A particular sawdust pile has a base diameter of 25 feet when the height is 20 feet. Find the volume of this sawdust pile when it is 30 feet high.

Answer:

Step-by-step explanation:

Conditions

Let the circular stones = x

Let the rectangular stones = y

Equations

x + y = 37                          Subtract x from both sides of this equation.

y = 37 - x                           Notice that x is on the right side of the equation

Solution

26x   +  34y = 1138                 Substitute for y

26x + 34(37 - x) = 1138           Remove the brackets

26x + 1258 -34x= 1138           Combine

-8x + 1258 = 1138                    Subtract 1258 from both sides

-8x +1258-1258 = 1138-1258  Combine.  

-8x = -120                                Divide both sides by -8

-8x/-8 = -120/-8

x = 15                                       Two minuses make a plus (last step)

x+ y = 37

15 + y = 37                               Subtract 15 from both sides

15-15 +y = 37-15                     Combine

y = 22

Answer

x = 15     Circular pizza dishes

y = 22   square pizza dishes

The consultant sold 15 circular pizza stones and 22 rectangular pizza stones.

Let's assume the number of circular pizza stones sold is "c" and the number of rectangular pizza stones sold is "r."

We are given two pieces of information:

1. The total number of stones sold: c + r = 37

2. The total amount earned from the sale of the stones: 26c + 34r = 1138

Now, we can use these two equations to solve for the values of "c" and "r."

First, let's use the first equation to express "c" in terms of "r":

c = 37 - r

Now, substitute this value of "c" into the second equation:

26c + 34r = 1138

26(37 - r) + 34r = 1138

962 - 26r + 34r = 1138

Combine the "r" terms:

8r = 1138 - 962

8r = 176

Now, divide by 8 to find the value of "r":

r = 176 / 8

r = 22

Now that we have the value of "r," we can find the value of "c" using the first equation:

c = 37 - r

c = 37 - 22

c = 15

So, the consultant sold 15 circular pizza stones and 22 rectangular pizza stones.

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Answer:

4/7

Step-by-step explanation: Multiply 2/3 x 6/7 Put your answer in lowest terms a. 4/7

Answer:

Difference: 4/21

Step-by-step explanation:

the difference between two quantities is the result of a subtraction

[tex]\frac{6}{7} -\frac{2}{3} =\frac{(6)(3)-(7)(2)}{(7)(3)} =\frac{18-14}{21} =\frac{4}{21}[/tex]

The fraction can no longer be reduced

Hope this helps

Answer:

first three expressions are polynomials and last three are not.

Step-by-step explanation:

last three expression has negative powers of X and  some powers of Xs are not integers.

Answer:

march 9

Step-by-step explanation:

10+3-4

=9

I think that's the answer

Answer:

67

Step-by-step explanation:

7 + 2 =9

9 + 4 = 13

13 + 16 = 29

29 + 38 = 67

Answer + Step-by-step explanation:

[tex]f(x) = 5|x-6|+2 = \begin{cases}5\left( x-6\right) +2&if\ x\geq 6\\ 5\left( 6-x\right) +2 &if\ x\leq 6\end{cases}[/tex]

[tex]\Longrightarrow f(x) = \begin{cases}5x-30+2&if\ x\geq 6\\ 30-5x +2 &if\ x\leq 6\end{cases}[/tex]

[tex]\Longrightarrow f(x) = \begin{cases}5x-28&if\ x\geq 6\\ -5x +32 &if\ x\leq 6\end{cases}[/tex]

case 1: x ≥ 6 → f(x) = 5x - 28

5(6) - 28 = 30 - 28 = 2

Then

the point A(6 ,2) lie on the graph (line) of f

5(7) - 28 = 35 - 28 = 7

Then

the point B(7 ,7) lie on the graph (line) of f

Graphing :

When x ≥ 6 ,the graph of f is the ray [AB) (just connect the points A and B)

case 2: x ≤ 6 → f(x) = -5x + 32

-5(6) +32 = -30 + 32 = 2

Then

the point A(6 ,2) lie on the graph (line) of f

-5(5) +32 = -25 + 32 = 7

Then

the point C(5 ,7) lie on the graph (line) of f

Graphing :

When x ≤ 6 ,the graph of f is the ray [AC) (just connect the points A and C)

By means of recurrence formulas and a given initial value, we find the following three results: f(5) = 19, f(125) = 469, f(3125) = 11719.

