What is the surface area of a right rectangular prism with a length of 2.5 ft, a width of 1.5 ft, and a height of 3.5 ft? Surface Area of Rectangular Prism

SA = 21w + 21h + 2wh SA=2( X ) + 2( x )+ 2(x ) SA=
2( )+ 2( ) + 2( ) SA= + +​

Using laws of the outside angle theorem, we can find the value of the arc x to be = 130°.

The measure of an exterior angle is equal to the sum of the measures of the two distant interior angles of the triangle, according to the external angle theorem. According to the exterior angle inequality theorem, any triangle's outside angle has a measure bigger than either of its opposing interior angles.

Here in the question,

As per the outside angle theorem,

50° = 180° - x°

Adding x° on both sides:

⇒ 50° + x° = 180°

Now subtracting 50° from both sides:

⇒ x° = 180° - 50°

⇒ x° = 130°

To know more about outside angle theorem, visit:

https://brainly.com/question/31507659

#SPJ1

The length of the bridge is 980 feet.

Let's denote the length of the bridge as x. According to the problem, one bank of the river holds 3/7 of the bridge, which means that the other bank holds 4/7 of the bridge.

Therefore, we can write the following equation:

3/7 x + 1400 + 4/7 x = x

Simplifying this equation, we get:

6/7 x + 1400 = x

Subtracting 6/7 x from both sides, we get:

1/7 x + 1400 = 0

Subtracting 1400 from both sides, we get:

1/7 x = -1400

Multiplying both sides by 7, we get:

x = -9800

Since the length of the bridge cannot be negative, we need to discard this solution. Therefore, the only valid solution is:

x = 980

So the length of the bridge is 980 feet.

Learn more about bridge

brainly.com/question/14555851

#SPJ11

Answer:9

Step-by-step explanation:

If three squares have sides that make an acute triangle, then the sum of the areas of the two small squares equals the area of the largest square. This is known as the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two smaller sides is equal to the square of the hypotenuse (the longest side).

2. If three squares have sides that make an obtuse triangle, then the sum of the areas of the two small squares is greater than the area of the largest square. This can be proven using the Law of Cosines, which states that in a triangle with sides a, b, and c and angle C opposite side c, c² = a² + b - 2ab cos(C). For an obtuse triangle, the cosine of the angle opposite the largest side is negative, which makes the right-hand side of the equation larger than c². Therefore, the sum of the squares of the smaller sides is greater than the square of the largest side.

3. If three squares have sides that make a right triangle, then the sum of the areas of the two small squares equals the area of the largest square. This is again the Pythagorean theorem. Let the sides of the squares be a, b, and c, with c being the hypotenuse. Then we have a² + b² = c². The areas of the squares are a², b², and c², respectively, so the sum of the areas of the two small squares is a² + b², which equals the area of the largest square (c²).

To know more about squares  here:

https://brainly.com/question/27307830

#SPJ1

Using the binomial probability formula, we get a probability of approximately 1 or 100%.

This problem involves a binomial probability distribution, where we are interested in the number of successes (colleges with distance learning courses) in a fixed number of trials (picking 13 institutions), where each trial has a constant probability of success (the probability that a college offers distance learning courses).

We can use the binomial probability formula

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

where X is the number of successes, k is the number of successes we are interested in, n is the total number of trials, p is the probability of success, and C(n, k) is the binomial coefficient.

Substituting the given values, we get

P(X = k) = C(13, k) * 0.96^k * 0.04^(13-k)

To find the probability that at least one college offers distance learning courses, we can find the probability that none of the 13 colleges offer distance learning courses and subtract it from 1

P(X ≥ 1) = 1 - P(X = 0)

P(X = 0) = C(13, 0) * 0.96^0 * 0.04^13 = 0.000000005096

P(X ≥ 1) = 1 - 0.000000005096 ≈ 1

Therefore, the probability that at least one college out of 13 offers distance learning courses is approximately 1 or 100%.

To know more about binomial probability distribution:

https://brainly.com/question/31197941

#SPJ4

Therefore , the solution of the given problem of ratio comes out to be the Udderly Delicious Cheese Factory needs 550 gallons of milk in total.

