What is the volume of the following triangular prism?

Answer: 3/80 = 0.0375

As per the volume of the rectangular tank, the dimensions are 13.78 x 379.82 x 13.78

Volume of rectangle:

The general formula to calculate the volume of the rectangle is

V = length x width x height.

Given,

A rectangular tank that is 5234 ft^3 with a square base and open top is to be constructed of sheet steel of a given thickness.

Here we need to find the dimensions of the rectangular tank,

As per the given volume of rectangular tank, when we equate this with the formula, then we get,

=> 5234 = length x width x height.

Let us consider the length and the width are equal then we get the value of height as.

=> height = 5234/length

So, the value is calculated by using the surface area formula,

=> A = length² + 5234/length

When we differentiate the surface area with respect to

=> dA/dl = 2l - 5234/l²

To minimize the surface area, so dA/dl = 0,

=> 2l = 5324/l²

=> 2l³ = 5234

=> l³ = 2617

=> l = ∛2617

Therefore, the value of length is 13.78

Then the height is calculated as.

=> h = 5234/13.78 = 379.82

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Answer:

Step-by-step explanation:

Measure of one angle= 96

one angle= 2x

other angle= x + 12

By using angle sum property, we know that sum of all angles in a triangle is 180 degree.

so,

96 + 2x + x+12 = 180

108 + 3x = 180

3x = 180 - 108

3x = 72

x = 72/3

x = 24

So,

one angle (2x) = 2 * 24

                        = 48

other angle ( x + 12 ) = 24 + 12

                                  = 36

Hence, the other two degree measures for the missing angles is [tex]36[/tex].

What is the angles?

Angles are an integral facet in the study of mathematics, particularly geometry. Angles are formed by two rays (or lines) that begin at the same point or share the same endpoint.

The point at which the two rays meet (intersect) is called the vertex.

Here given that,

One measure of an angle in a triangle is [tex]96[/tex] degree. The other two angle measures are represented by [tex]2x[/tex] and [tex]x + 12[/tex].

So,

Measurement of one angle= [tex]96[/tex] degree

One angle= [tex]2x[/tex]

Other angle= [tex]x + 12[/tex]

As we know that sum of all angles in a triangle is [tex]180[/tex] degree.

So,

[tex]96 + 2x + x+12 = 180\\\\108 + 3x = 180\\\\3x = 180 - 108\\\\3x = 72\\\\x = \frac{72}{3}\\\\x = 24\\\\[/tex]

So,

One angle  is

[tex](2x) = 2 (24)\\=48[/tex]

Other angle is ( x + 12 ) = 24 + 12

[tex]( x + 12 ) = 24 + 12\\=36[/tex]

Hence, the other two degree measures for the missing angles is [tex]36[/tex].

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The probability of choosing a letter other than the letter a from a bag that contains the fifteen letters of the Indian city Palasa Kasibugga is 11/15.

According to the question,

We have the following information:

Words are:

Palasa Kasibugga

Now, total number of letters = 15

Number of a in these words = 4

Number of letters other than a = 11

We know that the following formula is used to find the probability of an event:

Probability = Number of favorable outcomes/total number of outcomes

Probability = 11/15

Hence, the probability of choosing a letter other than the letter a from a bag that contains the fifteen letters of the Indian city Palasa Kasibugga is 11/15.

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Answer: 2/1 should be your answer

Step-by-step explanation:

4 x 3= 12/6

1 x 3= 3/3

12 divided by 2 = 2  3 divided 3= 1

2/1

The formula for f , the specific antiderivative of f  is F(u) = 4㏑(u) + u²/2 + 11/2  .

In the question ,

it is given that ,

the function f(u) is f(u) = 4/u + u and f(1) = 6 ,

to find the antiderivative of f , we integrate it with respect to u ,

∫f(u) = 4∫(1/u)du + ∫u.du

On integrating ,

we get ,

F(u) = 4㏑(u) + u²/2 + c      ......equation(1)

Substituting the value of u = 1 in equation(1) ,

we get ,

F(1) = 4㏑(1) + 1/2 + c

6 = 0 + 1/2 + c

c = 6 - 1/2

c = 11/2 .

