How can you interpret statements that use function notation without a graph?

Properties of log:

Evaluate given using the properties above:

Q1

Q2

Q3

Answer:

[tex]\textsf{1.} \quad 5 \ln x + 5 \ln y[/tex]

[tex]\textsf{2.} \quad \dfrac{1}{7} \ln t[/tex]

[tex]\textsf{3.} \quad \ln x - \dfrac{5}{2}\ln y \;\; \;\;\textsf{or} \;\;\;\; \ln x - 5\ln y[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Natural log laws}\\\\Product law: \;$\ln xy=\ln x + \ln y$\\\\Quotient law: $\ln \left(\dfrac{x}{y}\right) = \ln x - \ln y$\\\\Power law: \;\;\;\;$\ln x^n=n \ln x$\\\end{minipage}}[/tex]

Apply the power law followed by the product law:

[tex]\begin{aligned}\ln (xy)^5 & = 5 \ln (xy)\\ & = 5\left( \ln x + \ln y \right) \\ & = 5 \ln x + 5 \ln y\end{aligned}[/tex]

[tex]\textsf{Apply the exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}[/tex]

then apply the power law:

[tex]\begin{aligned}\ln \sqrt[7]{t} & = \ln t^{\frac{1}{7}} \\ & = \dfrac{1}{7} \ln t\end{aligned}[/tex]

It is not completely clear where the square root sign begins and ends, so I have provided answers for both permutations:

[tex]\begin{aligned}\ln \left(\sqrt{\dfrac{x^2}{y^5}}\right) & = \ln \left(\dfrac{\sqrt{x^2}}{\sqrt{y^5}}\right) \\\\& = \ln \left(\dfrac{x}{y^{\frac{5}{2}}}\right) \\\\&=\ln x - \ln y^{\frac{5}{2}}\\\\&=\ln x - \dfrac{5}{2}\ln y\end{aligned}[/tex]

[tex]\begin{aligned}\ln \left(\dfrac{\sqrt{x^2}}{y^5}\right)& = \ln \left(\dfrac{x}{y^5}\right) \\\\&=\ln x - \ln y^5\\\\&=\ln x - 5\ln y\end{aligned}[/tex]

a) The option that is a negation of the given statement is; The water temperature is not 70.

b) The conclusion of the given conditional statement is; Keisha likes the dress.

In mathematics, a conditional statement is defined as a statement that can be written in the form “If P then Q,” where P and Q are sentences.

a) We are given the statement as;

The water temperature is 70.

Now, negation is a false/opposite form of the given statement and as such among the options, the only one that is a negation is that

"The water temperature is not 70."

b) We are given the conditional statement as;

If the dress is red, then Keisha likes the dress.

Thus, the conclusion of this is that likes the dress.

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The formula to find the slope is m = (y₂ - y₁)/(x₂ - x₁), hence option B is correct and the slope of the line will be -1/2.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the data mentioned in the question,

1.

The formula to find the slope of the line between two points is,

m = (y₂ - y₁)/(x₂ - x₁)

2.

The given points are,

(-4, 3) and (12, -5)

So, the slope of the line that connects given points,

m = (-5 - 3)/(12+4)

m = -8/16

m = -1/2

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Therefore ,the the  the work done in propelling a 10-ton satellite to a height of 200 miles above Earth is 1904.7619 million ton.

An expression is composed of a number, a variable, both, or neither, and specific operation symbols. An equation is made up of two expressions, which are separated by an equal sign.

Here,

Use F(x) = C/[tex]x^{2}[/tex]

Where c is a constant and x is the radius of the earth

F(x) is satellite weight

We have to find c.

thus,

=> 10 = c /[tex]4000^{2}[/tex]

=> c =160000000

Therefore,

=> F(x) =  160000000/  [tex]x^{2}[/tex]

Workdone ,

=> W = [tex]\int\limits^{4200}_{4000} {F(x)} \, dx[/tex]

=>W = [tex]\int\limits^{4200}_{4000} {160000000 /x^{2} } \, dx[/tex]

=>W =[tex]\left \{ {{4200} \atop {4000}} \right. \frac{-160000000 }{x}[/tex]

=> W =1904.7619 million ton

Therefore ,the the  the work done in propelling a 10-ton satellite to a height of 200 miles above Earth is 1904.7619 million ton.

