4 √(20) + 6 √(45) - √(80)

Answer:

x ≈ 39.5°

Step-by-step explanation:

using the cosine ratio in the right triangle

cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{OP}{NP}[/tex] = [tex]\frac{64}{83}[/tex] , then

x = [tex]cos^{-1}[/tex] ( [tex]\frac{64}{83}[/tex] ) ≈ 39.5° ( to the nearest tenth )

The surface area of the rectangular pyramid is approximately 567.9 in².

What is rectangular pyramid?

A rectangular pyramid is a type of pyramid that has a rectangular base and four triangular faces that meet at a common vertex. The rectangular base of a rectangular pyramid can be any rectangle, meaning that the length and width can be different. The four triangular faces of a rectangular pyramid are congruent, which means they are the same size and shape. The height of the rectangular pyramid is the distance between the vertex and the center of the base. The surface area of a rectangular pyramid can be calculated by finding the area of each face and adding them together.

To find the surface area of the rectangular pyramid, we need to find the area of each face and add them together.

First, let's find the area of the rectangular base:

Area of base = length x width = 13 in x 17 in = 221 in²

Next, let's find the area of the larger triangular faces:

Area of each larger triangular face = (1/2) x base x height = (1/2) x 17 in x 11 in = 93.5 in²

Total area of both larger triangular faces = 2 x 93.5 in² = 187 in²

Finally, let's find the area of the smaller triangular face:

Area of smaller triangular face = (1/2) x base x height = (1/2) x 13 in x 12.3 in = 79.95 in²

Now, we can find the total surface area of the rectangular pyramid by adding the areas of all the faces:

Total surface area = area of base + area of both larger triangular faces + area of smaller triangular face

Total surface area = 221 in² + 187 in² + 79.95 in²

Total surface area = 488.95 in²

Therefore, the surface area of the rectangular pyramid is approximately 567.9 in².

To know more about rectangular pyramid visit:

https://brainly.com/question/27270944

#SPJ1

Answer:

The answer is B ([tex]x=\frac{6}{5}[/tex])

Step-by-step explanation:

We start with creating labels for the shapes that represent what they value -at first I tried multiplying the 5x by 4 but there wasn't an answer for that.

[tex]5x+4=10[/tex]

First we just simplify,

[tex]5x (-4)=10(-4)[/tex]

[tex]5x=6[/tex]

then divide,

[tex]\frac{5x}{5} =\frac{6}{5}[/tex]

and we end up with:

[tex]x=\frac{6}{5}[/tex]

or

B

Step-by-step explanation:

From 4:26 to 6:50  is   2 hr and 24 in = 2  24/60  hrs =  2.4 hours

2.4 hrs is what percent of 15 hrs ?

2.4  /  15  * 100% = 16%

The volume of a triangular prism will be reduced to half of it if the height is reduced by half

A prism is a solid shape that is bound on all its sides by plane faces. The volume of a prism is generally expressed as ;

V = base area × height

If the height is cut into half, then the volume will be affected in this way.

V = bh, where b is the base area and h is the height.

When the height is cut into half i.e h/2 then the volume will be;

V = b × h/2

Since the base is constant, this means the volume will also be reduced by half.

Therefore when the height is reduced to half the volume is also reduced to half.

learn more about volume of a prism from

https://brainly.com/question/23766958

#SPJ1

The volume of the prism is 87 and 1/2 cubic yards or 87.5 [tex]yd^{3}[/tex]

The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.

In this case, the length is 5 yards, the width is 5 yards, and the height is 3 and 1/2 yards. We can convert the height to a mixed number fraction of 7/2 yards.

Therefore, the volume of the prism is:

V = lwh = 5 yards × 5 yards × 7/2 yards = 87.5 cubic yards

So, the volume of the prism is 87 and 1/2 cubic yards or 87.5 [tex]yd^{3}[/tex]

to know more about volume

brainly.com/question/1578538

#SPJ1

Therefore, the area of the regular dodecagon with a side length of 8 units is approximately 1,843.21 square units.

In mathematics, area refers to the measure of the amount of space inside a two-dimensional shape or region. It is a measure of the size of a flat surface, and is typically expressed in square units, such as square meters (m²), square centimeters (cm²), or square feet (ft²). The area of a shape can be calculated using various formulas, depending on the type of shape. The concept of area is used in many areas of science and engineering, including physics, geometry, and architecture. It is particularly important in fields such as construction and landscaping, where the amount of material needed to cover a given area is often a key factor in planning and budgeting.

