b) [(p → q) ∧ (q → r)] → (p → r)

To show that the** conditional statement **[(p → q) ∧ (q → r)] → (p → r) is a tautology without using truth tables, we can use a logical proof known as the** Law of Implication.**

To show that the conditional statement [(p → q) ∧ (q → r)] → (p → r) is a tautology without using truth tables, we can employ a **logical proof **known as a direct proof.

First, let's assume that the antecedent, [(p → q) ∧ (q → r)], is true.

This means that both (p → q) and (q → r) are true simultaneously.

Using the definition of implication, (p → q) can be written as (~p ∨ q) and (q → r) can be written as (~q ∨ r).

So we have (~p ∨ q) ∧ (~q ∨ r) as the conjunction of the two implications.

Now, we need to prove that (p → r) is also true.

Using the definition of implication, (p → r) can be written as (~p ∨ r).

To show that (p → r) is true, we need to prove that ~p ∨ r is true.

We can do this by considering the two cases:

If ~p is true, then ~p ∨ r is true regardless of the truth value of r.

If ~p is false, then p is true, and since (p → q) and (q → r) are both true, q and r must also be true.

Thus, ~p ∨ r is true.

In both cases, ~p ∨ r is true, which means (p → r) is true.

Since both the antecedent [(p → q) ∧ (q → r)] and the **consequent **(p → r) are true, we can conclude that the conditional statement [(p → q) ∧ (q → r)] → (p → r) is a tautology.

Therefore, using a direct proof, we have shown that the given conditional statement is always true and satisfies the definition of a tautology.

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In The figure below, what are m<1,m<2,m<3,m<4? Give reasons for each one

The **measure** of unknown angles,

∠1 = ∠4 = 110 degree

∠2 = ∠3 = 70 degree

Labeling the figure,

Then from figure we have,

⇒ x + 40 + x = 180

⇒ 2x + 40 = 180

**Subtract **40 both sides,

⇒ 2x = 140

**Divide** both sides by 2

⇒ x = 70

From figure,

⇒ ∠1 + 70 = 180

⇒ ∠1 = 180 - 70

⇒ ∠1 = 110 degree

And from figure,

⇒ ∠1 + ∠2 = 180

⇒ 110 + ∠2 = 180

⇒ ∠2 = 70 degree

Since,

∠2 = ∠3 = 70 degree

And ∠1 = ∠4 = 110 degree

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Two math students were asked to write an exponential growth equation that had a starting value of 300 and a growth rate of 2%. Pierre thinks the answer is y=300(1.02)^x and Scott thinks that the answer is y=300(1.2)^x. Are either of them right and why?

Incorrect, the correct **exponential** growth equation as it accurately represents a starting value of 300 and a growth rate of 2%. Scott's equation

Neither Pierre nor Scott has the correct exponential growth equation.

The exponential growth **equation **represents a relationship where a quantity increases or grows exponentially over time. It is typically represented as y = a(1 + r)^x, where "a" represents the initial or starting value, "r" represents the growth rate (expressed as a decimal), "x" represents the time or number of periods, and "y" represents the resulting value after the growth.

In this case, Pierre's equation is y =[tex]300(1.02)^x.[/tex]This equation suggests a growth rate of 2% (0.02 as a decimal), which means that the quantity would increase by 2% with each **period**. This aligns with the given growth rate of 2%. Thus, Pierre's equation is correct.

On the other hand, **Scott's **equation is y = [tex]300(1.2)^x[/tex]. This equation suggests a growth rate of 20% (0.2 as a decimal), which means that the quantity would increase by 20% with each period. However, the given growth rate is 2%, not 20%. Therefore, Scott's equation is incorrect.

To summarize, Pierre's equation, y = 300(1.02)^x, is the correct exponential growth equation as it **accurately** represents a starting value of 300 and a growth rate of 2%. Scott's equation, y = 300(1.2)^x, does not match the given growth rate and is therefore incorrect.

