Simplifying the equation gives us 36π=9πh. Dividing both sides by 9π, we arrive at the solution, h=4 cm. Therefore, the height of the liquid in the new cylinder will be 4 cm.

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Answer:

Solution for (a)

Earlier Copper pennies are 22.

After 1983 pennies are 28.

Step-by-step explanation:

Pennies minted after 1983 weigh 2.50g

Earlier copper pennies weigh 3.11g

A roll of pennies contains 50 pennies.

A particular roll of pennies weighs 138.42g

Let the number of pennies minted after 1983 be x and;

Earlier copper pennies be 50 - x

2.50x + 3.11(50 - x) = 138.42

Opening the brackets gives;

2.5x + 155.5 - 3.11x = 138.42

Solving like terms together gives;

-0.61x = -17.08

Dividing through gives;

x = 28

So there are 28 after 1983 pennies and;

50 - 28 = 22 earlier pennies.

[tex]i=\sqrt{-1}-\text{the imaginary number}\\\\\sqrt{-36}=\sqrt{(36)(-1)}=\sqrt{36}\cdot\sqrt{-1}=\boxed{6i}[/tex]

Answer:

Answer is: A

Step-by-step explanation:

Because it is.

Answer:

A. $17.00

Step-by-step explanation:

$5.10 for 6 quarts.

Unit cost: ($5.10)/(6 qt) = $0.85/qt

Price for 5 gallons:

1 gallon = 4 quarts

5 gallons = 5 * 4 quarts = 20 quarts

Price for 5 gallons = unit price * number of quarts

Price for 5 gallons = $0.85/qt * 20 qt = $17.00

Answer: A. $17.00

Answer:

is your answer $3250

Step-by-step explanation:

so we dont know our I (interest) but :

P (principal) = 10000

R (rate) = 6.5%  we'll have to turn it into the decimal which is 0.065

T (time) = 5 years

and our basic formula of finding I is I = PxRxT   so :

I = 10000 x 0.065 x 5

I = 3250

Answer:

We have the following given

mileage = 70 miles per gallon

distance = 60 km

Required: amount of fuel in gallons

First, we must convert the distance to miles, so

60 km (1 mi/1.6 km) = 37.5 mi

So, the amount of fuel is

37.5 mi / (70 mi/gal) = 0.54 gallon

Answer:

B

Step-by-step explanation:

70 miles * [1.6 km/mile] = 112 km

Notice when you multiply by km/mile by miles the miles cancel out.

1 gallon will get 112 km

x gallon will get 60 km

Solution:

Considering  room to be in the shape of Cuboid as well as the Bed to be in the shape of Cuboid.

Dimensions of Room

Let Length of cuboid which is in the shape of room = L

Breadth of cuboid which is in the shape of  room = B

Height of cuboid which is in the shape of room = H

Considering, L>B>H

Dimension of Bed

Length=[tex]\frac{L}{6}[/tex] units

Breadth=[tex]\frac{B}{4}[/tex] units

Height=[tex]\frac{H}{6}[/tex] units

Taking one corner at origin i.e (0,0,0)

You can keep your bed at any place inside the room, but you want your bed to be at that place inside the room where the window is located so that proper ventilation and sunlight can enter your room.

Taking bed to be in the middle of room near the window and considering it's upper face

Distance from one corner i.e from length= B- [tex]\frac{B}{4}[/tex]=[tex]\frac{3B}{4}[/tex] Units

Distance from other corner=  0 Units

Distance from Breadth of one side of wall= [tex]\frac{L}{3}[/tex] units

Distance from one corner i.e from Breadth =L - [tex]\frac{L}{3}[/tex]-[tex]\frac{L}{6}[/tex]= [tex]\frac{L}{2}[/tex]

Distance from floor i.e surface=[tex]\frac{H}{6}[/tex] units

Distance from Ceiling= H -[tex]\frac{H}{6}[/tex] = [tex]\frac{5 H}{6}[/tex] units

To find the distance each bed edge should be from the corner in a scale drawing, determine the scale used (such as 1 inch = 6 feet), convert actual bed dimensions using the scale, and ensure measurements on the drawing are precise and noted with the correct line types.

