**Third quadrant **the **complex plane **is where the number -14 - 5i is situated.

Based on the common knowledge, the **complex** **number's **real and imaginary **components **are considered as the x- and y- **coordinates **of an ordered pair in a 2-D plane.

first quadrant a+bi =(a,b)

second quadrant -a+bi= (-a,b)

third quadrant -a-bi=(-a,-b)

fourth quadrant a,-b=(a,-b)

According to the question,-14-5i is located in third quadrant(-14,-5)

As a result, the complex plane's **third quadrant **is where the number -14 - 5i is situated.

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Which point is the solution to the inequality shown in this graph?? Help pls

a.(0,5)

b.(-3,-1)

c.(0,0)

d.(3,3).

Answer:

only (0,5)

Step-by-step explanation:

(0,5) is in the shaded region on the graph, so it is a solution.

One other point is in the unshaded region so it is NOT a solution. The other two points are on the dashed line, so they are NOT solutions. If the line was solid (not dashed) they would work, but since the line is dashed they are NOT solutions.

**Answer:**

A. (0,5)

**Step-by-step explanation:**

Which is a function?

look at pic

**Answer:**

option 2 {(12, 3), (11,2), ...}

**Step-by-step explanation:**

For functions, multiple x-values can have the same y-value but each y-value must have a unique x-value. The second option matches this criterion.

Someone please help me

**Step-by-step explanation:**

**Part A:** [tex]u^6[/tex] can be written as the square of u³, or [tex](u^3)^2[/tex]. Similarly, [tex]v^6=(v^3)^2[/tex]. Hence, we can write this as a difference of two squares by writing it as

[tex](u^3)^2-(v^3)^2[/tex]

**Part B:**

We can first factor a difference of two squares a² - b² into **(a+b)(a-b)**. Here, *a* would be u³ and *b* would be v³.

[tex](u^3+v^3)(u^3-v^3)[/tex]

Sum and Difference of Two CubesWe can factor this further by the use of two special formulas to factor a **sum of two cubes** and a **difference of two cubes**. These formulas are as follows:

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)\\a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]

Since u³ + v³ is a sum of two cubes, let's rewrite it.

[tex]u^3+v^3=(u+v)(u^2-uv+v^2)[/tex]

Since u³ - v³ is a difference of two cubes, we can rewrite it as well.

[tex]u^3-v^3=(u-v)(u^2+uv+v^2)[/tex]

Now, let's multiply them together again to get the final factored form.

[tex]u^6-v^6=(u+v)(u^2-uv+v^2)(u-v)(u^2+uv+v^2)[/tex]

**Part C:**

If we want to factor [tex]x^6-1[/tex] completely, we can just see that x to the sixth power is just [tex]x^6[/tex] and 1 to the sixth power is just 1. Hence, x can substitute for *u *and 1 can substitute for v.

[tex]x^6-1=(x+1)(x^2-x(1)+1^2)(x-1)(x^2+x(1)+1^2)\\x^6-1=(x+1)(x^2-x+1)(x-1)(x^2+x+1)[/tex]

We can repeat this for [tex]x^6-64[/tex], as 64 is just 2 to the sixth power.

[tex]x^6-64=(x+2)(x^2-x(2)+2^2)(x-2)(x^2+x(2)+2^2)\\x^6-64=(x+2)(x^2-2x+4)(x-2)(x^2+2x+4)[/tex]

3) angle of an isosceles triangle is 70°, find the value of If one remaining angles. a) 40°, 40° b) 45°, 45° c) 40°70° d)50⁰, 50⁰

The remaining two angles of the given **isosceles triangle** is Option(C) 40°,70° .

For an **isosceles triangle**, the two sides of the triangle are congruent and equal in length . Also the angles subtending the adjacent equal sides of the **isosceles triangle** are of same measure.

We also know that the sum of the three interior angles of any triangle is always equal to 180° .

In the options given, in Option(C) the angles measure 40° and 70° .

Thus as one angle of the **isosceles triangle** is given to be 70°, the other angle of its adjacent side is also 70° .

The sum of the interior angles of the triangle is equal to -

70° + 40° + 70° = 180° which satisfies the property.

