(10 points) Find the height y and length of a side of its base x of a square pyramid with congruent isosceles triangle sides whose volume is cubic meters and whose lateral surface area is as small as possible. (The lateral surface area includes the sides but excludes the base of the pyramid.) Justify that the dimensions you found give minimum lateral surface area.

Answer:

4

Step-by-step explanation:

Answer:

The rate of change is 4

Step-by-step explanation:

The rate of change is the slope.

Since the equation is written in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

y = 4x-3

The slope is 4 and the y intercept is -3

Answer:

first option

Step-by-step explanation:

using the property of logarithms

ln [tex]x^{n}[/tex] = nlnx ( ln is the natural logarithm )

given

[tex]17^{(0.3x+5)}[/tex] = 12

take the ln of both sides

ln [tex]17^{(0.3x+5)}[/tex] = ln 12 , then

(0.3x + 5) ln 17 = ln 12 ( divide both sides by ln 17 )

0.3x + 5 = [tex]\frac{ln12}{ln17}[/tex] ≈ 0.877063 ( subtract 5 from both sides )

0.3x ≈ - 4.12293 ( divide both sides by 0.3 )

x = [tex]\frac{-4.12293}{0.3}[/tex] ≈ - 13.7431 ( to the nearest ten thousandth )

The quantity that is multiplied by pi in the formula for the area of a circle is the square of the radius

From the question, we have the following parameters that can be used in our computation:

Area of a circle

The formula for the area of a circle is represented as

A = πr²

Express the formula as a product

So, we have the following representation

A = π * r²

In the above formula, we can see that the square of r is multiplied by pi

Hence, the required quantity is the square of the radius of the circle

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Answer:

Below

Step-by-step explanation:

Only the middle three are tri -nomials  ( three terms)

the third one reduces to  (x+ 2)^2

Answer:

3

Step-by-step explanation:

(x+2)^2

Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.

In a homomorphism, corresponding elements of two systems behave very similarly in combination with other corresponding elements. For example, let G and H be groups. The elements of G are denoted g, g′,…, and they are subject to some operation ⊕.

In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient

Let f:R⇒S be a surjective homomorphism of rings with identity.

We have to find if R is a PID, prove that every ideal in S is principal.

We know that,

Let I be the ideal of S

Since f is sufficient homomorphism.

So, f⁻¹(I) is an ideal of R.

Since R is PID so ∈ r ∈ R such that

f⁻¹(I) = <r>

I = <f(r)>

Therefore,

Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.

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The area of a rectangle with the sides of x+7 and 3x-4 is 3x² + 17x - 28.

Any shape's area can be calculated by counting how many unit squares will fit inside of it. A square with a side of 1 unit is referred to as a unit square in this context. Therefore, the quantity of unit squares that make up a rectangle's perimeter is its area. Alternately, the area of the rectangle is the area contained within the boundary of this shape. The unit-length tiles in your home are a good illustration of a rectangle form. By counting the number of tiles, you can quickly determine how much space the floor takes up. This will also enable you to calculate the rectangle floor's area.

Given

Sides = x+7 and 3x-4

Area of rectangle

Length ×Breadth

(x + 7) (3x - 4)

Multiplying,

x(3x - 4) + 7(3x - 4)

3x² - 4x + 21x - 28

3x² + 17x - 28

The area of a rectangle with the sides of x+7 and 3x-4 is 3x² + 17x - 28.

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Answer:

1) -10x + 5

2) 5p - 26

3) -5y + 6

The equation of the line would be y = x/3 + 1/2.

Option (B) is correct.

What is the slope-intercept form of the line?

The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.

As we can see in the graph the line cuts the y-axis at y = 1/2

so the y-intercept of the line would be c = 1/2.

And when x=4, y = 2

So we can prepare the equation as y = x/3 + 1/2.

Hence, the equation of the line would be y = x/3 + 1/2.

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The equation of the line would be y = x/3 + 1/2.

Option (B) is correct.

What is the slope-intercept form of the line?

The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.

As we can see in the graph the line cuts the y-axis at y = 1/2

so the y-intercept of the line would be c = 1/2.