To determine how far each edge of the bed should be from its own corner of the wall in a scale drawing, first establish the scale being used for the model. For example, if the scale is 1 inch = 6 feet, convert the actual dimensions of the bed into the scale size by using ratios that compare the scale distance to the actual distance. If the actual bed is 6 feet long, then the length on the scale model would be 1 inch. When recording measurements, both the actual size and the scale size should be clearly marked to prevent confusion. It is important to use correct line types and to make all the drawings to exact measurements within the constraints of the paper size.

For consistent and accurate representation, the edges of the bed should be measured from the corner of the walls based on the determined scale. This involves calculating the distance of the bed from the wall in actual size, then converting that distance to the scale model size. Pay attention to significant figures and the choice of units (inches, feet, centimeters, meters) to maintain precision in your scale drawing.

Answer:

A C B

Step-by-step explanation:

In sequence A. the numbers are being divided by 4.

In sequence B. the numbers are being multiplied by -3

In sequence C. the numbers are being add by 4

So the ratio from least to greatest would be A C B

Answer:

Sequence B, Sequence A, Sequence C

Step-by-step explanation:

Common ratio of a geometric sequence is the ratio of a term and its previous term of the sequence.

Thus, the common ratio of the sequence  A: 160,40,10,2.5,...

[tex]r_1=\frac{40}{160}=\frac{1}{4}[/tex]

The common ratio of the sequence B: -21,63,-189,567,...

[tex]r_2=\frac{63}{-21}=-3[/tex]

The common ratio of the sequence C : 8,12,18,27,....

[tex]r_3=\frac{12}{8}=\frac{3}{2}[/tex]

Since, -3 < [tex]\frac{1}{4}[/tex] < [tex]\frac{3}{2}[/tex]

Thus,

[tex]r_2 < r_1 < r_3[/tex]

Hence, the order the sequences from least common ratio to the greatest common ratio is,

Sequence B, Sequence A, Sequence C

Answer:

7/10 x 2/5 = 14/50 = 7/25

Step-by-step explanation:

mutipily 7 and 2 that gives you 14 and mutilpily 10 and 5 that gives you 50 = 14/50. In simplest form the answer is 7/25.

Answer:

7/10 x 2/5 = 14/50 = 7/25

Step-by-step explanation:

mutipily 7 and 2 that gives you 14 and mutilpily 10 and 5 that gives you 50 = 14/50. In simplest form the answer is 7/25.

Answer: 47 (choice B)

x+43 = 90

x = 90 - 43

x = 47

This works because triangle PQR is a right triangle (with angle Q as the 90 degree angle). We say that that P and R are complementary angles. I added point R to be located where the angle x is written.

Answer:

47

Step-by-step explanation:

Answer:

2700 cookies.

Step-by-step explanation:

A dozen is a grouping of twelve, that is a dozen = 12.

If there are 225 dozen cookies in the bakery, then there are

[tex]225\cdot 12=2700[/tex] cookies in the bakery.

there are 2700 cookies in total

Since there are 225 dozen cookies in the bakery, we need to determine the total number of cookies.

To convert dozen to individual units, we multiply the number of dozens ( 225 )  by 12, as there are 12 cookies in each dozen :

225 dozen * 12 cookies / dozen = 2700 cookies

Therefore, there are 2700 cookies in total. By multiplying the number of dozens by 12, we account for the fact that each dozen contains 12 cookies. This calculation allows us to determine the precise quantity of cookies in the bakery.

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Answer:

All you have to do is subtract 1500-785 in order to find the number of minutes left for him.

1500-785=715 more minutes left

Answer:

Its Option C

Step-by-step explanation:

The difference is 180 - 135 = $45

So  it is 45 * 100 / 135  

= 33.33% greater

Answer: Its Option C

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

74,000 x .48 = 35520. 35520 is the amount of property you have to pay for.

35520 x 0.031 = 1,101.12.  1.101.12 is the amount you owe in property tax.