Here,

To find the area of a regular dodecagon, you can use the formula:

Area = (3 * √3 / 2) * s² * n

where s is the length of each side and n is the number of sides.

Substituting s = 8 and n = 12, we get:

Area = (3 * √3 / 2) * 8² * 12

Area = 3 * √3 * 64 * 12

Area = 1,843.21 square units (rounded to two decimal places)

To know more area,

https://brainly.com/question/30106292

#SPJ1

Answer:

236 cm^2  and  8 cm

Step-by-step explanation:

width=w

240=6(5)(w)

w=8 cm

area=2[(6)(5)+(6)(8)+(5)(8)]

area=236 cm^2

The description of the polyomial roller coaster project is shown below

Proposal for the "Imaginary Rush" Roller Coaster:

The polynomial's graph is attached

Description of how client specifications are met:

Interpretation of the practicality of the design:

The design of Imaginary Rush is both exciting and practical. The coaster meets all the client's specifications while also providing a thrilling ride for coaster enthusiasts.

The dips and peaks of the coaster follow the behavior of the polynomial, providing a unique experience for riders.

The use of the imaginary root adds an additional level of excitement to the ride, making it stand out from other roller coasters.

Overall, the design of Imaginary Rush is both fun and practical, making it an excellent addition to any theme park.

Discussion of the polynomial's behaviors:

Read more about polynomial at

https://brainly.com/question/7693326

#SPJ1

Answer: It should be the same?

(edit) Answer: The direct answer is 6:2 or 6 (cups) flour 2 (cups) milk

Step-by-step explanation: I'm Confused, the ratio is 3:1 or 1:0/3 even if you double the ratio it would be 6:2 the portions of flour will always 3 times the amount (measurement) of the milk. Correct me if i'm wrong, a bit perplexed why this question is asked.

The margin of error for the school's claim  is 0.055 or approximately 5.5%.

To find the margin of error, we need to use the formula:

Margin of error = Critical value x Standard error

For a sample size of 500, the critical value can be found by:

critical value = 1.96

Next, we need to find the standard error. The formula for the standard error is:

standard error = sqrt(p_hat * (1 - p_hat) / n)

In this case, the sample proportion is 150/500 = 0.3.

standard error = sqrt(0.3 * (1 - 0.3) / 500) = 0.028

Finally, we can calculate the margin of error:

Margin of error = 1.96 x 0.028 = 0.055

To know more about margin of error, here

brainly.com/question/29101642

#SPJ4

--The complete Question is, What is the margin of error for the school's claim that 30% of grade 3 pupils stay in the playground after their classes, given the results of the survey of 500 grade 3 pupils, which revealed that 150 of them stay in the playground after their classes? Assume a confidence level of 95%.--

Compartmentalized is the type of data that is discussed in the problem researched by an employee rylie who is a newly hired cybersecurity expert for a government agency and has working experience in the private sector.

Data classification is the way of organizing data into different categories that make it easy to retrieve, sort and store for future use. In simple words, compartmentalization means to separate into isolated compartments or categories. In data language, A nonhierarchical grouping of information used to control access to data more finely than with hierarchical security classification alone is called Compartmentalization. Now, we have a rylie who is a newly hired cybersecurity expert for a government agency. She has working experience in the private sector. On basis of her experience she has discovered that, the private sector companies often had confusing hierarchies for data classification as compared to the government's classifications which are well known and standardized. During her training, she is researching data that requires special authorization beyond normal classification. The data type that she researched and that is authorization beyond normal classification is called compartmentalized data.

For more information about data classification, visit :

https://brainly.com/question/30580761

#SPJ4

The probability of the sample mean being less than 79 is 77.64%

In order to solve the given problem we have to take the help of Standard error mean

SEM = ∑/√(n)

here,

∑ = population standard deviation

n = sample size

hence, the z-score can be calculated as

z = ( x' - μ)/σ/√(n)

here,

x' = sample mean

μ = population mean

σ = population standard deviation

n = sample size

adding the values into the formula

SEM = σ / √(n)

= 21/√64

= 2.625

z = (x' - μ)/SEM

= (79-77)/2.625

= 0.76

now, using standard distribution table we find that probability of a z-score is less than 0.77 then converting it into percentage

0.77 x 100

= 77%

The probability of the sample mean being less than 79 is 77.64%

To learn more about probability,

https://brainly.com/question/13604758

#SPJ4

It is true that a linear programming problem can have an optimal solution that is not a corner point.