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Yes, I agree that this equivalent expression has been simplified.

Reorder and gather like terms: (8.4x +6.3 x) +12.6

Collect coefficients for the like terms: (8.4 +6.3)  ×  x +12.6

Calculate the sum or difference: 14.7 x +12.6

Answer : 14.7 x  + 12.6

What exactly is equivalent expression, and how do we recognize it?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

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The probability that a 6 occurs on exactly one of the rolls after rolling a fair die four times is 0.385.

The Three Kinds of Probability

Classical: (equally probable outcomes) (equally probable outcomes) Let S be the sample space (the collection of all unique outcomes that might occur).

Subjective Probability. Definition of Relative Frequency.

Formula used to find probability

The probability is often defined as the proportion of positive outcomes to all outcomes in the sample space. It is written as, the likelihood of an event

P(E) = (Number of favorable outcomes) ÷ (Sample space).

As die is rolled 4 times ,

X≈ binomial(4, 1/6)

P(X=r) = nCr (p)^r (q)^(n-r)

P(X = 1) = 4C1 × (1/6)^1 × (5/6)^3

           = 4 × 1/6 × (5/6)^3

∴P(X = 1) = 0.257

The probability that a 6 occurs on exactly one of the rolls after rolling a fair die four times is 0.385.

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Answer:

D) 48

Step-by-step explanation:

Let s = Scott

Let j - James

s = 5

s + 43 = j  Substitute 5 for s

5 + 43 = j

48 = j

The steps to construct a cumulative frequency distribution table are mentioned above.

Given is to construct a cumulative frequency distribution table.

Since the data is not given, we can write the steps to construct a frequency distribution table. The steps to create a cumulative frequency distribution table are mentioned below -

Therefore, the steps to construct a cumulative frequency distribution table are mentioned above.

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The range of possible values for x is 4/11 < x < 8

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

Triangles = 2

On these triangles, we have the following angles

Angle 1 = 11x - 4

Angle 2 = 84

Angle 1 cannot exceed angle 2

So, we have

11x - 4 < 84

Add 4 to both sides

11x < 88

Divide

x < 8

Angle 1 cannot exceed be negative or 0

So, we have

11x - 4 > 0

Add 4 to both sides

11x > 4

Divide

x > 4/11

Hence, the range is 4/11 < x < 8

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According to question,

Given data,

A hospital director is told that 54% of the emergency room visitors are insured.

A sample of 120 patients  found that 60 were insured.

We know that,

To determine the percentage,

we have to divide the value by the total value and then multiply the resultant by 100,

Percentage formula

Is /of=%?100

Or

Part/whole=%/100

With the help of formula,

Part/sample of patient=%/100

60×100/120=50%

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Answer:

6x+6x2+3

Step-by-step explanation:

6x2+5x+1+x+2

Combine 5x and x to get 6x.

6x2+6x+1+2

Add 1 and 2 to get 3.

6x2+6x+3

Answer:

.

Step-by-step explanation:

sorry i hit my daily limit and i need more answers

Answer:

Based on the information provided, it does not seem like this game is fair. Since region 1 and region 2 are the same size, each player has an equal chance of winning, but since region 3 is significantly larger than the other regions, neither player has a high chance of winning. This means that one player could potentially win multiple times in a row just by luck, without the other player having a chance to catch up. In order for the game to be considered fair, the relative sizes of the regions should be such that each player has a roughly equal chance of winning.