Therefore, the remaining two angles of the given **isosceles triangle** is **Option(C)** 40°,70° .

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A rectangle measures 3.5 ft by 7 ft. It is enlarged by a scale factor of two. What is the area of the enlarged rectangle? T a m a

**Answer:**

98

**Step-by-step explanation:**

Solution 1, (quick)

When enlarging by a scale factor, the shape's area is multiplied by the scale factor squared.

3.5*7*2^2=98

This works because for a rectangle width x and length y, width 2x and length is 2y, area is 4xy compared to area xy originally.

Solution 2, (technical)

Scale factor of 2 means multiplying by 2

3.5^2=7

7*2=14

7*14=98

PLEASE HELP QUICKLY️️️

**Answer:**

first option x = 7

**Step-by-step explanation:**

"x" is the cathetus opposite the angle of 30°

14 is the hypotenuse

use the sine function

[tex]sin30^{0} =\frac{x}{14}[/tex]

[tex]x=14sen30^{0} =14(0.5)=7[/tex]

Hope this helps

A firm offers routine physical examinations as part of a health service program for its employees. The exams showed that 16% of the employees needed corrective shoes, 23% needed major dental work, and 3% needed both corrective shoes and major dental work. What is the probability that an employee selected at random will need either corrective shoes or major dental work

**Probability** of people needing corrective shoes or dental work is **0.36**.

The proportion of favorable cases to all possible cases used to determine how likely an event is to occur.

What are mutually exclusive events?A statistical term used to describe events that cannot occur concurrently is "mutually exclusive".

Here, the two events getting corrective shoes and getting dental work are **not **mutually exclusive events.

P(corrective shoes or dental work) = P(corrective shoes) + P(dental work) - P(corrective shoes and dental work)

P(corrective shoes or dental work) = 0.16 + 0.23 - 0.03

**P(corrective shoes or dental work)** = 0.36

Hence, the probability of people needing corrective shoes or dental work is **0.36**.

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Janice bought 30 items each priced at 30 cents, 2 dollars, or 3 dollars. If her total purchase price was $\$$30.00, how many 30-cent items did she purchase

she bought **20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.**

According to the statement

Janice bought total items = 30

Price of items are 30 cents, 2 dollars, or 3 dollars.

Total purchase price of Janice = 30$

If we let she bought 10 items at price of 3$, Then it is not possible

So, **Number of items** which are bought by her** at price of $3 is less than 10. **Similarly **Number of items** which are bought by her** at price of $2 is less than 10. **

we know that** 1 CENT = 0.01 $**

We also know that** 10 30-cents will worth 3 dollars, so the number of cents **which are bought by her** at price of $0.01 is greater than 10.**

Now, Let she bought 20 items at price of 0.01$

Then **20*0.3 = 6$**

It means 30$-6$ = 24$

24$ are left to purchase the things which are at price of 2$ and 3$.

If we let she purchase 4 items at cost $3 then

Then** 4*$3 = 12$**

It means **24$-12$ = 12$**

Now, with remaining money she bought 6 items at cost $2.

So, she bought **20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.**

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**she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.**

**According to the statement**

**Janice bought total items = 30**

**Price of items are 30 cents, 2 dollars, or 3 dollars.**

**Total purchase price of Janice = 30$**

**If we let she bought 10 items at price of 3$, Then it is not possible**

**So, Number of items which are bought by her at price of $3 is less than 10. Similarly Number of items which are bought by her at price of $2 is less than 10.**

**we know that 1 CENT = 0.01 $**

**We also know that 10 30-cents will worth 3 dollars, so the number of cents which are bought by her at price of $0.01 is greater than 10.**

**Now, Let she bought 20 items at price of 0.01$**

**Then 20*0.3 = 6$**

**It means 30$-6$ = 24$**

**24$ are left to purchase the things which are at price of 2$ and 3$.**

**If we let she purchase 4 items at cost $3 then**

**Then 4*$3 = 12$**

**It means 24$-12$ = 12$**

**Now, with remaining money she bought 6 items at cost $2.**

**So, she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.**

find the equation of the line y=mx+b form with the slope 3 that passes through the point (5,19)

The **equation **of the line that has a slope of 3 and that passes through the point (5,19) is** y = 3x + 4**