In linear programming, the optimal solution represents the point where the objective function is optimized while still satisfying all the constraints.

In some cases, the optimal solution may occur at a corner point of the feasible region, where two or more of the constraints intersect.

However, it is possible for the optimal solution to occur at a point that is not a corner point, but rather lies on an edge or a line segment of the feasible region.

This can occur when the objective function is parallel to one of the constraint lines or when there are redundant constraints that limit the feasible region.

Therefore, it is true that a linear programming problem can have an optimal solution that is not a corner point.

Learn more about linear programming.

brainly.com/question/15417573

#SPJ11

Answer:

Step-by-step explanation:

Principal = 17,525. Rate = 1/2% = 0.005 time,t = 3

Interest, I = principal x rate x time

Interest, I = 17525 x 0.005 x 3

Interest, I = $262.875

Therefore, the time in minutes when the trough is empty is approximately 0.313 minutes.

To find the time in minutes when the trough is empty, we need to solve the equation f(x) = 0, since f(x) represents the volume of water in the trough.

So, we need to solve the quadratic equation:

[tex]10x^2 - 19x + 6 = 0[/tex]

To solve this equation, we can use the quadratic formula:

[tex]x = (-b ± \sqrt(b^2 - 4ac)) / 2a[/tex]

where a = 10, b = -19, and c = 6.

Plugging in these values, we get:

[tex]x = (-(-19) ± \sqrt((-19)^2 - 4(10)(6))) / 2(10)[/tex]

[tex]x = (19 ± sqrt(241)) / 20[/tex]

So, the two solutions are:

[tex]x = (19 + \sqrt(241)) / 20 \approx1.807 minutes[/tex]

[tex]x = (19 - \sqrt(241)) / 20 \approx0.313 minutes[/tex]

However, only the second solution makes sense in this context, since the trough cannot be empty before we start draining the water. Therefore, the time in minutes when the trough is empty is approximately 0.313 minutes.

To know more about quadratic visit:

https://brainly.com/question/22364785

#SPJ1

The required sample size is  8.90400.

Given a student wants to make a guess within 0.03 of the true ratio with a 90% confidence level.

Margin of Error, E = 0.03

significance level α=0.10  {90% confidence}

A given estimate of the percentage of population p is p = 0.79.

The critical value for the significance level α = 0.10 is Zc = 1.645. This can be determined using either Excel or a normal probability table.

Use the following formula to calculate the minimum sample size required to estimate the percentage of population p within the required margin of error.

n≥p(1-p)(Zc÷E)²

n = 0.796×(1-0.796)(1.645÷0.03)²

n = 0.796 x 0.204 x 54.833

n = 8.90400

Therefore, the resample size required to meet the condition is n ≥  8.90400 and must be an integer. From this, we conclude that the minimum sample size required is n =  8.90400

Lear more about confidence level here :-

https://brainly.com/question/22851322

#SPJ4

Answer:

The answer is 28

Step-by-step explanation:

sin0=opp/hyp

let hyp be x

sin30=14/x

0.5x=14

divide both sides by 0.6

x=14/0.5

x=28

The fraction of the year representing the Christian celebration of Easter on April 16 is equal to 0.3.

In 2017, there were 365 days in the year.

It was not a leap year.

Easter Sunday occurred on April 16th.

Number of days in months before Easter,

January = 31

February = 28

March = 31

April = 16

Total days in Easter = 31 + 28 + 31 +16

                                  =  106th day of the year

January 1 is the first day of the year.

Total number of days in a year = 365

Fraction of the year

= the number of days up to and including April 16th / the total number of days in the year

= 106 / 365

= 0.2904

= 0.3 (rounded to 1 decimal place)

Therefore, Easter Sunday in 2017 represented as 0.3 fraction of the year.

learn more about fraction here

brainly.com/question/25278844

#SPJ4

The above question is incomplete , the complete question is:

In 2017, the Christian celebration of Easter occurred on Sunday, 16 April. What fraction of the year was this? (to 1 decimal place).

The value of AC to the nearest tenth is 29.5

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

Angle B = 180-(33+58)

= 180-91 = 89°

using sine rule

represent AC by x

x/ sin89 = 25/sin 58

xsin58 = 25sin89

0.848x = 0.9998×25

0.848x = 24.995

x = 24.995/0.848

x = 29.5( nearest tenth)

therefore the value of AC is 29.5.

learn more about sine rule from

https://brainly.com/question/20839703

#SPJ1

There were 100 small pine cone patterns and 50 large pine cone patterns used in the camp.