Sequences are sets of values defined by at least one condition. In this case, we have three conditions to generate the required values:

f(n) = f(n/5) + 3 · n

f(1) = 4

[tex]n \in \mathbb{N}[/tex]

Now we proceed to find the elements by recurrence:

f(5) = f(1) + 3 · 5

f(5) = 4 + 15

f(5) = 19

f(25) = f(5) + 3 · 25

f(25) = 19 + 75

f(25) = 94

f(125) = f(25) + 3 · 125

f(125) = 94 + 375

f(125) = 469

f(625) = f(125) + 3 · 625

f(625) = 469 + 3 · 625

f(625) = 469 + 1875

f(625) = 2344

f(3125) = f(625) + 3 · 3125

f(3125) = 2344 + 9375

f(3125) = 11719

By means of recurrence formulas and a given initial value, we find the following three results: f(5) = 19, f(125) = 469, f(3125) = 11719.

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Answer:

Id say A but it's tricky.

Israel is in the Eurasian plate. Go ahead with A for the correct one

The first four terms in the sequence are 4, 9, 16 and 25.

Given that, the nth term of the sequence is 1 (n + 1)².

We need to find the first four terms in the sequence.

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

To find the first four terms of the sequence, replace n=1, 2, 3 and 4.

Now, when n=1

1(1+1)²=1×4=4

When n=2

1(1+2)²=1×9=9

When n=3

1(1+3)²=1×16=16

When n=4

1(1+4)²=1×25=25

Therefore, the first four terms in the sequence are 4, 9, 16 and 25.

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Answer:

a^11

Step-by-step explanation:

1) Simplify the numerator. Use the laws: (x^a)^y = x^ay, x^a × x^b = x^a+b.

= a¹⁵ × a^-6 / a^-2

= a⁹ / a^-2

2) Divide them. Use the law: x^a / x^b = x^a - b.

= a^9 - (-2) / 1

= a^9 + 2 / 1

= a^11

Answer:

C. Yes, △ABC~△CBD by the SAS similarity theorem

Step-by-step explanation:

i think

Answer:

C- SAS similarity theorem

Explantion:

Two sides and one 90 degree angle

Based on the data given, the length of line segment AC is 2.29

Based on the given data:

The triangle ABC is an isosceles triangle.

The line segment AC is the hypotenuse of the the triangle ACD.

The length of AD = 3/2

[tex]AC = \sqrt{(\sqrt{3)^{2}} + (\frac{3}{2})^{2}}= 2.29[/tex]

In conclusion, the length of  AC is 2.29

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Answer:

[tex]volume=558.9[/tex]

Step-by-step explanation:

find the volume of the cone and the hemisphere and add them together

cone:

[tex]Vcone=\pi r^{2} \frac{h}{3} \\\\V=\pi (5.3)^2(\frac{8.4}{3} )\\V=\pi (28.09)(2.8)\\V=247.09\pi \\V=247.1[/tex]

hemisphere:

[tex]Vhemisphere=\frac{2\pi r^3}{3} \\V=\frac{2\pi (5.3)^3}{3} \\V=\frac{2\pi (148.877)}{3} \\V=\frac{297.754\pi }{3} \\V=\frac{935.421}{3}\\ V=311.8[/tex]

add the volumes together:

[tex]Vol=247.1+311.8\\Vol=558.9[/tex]

The key features of the graph include the fact the graphs are periodic.

It should be noted that a graph is a diagram that represents ban interrelations between variables.

The tan graph is simply the visual representation of the tangent function for a range of angles.

In this case, the graphs have been attached and it can be seen that the tan graph repeats every 180° and is not a continuous curve.

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Answer: it is a ratio of vertical alignment w.r.t horizontal alignment

Step-by-step explanation:

The main difference is that graph of tan(x) is the ratio of sin(x)/cos(x) that is it is a ratio of vertical alignment w.r.t horizontal alignment whereas graph of x^3 is not trigonometric but algebraic in nature as ( x×x×x).

