12 in is 1 ft, 5 in is ~0.41 ft, 13 in is ~1.08 ft

16 oz is 1 lb, 9 oz is ~0.56 lbs, 18 oz is ~1.13 lbs

Write an equation for the absolute value function below:

The **absolute value **equation represented in the **graph **is

|x + 3|

What is absolute value?Without taking direction into account, **absolute value **describes how far away from zero a certain number is on the number line.

A number can never have a negative **absolute value**.

The equation is written in the form below

|x|

The a transformation which involves a translation of 3 units to the left took place. the transformation rule for 3 units to the left is addition of 3, hence we have the equation

|x + 3|

We can therefore conclude that the **absolute value **equation of the function is |x + 3|

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when conducting a study comparing more than two groups of parametric (normally distributed) data, which of the following statistical tests should be used? g

**Answer:**

.

**Step-by-step explanation:**

sorry i hit my daily limit and i need more answers

Jen drew a scale drawing of a summer camp

**Answer:**

This is a statement. Not a question.

**Step-by-step explanation:**

An investor decides to invest some cash in an account paying12%

annual interest, and to put the rest in a stock fund that ends up earning 8%over the course of a year. The investor puts $1500more in the first account than in the stock fund, and at the end of the year finds the total interest from the two investments was $1880. How much money was invested at each of the two rates? Round to the nearest integer.

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:

I = Interest.P = Principal amount.r = Interest rate (in decimal form).t = Time (in years).Account A:

P = x + 1500r = 12% = 0.12t = 1 year[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):

P = xr = 8% = 0.08t = 1 year[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:

Complete the following.

(a) Consider the following statement.

The water temperature is 70.

Check all the statements below that are negations of this statement.

The water temperature is less than 80.

It is not the case that the water temperature is 70.

The water temperature is not 70.

(b) Consider the following conditional statement.

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

What is the conclusion of this statement?

It is not true that Keisha owns a dress.

Keisha likes the dress.

The dress is red.

Keisha loves the dress.

The dress likes Keisha.

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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Solve the proportion using cross products. Round to the nearest hundredth if necessary.

12Miles/27hours=4miles/Xhours

A. 28

B. 12

C. 9

D. 18

**Answer:**

C) x = 9

**Step-by-step explanation:**

[tex]\frac{12}{27}[/tex] = [tex]\frac{4}{x}[/tex]

[tex]\frac{12}{27}[/tex] ÷ [tex]\frac{3}{3}[/tex] = [tex]\frac{4}{9}[/tex] This is the fraction simplified

[tex]\frac{4}{9}[/tex] = [tex]\frac{4}{x}[/tex] Simplified, I think that it is easier to see that x = 9

if the circumference of a circle is 5cm, then the diameter is ____cm.

a. 5 cm

b. 31.4 cm

c. 15.7 cm

d. 1.57 cm

Let’s start with the circumference of a circle formula and solve for “d” (diameter):

C=2πr

The circumference, “C,” is 5cm

5=2πr

Let’s rewrite the formula using the commutative property of multiplication so we can solve for “d:”

5=π2r

The order in which numbers are multiplied does not affect the product. Since the diameter is double the radius, 2r will equal the diameter since 2r equals r+r. So, we can substitute “d” in for 2r:

5=πd

Now, let’s solve for d

Divide both sides by pi:

5/π=d

1.591=d

We can check this back into the formula:

C=π(1.591)

C=4.998

So, your answer is 1.57 since it is the closest.

C=2πr

The circumference, “C,” is 5cm

5=2πr

Let’s rewrite the formula using the commutative property of multiplication so we can solve for “d:”

5=π2r

The order in which numbers are multiplied does not affect the product. Since the diameter is double the radius, 2r will equal the diameter since 2r equals r+r. So, we can substitute “d” in for 2r:

5=πd

Now, let’s solve for d

Divide both sides by pi:

5/π=d

1.591=d

We can check this back into the formula:

C=π(1.591)

C=4.998

So, your answer is 1.57 since it is the closest.

What values of v and w make Δ P Q R ≅ Δ K J I ?

v=_____

w=_____

The **values** of v and w that will make ΔPQR **congruent** to ΔKJI are:

v = 12; w = 20.

What are Congruent Triangles?Based on the **CPCTC**, every corresponding sides and corresponding angles of two **congruent triangles** are equal to each other.

Therefore, given that ΔPQR ≅ ΔKJI

PR = KI, and QR = JI

Substitute the **values**:

5v = 6v - 12

5v - 6v = -12

-v = -12

v = 12

w - 1 = 3w - 41

w - 3w = 1 - 41

-2w = -40

w = -40/-2

w = 20

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Which of the following is a subspace of R^3? (A) All vectors of the form(0, a, a^2), (B) All vectors of the form(a+2, a, 0), (C) All vectors of the form (a, b, 2), (D) All vectors of the form(a, b, a-2b)

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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NO LINKS!!

Find the average rate of change of the function from x1 to x2.

function f(x) = -9x + 4

x-values x1 = -5, x2 = 0

**Answer:**

-9

**Step-by-step explanation:**

Given function:

[tex]f(x)=-9x+4[/tex]

Given x-values:

x₁ = -5x₂ = 0**Calculate **the value of the **function **for the two given **values of x**:

[tex]\begin{aligned}\implies f(x_1)&=-9(-5)+4\\&=45+4\\&=49\end{aligned}[/tex]

[tex]\begin{aligned}\implies f(x_2)&=-9(0)+4\\&=0+4\\&=4\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Average rate of change of function $f(x)$}\\\\$\dfrac{f(b)-f(a)}{b-a}$\\\\over the interval $a \leq x \leq b$\\\end{minipage}}[/tex]

As -5 < 0:

a = x₁ = -5b = x₂ = 0Therefore:

[tex]\begin{aligned} \implies \textsf{Average rate of change}&=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}\\\\&=\dfrac{4-49}{0-(-5)}\\\\&=\dfrac{-45}{5}\\\\&=-9\end{aligned}[/tex]

Rory is an independent filmmaker and has great ideas for several movies. For each short film or full-length movie she makes, she has to raise money. She figures that it will take 7 months to raise money for each short film and 7 months to raise money for each full-length movie. She has given herself at most 49 months to raise money for the films before she abandons the project.