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Please help me solve this

There is 90% confidence that the **population mean **number of books people read is **between **11.55 and 13.25.

To construct a 90% **confidence interval **for the mean number of books people read, we can use the following formula:

Confidence Interval = x ± (Z * (s / √n))

Where:

x = sample mean (12.4 books)

s = sample standard deviation (16.6 books)

n = sample size (1017)

Z = Z-score

Since the **sample size **is large (n > 30), we can assume the sampling distribution is approximately normal.

We can use the standard normal **distribution **to find the Z-score for a 90% confidence level.

The Z-score for a 90% confidence level is approximately 1.645.

Now we can calculate the confidence interval:

Confidence Interval = 12.4 ± (1.645 (16.6 / √1017))

Confidence Interval ≈ 12.4 ± (1.645 (16.6 / √1017))

Confidence Interval ≈ 12.4 ± (1.645 (16.6 / 31.95))

Confidence Interval ≈ 12.4 ± (1.645 x 0.518)

Confidence Interval ≈ 12.4 ± 0.85

There is 90% confidence that the **population mean **number of books people read is **between **11.55 and 13.25.

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The size of a rectangular television screen is usually given by its diagonal measurement. If a flat television screen is 20 inches high and 25 inches wide, what is its size rounded to the nearest inch?

**Answer:**

32 inches Aprox

**Step-by-step explanation:**

To find the size of a rectangular television screen given its height and width, we can use the Pythagorean theorem. The diagonal measurement (size) is the hypotenuse of a right triangle formed by the height and width.

Given:

Height of the television screen (h) = 20 inches

Width of the television screen (w) = 25 inches

Using the Pythagorean theorem:

diagonal² = height² + width²

diagonal² = 20² + 25²

diagonal² = 400 + 625

diagonal² = 1025

Taking the square root of both sides:

diagonal ≈ √1025

diagonal ≈ 32.02

Rounding to the nearest inch, the size of the television screen is approximately 32 inches.

Therefore, the size of the rectangular television screen, rounded to the nearest inch, is 32 inches.

I have 12 teams that will play each other once, but have activities that each team will only play once. How many weeks and activities do I need.

==============================================

Explanation:

The formula to use is n*(n-1)/2

Plug in n = 12 to get 12*(12-1)/2 = 12*11/2 = 132/2 = **66**

That formula is from the nCr combination formula when r = 2.

---------------------

Here's a visual way to see why that rule works.

Imagine there are only 4 teams. We'll make a table that has 4 rows and 4 columns. The team names are A,B,C,D.

[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & & & & \\\cline{1-5}B & & & & \\\cline{1-5}C & & & & \\\cline{1-5}D & & & & \\\cline{1-5}\end{array}[/tex]

In the table, cross out the cells where one team pairs up with itself. That's along the main diagonal pointing to the northwest (or southeast).

[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & & X & & \\\cline{1-5}C & & & X & \\\cline{1-5}D & & & & X\\\cline{1-5}\end{array}[/tex]

Let's also cross out any cell below the main diagonal.

[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & X & X & & \\\cline{1-5}C & X & X & X & \\\cline{1-5}D & X & X & X & X\\\cline{1-5}\end{array}[/tex]

We do this because a mirrored copy is found above the diagonal.

We started with 4*4 = 16 cells. Then subtracted off the diagonal to get 16-4 = 12 cells left over. Then divide in half because we crossed off the lower half to get 12/2 = 6 different matchups among the 4 teams.

Those 6 matchups are:

A vs BA vs CA vs DB vs CB vs DC vs DThe order doesn't matter. A matchup like "A vs B" is the same as "B vs A".

We'll take this concept to extend it to n teams. We have n*n = n^2 cells to start with. Subtract off the n cells along the diagonal to get n^2-n = n(n-1) cells remaining.

Then we split that in half to get the formula n(n-1)/2.

you will have a total of 66 games (12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1).

If you have 66 games and each game is an activity that each team will play once, then you will need 66 activities.

If you want each team to have only one activity per week, then you will need 66 weeks to complete all the activities.