From the question, we are to determine the **equation **of the line that has a **slope **of **3 **and that passes through the **point (5,19) **

Using the **point-slope form** of an **equation **of a line

y - y₁ = m(x - x₁)

Where** m** is the **slope **

and** (x₁, y₁)** is a **point **on the **line **

From the given **information**

m = **3 **

x₁ = **5 **

y₁ =** 19**

Putting the **parameters **into the **equation**, we get

y - 19 = 3(x - 5)

y - 19 = 3x - 15

y = 3x -15 + 19

**y = 3x +4**

Hence, the **equation **of the line that has a slope of 3 and that passes through the point (5,19) is** y = 3x + 4**

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Help please you don’t know how much this means to me

Problem 6:a)

[tex]a(0) = 1 \: \: \: \: \: \: b(0) = 2 \: \: \: \: \: c(0) = 3 \\ a(1) = b(0) + c(0) = 2 + 3 = 5 \\ b(1) = a(0) + c(0) = 1 + 3 = 4 \\ c(1) = a(0) + b(0) = 1 + 2 = 3 \\ \\ a(2) = b(1) + c(1) = 4 + 3 = 7 \\ b(2) = a(1) + c(1) = 5 + 3 = 8 \\ c(2) = a(1) + b(1) = 5 + 4 = 9[/tex]

[tex]a(3) = b(2) + c(2) = 8 + 9 = 17\\ b(3) = a(2) + c(2) =7 + 9 = 16 \\ c(3) = a(2) + b(2) = 7 + 8 = 15 \\ \\ a(4) = b(3) + c(3) = 16 + 15 = 31 \\ b(4) = a(3) + c(3) = 17 + 15 = 32 \\ c(4) = a(3) + b(3) = 17 + 16 = 33[/tex]

[tex]a(5) = 32 + 33 = 65 \\ b(5) = 31 + 33 = 64 \\ c(5) =31 + 32 = 63 \\ \\ a(6) = 64 + 63 = 127 \\ b(6) = 65 + 63 = 128 \\ c(6) = 65 + 64 = 129 \\ [/tex]

[tex]a(7) = 128 + 129 = 257 \\ b(7) = 127 + 129 = 256 \\c (7) = 127 + 128 = 255 \\ \\ a(8) = 256 + 255 = 511 \\ b(8) = 257 + 255 = 512 \\ c(8) = 257 + 256 = 513[/tex]

[tex]a(9) = 512 + 513 = 1025 \\ b(9) = 511 + 513 = 1024 \\ c(9) = 511 + 512 = 1023 \\ \\ a(10) = 1024 + 1023 = 2047 \\ b(10) = 1025 + 1023 = 2048 \\ c(10) = 1025 + 1024 = 2049[/tex]

b)[tex]a(n) + b(n) + c(n) = \\ 2(a(n - 1) + b(n - 1) + c(n - 1)) \\ 6 \times 2 {}^{n } [/tex]

c)[tex]6 \times 2 {}^{n} > 100 \: 000 \\ 2 {}^{n} > \frac{100 \: 000}{6} \\ n > log {}^{2} ( \frac{100 \: 000}{6} ) \\ n > 14.02468 \\ n = 15[/tex]

Using the quadratic formula, solve the

equation below to find the two possible

values of t.

6x^2-35=-11x

Give each value as a fraction in its

simplest form.

The **two possible solutions **to the given **equation **( 6x^2-35 = -11x ) are x = **5/3** and x = **-7/2**

What are the two possible solution to the equation?

Given the equation; 6x² - 35 = -11x

The **quadratic formula **is expressed as;

**x = [ -b±√( b² - 4(ac) ]/2a**

First, we **re-arrange** our equation in the form of **ax² + bx + c = 0**

6x² + 11x - 35 = 0

a = 6b = 11c = -35We substitute into the formula.

x = [ -b±√( b² - 4(ac) ]/2a

x = [ -11±√( 11² - 4( 6 × -35 ) ]/2×6

x = [ -11±√( 121 + 840 ]/12

x = [ -11±√961 ]/12

x = [ -11 ± 31 ]/12

x = (-11 + 31)/12, (-11 + 31 )/12

x = 20/12, -42/12

**x = 5/3, -7/2**

Therefore, the **two possible solutions **to the given **equation **( 6x^2-35 = -11x ) are x = **5/3** and x = **-7/2**