Answer:

yes. they both have ⅓ chance of winning

Step-by-step explanation:

Answer: Measure less 90 degrees

Step-by-step explanation: Less than 90 degrees measure acute angle. 90 degrees in right corner. Obtuse corners are larger than 90 degrees

A)  A linear function that will yield the compensation y of the sales executive for a given amount of monthly sales x is;

B) The account executive's compensation for $90,000 in monthly sales is; $300

The general equation of a line in slope intercept form is;

y = mx + b

where;

m is slope

b is y-intercept

x and y are provided in the problem: x = monthly sales and y = compensation

We will have to find m (Slope), which represents the commission percentage, and b (y-intercept), which represents the the base salary.

    x₁        y₁         x₂        y₂      

(50000, 6500) (60000, 6800)

Slope;

m = (y₂ - y₁) / (x₂ - x₁)

m = (6800 - 6500) / (60000 - 50000)  

m = 300/10000

m = 3/100 = 0.03 = 3%

To find b, we have to take one of our ordered pairs [ (50000, 6500) or (60000, 6800) ] and plug it into the equation, y=mx+b.

Let's use (60000, 6800)

6800 = 0.03(60000) + b

6800 = 1200 + b  

b = 6800 - 1200

b = $5600

The base salary = $5600

The equation is y = 0.03x + 5600

b) For $90000 in monthly sales, the executive's compensation is;

y = 0.03(90000) + 5600

y = 2700 + 5600

y = $300

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following algorithms correctly updates the values, If num is less than the minimum, set the minimum equal to num. Otherwise, if num is greater than the maximum, set the maximum equal to num.

The game records the highest and lowest scores that were earned. This indicates that the game already has the highest and lowest score stored in its memory.

Now, if a new score, num, is achieved, the game must compare num with the minimum and maximum scores in order to update the minimum and maximum scores. The minimum score is updated to the score, num if the most recent score, num, is lower than the minimum score.

Additionally, the maximum score is updated to the score, num if the most recent score, num, is higher than the maximum score.

Complete Question :

A certain game keeps track of the maximum and minimum scores obtained so far. If num represents the most recent score obtained, which of the following algorithms correctly updates the values of the maximum and the minimum?

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Answer:

The value of the correlation coefficient is 0.87, which means there is a strong, positive association between discharge and speed. A positive correlation means that as one variable increases, the other variable also increases. In this case, as the discharge of the Colorado River increases, the speed of the river also increases. The strength of the association is indicated by the magnitude of the correlation coefficient, which ranges from -1 to 1. A value of 0.87 is considered a strong positive correlation, indicating that there is a strong relationship between the two variables.

Using percentages, we know that out of 20 people, 5 people that is 25% of the random sample consider themselves as republicans.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

So, we have a random sample of 20 people.

n = 20

And we also know that 25% of Americans identify themselves as republicans.

Then the number of republicans in 20 people would be:

20/100 * 25

.2 * 25

5

Therefore, using percentages, we know that out of 20 people, 5 people that is 25% of the random sample consider themselves as republicans.

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The value of variable x in the equation is x = -3y + 5/ 2

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Therefore, the equation 2x + 3y = 5 can be solved for x as follows:

We have to make x the subject of the formula in the equation.

Subject of the formula is the variable which is expressed in terms of other variables involved in the formula.

Hence,

2x + 3y = 5

subtract 3y from both sides of the equation

2x + 3y = 5

2x + 3y  - 3y = 5 - 3y

2x = 5 - 3y

divide both sides by 2

Therefore,

x = 5 - 3y / 2

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Emerson actually hit the ball 32% of times at bat.

What is percentage ?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

Since in Game 1, Emerson struck out 30 times in 90 times at bat;

in Game 2, he struck out 40 times in 120 times at bat;

in Game 3, Emerson struck out 42 times in 140 times at bat;

To determine what percentage of times at bat did Emerson actually hit the ball, the following calculation must be performed:

(30 + 40 + 42) / (90 + 120 + 140) = X

112/350 = X

0.32 = X

Therefore, Emerson actually hit the ball 32% of times at bat.

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The tangent AB is for circle in figure (a).The correct option is (a).

For a given circle there can only be one tangent at one point.

The tangent and the circle has only one point in common.

The tangent to a circle is always perpendicular to the radius at that point.

The tangent drawn to a circle is always at right angle to the radius at that point.

The given figures are examined one by one as follows,

(a) The sides of the triangle are given as 5, 12 and 13.

And, 13² = 5² + 12²

Which implies it is a right triangle by Pythagoras theorem.

