Darius is building a table. He cuts 12-foot-long boards into sections that are each ¼ foot long. How many sections of the board will Darius have when he is finished cutting?

Answer: 31363022. or 17

Step-by-step explanation:

Answer:

the width of the rectangle is 5.

Step-by-step explanation:

Let's assume that the width of the rectangle is x. Then, according to the problem statement, the length of the rectangle would be 3x.

The area of a rectangle is given by the formula:

Area = Length x Width

Substituting the values of length and width in the formula, we get:

75 = (3x) x (x)

Simplifying the right-hand side, we get:

75 = 3x^2

Dividing both sides by 3, we get:

25 = x^2

Taking the square root of both sides, we get:

x = ±5

Since the width cannot be negative, we take the positive value of x, which is 5.

Therefore, the width of the rectangle is 5

For part A the length of the perpendicular is approximately 156.18. Length of GH, the area of the rectangle is approximately 12336.22 square units.

FOR Part B the length of the perpendicular is approximately 182.48.

the area of the triangle is approximately 8954.96 square units.

How to solve the question?

To find the perpendicular of a right triangle, we need to use the Pythagorean theorem, which states that the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let the length of the perpendicular be h, and the length of the other leg of the triangle be b. Then, we can set up the equation:

175²= h²+ 79²

Simplifying, we get:

30,625 = h²+ 6,241

Subtracting 6,241 from both sides, we get:

24,384 = h²

Taking the square root of both sides, we get:

h ≈ 156.18

Therefore, the length of the perpendicular is approximately 156.18.

The area of a rectangle is given by the formula:

Area = length × width

Substituting the given values, we get:

Area = 156.18 × 79

Area = 12336.22 square units

Therefore, the area of the rectangle is approximately 12336.22 square units.

To find the perpendicular, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, we know the length of the hypotenuse and one of the other sides, so we can solve for the length of the perpendicular.

Using the Pythagorean theorem:

h²= b²+ p²

where h is the length of the hypotenuse, b is the length of the base, and p is the length of the perpendicular.

Substituting the given values:

207²= 98²+ p²

Simplifying:

42849 = 9604 + p²

Subtracting 9604 from both sides:

33245 = p²

Taking the square root of both sides (since p is a length, we only take the positive square root):

p = sqrt(33245)

p ≈ 182.48

Therefore, the length of the perpendicular is approximately 182.48.

To find the area of the triangle, we can use the formula:

Area = (1/2) x base x height

Substituting the given values:

Area = (1/2) x 98 x 182.48

Simplifying:

Area = 0.5 x 98 x 182.48

Area ≈ 8954.96

Therefore, the area of the triangle is approximately 8954.96 square units.

To know more about Area visit :-

https://brainly.com/question/25292087

#SPJ1

Answer:

V = 4,423.4

SA = 1,508.0

Step-by-step explanation:

r = d/2
V = πr²h

(3.14)(8)²(22) = 4,423.362456

SA = 2πr(h + r)

2(3.14)(8)(22 + 8) = 1,507.964474

Therefore, the width of the rectangle is 10.

So, the answer is (O) 10.

To find the width of a rectangle, you will need to have at least one of the following pieces of information:

Length and area: If you know the length and area of the rectangle, you can use the formula for area (A = length x width) and solve for the width (W = A/length).

Perimeter and length: If you know the perimeter and length of the rectangle, you can use the formula for perimeter (P = 2 x length + 2 x width) and solve for the width (W = (P - 2 x length)/2).

Diagonal and length: If you know the diagonal and length of the rectangle, you can use the Pythagorean theorem ([tex]a^2 + b^2 = c^2[/tex]) to solve for the width. [tex](W = \sqrt(c^2 - length^2)),[/tex] where c is the diagonal and a and b are the length and width (in some order).

Ratio of length to width: If you know the ratio of length to width, you can use this ratio to solve for the width. For example, if the ratio of length to width is 3:2, and the length is 15, then the width would be 10 (because 15/3 = 5 and 5 x 2 = 10).

