For the following, find f(2.1) and f(4).

Solution

- The question would like us to determine the difference expression that corresponds to the following logarithm

- In order to solve this question, we should apply the Law of Logarithm which states that:

- Applying this law, we have:

Final Answer

The answer to the question is

(a) Plan B, 8

(b) 250, Plan A

Let:

If the line is horizontal, then:

The slope is given by:

Zero over any quantity is always zero, so:

Answer:

Step-by-step explanation:

First you want to make the denominator the first multiple of both numbers so: 2/3 -3 5/6 = 2/6 - 3 5/6

Next you want to multiply the numerator by the amount of times you had to multiply the denominator so: 4/6 - 3 5/6

Then subtract the answer: 3 1/6

Answer:

Step-by-step explanation:

The base of the rectangle and triangle is same.

Triangle area formula:

Substitute the values:

Answer is 14 ft.

Triangle Area Use Formula.

A = 28 ft2

H = 4 ft

B Value.

28 = 4b/2

28 = (4/2)b

28 = 2b

b = 28/2

b = 14

_____________________

Class: Middle School

Lesson: Triangle

[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}[/tex]

Answer is option A

Because the other side (AB) is 15 and the other rectangle (JM) is 10, so the realation between them is 15/10 = 3/2

But, since DC and ML relation is NOT 3/2, then the rectanlges are not similar

Answer: We need to find the expression p(x) for profit.

Therefore the first option represents the profit of the company.

Let's express the mixed fraction in decimal.

Then, from least to greatest, the numbers are

Answer:

a

Step-by-step explanation:

to rotate 180 degrees, simply invert both signs

Answer: We have to calculate the (i) volume and (ii) the surface area of the cone:

The formula (1) is for the lateral surface of the cone and the formula (2) is for the volume of the cone, the unknowns are determined as follows:

Therefore the volume and the lateral surface area is calculated as follows:

Therefore x and y are the answers.

Let's begin by listing out the information given to us:

Amount spent = $240

discount = 25%

Therefore, the customer paid $180 for his purchase

Resolviendo una ecuación lineal veremos que el número es 76, y la mitad de ese número es 38.

Definamos la variable "x" como el número de la ecuación.

Tenemos la oración matematica:

"La cuarta parte de un número, disminuida en 17, es igual a 4"

Esto se puede escribir como la ecuacion:

(1/4)*x - 17 = 4

Esto es una ecuación lineal que puede ser resuelta para x.

(1/4)*x - 17 = 4

(1/4)*x = 4 + 17 = 19

x = 4*19 = 76

Entonces la mitad del número es:

x/2 = 76/2 = 38

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The number of cups of lemonade sold in each hour is 32.4.

The number of cups of lemonade in each hour is the rate of selling. The rate of selling will be calculated by the formula : number of cups ÷ time.

Keep the values in formula to find the number of cups of lemonade sold each hour

Number of cups of lemonade sold each hour = 162 ÷ 5

Performing division to find the number of cups sold each hour

Number of cups of lemonade sold each hour = 32.4

Thus, each hour, 32.4 cups of lemonade are sold.

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If we have the function

Then

This also can be written in the form

We see that both answer are the same, like it should be.

First determine the common ratio between consecutive terms.

4.5/3 = 9/6 = 3/2

6.75/4.5 = 27/18 = 3/2

and so on. The [tex]n[/tex]-th term in the sequence is given by

[tex]a_n = 3 \cdot \left(\dfrac32\right)^{n-1}[/tex]

Solve for [tex]n[/tex] that gives the last term to find how many terms are in the sum.

[tex]n = 1 + \log_{3/2}\left(\dfrac{a_n}3\right)[/tex]

Plug in the last term.

[tex]n = 1 + \log_{3/2} \left(\dfrac{34.171875}3\right) = 1 + 6 = 7[/tex]

Then the sum of the first 7 terms of this sequence is

[tex]\displaystyle \sum_{n=1}^7 3 \cdot \left(\frac32\right)^{n-1} = 3\cdot\frac{1 - \left(\frac32\right)^7}{1-\frac32} = \boxed{\frac{6177}{44}} = 96.515625[/tex]

where we use the formula

[tex]\displaystyle \sum_{n=1}^k r^{n-1} = \frac{1-r^n}{1-r}[/tex]

The sample space is the set of all different outcomes that can show up from the experiment.

