Write the expression as a single natural logarithm.3 ln x – 5 ln c

Final answer:

To determine the number of grams per serving of ice cream, use the formula y = x / 16, where x is the total number of grams in the container and y is the number of grams per serving.

Explanation:

To determine the number of grams per serving of ice cream, we can set up a formula using the variables x and y. Since the container has 16 servings of ice cream, the total number of grams in the container can be represented as 16y (16 servings multiplied by the number of grams per serving).

So, the formula to determine the number of grams per serving (y) is: y = x / 16

For example, if the total number of grams in the container (x) is 800g, then the number of grams per serving (y) would be 800g / 16 = 50g.

Answer:

12

Step-by-step explanation:

The possible values of the third side of the triangle can be written as, 8 < c < 12.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Given a triangle.

Side lengths of the triangle are 10 centimeters, 2 centimeters, and c centimeters.

We have to find the possible values of c.

By the triangle Inequality Theorem,

10 - 2 < c < 10 + 2

8 < c < 12

Hence the possible values of c are 9, 10 and 11.

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The equation of the conic section is [tex]\frac{145x\²}{24336} - \frac{145y\²}{169}=1[/tex]

The foci of the hyperbola are given as: (13,0) and (-13,0)

The asymptote is given as [tex]y =\pm 12x[/tex]

Divide both sides of [tex]y =\pm 12x[/tex] by x.

[tex]\frac yx = \pm 12[/tex]

Where y/x = a/b.

So, we have:

[tex]\frac ab = \pm 12[/tex]

Make a the subject

[tex]a = \pm 12b[/tex]

Recall that

[tex]c\²=a\²+b\²[/tex]

Where:

[tex]c = \pm13[/tex]

[tex]c\²=a\²+b\²[/tex] becomes

[tex](\pm 13)^2 = (\pm 12b)^2 +b^2[/tex]

[tex]169 = 144b^2 +b^2[/tex]

Evaluate like terms

[tex]169 = 145b^2[/tex]

Make b^2 the subject

[tex]b^2 = \frac{169}{145}[/tex]

Recall that [tex]a = \pm 12b[/tex]

Square both sides

[tex]a^2 = 144b^2[/tex]

Substitute  [tex]b^2 = \frac{169}{145}[/tex]

[tex]a^2 = 144 \times \frac{169}{145}[/tex]

[tex]a^2 = \frac{24336}{145}[/tex]

The equation of the conic section is represented as:

[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]

Substitute known values

[tex]\frac{x^2}{24336/145} - \frac{y^2}{169/145} = 1[/tex]

Rewrite as:

[tex]\frac{145x\²}{24336} - \frac{145y\²}{169}=1[/tex]

Hence, the equation of the conic section is [tex]\frac{145x\²}{24336} - \frac{145y\²}{169}=1[/tex]

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Answer:

Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.

Step-by-step explanation:

The equation of the line perpendicular to y = 3x -7 that passes through the point (6, 8) is Option D. y = -1/3x + 10. The slope of the perpendicular line is -1/3. Using point-slope form, we determine the final equation.

To find the equation of a line perpendicular to y = 3x - 7 that passes through the point (6, 8), we must determine the slope of the perpendicular line first.

The slope of the given line is 3. The slope of a line perpendicular to this one is the negative reciprocal of 3, which is -1/3.

We now use the point-slope form of the linear equation, which is:

y - y₁ = m(x - x₁)

Substitute m = -1/3 and the point (6, 8):

y - 8 = -1/3(x - 6)

Distribute -1/3:

y - 8 = -1/3x + 2

Add 8 to both sides:

y = -1/3x + 10

Thus, the equation is Option D. -1/3x + 10.

Answer:

[tex]x=2\text{ (or) }x=11[/tex]

Step-by-step explanation:

We have been given factors of a polynomial as [tex](x-2)[/tex] and [tex](x-11)[/tex]. We are asked to find the values of x that would make the polynomial equal to zero.

We will use zero product property of polynomials to solve our given problem. The zero product property of polynomials states that if any of two factors of a polynomial is zero, then their product will be equal to zero.