Measurements: If you have physical access to the rectangle, you can measure the width directly using a ruler or tape measure.

Let's assume the length of the rectangle as "L" and the width as "W".

From the given information, we know that:

The area of the rectangle is 40, so we have the equation:

[tex]L x W = 40[/tex]

The width is 2 less than 3 times the length, so we have the equation:

[tex]W = 3L - 2[/tex]

Now we can substitute the second equation into the first equation and get:

[tex]L x (3L - 2) = 40[/tex]

Expanding the left-hand side, we have:

3L^2 - 2L - 40 = 0

Dividing both sides by 1, we get:

[tex]3L^2 - 2L - 40 = 0[/tex]

Using the quadratic formula, we get:

[tex]L = 4 or L = -10/3[/tex]

Since the length of a rectangle cannot be negative, we take L = 4.

Then, we can use the equation W = 3L - 2 to find the width:

[tex]W = 3 x 4 - 2 = 10[/tex]

To know more about  rectangle, visit:

https://brainly.com/question/29123947

#SPJ1

The side length of each square is √225 in = 15 inches so the option B is correct

The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √. For example, the square root of 9 is 3 because 3 multiplied by 3 equals 9. The square root of 16 is 4 because 4 multiplied by 4 equals 16. The square root of a number is always a positive number, although it can be irrational (a non-repeating, non-terminating decimal) for some numbers.

The formula to find the length of one side of a square, s, when given the area, A, is:

s = √(A)

So, for the square with A = 225 in², the side length would be:

s = √(225) in

s = 15 inches

Therefore, the side length of the square with an area of 225 in² is 15 inches.

Learn more about Square root here

https://brainly.com/question/29775049

#SPJ1

As a result, the shaded region's area sector is **10.62 cm² cm.²

What is a sector?

A sector is a section of a circle in geometry that is bounded by two radii and an arc. It is a pie-shaped portion of a circle that touches the circle's center, has two straight edges (the two radius lines), and a curved edge created by the arc.

Arc Length = r is the formula for the arc length of a circle,

where is the radius of the circle and r is the radian measurement of the arc (or central angle).

The formula for arc length, L = r *, can be used to determine the value of zero. L is the length of the arc, r is the radius of the circle, and is the centre angle in radians. We can deduce from the facts provided that PQ equals 2 * OP.

Also obvious is that OR = 4 cm. We can claim that PQ = 2 * OR = 8cm because PQ is twice as long as OP. Now, we can calculate's value using the formula:

L = r * θ 8 = 4θ θ = 2

Consequently, = 2 radians.

We must know the length of arc RS in order to calculate the size of the shaded zone. PQ is twice RS, as we are aware. RS = PQ/2, which equals 4 cm. Now, we may apply the area of a formula.We may now apply the formula A = (1/2) * r² *, where A is the sector's area, r is the circle's radius, and is the centre angle in radians.

Sector PQR area equals (1/2) * OR2 * sector PQR area equals (1/2) * 16 * 2 sector PQR area equals (16)

Sector PSR area equals (1/2) * OR²2 * Sector PSR area equals (1/2) * 16 * π/3 Sector PSR area equals (8)/3

Sector PQR minus Sector PSR is equal to the area of the shaded region. Area of the shaded area is 16 - (8π)/3. Shaded area size: 10.62 cm²

To know more about sector visit:

brainly.com/question/12665895

#SPJ1

The required probability that Joy will give a chocolate ice cream cone to the first child and then second child get a vanilla ice cream cone is equal to 3/16.

Number of chocolate ice cream cones = 8

Number of vanilla ice cream cones = 10

Number of strawberry ice cream cones = 6

Total number of ice cream cones = 8+10+6

                                                        = 24 cones,

The probability of Joy giving a chocolate ice cream cone to the first child is 8 cones,

P(chocolate) = 8/(8+10+6) = 8/24 = 1/3

Now,

Assuming that Joy gave away a chocolate ice cream cone to the first child,

There are 8-1=7 chocolate ice cream cones left.

Similarly, there are 10-1=9 vanilla ice cream cones left.