When 50 students constructed one craft project each using two little pine cone patterns and one giant pine cone pattern, it is the question of how many small and large pine cone patterns were utilised overall:

We can begin by figuring out how many little pine cone patterns were utilized overall to solve this.

Since each student used 2 small pine cone patterns, we can multiply 2 by 50 (the number of students) to get:

2 x 50 = 100 small pine cone patterns used

Similarly, we can calculate the total number of large pine cone patterns used by multiplying the number of students (50) by 1 :

1 x 50 = 50 large pine cone patterns used

Therefore, in total, there were 100 small pine cone patterns and 50 large pine cone patterns used in the camp.

To know more about pine cone patterns, here

brainly.com/question/5057335

#SPJ4

--The complete Question is, If a camp has 50 students and each student made one craft project using 2 small pine cone patterns and 1 large pine cone pattern, how many small and large pine cone patterns were used in total? --

where t is measured in days, and A(t) represents the amount of flooded land at time t. This function has a B-value of -0.3118.

To model the situation of the flood, we can use an exponential decay function, which represents the decreasing amount of flooded land over time. The function can be written as:

[tex]A(t) = A0 * e^{(-kt)}[/tex]

where A(t) is the amount of flooded land at time t, A0 is the initial amount of flooded land, k is a constant representing the rate of decay, and e is the mathematical constant approximately equal to 2.718.

To determine the value of k, we can use the given information that after 2 days, only 3375 acres of land were under water. Substituting t = 2 and A(t) = 3375 into the equation above, we get:

[tex]3375 = A0 * e^{(-2k)[/tex]

We also know that initially, there were 6000 acres of land under water. Substituting A0 = 6000 into the equation above, we get:

Dividing both sides by 6000, we get:

ln(0.5625) = -2k[tex]ln(0.5625) = -2k[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(0.5625) = -2k[/tex]

Solving for k, we get:

[tex]k = -ln(0.5625)/2[/tex]

k ≈ 0.3118

Therefore, the function to model the situation of the flood is:

[tex]A(t) = 6000 * e^{(-0.3118t)}[/tex]

To learn more about function, visit

https://brainly.com/question/12431044

#SPJ1

Part A: A reasonable domain to plot the growth function would be from d = 0 to d = 11.

Part B: The y-intercept of the graph of the function f(d) is 7

Part C: The average rate of change of the function f(d) from d = 4 to d = 11 is approximately 0.64 mm/day.

The domain of a function represents the set of input values for which the function is defined and can produce a meaningful output.

The y-intercept of a function represents the value of the function when the input is equal to zero.

The average rate of change of a function from x = a to x = b is given by the slope of the secant line passing through the points (a, f(a)) and (b, f(b)).

Here we have

A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:

=> f(d) = 7(1.06)^d

Since it is given that the radius of the algae was approximately 13.29 mm when the biologist concluded her study, we can set f(d) = 13.29  

=> 13.29 = [tex]7(1.06)^{d}[/tex]

=> ln(13.29/7) = d ln(1.06)

=> d = ln(13.29/7)/ln(1.06) ≈ 11  

Therefore, A reasonable domain to plot the growth function would be from d = 0 to d = 11.

Part B: The y-intercept of the graph of the function f(d) represents the value of the function when d = 0.

Substituting d = 0 into the given equation, we get:

f(0) = 7(1.06)⁰ = 7

Therefore, The y-intercept of the graph of the function f(d) is 7

Part C: The average rate of change of the function f(d) from d = 4 to d = 11 is given by the slope of the secant line passing through the points (4, f(4)) and (11, f(11)). Using the given equation, we can evaluate f(4) and f(11):

f(4) = 7(1.06)⁴ ≈ 8.84

f(11) = 7(1.06)¹¹ ≈ 13.29

The slope of the second line passing through these two points is:

Slope = (f(11) - f(4))/(11 - 4) = [ 13.29 - 8.84]/7 = 0.64

Therefore,

The average rate of change of the function f(d) from d = 4 to d = 11 is approximately 0.64 mm/day.

Learn more about Functions at

https://brainly.com/question/24839787

#SPJ1

For the given integer, the maximum starting population size that will eventually lead to extinction is 98, since any larger value will result in the population either stabilizing at a positive value or growing indefinitely.

The equation in question is:

dN/dt = -0.001N(N - 110)(N - 99)

Here, N represents the population size, and dN/dt represents the rate of change of the population with respect to time. The right-hand side of the equation tells us how the population size changes over time, and it's determined by the current population size N, as well as the two constants 110 and 99.