The amount owed in property tax to the nearest dollar is $1,101

In real estate management, the market price is the price at which a buyer is willing to pay and which the seller is as agreed to receive at the present time.

From the parameters given:

From the property, the required amount of property to be paid for is:

= $74000 × 0.48

= $35520

If the state property tax rate is 0.31, the amount owe in property tax is:

= $35520 × 0.031

= $1,101

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First, by using the distance formula for just one side, we can find the length of all sides (a square has 4 equal sides.) Then, we can apply the area of a square formula, which is a^2.

Distance formula:

[tex]\sqrt{(x.2 - x.1)^{2} + (y.2 - y.1)^{2}}[/tex]

√((-2 + 5)^2 + (-8 + 4)^2)

√((3)^2 + (4)^2)

√9 + 16

√25

5

The side lengths of the square are each equal to 5, and by applying the formula for area, we can find the area of the square.

5^2 = 25

Final answer:

To find Tamia's age, an equation was set up based on the relationship between Jay and Tamia's ages. Jay is 20 years old and 4 years younger than three times Tamia's age. Solving the equation shows that Tamia is 8 years old.

Explanation:

Jay is 4 years younger than three times Tamia's age. Given that Jay is 20 years old, we can use this information to find out how old Tamia is. Let's denote Tamia's age as T. The relationship between their ages can be represented by the equation: Jay's age = 3 × Tamia's age - 4. Since Jay's age is 20, we can substitute this into the equation, giving us 20 = 3T - 4.

To solve for T, we first add 4 to both sides of the equation, which gives us 24 = 3T. Next, we divide both sides by 3 to find Tamia's age, resulting in T = 8. Therefore, Tamia is 8 years old.

This problem was solved by setting up an equation based on the relationship described between Jay and Tamia's ages, then using basic algebraic steps to solve for Tamia's age.

Answer:

x=56 and the exterior angle is 116

Step-by-step explanation:

We will call the unknown angle in the triangle y.  Angle y and the angle (2x +4) form a straight line so they make 180 degrees.

y + 2x+4 =180

Solve for y by subtracting 2x+4 from each side.

y + 2x+4 - (2x+4) =180 - (2x+4)

y = 180-2x-4

y = 176-2x

The three angles of a triangle add to 180 degrees

x+ y+ 60 = 180

x+ (176-2x)+60 = 180

Combine like terms

-x +236=180

Subtract 236 from each side

-x+236-236 = 180-236

-x = -56

Multiply each side by -1

-1*-x = -56*-1

x=56

The exterior angle is 2x+4.  Substitute x=56 into the equation.

2(56)+4

112+4

116

Answer:

B) 2

Step-by-step explanation:

Given expression,

48 ÷ ((2 + 6) × 2) − 1

In simplification we follows the following order,

B = Bracket

O = Of

D = Division

M = Multiplication

A = Addition,

S = Subtraction,

Thus, steps of solving the given expression by following BODMAS are as follow,

[tex]\frac{48}{(2 + 6) \times 2}-1[/tex]

[tex]=\frac{48}{8\times 2}-1[/tex]

[tex]=\frac{48}{16}-1[/tex]

[tex]=3-1[/tex]

[tex]=2[/tex]

Hence, OPTION B is correct.

The value equivalent to 48 ÷ ((2 + 6) × 2) - 1 is B) 2.

To solve this problem, we need to follow the order of operations (also known as PEMDAS or BODMAS).

First, we calculate the expression inside the parentheses: 2 + 6 = 8.

Next, we multiply the result by 2: 8 × 2 = 16.

Finally, we divide 48 by the result: 48 ÷ 16 = 3.

After that, we subtract 1: 3 - 1 = 2.

Therefore, the value equivalent to 48 ÷ ((2 + 6) × 2) - 1 is 2.

Answer:

I Think It Is 0.12*2

Because I See Both Of The Shadings Colored Differently And Each One Has 12 That Is The Reason For Me Thinking This.

Answer: Bradley would expect 94 times to get a blue or green gumball.

