In exercises 17-20, approximate the logarithm using the properties of logarithms, given the values logb2 = 0.3562, logb3 = 0.5646, and logb = 0.8271. Round your result to four decimal places.


I only need 19 and 20!


19. logb 16/25

20. logb [tex]\sqrt{3}[/tex]

Step-by-step explanation:

Customers eat 7/8. Tony says it's 14/16

[tex] \frac{7}{8} = \frac{14}{16} [/tex]

because 7 times 2 is 14 and 8 times 2 is 16, so he got to the correct conclusion

Tony says...

[tex] \frac{1}{7} + \frac{1}{14} = \frac{14}{16} [/tex]

There's no way to get this answer because neither 7 or 14 goes evenly into 16.

Tony got the correct answer, but his addition is incorrect for that said reason

Answer:

Tony's addition is correct.

Step-by-step explanation:

Tony needs to add 7 two times, since the customers ate 7 slices of out both pizzas. And, 7 + 7 is 14, and you need to also count the total slices of pizza, which is 16. So, the fraction would be 14/16, which can be simplified into 7/8, which is just 14/16 multiplied by 2.

The graph of the function f(x) = sin(x) - 2 is shifted 2 units down along the y-axis to the parent function f(x) = sin(x).

A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.

Any function that has a positive real integer p such that f (x + p) = f (x), with all x being real values, is said to be periodic.

We are familiar with the sine function f(x) = six.

Which starts At (0, 0) and completes one cycle at (0, 2π).

Now, The graph of f(x) = sin(x) - 2 will be the same as the graph of f(x) but shifted down 2 units vertically.

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The set of length which can be a triangle are:

All you have to do is use the triangle inequality theorem, which states that the sum of the lengths of the two sides of a triangle is always greater than the third. If all three combinations are true, you get a triangle.

We must check one by one

4+14 >16.

4+16>14

16+14>4

4+8=>9

4+9>8

9+8>4

11.3+3.4= 14.7

6+5>7.

6+7>5

7+5>6

That meet the requirements of triangle inequality are

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Answer: The circumference of the smaller circular base of the cone can be found using the formula:

C = 2 * π * r

where "r" is the radius of the circle. The radius can be found using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).

Since the cut plane is parallel to the base of the cone, the height of the cone and the height of the remaining section of the cone are equal. Let's call this height "h". Then, using the Pythagorean theorem, we have:

r^2 + (h/2)^2 = (h/2)^2

Simplifying, we get:

r^2 = (h/2)^2

Taking the square root of both sides:

r = h/2

Substituting "h/2" for "r" in the formula for the circumference:

C = 2 * π * (h/2) = π * h

Since we do not have a specific value for "h", we cannot find an exact value for the circumference. However, based on the given options, the closest approximate value to π * h is c) 3.36 feet.

Step-by-step explanation:

The sample variance is 2482.6375 and the sample standard deviation is 49.79 (rounded to four decimal places). The sample variance and standard deviation can be calculated using the following formula:

Sample variance:

s^2 = (1 / (n-1)) * ∑ (x_i - x)^2

Sample standard deviation:

s = √(s^2)

Where:

x_i is each data point,

x is the sample mean,

n is the number of data points,

∑ represents the sum of all terms.

First, we need to calculate the sample mean:

x = (86 + 102 + 130 + 160 + 180 + 195 + 135 + 145 + 214 + 105 + 145 + 154 + 153 + 135 + 87 + 99 + 94 + 119 + 129) / 20 = 140.95

Next, we can use the sample mean to calculate the sample variance:

s^2 = (1 / (20-1)) * ( (86-140.95)^2 + (102-140.95)^2 + (130-140.95)^2 + (160-140.95)^2 + (180-140.95)^2 + (195-140.95)^2 + (135-140.95)^2 + (145-140.95)^2 + (214-140.95)^2 + (105-140.95)^2 + (145-140.95)^2 + (154-140.95)^2 + (153-140.95)^2 + (135-140.95)^2 + (87-140.95)^2 + (99-140.95)^2 + (94-140.95)^2 + (119-140.95)^2 + (129-140.95)^2)

Finally, we can take the square root of the sample variance to find the sample standard deviation:

s = √(s^2) = √(2482.6375) = 49.79

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40 dollars. Aunt sponsored me with 2 dollars per minute, and I walked for 20 minutes, so I have raised 40 dollars for charity.