If you have 66 games and each game is an activity that each team will play once, then you will need 66 activities.

If you want each team to have only one activity per week, then you will need 66 weeks to complete all the activities.

I have 7/4 green counters, and 24 yellow counter, so how much green counters will i have

**Answer: the question doesn't give that much information but you would have 7/4 or 1.75 green counters.**

**Step-by-step explanation: 7/4 as a decimal is 1.75**

This number pattern -1:5 ;x; 35 ; ...

Is a quadratic number pattern.

a) Calculate x

b) Hence, or otherwise, determine the nth term of the sequence.

This sequence 4;9; x; 37; .... is a quadratic sequence.

a) Calculate x

b) Hence, or otherwise, determine the nth term of the sequence.

**Answer:**

[tex]\textsf{a)} \quad x = 17[/tex]

[tex]\textsf{b)} \quad T_n=3n^2-3n-1[/tex]

[tex]\textsf{a)} \quad x = 20[/tex]

[tex]\textsf{b)} \quad T_n=3n^2-4n+5[/tex]

**Step-by-step explanation:**

Given **quadratic number pattern**:

To find the equation for the **nth term**, we can use the general form of a **quadratic equation**:

[tex]\boxed{T_n=an^2 + bn + c}[/tex]

where **n** is the **position **of the term.

Let's **substitute **the **values **of T₁, T₂ and T₄ into the **quadratic equation**: to create three equations:

[tex]\begin{aligned}T_1=a(1)^2+b(1)+c&=-1\\a+b+c&=-1\end{aligned}[/tex]

[tex]\begin{aligned}T_2=a(2)^2+b(2)+c&=5\\4a+2b+c&=5\end{aligned}[/tex]

[tex]\begin{aligned}T_4=a(4)^2+b(4)+c&=35\\16a+4b+c&=35\end{aligned}[/tex]

Rearrange the first equation to **isolate c**:

[tex]c=-a-b-1[/tex]

Substitute this into the second and third equations:

[tex]\begin{aligned}4a+2b+(-a-b-1)&=5\\3a+b&=6\end{ailgned}[/tex]

[tex]\begin{aligned}16a+4b+(-a-b-1)&=35\\15a+3b&=36\end{ailgned}[/tex]

**Solve **the **equations simultaneously** by rearranged the first equation to isolate b and substituting this into the second equation and solving for a:

[tex]b=-3a+6[/tex]

[tex]\begin{aligned}15a+3(-3a+6)&=36 \\15a-9a+18&=36\\6a&=18\\a&=3 \end{aligned}[/tex]

**Substitute **the found **value of a **into the **equation for b** and **solve for b**:

[tex]\begin{aligned}b&=-3a+6\\&=-3(3)+6\\&=-9+6\\&=-3\end{aligned}[/tex]

Finally, **substitute **the found **values of a and b **into the **equation for c** and **solve for c**:

[tex]\begin{aligned}c&=-a-b-1\\&=-3-(-3)-1\\&=-3+3-1\\&=-1\end{aligned}[/tex]

Therefore, the **equation **for the **nth term **is:

[tex]\boxed{T_n=3n^2-3n-1}[/tex]

The** value of x** is the **3rd term**. Therefore, to find the value of x, **substitute n = 3** into the equation for the** nth term**:

[tex]\begin{aligned}T_3&=3(3)^2-3(3)-1\\&=3(9)-3(3)-1\\&=27-9-1\\&=18-1\\&=17\end{aligned}[/tex]

Therefore, the **value of x** is **17**.

[tex]\hrulefill[/tex]

Given **quadratic number pattern**:

To find the equation for the **nth term**, we can use the general form of a **quadratic equation**:

[tex]\boxed{T_n=an^2 + bn + c}[/tex]

where **n** is the **position **of the term.