And when x=4, y = 2

So we can prepare the equation as y = x/3 + 1/2.

Hence, the equation of the line would be y = x/3 + 1/2.

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Answer: C

Step-by-step explanation: Because

The angle A is an obtuse angle of the regular polygon.

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The interior angle of a polygon is [(n-2)180°]/n.

Where n is the number of sides of the polygon.

The number of sides of the polygon is 8.

The measure of the interior of the polygon is [(8-2)180°]/8

= 135°

The obtuse angle is an angle that more than 90°.

Therefore angle is an obtuse angle.

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As per the binomial distribution, the value of the normal approximation is 0.6573

The term binomial distribution refers the discrete probability distribution that gives only two possible results in an experiment, either success or failure.

Here we have given that n = 95 P = 0.96 and q = 0.04

Now, here we have to check  the binomial distribution to see whether it can be approximated by the normal distribution.

While we looking into the given question we know that the value of n = 95 P = 0.96.

Then as per the binomial distribution formula, the normal distribution is calculated as,

=> P(X=1) = 95C4 * (0.96)⁴ * (1-0.96)⁹⁵⁻⁴

When we simplify this one then we get the value as 0.6573

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The function f(x) is an absolute function and the function g(x) will be twice the function f(x). The table is completed below.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

f(x) = |x| - 2 and g(x) = 2 f(x)

The function g(x) is rewritten as,

g(x) = 2 (|x| - 2)

g(x) = 2|x| - 4

The function f(x) is an absolute function and the function g(x) will be twice the function f(x).

x           f(x) = |x| - 2               g(x) = 2f(x)

-2                0                               0

-1                -1                               -2

0                -2                              -4

 1                -1                               -2

2                0                                0

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The equation which can be used to determine n, the number of calories in each chicken nugget would be 193.5+12 n=288.5+8n

And n = 24.1

Option (C) is correct.

What is a linear equation?

A linear equation is an equation that describes a straight line. Linear equations have the form y = mx + b, where x and y are variables and m and b are constants. The constant m is the slope of the line, and the constant b is the y-intercept, which is the point where the line crosses the y-axis.

To derive this equation, we can start with the fact that the two meals have the same number of total calories. This means that the number of calories in the first meal is equal to the number of calories in the second meal. We can represent this relationship with the equation:

8 nuggets * calories/nugget + 193.5 calories = 12 nuggets * calories/nugget + 288.5 calories

We can then rearrange the terms on the left and right sides of the equation to get the equation in the form given in option C:

193.5 + 12 n = 288.5 + 8 n

Finally, we can solve this equation for n by subtracting 8n from both sides and then dividing both sides by 4:

n = (193.5 - 288.5) / 4 = (-95) / 4 = -23.75

Therefore, the number of calories in each chicken nugget is 24.1 calories.

Hence, option (C) is correct.

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Answer:

final answer would be $6,550

Step-by-step explanation:

To calculate the state income tax owed on a $50,000 per year salary, we can use the progressive tax rate provided in the question. We can divide the salary into three ranges, corresponding to the three tax rates:

Income Range: $0 - $10,000

Progressive Tax Rate: 3%

Tax Owed: $0 - $10,000 * 3% = $0 - $300

Income Range: $10,001 - $50,000

Progressive Tax Rate: 5%

Tax Owed: $10,001 - $50,000 * 5% = $500 - $2,500

Income Range: $50,001 - $100,000

Progressive Tax Rate: 5.5%

Tax Owed: $50,001 - $100,000 * 5.5% = $2,750 - $5,500

Thus, the total state income tax owed on a $50,000 per year salary would be $300 + $2,500 + $2,750 = $6,550. This amount should be rounded to the nearest whole dollar amount, so the final answer would be $6,550.