(b) The sides of the triangle are given as 4, 10 and 11.

And, 11² ≠ 10² + 4²

Which implies it is not a right triangle by Pythagoras theorem.

(c) The sides of the triangle are given as 18, 25 and 18.

And, 25² ≠ 18² + 18²

Which implies it is not a right triangle by Pythagoras theorem.

Thus, only for figure (a) the criteria for the tangent satisfies.

Hence, the line segment AB is tangent to the circle given in figure (a).

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Answer:

This is a statement. Not a question.

Step-by-step explanation:

Answer:

124 and 228

Step-by-step explanation:

Two numbers will be presented as x and y

x + y = 352

x - y = 104

x + y + x - y = 352 + 104

2x = 456

Divide both side by 2

x = 228

x + y = 352

y = 352 - x

y = 352 - 228

y = 124

Given the graph of f(x), the range of f⁻¹(x) is; (−∞, 2) ∪ (2, ∞)

The range of a function is defined as the set that is composed by all the output values on a function. Thus, on the graph, the range of a function is composed by the values of y of the function.

For the inverse function, the input and the output are exchanged, and as such given the graph of a function, we can say that the range of the inverse function is given by the domain of the initial function, which is, the values of x of the graph of the original function.

From the description of the rational function, we are told that the asymptote is given as: x = 2

Thus, the domain of the graphed function, would be the same as the range of the inverse function,  will be given by the interval:

(−∞, 2) ∪ (2, ∞).

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The required inequality expressions are 7x + 7y ≤ 49 and x + 2y ≤ 13 an the graph has been plotted with clarity.

The expression for inequality can be written by taking the suitable sign for the given problem and then relating the variable part to the constant terms.

(a) Suppose the number of short film and full movie are x and y respectively.

Then, the inequality expression for the given case can be written as follows,

The inequality for money raised is,

7x + 7y ≤ 49

And, the inequality for script writing is,

x + 2y ≤ 13

(b) These inequalities can be graphed as follows,

Hence, for the given case the required system of inequalities is 7x + 7y ≤ 49 and x + 2y ≤ 13 and the graph for the solution is drawn properly.

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Let A be the amount of money invested at a 12% annual interest rate and B be the amount of money invested at a 8% annual interest rate.

We know that A = B + 1500, and the total interest earned by the two investments is $1880.

The interest earned by the investment at a 12% annual interest rate is 0.12 * A = 0.12A

The interest earned by the investment at a 8% annual interest rate is 0.08 * B = 0.08B

Therefore, we can write the following equation to represent the situation:

0.12A + 0.08B = 1880

Since A = B + 1500, we can substitute this into the equation to get:

0.12(B + 1500) + 0.08B = 1880

Solving for B, we get:

0.12B + 180 + 0.08B = 1880

Combining like terms, we get:

0.2B + 180 = 1880

Subtracting 180 from both sides, we get:

0.2B = 1700

Dividing both sides by 0.2, we get:

B = 8500

Since A = B + 1500, we can substitute this value into the equation to find the value of A:

A = 8500 + 1500 = 10000

Therefore, the investor invested $8,500 at an 8% annual interest rate and $10,000 at a 12% annual interest rate.

Answer:

Account A (12%)= $10,000

Account B (8% stock fund) = $8,500

Step-by-step explanation:

Annual Interest Formula

[tex]\large \text{$ \sf I=P\left(1+r\right)^{t} -P$}[/tex]

where:

Account A:

[tex]\implies \sf Interest=(x+1500) (1+0.12)^1-(x+1500)[/tex]

[tex]\implies \sf Interest=(x+1500) (1+0.12)-(x+1500)[/tex]

[tex]\implies \sf Interest=(x+1500)+0.12(x+1500)-(x+1500)[/tex]

[tex]\implies \sf Interest=0.12(x+1500)[/tex]

[tex]\implies \sf Interest=0.12x+180[/tex]

Account B (stock fund):

[tex]\implies \sf Interest=x (1+0.08)^1-x[/tex]

[tex]\implies \sf Interest=x (1+0.08)-x[/tex]