A group comprising values both variable "a" and "" that seem to be equal is found using the straightforward formula "a / b," whenever "b" might be a greater number than zero. A ratio is created by combining two ratios. The ratio , fraction could have been 1:1 if there were just one guy and three women. There are 1/4 men and 3/4 women in the group.

Here,

For cheddar cheese, multiply the quantity of blocks by 200 and the amount of milk consumed by each block by 5.

200 blocks of cheddar cheese divided by 5 quarts per block equals a total of 1000 quarts.

For Swiss cheese, the formula is as follows: 200 blocks of Swiss cheese, or 6 quarts of milk per block.

200 blocks of Swiss cheese divided by 6 quarts per block equals 1200 quarts of milk in total.

Total milk used equals the sum of the milk required to make cheddar cheese and the milk used to make Swiss cheese, or 1000 quarts plus 1200 quarts, or 2200 quarts.

We can convert quarts to gallons by dividing by 4 because there are 4 quarts in a gallon.

= 1000 quarts + 1200 quarts

= 2200 quarts

We can convert quarts to gallons by dividing by 4 because there are 4 quarts in a gallon.

=> Total gallons of milk used = 2200 quarts / 4 quarts/gallon = 550 gallons

Thus, to make 200 blocks of cheddar cheese and 200 blocks of Swiss cheese each day,

the Udderly Delicious Cheese Factory needs 550 gallons of milk in total.

To know more about ratio visit:

brainly.com/question/13419413

#SPJ1

The measure of the supplementary angle of the given angle would be = 175.2°

A supplementary angles are those angles that sums up to 180° when added up together.

To calculate the supplementary angle represented by X;

That is,

X+ 4.8° = 180

X = 180-4.8 = 175.2°

Learn more about supplementary angles here:

https://brainly.com/question/30431434

#SPJ1

Answer:

2/3 pizza is left!

Step-by-step explanation:

You take 1/3 from a whole pizza (3/3), leaving 2/3 for ur 2 buddies :D

The standard form of the polynomial 2m-3m²+4m⁵+21 is 4m⁵ - 3m² + 2m + 21.

The standard form of a polynomial is when the polynomial is written with the terms in descending order of degree, with each term having a coefficient and an exponent. To convert the given polynomial 2m-3m²+4m⁵+21 to standard form, we need to rearrange the terms in descending order of degree.

The degree of a term is the exponent of the variable in that term. For example, the degree of the term 4m⁵ is 5, and the degree of the term -3m² is 2.

So, we start by arranging the terms in descending order of degree:

4m⁵ - 3m² + 2m + 21

Next, we can simplify the coefficients of each term if possible. In this case, all of the coefficients are already simplified, so we leave them as they are.

In summary, to convert a polynomial to standard form, we arrange the terms in descending order of degree and simplify the coefficients of each term if possible. This makes it easier to compare and manipulate polynomials, and is often required when solving equations or finding roots of polynomials.

To learn more about polynomial click on,

https://brainly.com/question/18275243

#SPJ1

The correct order from greatest to least is option G. 14.33, 4√13, 14

To convert a root number to a whole number, you simply need to evaluate the root expression by performing the indicated operation. The result of the evaluation will be a whole number.

Here are the steps to convert a root number to a whole number:

Determine the type of root: square root (√), cube root (∛), etc.

Write the root expression using the appropriate symbol and the radicand (the number inside the root symbol).

Evaluate the expression by performing the indicated operation. For example, if it is a square root, multiply the number inside the root symbol by itself. If it is a cube root, multiply the number inside the root symbol by itself three times.

The result of the evaluation will be a whole number.

To compare the diagonal lengths, we need to convert them to the same units. We can convert 4√13 ft to approximately 9.17 ft by using a calculator. Now we have:

14.33 ft

0.143 ft

9.17 ft

So, the order from greatest to least is:

G. 14.33, 4√13, 14

learn more about root expression: https://brainly.com/question/738531

#SPJ1

The unit rate of water dropped per day is [tex]$\frac{12}{5}$[/tex] gallons per day.