Probability of Joy giving a vanilla ice cream cone to the second child,

given that she gave a chocolate ice cream cone to the first child, is,

P(vanilla | chocolate)

= 9/(7+9)

= 9/16

Probability of Joy giving a chocolate ice cream cone to the first child and a vanilla ice cream cone to the second child is,

P(chocolate and vanilla)

= P(chocolate) × P(vanilla | chocolate)

= (1/3) × (9/16)

= 3/16

Therefore, the probability that Joy will give a chocolate ice cream cone to the first child and then a vanilla ice cream cone to the second child is 3/16.

Learn more about probability here

brainly.com/question/29800191

#SPJ4

The coordinate location of point C' after the dilation is (-10, 2).

What is coordinate location?

To find the coordinate location of point C' after the dilation by a scale factor of 4 about the center (-2,-2), we can use the following formula:

(x', y') = (k * (x - h) + h, k * (y - k) + k)

where (x, y) are the coordinates of the original point, (h, k) are the coordinates of the center of dilation, k is the scale factor, and (x', y') are the coordinates of the corresponding point after dilation.

For point C, the coordinates are (x, y) = (-2, -1) and the center of dilation is (h, k) = (-2, -2) with a scale factor of k = 4.

Plugging in these values, we get:

(x', y') = (4 * (-2 - (-2)) - 2, 4 * (-1 - (-2)) - 2)

= (-10, 2)

Therefore, the coordinate location of point C' after the dilation is (-10, 2).

What is coordinate?

A coordinate is a set of numbers or values that indicate the position or location of a point or object in a given space or system. Coordinates are often used in mathematics, geometry, physics, and other fields to describe the location of objects or points in a two- or three-dimensional space. The most common type of coordinates are Cartesian coordinates, which are represented by an ordered pair of numbers (x,y) that describe the location of a point on a two-dimensional plane, or an ordered triplet of numbers (x,y,z) that describe the location of a point in a three-dimensional space.

To know more about coordinate, visit:

https://brainly.com/question/30951761

#SPJ1

Complete question is: The preimage shown above is dilated by a scale factor of 4 about the center (-2,-2). the coordinate location of the point C'after the dilation is (-10, 2).

The total probability of winning is 0.75, which is not equal to 1, indicating that the game is not fair.

To decide in case this is a fair game, we ought to calculate the likelihood of each player winning.

Let H speak to the result of flipping a head and Tail speak to the result of flipping a tail. At that point, the conceivable results of three coin flips are:

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

The likelihood of getting each result is 1/8, accepting the coin flips are reasonable and autonomous.

Xenia wins on the off chance that there are 2 heads and 1 tail. Three conceivable results fulfill this condition:

HHT, HTH, and THH. Hence, the likelihood of Xenia winning is 3/8.

Yolanda wins in case there are 2 tails and 1 head. There are moreover three conceivable outcomes that fulfill this condition:

TTH, THT, and HTT. Subsequently, the likelihood of Yolanda winning is additionally 3/8.

Zoe wins if there are 3 heads or 3 tails. Two conceivable results fulfill this condition:

HHH and TTT. In this manner, the likelihood of Zoe winning is 2/8 = 1/4.

To check in case the diversion is reasonable, we include the probabilities of each player winning:

3/8 + 3/8 + 1/4 = 0.75

The full probability of winning is 0.75, which isn't break even with 1, indicating that the game is not fair.

One way to form it a fair diversion would be to alter the payouts or the rules of the amusement to guarantee that the full likelihood of winning includes up to 1.

learn more about probability

brainly.com/question/13957582

#SPJ4

The amounts of Alex's transactions in order are $50.00, $40.00, $24.00, $35.00, $149.00, and $98.67.