Step-by-step explanation:

Since we have given that

Number of blue gumballs = 15

Number of yellow gumballs = 12

Number of green gumballs = 2

Number of purple gumballs = 16

Total number of all gumballs = 45

Probability of getting either a blue gumball or green gumball be

[tex]\frac{15}{45}+\frac{2}{45}=\frac{17}{45}[/tex]

So, Expectation of getting a blue gumball or green gumball if a gumball was taken out 250 times :

[tex]\frac{17}{45}\times 250=94.4[/tex]

Since we know that it must be less than 94.4.

So, the nearest smallest integer will be 94 times .

Hence, Bradley would expect 94 times to get a blue or green gumball.

Answer:

The answer is A because if you subtract the 1 you get y=1 and the line of A is at the point 1 on the y-axis

Step-by-step explanation:

Answer:

b+9

Step-by-step explanation:

(b + 3) + 6 = b + (3 + 6) = b + 9

The percentage of its capacity is the large container​ filled will be 87.5%.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

A large container has a maximum capacity of 64 ounces.

And, The container is filled with 8 ounces less than its maximum capacity.

Now,

Calculate the percent of its capacity is the large container​ filled as;

Percent = (64 - 8) / 64  x 100

            = 56/64 x 100

            = 87.5%

Thus, The percentage of its capacity is the large container​ filled will be 87.5%.

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The complete question is this;

A large container has a maximum capacity of 64 ounces. The container is filled with 8 ounces less than its maximum capacity. To what percent of its capacity is the large container​ filled?

Brian rented the book for 12 days.

Brian rented a book with the condition that the shop charges $2 for the first day and $3 from the second day onwards. He paid a total of $35 upon returning the book. To determine how many days he kept the book, we must calculate the cost for each day and subtract the initial $2 from the total amount paid.

Steps to Calculate the Number of Days:

Therefore, Brian kept the book with him for 12 days.

Answer:

C) 8

Step-by-step explanation:

y = 3x-4

Substitute x=4 into the equation

y = 3*4 -4

y = 12-4

y=8

Put the value of x = 4 to the equation y = 3x - 4:

[tex]y=3(4)-4=12-4=8[/tex]

[tex]\bold{Given : 2^2^x^-^2 - 2^x^-^1 = 2^x - 2}[/tex]

[tex]\bold{\implies (2^2^x) (2^-^2) - (2^x)(2^-^1) = 2^x - 2}[/tex]

[tex]\bold{\implies \frac{(2^2^x)}{(2^2)} - \frac{(2^x)}{(2^1)} = 2^x - 2}[/tex]

[tex]\bold{\implies \frac{(2^2^x)}{4} - \frac{(2^x)}{2} = 2^x - 2}[/tex]

[tex]\bold{\implies \frac{[2^2^x - (2^x)(2)]}{4} = 2^x - 2}[/tex]

[tex]\bold{\implies [2^2^x - (2^x)(2)] = (4)(2^x) - 8}[/tex]

[tex]\bold{\implies 2^2^x - (2^x)(2) - (4)(2^x) + 8 = 0}[/tex]

[tex]\bold{\implies (2^x)^2 - (2^x)(6) + 8 = 0}[/tex]

[tex]\bold{Let\;us\;take : (2^x) = Z}[/tex]

[tex]\bold{\implies Z^2 - 6Z + 8 = 0}[/tex]

[tex]\bold{\implies Z^2 - 4Z - 2Z + 8 = 0}[/tex]

[tex]\bold{\implies Z(Z - 4) - 2(Z - 4) = 0}[/tex]

[tex]\bold{\implies Z = 4\;\;(or)\;\;Z = 2}[/tex]

[tex]\bold{But : Z = 2^x}[/tex]

[tex]\bold{\implies 2^x = 4\;\; (or) \;\; 2^x = 2}[/tex]

[tex]\bold{\implies 2^x = 2^2\;\; (or) \;\; 2^x = 2^1}[/tex]

[tex]\bold{\implies x = 2\;\;(or)\;\; x = 1}[/tex]