Now , substituting the value of c = 11/2 in equation(1) , we get

F(u) = 4㏑(u) + u²/2 + 11/2

Therefore , the formula for f is F(u) = 4㏑(u) + u²/2 + 11/2 .

The given question is incomplete , the complete question is

Write a formula for f, the specific antiderivative of f.  

f(u) = 4/u + u ; F(1) = 6  .

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When Ф(b)Ф(a) = Ф(ba) , then  Ф is an isomorphism G is abelian

Let ϕ:G→H be an isomorphism.

If G is abelian, we have xy = yx , for any x,y ∈ G. Consider any two element in H , say c and d . Since Ф is an isomorphism , we have c = Ф(a) and d = Ф(b) for some a,b ∈ G . Hence,

cd = Ф(a)Ф(b) = (ab) =Ф(ba)

=Ф(b)Ф(a) =  dc

This means H is an isomorphism.

If H is abelian, we have xy = yx, for any x,y ∈ H. Now consider two elements in G , say a and b .Since Ф is mapping , we have c = Ф (a) and d = Ф(b) for some c,d ∈ H. Hence ,

Ф(ab) = Ф(a)Ф(b) = cd = dc

= Ф(b)Ф(a) = Ф(ba)

Since,  is an isomorphism , we have ab = ba ,

This means G is also abelian  

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The scale of the model when the length of a model ship is 8 in its actual length is 100 ft is 1:150.

The term scale is used in mathematics to represent the relationship between a measurement on a model and the corresponding measurement on the actual object. Maps and blueprints would be useless without scales. A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size.

From the information, the length of a model ship is 8 in its actual length is 100 ft

It should be noted that;

1 foot = 12 inches

Therefore, 100 feet will be:

= 100 × 12

= 1200 inches

Therefore, the scale will be:

= 8/1200

= 1/150

= 1:150

The scale is 1:150.

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The number of Left Hand pitchers that the team have is 3 .

In the question ,

it is given that ,

the total number of pitchers in the baseball team is = 18

and the ratio of right hand to total pitchers is = 5 : 6

we have to find the number of left hand pitchers that the base ball team have .

From the ratio, the total number of pitchers is = 6x ,

and number of right hand pitchers = 5x ,

So , the number of left hand pitchers = x ,

that means , 6x = 18

Simplifying further ,

we get ,

x = 3,

Therefore , there are 3 left hand pitchers .

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Answer:55.9074

Step-by-step explanation:

The area of a circle with radius 4 is 50.24.

Writing the equation form for area and radius of two circles -

(Area/radius²) for circle 1 = (Area/radius²) for circle 2

Keep the values in the relation to find the area of small circle.

314/10² = Area/4²

Area = (314 × 16)/100

Performing multiplication on Right Hand Side of the equation to find the area of circle

Area = 5024/100

Performing division on Right Hand Side of the equation to find the area of circle

Area = 50.24

Hence, we see the decrease in area based on decrease in radius. Thus, the area of circle is 50.24.

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The length of the minute hand is stated as r=6 inches. We are aware that the minute hand will create a 90° angle in 15 minutes. The measurement is 9.4248 inches as a result.

What is an angle?

An angle is a shape made up of two rays that share an endpoint and is known as the vertex of the angle. These rays are known as the sides of the angle. The plane that contains the rays contains the angles created by two rays. The meeting of two planes can also result in an angle. They are referred to as dihedral angles.

The orientation of a line with another line or plane is represented by its angular position. How far the body has been rotated from the reference position is used to measure angular position.

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A tri-linear inequality for the estimate of the drug that would lower a typical patient's systolic blood pressure (using a 90% confidence level) is; 53.3   ≤  x-bar  ≤  58.3.