The amounts of Alex's transactions can be listed in the following order:

The amount he received from selling his bike: $50.00

The amount he deposited into his savings account, which is 80% of $50.00: $40.00

The first deposit he made of $24.00

The second deposit he made of $35.00

The total amount he had in his account before withdrawing 2/3 of it: $149.00 (which is the sum of $50.00, $40.00, $24.00, and $35.00)

The amount he withdrew to buy the used skateboard, which is 2/3 of $149.00: $98.67

Find out more about savings accounts

at brainly.com/question/27466480

#SPJ4

 so it is 2o bevuse

hi

Answer:148.38

Step-by-step explanation:

Population Density=Population of country÷Area of country

Population of country=23,023

Area of country=(18*8)+(4*5)=164 m²

Population Density=23023÷164=148.38 people/m²

The height of the building is approximately 62.4369 feet. The solution involves using trigonometry and solving for the opposite side of the triangle using the tangent function.

Let h be the height of the building, and x be the distance between the first point and the base of the building. Then we have:

tan(26.8°) = h/x ----(1)

tan(19.5°) = h/(x + 43.9) ----(2)

From equation (1), we have x = h/tan(26.8°)

Substituting this value of x in equation (2) and solving for h, we get:

h = (43.9 tan(19.5°) tan(26.8°))/(tan(26.8°) - tan(19.5°))

Plugging in the values, we get:

h ≈ 62.4369 feet

Therefore, the height of the building is approximately 62.4369 feet.

Learn more about trigonometry here: brainly.com/question/29002217

#SPJ1

The net loss is $1873.97.

What is the selling price?

The selling price formula is Selling Price = Cost Price + Profit Margin. Cost price is the price a retailer paid for the product. The profit margin is a percentage of the cost price.

Here, we have

Given: Suki purchased $9,600 worth of stock and paid her broker a 2.5% broker fee. She had an immediate need for cash and was forced to sell the stock when it was worth $8,000. She used a discount broker who charged $33.97 per trade transaction.

Purchase price: $9,600

Fee purchase:  2.5%

Selling price: $8,000

Fee scale: $33.97

The broker fee is the product of the broker fee rate of  2.5% and the purchase price:

Broker fee purchase = 2.5%× 9,600

= 240

The total purchase cost is the sum of the purchase price and the broker fee of the purchase:

Total purchase cost Purchase price =  Broker fee purchase

= 9600 + 240

= 9840

The total selling cost is the selling price decreased by the broker fee of the sale (flat rate):

Total selling cost = Selling price - Broker fee sale

= 8,000 - 33.97

= 7966.03

The net loss is then the difference between the total purchase cost and the total selling cost:

Net loss = Total purchase cost - Total selling cost

= 9840 - 7966.03

= 1873.97

Hence, the net loss is $1873.97.

To learn more about the selling price from the given link

https://brainly.com/question/31131809

#SPJ1

Assume that m arc VUX = 228° and m ∠UVW = 121° in the circle below.

m∠VUX = 66° and m m∠UXW = 59° respectively.

1) The given information is;

The angle of arc m∠VUX = 228°, the measured angle of ∠UVW = 121°

Given that m∠VUX = 228°, therefore, arc ∠XWV = 360 - 228 = 132°

Therefore, the angle subtended by arc ∠XWV at the centre = 88°

The angle subtended by arc ∠XWV at the circumference = m∠VUX

∴ m∠VUX = 132°/2 = 66° (Angle subtended at the center = 2×angle subtended at the circumference)

m∠VUX = 66°

2) Similarly, m∠XWV is subtended by arc m∠VUX, therefore, m∠XWV = (arc m VUX)/2 = 228°/2 = 114°

A quadrilateral's angles add up to 360°.

Therefore;

m∠VUX + m∠XWV + m∠UVW + m∠UXW = 360° (The sum of angles in a quadrilateral XWVU)

m∠UXW = 360° - (m∠VUX + m∠XWV + m∠UVW)

m∠UXW = 360° - (66 + 114 + 121)

m∠UXW = 360° - 301

m∠UXW = 59°.

To learn more about the arc, refer:-

https://brainly.com/question/18741430

#SPJ1

Answer:

60 degrees

Step-by-step explanation:

The total angles of a circle add up to 360 so to find a missing angle, subtract the figures already given from 60. The angles given total to (140+125+35) = 300. To find angle a, you subtract the 300 from 360. 360-300 = 60 degrees. Therefore, angle a is 60 degrees

The equation that represents the proportional relationship is [tex]y=\frac{1}{4}x[/tex].