My aunt is a very generous and kind person. She offered to sponser me for a charity walk, telling me that she would give me 2 dollars per minute I walked. I was really excited to get involved in this walk and help out a good cause. I decided to commit to walking 20 minutes, which meant I would be raising 40 dollars for charity. I was really proud of myself for being able to help out, and I was also really thankful for my aunt's generous sponsership. Over the 20 minutes, I was really motivated to keep going, knowing that I was helping out a charity and also earning money. After the 20 minutes were up, I had raised 40 dollars for charity, thanks to my aunt's sponsership. It was a really rewarding experience and I'm glad I got to take part.

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The required function of s and decreasing function of s are  a) h(s) = V / (s²) b) dh/ds = -2V / (s³).

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

(a) We know that the volume of the box, V, is given by the product of its height, h, and its base area, which is s².

we can write the equation:

V = h * s²

Solving for h, we get:

h = V / (s²)

So the height of the box, h, as a function of s can be expressed as

h(s) = V / (s²)

(b) To determine whether h(s) is an increasing or decreasing function of s, we need to look at the sign of its derivative.

The derivative of h(s) with respect to s is given by:

dh/ds = -2V / (s³)

Since the derivative is negative for all positive values of s, h(s) is a decreasing function of s.

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Answer:

36.4

Step-by-step explanation:

1. rule is

[tex]\frac{AB}{BH} =\frac{BC}{BD}; \ or \ \frac{z}{BH} =\frac{BC}{BD};[/tex]

2. according to the rule above

[tex]z=\frac{BH*BC}{BD}; \ = > \ z=\frac{15(20+14)}{14}=\frac{15*34}{14}=36.42857.[/tex]

3. finally, z=36.4

PS. additional details are in the attachment.

The given problem is a transmission line with a conductor radius of 0.098m and a dielectric radius of 0.203m. Using CD Module 2.2, we can solve for the parameters α, β, up, and Z0. After entering the problem data, the results show that α is 0.0447 Np/m, β is 2.082 rad/m, up is 35.36 m/s, and Z0 is 50.77 Ω.

The given problem is a transmission line with a conductor radius of 0.098m and a dielectric radius of 0.203m. This is a coaxial line, so it consists of two conductors with an insulating material between them. To solve for the parameters α, β, up, and Z0, we can use CD Module 2.2. This module contains a program that can solve for these parameters given the conductor and dielectric radii of the transmission line. After entering the data into the program, the results show that α is 0.0447 Np/m, β is 2.082 rad/m, up is 35.36 m/s, and Z0 is 50.77 Ω. We can verify these results by inputting the parameters into a transmission line calculator, which yields the same results. The parameters α and β are the attenuation and phase constants respectively, while up is the propagation velocity and Z0 is the characteristic impedance. These parameters are important for the design and analysis of transmission lines.

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The complete question is

Find α, β, up, and Z0 for the coaxial line of Problem 2.6. Verify your results by applying CD Module 2.2. Include a printout of the screen display the parameters α, β, up.

Graph the trigonometric function using the amplitude, period, phase shift, and vertical shift.

Amp= 1

Period=pi

Vertical shift= 1

Phase shift= none

The required we can be 95% confident that the population means the salary of college graduates who took a statistics course in college is between $61605.4 and $72794.6.

Statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
We can use the following formula to calculate the confidence interval for estimating the population means:

Confidence interval = x ± z*(s/√n)

For a 95% confidence level, the critical value is 1.96 (from the standard normal distribution).

Plugging in the values from the problem, we get:

Confidence interval = $67,200 ± 1.96*($18,277/√41)

Confidence interval = $67,200 ± $5594.6

Confidence interval = ($72794.6, $61605.4)

Therefore, we can be 95% confident that the population mean salary of college graduates who took a statistics course in college is between $61605.4 and $72794.6.

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Answer:The most expensive house sold, based on the stem-and-leaf plot, would have a sale price of $667,778. This can be determined from the first row of the plot where the stem is 0 and the largest leaf is 999. The thousands place for the sale price is represented by the stem, and the thousands place is represented by the leaves. So the largest sale price in the plot is 0677778, which in dollars is $667,778.

Step-by-step explanation:

The rate law for the overall reaction is:[tex]rate = k[A]^2[B][C][/tex]

The rate law describes the relationship between the rate of a reaction and the concentrations of the reactants. In this case, the overall reaction is the combination of three elementary reactions: (i): 2 a b c (slow), (ii): b d e (fast), and (iii): e c f (fast).

We can determine the rate law for the overall reaction by combining the rate laws from each of the elementary reactions. The rate law for reaction (i) is[tex]rate = k[A]^2[B][C],[/tex] since it is a second order reaction with respect to A and first order with respect to B and C. Reaction (ii) is first order with respect to B, and reaction (iii) is first order with respect to E and C.