Let's **substitute **the **values **of T₁, T₂ and T₄ into the **quadratic equation**: to create three equations:

[tex]\begin{aligned}T_1=a(1)^2+b(1)+c&=4\\a+b+c&=4\end{aligned}[/tex]

[tex]\begin{aligned}T_2=a(2)^2+b(2)+c&=9\\4a+2b+c&=9\end{aligned}[/tex]

[tex]\begin{aligned}T_4=a(4)^2+b(4)+c&=37\\16a+4b+c&=37\end{aligned}[/tex]

Rearrange the first equation to **isolate c**:

[tex]c=-a-b+4[/tex]

Substitute this into the second and third equations:

[tex]\begin{aligned}4a+2b+(-a-b+4)&=9\\3a+b&=5\end{ailgned}[/tex]

[tex]\begin{aligned}16a+4b+(-a-b+4)&=37\\15a+3b&=33\end{ailgned}[/tex]

**Solve **the **equations simultaneously** by rearranged the first equation to isolate b and substituting this into the second equation and solving for a:

[tex]b=-3a+5[/tex]

[tex]\begin{aligned}15a+3(-3a+5)&=33 \\15a-9a+15&=33\\6a&=18\\a&=3 \end{aligned}[/tex]

**Substitute **the found **value of a **into the **equation for b** and **solve for b**:

[tex]\begin{aligned}b&=-3a+5\\&=-3(3)+5\\&=-9+5\\&=-4\end{aligned}[/tex]

Finally, **substitute **the found **values of a and b **into the **equation for c** and **solve for c**:

[tex]\begin{aligned}c&=-a-b+4\\&=-3-(-4)+4\\&=-3+4+4\\&=5\end{aligned}[/tex]

Therefore, the **equation **for the **nth term **is:

[tex]\boxed{T_n=3n^2-4n+5}[/tex]

The** value of x** is the **3rd term**. Therefore, to find the value of x, **substitute n = 3** into the equation for the** nth term**:

[tex]\begin{aligned}T_3&=3(3)^2-4(3)+5\\&=3(9)-4(3)+5\\&=27-12+5\\&=15+5\\&=20\end{aligned}[/tex]

Therefore, the **value of x** is **20**.

2. Consider this dilation.

Pre-image

9 cm

B

Image

3 cm B

(a) Find the scale factor. Show your work. (5 points)

(2- a.) Scale factor= Image length

Pre-image length

1/3.

Explanation:

The scale factor is the ratio of the image length to the pre-image length.

Scale factor = Image length / Pre-image length

In this case, the image length is 3 cm and the pre-image length is 9 cm.

Scale factor = 3 cm / 9 cm = 1/3

Explanation:

The scale factor is the ratio of the image length to the pre-image length.

Scale factor = Image length / Pre-image length

In this case, the image length is 3 cm and the pre-image length is 9 cm.

Scale factor = 3 cm / 9 cm = 1/3

The line r represents f ( x ) = x − 4 3 . Therefore, the line that represents f - 1 is and f - 1 ( x ) = x + .

Given statement solution is :- The **Inverse** line that represents [tex]f^(-1[/tex]) is [tex]f^(-1)[/tex] (x) = 3x + 4.

To find the inverse function of f(x) = (x - 4)/3, we need to swap the roles of x and y and solve for y. Let's start by writing the** equation** with y instead of f(x):

y = (x - 4)/3

Now, let's **interchange** x and y:

x = (y - 4)/3

To solve for y, we can isolate it by multiplying both sides of the equation by 3:

3x = y - 4

Next, let's add 4 to both sides:

3x + 4 = y

Finally, we can write the inverse function as:

[tex]f^(-1)(x)[/tex] = 3x + 4

So, the **Inverse** line that represents [tex]f^(-1[/tex]) is [tex]f^(-1)[/tex] (x) = 3x + 4.

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Given the diagram below, determine the measure of angles A, B, and C.

Hello!

A = 115° => opposite

B = 115° => corresponding angles

C = 65° => 180° - 115°

**Answer:**

A = 115 degrees

B = 115 degrees

C = 65 degrees

**Step-by-step explanation:**

A is opposite of 115 so it is 115 degrees.