What is proportion?

Proportion is a mathematical concept that describes the equality of two ratios. In other words, it is a statement that two ratios or fractions are equal.

For example, if we have two fractions [tex]\frac{a}{b}[/tex] and [tex]\frac{c}{d}[/tex], we can say that they are in proportion if:

=> [tex]\frac{a}{b}=\frac{c}{d}[/tex]

Now the ratio between x and y = 4:1

Here x = 28 then y = [tex]\frac{1}{4}\times28 = 7[/tex]

Then, x = 12 then [tex]y=\frac{1}{4}\times12 = 3[/tex]

We can see that the ratio between X and Y is always 4:1, which means that Y is one-fourth of X. We can write this as:

=>[tex]y=\frac{1}{4}x[/tex]

Therefore, the equation that represents the proportional relationship is:[tex]y=\frac{1}{4}x[/tex].

To know more about proportions refer the below link

brainly.com/question/30241688

#SPJ1

The measure of angle LEP can be found using the angle addition postulate, which states that the measure of an angle formed by two adjacent angles is equal to the sum of their measures. Given that angle, LEW is 51 degrees and angle PEW is 27 degrees, we can find the measure of angle LEP by adding these two angles. Thus, the angle LEP is 78 degrees (51 + 27).

         L

        / \

       /   \

      /     \

     E-------P

        W

In mathematics, an angle is a geometric figure formed by two rays sharing a common endpoint, known as the vertex of the angle. There are two main ways to label angles: by giving the angle a name, usually a lowercase letter or a Greek letter, or by using the three letters that define the angle, with the middle letter being where the angle is located. Angles are typically measured in degrees using a protractor and are defined by their measure, which is not dependent upon the lengths of the sides of the angle. Coterminal angles share terminal sides but differ in size by an integer multiple of a turn.

Find out more about the angle

brainly.com/question/30474184

#SPJ4

Answer:

Let's start with the fixed cost, which is the cost to rent the room: $150. This is the y-intercept of the equation. Now, for each child attending the party, there is an additional cost of $5. We can represent the number of children attending with the variable x. Therefore, the equation in slope-intercept form is: y = 5x + 150 So the correct answer is D) y = 5x + 150

It is possible for her to exceed the speed limit and get a ticket if she is not paying attention or if the road conditions change.

What is speed?

she should always be aware of her speed and adjust it as necessary to stay within the legal limit.

Yes, this is an inequality problem. We can use an inequality to represent the situation:

David's speed ≤ Speed limit + 7 mph

Let's substitute the given values:

David's speed ≤ 60 mph + 7 mph

David's speed ≤ 67 mph

If David's speed is less than or equal to 67 mph, then she will not get a ticket, because she is within the allowable limit of going 7 mph over the speed limit. However, if David's speed is greater than 67 mph, then she will be going too fast and is at risk of getting a ticket.

Since David is driving on cruise control, it is possible for her to exceed the speed limit and get a ticket if she is not paying attention or if the road conditions change. Therefore, she should always be aware of her speed and adjust it as necessary to stay within the legal limit.

To know more about inequality visit:

https://brainly.com/question/30228778

#SPJ1

The answer is A. 1/4.

Step-by-step explanation:

The graph that represents all values of x such that x > -3 and x < 2 is the graph of a vertical line segment located between -3 and 2 on the x-axis, but excluding these two points. This can be represented graphically as:

|

|

|

---------x---------

|

|

|

-3 2

Here, the open circles indicate that the points -3 and 2 are not included in the range of values for x.

Hence, the response is (iv) 85 as the exterior angle is equal to the sum of the two opposite interior angles.