We can start by finding the unit rate of water dropped per hour.

If the sink drips [tex]$\frac{2}{5}$[/tex] gallon of water in 4 hours, then it drips [tex]\frac{1}{5}$[/tex] gallon of water in 2 hours (since [tex](\frac{2}{4} = \frac{1}{2}$).[/tex]

The unit rate of water dropped per hour is:

[tex]$\frac{1/5}{2} = \frac{1}{10}$[/tex] gallon per hour.

To find the unit rate of water dropped per day, we can multiply the unit rate per hour by the number of hours in a day:

[tex]$\frac{1}{10} \text{ gallon per hour} \cdot 24 \text{ hours per day} = \frac{12}{5} \text{ gallons per day}$[/tex]

Therefore, the unit rate of water dropped per day is [tex]$\frac{12}{5}$[/tex] gallons per day.

Learn more about  unit rate

https://brainly.com/question/29781084

#SPJ4

The unit rate of water dropped per day is 12/5 gallons.

To find the unit rate of water dropped per day for a sink that drips 2/5 gallons of water in 4 hours, we'll follow these

steps:

Determine how many gallons of water are dripped in one hour.

Calculate the gallons of water dripped in 24 hours (one day).

Calculate gallons per hour.

Since the sink drips 2/5 gallons in 4 hours, we'll divide the gallons by the number of hours:

(2/5) / 4 = (2/5) × (1/4) = 2/20 = 1/10

So, the sink drips 1/10 gallons per hour.

Calculate gallons per day.

Now, we'll multiply the gallons per hour by 24 hours to find the gallons per day:

(1/10) × 24 = 24/10 = 12/5

The unit rate of water dropped per day is 12/5 gallons.

for such more question on word problem

https://brainly.com/question/21405634

#SPJ11

The measure of the angles formed by the lines are 30°, 30°,  150° and  150° by definition of vertically opposite angles.

When two straight lines intersect each other at some angle, say line AB intersect line CD, then the opposite angles formed by the two lines are called vertically opposite angles. A pair of vertically opposite angles are equal to each other.

There are two pairs of opposite angles formed by intersection of two straight lines.

The total sum of all the angles formed by intersection of two straight lines is 360°.

Let angle X = x° and angle Y= y° be a pair of opposite angles.

Let the other pair of opposite angles be of angle M = m° and angle N = n°.

Thus, by definition of opposite angles and sum of all angles on intersection of two lines we get,

angle X + angle Y + angle M + angle N = 360°

⇒ x° + y° + m° + n° = 360°

⇒ x° + x° + m° + m° = 360°

⇒ 2( x° + m°) = 360°

⇒ x° + m° = 180° ___ (1)

Also, the measure of one of the angles is five times the measure of another of the angles formed by the lines.

This relation can be written as,

angle X = 5 times of angle M

⇒ x° = 5m° ___(2)

Since angle X and angle M are not a pair of opposite angles but are supplementary angles as observed in equation (1).

Putting equation (2) in equation (1) we get,

5m° + m° = 180°

⇒ 6m° = 180°

⇒ m° = 30°

Thus, x° = 5(30°) = 150°

Hence the angles are 30°, 30°,  150° and  150°.

To know more about  measures of angles and vertically opposite angles here

https://brainly.com/question/29147905

#SPJ4

Answer: To find the average change in temperature per hour, we need to divide the total change in temperature by the number of hours.

The temperature dropped 25 degrees over 8 hours, so the average change per hour is:

25 degrees / 8 hours = 3.125 degrees per hour

Therefore, the temperature on top of Mt. Katahdin dropped by an average of 3.125 degrees per hour.

Step-by-step explanation: The temperature on top of Mt. Katahdin dropped by an average of 3.125 degrees per hour.

Answer:

0.535 is the correct choice.

The value of the triple integral is 1920pi/3.