B is 115 because it is on a parellel line to the one of 115

C is 180 minus B, which is 180 - 115 = 65

Question 10 (1 point)

A

33

7 in.

B

C

The **value **of AB is,

⇒ AB = 5.9

(**rounded **to nearest tenth)

We have to given that,

A **right triangle** ABC is shown.

Now, By **trigonometry **formula,

we get;

⇒ cos 33° = Base / Hypotenuse

Substitute all the values, we get;

⇒ cos 33° = AB / 7

⇒ 0.84 = AB / 7

⇒ AB = 0.84 × 7

⇒ AB = 5.88

⇒ AB = 5.9

(rounded to nearest tenth)

Thus, We get;

AB = 5.9

(rounded to nearest tenth)

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d) Suppose you begin making a monthly payment of $75.00. Fill in the table.

Month Current balance

1

2

3

4

5

6

7

8

9

10

11

12

WYPIE

$2750.00

Interest

$45.38

Payment

$75.00

$75.00

$75.00

$75.00

$75.00

$75.00

$75.00

$75.00

$75.00

$75.00

$75.00

$75.00

Amount applied to principal

$29.62

**Answer:**

**Step-by-step explanation:**

**Answer:**

**For month 1, the current balance is $2750.00, the interest is $45.38, and the payment is $75.00. The amount applied to principal is $29.62.**

**For the remaining months, the interest and payment amount will stay the same, but the current balance and amount applied to principal will change based on the previous month's numbers. **

**Point of view:**

**Here's your answer but I prefer you to focus and study hard because school isn't that easy. But i'm glad I could help you!**

**:)**

The top of a kitchen table measures 160cm by 90cm. A beetle walks diagonally across the table from one corner to the other. Calculate how far the beetle walks.

**Answer: To calculate the distance the beetle walks diagonally across the table, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.**

**In this case, the two sides of the right triangle formed by the table are 160 cm and 90 cm. Let's call the hypotenuse (the distance the beetle walks) "d."**

**So, applying the Pythagorean theorem, we have:**

**d^2 = 160^2 + 90^2**

**Simplifying:**

**d^2 = 25600 + 8100**

**d^2 = 33700**

**Taking the square root of both sides:**

**d ≈ √33700**

**d ≈ 183.54 cm**

**Therefore, the beetle walks approximately 183.54 cm diagonally across the kitchen table.**

Use a table of values to graph the following exponential function. (see attachment)

y= 2^x

Please graph

By using the **table** of values, a **graph** of the exponential function is shown in the image below.

In Mathematics and Geometry, an **exponential function** can be modeled by using this mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

a represents the initial value or y-intercept.x represents x-variable.b represents theBased on the information provided above, we can logically deduce the following **exponential function**;

[tex]y = 2^x[/tex]

Next, we would create a **table** of values based on the **exponential function**;

when x = 0, the y-value is given by;

y = 2⁰

y = 1

when x = 1, the y-value is given by;

y = 2¹

y = 2

x y____

-2 0.25

-1 0.5

0 1

1 2

2 4

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Please answer: h^-1(x) for this question

All the **solutions **are,

g⁻¹ = { (7, - 7), (- 7, - 6), (6, - 1), (9, 3) }

h⁻¹ (x) = 5x - 13

⇒ (h⁻¹ о h ) (- 3) = 3

We have to given that,

**Functions **g and f are defined as,

g = {(- 7, 7), (- 6, - 7), (- 1, 6), (3, 9)

And, h (x) = (x + 13) / 5

Now, We can simplify for i**nverse function **as,

For inverse function of g,

g = {(- 7, 7), (- 6, - 7), (- 1, 6), (3, 9)

g⁻¹ = { (7, - 7), (- 7, - 6), (6, - 1), (9, 3) }

And, **Inverse **function of h is,

h (x) = (x + 13) / 5

y = (x + 13) / 5

Solve for x,

5y = x + 13

x = 5y - 13

h⁻¹ (x) = 5x - 13

So, We get;

⇒ (h⁻¹ о h ) (- 3)

⇒ (h⁻¹ (h (- 3))

⇒ (h⁻¹ (- 3 + 13)/5)

⇒ (h⁻¹ (2))

⇒ 5 (2) - 13

⇒ 10 - 13

⇒ - 3

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100 Points! Geometry question. Photo attached. Find x in the right triangle. Please show as much work as possible. Thank you!