Flipping a coin has two possible outcomes: heads or tails.

Spinning the spinner has three possible outcomes: A, B or C.

Draw a tree diagram to represent the sample space:

If we represent results using ordered pairs, the sample space is:

Where H stands for heads and T stands for tails.

Using a linear function, it is found that:

a) The table is completed in the first image at the end of the answer.

b) The function is: s(w) = 125 - 10.50w.

c) The graph of the function is given by the second image at the end of the answer.

The slope-intercept representation of a linear function is shown by the rule presented below:

y = mx + b

The coefficients of the function are presented as follows:

In the context of this problem, the slope and the intercept are given as follows:

Hence the function is given as follows:

s(w) = 125 - 10.50w.

The numeric values to complete the table are given as follows:

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Answer:

Step-by-step explanation:

z 3 = 0.64 Take the specified root of both sides of the equation to eliminate the exponent on the left side. z = 3 √ 0.64 The result can be shown in multiple forms. Exact Form: z = 3 √ 0.64 Decimal Form: z = 0.86177387

Answer:

$435,400

Step-by-step explanation:

Price of one ticket: $311,000/5,000

Price of one ticket: $62.20

Price of 7000 tickets: $62.20 x 7000

Price of 7000 tickets: $435,400

Given a normal distribution with m = 100 and s = 10, the probabilities are;

a) X > 75 = 0.0062

b) X < 70 = 0.00135

c) X < 80 or X > 110 = 0.053954

We are given;

Population mean; m = 100

standard deviation; s = 10

The z-score is gotten from the formula;

z = (X - m)/s

Thus;

1) Probability that X > 75 is;

z = (75 - 100)/10

z = -2.5

From online p-value from z-score calculator, we have;

probability = 0.0062

2) Probability that X < 70 is;

z = (70 - 100)/10

z = -3

From online p-value from z-score calculator, we have;

probability = 0.00135

3) Probability that X < 80 is;

z = (80 - 100)/10

z = -2

From online p-value from z-score calculator, we have;

probability = 0.02275.

Probability that X > 110 is;

z = (110 - 100)/10

z = -1

From online p-value from z-score calculator, we have;

probability = 0.158655

Thus, P(0.02275 < x < 0.158655) = 0.053954

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Answer:

perimeter = 310 yards

Step-by-step explanation:

If the length is 100 yards and the width is 55 yards, how many yards is the perimeter?

p =  2l + 2w

perimeter = 2(100) + 2(55)

perimeter = 200 + 110

perimeter = 310 yards

The set-builder form is { x | x is a calculus book}.

A set is a collection of quantities based  on a specific criteria. A set can be expressed in two forms.

We usually use the form {a, b, c,....} in which we include each element of the set separated with a comma in between. This form of set notation is called the roster form.

Another set notation is the set-builder form. This form is more concise and precise and easily understandable also. In this form, all the elements are included in the set which has a same property. That is, here we don't write each and every element separately in the set but just emphasize the property of the elements which are included in the set.

We are asked to write the set of all calculus books in set-builder form.

The set-builder form for 'The set of all calculus books' is { x | x is a calculus book}.

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Lionel should be the correct answer.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Dotty and Lionel are making a graph comparing a car's age with its gas mileage.

Dotty says the graph should show discrete points because the car sage is started in whole numbers of years.

Lionel says they should make a continuous line because age increases gradually, like time.

Now,

Clearly, The Lionel is correct because when we talk about the age, that means time and Time is continuous , never stopping or slowing down for anyone.

Thus, Lionel should be the correct answer.

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1) We need to find out a pattern for the powers that have a base 2:

Note that from 4 to 4 powers the last digit starts to repeat itself.

2) So, let's proceed with this dividing the exponent 2058 by 4:

Now, note that the remainder is 2, therefore we can state that:

As we can see from the given data, that, it gives some informtaion about, an on going process, that is almost in rythm.