Here are five other iterated integrals that are equal to the given iterated integral:

[tex]\Integral^2_0 \Integral^y_0 \Integral^1_0 f(x, y, z) dx dy dz[/tex]

[tex]\Integral^2_0 \Integral^z_0 \Integral^1_z f(x, y, z) dx dz dy[/tex]

[tex]\Integral^1_0 \Integral^y_0 \Integral^1_z f(x, y, z) dx dz dy[/tex]

[tex]\Integral^1_0 \Integral^z_0 \Integral^1_y f(x, y, z) dx dy dz[/tex]

[tex]\Integral^z_0 \Integral^1_0 \Integral^y_z f(x, y, z) dx dy dz[/tex]

To evaluate the triple integral of[tex](4 + 5x^2yz^2) dV[/tex]over the cylindrical region [tex]x^2 + y^2[/tex] <= 4, -2 <= z <= 2, we can use geometric interpretation and symmetry.

Note that the integrand [tex](4 + 5x^2yz^2)[/tex] is an even function of x and y, and an odd function of z.

Therefore, the integral over the region where z is positive is equal in magnitude but opposite in sign to the integral over the region where z is negative.

Hence, we can evaluate the integral over the region 0 <= z <= 2, and then double the result.

The region of integration is a cylinder of radius 2 and height 4.

Since the integrand is not dependent on x and y, we can factor out[tex](4 + 5z^2)[/tex]  from the integrand, and evaluate the remaining integral over the unit disc in the x-y plane.

Thus, the triple integral can be written as:

[tex]8 * \Integral^2_0 \Integral^2pi_0 \Integral^2_0 (4 + 5z^2) r^3 sin(\theta) dr d(\theta) dz[/tex]

Integrating with respect to r from 0 to 2 and with respect to [tex]\theta[/tex] from 0 to [tex]2\pi[/tex], we get:

[tex]8 * \Integral^2_0 \Integral^2pi_0 (4 + 5z^2) sin(\theta) d(\theta) dz[/tex]

Integrating with respect to theta from 0 to 2pi, we get:

[tex]16pi * \Integral^2_0 (4 + 5z^2) dz[/tex]

Integrating with respect to z from 0 to 2, we get:

16pi * (32/3 + 80) = 1920pi/3.

For similar question on integral.

https://brainly.com/question/24705479

#SPJ11

the least common multiple of 43, 24, and 17 is 87,672.To find the least common multiple (LCM) of three numbers, we first need to find their prime factorization.

what is prime factorization ?

Prime factorization is the process of finding the prime numbers that multiply together to give a given composite number. A composite number is any positive integer greater than 1 that is not itself a prime number.

In the given question,

To find the least common multiple (LCM) of three numbers, we first need to find their prime factorization.

Prime factorization of 43: 43 is a prime number, so its prime factorization is simply 43.

Prime factorization of 24: 24 can be factored as 2 × 2 × 2 × 3.

Prime factorization of 17: 17 is a prime number, so its prime factorization is simply 17.

Next, we find the highest power of each prime factor that appears in any of the three factorizations:

The prime factor 2 appears to the third power in the factorization of 24, and to the first power in the factorizations of 43 and 17.

The prime factor 3 appears to the first power in the factorization of 24, and to the zero power in the factorizations of 43 and 17.

The prime factor 17 appears to the first power in the factorization of 17, and to the zero power in the factorizations of 43 and 24.

The prime factor 43 appears to the first power in the factorization of 43, and to the zero power in the factorizations of 24 and 17.

Therefore, the LCM of 43, 24, and 17 is:

2³ × 3¹ × 17¹ × 43¹ = 87,672

Hence, the least common multiple of 43, 24, and 17 is 87,672.

To know more about prime factorization , visit:

https://brainly.com/question/29775157

#SPJ1

To ensure that the replica will fit on an 8.5-by-11-inch paper, we need to choose a scale that will result in dimensions that are smaller than or equal to 8.5 inches by 11 inches.

Choosing an appropriate scale for a replica depends on the size of the original object and the desired size of the replica. To fit a replica on an 8.5-by-11-inch paper, we need to determine the maximum size that the replica can be while still fitting on the paper.

One common method for determining the appropriate scale is to measure the dimensions of the original object and then divide them by the desired size of the replica. For example, if the original object is 20 inches wide and we want to create a replica that is 8 inches wide, the scale would be 20/8, or 2.5.