For the stated question-

Average of reduction in systolic blood pressure μ = 55.8.

Standard deviation s = 7.9.

Sample of size n = 29

The confidence interval is estimated as-

μ - t₀.₀₅(s/√n)  ≤  x-bar  ≤  μ + t₀.₀₅(s/√n)

Put the values-

55.8 - t₀.₀₅(7.9/√29)  ≤  x-bar  ≤  55.8 + t₀.₀₅(7.9/√29)

On simplifying,

53.3   ≤  x-bar  ≤  58.3

Thus, a tri-linear inequality for the estimate of the drug that would lower a typical patient's systolic blood pressure (using a 90% confidence level) is; 53.3   ≤  x-bar  ≤  58.3.

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The probability that all of them are real is 0.01875 or 1.875%

If the diamonds are replaced after each draw:

The probability of drawing a real diamond is 9/14, found by making the numerator the number of real diamonds and adding the total number of diamonds to find the denominator. 5+9 = 14.

To find the probability of all 9 diamonds drawn being real, multiply 9/14 by itself 9 times.  = 387420489/ 20661046784. This creates a probability of 387420489/ 20661046784. This cannot be reduced because there is no common factor. To express as a decimal, divide. 387420489/ 20661046784 = 0.01875. To turn this into a percent, multiply by 100. 0.01875*100 = 1.875

Hence, the probability that all of them are real is 0.01875 or 1.875%

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Answer:

Step-by-step explanation:

Every rational number can be expressed in decimal form. This argument cannot be used to demonstrate that rational numbers between 0 and 1 are countable. We frequently use this fact to demonstrate that rationals are countable since every rational number has a decimal representation that terminates on a non-teminating repeating sequence.

Rational number:

P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. Thus, natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers (terminating decimals and recurring decimals). The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.

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The degrees of freedom used to test the significance of the slope in a simple linear regression equation is n-2.

The maximum number of logically independent, or potentially different, values in the sample of data is referred to as the degree of freedom.

The degree of freedom is a fundamental concept that can be found throughout statistics in a variety of contexts, such as with hypothesis tests, probability distributions, and linear regression.

The degrees of freedom are n−k, however, in simple linear regression you estimate both a y-intercept and a slope, so k=2. Even though we generally don't worry about testing the intercept, it still uses up a degree of freedom, the slope would be very different and have a very different interpretation if we did not estimate an intercept along with the slope.

When we put the value of k=2 we get degrees of freedom are n-2.

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Answer:

The approximate area of the circle is:

50.24m²

Step-by-step explanation:

Circle area = 3.14 * (diameter/2)²

In this case:

Circle area = 3.14 * (8/2)²

Circle area = 3.14 * 4²

Circle area = 3.14 * 16

Circle area = 50.24 meters²

The mass that can rectangular air mattress can support in water before sinking is 97.2 kg

Consider the rectangular air mattress

The length = 2 meter

The width = 0.500 meter

The thickness = 0.100 meters

The volume = Length × width × thickness

The volume = 2 × 0.500 × 0.100

= 0.1 cubic meters

We know,

Total weight = Volume × Density × g

The density of water = 1000 kg/ meter square

Total mass = 0.1 × 1000 × 9.81

= 981 N

The the equation of mass will be

(2.8 + m) × 9.81 = 981

2.8 + m = 100

m = 100 - 2.8

m = 97.2 kg

Therefore, it will support 97.2 kg water before sinking

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The volume of the solid region common to both cylinder is 8/3 when two half-cylinders of diameter 2 come together at a right angle.

Given that,

In the following figure, two half-cylinders of diameter 2 come together at a right angle.

We have to determine the solid region's common volume for the two half-cylinders. (Hint: Take into account slices that are parallel to the solid's base.)