Upon equating our given factors to zero, we will get:

[tex](x-2)(x-11)=0[/tex]

[tex](x-2)=0\text{ (or) }(x-11)=0[/tex]

[tex]x-2=0\text{ (or) }x-11=0[/tex]

[tex]x-2+2=0+2\text{ (or) }x-11+11=0+11[/tex]

[tex]x=2\text{ (or) }x=11[/tex]

Therefore, [tex]x=2\text{ (or) }x=11[/tex] will make the polynomial equal to zero.

Answer:

q=171

Step-by-step explanation:

Hello there!

In this explanation k is constant and it means that q is some constant amount bigger than r.

q=kr

76=k×20

76÷20=k  

k= 3.8

q=3.8r

q=3.8×45

q=171

The total number of cups of juice that are left in the bottle are 8x.

Division is a process of splitting a number into two or more equal parts.

Given is that Olly drank 1/2 of a 16 fluid ounce bottle of juice.

Assume that 1 fluid ounce of bottle can fill {x} cups. So, we can write -

16 fluid ounce bottle of juice can fill {16x} cups.

So, 1/2 x 16 fluid ounce of juice will fill {1/2 x 16x} cups.

{1/2 x 16x} cups

8x cups

Therefore, the total number of cups of juice that are left in the bottle are 8x.

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To solve the equation -6/7m = -84, multiply both sides by the reciprocal of -6/7, which is -7/6. The solution is m = 98.

To solve the equation -6/7m = -84, we need to isolate the variable m on one side of the equation. We can do this by performing the inverse operation of what is currently being done to m. Since m is being divided by -6/7, we can multiply both sides of the equation by the reciprocal of -6/7, which is -7/6, to cancel out the division on the left side.

The steps to solve the equation are:

Multiply both sides of the equation by -7/6:

-7/6 *  (-6/7m) = -7/6 *  -84

The left side simplifies to m, and the right side becomes m = 98.

So, the solution to the equation is m = 98.

Final answer:

To find the probability of at least 90 rolls being necessary for the total sum of all rolls to exceed 375, we need to consider the probabilities associated with each roll.

Explanation:

To find the probability of at least 90 rolls being necessary for the total sum of all rolls to exceed 375, we need to consider the probabilities associated with each roll.

The maximum possible sum from a single roll of a six-sided die is 6, so after 90 rolls, the maximum possible sum is 90 * 6 = 540. If the total sum exceeds 375, it means that at least one roll resulted in a value greater than 2.

To calculate the probability, we need to find the complement of the event that the total sum is less than or equal to 375, which is the event of the total sum being greater than 375. Let's assume that the probability of rolling a value greater than 2 is p. The probability of at least 90 rolls being necessary is 1 - (1 - p)^90.

Given the lengths of the major and minor axes of an ellipse, one can derive the standard form equation of the ellipse. In this example, the lengths were 16 and 4, yielding a standard form equation of x²/4 + y²/64 = 1.

The subject of this question is about finding the standard form equation for an ellipse given the lengths of the major and minor axes. To find the equation of the ellipse, we need to identify the semi-major axis (a) which is half the length of the major axis, and the semi-minor axis (b), which is half the length of the minor axis.

In this case, the lengths of the major and minor axes are 16 and 4 respectively, which gives us a semi-major axis of 8 and a semi-minor axis of 2. The standard form equation of an ellipse with a vertical major axis is given by:

(x-h)²/b² + (y-k)²/a² = 1

Where (h, k) is the center of the ellipse. In this case, since the center of the ellipse is at the origin (0,0), the equation becomes:

x²/4 + y²/64 = 1

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The area of a given isosceles triangle with sides of 1 foot in length and a 45-degree angle between these sides is 0.5 square feet.

The area of an isosceles triangle can be calculated using the formula 1/2 base times height. But since we know that the triangle is isosceles and the angle between the equal sides is 45 degrees, this forms a 45-45-90 degree triangle which is a special kind of triangle. In a 45-45-90 degree triangle, the lengths of the sides are in the ratio 1:1:√2. Therefore, the length of the base (which also serves as the height in this case) will be the same length as the equal sides, 1 foot. Substituting these into the formula for area, we get Area = 1/2 * 1 ft * 1 ft = 0.5 square feet.

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