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Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 8% each week. The following function represents the weekly weed growth: f(x) = 86(1.08)x. Rewrite the function to show how quickly the weeds grow each day.

f(x) = 86(1.08)7x; grows approximately at a rate of 5.6% daily

f(x) = 86(1.087)x; grows approximately at a rate of 0.56% daily

f(x) = 86(1.01)x; grows approximately at a rate of 0.1% daily

f(x) = 86(1.01)7x; grows approximately at a rate of 1% daily

The **function **is f(x) = 86(1.01)^7x; grows **approximately **at a rate of 1% daily

The **function **is given as:

f(x) = 86(1.08)^x

There are 7 days in a week.

This means that:

1 day = 1/7 week

So, x days is

x day = x/7 week

Substitute x/7 for x in

f(x) = 86(1.08)^(x/7)

Rewrite as:

f(x) = 86(1.08^1/7)^x

Evaluate

f(x) = 86(1.01)^x

In the above, we have:

r = 1.01 - 1

Evaluate

r = 0.01

Express as percentage

r = 1%

Hence, the **function **is f(x) = 86(1.01)^7x; grows **approximately **at a rate of 1% daily

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**Answer: the answer is d**

**Step-by-step explanation:**

Can someone please help me with this? I'll give brainliest :)

Based on the information given find the slope from [2,5] Is interval notation and means from x=2 to x=5.

16. y = 3x - 4

17. y = 2x^2-4x - 2

The **slope **of y = 3x - 4 on the **interval** [2, 5] is 3 and the **slope **of y = 2x^2-4x - 2 on the **interval** [2, 5] is 10

The **interval **is given as:

x = 2 to x = 5

The **slope **is calculated as:

[tex]m = \frac{y_2 -y_1}{x_2-x_1}[/tex]

**16. y = 3x - 4**

Substitute 2 and 5 for x

y = 3*2 - 4 = 2

y = 3*5 - 4 = 11

So, we have:

[tex]m = \frac{11 - 2}{5 - 2}[/tex]

[tex]m = \frac{9}{3}[/tex]

Divide

m = 3

Hence, the **slope **of y = 3x - 4 on the **interval** [2, 5] is 3

**17. y = 2x^2-4x - 2**

Substitute 2 and 5 for x

y = 2 * 2^2 - 4 * 2 - 2 = -2

y = 2 * 5^2 - 4 * 5 - 2 = 28

So, we have:

[tex]m = \frac{28 + 2}{5 - 2}[/tex]

[tex]m = \frac{30}{3}[/tex]

Divide

m = 10

Hence, the **slope **of y = 2x^2-4x - 2 on the **interval** [2, 5] is 10

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Find the midpoint of a and b when a has coordinates (2,3) and b has coordinates (8,9)

The midpoint of co-ordinate is (5, 6)

Add both** "x"** coordinates, and divide by 2.

Add both **"y"** coordinates, and divide by 2.

Given that;

Coordinates of A =** (2,3)**

Coordinates of B =** (8,9)**

Find:

Midpoint of co-ordinate

Computation:

Midpoint of co-ordinate = [(x1 + x2) / 2], [(y1 + y2) / 2]

Midpoint of co-ordinate =** [(2 + 8) / 2], [(3 + 9) / 2]**

Midpoint of co-ordinate =** [10 / 2], [12 / 2]**

Midpoint of co-ordinate =** (5, 6)**

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What is the sum of the 12th square number and the 9th square number

**Answer: 225**

**Step-by-step explanation:**

What is a square number?

A square number is a product of a number times itself

So, the 12th square number would be 12 * 12, or 12²

The 9th square number would be 9 * 9, or 9²

The equation would be 12² + 9²

So:

12² + 9²

= 144 + 81

= 225

**So, the answer is 225**

Which search method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line

The **wide-area search method **employs the use of markers such as knots at **regular intervals** along the **search line.**

Given the **method** employs the use of markers such as knots at **regular intervals** along the search line to indicate distance from the **beginning** of the search line.

