How many cubic feet of dirt are there in a hole that is 3’ deep x 3’ wide x 3’ long?.

Answer:

10

Step-by-step explanation:

square root of 6^2 + 8^2

Answer:

r = 290°

Step-by-step explanation:

  In a triangle, exterior angles equals the sum of interior opposite angle.

In triangle A,

   x + 90 = 125   {Exterior angle property}

           x = 125 - 90

           x = 35°

In triangle B,

      y + 90 = 125

             y = 125 - 90

             y = 35°

    x + y + r = 360   {Complete angle}

35 + 35 + r = 360

         70 +r = 360

               r = 360 - 70

               r = 290°

Answer:

1 turn

Step-by-step explanation:

this is what the graph would look like:

If inspection department wants to estimate the mean amount with 95% confidence level with standard deviation 0.05 then it needed a sample size of 97.

Given 95% confidence level, standard deviation=0.05.

We know that margin of error is the range of values below and above the sample statistic in a confidence interval.

We assume that the values follow normal distribution. Normal distribution is a probability that is symmetric about the mean showing the data  near the mean are more frequent in occurence than data far from mean.

We know that margin of error for a confidence interval is given by:

Me=[tex]z/2* ST/\sqrt{N}[/tex]

α=1-0.95=0.05

α/2=0.025

z with α/2=1.96 (using normal distribution table)

Solving for n using formula of margin of error.

[tex]n=(z/2ST/Me)^{2}[/tex]

n=[tex](1.96*0.05)^{2} /(0.01)^{2}[/tex]

=96.4

By rounding off we will get 97.

Hence the sample size required will be 97.

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The given question is incomplete and the full question is as under:

If the inspection division of a county weights and measures department wants to estimate the mean amount of soft drink fill in 2 liters bottles to within (0.01 liter with 95% confidence and also assumes that standard deviation is 0.05 liter. What is the sample size needed?

Answer:

187

Step-by-step explanation:

Answer:

x = -15

Step-by-step explanation:

Answer:

The answer would be D    7mn+3m/2+5n/4

Step-by-step explanation:

A polynomial is a combination of terms separated by +

or  − signs. A polynomial does not contain variables raised to negative or fractional exponents, variables in the denominator or under a radical, or any special features such as trigonometric functions, or logarithms.

Answer:

a=-2π

b=-17/3

c=-sqrt18

Step-by-step explanation:

eyeball it.

-2π≈-6.28

-17/3 is less than -5 but more than -6, so it's between those 2

-sqrt 18 is between -sqrt 16 and -sqrt 25, so it's a little less than -4

Answer:

if you're supposed to be solving for x then the top one is x=-y+3 and the bottom is x=-y+5

Polynomial is an expression that consists of indeterminates(variable) and coefficients. The roots of the polynomial are ​1, 2.7321, and -0.7321.

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

The roots of the polynomial are:

x³ - 3x² + 2

If we divide the polynomial by (x-1), then

(x³ - 3x² + 2)/(x-1) = x² - 2x - 2

now, factorize the given polynomial,

x² - 2x - 2

x = 1 ± √3

x = ​1, 2.7321, -0.7321

​Hence, the roots of the polynomial are ​1, 2.7321, and -0.7321.

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The given expression will be written as follows:-

y = 6x

y = 6x + 6

y = 6x - 1

y = 6x +1

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

A) The total pages a person reads in x days, if the person reads 6 pages a day

y = 6x

B) The cost of x boxes of mangoes, if 1 box costs $6 and the shipping charge is $6 per order (for any number of boxes)

y = 6x + 6

C) The total cost of x notebooks if one notebook costs $6 and students receive a discount of $1 off their total bill

y = 6x - 1

D) The total cost of x novels and a pocket dictionary if you buy x novels each at $6 and get a pocket dictionary at $1

y = 6x + 1

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Considering the direction of the wind, it is found that the jet travels faster than the sound during it's journey.

The jet's speed, considering that there is a tailwind, is given by:

J = Plane speed + Wind speed.

In this problem, we have that the speeds are given as follows:

Hence the jet's speed is given by:

J = 550 + 120 = 670 knots.

670 knots > 661 knots, hence the jet travels faster than the sound during it's journey.

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Answer:

the y intercept is (0,2)

slope = -4

Step-by-step explanation:

from the graph the y intercept is (0,2) and we can consider it as p1

p2 (2,-6)

slope = y2-y1 / x2-x1

= -6 - 2/ 2 -0 = -8/2 = -4

Answer:

7 yds  1 ft 1 inch

Step-by-step explanation:

Quick Solve!