Answer:

0.25

Step-by-step explanation:

Step 1: Convert all fractions to decimals

Two-thirds = 0.6666

Three-quarters = 0.75

One-half = 0.5

Step 2: Multiply all fractions

0.6666 * 0.75 * 0.5 = 0.25

Step 3: The answer is 0.25

Answer:

[tex]\dfrac{1}{4}[/tex]

Step-by-step explanation:

Three-quarters of one half:

[tex]\implies \dfrac{3}{4} \times \dfrac{1}{2}=\dfrac{3 \times 1}{4 \times 2}=\dfrac{3}{8}[/tex]

Two-thirds of "Three-quarters of one half":

[tex]\implies \dfrac{2}{3} \times \dfrac{3}{8}=\dfrac{2 \times 3}{3 \times 8}=\dfrac{6}{24}=\dfrac{6 \div 6}{24 \div 6}=\dfrac{1}{4}[/tex]

The linear constraint form of the variables is X1 =< 0.75(X1 + X2 + X3)

The term linear refers the algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Here we have given that x1 must be at most 75% of the blend of x1 , x2 , and x3 ,

Abd here we must have to find the linear constraint of the form of the variables.

While we looking into the given question we have identified the three are three variables are given they are x1, x2 and x3.

And we have also given that x1 must be greater than 75% when we convert this into decimal then we get the value 0.75.

Here the term of blend refers the sum of the terms,

Then the linear constraint form of the variables is written as,

=> X1 =< 0.75 (X1 + X2 + X3)

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Step-by-step explanation:

boy come ladies yer wait for you

hvb-amor-jon

The required, subtraction of 7x-9 from 2x² - 11 is 2x²-7x-2. Option B is correct.

Arithmetic is a branch of mathematics that deals with the study of numbers, their properties, and their operations. It involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.

Here,

To subtract 7x-9 from 2x² - 11, we need to distribute the negative sign across 7x and 9, and then combine like terms.

=2x² - 11 - (7x - 9)

= 2x² - 11 - 7x + 9

= 2x² - 7x - 2

Therefore, the answer is 2x²-7x-2.

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In response to the question, we may say that As a result, the right answer  expression is OA: 0, 3, 6, 5, 8, corresponding to the participants assigned to therapy A.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

To carry out the random assignment, we may utilise the following table of random digits:

Allocate the first ten topics to the table's rows, beginning with 0 and ending with 9.

Read the numerals from left to right, top to bottom, until 5 participants have been allocated to treatment A and 5 subjects have been assigned to treatment B.

We can get the following random assignment using this method:

A: 0, 3, 6, 5, 8 \sB: 1, 7, 4, 2, 9

As a result, the right answer is OA: 0, 3, 6, 5, 8, corresponding to the participants assigned to therapy A.

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Answer:

A: 0, 7, 5, 8, 1  B: 3, 4, 2, 6, 9

Step-by-step explanation:

THE ANSWER IS D

Answer: i think 15/8 but, im not sure

Step-by-step explanation:

0.3% is the percentage rate of increase  in exponential function.

What exactly makes a function exponential?

A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.

                   The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.

We have,

y = 50( 1.3)ˣ

The equation represents exponential growth because the growth factor is greater than 1.

The general form equation is

y(x)= a(1-r)^x such that r is the growth percent.

   1 + r = 1.3

     r = 0.3 ⇒  0.3%

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third side,  AB= 14.318 Units  and  tanB = 0.461

given:

BC=13 units

AC=6 units

solution:

using pythagoras theorem, we get

AB² = BC² + AC²

AB² = 13² + 6²

AB² = 169 + 36

AB² = 205

AB = 14.318 units

tanB = side opposite/side adjacent

tanB = AC/BC

tanB = 6/13

tanB = 0.461

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Using Pythagoras theorem, Third side,  AB= 14.318 Units  and tanB = 0.461

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.

given:

BC=13 units

AC=6 units

solution:

using pythagoras theorem, we get

AB² = BC² + AC²

AB² = 13² + 6²

AB² = 169 + 36

AB² = 205

AB = 14.318 units

tanB = side opposite/side adjacent

tanB = AC/BC

tanB = 6/13

tanB = 0.461

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The vertex of the graph (3, 0)

What is Vertex of graph?

A vertex or node is the basic building block of a graph in discrete mathematics, and more precisely in graph theory. An undirected graph is made up of a set of vertices and a set of edges, whereas a directed graph is made up of a set of vertices and a set of arcs.