In order to **locate, relieve distress**, and **preserve** the life of a person who has been reported missing or is believed to be lost, stranded, or is considered a **high-risk missing person**, wide area search and rescue refers to activities occurring within **large geographic areas**. It also refers to the removal of any **survivors** to a safe location.

Hence, the **wide-area search **method employs the use of **markers** such as knots at **regular intervals** along the search line to indicate distance from the beginning of the** search line**

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Write the equation of the sinusoidal function shown.

A) y = cos x - 1

B)y=sin x - 1

C) y=2 sin x - 1

D) y = 2 cos x - 1

Answer:

A. y= cos x - 1

Step-by-step explanation:

short answer: this is basically the parent graph cos(x), just vertically shifted down 1 unit.

longer answer:

standard form is y = a cos(bx-c) +d

a = amplitude

b = 2pi/period

c = horizontal shift

d = vertical shift (also equal to midline)

for this graph

a=1

period is 2pi, so b=1

there is no horizontal shift so c=0

d= -1 because it is shifted down one unit from axis (midline is at -1)

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There is a pair of parallel sides in the following shape.

what is the area

The** area** of the given figure is **38 square units**

The area of the given trapezoid is expressed as:

A = 0.5(a+b)h

where

a and b are the sides

h is the height

**Substitute**

A = 0.5(9+10) * 4

A = 19 * 2

A = **38 square units**

Hence the** area** of the given figure is **38 square units**

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PLEASE HELP ME AS SOON AS POSSIBLE

**a) **The **linear function **that models the population in t years after 2004 is: P(t) = -200t + 29600.

**b)** Using the function, the **estimate **for the population in **2020 **is of 26,400.

A linear function is **modeled **by:

y = mx + b

In which:

The initial population in 2004, of **29600, is the y-intercept**. In 12 years, the population decayed 2400, hence the **slope **is:

m = -2400/12 = -200.

Hence the **equation **is:

P(t) = -200t + 29600.

2020 is **16 years after 2004**, hence the **estimate **is:

P(16) = -200(16) + 29600 = 26,400.

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How many solutions does this nonlinear system of equations have? NEED HELP ASAP!

**Answer:**

**Step-by-step explanation:**

two

Can u guys pls help me with this homework

The **value **of √(7 * 23 - 1)/8 is 4.47, the **values **of a, b and c are -14/11, -10/11 and 3, respectively and the **area **of the **shape **is 5√5 + 5 square meters

The question goes thus:

If √5 = 2.236, evaluate √(7 * 23 - 1)/8

We have:

√(7 * 23 - 1)/8

Evaluate the **product **of 7 and 23

√(7 * 23 - 1)/8 = √(161 - 1)/8

Evaluate the **difference **of 161 and 1

√(7 * 23 - 1)/8 = √160/8

Evaluate the **quotient **of 160 and 8

√(7 * 23 - 1)/8 = √20

Express 20 as the **product **4 and 5

√(7 * 23 - 1)/8 = √(4 * 5)

Expand the **product**

√(7 * 23 - 1)/8 = √4 * √5

Express √4 as 2

√(7 * 23 - 1)/8 = 2 * √5

Substitute √5 = 2.236

√(7 * 23 - 1)/8 = 2 * 2.236

Evaluate the **product **

√(7 * 23 - 1)/8 = 4.472

Approximate

√(7 * 23 - 1)/8 = 4.47

Hence, the **value **of √(7 * 23 - 1)/8 is 4.47

The expression is given as:

(3√2 + 5√6)/(3√2 - 5√6)

Rationalize the above **expression**

(3√2 + 5√6)/(3√2 - 5√6) * (3√2 + 5√6)/(3√2 + 5√6)

Evaluate the **product**

(3√2 + 5√6)²/((3√2)² - (5√6)²)

Simplify the **denominator**

(3√2 + 5√6)²/(18 - 150)

This gives

[(3√2)² + (5√6)² + 2 *(3√2) * (5√6)]/(-132)

Simplify the **numerator**

[168 + 120√3]/(-132)

Simplify the fraction

-14/11 - 10√3/11

Hence, the **values **of a, b and c are -14/11, -10/11 and 3, respectively

The **area **is calculated as:

A = 1/2 * (Sum of parallel bases) * Height

So, we have:

A = 1/2 * (4 + 3√5 + 6 - √5) * √5

Evaluate the like terms

A = 1/2 * (10 + 2√5) * √5

Evaluate the **product**

A = (5 + √5) * √5

Evaluate the **product**

A = 5√5 + 5

Hence, the **area **of the **shape **is 5√5 + 5 square meters

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What is the slope of a line that is parallel to the line y = 3/4x+2?

