Exercise: Determine if x = 64 is a solution to the logarithmic equation.
log4(x)=3-log4(x - 63)

The height of the can is approximately 1.26 cm.

The formula for the surface area of a cylinder is:

SA = 2πr² + 2πrh

where r is the radius of the cylinder and h is its height.

Since the diameter of the can is 7 cm, the radius is 7/2 = 3.5 cm.

We are given that the surface area of the can is 180 square centimeters, so we can set up an equation:

180 = 2π(3.5)² + 2π(3.5)h

Simplifying:

180 = 24.5π + 7πh

180 = 45.5πh

h = 180 / (45.5π)

h = 1.25924790139

h ≈ 1.26 cm (rounded to the nearest hundredth)

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1. The lateral surface area of the prism is 200 units²

2. The lateral surface area of the cylinder is 125.6 cm²

The lateral surface area is the area of the lateral surface.

The lateral surface area of a prism is expressed as;

LSA = (a+b+c)h

or perimeter of the base × height

LSA = (6+12+7)8

= 25 × 8

= 200 units²

The lateral surface area of a cylinder

= 2πrh

r = 4cm and h = 5cm

LSA = 2 × 3.14 × 4 × 5

LSA = 40 × 3.14

= 125.6cm²

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Answer:

0.039 or 0.040

Step-by-step explanation:

this is due to how when u get things like 3.9 and you need to round u just round up bye it to get the closest answer

The time it takes (1/x) + (1/(x + 5)) + (1/(4x + 20))

​

From the question,

Marla takes 5 hours more than Tom: M = T + 5

Bob takes 4 times as long as Marla: B = 4M

work is inversely proportional to the time hence

Tom: 1/T

Marla: 1/M

Bob: 1/B

When we express this,

Marla: 1/(T + 5)

Bob: 1/(4*(T + 5))

We would have to solve for the total work in a given hour

= (1/T) + (1/(T + 5)) + (1/(4*(T + 5))

In one hour, Tom cаn clеan 1/х оf thе building, Mаrlа cаn clеan 1/(x + 5) оf thе building, and Вob cаn clеan 1/(4х + 20) оf thе building.

then 1/T = 1/x

1/(T + 5) = 1/(x + 5)

1/(4*(T + 5)) = 1/(4x + 20)

The expression would be written as:

work in one hour = (1/x) + (1/(x + 5)) + (1/(4x + 20))

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The value of m in terms of other variables of the right angle triangle is: m = √(p² - n²)

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

However, it can also be written in the form of c² = a² + b²

From the given triangle, we can write as:

p² = m² + n²

m² = p² - n²

m = √(p² - n²)

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We can see here that filling up the remaining spaces:

AB ≅ CD: Opposite sides are congruent.

∠ABC and ∠BCD are supplementary: Consecutive angles are supplementary.

An angle is actually known to be a geometric figure that is formed by the joining together of two rays or endpoints which are known as vertex.

The sides or legs of the angle are known to be make up the rays.

Angles are actually known to be measured in degrees, with a full circle containing 360 degrees.

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The equation that has an initial value of 10 and has a rate of change of 4 is y= 4x+ 10.

We have,

Initial value= 10

Rate pf change= 4

We know from slope intercept form

y= mx+ b

where is m is slope or rate of change and b is y intercept or initial value.

So, we can take m = 4 and b= 10

Then, the required equation is

y= 4x +10.

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The best response to such statement will be "Let me explain how my questions are related to our discussion" which is option (A)

The statement the customer made shows that he is disappointed with whatever the situation is.

Customer dissatisfaction refers to the feeling of displeasure, frustration, or disappointment that a customer experiences when their expectations are not met by a product or service they have purchased or received. It can arise from various factors, such as poor quality, ineffective communication, slow response times, inadequate support, or a mismatch between customer needs and what is being offered.