The apex of the angle is the intersection of two rays that together form the geometric shape known as an angle. Angles, which are commonly measured in degrees or radians, are employed in a variety of mathematical and scientific contexts, including engineering, physics, geometry, and trigonometry.

given

We can utilise the above details to construct an equation because the exterior angle is equal to the sum of the two opposite interior angles:

x + 35 = 120

35 is subtracted from both sides to yield:

x = 85

Hence, the response is (iv) 85 as the exterior angle is equal to the sum of the two opposite interior angles.

To know more about angles visit:

https://brainly.com/question/14569348

#SPJ1

The complete question is :-  

Use the Exterior Angle Theorem to solve for x.

Exterior angle = 120°

60

120

O 155

85

35°

The event where two or more things happen at the same time is called a "compound event."  the correct answer is B.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

A compound event refers to a situation where two or more events occur at the same time. In other words, it is an event that consists of multiple outcomes happening simultaneously.

For example, if you flip a coin and roll a dice at the same time, the resulting event would be a compound event because it involves the outcomes of both actions occurring simultaneously. It is important to distinguish between compound events and independent or dependent events, as they have different probabilities and methods of calculation. Compound events are often used in probability theory and statistics to analyze and predict the likelihood of multiple outcomes occurring at the same time.

The event where two or more things happen at the same time is called a "compound event." Therefore, the correct answer is B.

To learn more about probability from the given link:

https://brainly.com/question/30034780

#SPJ1

The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height of the prism, respectively. If the width is changed by a scale factor of 1/3, then the new width is (1/3)w. The length and height remain the same. Therefore, the new volume of the rectangular prism is:

V' = l(1/3w)h

Multiplying both sides by 3 to simplify the expression, we get:

3V' = lw(3h)

Since the original volume of the rectangular prism is 768 ft3, we have:

V = lwh = 768

Multiplying both sides by 3 to simplify the expression, we get:

3V = lw(3h)

Substituting 3V for lw(3h), we get:

3V' = 3V(1/3w) = Vw

Therefore, the new volume of the rectangular prism is:

V' = Vw = (768 ft3)(1/3) = 256 ft3

So, the volume of the same shape if the width is changed by a scale factor of 1/3 is 256 ft3.

The values x and y that make the quadrilaterals parallelograms are:

a. x = 2 and y = 41

b. x = 4 and y = 3

a. Since opposite sides of parallelograms are equal in length. We can say:

2x + 7 = x + 9

2x - x = 9 - 7

x = 2

Also, two adjacent  angles of parallelograms adds up to 180 degrees. That is:

(2y - 5)° + (2y + 21)° = 180°

4y + 16 = 180

4y = 180 - 6

4y = 164

y = 164/4

y = 41

b. Since the diagonals divide each other equally. We can say:

x + 8 = 16 - x

x + x = 16 - 8

2x = 8

x = 8/2

x = 4

5y + 4 = 2y + 13

5y - 2y = 13 - 4

3y = 9

y = 9/3

y = 3

Learn more about parallelograms on:

https://brainly.com/question/970600

#SPJ1

The evidence supports the conclusion that the account is not materially misstated if both the upper and lower limits are within the bounds of tolerable misstatement.

The combined total of his annual contribution and his employer's contribution is $13,000.

The term "combined total" refers to the sum or aggregate of two or more individual quantities, values, or amounts. It represents the cumulative or total amount resulting from the combination or addition of multiple components.

According to the given information:

First, let's calculate Caleb's annual contribution to his 401k account.

Caleb contributes $250 from each biweekly paycheck, so his biweekly contribution is $250.

Since there are 26 biweekly pay periods in a year (52 weeks), his total biweekly contributions in a year would be 26 * $250 = $6,500.

Caleb's annual salary is $45,000 per year, and his employer matches 75% of his 401k contributions up to 10% of his annual salary. So, the maximum employer match would be 75% of 10% of $45,000, which is 0.75 * 0.10 * $45,000 = $3,375.

Since Caleb's annual contribution ($6,500) is less than the maximum employer match ($3,375), his employer will match his entire contribution.

Therefore, the combined total of Caleb's annual contribution and his employer's contribution would be $6,500 + $6,500 = $13,000.

To know more about the combined total visit:

https://brainly.com/question/27119511

#SPJ1