Side #1:

144 inches + 24 inches + 7 inches = 175 inches

Side #2:

72 inches + 18 inches = 90 inches + 6 inches = 96 inches

Conclusion:

175 inches + 96 inches = 271 inches

Answer:

⇒ 7 yds  1 ft 1 inch

Answer:

7 yards 1 foot 1 inch

Step-by-step explanation:

Adding both of them together, you get:

6 yards 3 feet 13 inches

Since 1 foot = 12 inches, and 13 inches exceeds that, add a foot to the previous 3 feet and subtract 12 from the 13 inches

Therefore: 6 yards 4 feet 1 inch

Since 1 yard = 3 feet, and 4 feet exceeds that, add a yard to the previous 6 yards and subtract 3 feet from the remaining 4 feet

Hence:

7 yards 1 foot 1 inch

Answer:

1.4y

Step-by-step explanation:

Answer:

b(n) = -11 + (n-1)*8

Step-by-step explanation:

Let n be the sequence number, with n=1 the first number b(1) -11

The sequence changes by +8 each step.

b(1)   -11         + 8 =   -3

b(2)   -3          + 8 =    5

b(3)   5         + 8 =   13

b(4) 13

b(1) = -11

b(2) = -3.   or b(1) + 1*8

b(3) =  5,    or b(1) + 2*8

b(4) =  13,   or b(1) + 3*8

We note that each step adds a multiple of 8 to the initial value of -11.  This can be stated as (n-1)*8

The formula for this sequence would be b(n) = b(1) + (n-1)*8

b(n) = -11 + (n-1)*8

Check:  Does n=3 return the value of 5?

b(n) = -11 + (n-1)*8

b(3) = -11 + ((3)-1)*8

b(3) = -11 + (2)*8

b(3) = -11 + 16

b(3) = 5   YES

The probability that you lose all five times will be 0.59.

From the information given, the chances of winning are 0.1. Therefore, the chance of losing will be:

= 1 - 0.1 = 0.9

Therefore, the probability that you lose all five times will be:

= 0.9 × 0.9 × 0.9 × 0.9 × 0.9

= 0.59

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Answer:

148.7804878

Step-by-step explanation:

All you have to do is divide!

Answer:

8 + 7.

Step-by-step explanation: It is absolute value.

The circumference of the base of the cone is 8π - x since the base is equal to go the arc length of the remainder of the circle.

The radius r as a function of x will be:

8π - x = 2πr

r = (8π - x)/2π

r = 4 - x/2π

The height has a function of x will be:

r² + h² = 16

h² = 16 - r²

where r = 4 - x/2π

h = √16 - ✓(4 - x/2π)²

h = 4✓(4 - x/2π)²

The volume V of the cone as a function of x will be:

= 1/3 πr²h

= π/3(4 - x/2π)² 4✓(4 - x/2π)²

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[tex] \underline{\large \bf{Required \: Answer}} : - [/tex]

[tex] \dashrightarrow \: \red{\large8}[/tex]

[tex] \sf[/tex]

[tex] \underline{ \large{ \rm \pink{SolutioN}}} \: -[/tex]

[tex] \quad \qquad\sf \: {(a + b)}^{2} = 10[/tex]

[tex] \qquad \: \: \to\: \: \sf{a}^{2} + {b}^{2} + 2ab = 10[/tex]

[tex] \qquad\: \: \to\: \: \sf{a}^{2} + {b}^{2} + 2(1) = 10[/tex]

[tex] \qquad\: \: \to\: \: \sf \: {a}^{2} + {b}^{2} = 10 - 2[/tex]

[tex] \qquad\: \:\bf \to\: \: \: {a}^{2} + {b}^{2} = 8[/tex]

[tex] \sf[/tex]

[tex] \sf \therefore \: 8 \: \: is \: \: the \: \: required \: \: answer[/tex]

[tex] \rule{200pt}{2pt}[/tex]

Answer:

1.596

Step-by-step explanation:

So you can rewrite log as: [tex]log_{b}a=x = > b^x=a[/tex] So in this case it's already in exponential form which we'll use to rewrite into logarithm form.

[tex]4^{x+3} = 7\\log_47=x+3\\\\\frac{log7}{log4}=x+3\\1.404\approx x+3\\x\approx1.596[/tex]

Answer:

x = -1.596

Explanation:

[tex]\rightarrow \sf 4^{x + 3} = 7[/tex]

take log on both sides

[tex]\rightarrow \sf log(4^{x + 3}) = log(7)[/tex]

[tex]\rightarrow \sf (x + 3)log(4) = log(7)[/tex]

[tex]\rightarrow \sf x + 3= \dfrac{log(7)}{log(4)}[/tex]

[tex]\rightarrow \sf x= \dfrac{log(7)}{log(4)} -3[/tex]

calculate

[tex]\rightarrow \sf x= -1.596322539[/tex]

[tex]\rightarrow \sf x= -1.596 \quad (rounded \ to \ nearest \ thousand)[/tex]