**Answer:**

x = 12

**Step-by-step explanation:**

sin45 = x/17 (sin = opposite/hypotenuse)

x = (sin45)(17) = 12.02 ≈ 12

there's 240 candy bars 1/4 of candy bars are snickers 1/3 of the candy bars are twix 1/8 of the candy bars are hershey. how many candy bars are Mars? explain not with a lot of words but in numbers please.

**Answer:**

1/4+1/3+1/8

=17/24

subtract from 1**Step-by-step explanation:**

1-17/24

=7/24

multiply with the total number of candy7/24×240

=70

A jug contains 36 fluid ounces of apple juice. How many pints of apple juice does the jug contain?

**Answer: There are 16 fluid ounces in 1 pint. To determine the number of pints in the jug, we need to divide the total number of fluid ounces by 16.**

**Given that the jug contains 36 fluid ounces of apple juice, we divide 36 by 16:**

**36 fluid ounces ÷ 16 fluid ounces/pint = 2.25 pints**

**Therefore, the jug contains 2.25 pints of apple juice.**

50 Points! Multiple choice geometry question. Photo attached. Thank you!

**This is a simple one.**

**All you need to do is find the scale factor of the shapes. (How much has it decreased by?)**

**Wecan find this by doing 15 ÷ 20 (not the other way round because we want to find the scale factor for the bigger rectangle to the smaller)**

**15 ÷ 20 = 0.75**

**So to find the area all you need to do is times the area with the scale factor which is 0.75**

**500 x 0.75 = 375cm²**

**So the answer is**

**(A) 375cm²**

The answer is b)375m2

50 Points! Multiple choice geometry question. Photo attached. Thank you!

The **value of x** in triangle STU is given as follows:

**b) **8.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the **hypotenuse**, which is the longest side, is equals to the sum of the squares of the lengths of the other two sides.

Hence the **equation **for the theorem is given as follows:

c² = a² + b².

In which:

c > a and c > b is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.Applying the Pythagorean Theorem for this problem, the **value of x** is obtained as follows:

x² + 15² = 17²

x² = 17² - 15²

x² = 64.

x = 8.

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(a) Dewi has £460 to buy Chinese yuan.

Calculate

.

the maximum number of CYN Dewi can buy, and

how much, to the nearest penny, this will cost him.

The **maximum** number of CYN Dewi can **buy** is 4268.8 CYN and cost in pounds is £453.20.

**Maximum** number of CYN Dewi can buy:

Since £1 buys 9.28 CYN, Dewi's £460 can be converted to Chinese yuan by multiplying it by the** exchange rate**:

Maximum CYN = £460 × 9.28 CYN/£1

To calculate this, we multiply the pound amount by the exchange rate:

**Maximum** CYN = £460 × 9.28 CYN/£1 ≈ 4268.8 CYN

Cost in pounds to the nearest penny:

To calculate the cost in pounds, we divide the desired amount of Chinese yuan by the exchange rate:

Cost in pounds = 4268.8 CYN ÷ 9.42 CYN/£1

To calculate this, we **divide** the Chinese yuan amount by the exchange rate:

Cost in pounds = 4268.8 CYN ÷ 9.42 CYN/£1

= £453.20

Therefore, the cost in pounds, to the nearest penny, will be £453.20.

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Complete question

Buying chinese yuan (CYN) £1 buys 9.28 CYN

Selling chinese yuan (CYN) 9.42 CYN buys £1

(a) Dewi has £460 to buy Chinese yuan.