The table that represents a linear function is y=3,7,11,15

For a table to represent a linear function, the table must have a constant rate of change i.e. a common difference

From the list of options, we have:

y=3,7,11,15

The difference between each y value is 4

i.e. 7 - 3 = 11 - 7 = 15 - 11 = 4

Hence, the table that represents a linear function is y=3,7,11,15

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Answer:

Step-by-step explanation:

So in this example we'll be using the difference of squares which essentially states that: [tex](a-b)(a+b)=a^2-b^2[/tex] or another way to think of it would be: [tex]a-b=(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})[/tex]. So in this example you'll notice both terms are perfect squares. in fact x^n is a perfect square as long as n is even. This is because if it's even it can be split into two groups evenly for example, in this case we have x^8. so the square root is x^4 because you can split this up into (x * x * x * x) * (x * x * x * x) = x^8. Two groups with equal value multiplying to get x^8, that's what the square root is. So using these we can rewrite the equation as:

[tex]x^8-16 = (x^4-4)(x^4+4)[/tex]

Now in this case you'll notice the degree is still even (it's 4) and the 4 is also a perfect square, and it's a difference of squares in one of the factors, so it can further be rewritten:

[tex]x^4-4 = (x^2-2)(x^2+2)[/tex]

So completely factored form is: [tex](x^2-2)(x^2+4)(x^4+4)[/tex]

I'm assuming that's considered completely factored but you can technically factor it further. While the identity difference of squares technically only applies to difference of squares, it can also be used on the sum of squares, but you need to use imaginary numbers. Because [tex]x^2+4 = x^2-(-4)[/tex]. and in this case a=x^2 and b=-4. So rewriting it as the difference of squares becomes: [tex]x^4+4 = x^4 - (-4) = (x^2-\sqrt{-4})(x^2+\sqrt{-4}) = (x^2-2i)(x^2+2i)[/tex] just something that might be useful in some cases.

We can factor this into [tex](x^{4}+4)(x^{4} -4)[/tex].

This is because we use  difference of two squares where [tex]x^{2} -y^{2} = (x+y)(x-y)[/tex]

So we rewrite x^8-16 to x^8-4^2.

This can then be written to the equation I put at the start.

p.s. The reason its [tex]x^{4}[/tex] is because [tex]x^{4} * x^{4} = x^{8}[/tex]
(P.S.S I just found that the other helper did it fully so I stopped here, read his, its correct)

Answer:26

Step-by-step explanation:

Answer:

102cm^3

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

3x isnt used because it stated when x>1.

so -2(1) is -2, because x =< 1 is true

Answer:

D

Step-by-step explanation:

Answer:

D. 1/125

Step-by-step explanation:

[tex]f(3)=(\frac{1}{5} )^{3} =\frac{1^{3} }{5^{3} } =\frac{1}{125}[/tex]

Hope this helps

Equations are written by equating two expressionsThe value of x - 2y is 8/3

Equations are written by equating two expressions. Given the following equation

3x - 6y = 8

Divide through by 3 to have:

3x/3 - 6y/3 = 8/3

x - 2y = 8/3

Hence the value of x - 2y is 8/3

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The value of the correlation is -0.0721 and it is a weak negative correlation

The points are given as:

(12, 28), (15, 50), (18, 14), (21, 28), (24, 36)

Enter the above points in a graphing calculator.

From the graphing calculator, we have the following summary:

X Values

Y Values

X and Y Combined

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

This gives

r = -18 / √((90)(692.8)) = -0.0721

So, the correlation coefficient is -0.0721

The above is a negative correlation because it is less than 0 and it is a weak correlation because it is closer to 0 than -1

Hence, the correlation is a weak negative correlation

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Answer:

Negative

Step-by-step explanation:

When you move the decimal place to the right, the exponent in scientific notation is negative. In other words, when you are converting a number smaller than 1 into scientific notation, the exponent will be negative. In this case, because you are moving the decimal place to the right 3 places, the new number would be 4.430 x 10⁻³ cm.

When you move the decimal place to the left, the exponent in scientific notation is positive.

H_TM is reduced to HALT_TM and as such, HALT_TM is undecidable.

A language is referred to as Decidable or Recursive if there is a Turing machine that accepts and halts on every input string w. This tells us that every decidable language is Turing-Acceptable.

Now, we are told that the halting language is reducible to some language B. This means that it is an undecidability via reduction.

Now, Using the idea that “ If A is undecidable and reducible to B, then B is undecidable.” Suppose R decides HALT_TM, we will construct S to decide ATM .

S = “On input (M, B)

This means that H_TM is reduced to HALT_TM and as such, HALT_TM is undecidable.