We know that,

Using the Pythagoras theorem,

S²+x²=r²

Diameter=2

2r=2

r=1

S²+x²=1

S²=1-x²

S=√(1-x²)

[tex]\int\limits^1_0 {Area(x)} \, dx[/tex]

4[tex]\int\limits^1_0 {1-x^{2} } \, dx[/tex]

4(x-x³/3)₀¹

4(1-1/3)

4(2/3)

8/3

Therefore, The volume of the solid region common to both cylinder is 8/3 when two half-cylinders of diameter 2 come together at a right angle.

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The circle's area is 200.96 square inches.

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.

Any round form without edges or line segments is called a circle. In geometry, it has the shape of a closed curve.

radius, r =  8 inches

Area of a circle:

A = π r²

  = 3.14 * 8²

  = 200.96 square inches

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Answer:

Step-by-step explanation:

o

The outcome of this question is determined by the number of alternative possibilities and their probability.

If there are only two conceivable outcomes, one of which is success and one of which is a failure, the theoretical chance of success is 50%. The theoretical probability of success is the sum of the probabilities of the two successful outcomes if there are three alternative outcomes.

If you know anything about probability, you're undoubtedly aware that the theoretical likelihood of any given result occurring in a given circumstance is always the same. Finally, the theoretical likelihood that any of the outcomes will be successful if a circumstance is repeated is the sum of the probabilities of each successful outcome divided by the entire number of alternatives.

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What is the theoretical probability that any one of the outcomes will be a success if a situation is repeated again and again?

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The equation of the parabola is  y -5 = (5/6) (x - 2)^2

a curve produced by the intersection of a cone's surface with a plane perpendicular to a straight line; a curve produced by a moving point whose distance from a fixed point is equal to its distance from a fixed line.

A quadratic function's U-shaped curve is shown on a parabola graph. A right circular cone and a plane surface intersect to form one of the conic sections known as a parabola in mathematics. The plane is symmetrical. U-shaped bend

y - k = a (x - h)2

where the vertex is (h,k). Since the vertex is known to be at (7,-3), we know that h = 7 and k = -3. Consequently, the equation is

y -5 = a (x - 2)2

We utilize the fact that the parabola passes through point to determine a for (4,0). With x =- 4 and y = 0, we obtain

0 - 5 = a (-4 - 2)

-5 = a (-6)2

-5 = -6a

a = 5/6

Consequently, the parabola's equation is

y -5 = (5/6) (x - 2)^2

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The area of the actual office space is 36 yards if the scale is 1:6 yards.

An item is enlarged in a scale drawing. An expansion increases or decreases the size of an item by multiplying each of its lengths by a scale factor. A scale of 1:5, for instance, indicates that the size of 1 unit in the picture corresponds to the size of 5 units in the actual world.

The scale of office space is 1:6 yards. The scale drawing has an area of 6 square inches. This means that 1 scale represents 6 square inches of office. For the actual area multiply 6 by the area of the scale drawing which will give 36 yards.

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the absolute extrema of the linear equation f(x) =  12x^2 -11x +2 are 27 (absolute maximum) for x = - 8 and - 9 (absolute minimum) for x = 4. (- 8, 27) and (4, - 9).

What are the absolute extrema of a linear equation within a closed interval?

According to the functions theory, linear equations have no absolute extrema for all real numbers, but things are different for any closed interval as absolute extrema are the ends of linear function. Now we proceed to evaluate the function at each point:

Absolute maximum

f(- 8) =   12x^2 -11x +2

f(- 8) = 27

Absolute minimum

f(4) = - 3 · 4 + 3

f(4) = - 9

By means of functions theory and the characteristics of linear equations, the absolute extrema of the linear equation f(x) = 12x^2 -11x+2  are 27 (absolute maximum) for x = - 8 and - 9 (absolute minimum) for x = 4. (- 8, 27) and (4, - 9).

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Answer: -6

Step-by-step explanation:

You're welcome I'm not sure if it corrects correct, but this is my answer