Calculate the maximum number of CYN Dewi can buy, and

how much, to the nearest penny, this will cost him.

Which graph represents the solution set to the system of inequalities?

Y ≤ 2X+2

1/2X + Y <7

Y- 3 ≥ 0

ANSWER is Down Below

The solution set to the system of **inequalities** will be the overlapping region or the intersection of the shaded regions from all three inequalities.

The system of inequalities consists of three inequalities:

y ≤ 2x + 2

(1/2)x + y < 7

y - 3 ≥ 0

Let's **analyze **each inequality:

y ≤ 2x + 2 represents a shaded region below the line with a **slope **of 2 and a y-intercept of 2.

(1/2)x + y < 7 represents a shaded region below the line with a slope of -1/2 and a y-**intercept **of 7.

y - 3 ≥ 0 represents a shaded region above the line with a slope of 0 and a y-intercept of 3.

The solution set to the system of inequalities will be the **overlapping **region or the intersection of the shaded regions from all three inequalities.

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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

**Answer:**

100°

**Step-by-step explanation:**

tThe sum of all arc measures that make up that circle is 360 degrees.

QS + RQ + RS = 360

QS = 360 - 120 - 140 = 100

An arc angle is the degree measurement of that angle inside the circle, opposite the arc

m∠R = arc QS = 100°

**Answer:**

∠ R = 50°

**Step-by-step explanation:**

the inscribed angle R is half the measure of its intercepted arc QS

the sum of the arcs on a circle is 360° , that is

RQ + QS + SR = 360°

120° + QS + 140° = 360°

QS + 260° = 360° ( subtract 260° from both sides )

QS = 100°

Then

∠ R = [tex]\frac{1}{2}[/tex] × 100° = 50°

A bucket contains 4 green, 3 yellow, 6 red, and 4 blue marbles. Jessi removes 2 marbles, without replacement, from the bucket shown in the image. What is the probability that Jessi removes 1 red marble on her first try and 1 green marble on her second try?

A.

8.8%

B.

3.7%

C.

62.5%

D.

58.9%

**Answer: A**

**Step-by-step explanation: **

!!!!!PLEASE HELP 100 POINTS AND WILL MARK BRAINLIEST!!!!!

Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth of a percent (!!!!!SHOW YOUR WORK!!!!!)

A) Inside the Square

B) Outside the Triangle

Lets solve this ~

A square and a traingle are present in a large rectangle with given dimensions in the figure.

Area of the rectangle is :[tex]\qquad\displaystyle \tt \dashrightarrow \: 12 \times 8[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 96 \: \: unit {}^{2} [/tex]

Area of square :[tex]\qquad\displaystyle \tt \dashrightarrow \: 4 \times 4[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 16 \: \: unit {}^{2} [/tex]

Area of triangle :[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times 4 \times 5[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times 4 \times 5[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 2 \times 5[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 10 \: \: unit {}^{2} [/tex]

Problem 1 : Inside the square[ area of square / total area ]

[tex]\qquad\displaystyle \tt \dashrightarrow \: p(inside \: \: the \: \: square) = \frac{16}{96} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: p(inside \: \: the \: \: square) = \frac{1}{6} [/tex]

Problem 2 : Outside the triangle[ total area except area of triangle / total area ]

[tex]\qquad\displaystyle \tt \dashrightarrow \: p(outside \: the \: triangle) = \frac{96 - 10}{96} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: p(outside \: the \: triangle) = \frac{86 }{96} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: p(outside \: the \: triangle) = \frac{43}{48} [/tex]

The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 43

minutes of calls is $19.41, and the remaining credit after 56 minutes of calls is $17.72. What is the remaining credit after 65 minutes of calls?

The **remaining credit** after 65 minutes of calls is approximately $15.45.

To find the remaining credit after 65 minutes of calls, we can use the given information to determine the **linear function** that relates the remaining credit to the **total calling time**.

Let's assume the **total calling time **in minutes is represented by the variable "x," and the **remaining credit** in dollars is represented by the variable "y."