In order to fit the replica on an 8.5-by-11-inch paper, we need to make sure that the dimensions of the replica are smaller than or equal to 8.5 inches by 11 inches.

We can use the scale factor to determine the maximum dimensions of the replica. For example, if the scale factor is 2.5 and we want the replica to be 8 inches wide, the maximum height of the replica would be 8/2.5, or 3.2 inches.

To learn more about scale click on,

https://brainly.com/question/2897262

#SPJ4

The quadratic equation that has solutions of 3 and -4 and includes f(7) = 88 is f(x) = 2(x - 3)(x + 4).

A quadratic equation is a second-degree polynomial equation that can be written in the general form:ax^2 + bx + c = 0

where x represents the variable, and a, b, and c are coefficients that represent real numbers, with a ≠ 0. The highest power of x in a quadratic equation is 2, and it typically forms a parabolic shape when graphed on a coordinate plane.

According to the given information:

A quadratic equation is typically written in the form:

f(x) = ax^2 + bx + c

where a, b, and c are coefficients.

Given that the solutions of the quadratic equation are 3 and -4, we can write the equation in factored form as:

f(x) = a(x - 3)(x + 4)

where (x - 3) and (x + 4) are the factors corresponding to the solutions 3 and -4, respectively.

Now, we are given that f(7) = 88. We can substitute x = 7 and f(x) = 88 into the equation above to obtain:

88 = a(7 - 3)(7 + 4)

Simplifying the expression inside the parentheses, we get:

88 = a(4)(11)

88 = 44a

Dividing both sides by 44 to solve for a, we get:

a = 88 / 44

a = 2

So, the value of a is 2.

Substituting the value of an into the factored form of the equation, we get:

f(x) = 2(x - 3)(x + 4)

Therefore, the quadratic equation that has solutions of 3 and -4 and includes f(7) = 88 is: f(x) = 2(x - 3)(x + 4)

To know more about Quadratic equations visit:https://brainly.com/question/17177510

#SPJ1

Thus,  the store sold 9 purses and 27 blouses on that day, and the total revenue from selling these items was $1107.

To solve this problem, we need to use algebraic equations. Let's start by assigning variables to the unknown quantities. Let x be the number of purses sold and y be the number of blouses sold.

From the problem, we know that the blouses cost $28 each and the purses cost $39 each. Therefore, the total revenue from selling x purses and y blouses is given by:

Revenue = 28y + 39x

We also know that the store sold three times as many blouses as purses. Therefore, we can write:
y = 3x

Now we can substitute y = 3x into the revenue equation and solve for x:
1107 = 28y + 39x
1107 = 28(3x) + 39x
1107 = 84x + 39x
1107 = 123x
x = 9

So the store sold 9 purses. To find the number of blouses, we can use the equation y = 3x:
y = 3x = 3(9) = 27

Therefore, the store sold 27 blouses.

In summary, the store sold 9 purses and 27 blouses on that day, and the total revenue from selling these items was $1107.

know more about the total revenue

https://brainly.com/question/30760779

#SPJ11

The length of curve DE, which is 5% longer than line segment AB, is 10.5 units.

To calculate the length of curve DE, we first need to determine the length of line segment AB. Let's say, for example, that line segment AB has a length of 10 units. To find the length of curve DE, we need to add 5% of line segment AB's length to line segment AB.

To calculate 5% of line segment AB's length, we can multiply the length of line segment AB by 0.05. This gives us:

5% of 10 = 0.05 x 10 = 0.5

So, 5% of line segment AB's length is 0.5 units. To find the length of curve DE, we need to add 0.5 units to the length of line segment AB. This gives us:

Length of curve DE = Length of line segment AB + 5% of Length of line segment AB

= 10 + 0.5

= 10.5 units

To know more about line segment here

https://brainly.com/question/30072605

#SPJ4

Complete Question:

You are trying to help Matt understand the concept of a 5% slack in the line. You explain that having a 5% slack means that the length is 5% longer than it would be if it were completely straight. You compare ABC to Figure DEF, where curve DE is 5% longer than line segment AB.