To prevent customer dissatisfaction, businesses must focus on providing high-quality products and services, being responsive and attentive to customer needs, and proactively addressing any issues or concerns that arise.

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The condition that must be true in order to get a correct answer will be that the number found in the columns of the first matrix must be equal to the numbers in the rows of the second matrix.

A matrix is a rectangular arrangement of numbers that can be used to demonstrate mathematical properties. Often, two or three matrices can be evaluated to determine an outcome.

For the given matrices, a × b  and c x d the only way to arrive at a correct answer will be if the figures found in the columns of the first matrix equal the figures found in the rows of the second matrix.

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The volume of the prism will be 88 cubic units. Then the correct option is B.

Given that:

Length, L = 4 units

Width, W = 4 units

Height, H = 5.5 units

The volume of the prism is given as,

V = L x W x H

The volume of the prism is calculated as,

V = 4 x 4 x 5.5

V = 88 cubic units

The volume of the prism will be 88 cubic units. Then the correct option is B.

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The complete question is given below.

The length of AB in the right triangle is 8 units.

The sides of a right angle triangle can be found as follows:

The right angle triangle has one of its angles as 30 degrees. The side AB can be found using trigonometric ratios.

Hence,

sin 30 = opposite / hypotenuse

where

opposite side = AB

hypotenuse side = 16 units

Therefore,

sin 30 = AB / 16

cross multiply

AB = 16 sin 30

AB = 16 × 0.5

AB = 8 units

Therefore,

AB = 8 units

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The balance of the account after 20 years is given as follows:

A(20) = $13,268.58.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

P = 6500, r = 0.036, n = 2, t = 20.

Hence the balance of the account after 20 years is given as follows:

A(20) = 6500 x (1 + 0.036/2)^(2 x 20)

A(20) = $13,268.58.

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Answer:  the best answer is option A: the data is symmetric with an approximate range of 20. The lowest value of 6 might mean that most students did not participate in activities.

Step-by-step explanation: From the line plot, we can see that the data is not symmetric because the dots are not equally distributed on both sides of the plot. Therefore, we can eliminate options A and C.

Option D suggests that the data is bimodal, meaning that there are two peaks in the distribution. However, there is no clear indication of two peaks in the plot. Therefore, we can eliminate option D.

Option B suggests that the data is skewed, and the most frequent number of activities is 16 or more. However, this is not the case as the highest number of dots is above 14 and 16. Therefore, we can eliminate option B.

Answer:

180

Step-by-step explanation:

The word HORSES has 6 distinct letters, so we can arrange them in 6! = 720 ways if all the letters were unique.

However, in this case, the letters E and S are repeated twice. Therefore, we must divide by the number of arrangements of the repeated letters to avoid counting the same arrangement more than once.

The letter E appears twice, so there are 2! = 2 ways to arrange the E's within the word. Similarly, the letter S appears twice, so there are 2! = 2 ways to arrange the S's within the word.

Thus, the total number of unique arrangements of the letters in the word HORSES is:

6! / (2! × 2!) = 720 / 4 = 180

Therefore, there are 180 unique arrangements of the letters in the word HORSES.

No, the relation is not a function.

Given the relation in the question:

x: -2, -4, -1, -4, 5, 3

y: 1, -3, 2, 8, 0, -1

A function is simply a relationship that maps one input to one output.

To determine whether the relation is a function, we need to check whether each x-value in the relation is associated with a unique y-value.

Looking at the x-values, we see that there are repeated values of -4, which means that there are multiple y-values ( -3 and 8 ) associated with x = -4.

The mapping of x to y is not well-defined for all values of x, since one value of x is associated with multiple values of y, hence, it is not a function.

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The sum of the first 5 terms of the sequence is 183.

We have,

The first term of the sequence is 3 and the common ratio is -3.