[tex]\implies \sf Interest=x+0.08x-x[/tex]

[tex]\implies \sf Interest=0.08x[/tex]

If the total interest from the two investments was $1880:

[tex]\implies \sf 0.12x+180+0.08x=1880[/tex]

[tex]\implies \sf 0.2x+180=1880[/tex]

[tex]\implies \sf 0.2x=1700[/tex]

[tex]\implies \sf x=8500[/tex]

Therefore, the money invested in each of the two accounts is:

Consequently, the rectangular garden's length is [tex]x^{2} +2x+2[/tex]

option D is correct

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. Surface area refers to an open surface or the perimeter of a three-dimensional object, whereas plane region or plane area refers to a shape or planar lamina.

given

the width(w) of the rectangular garden= [tex]x[/tex][tex]-2[/tex]

area of the rectangular garden = [tex]x^{3} -2x-4[/tex]

The area of a rectangle is,

area = length × width(w) ,

If l is the rectangle's length,

w is the width of the rectangle,

By substituting values,

[tex]x^{3}-2x-4[/tex] = ([tex]x-2[/tex]) *  length ( l )

[tex]l=\frac{x^{3}-2x-4 }{x-2}[/tex] = [tex]x^{2} +2x+2[/tex]   (by long division method)

Consequently, the rectangular garden's length is [tex]x^{2} +2x+2[/tex]

option D is correct

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All vectors of the form(a, b, a - 2b) is a subspace of R³. So, the correct option is option(D).

If W is a set of one or more vectors from a vector space V, then W is a subspace of V if and only if

Now, check the options and find out the option which satisfy the subspace conditions.

A) All the vectors are of form (0, a,a²)

let (0,1,1) = u and v=(0,2,4) and both are belongs to { 0, a,a² : a∈R }, (0,0,0)∈ {0, a,a² : a∈R }.

u + v = (0,1,1) + (0,2,4) = (0,3, 5) not belongs to

{ 0, a,a² : a∈R }. So, this is not correct option.

B) Here, (0,0,0) does not belongs to

{0, a, a+2 : a∈R } because if a= 0 then a+2 =/ 0 .

So, it is also not subspace.

C) All vectors of the form (a, b, 2)

The third tuple is 2 which never be equal to zero. Hence, (0,0,0) does not belongs to (a, b, 2) and it is not form subspace.

D) All vectors of the form (a, b, a - 2b)

When a = 0 , b = 0 => (0,0,0) ∈(a, b, a - 2b)

let u = ( a1, b1 , a1- 2b1) and v = ( a₂, b₂ , a₂ - 2b₂)

and α∈R

u + v = ( a₁, b₁ , a₁- 2b₁ ) + ( a₂, b₂ , a₂ - 2b₂)

= ( a₁ +a₂ , b₁+b₂ , a₁+a₂ -2(b₁ - b₂)) €(a, b, a - 2b)

αu = α(a₁ , b₁ , a₁- 2b₁)

=( αa₁ , αb₁ , α(a₁ - 2b₁))∈(a, b, a - 2b)

both the conditions are satisfied, so it is Subspace of R³.

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Using combination we get  20475 teams can made up of 3 girls and 2 boys and 37128  teams can be selected with at least 3 girls.

Since this is just a team of 5 children,

we have   no of girls = 15

No of boys = 10

teams made up of 3 girls and 2 boys

girls out of 3 girls can be selected in  ¹⁵C₃ ways and

2 boys out of 10 boys can be selected in  ¹⁰C₂  ways.

[tex]\implies[/tex] ¹⁵C₃ X  ¹⁰C₂

= 455*45 =20475 Ways

Teams can be selected with at least 3 girls

It is the probability of at least 3 girls which means P(3 girls,2 boys) or P(4 girls,1 boy) or P(5 girls, 0 boys)

[tex]\implies[/tex] ¹⁵C₃ X  ¹⁰C₂  + ¹⁵C₄ X  ¹⁰C₁ + ¹⁵C₅ X  ¹⁰C₀

= 455 * 45 +1365*10+3003*1

=20475 +13650 +3003

=37128 ways

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