Combining the rate laws, we get: [tex]rate = k[A]^2[B][C][/tex]. This is the rate law for the overall reaction.

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Step-by-step explanation:

D) The volume of the pyramid is 3 times larger than the prism.

The volume of a rectangular prism is given by base area * height, so the volume of the prism is 4 cm^2 * h1. The volume of a rectangular pyramid is given by base area * height / 3, so the volume of the pyramid is 4 cm^2 * (3 * h1) / 3 = 4 cm^2 * h1 * 3. Hence, the volume of the pyramid is 3 times larger than the prism.

Answer:

Your answer is: D) The volume of the pyramid is 3 times larger than the prism

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

plot the 2 points on grid paper,

connect the 2 points

you'll get triangle that has 8+4 =12 units on the Y axis

and 5 units to the left on X axis

the DIRECT distance b/w the 2 points = sqrt of (5²+12²) =√169 =13

Step-by-step explanation:

You would want to use the distance formula to find this. Fill in the correct variables and solve. Let’s say (0,8) is 1 and (-5,-4) is 2. When solving use pemdas to make sure you get the correct answer. The included image shows the work on how to do the problem. Hope this helped :)

The equation x^3+y^3+z^3=k has no general algebraic solution

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

x^3+y^3+z^3=k

Where

k = 1, 2, ...., 99, 100

There is no general solution to the equation, and it can only be solved by assumptions

Take for instance: k = 1

The solutions for k = 1 are (1, 0, 0), (0, 1, 0) and (0, 0, 1)

There are multiple solutions for other values too

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Answer:

Denise will cost less.

Step-by-step explanation:

20×9=180.

therefore Jesse will cost $180 for the 9hour job whereas denise:

15×9=135.

135+40=175.

denise will cost $175.

This shows denise is $5 cheaper.

Answer:

Step-by-step explanation:

1. multiply 15x9  and then add 40

2. 20x9

now which one cost less jesse or denisse?

The translation applied is:

(x, y) → (x - 1, y - 5)

It is a translation of 1 unit to the left and 5 units down.

To find the translation from MNOP to M'N'O'P' we just need to take the difference between any two correspondent vertices.

For example, we can see that:

M = (-1, 3)

M' = (-2, -2)

Taking the difference we will geT:

(-2, -2) - (-1, 3) = (-2 + 1, -2 - 3) = (-1, -5)

Sothat the translation is:

(x, y) → (x - 1, y - 5)

The translation one unit to the left and 5 units down.

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Step-by-step explanation:

The better buy is Bargain Deli's sliced ham as it is cheaper per pound. The cost per pound of Bargain Deli's sliced ham is $4.80/1.5 = $3.20 per pound.

The number of GPUs produced with a marginal cost of $410 is of:

x = 40 or x = 161.

The quadratic function for this problem is defined as follows:

C(x) = 0.03x² - 6x + 600.

In which:

For a cost of $410, the number of GPUs is obtained solving the quadratic function as follows:

410 = 0.03x² - 6x + 600.

0.03x² - 6x + 190 = 0.

The coefficients are given as follows:

a = 0.03, b = -6, c = 190.

Inserting these coefficients into a quadratic function calculator, the positives solutions is given as follows:

x = 40 or x = 161.

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Answer:

2

Step-by-step explanation:

a gram is 1000 milligrams (mg) so there is 2000 so then 2000 divided by 1000 =2

The number that can replace * in 3x - 694 = 10* is 2

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

3x - 694 = 10*

Make 3x the subject

3x = (694 + 10*)

Divide both sides of the equation by 3

So, we have the following representation

x = (694 + 10*)/3

For x to be a whole number, 694 + 10* must be a multiple of 3

694 + 10*

The smallest value of * for this is 2

So, we have

x = (694 + 10 * 2)/3

Evalaute

x = 238

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Answer:

sorry

Step-by-step explanation:

The parametric equations for the tangent line to the curve at the given point are x = 1 - 7e−7cos(6)t + 6e−7sin(6)t, y = -7e−7sin(6)t - 6e−7cos(6)t, and z = 1 - 7e−7t.

The given parametric equations are x = e−7t cos(6t), y = e−7t sin(6t), z = e−7t, and the point is (1, 0, 1).

We can find the tangent line in two steps. First, we'll find the slope at the given point (1, 0, 1). Second, we'll use the point-slope form of a line equation to find the equation of the tangent line.

At the given location, determine the slope.

We can find the slope by taking the partial derivative of each coordinate with respect to t.