We can use the formula for the sum of the first n terms of a geometric sequence:

Sn = a(1 - r^n) / (1 - r)

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

Plugging in the values we have:

S5 = 3(1 - (-3)^5) / (1 - (-3))

Simplifying:

S(5) = 3(1 + 243) / 4

S(5) = 3(244) / 4

S(5) = 183

Therefore,

The sum of the first 5 terms of the sequence is 183.

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Answer:28

Step-by-step explanation:

•C= 2(3.14 x r)

•C= 2(3.14 x4.5)

•C=2(14.13)

•C=28.26

Answer:

(1)

Step-by-step explanation:

11111111111111111111111

Miriana rolled the sequence of 3 and then 6 two more times than the theoretical probability would have predicted.

The theoretical probability of rolling a three-on-one number cube is 1/6, and the same is true for rolling a six. Since the two rolls are independent,

The probability of rolling a three and then a six in the sequence is the product of the probabilities: (1/6) x (1/6) = 1/36.

To find the expected number of times this sequence would occur in 180 experiments, we multiply the probability by the number of experiments: (1/36) x 180 = 5.

So, if Miriana had rolled the number of cubes according to the theoretical probability, we would have expected her to roll the sequence of 3 and then 6 five times in 180 experiments.

However, she actually rolled this sequence 7 times, so she rolled it 2 more times than the theoretical probability would have predicted.

Therefore, Miriana rolled the sequence of 3 and then 6 two more times than the theoretical probability would have predicted.

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Answer:

y = -x + 4

Step-by-step explanation:

The slope-intercept form is y = mx + b

4x + 4y = 16

4y = - 4x + 16

y = -x + 4

So, the answer y = -x + 4

Answer:

Step-by-step explanation:

The statement "70 decreased by twice chai’s height" as an expression is 70 - 2c

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

70 decreased by twice chai’s height

Represent chai’s height with c

So, we have the following representation

70 decreased by 2c

When the above statement is then represented as an expression, we have the following

Expression: 70 - 2c

Hence, the expression of the statement "70 decreased by twice chai’s height"  is 70 - 2c

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The numeric value of the function f(x) at x = 5 is given as follows:

f(5) = 74.75.

The second derivative of the function f(x) is given as follows:

f''(x) = 2x + 6sin(x).

Integrating the second derivative, the first derivative of the function is given as follows:

f'(x) = x² - 6cos(x) + K.

When x = 0, y' = 2, hence the constant K is given as follows:

2 = -6 + K

K = 8.

Hence:

f'(x) = x² - 6cos(x) + 8.

Integrating the first derivative, the function is given as follows:

f(x) = x³/3 - 6sin(x) + 8x + K.

When x = 0, y = 4, hence the constant K is given as follows:

K = 4.

Then:

f(x) = x³/3 - 6sin(x) + 8x + 4.

The numeric value at x = 5 is given as follows:

f(5) = 5³/5 - 6sin(5) + 8(5) + 4

f(5) = 74.75.

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Answer:

Step-by-step explanation:

You want to compare the future values of two accounts after 10, 20, 50, and 85 years:

The formula for account value with compounding monthly is ...

  A = P(1 +r/12)^(12t) . . . . . . principal P invested at rate r for t years

  A = 4500(1 +0.075/12)^(12·t) . . . . . using given values for P and r

The first line of calculator output shown in the attachment gives the value after 10, 20, 50, and 85 years.

The formula for account value with continuous compounding is ...

  A = P·e^(rt)

  A = 5500·e^(0.0675t) . . . . . using given values for P and r

The second line of calculator output shown in the attachment gives the value after 10, 20, 50, and 85 years.

You will notice this (second) account has higher value up to 20 years, then lower value after that.

The account with the higher interest rate will make more money after the "break-even" period of about 20.6 years.

__

Additional comment

We have rounded the account values to the nearest dollar. For the purpose of value comparison, three significant figures would be sufficient.

The second attachment shows the different account values over the long term. You can see the higher interest rate really makes a difference.

The third attachment shows the shorter-term account values, and the "break-even" time period of about 20.6 years, when the values in both accounts are about $22,063.