1

While Rory is raising money, she also has to write the scripts. It will take her of a month to write each short film script and 2 months to write each full-length movie script. She is committed to spending at most 13 months on writing scripts.

a. What is the system of inequalities that models this scenario?

b. What is the graph of the solutions?

continued

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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Solve:(6x^2+5x+1)÷(x+2)

**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**

*What two numbers have a sum of 352 and a difference of 104?

**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

A dance teacher divides 5 dance classes into 6 equal groups. Each dance class has 18 students. How many dance students are in each group

First, multiply [tex]18*5 = 90[/tex]

Then, divide [tex]90 / 6 = 15[/tex]

Therefore, each group has 15 students.

what is a acute angle

**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

An account executive receives a base salary plus a commission. On $50,000 in monthly sales, the account executive receives $6500. On $60,000 in monthly sales, the account executive receives $6800.

(a) Determine a linear function that will yield the compensation y of the sales executive for a given amount of monthly sales x.

(b) Use this model to determine the account executive's compensation for $90,000 in monthly sales.

$

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

How to model a linear equation?

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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Convergence or Divergence? Prove using a test.

Lim. (√1+2/n / 2+1/n+1/n^2)

√1+2•0/2+0+0

1/2

N—> ∞

Converges

√1+2•0/2+0+0

1/2

N—> ∞

Converges

Given the graph of f(x), determine the range of f−1(x).

Rational function with one piece decreasing from the left in quadrant 2 asymptotic to the line y equals 3 and passing through the point 0 comma 2 and asymptotic to the line x equals 2 and another piece decreasing from the left in quadrant 1 asymptotic to the line x equals 2 passing through the point 4 comma 4 asymptotic to the line y equals 3.

ℝ

(2, ∞)

(−∞, 2) ∪ (2, ∞)

(−∞, 3) ∪ (3, ∞)

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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A quiz team of 5 children is to be selected from a class of 25 children. There are 15 girls and 10 boys in the class. (a) How many teams made up of 3 girls and 2 boys can be selected? (b) How many teams can be selected with at least 3 girls?

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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Neglecting air resistance and the weight of the propellant, determine the work done in propelling a 10-ton satellite to a height of 200 miles above Earth. Assume that the Earth has a radius of 4000 miles. O 4.190.48 mi-ton 1,142.86 mi-ton O 1,904.76 mi-ton 2,857.14 mi-ton 1,523.81 mi-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.

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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-16(d + 1) = -21 solve for d

**Step-by-step explanation:**

To solve the equation -16(d + 1) = -21 for d, we can first use the distributive property to expand the expression -16(d + 1):

-16(d + 1) = -16d - 16

Then, we can set the two sides of the equation equal to each other and solve for d:

-16d - 16 = -21

-16d = -5

d = 5/16

Therefore, the value of d that satisfies the equation -16(d + 1) = -21 is d = 5/16.

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.

What percentage of times at bat did Emerson actually hit the ball?

%

**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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It is known that 25 % percent of Americans identify themselves as republican . In a random sample of n=20 Americans , what is the expected number of republicans ? It is known that 25 % percent of Americans identify themselves as republican . In a random sample of n=20 Americans , what is the standard deviation of the number of republicans ? ( Round to 2 decimal places )

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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can I get help with this practice I'm having a lot of trouble with this can I get some help

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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For each diagram below, work out whether AB is a tangent to the circle, is not a

tangent to the circle, or if it is not possible to tell.

Justify your answers.

13 cm

5 cm

12 cm

10 cm

4 cm

11 cm

18 cm

18 cm

25 cm

Not drawn accurately

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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2. The width, w, of a rectangular garden is x-2. The area of the garden is ³-2x-4. What is

an expression for the length of the garden?

Ox²-2x-2

Ox²+2x-2

Ox²-2x+2

Ox²+2x+2

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

option D is correct

what is area?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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Question 1-28

What is the range of possible values for x?

B

A

8.2

11.7

(11x-4)

D

84°

C

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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A hospital director is told that 54% of the emergency room visitors are insured. The director wants to test the claim that the percentage of insured patients is under the expected percentage. A sample of 120 patients found that 60 were insured. Find the value of the test statistic. Round your answer to two decimal places.

**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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NO LINKS!!

Use the properties to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive)

1. ln((xy)^5)

2. ln (seventh root(t))

3. ln (√x²/y^5)

*Properties of log:*

**Evaluate given using the properties above:**

Q1

[tex]ln((xy)^5) = 5ln(xy) = 5(ln x + ln y) = 5\ ln\ x + 5\ ln\ y[/tex]Q2

[tex]ln(\sqrt[7]{t} ) = ln(t^{1/7})=1/7\ ln\ t[/tex]Q3

[tex]ln(\sqrt{x^2}/y^5)=ln(x/y^5)= ln\ x - ln\ y^5 = ln\ x - 5\ ln\ y[/tex]**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]

Question 1Apply 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]

Question 2[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]

Question 3It 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]

Emma wrote 8.4x+6.3x+12.6 as an equivalent expression for 4.2(2x+1.5x+3). She said that her equivalent expression is simplified. Do you agree? Explain.

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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