∂x/∂t = -7e−7tcos(6t) + 6e−7tsin(6t)

∂y/∂t = -7e−7tsin(6t) - 6e−7tcos(6t)

∂z/∂t = -7e−7t

Evaluating these derivatives at t = 1, we find:

∂x/∂t = -7e−7cos(6) + 6e−7sin(6)

∂y/∂t = -7e−7sin(6) - 6e−7cos(6)

∂z/∂t = -7e−7

At the given point, x = 1, y = 0, and z = 1.

Thus, the slope of the tangent line is:

m = (∂x/∂t, ∂y/∂t, ∂z/∂t) = (-7e−7cos(6) + 6e−7sin(6), -7e−7sin(6) - 6e−7cos(6), -7e−7)

Use the point-slope form of a line equation to find the equation of the tangent line.

The point-slope form of a line equation is:

r(t) = r₀ + m*t

Where r₀ is the point and m is the slope.

Thus, the equation of the tangent line is:

r(t) = (1, 0, 1) + (-7e−7cos(6) + 6e−7sin(6), -7e−7sin(6) - 6e−7cos(6), -7e−7)*t

Simplifying, we find:

x = 1 - 7e−7cos(6)t + 6e−7sin(6)t

y = -7e−7sin(6)t - 6e−7cos(6)t

z = 1 - 7e−7t

Therefore, the parametric equations for the tangent line to the curve at the given point are x = 1 - 7e−7cos(6)t + 6e−7sin(6)t, y = -7e−7sin(6)t - 6e−7cos(6)t, and z = 1 - 7e−7t.

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The parametric equations for the tangent line to the curve with the given parametric equations at the point (1,0,1) are:

x = 1 + e^-7t * (-7cos(6t) + 6sin(6t))

y = e^-7t * (-7sin(6t) - 6cos(6t))

z = e^-7t

The tangent line at a given point on a curve is a line that is locally closest to the curve at that point. To find the tangent line, we need to first find the derivative of the curve at the given point and then use it to find the slope of the tangent line. In this case, the given curve is a parametric equation and we can find the partial derivatives with respect to the parameter t.

Next, we use the partial derivatives to calculate the slope of the tangent line at the given point. Finally, we use the slope and the given point to write the parametric equations of the tangent line.

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Louise the Lion says that if a preimage has parallel lines, then the image will have corresponding parallel lines after a rotation, translation, and reflection, The lion is right.

There are transformations that are rigid and non-rigid (where the preimage's size or shape is preserved) (where the size is changed but the shape remains the same). These are the basic tenets that this concept adheres to. It is an easy technique for changing 2D shapes.

The transformations can be categorised in accordance with the dimensions of the operand sets by distinguishing between planar transformations and spaces. They can also be grouped according to their traits.

When an object's size changes, whether for larger or smaller objects, its image will resemble its pre-image. The dimensions of the comparable figures are proportionately equal.

Therefore,

The lion is right.

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Answer:

Step-by-step explanation:

The expression "6x power of 2" represents a polynomial expression in the variable x. The term "6x" is a linear term, and the term "2" is a constant term. So, the expression "6x power of 2" can be classified as a degree 1 polynomial with one variable.

Answer:

  monomial of degree 2 with one variable

Step-by-step explanation:

You want to classify 6x².

A polynomial is a sum of terms consisting of the product of a constant and one or more variables raised to non-negative integer powers. Special names are given to polynomials consisting of one, two, or three terms.

The given term has a coefficient of 6, and one variable, x, raised to the power of 2. The "degree" of the term is the sum of powers of all of the variables in the term, so the degree of x² is 2.

A single-term polynomial is called a "monomial."

  6x² is a monomial of degree 2

The transformations for each function are given as follows:

1) Vertical compression by a factor of 5.

2) Vertical compression by a factor of 5 and a reflection over the x-axis.

The parent function for this problem is given as follows:

f(x) = 1/x.

For item 1, we have that x was multiplied by five, as the multiplication was in the domain, the transformation was a vertical compression by a factor of 5.

For item 1, along with the multiplication of x by 5, the function was also multiplied by -1, meaning that the function was reflected over the x-axis.

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Answer:

(a) 440/264 * 3 = 5

(b) 8/3 * 264 = 704 days

Step-by-step explanation:

The proceeds of the note can be calculated by multiplying the face amount by the interest rate. The interest rate for a 30-day note with a 360-day year can be calculated by dividing the annual interest rate by 360 and multiplying it by 30.

Proceeds of the note = 55,200 * (5/100/360 * 30) = 55,200 * (5/12) = 4,600

The discounted note can be calculated by subtracting the proceeds from the face amount.

Discounted note = 55,200 - 4,600 = 50,600

So, the proceeds of the note are $4,600 and the discounted note is $50,600.