We are given two data points:

When x = 43, y = $19.41.

When x = 56, y = $17.72.

We can use these data points to form a **system of linear equations**.

Let's solve it to find the equation of the linear function.

Using the point-slope form of a **linear equation**:

y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute the values:

For the first data point:

x1 = 43

y1 = 19.41

Using the second data point:

x2 = 56

y2 = 17.72

The slope (m) can be calculated as:

m = (y2 - y1) / (x2 - x1)

m = (17.72 - 19.41) / (56 - 43)

m = -1.69 / 13

m ≈ -0.13

Now, we can use the **point-slope form **with one of the data points to find the equation of the linear function:

Using (x1, y1) = (43, 19.41):

y - 19.41 = -0.13(x - 43)

Simplifying the equation:

y - 19.41 = -0.13x + 5.59

y = -0.13x + 24

Now that we have the **equation** of the linear function, we can substitute x = 65 to find the remaining credit after 65 minutes:

y = -0.13(65) + 24

y ≈ $15.45

Therefore, the **remaining credit** after 65 minutes of calls is approximately $15.45.

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The average national utility price is $270.48. Over a 6-month period, what is the average utility price in Orlando? How

does this compare with the national average?

The** **average **utility price** in **Orlando **for the 6 month period, and the way it compares to the national average is d. $ 308. 83 ; higher than the national average .

The information for Orlando is **April**, the **cost **was 288 dollars; May, 310 dollars; June, 325 dollars; July, 294 dollars; August, 293 dollars; September, 343 dollars.

The **average **is:

= ( 288 + 310 + 325 + 294 + 293 + 343 ) / 6

= 1, 853 / 6

= $ 308. 83

This average is **higher **than the national average of $ 308. 83.

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Full question is:

A graph titled Orlando, Florida, has month on the x-axis and utility price on the y-axis. In April, the cost was 288 dollars; May, 310 dollars; June, 325 dollars; July, 294 dollars; August, 293 dollars; September, 343 dollars.

a. $370.60; higher than the national average

b. $292.17; higher than the national average

c. $38.35; lower than the national average

d. $308.83; higher than the national average

Why is °=(−°)? PLSS HELP NOW

The equation ° = (-°) is not true. It is incorrect mathematically. The equals sign in an equation indicates that the expression on the left side is equal to the expression on the right side. In this case, the equation is attempting to equate a positive degree with its negative counterpart.

However, a positive degree (°) is not equal to its negative counterpart (-°). They represent opposite directions on the temperature scale or angles in mathematics. For example, 30 degrees is not equal to -30 degrees; they are opposite values.

Therefore, the equation ° = (-°) is false.

I hope this helps! :)

However, a positive degree (°) is not equal to its negative counterpart (-°). They represent opposite directions on the temperature scale or angles in mathematics. For example, 30 degrees is not equal to -30 degrees; they are opposite values.

Therefore, the equation ° = (-°) is false.

I hope this helps! :)

Find x to the nearest hundredth.

16

X

40°

O A x = 24.89

O

OB. x = 13.43

O C. x 10.28

D. x = 12.26

Option C is correct, the **value** of x in the **triangle** is 10.28 units.

The given triangle is right angled **triangle**.

We know that the sine function is a ratio of opposite side and hypotenuse.

To the **angle** 40 degrees the opposite side is x.

The hypotenuse is 16.

Sin 40 degrees=x/16

0.6428=x/16

Apply** cross multiplication**:

x=16×0.6428

x=10.28

Hence, the value of x in the **triangle** is 10.28 units.

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Multiply out

5x(3x-2)=

The solution is the** multiplication** is: 5x × (3x-2) = 15x² - 10x.

Here, we have,

given that,

the **expression** is:

5x(3x-2)

now, we have to **Multiply** out

so, we have,

5x × (3x-2)

= 5x×3x - 5x×2

=15x² - 10x

Hence, The solution is the** multiplication** is: 5x × (3x-2) = 15x² - 10x.

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