Enter the length of curve DE given that the curve is 5% longer than line segment AB.

The statement that is true of the pizza is A. About half of the pizza is left.

The answer to the subtraction of the fractions is 7/24.

Miron was 1/3 of an hour faster today than yesterday.

Initially, 2/3 of the pizza was left over. Marcy ate 2/9 of the pizza.

2/3 - 2/9

(2/3) x (3/3) = 6/9

6/9 - 2/9 = 4/9

So, 4/9 of the pizza is left. Since 4/9 is less than half but more than very little.

2/3 - 3/8

Find a common denominator, which in this case is 24:

(2/3) x (8/8) = 16/24

(3/8) x (3/3) = 9/24

Now subtract:

16/24 - 9/24 = 7/24

The answer in simplest form is 7/24

Miron finished his tasks in 3/4 of an hour yesterday and 5/12 of an hour today.

3/4 - 5/12

Find a common denominator, which in this case is 12:

(3/4) x (3/3) = 9/12

9/12 - 5/12 = 4/12

4/12 = 1/3

Miron was 1/3 of an hour faster today than yesterday.

Find out more on fractions at https://brainly.com/question/18175484

#SPJ1

Answer:

4138158

Step-by-step explanation:

1+1+1+1+1+1+1+1+1+1+1+1+1+3+3+34

-13+6+34

-19+34

=59

4748957+84765

=4833722

59+4833722

=4833781

keep counting all of the number and then you get the same (?? iguess) answer as mine.

48πft² is the amount of plastic was used to make the packages.

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases connected by a curved surface. It can be thought of as a solid object with a circular cross-section. Cylinders are commonly used in engineering, architecture, and mathematics.

A sphere is a three-dimensional geometric object that is perfectly round in shape, like a ball. It is defined as the set of all points in space that are equidistant from a given point, called the center. Spheres are commonly used in mathematics, physics, and engineering to model objects such as planets, bubbles, and particles.

Surface area= 2×base area+lateral area

= 2πr²+πd×h

=2π×3²+π×(3×2)×5

=2π×9+30π

=(18π+30π)

=48πft²

Learn more about shapes here:

https://brainly.com/question/28633340

#SPJ1

Answer:

volume

Step-by-step explanation:

Victoria should use volume measurement to determine how much sand she should buy.

Horatio has 6 trophies by equating the resultant linear equation in one variable.

Hence option b  is the correct option.

Patel has 19 trophies in total.

Its is said that Patel has five less than four times as many trophies as Horatio has.

Let the number of trophies Horatio has be x and that of Patel be y.

From the given relation of trophies of Patel and Horatio we get,

y = 4x - 5

This forms a linear equation.

We have y = 19.

Thus y = 4x - 5 can be written as,

19 = 4x - 5

Thus we have the equation in the form of a linear equation in one variable.

Simplifying the linear equation in one variable we get,

19 = 4x - 5

⇒ 19 + 5 = 4x

⇒ 24 = 4x

or, 4x = 24

⇒ x = 24/4

⇒ x = 6

Hence, Horatio has x = 6 trophies in total.

Hence option b is correct option.

To know more about linear equation in one variable here

https://brainly.com/question/31120842

#SPJ4

We can rewrite the following logarithms to common logarithms as follows:

1. 2.3768

2. 3.8173

To rewrite the logarithms in the common format we can use the following formula.

loga b = log10 b / log10 a

So, we have:

log5 46 = log10 46 / log10 5

Using a calculator, we find that log10 46 ≈ 1.66276 and log10 5 ≈ 0.69897, so:

log5 46 ≈ 1.66276 / 0.69897 ≈ 2.3768

For the second one, we can approach the problem this way:

loga b = log10 b / log10 a

So, we have:

log3 66 = log10 66 / log10 3

Using a calculator, we find that log10 66 ≈ 1.81954 and log10 3 ≈ 0.47712, so:

log3 66 ≈ 1.81954 / 0.47712 ≈ 3.8173

Learn more about common logarithms here:

https://brainly.com/question/30467932

#SPJ1