So, from that we can see that, Mile had increased the running time in a particular pattern, at first he had increased the time by 2, then by 3, then by 4, and so on.

So to find the running time for sunday, we can solve this problem by analysing this pattern.

Therefore the answer is (D): looking for patterns.

We are asked to evaluate the mathematical expression below;

To do this we would use "PEMDAS". PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction.

Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third, and so on, until the calculation is complete.

We will then proceed to solve the expression according to PEMDAS.

Answer: 28

The quadratic function in vertex form is y = -1/2(x + 1)^2 - 2

The vertex is given as

(h, k) = (-1,-2)

The point is also given as

(x, y) = (3, -10)

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

Substitute (h, k) = (-1,-2)  in y = a(x - h)^2 + k

y = a(x + 1)^2 - 2

Substitute (x, y) = (3, -10)

-10 = a(3 + 1)^2 - 2

So, we have

-10 = a(4)^2 - 2

Add 2 to all sides

-8 = a(16)

Divide by 16

a = -1/2

Substitute a = -1/2 in y = a(x + 1)^2 - 2

y = -1/2(x + 1)^2 - 2

Hence, the equation is y = -1/2(x + 1)^2 - 2

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ANSWER :

f(x) = (3x-2)(x-3)(x-4)(x-2)^3

EXPLANATION :

A polynomial with a degree of 6 has 6 factors.

f(x) = (x - a)(x - b)(x - c)(x - d)(x - e)(x - f) with 6 roots or x-intercepts.

But the problems states that it has 4 x-intercepts, so we will reduced the number of roots but maintaining the number of factors.

f(x) = (x - a)(x - b)(x - c)(x - d)(x - a)(x - a).

From here, we still have 6 factors but only 4 x-intercepts, the last two factors (x - a) is the same as the first factor.

So we can rewrite this as :

Next is to have a y-intercept of 64, y-intercept is the value of f(x) when x = 0

Substitute 0 to the function.

Now we have f(0) = a^3bcd and f(0) = 64 as the definition from above.

We need to find the factors of 64,

64 = 8 x 4 x 3 x 2/3

And we can rewrite the equation as :

From here, we can observe that,

a^3 = 8 ⇒ a = 2

b = 4

c = 3

d = 2/3

So the function will be :

Explanation in 2/3

Since we only need 4 distinct factors of 64.

8 x 4 x 3 x 2/3

8 x 4 = 32

The product of the 3rd and 4th factor should be 2, in order to get 64.

Since from the first

The type of function we are going to work with here is an exponential function. These functions are given by equations like:

Where x is the variable and a, b and c fixed parameters. In this case c=0, a=1 and b=13/4. This number b, i.e. the one affected by the exponent is called the base so I'm going to refer to it with that word.

All exponential functions have similar graphs, they pass from being very close, almost pararel to the x-axis and then they begin to rapidly increase toward infinite y values. In the following picture you can see the graph of two exponential functions:

The red graph tends to zero for positive x values, this means that its equation has a negative sign in the exponent:

The blue graph on the other hand tends to zero for negative x values which means that there's no negative sign in the exponent. This is the case of our function r(x) so we can discard the upper left option.

Another thing to take into account is the offset of the function, that number that I labeled as "c" in the first equation. This offset translates the graph upwards or downwards depending on its sign.

For example, in this image the graphs decrease for negative x values which means their exponents don't have a negative sign but they all tend to different values which means their offsets are different. Blue's offset is 0 since it tends to 0 while gray's offset is 1 because it tends to 1. The same way you can deduce that the orange graph has an offset of -2. In the case of our problem, function r(x) doesn't have an offset which means that in one direction it has to tend to 0. This means we can discard the lower rigth option.

We have already discarded two options, if we discard one more we have the answer.

Now let's take r(x) and evaluate it in x=0:

You don't need a calculator for this because any number raised to 0 lays 1. This means that at x=0 ,i.e. the y-intercept of the graph, the function has y=1.

Lower left graph intercepts the y-axis in 1 while the upper right does it closer to 0 so we can discard this last option.

In summary, we have only one possible option left, the one in the lower left. This is the correct option.