The value of y when x = 2 is -2.

We are given that;

x = 4

y = -1

Now,

To write an equation relating x and y for inverse variation, you can use the formula123:

xy = k

where k is a constant.

To find the value of k, you can use the given values of x and y:

x = 4

y = -1

xy = k

(4)(-1) = k

k = -4

So, the equation relating x and y is:

xy = -4

To find y when x = 2, you can substitute x = 2 in the equation and solve for y:

xy = -4

(2)y = -4

y = -4/2

y = -2

Therefore, by the given equations the answer will be -2.

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The solution to the system of equations is (d) More than 1 solution

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

3y-12x=18

2y-8x=12

Using the graphing function on a calculator, we have the solution to be

Infinite many solutions

This is so because the equations 3y-12x=18 and 2y-8x=12 are equivalent equations

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The probability of picking L and another A with replacement is: 2/49

Probability of picking A and then another A with replacement is:  1/49

We are given the letter DALLAS.

There are a total of 7 letters. Thus, the probability of picking L is:

2/7

Probability of picking A after that with replacement is: 1/7

Thus, probability of picking L and another A with replacement is:

(2/7) * (1/7) = 2/49

Probability of picking A and then another A with replacement is:

(1/7) * (1/7) = 1/49

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Aisha and Jordan need 63 carpet tiles to cover the maximum amount of floor with the whole tiles.

To find the area of the greatest amount of floor that can be covered with carpet tiles, we need to figure out how many tiles can fit in that area. Since each tile has a side length of 1.5 feet, we can divide the grid into squares with side lengths of 1.5 feet to see how many tiles can fit.

Dividing the grid in this way, we can see that the area of each square is 2.25 square feet (1.5 ft x 1.5 ft). To find the maximum area that can be covered with whole tiles, we need to find the dimensions of the largest rectangle that can be formed using these squares.

In the grid, the longest side that can be formed using whole tiles is 9 squares long (13.5 feet), and the shortest side that can be formed using whole tiles is 7 squares long (10.5 feet). Therefore, the maximum area that can be covered with whole tiles is:

Area = Length x Width = 13.5 ft x 10.5 ft = 141.75 square feet

To find out how many tiles are needed to cover this area, we need to divide the area by the area of each tile:

Number of tiles = Area / Area of each tile = 141.75 sq ft / 2.25 sq ft per tile = 63 tiles

Therefore, Aisha and Jordan need 63 carpet tiles to cover the maximum amount of floor with the whole tiles.

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The numeric value of the function f(x) at x = 5 is given as follows:

f(5) = 74.75.

The second derivative of the function f(x) is given as follows:

f''(x) = 2x + 6sin(x).

Integrating the second derivative, the first derivative of the function is given as follows:

f'(x) = x² - 6cos(x) + K.

When x = 0, y' = 2, hence the constant K is given as follows:

2 = -6 + K

K = 8.

Hence:

f'(x) = x² - 6cos(x) + 8.

Integrating the first derivative, the function is given as follows:

f(x) = x³/3 - 6sin(x) + 8x + K.

When x = 0, y = 4, hence the constant K is given as follows:

K = 4.

Then:

f(x) = x³/3 - 6sin(x) + 8x + 4.

The numeric value at x = 5 is given as follows:

f(5) = 5³/5 - 6sin(5) + 8(5) + 4

f(5) = 74.75.

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The time it will take for him to have enough money for the project is given as follows:

t = 8.5 years.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

P = 4000, r = 0.062, n = 2, A(t) = 6720.

Hence the time needed is obtained as follows:

[tex]4000\left(1 + \frac{0.062}{2}\right)^{2t} = 6720[/tex]

(1.031)^2t = 672/400

(1.031)^2t = 1.68

2tlog(1.031) = log(1.68)

t = log(1.68)/[2 x log(1.031)]

t = 8.5 years.

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