**Answer: 3/4**

**Step-by-step explanation:**

Parallel lines have the same slope.

From the top of a 16 m tall building, the angle of depression to a car on the road is 35°. To the nearest metre, how far is the car from the base of the building?

The distance of the car to the base of the building is 23 metres.

How to find the distance of the car from the building using angle of depression?The situation will form a right angle triangle.

Therefore, the distance of the car to the base of the building is the adjacent side of the** right angle triangle** formed.

Therefore,

**tan 35 = opposite / adjacent**

tan 35 = 16 / x

x tan 35 = 16

x = 16 / tan 35

Therefore,

x = 16 / 0.70020753821

x = 22.8506141103

**x = 23 meters**

Therefore, the distance of the car to the base of the building is 23 metres.

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The temperature was -20.5°F at 5 A.M. and rose 5 degrees per hour for the next 5 hours. Melissa says the temperature at 10 A.M. was -5.5°F. Which statement identifies Melissa’s error and the correct answer?A.Melissa multiplied incorrectly. The correct answer is -0.5°F.B.Melissa multiplied incorrectly. The correct answer is 9.5°F.C.Melissa added incorrectly. The correct answer is 4.5°F.D.Melissa added incorrectly. The correct answer is 5.5°F.

The statement which identifies **Melissa’s error** and the correct answer is; Melissa **added** **incorrectly**. The correct answer is **4.5°F**

New temperature = Initial temperature + (Change in temperature per × Number of hours)

= -20.5°F + (5°F × 5)

= -20.5°F + (25°F)

= **4.5°F**

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**Answer:**

C

**Step-by-step explanation:**

In the diagram AB/BC = AD/DE

Substitute the known values into the proportion and solve for DE

**Answer:**

[tex]\huge\boxed{\sf DE = 9}[/tex]

**Step-by-step explanation:**

From the figure,

**AB = 2**

**BC = 3**

**AD = 6**

**Substitute **in the given formula

[tex]\displaystyle \frac{AB}{BC} =\frac{AD}{DE} \\\\\frac{2}{3} = \frac{6}{DE} \\\\Cross \ Multiply \\\\2 \times DE = 6 \times 3\\\\2DE = 18\\\\Divide \ 2 \ to \ both \ sides\\\\DE = 18/2\\\\DE = 9\\\\\rule[225]{225}{2}[/tex]

Half of a set of the parts are manufactured by machine A and half by machine B. Eight percent of all the parts are defective. Two percent of the parts manufactured on machine A are defective. Find the probability that a part was manufactured on machine A, given that the part is defective. (Round your answer to 4 decimal places.)

The **probability **that a part was manufactured on machine A, given that the part is defective is P ( A | D ) = 0.024.

**To find the probability that a part was manufactured on machine A, given that the part is defective:**

The probability that a part was manufactured on machine A given that part is defective:

**P ( A | D )**

**P ( A | D ) = [P (A) * P ( D | A )]/ P ( D )**

Where: P (A) is the **probability **that the part is manufactured in machine A which is 0.2 (half of the parts are manufactured in machine A)

P (D/A) is the **probability **of a defective part given that the part was manufactured in machine A which is 2% or 0.02

And finally, the **probability **of defective part in the production is 8% or 0.08 hence :

**P ( A | D ) = [ ( 0.2 ) * 0.02 ] / 0.08**

**P ( A | D ) = 0.024**

Therefore, the **probability **that a part was manufactured on machine A, given that the part is defective is P ( A | D ) = 0.024.

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Solution

We can start with the pythagorean theorem:

(leg 1)² + (leg 2)² = (hypotenuse)²

Substitute the values we know.