According to question

when f(x) = 0

that's the minimum point, the vertex, or the intersection of two lines,  g(x) = 0.25x − 0.75 and h(x) =  0.75 - 0.25x

Therefore

find the intersection of Two line which are

⇒ y = x/4 - 3/4

⇒ 4y = x - 3 → First line

⇒ y = 3/4 - x/4  

⇒ 4y = 3 - x → Second line

So x - 3 = 3 - x

2x = 6 ,

x = 3

And y = 0

hence the vertex of f(x) = (3, 0)

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Answer:

1st {-6, -3, 0, 3, 6}

Step-by-step explanation:

range is the output that is "y", so the range is a set of {-6, -3, 0, 3, 6}

The statements best describe probability as the relative likelihood that an event will occur. It is a number between 0 and 1 inclusive.

Probability

A mathematical tool used to examine unpredictability is probability. It discusses the likelihood that an event will occur. For instance, you might not get two heads and two tails if you flip a fair coin four times. But if you flip the same coin 4,000 times, you'll get results that are almost evenly split between heads and tails. The theoretically predicted chance of heads in any given toss is 12, or.5. There is a predictable pattern of results when there are numerous repetitions, even though the results of a few repetitions are unknown. One of the authors tossed a coin 2,000 times after reading about the English statistician Karl Pearson, who threw a coin 24,000 times and got 12,012 heads. The outcome was 996 heads. The expected chance of 5 is quite near to being reached by the fraction of 9962,000, which is equivalent to 498.

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Answer:

42

Step-by-step explanation:

If 2/7 left that means that 5/7 are still there.

5/7x = 30  Multiple both sides by 7/5

x = [tex]\frac{30}{1}[/tex] x [tex]\frac{7}{5}[/tex]

x = 42

The perimeter of the checker board  118.4 cm

Area of each square = 14 sq. cm.

What is the length?

Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The meter serves as the foundational unit of length in the International System of Units.

The square root of area is the length of one side

[tex]\text { lengthofeachsquare }=\sqrt{14}=3.7 \mathrm{~cm}[/tex]

[tex]\text { lengthofoneside }=8 * 3.7=29.6 \mathrm{~cm}[/tex]

[tex]P=4 a[/tex]

[tex]=4 * 29.6=118.4 \mathrm{~cm}[/tex]

[tex]\text { Perimeterofthecheckerboard }[/tex]

Therefor we get the perimeter of the checker board  118.4 cm

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Step 3 shows the result of applying the subtraction property of equality

Two or more expressions with an Equal sign is called as Equation.

The given equation is 1/4(12x+8)+4=3.

We need to find which step has the property of substitution.

The Subtraction Property of Equality states that an equal value subtracted or removed from two equal items will result in a new equal amount.

Given step 1 is 3x+2+4=3

Opened the brackets on left side and multiplied with 1/4.

Step 2: 3x + 6 = 3.

Added the numbers on the left.

Step 3: 3x = -3

Equal value subtracted or removed from two equal items will result in a new equal amount. So Subtracted both sides by 6.Step 3 shows the result of applying the subtraction property of equality

Step 4: x = -1

Divided both sides by 3.

Hence, in step 3 we have used the property of subtraction.

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Least time required to reach the point Q as per the distance and the speed rate is equal to 2 hours.

As given in the question,

Nearest point on the coast is 2 miles far away

rate of the row = 1mile per hour

Walk at the rate of 3 miles per hour

Let 'x' hours be the least time to reach point Q.

Time = distance / speed

Time taken to reach the point Q = [√ 1 + ( 3 - x)² ]/ 3

Time taken to reach the coast = (√ 4 + x² ) / 1

Total  time taken 't' = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

To find least time dt/dx = 0

t  = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

⇒dt/dx = [ x / √ 4 + x² ] + ( 3 - x) / √( 10 -6x + x² )

⇒x / √ 4 + x² = ( x - 3) / √( 10 -6x + x² )

Squaring both the side we get,

x² / (4 + x²) = ( x - 3)² / ( 10 -6x + x² )

⇒3x² -24x +36 =0

⇒ x² -8x + 12 = 0

⇒ x = 2 or 6 hours

Therefore , the least time taken to reach the point Q is equal to 2 hours.

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