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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Determine the slope of a line that is parallel to the equation [tex]\bf{3x+6y=18}[/tex].

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

First we should divide the whole equation by 6,

[tex]\bf{\dfrac{3}{6}x+\dfrac{6}{6}y=\dfrac{18}{6}}[/tex] | simplify

[tex]\bf{\dfrac{1}{2}x+y=3}[/tex] | subtract 1/2 x

[tex]\bf{y=-\dfrac{1}{2}x+3[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

            [tex]\bf{=Slope-\dfrac{1}{2}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]

Step-by-step explanation:

so, if I understand this correctly, the original function (shown in the graph) is

f(x) = sqrt(x)

the following transformations were done going from f(x) to h(x) :

x -> x + 4 as variable term moved the whole curve 4 units to the left. because now a specific functional value is calculated for a smaller x (by 4 units) than for the original f(x). e. g. let's call g(x) = sqrt(x + 4). then g(-4) = f(0). as mentioned, everything moved over to the left by 4 units.

sqrt(x) -> 3×sqrt(x) increased the range of the function (the generated y values) by the factor 3. was the functional result for a x value = 1, then it is now 3 for the same x value.

sqrt(x) -> sqrt(x) - 1 moved the whole curve down by 1 unit.

in summary, the whole original curve was moved 4 units to the left, then stretched upwards by the factor 3, and then that result was moved down by 1 unit.

so, e.g.

h(-4) = 3×f(0) - 1 = -1 point (-4, -1) corresponds to old (0, 0)

h(-3) = 3×f(1) - 1 = 2 point (-3, 2) corresponds to old (1, 1)

h(0) = 3×f(4) - 1 = 5 point (0, 5) corresponds to old (4, 2)

If a, b and c are integers then the correction option in the above case is that both equation 1 and 2 are correct.

Note that:

Because:

Suppose  one say a|b. Then one can see that   an integer  do exist which is n such that  b = an.

Hence:

bc = (an)c = a(nc), so a|(bc) (the reverse is still the case or still applies)

Therefore, If a, b and c are integers then the correction option in the above case is that both equation 1 and 2 are correct.

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The first set of integers are: 8 and 32

The second set of integers are: -8 and -32

An integer is a whole number.

It is also the ratio of any real number and 1.

It does not have a decimal part or the decimal part of the integer is zero.

Analysis:

Let the two inters be x and 4x

product of integers  = 4x(x) = 256

4[tex]x^{2}[/tex] = 256

[tex]x^{2}[/tex] = 256/4

[tex]x^{2}[/tex] = 64

x = ±[tex]\sqrt{64}[/tex]

x = -8 0r 8

The other integer = 4 x -8 = -32 or 32

In conclusion the two integers are -8 and -32 or 8 and 32

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Answer: [tex]4i\sqrt{5}[/tex]

Step-by-step explanation:

[tex]\sqrt{-80}\\\\=\sqrt{-1} \sqrt{80}\\\\=\sqrt{-1} \sqrt{16} \sqrt{5}\\\\=4i\sqrt{5}[/tex]

None of the provided options is equivalent to √-80.

We have,

To simplify the expression √-80, we need to determine the square root of -80.

However, since -80 is a negative number, its square root is not a real number.

The square root of a negative number is usually expressed using the imaginary unit "i," where i = √(-1).

In this case, we can rewrite the expression as:

√(-1 * 80) = √(-1) * √(80) = i * √(80).

Therefore,

None of the provided options is equivalent to √-80.

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The end behavior is that as the value of x increases the value of function increases.

A) We want to completely factor; f(x) = 2x² - x - 10

⇒ f(x) = 2x² - 5x + 4x - 10

⇒ 2x(x + 2) - 5(x + 2)

⇒ (2x - 5)(x + 2)

B) The x-intercept occurs at y = 0. Thus;

(2x - 5)(x + 2) = 0

x  =5/2  and x = -2

C) f(x) = 2x² - x - 10

Thus, the end behavior is that as the value of x increases the value of function increases.

D) The graph steps has been attached

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Answer: A

Step-by-step explanation:

Letting [tex]f(y)=x[/tex],

[tex]x=\sqrt{y}-5\\\\x+5=\sqrt{y}\\\\y=(x+5)^{2}[/tex]

Also, the domain of an inverse is the same as the range of the original function, so the range is [tex]x \geq 0[/tex]