Answer:

1

Step-by-step explanation:

the number of solutions corelatea with number of cross-points in the graphs, in our exame, 1 point, hence 1 solution

Answer:

B and D

Step-by-step explanation:

vertex(2,5) so D is correct

there are no real roots for the function B is correct

Answer:

[tex]\boxed {\frac{dy}{dx}= 2x}[/tex]

Step-by-step explanation:

Solving :

⇒ log y = log (x²)

⇒ log y = 2 log x

⇒ [tex]\mathsf {\frac{1}{y} \frac{dy}{dx} = \frac{1}{x} \times 2}[/tex]

⇒ [tex]\mathsf {\frac{dy}{dx}= 2x}[/tex]

Answer:

y’ = 2x

Step-by-step explanation:

Let y = f (x), take the natural logarithm of both sides ln (y) = ln (f (x))

ln (y) = ln (x²)

Differentiate the expression using the chain rule, keeping in mind that y is a function of x.

Differentiate the left hand side ln (y) using the chain rule.

y’/y = 2 In (x)

Differentiate the right hand side.

Differentiate 2 ln (x)

y’/y = d/dx = [ 2 In (x) ]

Since 2 is constant with respect to xx, the derivative of 2 ln (x) with respect to x is 2 d/dx [ln (x)]

y’/y = 2 d/dx [In (x)]

The derivative of ln (x) with respect to x is 1/x.

y’/y = 2 1/x

Combine 2 and 1/x

y’/y = 2/x

Isolate y' and substitute the original function for y in the right hand side.

y’ = [tex]\frac{2}{x}[/tex] x²

Factor x out of x².

y’ = [tex]\frac{2}{x}[/tex] (x * x)

Cancel the common factor.

y’ = [tex]\frac{2}{x}[/tex] (x * x)                     (The x that is under 2 and the other x that I have underlined are the ones that cancel out)  

Rewrite the expression.

y’ = 2x

So therefore, the answer would be 2x.

1. The range of the given function y = 3x² for the given domain: {- 2, - 1, and 0} is {12, 3, 0}.

2. The range of the given function y = 8x + 1, where x > 2 is (17, ∞).

3. The range of the given function y = 5x + 2, where x > -2 is (- 8, ∞).

We know that the range of a function is the entire set of all possible values for the dependent variable (typically y), after substituting the domain.

1. For the function y = 3x²,

Here the domain is {- 2, - 1, and 0}. So, we have to find the y values for the x values - 2, - 1, and 0 to find the range of the function.

Now, at x = - 2,

y = 3(- 2)² = 3 × 4 = 12

At x = - 1,

y = 3(- 1)² = 3 × 1 = 3

At x = 0,

y = 3(0)² = 3 × 0 = 0

So, the range of this function is {12, 3, 0}.

2. Now, for the function y = 8x + 1,

At x = 2,

y = 8 × 2 + 1 = 16 + 1 = 17

Since the domain is x > 2, we can say that the range set will contain values greater than 17.

So, the range of this function is (17, ∞).

3. For the function y = 5x + 2,

Now, at x = - 2,

y = 5 × (- 2) + 2 = - 10 + 2 = - 8

Since the domain is x > - 2, we can say that the range set will contain values greater than - 8.

So, the range of this function is (-8, ∞).

1. Therefore, the range of the given function y = 3x² for the given domain: {- 2, - 1, and 0} is {12, 3, 0}.

2. The range of the given function y = 8x + 1, where x > 2 is (17, ∞).

3. The range of the given function y = 5x + 2, where x > -2 is (- 8, ∞).

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Based on the triangle inequality theorem, the possible values of h in cm is: A. 4x < h < 10x

Based on the triangle inequality theorem, two sides of a triangle must be equal or more than the third sides.

Given a values of the side lengths of a triangle as, 3x, 6x, and h cm, the possible values would be determined as shown below:

h < 3x + 7x or 7x - 3x < h

h < 10x or 4x < h

The possible values of h would be: 4x < h < 10x.

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The volume of the air space surrounding the cone inside the cylinder is 1055.04 cm³

The volume of the air space surrounding the cone inside the cylinder is as follows:

volume of the air space = volume of cylinder - volume of a cone

volume of cylinder = πr²h

volume of cylinder = π16 × 5²

volume of cylinder = 400π

volume of the cone = 1 / 3 πr²h

volume of the cone = 1 / 3 × π × 12 × 4²

volume of the cone = 64π

Therefore,

volume of the air space = 400π - 64π

volume of the air space = 336π

volume of the air space = 1055.04 cm³

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Inequalities help us to compare two unequal expressions. The correct option is A.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

The set of numbers that the number line represents is -1, -2,-3, and -4. Thus, The inequalities that can express the given set are -4≤x≤-1.

Hence, the correct option is A.

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