We can do this by setting dN/dt equal to zero and solving for N:

dN/dt = -0.001N(N - 110)(N - 99) = 0

=> N = 0, N = 99, N = 110

We can then plot the direction field (i.e., arrows indicating the direction of change) on each interval, and use this to determine the behavior of the solution curve. In this case, we can see that the direction of the arrows changes at each critical point, indicating that the population behavior switches between growing and declining as we move from one interval to the next.

Specifically, we can see that if the initial population size A is less than 99, the population will decline to extinction. If the initial population size is between 99 and 110, the population will initially decline but then grow and eventually stabilize at N = 110. If the initial population size is greater than 110, the population will grow exponentially and tend towards infinity.

To know more about integer here

https://brainly.com/question/15276410

#SPJ4

Answer:

19.5625

Step-by-step explanation:

Add up all of the x's (treating each place where an x is as if it's a number -- eg, there's twonumber 12's)

12+12+15+15+15+15+16+18+20+20+22+25+25+25+29 = 313

Divide by the number of x's

313 / 16 = 19.5625

The range of 49 is the most appropriate measure of variability to use to represent the spread of donations received by the charity in this data set.

what is statistics?

Statistics is a branch of mathematics that deals with collecting, analyzing, interpreting, presenting, and organizing data. It involves the study of methods for designing experiments and surveys, analyzing and interpreting data, and making decisions based on data. Statistics plays an important role in a wide range of fields, including science, social science, economics, finance, engineering, and many others. It is used to draw conclusions, make predictions, and inform decision-making by providing a quantitative and objective approach to understanding and analyzing data.

The most accurate measure of variability to use for this data set is the range of 49. The range is the difference between the highest and lowest values in the data set, which in this case is 59 - 10 = 49. The range provides a simple and straightforward measure of the spread of the data and is useful when the data is not too skewed.

While the data in this set is skewed, the range is still an appropriate measure of variability because there are no extreme outliers that would significantly affect the range. The IQR (interquartile range) is another measure of variability that is useful for skewed data, but in this case, it would not be the most appropriate choice because the data set is not divided into quartiles and the IQR would not provide additional information beyond what the range already shows.

Therefore, the range of 49 is the most appropriate measure of variability to use to represent the spread of donations received by the charity in this data set.

To learn more about statistics from the given link

https://brainly.com/question/29093686

#SPJ1

Emmy and Liam each played 4 games according to the given statement.

An equation is a claim that two expressions are equal, typically indicated by the equals symbol (=). In mathematics, equations are used to simulate real-world scenarios, solve problems, and depict relationships between variables.

Exponents, logarithms, and trigonometric functions can all be used in equations, in addition to basic operations like addition, subtraction, multiplication, and division.

Let us suppose the number of games played = x.

Thus, for Emmy we have:

E = 1 + 2x

For Liam the equation is:

L = 5 + 1x

Equating the two equations we have:

1 + 2x = 5 + 1x

x = 4

Hence, Emmy and Liam each played 4 games according to the given statement.

Learn more about equation here:

https://brainly.com/question/10413253

#SPJ1

Thus, the on average the contents weight for the transatlantic shipping is found as  24.7  pounds.

Given dimension of rectangular prism

Length l = 4ft

width w = 9.5 ft

height h = 13 ft

Volume of rectangular prism = l*w*h

V = 4*9.5*13

V = 494 ft³

Now,

1  ft³ = 0.05 pounds

So,

weight of  494 ft³ =  494*0.05 pounds

weight of 494 ft³ =  24.7  pounds

Thus, the on average the contents weigh for the transatlantic shipping is found as  24.7  pounds.

know more about the rectangular prism

https://brainly.com/question/24284033

#SPJ1

The volume of the pyramid is approximately 574,533.33 cubic meters.

To find the volume of a pyramid, you use the formula: V = (1/3) × base area × height, where B is the area of the base and h is the height of the pyramid.

Given that the side length of the square base is 140 m and the height is 91 m.

Since the base of the pyramid is a square with a side length of 140 m, we can find its area by multiplying the side lengths: B = 140m x 140m = 19,600 square meters.
By calculating this expression, you'll find the volume of the pyramid.

Now we can plug in the values for B and h into the formula: V = (1/3)(19,600 square meters)(91 meters) = 574,533.33 cubic meters.

To learn more about volume visit;

brainly.com/question/16788902

#SPJ11