15² + x² = 32²

Solve for x.

X =

**Answer:**

28.26658805 (I included every digit in case your teacher needs you to round)

**Step-by-step explanation:**

In order to find x, we need to isolate x by subtracting 15^2 and taking the square root of both sides.

Thus, we have:

[tex]15^2+x^2=32^2\\x^2=32^2-15^2\\\sqrt{x^2} =\sqrt{(32^2-15^2)} \\\sqrt{x^2}=\sqrt{799} \\x=28.26658805[/tex]

When you roll two number cubes, what are the odds in simplest form against getting two numbers greater than 4?

A. 4:1

B. 1:4

C. 1:8

D. 8:1

The** odds i**n simplest form against getting **two numbers greate**r than **4 **is **1 : 4. **

**Probability** determines the **odds **that a random event would happen. The **odds t**he event occurs is 1 and the probability that the event does not occur is 0.

The** odds **of getting **two numbers greate**r than **4 = **2 x (numbers greater than 3 in a cube / total number of sides in a cube)

2(3/6)

2 x 1/2 = **1 : 4**

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In the 1980’s, a clinical trial was conducted to determine if taking an aspirin daily reduced the incidence of heart attacks. Of 22,071 medical doctors participating in the study, 11,037 were randomly assigned to take aspirin and 11,034 were randomly assigned to the placebo group. Doctors in this group were given a sugar pill disguised to look like aspirin. After six months, the proportion of heart attacks in the two groups was compared. Only 104 doctors who took aspirin had a heart attack, whereas 189 who received the placebo had a heart attack. Can we conclude from this study that taking aspirin reduced the chance of having a heart attack? the purpose of this study was to determine whether taking an aspirin daily reduces the proportion of heart attacks.

There is enough **evidence** to conclude that taking aspirin cannot reduces the chance of cancer.

Given **sample size** of patients take aspirin 11037, sample size of patients who have assigned placebo group be 11034. 104 doctors who take aspirin had a heart attack, 189 doctors had placebo had heart attacks.

First we have to form **hypothesis**.

[tex]H_{0} :p{1} -p_{2} =0[/tex]

[tex]H_{1}:p_{1} -p_{2} < 0[/tex]

We have to find the respective **probabilities**.

[tex]p_{1}[/tex]=104/11037

=0.0094

[tex]p_{2}[/tex]=189/11034

=0.0171

Now their respective **margin of errors**.

[tex]s_{1}[/tex]=[tex]\sqrt{ {(0.0094*0.9906)/11037}[/tex]

=0.0009

[tex]s_{2}[/tex]=[tex]\sqrt{0.0171*0.9829}[/tex]

=0.0011

Hence the distribution of the **differences**,they are given by:

p=[tex]p_{1} -p_{2}[/tex]

=0.0094-0.0171

=-0.0077

S=[tex]\sqrt{s_{1} ^{2}+s_{2} ^{2} }[/tex]

=[tex]\sqrt{(0.0009)^{2} +(0.0011)^{2} }[/tex]

=0.00305

z=(p -f)/S (In which f=0 is the value tested at the null **hypothesis**)

=(-0.0077-0)/0.00305

=-2.52

p value will be 0.005.

p value of 0.05 **significance level**.

z=1.96.

1.96>0.005

So we will reject the null **hypothesis** which means it cannot reduce the whole chance of becomming a heart attack.

Hence there is enough **evidence** to conclude that taking aspirin cannot reduces the chance of cancer.

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If the parabola of equation y=k−x2 is tangent to the line of the equation y=x then what is the value of k ?

The value of **k is 1/4.**

According to the statement

we have given

The equation of parabola is y=k−x2

And **tangent to the line of equation is y = x**

and we have to find the value of K.

So, let y=k−x2 -(1)

and let y = x -(2)

(2) is the tangent to the (1) then

therefore they cut at

y=k−x2 -(1)

y = x -(2)

so, put (2) in the (1) then

x = k- (x)^2

(x)^2 + x = k

The above written equation has one real number then for this D =0

so, (x)^2 + x - k = 0

-1 -1*4*k = 0

-1 - 4k = 0

-4k = 1

The value of k is -1/4.

So, The value of **k is 1/4.**

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